![as the temperature and pressure change? These monolayers are named after Langmuir because
he was the first to see isotherm discontinuities indicating phase transitions, but pressure and
density are macroscopic averages and do not tell us what is happening to the molecules at these
phase transitions. This was not known until new experimental techniques (including X-ray
diffraction and a variety of microscopies) were applied to this system starting in the 1980's and
especially in the 1990's.
It is probably safe to say that, of the various techniques, synchrotron X-ray diffraction has had
the most impact in this area. In general one should not overestimate the power of X-ray
scattering: it does not generate real-space pictures, and it is not useful in disordered systems
such as monolayers on very rough surfaces or monolayers with no lateral order or tilt order.
But in the case of Langmuir monolayers of simple, rod-like molecules (e.g. saturated fatty
acids and alcohols), X-ray scattering has provided important and vivid new information that
has explicitly contradicted the conventional wisdom. Many phases of these monolayers turned
out not to be liquids ('liquid expanded', 'liquid condensed', 'superliquid' etc); rather, they are
mesophases with some degree of positional order and are therefore characterizable by X-ray
diffraction.
A 1999 review [1] describes the general features of the fatty acid/alcohol Langmuir monoIayer
phase diagram in some detail, and contains much more information than can be included here.
The following section contains a brief overview of X-ray results. In subsequent sections some
newer information is surveyed that was not available at the time Ref. 1 was published,
regarding the ordering of the molecular backbones and positional order in the underlying
aqueous subphase.
2. THE PHASE DIAGRAM OF FATTY ACID AND ALCOHOL LANGMUIR
MONOLAYERS
In 1945, St~illberg-Stenhagen and Stenhagen [2] published an unexpectedly complex pressure-
temperature phase diagram for fatty acid monolayers, containing a variety of phase boundaries
and not explainable by the popular solid/ liquid expanded/ liquid condensed hierarchy of
phases. These results were considered dubious and widely ignored; most studies continued to
be performed only at room temperature. The 1966 book by Gaines [3], which was the bible of
this field through the 1980's, says that "In view of the experimental difficulties attendant on the](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-19-320.jpg)
![demonstration of these effects, it seems that further study is needed before any of them can be
considered well understood. No detailed discussion of them is given here..."
When such further studies were finally conducted [4], it was found that the phase diagram of
ref. 2 was largely accurate. A 'modem' phase diagram is shown in Fig.l; the labels used for the
phases have historical origins and don't really mean anything. All phase boundaries except the
Ov-L2 boundary can be seen as discontinuities in isotherms. The phase diagram is applicable to
all insoluble fatty acids irrespective of chain length if the temperature range is appropriately
shifted; the pressures change slightly as well, but the topology is not changed. The L2 phase is
not seen in saturated fatty alcohols.
X-ray diffraction can also be used to locate the phase boundaries, but it is much easier to do
this with isotherms, Brewster angle microscopy, etc. Once the boundaries are located, and the
next step is to identify what these phases and phase transitions are, that is when X-rays become
invaluable. An explanation of how this technique is used to determine not just the lattice but
also the tilt magnitude and direction is given in Ref. 1. The schematic diagrams in Fig. 1 show
the structures thus determined. There are
(a) two phases with distorted hexagonal (DH) i.e. centered rectangular lattices and vertical
molecules: CS and S;
(b) one phase with a hexagonal lattice and vertical molecules (LS);
(c) two phases with DH lattices and chains tilted towards a near neighbor (L2, L2"),
(d) two phases with DH lattices and tilts towards a next-nearest neighbor (L2', Ov).
All these phases have at least medium-range order. The high-pressure low-temperature CS
phase appears to be long-range-ordered. The L2 phase is anisotropically ordered (better-ordered
in one direction than in the direction normal to it). At higher temperatures there is finally a
liquid phase (not shown). Another phase not shown in Fig. 1 is a thin sliver of the 'I' phase
between the L2 and L2' phases, in which the tilt direction is intermediate between the near-
neighbor and next-nearest-neighhbor directions. A simple Landau theory [5] perfectly
reproduces the details of the phase transition between the L2 and I phases (first order) and
between the I and L2' phases (continuous).](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-20-320.jpg)
![CS I S ~." ! LS
! :I* ,o.
r
~.., --'~ t !":.M:
m m
temperature
Fig.1 Saturated fatty acid monolayerphase diagram, schematically showing the latticc distortions and tilt
directionsdeterminedby X-raydiffractiondata.[FromRef. 1.]
The story of the recently identified Ov phase illustrates the strengths and weaknesses of the
various experimental techniques and the advantages of bringing multiple techniques to bear on
this problem. The L2/Ov phase boundary is not seen in isotherms; in other words, there is no
discontinuity in the density and in that narrow sense there is no phase transition at all. This
phase boundary was located by Overbeck and M6bius [6] using Brewster Angle Microscopy:
they saw changes in texture when crossing specific points in the isotherm. X-ray scattering had
never been used in this region to look for phase boundaries, since this is time-consuming and
there was no reason to explore this area. Once the mysterious phase boundary was detected,
however, we rather quickly established [7] using X-rays that there was a distinct change in the
diffraction pattern upon crossing the phase boundary (Fig. 2). The tilt direction changes, from
towards a nearest-neighbor (L2 phase) below the phase boundary to towards a next-nearest-
neighbor (Ov phase) above the phase boundary. We also discovered why isotherm studies had
seen nothing: the tilt angle and the packing of the tilted molecules remain unchanged even
though the tilt direction (relative to the lattice) changes. Thus there is no change in the areal](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-21-320.jpg)
![density, but there is a change of symmetry. The phase transition is first-order even though there
is no flat coexistence region in the isotherm.
0.7
15 dyn es/cm
0.6
0.5
0.4
0.3
0.2
0.1
"--" 0.0
0.40.50.6~ 13 dyn es/cm
0.3
Ol
00
1.4o 1.45
Kxy(A1)
150 1.55
Fig. 2: SampleX-ray diffraction data fromC~9acid monolayers at 30°C,just below the transition to the Ov phase
(13 mN/m) and just above (15 mN/m). Data are plotted as Kp/Kzintensity contours; each contourrepresents an
equal intensitystep (arbitrary units) above the contour immediatelyoutside it. [FromRef. 7]
3. BACKBONE ORDERING IN FATTY ACID MONOLAYERS
The various phases listed above differ in the lattice symmetry; tilt or lack thereof; tilt direction;
and range of positional order. However, there is one more parameter. The alkane chains are not
cylinders with circular cross-sections; to fully specify how the molecules are arranged, one
needs to also specify the orientation of the molecule about its long axis. Since the carbon atoms
in the alkane tail define a plane, specifying the orientation of this backbone plane is a
convenient way to specify the orientation of the entire molecule.
In single crystals where a large number of diffraction peaks can be observed, it is possible to
deduce, from the peak intensities, the molecular form factor and thus the orientation relative to
the lattice. In Langmuir monolayers, even the second-order diffraction peaks are sometimes](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-22-320.jpg)
![hard to see, and most structures are derived (or rather surmised) from the first-order peak
positions. Recently [8], however, we obtained direct X-ray evidence of backbone order. Fig. 2
shows diffraction peaks for the CS phase indexed in terms of a rectangular non-primitive unit
cell. We see not only the known first-order (11) and (20) peaks [9], and the known second-
order (02) and (31) peaks [10], but a (21) peak. Now the rectangular unit cell contains two
molecules, and if these molecules are identical, the (21) peak is forbidden. This immediately
tells us that there are two inequivalent sites. Any differences between inequivalent sites will
cause the (21) peak to be visible, but they will in general also cause the (01) peak to be visible;
we do not see the (01) peak. This argues strongly for a herringbone arrangement of molecular
cross-sections, just like some phases of paraffins. As can be seen from the inset to Fig. 2, when
there is herringbone order the backbones at the two inequivalent sites make equal (although
opposite) angles relative to the (01) direction; therefore the molecules at the two sites have
identical structure factors for the (01) peak and this peak remains forbidden. However, relative
to the (21) direction, the backbones at the two sites are oriented very differently (again, see
inset); thus the two molecular structure factors are not the same and the (21) peak is not
forbidden.
Similar results are obtained for the tilted L2" phase; these data are not shown here but can be
found in ref. 8. We do not see 'forbidden' peaks in any of the other phases, which means they
can have at most short-range backbone order.
4. ORDER IN THE AQUEOUS SUBPHASE
When polyvalent metal ions are added to the subphase, the monolayer generally becomes much
better ordered [11], changes its viscoelastic response [12], and transfers more easily to a solid
substrate [13]. As always, a change in properties indicates a change in structure. As we shall
see below, what changes is that the underlying aqueous solution becomes ordered. It is
tempting to think of this as an ordering or the metal ions, since their presence is necessary to
see this effect, but that may not be true.
Some years ago, X-ray diffraction was used by another group to detect the formation of a
monolayer superlattice in the subphase when Cdz+ ions were present [14]. The unit cell was
mysteriously large (a 2x3 supercell of the Langmuir monolayer unit cell). We have confirmed
the observation in our own experiments, and we have also observed superlattices in the](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-23-320.jpg)
![presence of Mn 2+, Mg 2+ and Pb2+. The presence of each of these ions results in a different
subphase lattice.
.4,,,,a
.E
, w,,,,i
tD
o.1
expected
(ol)
(1 i) (20)
o 8
~ o
peak o o°
pos tion co
o O
o oo
oo o
O
o °o
o O o
8o ~o
~,o eo
(21)
(02)
• , , , ,1t,, /t , , , //
!
1.2 i.4 1.6 2.1 2.5 2.7
CS phase
~ ,/'3,
(31)
o
O0
o
oo
! i
2.8 2.9
K (A ~ )
Fig. 3 Sample x-ray data (in the horizontal plane, i.e. at Kz=0)from a heneicosanoic (C2~)acid monolayer in the
CS phase (T=7°C, rt=30 mN/m). Peaks are indexed according to a centered orthorhombic lattice with two
molecules per unit cell. The inset shows a centered orthorhombic lattice with a herringbone arrangement of the
molecular backbones. [From Ref. 8]
With Mn 2+ we see a l x2 superlattice of the organic structure; with Mg we see a 2x2
superlattice [15]. Perhaps the strangest subphase structure is seen in the presence of Pb2+, and
we will therefore show the Pb2+ data [16] here as an example. Fig. 4 shows the large number of
peaks seen. These can all be indexed, and the resulting unit cell is rotated with respect to the
organic lattice and is very large (bottom of Fig. 4). Its area is 14 times the organic unit cell, i.e.
nearly 280~ 2. While the diffraction data are unambiguous, they make it entirely impossible to
believe that what we are seeing are lattices of isolated ions.
We therefore sought to test for the presence of lead within the superlattice. If the superlattice
peaks were solely due to lead ions, the contribution to the intensity of each weak peak should](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-24-320.jpg)
![be proportional to the square of the lead form factor. Tuning the x-ray energy from 12.885KeV
(below the L3 absorption edge of the lead atom) to 13.100KeV (slightly above the edge) should
decrease the absolute intensity of a diffraction peak due to scattering from lead atoms by
-20%.
,r~
0.05 -
0,2
5 0.0
A
v
005
0.3 0.4 0.5
0.4.
06 0.7 0.8
~= 0.2 '¢
"7
- ]~ 0.04
II
It 0.03
0,0 0
1,5 1.6 1.7
,~- ~-
'~" ,~ ,R
'~~ '~
:a!....~'~
0.9 1.0 1.1 1.2 1.3 1.4 1.5
,~" ...
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
K y(A"~)
o ? o-Q.~5.~ o f o o
oo o 5~.~o oo o o
° ° °° ° ~-s..°
° o
o o o o ~ o,o o.o o~°
O organic molecules
inorganic superlattice
Fig. 4: TOP: Grazing incidence synchrotron x-ray diffraction data from a heneicosanoic acid Langmuir monolayer
with lead ions in the subphase. The lower-order peaks (2 2), (2 5 ) and (4 3 ), and higher-order peaks (0 7), (6 1 ),
(6 8 ), (4, 4), (4 10), are from the Langmuir monolayer. All other peaks are due to the superlattice. BOTTOM:
Real space lattices of the fatty acid monolayer and the superlattice. The heneicosanoic acid molecules are
represented by circles; the 'lead' supercell is shown by lines.. The lattices are commensurate' the basis vectors are
related through a'=4a+2b and b'=-3a+2b, so that area' =14xarea. [From Ref. 16]](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-25-320.jpg)
![We have measured the intensities of 13 weak peaks with K~.vbetween 0.6/1, ~ and 1.4 ,~-i at
these two energies (data for some representative superlattice peaks, and also some organic
peaks, are shown in Fig. 5). Within an experimental error of----5%, we observed no change for
any of these peaks.
1.2
0.8
0.4
0.0
o
om,
&n
C:
e. 008
0 04
0.00
Ilu
u
E,
[]
¢
J
un
[]
.d,
& 13.100KeV
u 12.EIBSKeV
U
0
' I ' I ' I ' I ' I ' I '
I .45 1 5(3 1.55 1.69 1 65 1.70
an
,L, On n
. e~n~l~
~
mrS" '~2~' ~ ~ ~. ~.
I ' I ' I ' I I | , 1 ~' I
D.60 0.65 0.70 0.75 0.80 0.85 090
K~(A")
Fig. 5 In-plane diffraction scan with x-ray energy below and slightly above the L3 absorption edge of lead. (a)
Three peaks from the organic monolayer plus weak superlattice peaks. (b) Four representative superlattice peaks.
We also looked at 9 other superlattice peaks not shown here, with the same results. If the superlattice consisted of
lead atoms only, a 20% change in the peak intensities would be expected. There was no observable change in
intensity for any of the peaks studied. [Fromref. 16]](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-26-320.jpg)
![10
If lead does not contribute measurably to the diffraction peak intensity, scattering from the
superstructure must be dominated by other atoms. In principle, superlattice reflections can arise
from a periodic superstructure within the organic monolayer, but the Bragg rod widths we
observe are not consistent with horizontal or vertical density modulations in the entire organic
monolayer. The only reasonable possibility is that the superlattice peaks are due to a thin layer
in the aqueous subphase. Since no superlattice is seen when no multivalent metal ions are
added to the subphase (even at very high pH), and different lattices are seen when different
ions are added, the lattice cannot be due to impurities in the water. However, it is well
established [17] that metal ions undergo hydrolysis and hydration in aqueous solution, and a
wide range of complex polynuclear oxo(hydroxo)-bridged structures can be formed. The
observation of changes in the organic monolayer structure as a function of the subphase pH and
subphase ion concentration [18] is further evidence that pH- and concentration-sensitive
hydrolysis products, rather than isolated ions, are present at the interface.
Thus, we expect that hydrolysis products and water molecules arrange themselves under the
Langmuir monolayer, interacting with the carboxyl head groups in such a way as to form a
large commensurate superlattice. The ratio of metal atoms to other atoms (hydroxyl ions,
water) can be small enough that their presence is undetectable in our anomalous scattering
studies.
5. ONGOING AND FUTURE STUDIES
Langmuir monolayers have been used by others [19, 20] as templates to grow inorganic
crystals. This is a somewhat simplified experimental model of the real-world process of
biomineralization. More generally, biomineralization is just one example of the possible use of
an organic template to control the nucleation of an inorganic mineral, and one can ask how and
when such template-directed nucleation occurs and whether there are any advantages to using
controllable organic lattices such as Langmuir monolayers as templates.
The monolayer structures mentioned in the previous section can be considered precursors to
bulk crystal growth. We had originally expected that unusual interfacial structures would serve
to mediate between otherwise incompatible monolayer and mineral structures. Unfortunately, it
is not easy to nucleate bulk Mnz+, Mg2+ and Pb2+ crystals at the interface because of the
difficulty of making stable supersaturated solutions. It is much easier to make supersaturated
CaCO3, which is of great interest because it is a biological mineral. Others have grown such](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-27-320.jpg)
![crystals at Langmuir monolayers, and reported oriented growth on the basis of selected crystals
lifted off the surface [19]. However, in our in situ studies we see that calcium carbonate does
grow preferentially at the interface but is misoriented - a powder. There is also no relationship
between the calcite (or vaterite) structure and the monotayer structure observed in sire.
Another crystal that grows weIl under a Langmuir monolayer is BaF2 [20]. Our in situ studies
confirm that in this case, perfectly aligned crystals grow under a Langmuir monolayer.
Unexpectedly, the BaF2 lattice spacings vary with the solution concentration: at high
concentrations they are exactly the same as for bulk BaF2, but at the lowest concentrations
(smallest nuclei) the lattice is commensurate with the Langmuir monolayer lattice. Strained
epitaxy is well known in inorganic thin film deposition under high vacuum, but if confirmed,
this will be the first report of strained epitaxial growth during nucleation from solution. Further
studies are in progress.
6. ACKNOWLEDGEMENT
The work of our group was supported by the US Department of Energy under grant no. DE-
FG02-ER45125.
7. REFERENCES
V.M. Kaganer, H. M6hwald and P. Dutta, Revs. Mod. Phys.,71,779 (1999)
S. StNlberg-Stenhagen and E. Stenhagen, Nature 156, 239 (1945)
G.L. Gaines, "Insoluble monolayers at liquid-gas interfaces", lnterscience Publishers,
New York, !966, pg. "184
A.M. Bibo and I.R. Peterson, Adv. Mater. 2,309 (1990).
M.K. Durbin, A. Malik, A.G. Richter, R. Ghaskadvi, T. Gog and P. Dutta, J. Chem.
Phys. 106, 8216 (1997)
G.A. Overbeck, and D. M6bius, D.J. Phys. Chem. 97, 7999 (1993)
M.K. Durbin, A. Malik, R. Ghaskadvi, M.C. Shih, P. Zschack and P. Dutta, J. Phys.
Chem. 98, 1753 (1994)](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-28-320.jpg)
![CHAPTER 2
ANALYTIC MODEL OF FLOW ORIENTATION IN
LANGMUIR-BLODGETT FILMS
Michio Sugil, Yuka Tabe2and Keiichi Ikegami2
i Faculty of Engineering, Toin University of Yokohama, Aoba-ku, Yokohama (Japan)
2Nanotechnology Research Institute, National Institute of Advanced Industrial Science and
Technology, Tsukuba, Ibaraki (Japan)
1. INTRODUCTION
The Langmuir-Blodgett (LB) technique, devised in the middle of 1930's, consists of the
manipulation of a monolayer condensed at an air-water interface and the deposition of it by
dipping and raising through the interface onto a fiat substrate which is kept upright [1]. This
technique is often referred to as the vertical dipping method. Three different types are
recognized in the manner of deposition: Y-type which picks up monolayers onto the substrate
for both dipping and raising, X-type picking only for the dipping, and Z-type picking for the
raising [1].
The products, called Langmuir-Blodgett films or simply LB films, have been attracting
continued interest in various fields of science and engineering. The origin of the present
interest can be traced back to the early 1960's to the pioneer work of H. Kuhn and his](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-30-320.jpg)
![14
collaborators, who utilized the LB technique as a means of arranging various molecules in the
form ofultrathin ordered films as a new class of assembly systems [2].
Characterization of the precursors of LB films, i.e., monolayers at the air-water interface, has
been fairly advanced as well as that of the end products, i.e., LB films. Now there are indeed
many guidelines for "good LB films" referring to some of the characteristic aspects associated
with the LB deposition process [3]. Most of them are, however, empirical laws to give
qualitative guidelines, and only a few analytic approaches are found to be effective in deriving
quantitative guidelines. The in-plane anisotropy in LB film system, for instance, is reported in
the early stages [4], and its occurrence has been known to depend on the deposition conditions.
Until the late 1980's, however, the origin of the in-plane anisotropy had been far from fully
understood.
Let us consider now the vertical dipping method. During the deposition, the substrate moves
either upward or downward between the upper and the lower dead centers. The direction of the
movement, however, does not matter very much if the consideration is confined to the motion
of the monolayer on the water surface: the monolayer is drawn closer to the upright substrate
and fades away from the water surface as the deposition proceeds, i.e., the deposition process is
inevitably associated with the flow and the deformation of monolayer.
The LB deposition process might be compared to a two-dimensional cosmos with black holes
distributed on a finite line with a uniform density. The former is the water surface with the
monolayer being the interstellar matter and the latter is the substrate moving upward or
downward. The monolayer is, however, different from the dispersed interstellar matter, a
condensed film like a two-dimensional solid [1]. These considerations suggest that the flow
and the deformation of the solid state should be appropriately taken into account for the better](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-31-320.jpg)
![15
understanding of the LB deposition process.
The continuous deformation of a solid by an external force is referred to as the plasticity [5].
The standard mechanical processing techniques as forging, rolling, squeezing and plucking of
metals, for instance, are nothing other than the utilization of the plasticity. A tiny pellet of a few
grams of gold is plastically extended to cover some ten square meters, and copper lead wires,
thick or thin, are produced using the plucking process, it is well known that these plastic
deformations are often associated with the changes in the microscopic texture such as size,
shape and orientation of the crystallites, resulting in the changes in the physical properties such
as mechanical, magnetic and electric ones. What would then happen in the case of
two-dimensional monolayers during the LB deposition process, and how can we describe it
quantitatively in relation to the in-plane anisotropy observed in the resultant LB films?
In this respect, endeavors have been made to describe the in-plane anisotropy observed in LB
films employing the morocyanine - fatty acid mixed films as a model system. Their chemical
structures are shown in Fig. 1, where DX with X--O, S or Se and C,, with n=16 - 22 refer to the
merocyanine and the fatty acid, respectively.
Ca)
D.~>CH CH..~s
"s DX
, O" t~
C18H37 CH;~COOH (X-O, S o~Se)
(b)
CH3(CH2)._~COOH C2o
Fig. 1 Chemical structures of (a) surface-activemerocyaninedye (DX with X=O, S or Se) and (b) straight-chain
fattyacid(C,,with n=]6 - 22).
The merocyanine dye family is generally characterized as a conjugate n--electron system that](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-32-320.jpg)
![17
anisotropy due to the compression and other anomalies, and also the problems associated with
them. In §5, another approach, describing the LB deposition as a Markov process, is reviewed
together with the results of numerical calculation. The thermal equilibrium assumption adopted
in the analytic approach is critically examined referring to the Markovian approach, and the
in-plane anisotropy due to the compression is also touched upon. §6 describes the advanced
methods to control the in-plane anisotropy in LB films by regulating the plastic flow in a
monolayer by the use of rotating disks, reviewing the quantitative model together with the
experimental results.
2. IN-PLANE ANISOTROPY IN LB FILMS
It is well known that the DX-C20 mixture form stable monolayers at the air-water interface
when it is dissolved in chloroform and spread on an aqueous subphase containing Cd2+, and
that, for the molar ratio up to [DX] : [C20]=1 : 2, these monolayers are easily deposited to form
Y-type LB films [6]-[17] . The as-deposited LB films of DS-C20 and DSe-C20 as well, are blue
in color and associated with a characteristic red-shifted band (J-band [18]-[20]) in the optical
absorption spectrum.
It is indicated that an ordered arrangement of the dye molecules, referred to as the J-aggregate,
is formed in these LB films, and that they are associated with stable spins of n-electron
character in the dark state. Both optical and ESR spectra have been found to exhibit the
in-plane anisotropy that has opened the way to the analytic model of flow orientation in the
present form. The results from the DS-C20 films are outlined in the following.
2.1. OpticalAnisotropyofJ-Aggregate
Figure 2 shows an example of anisotropic optical absorbance observed in a mixed LB film of](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-34-320.jpg)
![18
[DS] : [C20]=1 : 2 with a J-band centered around 590 nm, where the solid and the dashed lines
refer to the absorbances All and A± measured using the incidents normal to the layer plane with
the electric vector parallel and perpendicular to the dipping direction, respectively [21 ], [22].
2~
0 /"/"
4OO 5OO 7oo
,I. (nP,~)
Fig. 2 Anisotropicopticalabsorptionspectrumin a DS-C201 : 2 mixed LB filmfor a linearlypolarized lightwith
an incidentangleof 90°to the substrate.The absorbanceper monolayerA is plottedagainstthe wavelength2. The
solid and the dashed lines refer to Aliand A~ for the electricvector parallel and perpendicular to the dipping
direction in the filmplane, respectively.(Reproducedfrom[22]by permissionof the PhysicalSocietyof Japan.)
The dichroic ratio defined by R=AII/A ± is conventionally used to represent the in-plane
anisotropy observed in the optical absorbance: the transition dipole moment of the dye
chromophore is preferentially oriented in the direction of dipping and raising the substrate if
R>I; it prefers the direction perpendicular to the dipping direction if R<I, and it may be
isotropically distributed if R=I, while the angle of 45 ° between the dipole moment and the
dipping direction will also result in R=I.
The larger magnitude for Ali seen in Fig. 2 indicates that R> 1, i.e., the transition dipole moment
is preferentially oriented in the dipping direction. The value of R has been found to increase
with the deposition velocity or the speed of dipping and raising the substrate va, but to remain
in any case appreciably greater than unity at the J-band peak: R_>1.3, typically [22].
It has been found that the J-band can be dissociated and restored by the secondary treatments
using heat, acid and base [13], [23]. When an as-deposited film, blue in color, is kept at 90°C
for 30 min, for instance, the J-band and its in-plane anisotropy disappear and the film turns red](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-35-320.jpg)
![19
with the absorption maximum shifted to 540 nm. If the film is further treated by an exposure to
the vapor from ammonia water, then it turns again blue, with the J-band and its anisotropy
restored. These facts indicate that the DS chromophores in the J-aggregate are bound by such
relatively weak forces as the dipole-dipole interactions. Here, it is noted that the spectral shape
of the DS-C20 mixed fihn is found to be insensitive or essentially invariant to the molar mixing
ratio down to [DS] : [C:0]=I : 20 [9]. It is suggested that DS and C20 are immiscible with each
other forming a phase-separated monolayer consisting of the DS aggregates embedded in a
C20-rich matrix, and that the 540-nm isotropic band in the heat-treated film reflects the
disorders introduced in the aggregates.
2.2 Anisotropy in ESR Line Shape
Electron spin resonance (ESR) studies by Kuroda et al. have shown that the DS-C20 mixed LB
film is associated with stable spins of a'-electron character with a concentration as high as one
spin per several hundred DS molecules in the dark state [10], [15], [24]-[27]. The spins have
been found to involve two different species, A and B, of which the former is anisotropic and
the latter is featureless in ESR line shape as shown in Fig. 3 [24].
The concentrations of A and B are essentially equal to each other as seen in the figure,
suggesting that A and B form pairs in occurrence.
if we assume that a spin A and a spin B are associated with each other in an aggregate of
several hundred DS molecules, the aggregate will be more or less one-dimensional in shape so
that the spin pair is stabilized at its ends: a situation reminiscent of a cation or an anion radical
stabilized at each end of a polymer chain [24]. This picture is quite compatible with the fact
that both A and B disappear when the film is heat-treated at 90°C for 30 rain as is the case with
the J-band and its anisotropy mentioned in §2.1.
The species A was later successfully assigned to the donor radical by the ESR studies using the
15N-substituted donor and acceptor [28]-[30]. It is therefore indicated that the intermolecular](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-36-320.jpg)
![20
distance in the J-aggregate is small enough to allow the intermolecular charge transfer, and that
A and B originate from the cation and the anion radicals, respectively, located at the opposite
ends of the one-dimensionally developed J-aggregate.
(a) 12.007' ...........
~.f ....
I ~ - _
4"-2.OO9
.... I~ ^
lii i i i
Fig. 3 First-derivative ESR spectra of a 1000-layered DS-C2o 1 : 2 mixed LB films at room temperature (solid
curves). The external magnetic field is normal to the film plane (a). It makes the angle of 0°, 45" and 90° with the
dipping direction of the substrate from(b) to (d), respectively. Numbers show g-values of the fields as indicated.
Dashed lines show the simulated curves of the spin species A. Stick lines at the bottom of(d) show the resonance
fields corresponding to principal components of g and hyperfine tensors. (Reproduced from Ref. [24] by
permission of the Physical Society of Japan.)
Analysis of the anisotropic line shape of A has revealed that the pn orbital axis of DS
chromophore lies in the layer plane with its distribution function simulated by the
superposition of two components having maxima at about +60 ° with respect to the dipping
direction [15].
Figure 4 shows the model of the in-plane alignment of the DS chromophores deduced from the
analysis. This is compatible with the dichroic ratio R>I of the optical absorbance if the](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-37-320.jpg)
![21
aggregate of DS in the ESR study is identified with the optical J-aggregate, since the pa orbital
axis and the transition dipole moment are approximately orthogonal to each other, suggesting
the deviation angle of a=+30 ° which indicates R> 1.
(a) (b)
Dippingdirection
H,,t l y
~""'O~pr,orbitaI
Substrate
Dipping
direction
Fig. 4 Model of thc in-plane alignment of DS chromophorcs.(a) The external magnetic field and the proorbital
axis make angles ~'~,tand 0;,~with the dipping direction, respectively. The long axis of the chromophore is
schematically expressed by a thick line. (b) The long axis makes an angle a with the direction connecting the
centers of adjacentmolecules.<Ow>
denotesthe averageof 0p,~.(Reproducedfrom Ref. [24]by permissionof the
Physical Societyof Japan.)
Models of the J-aggregate structure have been proposed from various viewpoints including the
remarks from the optical and the ESR measurements. A comparable value a=±30 ° has been
estimated, e.g., by Nakahara et al. [16] by analyzing the optical anisotropy based on an
extended dipole model, although there still remain controversies to be solved among the
models [16], [20], [24], [30]-[34]. The detailed discussion is, however, beyond the scope of the
present article.
2.3. PossibleOrigin ofIn-planeAnisotropy
Let us imagine a stream in autumn, flowing gently, with its surface covered with a lot of leaves
fallen from the trees on the banks. Each of them is drifting down the stream as if it were](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-38-320.jpg)
![22
destined to trace its own path. Looking down from a height, however, one would recognize a
steady pattern like a bundle of stripes woven from numberless leaves drifting on the water
surface. If they are elongated in shape like those of willow, one would find that they are
aligned one after another in each stripe, forming head-to-tail, side-by-side or randomly stacked
chains.
TITTTT wTTT
iTTTTT.
1
TTTTTT ,wTT
. . . . . . • x ~, ,7:.
(a) (b)
TTTTTT
Y Y
, TTTTTt
.................. ~ X, • 1,"
(c) (d)
Fig. 5 Examplesof simple flows and typesof stacking. In each case, all the streamlinesare assumedto be parallel
to they-axis, i.e., vx=O.(a) vy=vo,random;(b) vy=vo+gx,head-to-tail;(c) v.~,=v0+gywithg>O,head-to-tail; (d) vy=vo
-gy with -g<O,side-by-side.
Such a pattern reflects the Iocat variation of the velocity field on the water surface. The center
of the leaf at a given place moves in accordance with the local velocity vector, as a matter of
course. Then, why a willow leaf sometimes prefers orienting its long axis towards a specific
direction? The clue for answering the question may be found in the velocity gradient that exerts
a torque on the leaf to orient to a specific direction [36], [37].](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-39-320.jpg)
![23
Let us consider four extreme cases (a) - (d) as shown in Fig. 5. In each case, all the streamlines
are assumed to be parallel to the y-direction, i.e., v.~(x,y)=Ofor simplicity.
Case (a) refers to the uniform velocity v~,(x,y)=v0=const. All the elements of the velocity
gradient tensor G are then equal to zero. As a result, the orientation of each leaf remains
unchanged, and the leaves may be randomly stacked.
Case (b) exemplifies the x-dependent velocity with a function vy(x,y)=vo+gx,which results in a
non-zero element in G, i.e., @x=OvJc3x=g,orienting the long axis to the y-direction. A
head-to-tail stacking of the leaves will be realized as a consequence.
Case (c) represents the increasing function of y by vy(x,y)=vo+gywith g>0, resulting in a
non-zero element Gyy=Ov),/Oy=g>Oto orient the axis to the y-direction. The resultant stacking
will also be head-to-tail.
Case (d) refers to a decreasing function vy(x,y)=vo-gywith G),y=-g<0, which orients the axis to
the x-direction. In this case, therefore, a side-by-side stacking will be realized, in contrast to
Cases (b) and (c).
There arises a question as to what extent this naive picture can be effective as the starting point
for elaborating a quantitative model to explain the in-plane anisotropy actually observed in the
LB films of DS-C20 and others. The endeavor of answering this question has led to the analytic
model of flow orientation [21], [22], [38]-[40], of which the basic framework will be reviewed
in the next section.](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-40-320.jpg)
![24
3. BASIC FRAMEWORK OF THE MODEL
In the analytic model of flow orientation for the conventional LB dipping process, the
monolayer on the water surface is assumed to be a continuum, ~ and the model consists of two
stages: the evaluation of the velocity potential on the water surface and the description of the
rotatory motion of a particle in this potential field.
3.1. Velocity Potential of the Monolayer Flow
In evaluating the flow of monolayer at the air-water interface, we have assumed:
(1) the monolayer is a two-dimensional ideal fluid;
(2) the substrate, i.e., a flat plate on which the monolayer is deposited, is a two-dimensional
fine sink;
(3) the monolayer is infinite in its dimensions [21], [22].
3.1. I. Ideal Fluid Approximation
The assumption (1) involves the incompressible and irrotational conditions. The former and the
latter enables us to introduce the velocity potential U(x,y) and the stream function V(x,y) to
describe the flow in an x-y plane which represents the water surface.
Here, the velocity vector v=(vx,vy)Taround a point (x,y) is given by,
8U 8U
v = -U x, vy=~==-U;,, (1)
Ox ay
and also by,
The continuumapproximation is implausible to very brittle monolayers, for which case Matsumoto et al. have
proposed the "channel-and-iceberg"modelin Refs. [4l] and [42].](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-41-320.jpg)
![25
OV OV
v,.=~--Vy, vy=-~--V,. (2)
Oy ax
Equations (1) and (2) are nothing but the well-known Cauchy-Riemann relation, Ux=Vyand
Uv=-Vx, which guarantees the existence of the complex velocity potential W(z)=U+iVin the
Gaussian plane, where z=x+iy [35], [36]. The velocity vector v is then written using the first
derivative dW/dz as,
• (@z
W ) = -Im(dW /
v~ = Re , v,, ~,--&z)" (3)
The deformation rates of an area element are given by the velocity gradient tensor G written as,
G =(G~:~ G ' (4)
where Gxx=Ovx/Ox,Gxy=Ovx/Sy,Gyx=Svy/c3xand Gyy=Ov/Sy. In Eq. (4), the diagonal elements,
Gxx and Gyy,denote the expansion-compression rates, and the off-diagonal elements, Gzy and
Gyx, are the shear rates. Using the second derivative d2W/dx 2, each element in Eq. (4) is
written as,
Re(dZWi (5)
and,
ira( d2W )
G.,, = Gyx =- ~dz2) (6)
The incompressible condition is referred to by Eq. (5), i.e., the expansion or compression of
the area element in the x-direction is canceled by that in the y-direction. Equation (6) is related
with the irrotational condition: G is a symmetric tensor associated with a pair of principal axes,](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-42-320.jpg)
![26
orthogonal to each other, at which directions the flow torque vanishes.
3.1.2 Normal Deposition with a Single Substrate
The assumptions (2) and (3) refer to the neglect of the thickness of the substrate in comparison
with its width, and also the complicated boundary conditions due to the shape and dimensions
of the trough and the barriers.
Let us consider the normal case that the monolayer is symmetrically deposited onto both
surfaces of one single substrate, which is represented by a line sink. If the substrate occupies a
range -a/2<x<a/2 on the real axis, the complex potential W=U+iV is written as [21],
W(z) = - v---g-a[ ~/2 log(z - x') dx',
7l" ,l-at2
(7)
where va is the deposition velocity, i.e., the speed of dipping and raising the substrate, and we
assume that the transfer ratio of rd--1, indicating that the monolayer is transferred from the
water surface onto the substrate without compression or expansion. Eq. (7) is regular except for
lx[<a/2 on the x-axis, and the factor -vd/~r at the right-hand side is so chosen that the condition
vy--,. -T-Va for ixl<a/2 is satisfied when y --~ +0.
Equation (7) is easily integrated as,
(8)
with the real and the imaginary parts,
IC~1 f/~/2 }l ~1 {I ~12 }
- va x y2
U(x,y) ~ - log x- + - x+ log x+ +y2
1
+2y arctan x-a/2 _arctan +a , (9)
lyl Jy](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-43-320.jpg)
![and,
V(x,y) ~ x+a/
+ylog x- +y2 _ylog x+ +y2 ,
respectively.
(lo)
27
dipping direction
y
-x4. x ,
(a) (b)
Fig. 6 (a) Streamlines and equipotential lines shown by the solid and the dashed lines, respectively for a
two-dimensional ideal fluid with a line-sink on the x-axis represented by the thick rod. (b) Schematic
representation of the normal LB deposition process. (Reproduced from Ref. [22] by permission of the Physical
Society of Japan.)
Figure 6 shows the equipotential and the streamlines, U(x,y)=constand V(x,y)=const,
respectively, for the single-substrate case [22]. The first derivative of W(z)is given as,
I I I all
dW__v~ log z- -log z+~ ,
dz tr
with the velocity vector expressed by,
(11)
vx(x'Y)= It, dz ) = ~---~log.
(x_a12)2 +yZ1
(x + ~/2) ~ + y~ '
vj,(x,y) = - t~---dZ-Z
) ¢c{ kx-al2,) x+al2)J
(12)](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-44-320.jpg)
![29
and the rotatory Brownian motion, while the inertia term is assumed to be neglected. Let (~', q)
be a coordinate with the (- and q-axes parallel to the x- and y-axes, respectively, and its origin
is fixed at the center of particle (x, y), as shown in Fig. 7. The relative velocity (~,¢/) of point
(~x,q) with respect to the origin is expressed by,
Gyx G~ '
(16)
using Eq. (4).
1
7 Long
axis
ofaggregate
Dipping ~ ,,
direction ~ ~ ~- c,
Fig. 7 Definition of ~, q-coordinate with the origin fixed at the center of particle. The long axis of the aggregate
forms angles ~0and 0 with the 4'- and q-axes, respectively, a refers to the angle between the long axis of the
aggregate and the transition dipole moment. ~b is the angle between the electric vector of lhe incident and the
q-axis. (Reproduced from Ref. [22] with modification by permission of the Physical Society of Japan.)
Let ¢ be the angle between the position vector and the ~'-axis as shown in Fig. 7, i.e., ~X=rcos¢
2
and ~/=rsintp with r = x/4'2 + 17 •The angular velocity is written as,
do G~, -G~ 2 z
(°-dt~ = ~ 2 sin 2rp + Gy.~cos ~ - Gxy sin co, (17)
or,
0 dO G~ -G~
- ~ = ~ s i n 20 + Gyx cos20 + (G~/- Gy~)cos 2 0, (18)
dt 2
if we use the angle 0 -- ~/2-(p instead of ~o.](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-46-320.jpg)
![30
In the incompressible, irrotational case, we derive,
t) = G= sin 20 + Gy~cos 20, (19)
referring to Eqs. (5) and (6). Substituting t)= 0 for Eq. (19), we obtain the expressions for the
principal axes as,
0+ 1 ~G.~¢)
( Gy,."] ( dtg)
~-
= -- arctan/ " l, with, + < 0, (20)
- 2 - dOo_o"
and the associated eigenvalues are,
< =_+#oS+c:.,.
where the double signs are taken in the same order. Here, the positive and negative eigenvalues,
G+ and G_, correspond to the maximum expansion and compression rates, respectively, and the
mechanically stable point is identical with 0+. The extreme values of the shear rate and their
positions are easily derived in a similar manner using the conditions with dO~dO = 0 and
+d20/dO 2<0as,
max min
= -G+, (22)
which are located at 0 = 0_+-n"/4, respectively. Thus, we have reconfirmed the naive view in
§2.3, i.e., the preferred direction of the long axis is not identified with the tangential of a
streamline, but determined by the velocity gradient.
The angular distribution function P can be derived starting from an equation of continuity [43],
OP c3S
. . . . (23)
Ot 00'](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-47-320.jpg)
![31
where P(O)dO gives the probability for 0 to lie in a range 0- O+dO, and S is the flow of
probability passing through a point 0. Here, S is written as,
S = t)P- D -~,0P (24)
O0
where D is the rotatory diffusion coefficient. In Eq. (24), the first term at the right-hand side
refers to the drift flow to orient the long axis of a particle towards the preferred direction, and
the second term corresponds to the diffusion flow to randomize the orientation.
Substituting Eq. (24) for Eq. (23), we obtain the diffusion equation,
oR o(oP) o~P
. . . . +D~ (25)
Ot O0 002 '
which expresses the compromise between the flow due to t) and the Brownian motion.
The rotatory diffusion coefficient D is related with the rotatory friction coefficient (between
the particle and the medium through the Einstein relation,
D = ksT , (26)
(
where k8 and T are the Boltzmann constant and the absolute temperature, respectively. It is
noted that D is generally a function of t since (may change as the particle moves towards the
substrate.
3.2.2. Local Thermal Equilibrium Approximation
If we assume that thermal equilibrium is quickly attained in comparison to the change in G, i.e.,
the local thermal equilibrium approximation, only the values of t) and D near the substrate
are referred to as determining the orientation [21], [22]. In this case, OP/& = 0, and Eq. (25)
is readily integrated as,
OP- O --c3P= So , (27)
00](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-48-320.jpg)
![33
(G sin 20)P + --~ = O, (31)
using Eqs. (19), (26) and (29). We integrate Eq. (31) to derive the angular distribution function
P(0) of Boltzmann-type as,
(32)
whose maximum is located at 0=-0. Allowing for the normalization condition ["2 P(O)dO =1
-ttl2
Eq. (32) is rewritten as,
P(O) = exp(-2c sin 2 0), (33)
where I0 is the modified Bessel function of the zeroth order, and c is defined as,
c= (O (34)
2k~T '
which is referred to as the flow orientation parameter or the c-parameter [22].
According to Eqs. (33) and (34), P(O) is determined by the c-parameter alone. The width of
P(O), for instance, is evaluated with a quantity <sin20> given by,
r,,, ,(,,<c))
< sin 20 >= sin 20P(O)dO = -~ 1- ,
"-"~ :o(~))
(35)
where I1 is the modified Bessel function of the first order.
3.3. Dichroic Ratio
Experimentally, we obtain the dichroic ratio R=-A(O)/A(1r/2) as representing the orientation of
the particle. Here, A(~b) is the absorbance of incident light polarized to an angle ¢ with
respect to the direction of dipping and raising of the substrate during the deposition process.
For evaluating R, the particle is assumed to be an aggregate of molecules as shown in Fig. 7.](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-50-320.jpg)
![34
The transition dipole moment of each molecule forms an angle a with the long axis of the
aggregate, which is at an angle 0 from the dipping direction. The absorbance A(¢) is written
as,
f ~'~ {cos~(o + ~ ~) + cos2(O ~ 0)} P(o)ao,
" -1r12
(36)
allowing for the symmetry with respect to the dipping direction [22]. The dichroic ratio is
therefore given by,
f ,~/2.tcos2(0 + Jr) + cos 2(0 - rr)l
~ P(O)dO
A(O) --~2
R = ~ = , (37)
A(n'/2) f_~]i22
{sinz(0 + re)+ sin 2(0.7r)} P(O)dO
If we substitute Eq. (33) derived assuming the local thermal equilibrium for Eq.(37), we obtain
the expression for the normal deposition with a single substrate as,
R = I° (c) + I~(c) cos 2a (38)
Io(c)-Ii(c)cos2a
using Eq. (35) and a relation <cos220>=l-<sin220>. Therefore, R is governed by c and a in this
case: it tends to R= 1 for c --~ 0 and R=cot2a for c ~ or.
3.4. BinghamModelofPlasticity
The rotatory friction coefficient (is determined by the size and shape of the particle and the
viscosity of the surrounding medium. If the medium is a Newtonian fluid, (is a constant
independent of the shear rate. It is however well known that condensed monolayers at the
air-water interface often show plasticity [1], which is characterized with the shear-dependence
of;'.
Of many models of visco-elasticity available so far [5], [44], a Bingham fluid model [45]](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-51-320.jpg)
![35
has been introduced to take the plastic behaviour into account. ( is then a function of the
maximum shear rate 0 m,x= G+ = G (cf. Eqs. (22) and (30)) and given by
72o
£" = ((G) = £" +--, (39)
G
where (' and ~:0refer to the Newtonian viscosity and the Bingham yield value, respectively [22].
Accordingly, the expression of ((7 is replaced by,
((7 = ('G + 720, (40)
which indicates that the system remains an elastic body if the maximum torque CG acting on
the particle does not exceed z'0, and that plastic deformation takes place for ~'G> r o and a
proportional relationship similar to the Newtonian case is held between the excessive torque
and the shear rate. The flow orientation parameter for the Bingham case is therefore expressed
as,
~"~+ r O
c = ~ , (41)
2keT
by substituting Eq. (40) for Eq. (34). It is noted that c ---, r ot(2keT)>Oeven when G --, 0.
3.5. Predictions from the Model
According to Eqs. (30), (33) and (41), the distribution function P(O) for the Bingham case is
governed by six parameters involved in the c-parameter, which is explicitly written as,
.k, rjt a
--F)
72o
2k~T
(42)
by substituting Eq. (30) for Eq. (41) [22].
The six parameters are the temperature T, the width of the substrate a, the deposition velocity
Vd, the relative position on the substrate lxl/a, and the two parameters (' and r0 involved in](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-52-320.jpg)
![36
the Bingham model of rotatory friction coefficient. According to Eq. (42), the dichroic ratio R
is determined by seven parameters, i.e., the above six and the deviation angle of the transition
dipole moment a. Among the seven, a, vd and ]xl/a are characteristic of the LB deposition
process, while C', r oand a are the properties of the monotayer.
3.5.1 Law of Similarity
The c-parameter given by Eq. (42) involves three dimensionless terms. They are (1) ('va
/(akeT), (2) (l-4x2/a2)-1 and (3) ~:0/(2keT),each leading to a law of similarity which governs the
degree of orientation.
(1) ~"'Vd I(akBT) involves four parameters, of which the deposition velocity Vdand the substrate
width a are adjustable independently of any other parameter involved in c, while the
Newtonian friction coefficient ~", and the Bingham yield value r0 as well, are generally
known to be temperature-dependent, vd and a are competitive against each other in their
contributions to the c-parameter: c increases with vd, but decreases with a, and the increment in
c for 2 vd is exactly equal to that for a/2.
(2) (1-4x2/a2) -1 represents the effect of the position on the substrate. It exhibits its minimum at
the center [x[/a=O, and increases slowly when [xl/a>>l/2, but diverges to infinity for [xl/a ---, 1/2.
Accordingly, the c-parameter, with its minimum Cmi,at the center, may have any value up to
c + co. In other words, starting from the lowest degree of orientation at the center, any high
degree up to the complete orientation is realized in one and the same substrate towards the edges.
(3) r0/(2kBT) refers to the effect of Bingham plasticity. For r0>0, the c-parameter remains
non-zero even for va --* O. In this case, c is determined by r0/(2ksT) alone, and its dependence
on the dimensionless terms (1) and (2) disappears, resulting in a constant c-value all over the
substrate except for the singular points Ix]/a--1/2 associated with the edges. As a consequence,](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-53-320.jpg)
![37
the dichroic ratio R is always R>I for a<45 ° and R<I for a>45 °.
3.5.2. Effect of the Length of Particles
Both (' and r0 depend on the geometry of the particle and the viscoelasticity of the monolayer
as a two-dimensional system. In the case of rod-like particles, e.g., rigid polymers or
needle-like crystallites, it is well known that,
(' ,~rfb2,
ro =f0b z, (43)
where b is the length of the particle, and r/' andJ~ are the surface Newtonian viscosity and the
corresponding Bingham yield value, respectively [37]. Here, the Bingham viscosity q at a shear
rate g is written as,
11 = q(g) = rl'+ fo (44)
Igl'
The sharpness of orientation increases therefore with the length b of the particle. Furthermore,
q' and j~ of the monolayer may also be increased with b, resulting in the enhanced flow
orientation effect.
3.6. Comparison with Experimental Results
The analytic model summarized in §3.1 - §3.5 is compared with the dichroic behaviour
observed in the absorption spectra of the mixed LB films of merocyanine DS and arachidic
acid C20 as exemplified in Fig. 2 [22]. The chemical structures of DS and C20 are shown in
Fig.1.
The dichroic data to be reviewed are from the 590-nm J-band seen in the Y-type LB films of a
mixture [DS] : [C20]= 1 : 2, prepared using the standard vertical dipping method with one single
substrate. The monolayers were formed at 20°C on an aqueous subphase containing Cd2+](https://image.slidesharecdn.com/907817-250615093105-c1432494/85/Organized-Monolayers-And-Assemblies-Structure-Processes-And-Function-1st-Edition-D-Mbius-And-R-Miller-Eds-54-320.jpg)
Organized Monolayers And Assemblies Structure Processes And Function 1st Edition D Mbius And R Miller Eds
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- 6. STUDIES IN INTERFACE SCIENCE Organized Monolayers and Assemblies: Structure, Processes and Function
- 7. STUDIES IN INTERFACE SCIENCE SERIES EDITORS D. Mfbius and R. Miller Vol. 1 Dynamics of Adsorption at Liquid Interfaces. Theory, Experiment, Application. By S.S. Dukhin, G. Kretzschmar and R. Miller Vol. 2 An Introduction to Dynamics of Colloids. By J.K.G. Dhont Vol. 3 Interfacial Tensiometry. ByA.I. Rusanov and V.A. Prokhorov Vol. 4 New Developments in Construction and Functions of Organic Thin Films. Edited by T. Kajiyama and M. Aizawa Vol. 5 Foam and Foam Films. By D. Exerowa and P.M. Kruglyakov Vol. 6 Drops and Bubbles in Interfacial Research. Edited by D. M6bius and R. Miller Vol. 7 Proteins at Liquid Interfaces. Edited by D. M6bius and R. Miller Vol. 8 Dynamic Surface Tensiometry in Medicine. ByV.M. Kazakov,O.V. Sinyachenko, V.B. Fainerman, U. Pison and R. Miller Vol. 9 Hydrophile-Lipophile Balance of Surfactants and Solid Particles. Physicochemical Aspects and Applications. By P.M. Kruglyakov Vol. lo Particles at Fluid Interfaces and Membranes. Attachment of ColloidParticles and Proteins to Interfaces and Formation of Two-Dimensional Arrays. By P.A. Kralchevsky and K. Nagayama Vol. 11 Novel Methods to Study Interfacial Layers. By D. M6bius and R. Miller Vol. 12 Colloid and Surface Chemistry. By E.D. Shchukin, A.V. Pertsov, E.A.Amelina and A.S. Zelenev Vol. 13 Surfactants: Chemistry, Interfacial Properties, Applications. Edited by V.B. Fainerman, D. M6bius and R. Miller Vol. 14 Complex Wave Dynamics on Thin Films. By H.-C. Chang and E.A. Demekhin Vol. 15 Ultrasound for Characterizing Colloids. Particle Sizing, Zeta Potential, Rheology. ByA.S. Dukhin and P.J. Goetz Vol. 16 Organized Monolayers and Assemblies: Structure, Processes and Function. Edited by D. M6bius and R. Miller
- 8. Organized Monolayers and Assemblies: Structure, Processes and Function Edited by D. M6bius Max-Planck-Institut fiir Biophysikalische Chemie, P.O. Box 2841, GSttingen, Germany R. Miller Max-Planck-Institut fiir Kolloid-und Grenzfl~ichenforschung, Am Miihlenberg 1, Potsdam/Golm, Germany 2002 ELSEVIER Amsterdam - Boston - London - New York - Oxford - Paris - Tokyo - San Diego San Francisco - Singapore - Sydney
- 9. ELSEVIER SCIENCE B.V. Sara Burgerhartstraat 25 P.O. Box 211, 1000 AE Amsterdam, The Netherlands 92002 Elsevier Science B.V. All rights reserved. This work is protected under copyright by Elsevier Science, and the following terms and conditions apply to its use: Photocopying Single photocopies of single chapters may be made for personal use as allowed by national copyright laws. Permission of the Publisher and payment of a fee is required for all other photocopying, including multiple or systematic copying, copying for advertising or promotional purposes, resale, and all forms of document delivery. Special rates are available for educational institutions that wish to make photocopies for non-profit educational classroom use. Permissions may be sought directly from Elsevier Science Global Rights Department, PO Box 800, Oxford OX5 IDX, UK; phone: (+44) 1865 843830, fax: (+44) 1865 853333, e-mail: permissions@elsevier.co.uk. You may also contact Global Rights directly through Elsevier's home page (http://www.elsevier.nl), by selecting 'Obtaining Permissions'. In the USA, users may clear permissions and make payments through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA; phone: (+1) (978) 7508400, fax: (+1) (978) 7504744, and in the UK through the Copyright Licensing Agency Rapid Clearance Service (CLARCS), 90 Tottenham Court Road, London WIP 0LP, UK; phone: (+44) 207 631 5555; fax: (+44) 207 631 5500. Other countries may have a local reprographic rights agency for payments. Derivative Works Tables of contents may be reproduced for internal circulation, but permission of Elsevier Science is required for external resale or distribution of such material. Pcrmission of the Publisher is required for all other derivative works, including compilations and translations. Electronic Storage or Usage Permission of the Publisher is required to store or use electronically any material contained in this work, including any chapter or part of a chapter. Except as outlined above, no part of this work may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written permission of the Publisher. Address permissions requests to: Elsevier Science Global Rights Department, at the mail, fax and e-mail addresses noted above. Notice No responsibility is assumed by the Publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made. First edition 2001 Library of Congress Cataloging in Publication Data A catalog record from the Library of Congress has been applied for. ISBN: 0 444 51256 X ISSN: 1383 7303 The paper used in this publication meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper). Printed in The Netherlands.
- 10. V PREFACE The gas-water interface provides excellent possibilities to organise appropriate molecules in ultrathin films that are called monomolecular layers (monolayers or Langmuir and Gibbs films, respectively), since generally these films are only one molecule thick. Different to ultrathin films formed by surface chemical reaction on solid surfaces (self-assembly), the intermolecular interactions and resulting order may be controlled externally in the monolayers by variation of relevant parameters like the area per molecule or the lateral pressure. Therefore, these ultrathin films are particularly suited as model systems for the investigation of interfacial phenomena as well as membrane processes. The various contributions in this monograph range from reviews of fundamental studies of long range order e.g. of the hydrocarbon chains of simple insoluble amphiphilic molecules to reports and discussion of potential applications in sensors or opto-electronic devices. Monolayers of long chain fatty acids or alcohols exhibit a rich phase diagram as detected by optical techniques and X-ray diffraction. The incorporation of functional molecules like dyes or components of molecular recognition systems has opened a wide field of constructing molecular machines, i.e. devices on the nanometer scale. A large variety of analytical tools including different spectroscopic methods has been used to collect sufficient information for the evaluation of molecular orientation and association and ordering of large aggregates as well as understanding the underlying processes. Examples are the interplay between insoluble and soluble amphiphiles at the air-water interface, the influence of monolayer rheology on aggregate flow orientation, or the effects of trigger molecules and subtle variations of the molecular structure on orientation and association. The monolayers organised at the air-water interface may be transferred to solid substrates, and molecular architectures may be constructed by sequential transfer. For possible applications, however, the ultrathin organic layers formed by chemisorption and/or by molecular recognition with strong interaction of the components as in the system biotin/streptavidin may be more stable and easier to build. In the last two chapters of this monograph the potential of such ultrathin organic films for practical application is discussed providing a projection of the field to the near future. July 2002 D. MObius and R. Miller
- 11. This Page Intentionally Left Blank
- 12. Contents Preface CHAPTER 1 ORDER IN LANGMUIR MONOLAYERS AND IN THE AQUEOUS SUBPHASE Pulak Dutta Introduction The phase diagram of fatty acid and alcohol Langmuir monolayers Backbone ordering in fatty acid monolayers Order in the aqueous subphase Ongoing and future studies Acknowledgement References 1 2 5 6 10 11 I1 vii CHAPTER 2 ANALYTIC MODEL OF FLOW ORIENTATION IN LANGMUIR-BLODGETT FILMS Michio Sugi, Yuka Tabe and Keiichi Ikegami , 2. 2.1. 2.2. 2.3. 3. 3.1. 3.2. 3.3. 3.4. Introduction In-plane Anisotropy in LB Films Optical Anisotropy of J-Aggregate Anisotropy in ESR Line Shape Possible Origin of In-plane Anisotropy Basic Framework of the Model Velocity Potential of the Monolayer Flow Rotatory Motion of Particles Dichroic Ratio Bingham Model of Plasticity 13 13 17 17 19 21 24 24 28 33 34
- 13. viii 3.5. 3.6. 4. 4.1. 4.2. 4.3. 5. 5.1. 5.2. 5.3. 6. 6.1. 6.2. 6.3. 6.4. 7. 8. Predictions from the Model Comparison with Experimental Results Application to Complicated Cases Batch Production of LB Films Deposition in Small Troughs Anomalous Deposition Processes Numerical Calculation Based on a More Precise Model Flow Orientation Effect as a Markov Process Comparison with Experimental Results General Remarks Flow Orientation with Rotating Disks Rotating-disk Method Monolayer Flow Generated by a Rotatory Disk Orientation due to Shearing Multi-disk Versions Concluding Remarks Acknowledgements Bibliography CHAPTER 3 EQUILIBRIUM AND DYNAMICS OF 2D AGGREGATING MIXED MONOLAYERS CONSISTING OF SOLUBLE AND INSOLUBLE AMPHIPHILES Valentin B. Fainerman and Dieter Vollhardt Introduction General principles of penetration thermodynamics Description of the Gibbs monolayers with 2D aggregation Equation of state for Langmuir monolayers with 2D aggregation Penetration thermodynamics for homologues 35 37 43 44 51 59 65 66 70 75 77 77 79 85 91 95 98 98 105 105 107 113 115 118
- 14. 5.1 Generalised Szyszkowski-Langmuir equation 5.2. Generalised Volmer equation 5.3. Influence of the soluble amphiphile adsorption on the aggregation conditions 6. Penetration dynamics 7. Adsorption of soluble component in the compressed mixed monolayer 8. Experimental technique 9. Experimental studies of penetration and 2D aggregation 9.1. Mixed monolayer of soluble and insoluble dimethyl phosphine oxides 9.2. Mixed monolayer of soluble and insoluble amino acids 9.3. Protein penetration into DPPC phospholipid monolayers 9.4. Coadsorption of SDS/dodecanol mixtures 10. Conclusions 11. References I(-t CHAPTER 4 ORGANISATION OF PORPHYRINS IN MONOLAYERS AND MONOLAYER ASSEMBLIES Maria Teresa Martin Romero and Dietmar MObius 119 122 125 127 129 133 136 136 139 144 151 155 157 161 . 2. 2.1 2.2 2.3 3. 3.1 3.2 3.3 4. Introduction Monolayers at the Gas-Water Interface Location and orientation in monolayers at the gas-water interface Association phenomena Protonation and metallation equilibria Monolayer Assemblies Porphyrin organisation in monolayer assemblies Porphyrins as components of supermolecules Potential applications Abbreviations 161 162 163 172 185 190 190 196 199 200
- 15. 5. List of Symbols 6. References 201 202 CHAPTER 5 ENZYMATIC REACTIONS AT INTERFACES Marie H61/~n Ropert, Gerald Brezesinski and Helmuth Mfihwald 1. Introduction 2. Methods 3. Results and Discussion 3.1. Polymorphism of phospholipid monolayers 3.2. Interfacial reactions 3.2. I. The binding step 3.2.2. The catalyzed reactions 3.2.3. Inhibition- Activation 4. Concluding remarks 5. Abbreviations 6. References 207 207 208 212 212 216 216 223 234 238 239 240 CHAPTER 6 ELECTRON SPIN RESONANCE SPECTROSCOPY OF LANGMUIR- BLODGETT FILMS CONTAINING FUNCTIONAL MOLECULES Shin-ichi Kuroda l~ 2. 3. 3.1. 3.1.1. 247 Introduction 247 Parameters determined by ESR spectroscopy 248 Examples of ESR analysis of LB films 250 Characterization of in-plane molecular orientation in merocyanine dye 250 LB films Anisotropic ESR spectra of stable radicals -Characterization of in-plane 250 and out-of-plane molecular orientation
- 16. 3.1.2. 3.1.3. 3.2. 3.2.1. 3.2.2. 3.3. 4. 5. 6. ESR spectroscopy using isotope-substituted dyes Light-induced ESR of merocyanine dye LB films ESR studies of Cu-porphyrin films mixed with "trigger molecules" Monomer porphyrin with hexatriacontane, the trigger Dimer-type porphyrin with trigger Other examples Concluding remarks Acknowledgment References CHAPTER 7 BIOTIN-STREPTAVIDIN SENSOR SURFACE: A VERSATILE PLATFORM FOR PERFORMING DNA HYBRIDIZATION INTERACTIONS Dev Kambhampati and Wolfgang Knoll . 2. 2.1. 2.2. 2.3. 2.4. 3. 3.1. 3.2. 3.3. 3.4. 3.5. 3.6. 258 260 264 264 269 272 275 276 276 279 Introduction 279 Experimental Methods 281 Materials 281 Surface Architecture 281 Detection Techniques 283 Kinetic Models 284 Results and Discussion 285 Sensor Surface Topology 285 Non-specific Interaction Analysis 285 Regeneration of Sensor Surface 287 DNA Hybridization Interactions using P1 probes (15 T spacer and 15mer 290 recognition sequence) DNA Hybridization Interactions using P2 probes (30 T spacer and 15mer 295 recognition sequence) Melting' Analysis of Hybridization Interactions 299
- 17. xii 3.7. Effect of Temperature on Hybridization Interactions 4. Conclusions 5. Acknowledgements 6. References 306 312 313 313 CHAPTER 8 APPLICATIONS OF ORGANISED MOLECULAR FILMS TO ELECTRONIC AND OPTO-ELECTRONIC DEVICES Michael C. Petty 1. Introduction 2. Electrical Conductivity of Molecular Assemblies 2.1. D.C. Conductivity 2.2. A.C. Conductivity 3. Application of Organic Multilayer Assemblies 3.1. Organic Diodes and Transistors 3.2. Light Emitting Displays 3.3. Gas Sensors 3.4. Ion Sensors 3.5. Heat Sensors- Pyroelectric Devices 4. Conclusions 5. Acknowledgements 6. References 317 318 319 319 324 328 328 331 338 348 358 359 360 360 SUBJECT INDEX 369
- 18. CHAPTER 1 ORDER IN LANGMUIR MONOLAYERS AND IN THE AQUEOUS SUBPHASE Pulak Dutta Dept. of Physics & Astronomy, Northwestern University, Evanston, IL 60208, USA A variety of recent experiments have revealed a wide range of phases and phase transitions in simple amphiphilic monolayers on the surface of water. This paper describes some of the ordering phenomena revealed by X-ray diffraction. Recent experiments probing order in the underlying subphase are also described. /,,, 1. INTRODUCTION Floating monolayers of insoluble amphiphilic molecules---Langmuir films---are deceptively easy to make and to manipulate. A grainy back-and-white 1940's newsreel from General Electric shows Irving Langmuir casually putting these monolayers through their paces using tools available in every kitchen. (The monolayers were made 'visible' by the use of a macroscopic floating film of oil that is displaced by the amphiphiles.) It can be a shock to realize that, in this movie, Langmuir is playing with materials at the molecular scale---he is manipulating rnolecules. In other words, it's not necessarily difficult or expensive to do nanoscience. Until recently, however, a rather basic question about Langmuir monolayers remained: exactly what are the molecules doing when we manipulate the monolayer (e.g. change its pressure, density or temperature)? Hypotheses had been made and some were generally accepted in the field, but they had not been proved. It is reasonable that at the highest possible areal densities, the molecules are oriented so as to occupy the smallest area (simple linear-chain molecules would be oriented vertically). But how are they packed within the monolayer plane, and what happens
- 19. as the temperature and pressure change? These monolayers are named after Langmuir because he was the first to see isotherm discontinuities indicating phase transitions, but pressure and density are macroscopic averages and do not tell us what is happening to the molecules at these phase transitions. This was not known until new experimental techniques (including X-ray diffraction and a variety of microscopies) were applied to this system starting in the 1980's and especially in the 1990's. It is probably safe to say that, of the various techniques, synchrotron X-ray diffraction has had the most impact in this area. In general one should not overestimate the power of X-ray scattering: it does not generate real-space pictures, and it is not useful in disordered systems such as monolayers on very rough surfaces or monolayers with no lateral order or tilt order. But in the case of Langmuir monolayers of simple, rod-like molecules (e.g. saturated fatty acids and alcohols), X-ray scattering has provided important and vivid new information that has explicitly contradicted the conventional wisdom. Many phases of these monolayers turned out not to be liquids ('liquid expanded', 'liquid condensed', 'superliquid' etc); rather, they are mesophases with some degree of positional order and are therefore characterizable by X-ray diffraction. A 1999 review [1] describes the general features of the fatty acid/alcohol Langmuir monoIayer phase diagram in some detail, and contains much more information than can be included here. The following section contains a brief overview of X-ray results. In subsequent sections some newer information is surveyed that was not available at the time Ref. 1 was published, regarding the ordering of the molecular backbones and positional order in the underlying aqueous subphase. 2. THE PHASE DIAGRAM OF FATTY ACID AND ALCOHOL LANGMUIR MONOLAYERS In 1945, St~illberg-Stenhagen and Stenhagen [2] published an unexpectedly complex pressure- temperature phase diagram for fatty acid monolayers, containing a variety of phase boundaries and not explainable by the popular solid/ liquid expanded/ liquid condensed hierarchy of phases. These results were considered dubious and widely ignored; most studies continued to be performed only at room temperature. The 1966 book by Gaines [3], which was the bible of this field through the 1980's, says that "In view of the experimental difficulties attendant on the
- 20. demonstration of these effects, it seems that further study is needed before any of them can be considered well understood. No detailed discussion of them is given here..." When such further studies were finally conducted [4], it was found that the phase diagram of ref. 2 was largely accurate. A 'modem' phase diagram is shown in Fig.l; the labels used for the phases have historical origins and don't really mean anything. All phase boundaries except the Ov-L2 boundary can be seen as discontinuities in isotherms. The phase diagram is applicable to all insoluble fatty acids irrespective of chain length if the temperature range is appropriately shifted; the pressures change slightly as well, but the topology is not changed. The L2 phase is not seen in saturated fatty alcohols. X-ray diffraction can also be used to locate the phase boundaries, but it is much easier to do this with isotherms, Brewster angle microscopy, etc. Once the boundaries are located, and the next step is to identify what these phases and phase transitions are, that is when X-rays become invaluable. An explanation of how this technique is used to determine not just the lattice but also the tilt magnitude and direction is given in Ref. 1. The schematic diagrams in Fig. 1 show the structures thus determined. There are (a) two phases with distorted hexagonal (DH) i.e. centered rectangular lattices and vertical molecules: CS and S; (b) one phase with a hexagonal lattice and vertical molecules (LS); (c) two phases with DH lattices and chains tilted towards a near neighbor (L2, L2"), (d) two phases with DH lattices and tilts towards a next-nearest neighbor (L2', Ov). All these phases have at least medium-range order. The high-pressure low-temperature CS phase appears to be long-range-ordered. The L2 phase is anisotropically ordered (better-ordered in one direction than in the direction normal to it). At higher temperatures there is finally a liquid phase (not shown). Another phase not shown in Fig. 1 is a thin sliver of the 'I' phase between the L2 and L2' phases, in which the tilt direction is intermediate between the near- neighbor and next-nearest-neighhbor directions. A simple Landau theory [5] perfectly reproduces the details of the phase transition between the L2 and I phases (first order) and between the I and L2' phases (continuous).
- 21. CS I S ~." ! LS ! :I* ,o. r ~.., --'~ t !":.M: m m temperature Fig.1 Saturated fatty acid monolayerphase diagram, schematically showing the latticc distortions and tilt directionsdeterminedby X-raydiffractiondata.[FromRef. 1.] The story of the recently identified Ov phase illustrates the strengths and weaknesses of the various experimental techniques and the advantages of bringing multiple techniques to bear on this problem. The L2/Ov phase boundary is not seen in isotherms; in other words, there is no discontinuity in the density and in that narrow sense there is no phase transition at all. This phase boundary was located by Overbeck and M6bius [6] using Brewster Angle Microscopy: they saw changes in texture when crossing specific points in the isotherm. X-ray scattering had never been used in this region to look for phase boundaries, since this is time-consuming and there was no reason to explore this area. Once the mysterious phase boundary was detected, however, we rather quickly established [7] using X-rays that there was a distinct change in the diffraction pattern upon crossing the phase boundary (Fig. 2). The tilt direction changes, from towards a nearest-neighbor (L2 phase) below the phase boundary to towards a next-nearest- neighbor (Ov phase) above the phase boundary. We also discovered why isotherm studies had seen nothing: the tilt angle and the packing of the tilted molecules remain unchanged even though the tilt direction (relative to the lattice) changes. Thus there is no change in the areal
- 22. density, but there is a change of symmetry. The phase transition is first-order even though there is no flat coexistence region in the isotherm. 0.7 15 dyn es/cm 0.6 0.5 0.4 0.3 0.2 0.1 "--" 0.0 0.40.50.6~ 13 dyn es/cm 0.3 Ol 00 1.4o 1.45 Kxy(A1) 150 1.55 Fig. 2: SampleX-ray diffraction data fromC~9acid monolayers at 30°C,just below the transition to the Ov phase (13 mN/m) and just above (15 mN/m). Data are plotted as Kp/Kzintensity contours; each contourrepresents an equal intensitystep (arbitrary units) above the contour immediatelyoutside it. [FromRef. 7] 3. BACKBONE ORDERING IN FATTY ACID MONOLAYERS The various phases listed above differ in the lattice symmetry; tilt or lack thereof; tilt direction; and range of positional order. However, there is one more parameter. The alkane chains are not cylinders with circular cross-sections; to fully specify how the molecules are arranged, one needs to also specify the orientation of the molecule about its long axis. Since the carbon atoms in the alkane tail define a plane, specifying the orientation of this backbone plane is a convenient way to specify the orientation of the entire molecule. In single crystals where a large number of diffraction peaks can be observed, it is possible to deduce, from the peak intensities, the molecular form factor and thus the orientation relative to the lattice. In Langmuir monolayers, even the second-order diffraction peaks are sometimes
- 23. hard to see, and most structures are derived (or rather surmised) from the first-order peak positions. Recently [8], however, we obtained direct X-ray evidence of backbone order. Fig. 2 shows diffraction peaks for the CS phase indexed in terms of a rectangular non-primitive unit cell. We see not only the known first-order (11) and (20) peaks [9], and the known second- order (02) and (31) peaks [10], but a (21) peak. Now the rectangular unit cell contains two molecules, and if these molecules are identical, the (21) peak is forbidden. This immediately tells us that there are two inequivalent sites. Any differences between inequivalent sites will cause the (21) peak to be visible, but they will in general also cause the (01) peak to be visible; we do not see the (01) peak. This argues strongly for a herringbone arrangement of molecular cross-sections, just like some phases of paraffins. As can be seen from the inset to Fig. 2, when there is herringbone order the backbones at the two inequivalent sites make equal (although opposite) angles relative to the (01) direction; therefore the molecules at the two sites have identical structure factors for the (01) peak and this peak remains forbidden. However, relative to the (21) direction, the backbones at the two sites are oriented very differently (again, see inset); thus the two molecular structure factors are not the same and the (21) peak is not forbidden. Similar results are obtained for the tilted L2" phase; these data are not shown here but can be found in ref. 8. We do not see 'forbidden' peaks in any of the other phases, which means they can have at most short-range backbone order. 4. ORDER IN THE AQUEOUS SUBPHASE When polyvalent metal ions are added to the subphase, the monolayer generally becomes much better ordered [11], changes its viscoelastic response [12], and transfers more easily to a solid substrate [13]. As always, a change in properties indicates a change in structure. As we shall see below, what changes is that the underlying aqueous solution becomes ordered. It is tempting to think of this as an ordering or the metal ions, since their presence is necessary to see this effect, but that may not be true. Some years ago, X-ray diffraction was used by another group to detect the formation of a monolayer superlattice in the subphase when Cdz+ ions were present [14]. The unit cell was mysteriously large (a 2x3 supercell of the Langmuir monolayer unit cell). We have confirmed the observation in our own experiments, and we have also observed superlattices in the
- 24. presence of Mn 2+, Mg 2+ and Pb2+. The presence of each of these ions results in a different subphase lattice. .4,,,,a .E , w,,,,i tD o.1 expected (ol) (1 i) (20) o 8 ~ o peak o o° pos tion co o O o oo oo o O o °o o O o 8o ~o ~,o eo (21) (02) • , , , ,1t,, /t , , , // ! 1.2 i.4 1.6 2.1 2.5 2.7 CS phase ~ ,/'3, (31) o O0 o oo ! i 2.8 2.9 K (A ~ ) Fig. 3 Sample x-ray data (in the horizontal plane, i.e. at Kz=0)from a heneicosanoic (C2~)acid monolayer in the CS phase (T=7°C, rt=30 mN/m). Peaks are indexed according to a centered orthorhombic lattice with two molecules per unit cell. The inset shows a centered orthorhombic lattice with a herringbone arrangement of the molecular backbones. [From Ref. 8] With Mn 2+ we see a l x2 superlattice of the organic structure; with Mg we see a 2x2 superlattice [15]. Perhaps the strangest subphase structure is seen in the presence of Pb2+, and we will therefore show the Pb2+ data [16] here as an example. Fig. 4 shows the large number of peaks seen. These can all be indexed, and the resulting unit cell is rotated with respect to the organic lattice and is very large (bottom of Fig. 4). Its area is 14 times the organic unit cell, i.e. nearly 280~ 2. While the diffraction data are unambiguous, they make it entirely impossible to believe that what we are seeing are lattices of isolated ions. We therefore sought to test for the presence of lead within the superlattice. If the superlattice peaks were solely due to lead ions, the contribution to the intensity of each weak peak should
- 25. be proportional to the square of the lead form factor. Tuning the x-ray energy from 12.885KeV (below the L3 absorption edge of the lead atom) to 13.100KeV (slightly above the edge) should decrease the absolute intensity of a diffraction peak due to scattering from lead atoms by -20%. ,r~ 0.05 - 0,2 5 0.0 A v 005 0.3 0.4 0.5 0.4. 06 0.7 0.8 ~= 0.2 '¢ "7 - ]~ 0.04 II It 0.03 0,0 0 1,5 1.6 1.7 ,~- ~- '~" ,~ ,R '~~ '~ :a!....~'~ 0.9 1.0 1.1 1.2 1.3 1.4 1.5 ,~" ... 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 K y(A"~) o ? o-Q.~5.~ o f o o oo o 5~.~o oo o o ° ° °° ° ~-s..° ° o o o o o ~ o,o o.o o~° O organic molecules inorganic superlattice Fig. 4: TOP: Grazing incidence synchrotron x-ray diffraction data from a heneicosanoic acid Langmuir monolayer with lead ions in the subphase. The lower-order peaks (2 2), (2 5 ) and (4 3 ), and higher-order peaks (0 7), (6 1 ), (6 8 ), (4, 4), (4 10), are from the Langmuir monolayer. All other peaks are due to the superlattice. BOTTOM: Real space lattices of the fatty acid monolayer and the superlattice. The heneicosanoic acid molecules are represented by circles; the 'lead' supercell is shown by lines.. The lattices are commensurate' the basis vectors are related through a'=4a+2b and b'=-3a+2b, so that area' =14xarea. [From Ref. 16]
- 26. We have measured the intensities of 13 weak peaks with K~.vbetween 0.6/1, ~ and 1.4 ,~-i at these two energies (data for some representative superlattice peaks, and also some organic peaks, are shown in Fig. 5). Within an experimental error of----5%, we observed no change for any of these peaks. 1.2 0.8 0.4 0.0 o om, &n C: e. 008 0 04 0.00 Ilu u E, [] ¢ J un [] .d, & 13.100KeV u 12.EIBSKeV U 0 ' I ' I ' I ' I ' I ' I ' I .45 1 5(3 1.55 1.69 1 65 1.70 an ,L, On n . e~n~l~ ~ mrS" '~2~' ~ ~ ~. ~. I ' I ' I ' I I | , 1 ~' I D.60 0.65 0.70 0.75 0.80 0.85 090 K~(A") Fig. 5 In-plane diffraction scan with x-ray energy below and slightly above the L3 absorption edge of lead. (a) Three peaks from the organic monolayer plus weak superlattice peaks. (b) Four representative superlattice peaks. We also looked at 9 other superlattice peaks not shown here, with the same results. If the superlattice consisted of lead atoms only, a 20% change in the peak intensities would be expected. There was no observable change in intensity for any of the peaks studied. [Fromref. 16]
- 27. 10 If lead does not contribute measurably to the diffraction peak intensity, scattering from the superstructure must be dominated by other atoms. In principle, superlattice reflections can arise from a periodic superstructure within the organic monolayer, but the Bragg rod widths we observe are not consistent with horizontal or vertical density modulations in the entire organic monolayer. The only reasonable possibility is that the superlattice peaks are due to a thin layer in the aqueous subphase. Since no superlattice is seen when no multivalent metal ions are added to the subphase (even at very high pH), and different lattices are seen when different ions are added, the lattice cannot be due to impurities in the water. However, it is well established [17] that metal ions undergo hydrolysis and hydration in aqueous solution, and a wide range of complex polynuclear oxo(hydroxo)-bridged structures can be formed. The observation of changes in the organic monolayer structure as a function of the subphase pH and subphase ion concentration [18] is further evidence that pH- and concentration-sensitive hydrolysis products, rather than isolated ions, are present at the interface. Thus, we expect that hydrolysis products and water molecules arrange themselves under the Langmuir monolayer, interacting with the carboxyl head groups in such a way as to form a large commensurate superlattice. The ratio of metal atoms to other atoms (hydroxyl ions, water) can be small enough that their presence is undetectable in our anomalous scattering studies. 5. ONGOING AND FUTURE STUDIES Langmuir monolayers have been used by others [19, 20] as templates to grow inorganic crystals. This is a somewhat simplified experimental model of the real-world process of biomineralization. More generally, biomineralization is just one example of the possible use of an organic template to control the nucleation of an inorganic mineral, and one can ask how and when such template-directed nucleation occurs and whether there are any advantages to using controllable organic lattices such as Langmuir monolayers as templates. The monolayer structures mentioned in the previous section can be considered precursors to bulk crystal growth. We had originally expected that unusual interfacial structures would serve to mediate between otherwise incompatible monolayer and mineral structures. Unfortunately, it is not easy to nucleate bulk Mnz+, Mg2+ and Pb2+ crystals at the interface because of the difficulty of making stable supersaturated solutions. It is much easier to make supersaturated CaCO3, which is of great interest because it is a biological mineral. Others have grown such
- 28. crystals at Langmuir monolayers, and reported oriented growth on the basis of selected crystals lifted off the surface [19]. However, in our in situ studies we see that calcium carbonate does grow preferentially at the interface but is misoriented - a powder. There is also no relationship between the calcite (or vaterite) structure and the monotayer structure observed in sire. Another crystal that grows weIl under a Langmuir monolayer is BaF2 [20]. Our in situ studies confirm that in this case, perfectly aligned crystals grow under a Langmuir monolayer. Unexpectedly, the BaF2 lattice spacings vary with the solution concentration: at high concentrations they are exactly the same as for bulk BaF2, but at the lowest concentrations (smallest nuclei) the lattice is commensurate with the Langmuir monolayer lattice. Strained epitaxy is well known in inorganic thin film deposition under high vacuum, but if confirmed, this will be the first report of strained epitaxial growth during nucleation from solution. Further studies are in progress. 6. ACKNOWLEDGEMENT The work of our group was supported by the US Department of Energy under grant no. DE- FG02-ER45125. 7. REFERENCES V.M. Kaganer, H. M6hwald and P. Dutta, Revs. Mod. Phys.,71,779 (1999) S. StNlberg-Stenhagen and E. Stenhagen, Nature 156, 239 (1945) G.L. Gaines, "Insoluble monolayers at liquid-gas interfaces", lnterscience Publishers, New York, !966, pg. "184 A.M. Bibo and I.R. Peterson, Adv. Mater. 2,309 (1990). M.K. Durbin, A. Malik, A.G. Richter, R. Ghaskadvi, T. Gog and P. Dutta, J. Chem. Phys. 106, 8216 (1997) G.A. Overbeck, and D. M6bius, D.J. Phys. Chem. 97, 7999 (1993) M.K. Durbin, A. Malik, R. Ghaskadvi, M.C. Shih, P. Zschack and P. Dutta, J. Phys. Chem. 98, 1753 (1994)
- 29. 12 M.K. Durbin, A. Richter, C-J. Yu, J. Kmetko, J.M. Bai and P. Dutta, Phys. Rev. E 58, 7686 (1998) B. Lin, M.C. Shih, T.M. Bohanon, G.E. Ice, and P. Dutta, Phys. Rev. Lett. 65, 191 (1990) 10 T. Bohanon, B. Lin, M. Shih, G. Ice and P. Dutta, Phys. Rev. B (Rapid Comm.) 41, 4846 (1990) 11. D.K. Schwartz, Surf Sci. Rep. 27, 241 (1997) 12. R.S. Ghaskadvi,, S. Carr and M. Dennin, J. Chem. Phys. 111, 3675 (1999) 13. J.A. Zasadzinski, R. Viswanathan, L.Madsen, J. Garnaes, and D.K. Schwartz, Science 263, 1726 (i 994) 14. F. Leveiller, D. Jacquemain, M. Lahav, L.Leiserowitz, M.Deutsch, K. Kjaer and J. Als- Nielsen,, Science 252, 1532 (1991) 15. J. Kmetko, A. Datta, G. Evmenenko, and P. Dutta, J. Phys. Chem.B 105, 10818 (2001) 16. J. K_metko, A. Datta, G. Evmenenko,M.K. Durbin, A.G. Richter, P. Dutta,Langmuir 17, 4697 (2001) 77. D.T. Richens, The chemistry ofaqua ions: Wiley, New York, 1997; Chapter 2.5.4 18. A. Datta, J. Kmetko, C.J.Yu, A,G. Richter, K.S.Chung, J.M. Bai, and P. Dutta, J. Phys. Chem. B 104, 5797 (2000) I9. S. Mann, in Inorganic materials D. W. Bruce, D. O'Hare, Eds. (Wiley, Chichester, England, 1992) pp. 238.; S. Mann, Nature 365, 499-505 (1993); S. Mann, et al., Science 261, 1286-1292 (1993); B. R. Heywood, S. Mann, Adv. Mater. 4, 278-282 (1992); B. R. Heywood, S. Mann, Langmuir 8, 1492-1498 (1992).; B. Heywood, S. Mann, J. Am. Chem. Soc. 114, 4681-4686 (1992). 20. B. Li, et al., Langmuir 15, 4837-4841 (1999).; L. Lu, H. Cui, W. Li, H. Zhang, S. Xi, J. Mater. Res. 16, 2415-2420 (2001).
- 30. CHAPTER 2 ANALYTIC MODEL OF FLOW ORIENTATION IN LANGMUIR-BLODGETT FILMS Michio Sugil, Yuka Tabe2and Keiichi Ikegami2 i Faculty of Engineering, Toin University of Yokohama, Aoba-ku, Yokohama (Japan) 2Nanotechnology Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki (Japan) 1. INTRODUCTION The Langmuir-Blodgett (LB) technique, devised in the middle of 1930's, consists of the manipulation of a monolayer condensed at an air-water interface and the deposition of it by dipping and raising through the interface onto a fiat substrate which is kept upright [1]. This technique is often referred to as the vertical dipping method. Three different types are recognized in the manner of deposition: Y-type which picks up monolayers onto the substrate for both dipping and raising, X-type picking only for the dipping, and Z-type picking for the raising [1]. The products, called Langmuir-Blodgett films or simply LB films, have been attracting continued interest in various fields of science and engineering. The origin of the present interest can be traced back to the early 1960's to the pioneer work of H. Kuhn and his
- 31. 14 collaborators, who utilized the LB technique as a means of arranging various molecules in the form ofultrathin ordered films as a new class of assembly systems [2]. Characterization of the precursors of LB films, i.e., monolayers at the air-water interface, has been fairly advanced as well as that of the end products, i.e., LB films. Now there are indeed many guidelines for "good LB films" referring to some of the characteristic aspects associated with the LB deposition process [3]. Most of them are, however, empirical laws to give qualitative guidelines, and only a few analytic approaches are found to be effective in deriving quantitative guidelines. The in-plane anisotropy in LB film system, for instance, is reported in the early stages [4], and its occurrence has been known to depend on the deposition conditions. Until the late 1980's, however, the origin of the in-plane anisotropy had been far from fully understood. Let us consider now the vertical dipping method. During the deposition, the substrate moves either upward or downward between the upper and the lower dead centers. The direction of the movement, however, does not matter very much if the consideration is confined to the motion of the monolayer on the water surface: the monolayer is drawn closer to the upright substrate and fades away from the water surface as the deposition proceeds, i.e., the deposition process is inevitably associated with the flow and the deformation of monolayer. The LB deposition process might be compared to a two-dimensional cosmos with black holes distributed on a finite line with a uniform density. The former is the water surface with the monolayer being the interstellar matter and the latter is the substrate moving upward or downward. The monolayer is, however, different from the dispersed interstellar matter, a condensed film like a two-dimensional solid [1]. These considerations suggest that the flow and the deformation of the solid state should be appropriately taken into account for the better
- 32. 15 understanding of the LB deposition process. The continuous deformation of a solid by an external force is referred to as the plasticity [5]. The standard mechanical processing techniques as forging, rolling, squeezing and plucking of metals, for instance, are nothing other than the utilization of the plasticity. A tiny pellet of a few grams of gold is plastically extended to cover some ten square meters, and copper lead wires, thick or thin, are produced using the plucking process, it is well known that these plastic deformations are often associated with the changes in the microscopic texture such as size, shape and orientation of the crystallites, resulting in the changes in the physical properties such as mechanical, magnetic and electric ones. What would then happen in the case of two-dimensional monolayers during the LB deposition process, and how can we describe it quantitatively in relation to the in-plane anisotropy observed in the resultant LB films? In this respect, endeavors have been made to describe the in-plane anisotropy observed in LB films employing the morocyanine - fatty acid mixed films as a model system. Their chemical structures are shown in Fig. 1, where DX with X--O, S or Se and C,, with n=16 - 22 refer to the merocyanine and the fatty acid, respectively. Ca) D.~>CH CH..~s "s DX , O" t~ C18H37 CH;~COOH (X-O, S o~Se) (b) CH3(CH2)._~COOH C2o Fig. 1 Chemical structures of (a) surface-activemerocyaninedye (DX with X=O, S or Se) and (b) straight-chain fattyacid(C,,with n=]6 - 22). The merocyanine dye family is generally characterized as a conjugate n--electron system that
- 33. 16 has a donor nucleus at one end and an accepter at the other. Another feature of this family is the resonance between two extreme forms, non-polarized and polarized, caused by the intramolecular charge transfer between the donor and the acceptor. The non-polarized form of DX is referred to in Fig. 1. The resonance structure is represented by >N-C=C-C=C-C=O >N+=C-C=C-C=C-O -. The donor nucleus, shown at the left-hand side, is either of benzoxazole, benzothiazole and benzoselenazole nuclei for X=O, S and Se, respectively, each substituted with a straight-chain long alkyl, while the acceptor is a rhodanine acetic acid radical in each case. On the basis of the experimental remarks on the in-plane anisotropy in the DX-C,, mixed system, we have derived the "analytical model of flow orientation", which expresses the orientation effect due to the plastic flow of monolayers by six parameters as representing the LB vertical dipping process. This approach, assuming a local thermal equilibrium, has been further extended to lead to new methods to control the in-plane anisotropy, clarifying the limitations, at the same time, to be amended for further development in this approach. This article deals with the present status of the flow orientation model together with its problems to be solved. The qualitative features of the in-plane anisotropy in the LB films are exemplified in §2, referring to the optical absorption and the ESR measurements of the DS-C20 and other mixed films, which have led to the quantitative model of flow orientation. The framework of the model is summarized in §3 together with a brief description of the experimental results, referring to the simplest case of the LB deposition using a single substrate and a sufficiently large trough. §4 deals with the attempts of extending the model to the more complicated cases such as batch production of LB films, deposition using a trough of finite dimensions, transfer processes with peeling-off of the monolayer, slipping, stretching,
- 34. 17 anisotropy due to the compression and other anomalies, and also the problems associated with them. In §5, another approach, describing the LB deposition as a Markov process, is reviewed together with the results of numerical calculation. The thermal equilibrium assumption adopted in the analytic approach is critically examined referring to the Markovian approach, and the in-plane anisotropy due to the compression is also touched upon. §6 describes the advanced methods to control the in-plane anisotropy in LB films by regulating the plastic flow in a monolayer by the use of rotating disks, reviewing the quantitative model together with the experimental results. 2. IN-PLANE ANISOTROPY IN LB FILMS It is well known that the DX-C20 mixture form stable monolayers at the air-water interface when it is dissolved in chloroform and spread on an aqueous subphase containing Cd2+, and that, for the molar ratio up to [DX] : [C20]=1 : 2, these monolayers are easily deposited to form Y-type LB films [6]-[17] . The as-deposited LB films of DS-C20 and DSe-C20 as well, are blue in color and associated with a characteristic red-shifted band (J-band [18]-[20]) in the optical absorption spectrum. It is indicated that an ordered arrangement of the dye molecules, referred to as the J-aggregate, is formed in these LB films, and that they are associated with stable spins of n-electron character in the dark state. Both optical and ESR spectra have been found to exhibit the in-plane anisotropy that has opened the way to the analytic model of flow orientation in the present form. The results from the DS-C20 films are outlined in the following. 2.1. OpticalAnisotropyofJ-Aggregate Figure 2 shows an example of anisotropic optical absorbance observed in a mixed LB film of
- 35. 18 [DS] : [C20]=1 : 2 with a J-band centered around 590 nm, where the solid and the dashed lines refer to the absorbances All and A± measured using the incidents normal to the layer plane with the electric vector parallel and perpendicular to the dipping direction, respectively [21 ], [22]. 2~ 0 /"/" 4OO 5OO 7oo ,I. (nP,~) Fig. 2 Anisotropicopticalabsorptionspectrumin a DS-C201 : 2 mixed LB filmfor a linearlypolarized lightwith an incidentangleof 90°to the substrate.The absorbanceper monolayerA is plottedagainstthe wavelength2. The solid and the dashed lines refer to Aliand A~ for the electricvector parallel and perpendicular to the dipping direction in the filmplane, respectively.(Reproducedfrom[22]by permissionof the PhysicalSocietyof Japan.) The dichroic ratio defined by R=AII/A ± is conventionally used to represent the in-plane anisotropy observed in the optical absorbance: the transition dipole moment of the dye chromophore is preferentially oriented in the direction of dipping and raising the substrate if R>I; it prefers the direction perpendicular to the dipping direction if R<I, and it may be isotropically distributed if R=I, while the angle of 45 ° between the dipole moment and the dipping direction will also result in R=I. The larger magnitude for Ali seen in Fig. 2 indicates that R> 1, i.e., the transition dipole moment is preferentially oriented in the dipping direction. The value of R has been found to increase with the deposition velocity or the speed of dipping and raising the substrate va, but to remain in any case appreciably greater than unity at the J-band peak: R_>1.3, typically [22]. It has been found that the J-band can be dissociated and restored by the secondary treatments using heat, acid and base [13], [23]. When an as-deposited film, blue in color, is kept at 90°C for 30 min, for instance, the J-band and its in-plane anisotropy disappear and the film turns red
- 36. 19 with the absorption maximum shifted to 540 nm. If the film is further treated by an exposure to the vapor from ammonia water, then it turns again blue, with the J-band and its anisotropy restored. These facts indicate that the DS chromophores in the J-aggregate are bound by such relatively weak forces as the dipole-dipole interactions. Here, it is noted that the spectral shape of the DS-C20 mixed fihn is found to be insensitive or essentially invariant to the molar mixing ratio down to [DS] : [C:0]=I : 20 [9]. It is suggested that DS and C20 are immiscible with each other forming a phase-separated monolayer consisting of the DS aggregates embedded in a C20-rich matrix, and that the 540-nm isotropic band in the heat-treated film reflects the disorders introduced in the aggregates. 2.2 Anisotropy in ESR Line Shape Electron spin resonance (ESR) studies by Kuroda et al. have shown that the DS-C20 mixed LB film is associated with stable spins of a'-electron character with a concentration as high as one spin per several hundred DS molecules in the dark state [10], [15], [24]-[27]. The spins have been found to involve two different species, A and B, of which the former is anisotropic and the latter is featureless in ESR line shape as shown in Fig. 3 [24]. The concentrations of A and B are essentially equal to each other as seen in the figure, suggesting that A and B form pairs in occurrence. if we assume that a spin A and a spin B are associated with each other in an aggregate of several hundred DS molecules, the aggregate will be more or less one-dimensional in shape so that the spin pair is stabilized at its ends: a situation reminiscent of a cation or an anion radical stabilized at each end of a polymer chain [24]. This picture is quite compatible with the fact that both A and B disappear when the film is heat-treated at 90°C for 30 rain as is the case with the J-band and its anisotropy mentioned in §2.1. The species A was later successfully assigned to the donor radical by the ESR studies using the 15N-substituted donor and acceptor [28]-[30]. It is therefore indicated that the intermolecular
- 37. 20 distance in the J-aggregate is small enough to allow the intermolecular charge transfer, and that A and B originate from the cation and the anion radicals, respectively, located at the opposite ends of the one-dimensionally developed J-aggregate. (a) 12.007' ........... ~.f .... I ~ - _ 4"-2.OO9 .... I~ ^ lii i i i Fig. 3 First-derivative ESR spectra of a 1000-layered DS-C2o 1 : 2 mixed LB films at room temperature (solid curves). The external magnetic field is normal to the film plane (a). It makes the angle of 0°, 45" and 90° with the dipping direction of the substrate from(b) to (d), respectively. Numbers show g-values of the fields as indicated. Dashed lines show the simulated curves of the spin species A. Stick lines at the bottom of(d) show the resonance fields corresponding to principal components of g and hyperfine tensors. (Reproduced from Ref. [24] by permission of the Physical Society of Japan.) Analysis of the anisotropic line shape of A has revealed that the pn orbital axis of DS chromophore lies in the layer plane with its distribution function simulated by the superposition of two components having maxima at about +60 ° with respect to the dipping direction [15]. Figure 4 shows the model of the in-plane alignment of the DS chromophores deduced from the analysis. This is compatible with the dichroic ratio R>I of the optical absorbance if the
- 38. 21 aggregate of DS in the ESR study is identified with the optical J-aggregate, since the pa orbital axis and the transition dipole moment are approximately orthogonal to each other, suggesting the deviation angle of a=+30 ° which indicates R> 1. (a) (b) Dippingdirection H,,t l y ~""'O~pr,orbitaI Substrate Dipping direction Fig. 4 Model of thc in-plane alignment of DS chromophorcs.(a) The external magnetic field and the proorbital axis make angles ~'~,tand 0;,~with the dipping direction, respectively. The long axis of the chromophore is schematically expressed by a thick line. (b) The long axis makes an angle a with the direction connecting the centers of adjacentmolecules.<Ow> denotesthe averageof 0p,~.(Reproducedfrom Ref. [24]by permissionof the Physical Societyof Japan.) Models of the J-aggregate structure have been proposed from various viewpoints including the remarks from the optical and the ESR measurements. A comparable value a=±30 ° has been estimated, e.g., by Nakahara et al. [16] by analyzing the optical anisotropy based on an extended dipole model, although there still remain controversies to be solved among the models [16], [20], [24], [30]-[34]. The detailed discussion is, however, beyond the scope of the present article. 2.3. PossibleOrigin ofIn-planeAnisotropy Let us imagine a stream in autumn, flowing gently, with its surface covered with a lot of leaves fallen from the trees on the banks. Each of them is drifting down the stream as if it were
- 39. 22 destined to trace its own path. Looking down from a height, however, one would recognize a steady pattern like a bundle of stripes woven from numberless leaves drifting on the water surface. If they are elongated in shape like those of willow, one would find that they are aligned one after another in each stripe, forming head-to-tail, side-by-side or randomly stacked chains. TITTTT wTTT iTTTTT. 1 TTTTTT ,wTT . . . . . . • x ~, ,7:. (a) (b) TTTTTT Y Y , TTTTTt .................. ~ X, • 1," (c) (d) Fig. 5 Examplesof simple flows and typesof stacking. In each case, all the streamlinesare assumedto be parallel to they-axis, i.e., vx=O.(a) vy=vo,random;(b) vy=vo+gx,head-to-tail;(c) v.~,=v0+gywithg>O,head-to-tail; (d) vy=vo -gy with -g<O,side-by-side. Such a pattern reflects the Iocat variation of the velocity field on the water surface. The center of the leaf at a given place moves in accordance with the local velocity vector, as a matter of course. Then, why a willow leaf sometimes prefers orienting its long axis towards a specific direction? The clue for answering the question may be found in the velocity gradient that exerts a torque on the leaf to orient to a specific direction [36], [37].
- 40. 23 Let us consider four extreme cases (a) - (d) as shown in Fig. 5. In each case, all the streamlines are assumed to be parallel to the y-direction, i.e., v.~(x,y)=Ofor simplicity. Case (a) refers to the uniform velocity v~,(x,y)=v0=const. All the elements of the velocity gradient tensor G are then equal to zero. As a result, the orientation of each leaf remains unchanged, and the leaves may be randomly stacked. Case (b) exemplifies the x-dependent velocity with a function vy(x,y)=vo+gx,which results in a non-zero element in G, i.e., @x=OvJc3x=g,orienting the long axis to the y-direction. A head-to-tail stacking of the leaves will be realized as a consequence. Case (c) represents the increasing function of y by vy(x,y)=vo+gywith g>0, resulting in a non-zero element Gyy=Ov),/Oy=g>Oto orient the axis to the y-direction. The resultant stacking will also be head-to-tail. Case (d) refers to a decreasing function vy(x,y)=vo-gywith G),y=-g<0, which orients the axis to the x-direction. In this case, therefore, a side-by-side stacking will be realized, in contrast to Cases (b) and (c). There arises a question as to what extent this naive picture can be effective as the starting point for elaborating a quantitative model to explain the in-plane anisotropy actually observed in the LB films of DS-C20 and others. The endeavor of answering this question has led to the analytic model of flow orientation [21], [22], [38]-[40], of which the basic framework will be reviewed in the next section.
- 41. 24 3. BASIC FRAMEWORK OF THE MODEL In the analytic model of flow orientation for the conventional LB dipping process, the monolayer on the water surface is assumed to be a continuum, ~ and the model consists of two stages: the evaluation of the velocity potential on the water surface and the description of the rotatory motion of a particle in this potential field. 3.1. Velocity Potential of the Monolayer Flow In evaluating the flow of monolayer at the air-water interface, we have assumed: (1) the monolayer is a two-dimensional ideal fluid; (2) the substrate, i.e., a flat plate on which the monolayer is deposited, is a two-dimensional fine sink; (3) the monolayer is infinite in its dimensions [21], [22]. 3.1. I. Ideal Fluid Approximation The assumption (1) involves the incompressible and irrotational conditions. The former and the latter enables us to introduce the velocity potential U(x,y) and the stream function V(x,y) to describe the flow in an x-y plane which represents the water surface. Here, the velocity vector v=(vx,vy)Taround a point (x,y) is given by, 8U 8U v = -U x, vy=~==-U;,, (1) Ox ay and also by, The continuumapproximation is implausible to very brittle monolayers, for which case Matsumoto et al. have proposed the "channel-and-iceberg"modelin Refs. [4l] and [42].
- 42. 25 OV OV v,.=~--Vy, vy=-~--V,. (2) Oy ax Equations (1) and (2) are nothing but the well-known Cauchy-Riemann relation, Ux=Vyand Uv=-Vx, which guarantees the existence of the complex velocity potential W(z)=U+iVin the Gaussian plane, where z=x+iy [35], [36]. The velocity vector v is then written using the first derivative dW/dz as, • (@z W ) = -Im(dW / v~ = Re , v,, ~,--&z)" (3) The deformation rates of an area element are given by the velocity gradient tensor G written as, G =(G~:~ G ' (4) where Gxx=Ovx/Ox,Gxy=Ovx/Sy,Gyx=Svy/c3xand Gyy=Ov/Sy. In Eq. (4), the diagonal elements, Gxx and Gyy,denote the expansion-compression rates, and the off-diagonal elements, Gzy and Gyx, are the shear rates. Using the second derivative d2W/dx 2, each element in Eq. (4) is written as, Re(dZWi (5) and, ira( d2W ) G.,, = Gyx =- ~dz2) (6) The incompressible condition is referred to by Eq. (5), i.e., the expansion or compression of the area element in the x-direction is canceled by that in the y-direction. Equation (6) is related with the irrotational condition: G is a symmetric tensor associated with a pair of principal axes,
- 43. 26 orthogonal to each other, at which directions the flow torque vanishes. 3.1.2 Normal Deposition with a Single Substrate The assumptions (2) and (3) refer to the neglect of the thickness of the substrate in comparison with its width, and also the complicated boundary conditions due to the shape and dimensions of the trough and the barriers. Let us consider the normal case that the monolayer is symmetrically deposited onto both surfaces of one single substrate, which is represented by a line sink. If the substrate occupies a range -a/2<x<a/2 on the real axis, the complex potential W=U+iV is written as [21], W(z) = - v---g-a[ ~/2 log(z - x') dx', 7l" ,l-at2 (7) where va is the deposition velocity, i.e., the speed of dipping and raising the substrate, and we assume that the transfer ratio of rd--1, indicating that the monolayer is transferred from the water surface onto the substrate without compression or expansion. Eq. (7) is regular except for lx[<a/2 on the x-axis, and the factor -vd/~r at the right-hand side is so chosen that the condition vy--,. -T-Va for ixl<a/2 is satisfied when y --~ +0. Equation (7) is easily integrated as, (8) with the real and the imaginary parts, IC~1 f/~/2 }l ~1 {I ~12 } - va x y2 U(x,y) ~ - log x- + - x+ log x+ +y2 1 +2y arctan x-a/2 _arctan +a , (9) lyl Jy
- 44. and, V(x,y) ~ x+a/ +ylog x- +y2 _ylog x+ +y2 , respectively. (lo) 27 dipping direction y -x4. x , (a) (b) Fig. 6 (a) Streamlines and equipotential lines shown by the solid and the dashed lines, respectively for a two-dimensional ideal fluid with a line-sink on the x-axis represented by the thick rod. (b) Schematic representation of the normal LB deposition process. (Reproduced from Ref. [22] by permission of the Physical Society of Japan.) Figure 6 shows the equipotential and the streamlines, U(x,y)=constand V(x,y)=const, respectively, for the single-substrate case [22]. The first derivative of W(z)is given as, I I I all dW__v~ log z- -log z+~ , dz tr with the velocity vector expressed by, (11) vx(x'Y)= It, dz ) = ~---~log. (x_a12)2 +yZ1 (x + ~/2) ~ + y~ ' vj,(x,y) = - t~---dZ-Z ) ¢c{ kx-al2,) x+al2)J (12)
- 45. 28 the latter of which leads to, limv (x,y)=gva, for Ixl<a 3,---*__.0 Y 2 ' a =0, for Ix I>-~, (13) where the double signs are taken in the same order. The second derivative d2W/dx 2 is given by, d2W_va(l_ 1), (14) dz 2 x z-a~2 z +a/2 and the elements of G are derived as, v,_.L { x-a~2 c, = -a ,, = ~ (x - a / 2 )~ + y~ x+a/2 } (x+a/2)2 +y2 ' ( G va ~ 1 Gx,. = ~=--Y[ y2 lr (x - a / 2)~ + 1) (x+a/2)2+ y2 ' using Eqs. (5) and (6). 3.2. Rotatory Motion of Particles Let us examine the motion of a particle, elongated in shape, put in the velocity potential field. This particle may be a rod-like crystallite in the actual case. In this stage, the ideal fluid approximation adopted for evaluating the potential functions, W, etc., ceases to work, and the friction between the particle and the surrounding medium should now be explicitly taken into account. 3.2.1. Equation ofAngular Distribution Function The center of the particle moves along a streamline with a velocity vector v (e.g., cf. Eq. (1)). The orientation of the particle is governed by the velocity gradient tensor G (e.g., cf. Eq. (4))
- 46. 29 and the rotatory Brownian motion, while the inertia term is assumed to be neglected. Let (~', q) be a coordinate with the (- and q-axes parallel to the x- and y-axes, respectively, and its origin is fixed at the center of particle (x, y), as shown in Fig. 7. The relative velocity (~,¢/) of point (~x,q) with respect to the origin is expressed by, Gyx G~ ' (16) using Eq. (4). 1 7 Long axis ofaggregate Dipping ~ ,, direction ~ ~ ~- c, Fig. 7 Definition of ~, q-coordinate with the origin fixed at the center of particle. The long axis of the aggregate forms angles ~0and 0 with the 4'- and q-axes, respectively, a refers to the angle between the long axis of the aggregate and the transition dipole moment. ~b is the angle between the electric vector of lhe incident and the q-axis. (Reproduced from Ref. [22] with modification by permission of the Physical Society of Japan.) Let ¢ be the angle between the position vector and the ~'-axis as shown in Fig. 7, i.e., ~X=rcos¢ 2 and ~/=rsintp with r = x/4'2 + 17 •The angular velocity is written as, do G~, -G~ 2 z (°-dt~ = ~ 2 sin 2rp + Gy.~cos ~ - Gxy sin co, (17) or, 0 dO G~ -G~ - ~ = ~ s i n 20 + Gyx cos20 + (G~/- Gy~)cos 2 0, (18) dt 2 if we use the angle 0 -- ~/2-(p instead of ~o.
- 47. 30 In the incompressible, irrotational case, we derive, t) = G= sin 20 + Gy~cos 20, (19) referring to Eqs. (5) and (6). Substituting t)= 0 for Eq. (19), we obtain the expressions for the principal axes as, 0+ 1 ~G.~¢) ( Gy,."] ( dtg) ~- = -- arctan/ " l, with, + < 0, (20) - 2 - dOo_o" and the associated eigenvalues are, < =_+#oS+c:.,. where the double signs are taken in the same order. Here, the positive and negative eigenvalues, G+ and G_, correspond to the maximum expansion and compression rates, respectively, and the mechanically stable point is identical with 0+. The extreme values of the shear rate and their positions are easily derived in a similar manner using the conditions with dO~dO = 0 and +d20/dO 2<0as, max min = -G+, (22) which are located at 0 = 0_+-n"/4, respectively. Thus, we have reconfirmed the naive view in §2.3, i.e., the preferred direction of the long axis is not identified with the tangential of a streamline, but determined by the velocity gradient. The angular distribution function P can be derived starting from an equation of continuity [43], OP c3S . . . . (23) Ot 00'
- 48. 31 where P(O)dO gives the probability for 0 to lie in a range 0- O+dO, and S is the flow of probability passing through a point 0. Here, S is written as, S = t)P- D -~,0P (24) O0 where D is the rotatory diffusion coefficient. In Eq. (24), the first term at the right-hand side refers to the drift flow to orient the long axis of a particle towards the preferred direction, and the second term corresponds to the diffusion flow to randomize the orientation. Substituting Eq. (24) for Eq. (23), we obtain the diffusion equation, oR o(oP) o~P . . . . +D~ (25) Ot O0 002 ' which expresses the compromise between the flow due to t) and the Brownian motion. The rotatory diffusion coefficient D is related with the rotatory friction coefficient (between the particle and the medium through the Einstein relation, D = ksT , (26) ( where k8 and T are the Boltzmann constant and the absolute temperature, respectively. It is noted that D is generally a function of t since (may change as the particle moves towards the substrate. 3.2.2. Local Thermal Equilibrium Approximation If we assume that thermal equilibrium is quickly attained in comparison to the change in G, i.e., the local thermal equilibrium approximation, only the values of t) and D near the substrate are referred to as determining the orientation [21], [22]. In this case, OP/& = 0, and Eq. (25) is readily integrated as, OP- O --c3P= So , (27) 00
- 49. 32 where So is the integration constant. The left-hand side of Eq. (27) is identical with the flow of probability S given by Eq. (24). As a consequence, SOu: 0 indicates that there exists a steady flow of probability. This does not contradict the conservation of the total probability since 0 is a periodic variable, and it may well happen in a vortical velocity field,z For the ideal fluid, however, S0=0 due to the irrotationality. Thus, the expression for P is written as, OP- D c3_ff_P = 0. (28) ~30 For the normal deposition with a single substrate, we derive from Eq. (15), Gx. =-Gyy =-G, Gxy=Gyx=O, [xl<_a/2 and y-++0, (29) and, 1-' a 2 ) ' (30) which corresponds to the positive eigenvalue G+ in Eq. (21) for the normal deposition, as a matter of consequence. The preferred direction is obtained as 0+=0 using Eq. (20), i.e., the long axis tends to orient in parallel with the y-axis. Here, the area element is compressed in the x-direction and stretched in the y-direction. The y-direction is identical with the direction of dipping and raising, if the orientation of the particle is assumed to remain as it was immediately before the transfer onto the substrate. As a consequence, Eq. (28) is rewritten as, 2 A non-zeroSo corresponds to a steady rotation of the particle. This is actuallythe case with the rotating-disk methoddescribed in §6.
- 50. 33 (G sin 20)P + --~ = O, (31) using Eqs. (19), (26) and (29). We integrate Eq. (31) to derive the angular distribution function P(0) of Boltzmann-type as, (32) whose maximum is located at 0=-0. Allowing for the normalization condition ["2 P(O)dO =1 -ttl2 Eq. (32) is rewritten as, P(O) = exp(-2c sin 2 0), (33) where I0 is the modified Bessel function of the zeroth order, and c is defined as, c= (O (34) 2k~T ' which is referred to as the flow orientation parameter or the c-parameter [22]. According to Eqs. (33) and (34), P(O) is determined by the c-parameter alone. The width of P(O), for instance, is evaluated with a quantity <sin20> given by, r,,, ,(,,<c)) < sin 20 >= sin 20P(O)dO = -~ 1- , "-"~ :o(~)) (35) where I1 is the modified Bessel function of the first order. 3.3. Dichroic Ratio Experimentally, we obtain the dichroic ratio R=-A(O)/A(1r/2) as representing the orientation of the particle. Here, A(~b) is the absorbance of incident light polarized to an angle ¢ with respect to the direction of dipping and raising of the substrate during the deposition process. For evaluating R, the particle is assumed to be an aggregate of molecules as shown in Fig. 7.
- 51. 34 The transition dipole moment of each molecule forms an angle a with the long axis of the aggregate, which is at an angle 0 from the dipping direction. The absorbance A(¢) is written as, f ~'~ {cos~(o + ~ ~) + cos2(O ~ 0)} P(o)ao, " -1r12 (36) allowing for the symmetry with respect to the dipping direction [22]. The dichroic ratio is therefore given by, f ,~/2.tcos2(0 + Jr) + cos 2(0 - rr)l ~ P(O)dO A(O) --~2 R = ~ = , (37) A(n'/2) f_~]i22 {sinz(0 + re)+ sin 2(0.7r)} P(O)dO If we substitute Eq. (33) derived assuming the local thermal equilibrium for Eq.(37), we obtain the expression for the normal deposition with a single substrate as, R = I° (c) + I~(c) cos 2a (38) Io(c)-Ii(c)cos2a using Eq. (35) and a relation <cos220>=l-<sin220>. Therefore, R is governed by c and a in this case: it tends to R= 1 for c --~ 0 and R=cot2a for c ~ or. 3.4. BinghamModelofPlasticity The rotatory friction coefficient (is determined by the size and shape of the particle and the viscosity of the surrounding medium. If the medium is a Newtonian fluid, (is a constant independent of the shear rate. It is however well known that condensed monolayers at the air-water interface often show plasticity [1], which is characterized with the shear-dependence of;'. Of many models of visco-elasticity available so far [5], [44], a Bingham fluid model [45]
- 52. 35 has been introduced to take the plastic behaviour into account. ( is then a function of the maximum shear rate 0 m,x= G+ = G (cf. Eqs. (22) and (30)) and given by 72o £" = ((G) = £" +--, (39) G where (' and ~:0refer to the Newtonian viscosity and the Bingham yield value, respectively [22]. Accordingly, the expression of ((7 is replaced by, ((7 = ('G + 720, (40) which indicates that the system remains an elastic body if the maximum torque CG acting on the particle does not exceed z'0, and that plastic deformation takes place for ~'G> r o and a proportional relationship similar to the Newtonian case is held between the excessive torque and the shear rate. The flow orientation parameter for the Bingham case is therefore expressed as, ~"~+ r O c = ~ , (41) 2keT by substituting Eq. (40) for Eq. (34). It is noted that c ---, r ot(2keT)>Oeven when G --, 0. 3.5. Predictions from the Model According to Eqs. (30), (33) and (41), the distribution function P(O) for the Bingham case is governed by six parameters involved in the c-parameter, which is explicitly written as, .k, rjt a --F) 72o 2k~T (42) by substituting Eq. (30) for Eq. (41) [22]. The six parameters are the temperature T, the width of the substrate a, the deposition velocity Vd, the relative position on the substrate lxl/a, and the two parameters (' and r0 involved in
- 53. 36 the Bingham model of rotatory friction coefficient. According to Eq. (42), the dichroic ratio R is determined by seven parameters, i.e., the above six and the deviation angle of the transition dipole moment a. Among the seven, a, vd and ]xl/a are characteristic of the LB deposition process, while C', r oand a are the properties of the monotayer. 3.5.1 Law of Similarity The c-parameter given by Eq. (42) involves three dimensionless terms. They are (1) ('va /(akeT), (2) (l-4x2/a2)-1 and (3) ~:0/(2keT),each leading to a law of similarity which governs the degree of orientation. (1) ~"'Vd I(akBT) involves four parameters, of which the deposition velocity Vdand the substrate width a are adjustable independently of any other parameter involved in c, while the Newtonian friction coefficient ~", and the Bingham yield value r0 as well, are generally known to be temperature-dependent, vd and a are competitive against each other in their contributions to the c-parameter: c increases with vd, but decreases with a, and the increment in c for 2 vd is exactly equal to that for a/2. (2) (1-4x2/a2) -1 represents the effect of the position on the substrate. It exhibits its minimum at the center [x[/a=O, and increases slowly when [xl/a>>l/2, but diverges to infinity for [xl/a ---, 1/2. Accordingly, the c-parameter, with its minimum Cmi,at the center, may have any value up to c + co. In other words, starting from the lowest degree of orientation at the center, any high degree up to the complete orientation is realized in one and the same substrate towards the edges. (3) r0/(2kBT) refers to the effect of Bingham plasticity. For r0>0, the c-parameter remains non-zero even for va --* O. In this case, c is determined by r0/(2ksT) alone, and its dependence on the dimensionless terms (1) and (2) disappears, resulting in a constant c-value all over the substrate except for the singular points Ix]/a--1/2 associated with the edges. As a consequence,
- 54. 37 the dichroic ratio R is always R>I for a<45 ° and R<I for a>45 °. 3.5.2. Effect of the Length of Particles Both (' and r0 depend on the geometry of the particle and the viscoelasticity of the monolayer as a two-dimensional system. In the case of rod-like particles, e.g., rigid polymers or needle-like crystallites, it is well known that, (' ,~rfb2, ro =f0b z, (43) where b is the length of the particle, and r/' andJ~ are the surface Newtonian viscosity and the corresponding Bingham yield value, respectively [37]. Here, the Bingham viscosity q at a shear rate g is written as, 11 = q(g) = rl'+ fo (44) Igl' The sharpness of orientation increases therefore with the length b of the particle. Furthermore, q' and j~ of the monolayer may also be increased with b, resulting in the enhanced flow orientation effect. 3.6. Comparison with Experimental Results The analytic model summarized in §3.1 - §3.5 is compared with the dichroic behaviour observed in the absorption spectra of the mixed LB films of merocyanine DS and arachidic acid C20 as exemplified in Fig. 2 [22]. The chemical structures of DS and C20 are shown in Fig.1. The dichroic data to be reviewed are from the 590-nm J-band seen in the Y-type LB films of a mixture [DS] : [C20]= 1 : 2, prepared using the standard vertical dipping method with one single substrate. The monolayers were formed at 20°C on an aqueous subphase containing Cd2+
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- 56. possession of Eugénie, and her husband joined me. He talked to me in what, as I thought, he intended as a sly tone. He had evidently heard that I was paying court to Mademoiselle Dumeillan; he thought that perhaps I would ask him to negotiate my marriage, to speak for me, to arrange the provisions of the contract. Poor Giraud! I saw what he was driving at; I pretended not to understand his hints and allusions. When he mentioned Eugénie, I changed the subject. He was offended; he rose and left me. That was what I wanted. I was sure that his wife was going through the same manœuvres with Eugénie. Bélan was right: those people would never forgive us if we married without letting them have a hand in it; but we could do without their forgiveness. Madame Giraud walked away from Eugénie with evident displeasure. Eugénie glanced at me with a smile; I had guessed aright the subject of their conversation. The husband and wife met and whispered earnestly together; then they walked toward Madame Dumeillan and surrounded her, one at her right, and the other at her left; she could not escape them. They evidently proposed to try to learn more from Eugénie’s mother; but I knew that they would waste their time, that Madame Dumeillan would tell them nothing; she invented an excuse for leaving them after talking a few moments. Giraud and his wife were very angry. They came toward me again, and I expected that they would hurl epigrams at me and tear me with their claws. I was not mistaken; Madame Giraud began, speaking to her husband so that I should hear: “It is very amusing, isn’t it, Monsieur Giraud?” “Yes, Madame Giraud, very amusing; there is a great deal of diplomacy here.” “Yes, they make a mystery of something that is everybody’s secret.” “Aha! they evidently take us for fools.” “It seems that way to me.” “Wouldn’t anyone say that it was a question of uniting two great powers?” “Perhaps they are afraid they will have to invite us to the wedding.” “Great heaven! weddings! we have no lack of them; in fact, we have so many that it is fairly sickening.”
- 57. “I declined an invitation to another to-morrow. And there is poor Bélan who has already invited us to his, which is to be at Lointier’s.” “That young man will make a very good husband. Does he get along all right with Madame de Beausire?” “Oh, yes! since I went to see the mother-in-law, all the obstacles have disappeared. There are some people who aren’t afraid to let me take a hand in their affairs, and who are greatly benefited by it.” “Let us go, Monsieur Giraud; we still have time to go and see our good friends who have that expensive apartment on Rue de la Paix, and whose daughter you found a husband for two months ago.” “You are right; I am sure that they expect us to have a cup of tea.” The husband and wife disappeared without a word to anyone. And those creatures were offended with us because we found it natural and convenient to manage our own affairs! But in society it takes so little to make enemies, especially of narrow-minded people. The guests began to leave, and I found a moment to talk with Eugénie. I told her that my mother would come to see her the next day. She blushed and sighed as she replied: “Suppose she doesn’t like me? suppose she isn’t willing to have me for her daughter?” Not like her! who could fail to like her? I was not at all disturbed. I reassured Eugénie, and I left her at last when the clock so ordered, as I had not as yet the right not to leave her at all. On returning home, I met Ernest coming down from his mistress’s room. Since I had been spending all my time at Madame Dumeillan’s, I had sadly neglected my friends of the fifth floor. Ernest reproached me for it mildly, but they were not offended; they knew that I was in love, and thought it quite natural that I should think of no one but my love. But Ernest said to me: “I hope that you will come to see us sometimes, although Marguerite will soon cease to be your neighbor.” “Is she going to move?” “In a week. She is not going to live in an attic any longer, thank heaven! Poor child! she has been miserable enough; she has made so many sacrifices for me, that I may well be glad to offer her a pleasanter position at
- 58. last. Thank heaven! my affairs are prosperous. I have been successful, my friend, and I have made money. I have not squandered it at the cafés or restaurants, because I have always remembered Marguerite, in her attic, poor and destitute of everything. You see that, whatever my parents may say, it is not always a bad thing to have a poor mistress, for it has made me orderly and economical in good season.” “I see that you are not selfish, and that you are not like many young men of your age, who think that they have done enough for a woman when they have taken her to a theatre and to a restaurant,—pleasures which they share with her,—but who cease to think about her as soon as they have left her at home.” “I have hired a pretty little apartment on Rue du Temple, nearly opposite the baths. That is where we are going to live; I say we, because I hope that before long Marguerite and I shall not be parted. It matters little to me what people say; I propose to be happy, and I shall let evil tongues say what they will.” “You are right, my dear Ernest; happiness is rare enough for a person to make some sacrifices to obtain it. I am going to marry my Eugénie! I have attained the height of my ambition!” “I might marry Marguerite too; but we are so happy as we are! Why should we change? Besides, we have plenty of time, haven’t we? Adieu, my dear Blémont. You will come to see us, won’t you?” “Yes, I promise you that I will.”
- 59. VIII MARRIAGE.—A MEETING.—THE BALL My mother went to see Madame Dumeillan, and they suited each other. It is a miracle when two women of mature years suit each other. My mother found Eugénie very attractive; she complimented me on my choice, and she was very hard to suit, too. I was overjoyed, in ecstasy. The provisions of the contract were very soon arranged by the two ladies, each of whom had but one child. For my part, I hurried forward the wedding day to the best of my ability. And yet, I was very happy. I passed three-quarters of my afternoons and all my evenings with Eugénie. If the ladies went out, I escorted them. Our approaching union was no secret, and many young men congratulated me on my good fortune. Some of them sighed as they glanced at Eugénie; perhaps they were in love with her. Poor fellows! I pitied them; but I could do nothing for them. It was decided that I should retain the apartment which I occupied. It was large enough for my wife, and I had it decorated carefully in accordance with her taste. It would not have been large enough if Madame Dumeillan had come to live with us, as I expected at first. Eugénie too hoped that she would not leave her; but Madame Dumeillan said to her affectionately but firmly: “No, my child, I shall not live with you. When a man marries, he wishes to take but one wife; why give him two? I know that Henri is fond of me; that he would be glad to have me live with him; but I know also, my children, that a young couple often have a thousand things to say to each other, and that a third person, no matter how dearly loved, is sometimes in the way. In love, in jealousy, in the most trivial disputes, the presence of a third person may be most harmful, and may prolong for a week what need have lasted but a moment; it checks the outpouring of love and intensifies the bitterness of reproach. But I will live near you, and I shall see you often, very often. And whenever you want me, you will always be able to find me.”
- 60. Eugénie was obliged to yield to her mother, and for my part, I considered that Madame Dumeillan was right. Should we have a wedding party? That was a question which I asked myself, and which I was tempted more than once to put to Eugénie. But a little reflection convinced me that I should be wrong not to celebrate my marriage. To please me, Eugénie would pretend that she did not care about a ball; but at twenty years of age, possessed of innumerable charms, endowed with all the graces which attract and subjugate, is it not natural for a woman to long to show herself in all the glory of her happiness? Is that not a marked day in her life when she is called madame for the first time, although she has not absolutely ceased to be a maiden; when she has not as yet the assurance of the former, but on the contrary has all the shrinking modesty of the other in an intensified form? Yes, at the age of love and enjoyment, it is essential to have a wedding party; doubly so, when one marries the object of one’s passion; for happiness is always an embellishment. My Eugénie needed no embellishment; but why should I not have a little vanity? Why should I not be proud of my triumph? So it was decided that we should have a wedding party: that is to say, a grand breakfast after the ceremony, and in the evening a supper and ball at Lointier’s. I determined to look to it that my Eugénie should have magnificent dresses for that great day; not that she could possibly be more beautiful in my eyes, but I wished that she should enjoy all those triumphs which mark an epoch in a woman’s life. I gave her leave to be a coquette on that day. The moment of my happiness drew near. We turned our attention to the list of guests. For the breakfast there would be very few, enough however to make sure that they would not be bored, and that it should not have the aspect of a family party. For the evening, many people were invited; the salons were large, and it was necessary to fill them. We simply tried to make sure that in the throng none of those fine gentlemen should worm themselves in, who are known neither to the groom nor to the bride, nor to their relations, but who boldly present themselves at a large party, where, under cover of their decent exterior, they consume ices and often cheat at écarté. We had already written a multitude of names; I had not forgotten Bélan, and as the ladies were slightly acquainted with Madame de Beausire and
- 61. her daughter, we sent them an invitation too; I knew that that would rejoice poor Ferdinand. Suddenly I stopped, and looking at Eugénie and her mother with a smile, I said to them: “Shall we put down their names too?” “I am sure that I know whom you mean!” cried Eugénie. “Henri is thinking of the Giraud family.” “Exactly.” “Why invite them?” asked Madame Dumeillan; “they are terrible bores, and their inquisitiveness actually amounts to spying.” “I agree with you, and the last time they came to your reception they made themselves ridiculous. But I cannot forget that it was at their house that I first met Eugénie. And then our invitation will please them so much! and when I am so happy, I like others to be so.” “Henri is right, mamma; let us invite them.” So Giraud’s name was put down on the list. At last, the solemn day arrived. I rose at six o’clock in the morning, having slept hardly at all. I could not keep still. What should I do until eleven o’clock, when I was to call for my mother, and then for my Eugénie? To read was impossible; to draw or to paint was equally impossible. To think of her—ah! I did nothing else; but it fatigued me and did not divert my thoughts. After dressing, I went all over my apartment, where I was still alone; I made sure that nothing was lacking. I hoped that she would be comfortable there. That apartment, which I had occupied four years, involuntarily reminded me of a thousand incidents of my bachelor life. That room, that little salon had seen more than one female figure. I had received many visits. When a lady had promised to come to breakfast or to pass the day with me, how impatiently I counted the minutes! How, until the time arrived, I dreaded lest some inopportune visitor should ring the bell in place of her whom I expected! How many kisses, oaths and promises had been exchanged on that couch! And all those things were so soon forgotten!—Ah! I was very happy in those days too! But suddenly I thought of all the letters I had received; I had not burned them, and they were in a casket on my desk. I had often enjoyed reading them over; but suppose Eugénie should find them! I determined to burn them, to burn them all; for what was the use of them now?
- 62. I took out the casket which contained them; I opened it; it was stuffed with them. There are some women who are so fond of writing, either because they write well, or because they think they do, or simply because they love one. I took all the letters and carried them to the fireplace, where I made a pile of them. But before setting fire to them, I opened one, then another, then another; each of them reminded me of an episode, some day of my life. It is strange how quickly time passes amid such old souvenirs. The clock struck nine, and I was still reading. I was no longer in love with any of those women, but it was my last farewell to bachelorhood. I set them afire, not without a faint sigh. At last my bachelor amours were burned, and only a pinch of ashes remained; some day nothing more will remain of all the riches, of all the marvels of this earth. Those were very serious thoughts for a wedding day, but they served to pass the time, and that was something. Moreover, extremes always meet: the happier one is, the more disposed is one’s mind to melancholy thoughts. A grocer weighing sugar, or a postman delivering letters, does not feel such impressions. But I almost forgot something else; for since I had thought of nothing but Eugénie from morning until night, it was not surprising that I had not set all my affairs in order. I had once amused myself by painting miniatures of some of the ladies whose letters I had just burned. Those portraits were in the desk upon which I painted; there were eight of them. Should I sacrifice them as well? It would have been a pity; not because of the models, but because the miniatures were really not bad. Why destroy them? In the first place, Eugénie would never see them; and even if she should see them, they were fancy portraits. When one paints from life, one must necessarily paint portraits. So I had mercy upon those ladies, and replaced their pretty faces in the depths of the desk, whence I thought that they would never come forth. Now I had carefully scrutinized and examined everything; nothing was left which could possibly offend Eugénie’s eye. No, she could come there now and reign as mistress; thenceforth no other woman should enter those rooms than such as she should choose to receive. It was time to think about dressing. I thought it would do no harm if I were at my mother’s a little before the hour. If only the carriages did not keep me waiting. But someone entered my room; it was my concierge and
- 63. his wife, with a big bouquet. Did they think I was going to put it in my buttonhole? The husband came forward with an affable expression and was about to speak, but his wife did not give him time. “Monsieur,” she said, “this is your wedding day; we are very glad to be able to congratulate you on such a happy day, by offering you this bouquet and our compliments; these immortelles are the symbol of your happiness, which will last forever.” While his wife glibly delivered this speech, the concierge tried to slip in a few words, but he did not succeed. I took the bouquet, gave them some money and dismissed them. A wedding day would have little charm if one must submit to many congratulations of that sort. At last a carriage arrived. I went downstairs and passed rapidly before a long line of cooks and some gossiping old women who lived in the house, who were stationed in the courtyard to see me, as if a man who was going to be married had his nose placed otherwise than usual on that day. I was driven to my mother’s, and found that she had just begun to dress. “It isn’t eleven o’clock yet,” she said; “we have plenty of time; go and read the newspaper.” Read the newspaper! just at the moment that I was to be married! I, who could not read one through when I had nothing to do! No, I preferred to remain there, and each five minutes I knocked at the door of her dressing- room to enquire if she were ready. At a quarter-past eleven I carried my mother off, I almost dragged her away, although she declared that her bonnet was on crooked and that she wanted to have the ribbons changed. I refused to listen, we entered the carriage, and I swore to my mother that her headgear was in perfect order; she became calmer and consented to be amiable once more. We arrived at Madame Dumeillan’s. Eugénie was ready; I was confident that she would not keep me waiting, that she would have pity on my impatience. Her dress was charming, according to all the people who were there; for my part, I did not notice her dress, I saw only her, and I should have thought her a thousand times lovelier if it had been possible. One of our witnesses kept us waiting. There are people who would not hurry one iota to please others, and who know of nothing in the world that is important enough for haste. I could not live with such people.
- 64. At last the tardy witness arrived and we started for the mayor’s office. I was not allowed to escort Eugénie. On that day everything was subordinate to ceremony; a man must be happier on the day after his wedding than on his wedding day. I have never cared much for ceremonial, and that of my marriage seemed extremely long. To give me courage, I looked at my wife; she was more impressed than I by the solemnity of the moment; she was deeply moved and was weeping. Dear Eugénie! I thought of nothing but loving her forever, and it was certainly not necessary for anyone to order me to do it. It came to an end at last. We returned to the carriages, still in procession, and through a crowd of curious folk who devoured us with their eyes. I felt more buoyant, happier. I was so glad that it was over! I spied Giraud and his wife at the church, in full array; they had offered us congratulations which I had not listened to; but I had said to them: “until this evening;” and they replied with a low bow. We drove to Lointier’s, where a handsome breakfast awaited us. But a wedding breakfast is generally a decidedly gloomy affair. The bride can hardly be expected to laugh, and even when she is happiest, she is thoughtful and talks little; the grandparents are always intent upon preserving their dignity. For my part, I was engrossed, or rather annoyed, by the reflection that it was still early in the day. There were in the party some jokers, or persons who tried to joke; one stout gentleman, a kinsman of my mother, regaled us with some of those superannuated jests concerning the occasion and happiness that awaited us; but his sallies met with no success; nobody laughed at them, and he was forced to keep to himself the ample store of bons mots with which I am sure that he was provided. I was delighted, because I considered such jests very bad form; they should be left for the weddings of concierges or servants; the modesty of a young woman who has but one day of innocence left should be respected; and we should assume innocence in those who have none. Eugénie and I were at a distance from each other; we could not talk, but we glanced furtively at each other and our eyes mutually counselled patience. The clock struck five, and the ladies left to change their dresses. I escorted my wife to the carriage which was to take her home with her mother. I would have been glad to go with her, but Madame Dumeillan and
- 65. my mother persuaded me that it was my duty to remain with the guests who were still at table. Eugénie leaned toward me and whispered in my ear: “Oh! we shall be much happier to-morrow, my dear! we shall not be separated then, I trust.” Dear Eugénie, you were quite right. I had to return to the table, because it pleased some of our guests to eat and drink through four hours. If only I had been hungry! We left the table at last, at six o’clock. Several of the gentlemen began to play cards. As courtesy did not require me to watch them lose their money, I left the restaurant and drove to my wife’s house. The hairdresser had just arrived, and she had abandoned her lovely hair to him. Really, those hairdressers are too fortunate, to be able to pass their fingers through those lovely locks and to gaze constantly at the pretty head which is entrusted to them. That one took at least three-quarters of an hour to arrange Eugénie’s hair, as if it were difficult to make her look charming! But women are wonderfully patient with respect to everything that pertains to their toilet. Her hair was arranged at last; but they took her away, for she was not dressed. My wife was not yet mine; she was still in the grasp of the conventionalities of that day. I was fain to be patient, until I once had possession of her. But that night I would bolt all the doors, and no one should see her the next morning until I chose. I saw that Eugénie would not be dressed for at least an hour, so I went out and tried to kill time. I jumped into one of the carriages which were waiting at the door, and was driven to the Tuileries. I alighted on Rue de Rivoli, and entered the garden. The day was drawing to a close; the weather was gloomy and uncertain. There were very few people under those superb chestnuts toward which I walked. I was delighted, for I do not care for a promenade where there is a crowd; the people who stare at you or jostle you every moment prevent you from dreaming, from thinking at your leisure. I rarely went to the Tuileries; to my mind that great garden was melancholy and monotonous; but on that day it seemed pleasanter to me, for I could think freely of my wife. My wife! those words still had a strange sound to me. I was married, I who had so often laughed at husbands! Had I been wrong to laugh at them, or should I prove an exception to the rule?
- 66. I walked at random. Finally I found myself in front of the enclosure where the statues of Hippomenes and Atalanta stand. That reminded me of a certain assignation. It was three years before, in the middle of winter. There had been a heavy fall of snow; the garden, the benches were covered with it, and it was very cold. But I had an assignation, and on such occasions one does not consult the thermometer. It was with a certain Lucile, who, for decency’s sake, called herself Madame Lejeune, and who mended cashmere shawls. She was very pretty, was Lucile. About twenty-three years old at that time, with a pretty, shapely figure, and an almost distinguished face which did not betray the grisette. I had an idea that her portrait was among those that I had preserved. She was accustomed to love madly for a fortnight; during the third week she calmed down, and ordinarily she was unfaithful by the end of the month. As I had been warned, I considered it more amusing to anticipate her, and to take up with another before the fortnight had expired. She did not forgive me; her self-esteem was wounded, for I have no idea that she would have been more constant with me than with others; but she tried to make me believe that she would have, and whenever I met her I could always detect a flavor of bitterness in her speech and anger in her glance. It was in front of that enclosure, close by those statues, that we had arranged to meet. I remembered that Lucile was there before me, despite the extreme cold. We had not known each other four days, and we adored each other. She did not reprove me for keeping her waiting, and yet her nose and chin were purple with cold, and her fingers were stiff; but her eyes burned. I put her into a cab and took her to dine at Pelletan’s, at the Pavillon- Français. It was one of the red-letter days of my bachelorhood. Very good, but the whole business was not worth one smile from Eugénie. I was about to turn away from Atalanta, when I saw within a few feet of me a lady dressed with some elegance, who was looking at me with a smile on her lips. “You must admit,” she said, “that the snow is all that is needed to make the resemblance complete.” It was Lucile! What a strange chance! I walked toward her. “You here, madame?” “Yes, monsieur; and I beg you to believe that I have not come here in search of memories.”
- 67. “I am here, madame, by the merest chance. But, as I passed these statues, I remembered a certain assignation, one winter, and I confess that I was thinking of you.” “Really! Ah! that is most flattering on your part! You have to come to the Tuileries to do that, do you not, monsieur?” “If that were so, madame, you must admit that other men devote their thoughts to you. One aspirant more or less—you can hardly detect the difference.” “Ah! your remarks are exceedingly polite! But I am not surprised: you have never been anything but agreeable to me! You are the same as ever!” “I do not see that I have said anything to you that——” “Oh! mon Dieu! let us drop the subject. You might conclude that I attach great value to memories of you, and you would be much mistaken. But how fine you are! Are you going to a wedding?” “Just so; I have been one of a wedding party since morning, and I came here for a walk while the bride is dressing herself for the ball.” “Oho! you are a wedding guest to-day! Is the bride pretty?” “Lovely.” “A widow or unmarried?” “Unmarried.” “How old?” “Twenty years.” “Has she—you know what?” “I can tell you that better to-morrow, if I should happen to see you.” “Are you the best man?” “Better than that.” “Better than that! What! Do you mean—Oh, no! that is impossible. You are not going to be married?” “Why is it impossible?” “Because you don’t do such crazy things as that.” “I don’t know whether marriage is always a crazy thing, but I can assure you that I was married this morning, and that, far from regretting it, I congratulate myself upon it.”
- 68. “Oh! if it was only this morning, that is easy to understand.—What! are you really married, Henri? Ha! ha! how amusing it is!” “What is there so amusing about it?” “Ha! ha! ha! Poor Henri! You are married! Upon my word, I can’t get over it. But I promise you that it gives me the very greatest pleasure! Ha! ha! ha!” Lucile’s sneering laughter had an ironical note that began to irritate me. I bowed to her and turned away, but she detained me. “By the way, one moment, monsieur; it is probable that I shall not have the pleasure of talking with you again for a long time, for a married man doesn’t go out without his wife. So yours is very pretty, is she?” “Yes.” “And are you very much in love with her?” “More than I have ever been.” “Oh! how frank!” “Why shouldn’t I say what I think?” “To be sure. Then you must try to make her love you more than you have ever been loved. Ha! ha!” “I think that that will not be difficult.” “Do you think so? You may be mistaken.” “Excuse me, madame, if I leave you; but my wife must have finished dressing, and I must return for her.” “If your wife is waiting for you, why, go, monsieur; and see to it that she never waits for anybody else. Ha! ha!” I saw that Lucile had not forgiven me. I left her. I was unable to conceal the vexation that that woman caused me to feel. I jumped into the carriage which took me back to Eugénie. She was waiting for me; the sight of her, a single word from her lips, speedily dissipated that slight cloud. Eugénie was dazzling; her charms, her graces, her lovely dress, everything combined to add fascination to her aspect. I took her hand. “It is time to go to the ball; let us start,” said Madame Dumeillan and my mother. I held Eugénie’s hand, I was looking at my wife, and I had forgotten everything else.
- 69. Our appearance in the salons was greeted with a flattering murmur. Words of praise rang in my ears, and I admit that they flattered my heart too; it was my wife who was the object of universal admiration. Eugénie blushed and lowered her eyes; but it would have been difficult for her to avoid hearing the compliments which were rained upon her as she passed. There were many people already there, and my acquaintances came forward to greet me. Giraud took my hand and pressed it. I felt inclined to be friendly with everyone, I was so happy! The men crowded about my wife to obtain the favor of dancing with her; they took their numbers, and I overheard one of them say that he was number twenty-six. Judging from that, it was evident that I could not look forward to dancing with my wife that night. But I made the best of it, and invited other ladies to dance. I spied a little man, pushing and jostling everybody to make a passage for himself; it was Bélan, escorting a young lady who was at least a head taller than he, and with whom he was about to dance. When they passed me, they stopped, and he said to me: “My friend, this is Mademoiselle Armide de Beausire, of whom I have spoken to you so often.” I bowed low before Mademoiselle Armide, who was neither beautiful nor ugly, and whose eyes were almost as large as her mouth; but there was in her face and in her whole person something stiff and prim which smelt of the province a league away. People crowded around Bélan and Mademoiselle Armide to see them dance. The little man danced very well; and as he had a very good figure, he had procured tight trousers, a tight coat and a tight waistcoat; there was not a fold to be seen on his whole body; if his face had been black you would have thought that he was a little negro in puris naturalibus. Between the contradances I struggled through the crowd, to try to introduce to my wife a crowd of people whom I hardly knew, but who said to me: “Won’t you present me to madame?” At midnight the crowd had become so great that it was difficult to move. Did I know all those people? No; but I had told several of my acquaintances to bring their acquaintances, and that sort of thing extends very far sometimes. However, it was a brilliant affair. There were lovely dresses and very pretty women; the men were well-dressed, and I saw none of those
- 70. expressionless, ignoble faces, none of those old creased caps which one is surprised sometimes to see at a fashionable party, where however they often have more right to be than most people; for those unattractive, common faces which we see in corners at a wedding party usually belong to some uncle or some cousin whom it was impossible not to invite. Three times I found Giraud eating ices or carrying them to his wife. He had brought only two of his children; the two older ones; that was very considerate of him. I was so happy that I asked Madame Giraud to dance, and she seemed highly flattered by that courtesy. But what did it matter to me with whom I danced when it was not Eugénie? I no longer thought of paying court to ladies; other times, other ideas. “Your ball is delightful,” said Bélan, leading me into a salon where card playing was in progress, but where it was possible to move about. “There are at least four hundred people here.” “Faith! I should be hard put to it to say how many there are here. If they are enjoying themselves, that is all that is necessary.” “It will be like this at my wedding. What do you think of Armide?” “She is very attractive.” “And her eyes?” “They are superb.” “They are extraordinary, are they not? Well, my dear fellow, she has everything like that,—wit, talents, and such an air of distinction! Did you see us dancing together?” “Yes.” “Didn’t we get along well?” “It is a pity that you are a little short beside her.” “Short! you are joking. She is a little tall! However, when a man is built as I am, it is worth three inches of height. I certainly wouldn’t change figures with that tall, lanky man in front of us. Those tall fellows are always awkward. Have you seen Madame de Beausire?” “I don’t think so.” “Come then, and let me present you to her. You will see a woman who hasn’t a single touch of the plebeian; she is the type of true distinction.”
- 71. I submitted to be led away; I did whatever anyone wanted that night. I saw a tall, yellow woman who resembled a piece of old tapestry, and who looked as if she had never laughed since she came into the world. I made haste to bow and to run away. It seemed to me that one must necessarily catch the spleen in Madame de Beausire’s company. The supper hour arrived; at last the ball was drawing to a close; and although I was not exactly bored, still I should have been very glad to be at home with my wife. The ladies were conducted to their seats. I looked after the comfort of everybody; I saw that the tables, large and small alike, were properly waited upon. “Pray rest a moment and eat something,” people said to me. Much I thought about eating! I preferred to hurry the supper of that multitude. I found Giraud and his two children sitting at a small table with three young men. Giraud had a currant cake on his knees, and he had slipped a bowl of jelly under the table, not choosing to pass it, for fear it would not come back to him. I called for fish, chickens, and pâté; I covered his children’s plates with cakes. Giraud was in ecstasy; he shook my hand, murmuring: “This is one of the finest weddings I have ever seen, and God knows that I have seen a tremendous number of them!” Madame Giraud, who had been obliged to leave the large table when the other ladies rose, walked behind her husband and children at that moment, with an enormous reticule hanging on her arm. While pretending to pass the gentlemen what they wanted, I saw that she kept opening the bag and thrusting cakes, biscuit, and even pie crust into it. Giraud, seeing that I had noticed his wife’s manœuvring, said to her angrily, as she was trying to force some macaroons into her bag:
- 72. “What on earth are you doing, Madame Giraud? What sort of manners are these? You are putting macaroons into your bag!” “Just for Azor, my dear, the poor beast. He is so fond of macaroons, you know. They would be wasted, so what harm does it do? I want poor Azor to have a little of the pleasure of this party.” “You know very well that I don’t like such things, Madame Giraud.” I appeased Giraud, who pretended to be very angry; then I walked away, in order to leave his wife at full liberty; and she ended by making a perfect balloon of her bag. Meanwhile, the tables were gradually deserted; many people returned to the ballroom, but many others entered their carriages, and I considered that the latter acted wisely. The ball was more agreeable perhaps, because it was more comfortable to dance. Eugénie continued to be invited, and I must needs content myself with dancing opposite her; but there were figures in which we took each other’s hands, and then how many things we said by a soft pressure! it seems that the heart, that the very soul, passes into the beloved hand which presses ours lovingly. The ranks became thinner. My mother had gone, and Madame Dumeillan was only awaiting our departure to follow her example. It was five o’clock. The daylight was beginning to show through the windows, and to lessen the brilliancy of the candles. The number of ladies diminished every moment. I went to Eugénie’s side. “I am tired of dancing,” she said, “and yet I am afraid to refuse.” “Why, it seems to me that we might venture to go now.” She lowered her eyes and made no answer. I concluded that I had done enough for others and that I might think of myself at last. I took my wife’s hand and led her from the room; Madame Dumeillan followed us; we entered a carriage and drove away. We had to take Madame Dumeillan home first. It was a short distance, but it seemed very long to me. The nearer one’s happiness approaches, the more intense one’s impatience becomes. We spoke but little in the mother’s presence. At last we reached her house, and I alighted. Madame Dumeillan embraced her daughter; it seemed to me that their embrace was interminable. Selfish creatures that we
- 73. are! it did not occur to me that that was the last embrace in which a mother would hold her daughter, still a virgin, in her arms, and that I should have all the rest of my life to enjoy my privileges as a husband. Madame Dumeillan entered her house. I returned to the carriage, and we drove on. At last I was alone with Eugénie, with my wife. I believe that that was the sweetest moment that I have ever known; it had seemed to me that it would never arrive. I put my arms about Eugénie; she wept when she embraced her mother; but I embraced her, and she ceased to weep, for I overwhelmed her with caresses, and unfamiliar sensations made her heart beat fast. At last we reached my apartment, our apartment. The servant who was to live with us, and who had been in her mother’s service, was waiting for us in the concierge’s room, with a light; but it was broad day; we needed no service. My wife and I entered our home. I led her by the hand, I felt that she was trembling and I believe that I trembled too. It is a strange effect of happiness that it suffocates one, that it almost makes one ill. I closed the doors and shot the bolts. I was alone with my wife! At last there was no third person with us! We were at liberty to love each other, to tell each other of our love, and to prove it!
- 74. IX THE HONEYMOON.—BÉLAN’S WEDDING How happiness makes the time fly! A fortnight after I became Eugénie’s husband it seemed to both of us that we had been married only the day before. That fortnight had passed so rapidly! It would be very difficult for me to say how we employed the time; we had no leisure to do anything. In the first place, we rose late, we breakfasted tête-à-tête, and then we talked; often I held Eugénie on my knees; people can understand each other better when they are close together. We made a multitude of plans, our conversation being often interrupted by the kisses which I stole, or which she gave me. We were much surprised, when we glanced at the clock, to find that it was almost noon and that we had been talking for two hours. Then we had to think about dressing to go to see Madame Dumeillan, and sometimes to take a walk or drive. We continued to talk while we dressed. I would ask Eugénie to sing me a song, or to play something on the piano. If I chanced to have a visitor, or a client who kept me in my office fifteen minutes, when I came out I would find my wife already impatient at my long absence, and we would talk a few minutes more to make up to ourselves for the annoyance caused by my visitor. At last we would go out; but we always acted like school children and chose the longest way, so that it was almost dinner time when we reached my mother-in-law’s. We had been to the theatre twice since we were married; we preferred that to going to parties. At the theatre we were still alone and could talk when the play was dull; but in society one is never free to do whatever one pleases. We always returned home early, and we were always glad to get home. But, I say again, the time passed like a flash. My wife found my apartment much to her liking; she told me that it was a pleasure to her to live where I had lived as a bachelor. She often questioned me about that period of my life, and listened to my answers with interest and curiosity; but I did not tell her everything; I slurred over many episodes; for I had discovered that Eugénie was jealous. Her brow darkened
- 75. when there were women in my adventures, and she often interrupted me, saying angrily: “That’s enough, hush! I don’t want to know any more!” Then I would kiss her and say: “My dear love, I didn’t know you then.” But, despite my caresses, her ill humor always lasted some minutes. However, it was necessary that we should do something else than talk and embrace. Eugénie agreed to teach me to play on the piano, and I to give her lessons in painting. But first of all, I began her portrait. That was an occupation which took an endless time, for we were constantly distraught; when I looked at my model, and she fastened her lovely eyes upon me and smiled affectionately at me, how could I always resist the desire to kiss her? And she would pout so prettily when I failed to lay aside my brush for a long while! At that I would rise and rush to my model and embrace her. Such episodes led me to think that painters must be very self-restrained, to resist the temptations they must experience when they are painting the portrait of a young and pretty woman. A woman whom we are painting looks at us as we wish her to look; we request a very sweet glance and smile, and she exerts herself to make her expression as pleasing and amiable as possible; for a woman always desires her picture to be fascinating. For my own part, I had never needed to resist my desires, for I had painted none but my mistresses; but when one must needs scrutinize in detail innumerable charms, and stand quietly by one’s easel—ah! then, I repeat, one must be most virtuous, and that particular sort of virtue is not the characteristic quality of painters. Despite our frequent distractions, I worked assiduously at my wife’s portrait; in ten sittings it was finished, and I was delighted with my work; the likeness was striking. Eugénie herself uttered a cry of surprise when she saw herself; but she feared that I had flattered her. No; I had not painted her, to be sure, as she was in company, when she looked at everybody indifferently, but as she was when she looked at me while I was painting her, with eyes overflowing with love. It seemed to me that I had done wisely to select that expression; for it was for myself and not for others that I had painted her portrait.
- 76. Next, I must needs paint my own; Eugénie insisted upon it. That was a much less amusing task, and I feared that it would be a long one. I had already given myself several sittings, and it seemed to me that it did not progress satisfactorily. Eugénie was not satisfied; she said: “You have given yourself a sulky, sober look; that isn’t the way you look at me.” “My dear love, it is because it is a bore to me to look at myself.” “Oh! wait a moment, I have an idea. I will sit beside you; then, when you look in the glass, you will see me too, and I trust, monsieur, that you will not make faces at me.” Eugénie’s idea impressed me as a charming one. Thanks to her invention, I was no longer bored when I sat for myself; for she was always there beside me, and when I looked in the mirror she was the first thing I saw; my portrait gained enormously thereby; I was able to paint myself as she wished, and she was as well pleased as I had been with hers. I had her portrait set in a locket which I always wore; she had mine set in a bracelet which she always had on her arm. We were not content to have each other in reality, we must needs have each other’s image as well; if we could have possessed each other in any other way, we would have done it. But is it a mistake to love too dearly? Her mother and mine both declared that we were unreasonable, that we were worse than lovers; but Eugénie and I were determined never to change; we liked each other well enough as we were. My wife insisted that I should begin to learn the piano; and I showed her how to use a brush. Those lessons were most delicious to us; and they occupied a large part of the day. I realized however that piano playing and painting would not make me eminent at the bar. Since my marriage I had neglected the Palais, and paid almost no attention to business; but when I would propose to study, to shut myself up in my office, Eugénie would detain me, saying: “What is the use of worrying yourself, of tiring your brain over your Code and your Pandects? Are we not rich enough? Are we not happy? What is the need of your trying cases, of your tormenting yourself for other people? Stay with me, give me a lesson in painting, and don’t go to the Palais.”
- 77. I could not resist my wife. My mother scolded me sometimes for what she called my laziness. Love is not laziness, but a happy love makes us unfit for anything except making love. Three months passed almost as rapidly as the first fortnight of our married life. But I had learned to play On Dit qu’à Quinze Ans on the piano, and Eugénie was making rapid progress in painting. A new subject of rejoicing added to our happiness: my wife was enceinte. We leaped for joy, we danced about the room, thinking that we were to have a child. We talked of nothing else, we made no plans for the future in which our son or daughter had not a share. Good Madame Dumeillan shared our delight; my mother complimented me, but without enthusiasm, and as if it were a very trifling matter; whereas it seemed to me that it ought to mark an epoch in the world’s history. We went into society very rarely, and we had been to but two balls since our wedding. But one morning we received cards and an invitation to the wedding party of Monsieur Ferdinand de Bélan and Mademoiselle Armide de Beausire. Eugénie was not far enough advanced to fear that dancing would injure her; moreover, she promised to dance only a little; so we determined to go to Bélan’s wedding, where I had an idea that we should find something to laugh at. My wife agreed with me. Bélan had been to see us twice since we were married, and Eugénie considered that he made himself rather ridiculous by his chatter and his affectations. As for the Beausire family, the little that I had seen of them seemed to me rather amusing. The invitation included, upon a separate sheet, an intimation that we were expected to attend the breakfast also. That was a pleasure of which we determined to deprive ourselves. We mistrusted wedding breakfasts, which are about as amusing as an amateur concert or a parlor reading; we had made up our minds to go to the ball only, when Bélan appeared in our apartment. The little dandy bowed to the floor before my wife, which was not a difficult feat for him; then he shook hands with me and said with an air of triumph: “Did you receive our invitations?” “Yes, my dear fellow. First, let us congratulate you.”
- 78. “I accept your congratulations with pleasure. I certainly have reason to be flattered by the preference accorded me. I had seventeen rivals, three of whom were millionaires who owned iron foundries, factories or coal mines; and two marquises, one of them with six decorations; but I beat them all; and like Cæsar, veni, vidi, vici. We may rely upon you, may we not?” “Oh yes, we shall be at your ball.” “And at the breakfast?” “As to the breakfast, we cannot promise.” “Oh! I beg your pardon, but I insist upon a promise. It would be horrid of you to fail us. We have invited only a small number of people for the morning, but most select. Two of my wife’s uncles, three cousins, and five aunts, all of whom are women of my mother-in-law’s type. Great heaven! my mother-in-law has done nothing but weep since our wedding day was fixed; she drenches at least four handkerchiefs a day, and she doesn’t let her daughter out of her sight. That embarrasses me a little in my effusions of sentiment, but my time will come. However, you must attend all the festivities. I address my entreaties to you, madame; Henri will not refuse you.” Eugénie had not the heart to refuse; she glanced at me and we promised. Bélan thanked my wife and kissed her hand, then he asked me for two minutes in my office. “Have you any lawsuit on hand?” I asked him when we were alone. “No, but I want to consult you. Having just married a woman whom you adored, you will be able to tell me——” “Tell you what?” “I don’t know just how to put it. You know that I have been, like you, a lady’s man, never embarrassed in a tête-à-tête. I was like a flash of powder.” “Well?” “Well, it is very strange, but with Mademoiselle de Beausire, although I adore her, the effect is entirely different. It seems to me that I dare not squeeze the end of her finger. In short, I do not feel the slightest inclination to be enterprising. I confess that that worries me and makes me anxious; I don’t sleep at night; and the nearer my wedding day approaches, the more apprehensive I feel.”
- 79. “Ha! ha! Poor Bélan! nonsense! don’t be afraid! Real love, love that is too ardent, sometimes produces the effect which you complain of; but it does not last. And besides, what have you to fear with your wife? You are sure that she won’t escape you. She isn’t like a mistress, who often refuses to give you a second assignation when she is not pleased with the first. With one’s wife, what doesn’t happen the first night, will happen the second.” “True; it might not happen till the eighth even. You make me feel a little easier in my mind. You see, Mademoiselle de Beausire—such a well-bred young woman as she is—isn’t like a grisette. Oh! with a grisette, it goes all alone.—And then the mother-in-law is always there!” “I imagine that she won’t be there on your wedding night.” “Faith! I wouldn’t swear to it. She does nothing but talk about not being parted from her daughter, and says that she can’t sleep away from her. I believe that she means to sleep in a closet adjoining our bedroom.” “That will be very amusing for you!” “It is that sort of thing that keeps going through my head and takes away my natural ardor. But no matter, between now and my wedding I will have everything I eat flavored with vanilla; I will even have some put in my soup. Adieu, my dear Blémont. We rely upon you. Your wedding was very fine, but just wait till you see mine. That’s all I have to say.” Bélan went away. So we were simply compelled to attend the breakfast; we had promised. However, perhaps it would be more amusing than we thought. Indeed, there are parties which are so tiresome that they are actually comical. The only remedy was to make the best of things; they say that there is a good side to everything. Eugénie gave her attention to her dresses; for she must have two for that day. I urged her not to lace herself too tightly; you can guess why. A woman should think about being a mother rather than try to make herself slender; but that is what she often forgets. Bélan’s great day arrived. A carriage came for us, the coachman, and the groom behind, both dressed in apricot livery. I was compelled to admit that that feature already excelled my wedding, and I expected to see some magnificent things. We were to meet at Madame de Beausire’s, where I had never been. It was an old house, on Rue de la Roquette. We passed an old concierge; we ascended an old staircase, upon which rose leaves had been scattered profusely. I was sure that that was an idea of Bélan, and I did not
- 80. consider it a very happy one, for it nearly caused my wife to fall; but I caught her in time, and she said with a smile: “We were married without rose leaves, my dear.” “Yes, my dear love; it was less romantic, but there was no slipping.” We entered an apartment of extraordinary height, on the first floor. It was so high that I could hardly distinguish the mouldings of the ceiling. We were announced by an old servant, who seemed to have been weeping; perhaps that was a custom of the house. We were ushered into an immense salon, where Bélan, who was doing the honors, produced the impression of a dwarf amid a lot of Patagonians. We discovered a row of old faces, a sort of continuation of the tapestry of which Madame de Beausire had given me a specimen. The men were solemn, sententious and pretentious; the women stiff, affected and painted. There were a few people of our own set, but only a few. I concluded that Bélan had not obtained permission to invite many of his acquaintances. The poor fellow did not seem at his ease amid the Beausire family; he was afraid to be jovial, he dreaded to be dismal; he hovered about his new kindred, who did not talk for fear of compromising their dignity. The groom was delighted when we arrived; he felt more at ease with us. “You will see my wife presently,” he said to us; “just now she is with her mother, who is finishing her toilet, weeping.” “What! is your mother-in-law weeping still?” “Yes, my friend, that woman is a regular fountain.” “But what is she weeping for?” “Grief at separating from her daughter. And yet she does not propose to separate from her, for she declares that she will sleep in the same room with us.” “In the same room? Ha! ha! that is rather strong.” “I swear to you that that is what she says. Indeed, I believe that she hoped that I would not sleep with my wife; but on my word, despite all my respect for Madame de Beausire, I refused to give in on that point, and I think that Armide was glad of it. But here come the ladies.” The bride entered, escorted on one side by an old aunt with a nose like a snail’s shell, and on the other by her mother, who, with her tall, spare figure, her red eyes, and her leaden complexion, really looked like a ghost.
- 81. From the sighs heaved by those ladies, one would have thought that they were leading a second Iphigenia to the sacrifice. The relations came forward and delivered congratulations of the same style as their costumes. In the midst of it all, the bridegroom was the person to whom the least attention was paid. When he addressed his wife, she made no answer; when he turned to his mother-in-law, she took out her handkerchief and turned her back on him; and if he accosted any of the relations, they pretended to pay no attention to him. We started for the church, each man escorting a lady; I gave my arm to my wife; for I did not see why I should deprive myself of that pleasure in favor of those creatures. We went downstairs, in the conventional order, Bélan at the head, escorting his mother-in-law. The rose leaves produced a wonderful impression. “This is lovely!” said an old aunt; “it’s like a procession!” “It’s an idea of mine!” cried Bélan; “I thought of it last night, while thinking of my wedding; and I am delighted that——” Bélan had reached this point in his speech, when a tall cousin, who was escorting the bride, slipped down two steps and fell, dragging the fair Armide after him. Shrieks arose on all sides. Thank heaven, Armide had fallen decently, and had made no exposé for the benefit of the company, which would have been most unpleasant for the husband, who hoped to be the first to behold her charms; and which would probably have made the mother-in-law sob anew. The bride was quickly assisted to her feet, and the tall cousin rose unassisted, uttering a most vulgar oath and exclaiming: “The devil take the rose leaves! A man must be an infernal fool to scatter them on a staircase! I have hurt my scrotum.” Bélan was speechless with confusion at the accident due to his idea. “Monsieur de Bélan, you must have all this swept away,” said the mother-in-law; and the bridegroom replied with a low bow: “Yes, Madame de Beausire, I will look after it.” Our betrothed were united in a small church in the Marais. Nothing extraordinary took place during the ceremony, except that the mother-in-law
- 82. used two handkerchiefs, and that Bélan made horrible faces in his attempts to weep with her, but without success. I had hoped that the breakfast would be at a restaurant; but we were bidden to return to the mother-in-law’s. That certainly required courage. Eugénie and I looked at each other, vowing, albeit a little late, that we would never be caught in such a scrape again. The bridegroom went ahead, doubtless to have his rose leaves swept away. I was sure that he would do the sweeping himself rather than expose himself to his mother-in-law’s wrath. A long table was laid in the dining-room. We took our seats; I was between the old aunt with a nose like a snail’s shell and the tall cousin who had fallen so hard on the stairway; my wife was a mile away from me, between two old uncles with lace cuffs and curly wigs. How we were likely to enjoy ourselves! I expected to see Giraud and his wife at the breakfast, for Giraud had been declaring everywhere that it was he who had arranged Bélan’s marriage. But evidently the mother-in-law had not deemed them worthy of that honor, and we should not see them until evening. The bride kept her eyes on the floor and did not eat. The mother-in-law looked at her daughter, wiped her eyes, and seemed not to realize that there was anybody there. We sat at the table two minutes without touching anything, no one having been requested to serve. Bélan, uncertain whether he was expected to do the honors, glanced at his wife and his mother-in-law in turn, and faltered: “Who is to serve? Does Madame de Beausire desire me to serve?” But Madame de Beausire replied only by blowing her nose and sighing. I looked at my wife; I had such a mad desire to laugh that I dropped my knife and fork on the floor, so that I might indulge it a little while fumbling under the table. I chose to be considered awkward rather than discourteous. At last an old uncle, who had not come to the wedding simply to look at the dishes, although that would have been more dignified than to eat them, drew an enormous pie toward him and gave the signal for the attack. We decided to breakfast, notwithstanding Madame de Beausire’s sighs; but we did it with a decorum and gravity which were interrupted only by the noise of the plates and the forks.
- 83. When the first edge of the appetite was dulled, some of the uncles and cousins were pleased to indulge in various significant phrases, dwelling upon every word they uttered, as if they considered that necessary in order that we should understand them. Bélan put in a word here and there, but it was not noticed. I discovered that he was trying to lead the conversation around to the subject of poetry. I felt certain that he had written some, or had had some written, and that he did not know how to set to work to recite it. Whenever he reached the subject, an uncle or an aunt would cut him short by speaking of something else. I felt sorry for him and said: “My dear Bélan, has anyone written any poetry for your wedding?” “Yes, just so; I myself have dashed off something in honor of this day, and with your permission, I will——” “What! do you mean to say that you are going to sing, Monsieur de Bélan?” cried Madame de Beausire, with an almost threatening glance at her son-in-law. “For shame, monsieur! what sort of people have you lived with, where it was customary to sing at the table?” “I never had any idea of singing, mother-in-law; nor have I any desire to. I meant simply to recite some verses,—verses which do not in the least degree resemble a song.” “Verses at a wedding! You should leave that to the Almanach des Muses,” said the tall cousin, who sat beside me, and who still bore the groom a grudge on account of his fall on the stairs. At the same instant Madame de Beausire shrieked aloud: “You are pale, Armide! Don’t you feel well, my child?” I had not noticed that the bride had changed color; but as her mother told her that she had, Armide probably thought it best not to feel well. She passed her hand over her eyes and said in a faltering tone: “No, I feel——” Her mother did not allow her to finish. She sprang to her feet, crying: “Mon Dieu! mon Dieu! Armide is dying! We must carry her to her bed.” Instantly there was a general uprising. The aunt who was at my side thrust her elbow in my face in her attempt to rise quickly in order to go to the assistance of her niece, who thereupon concluded that she had best be ill altogether. While they were taking Armide to her room, and Bélan was
- 84. running hither and thither like a madman, I went to my wife, took her hand and led her to the door, saying: “This is quite enough for one morning.” Bélan overtook us on the stairs, and called out to us: “What! going already? Why, my wife will come to herself in a minute; I am not worried about her health; my mother-in-law is forever telling her that she is going to die, when she has no idea of doing anything of the kind.” “We have an engagement.” “Until this evening, then.” “The ball is not to be at your mother-in-law’s, is it?” “No, at Lointier’s. It will be magnificent.” “We will be there.” How glad we were to be alone again! We had plenty to laugh about, as we passed in review the original creatures whom we had met; and although my wife is not malicious, she was fully alive to the absurdities of the company. We had promised to attend the ball, so we had no choice but to go; moreover, it was impossible that it should be so dreary a function as the breakfast; and then it was to take place in the same salons in which we had given ours, and we were not sorry to see them once more. We went late, because we hoped to find the dancing well under way; but we were surprised to find the salons almost empty, and only two quadrilles in progress, so that everybody had plenty of room to dance. And yet it was after eleven o’clock. Bélan came to meet us. His face was a yard long, and he said to me: “It is most annoying: my mother-in-law would not allow me to invite more than thirty people; for she said that, with her family and acquaintances, that would be quite enough; and you see how much empty space there is. I am aware that the party is very select, but a few more people would do no harm.” “One result, my dear Bélan, is that it is much more comfortable to dance.” “Yes, that is so; the dancers will gain by it.”
- 85. “And madame is no longer ill?” “No, that didn’t last. But now it is my mother-in-law’s turn to have fits of suffocation. Just look at her eyes; she’s a regular rabbit; she makes me sick. She is crying now because my wife dances every contradance; she declares that her daughter will be killed. Great heaven, what an emotional creature she is!” “But I don’t see the Giraud family here, and that surprises me, for of course you invited them?” “Mon Dieu! my dear Blémont, don’t speak of it. I was distressed to death, but my mother-in-law declared that the Girauds had manners which would be entirely out of place with her family, and she would not allow me to invite them.” “But Madame de Beausire used to go to their house, if I remember aright?” “Yes, but since the little Giraud girl stuck her tongue out at her, she has sworn that she will never put her foot inside their door.” “I thought that Giraud was instrumental in arranging your marriage?” “True, he did start the business.” “And you haven’t invited him? He will never forgive you as long as he lives.” “What could I do? My mother-in-law—But excuse me, I believe that she is motioning to me.” We left Bélan, and I danced with my Eugénie. We were happy to dance together, to be again in those rooms which had been the scene of our own wedding. Our eyes expressed love and contentment. Surely we looked more as if we were at a wedding than anybody else there. To dance is the best thing that one can do at a ball where one knows nobody. All those Beausires, who stalked solemnly about the quadrilles, and the old aunts who sat against the wall, seemed almost displeased to see other people apparently enjoying themselves. I felt sure that they considered us very ill-bred. Eugénie proposed to me that we should go before the supper; but I preferred to remain, because I expected that there would be some amusing scenes at the close of the festivity. The supper was not served as mine was; the ladies alone were seated, and the men had to stand behind them.
- 86. Madame de Beausire insisted upon having it so, because it was much less jolly than sitting at small tables. The feast lasted a very short time. Madame de Beausire gave the signal by rising, and the other ladies had no choice but to follow her example. I heard one old aunt mutter as she rose: “This is ridiculous; I didn’t have time to finish my chicken wing.” As the fatal moment drew near, Madame de Beausire’s eyes became more and more full of tears. At last, when the dancing drew to a close, Bélan approached his Armide and suggested that they should go; whereupon Madame de Beausire rushed between them, sobbing, and threw her arms about her daughter. “You shall not separate us, monsieur!” she cried. Bélan stood as if turned to stone before his mother-in-law. The kinsfolk surrounded them, and I heard the uncles and cousins say to one another: “That little fellow is behaving in the most indecent way. It makes me ill to have him come into our family.” The aunts and the old maids had led Madame de Beausire away, and she left the restaurant with her daughter, while Bélan remained. He saw us and came to bid us good-night, faltering: “I have let my wife and her mother go before, because, you know, they have to put the bride to bed; and of course I cannot be there.” “My dear Bélan, I am afraid that Madame de Beausire will make another scene to-night.” “Oh, no! At all events, if she does, I will show my spirit.” We drove away, and as we returned home, Eugénie and I agreed that a man is always very foolish to enter a family which thinks that it does him much honor by allying itself with him. If chance has willed that he should be born in a lower class, he should, by his intellect or his character, show himself superior to those who try to humiliate him.
- 87. X A QUARREL.—THE FIRST VEXATION A few days after Bélan’s wedding, we received a visit from Monsieur and Madame Giraud. I divined what brought them, and in truth they were hardly seated before Giraud exclaimed: “You must have been greatly surprised not to see us at Bélan’s wedding?” “In fact,” added Madame Giraud, “it made an impression on everybody. It was so terribly vulgar! So extraordinary! Just think of it! It was at our house that they met, and it was Giraud who took the first steps, who sounded Madame de Beausire, and who enumerated to her the young man’s property and good qualities; and yet we were not invited to the breakfast, or even to the ball! It’s an outrage!” “More than that, it was indecent!” cried Giraud; “and if my wife hadn’t restrained me, I would have demanded satisfaction.” “No, no; people would have thought that we cared about a wedding party; but thank God! we have more of them than we want. By the way, they say that that one was very dismal and tiresome!” “Why, it was not very lively,” said Eugénie. “Ah! yours was the lovely one, my dear Madame Blémont, and managed with such taste and such profusion! I confess that I had thirteen ices; salvers kept passing me, and I forgot myself.” “Yes, that was a charming wedding,” said Giraud; “but they tell me that at Bélan’s there weren’t enough people to form two quadrilles of twelve, and that they were almost all outlandish creatures of the last century. And that old Beausire woman did nothing but cry. And then that night—do you know what happened?” “No, we don’t know.” “Well, I know all about it, because I have a maid who used to live in the house where the Beausires live, and who still has friends there. Well, that
- 88. night the mother-in-law refused to leave her daughter. When the husband arrived, Madame de Beausire sobbed so that she woke the neighbors. Bélan lost his temper, and they had a terrible scene; finally, in a rage, he went to bed in a little closet where they keep coal, and the next morning he came out looking like a coal heaver! Poor fellow! If he doesn’t look out, those two women will shut him up in a foot-warmer, and feed him through the holes when he’s a good boy.—Ha! ha! It is too funny!” said Madame Giraud. “However, I won’t give him a year to be—you know what—and he will well have deserved it.” Monsieur and Madame Giraud took leave of us, renewing the assurances of their friendship, and they probably went about to all their acquaintances to do the same thing. As her pregnancy advanced, my wife felt called upon to attend to a thousand little duties which made it necessary for her to neglect music and painting. Moreover, her health was often poor, and she needed a great deal of rest; the result was that I had much more time to work in my office. Besides, the title of father, which I hoped soon to have, made me reflect more reasonably than I had done for some months past. Although our fortune was large enough for Eugénie and myself, it would cease to be large enough if we should have several children, and on their account it would be well for me to think of increasing it. Bélan made his wedding call with his wife, who had lost none of her stiffness and primness since her marriage. I found that the new husband’s eyes were as red as his mother-in-law’s. Perhaps he too wept sometimes to gratify Madame de Beausire. He was so attentive, so devoted to his Armide, and he waited upon her with such humility, that he seemed like his wife’s servant. We returned their visit ceremoniously, and we did not go again; we remembered their breakfast. Since I had given my attention to business once more and had returned to the practice of my profession, my mother said that we had become reasonable and that I now had the aspect of a married man. I do not know what aspect I may have had, but I know that I considered that we were becoming altogether too sedate; we no longer played together or fooled the time away, as we did in the early days of our marriage.
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