![Additions to the Existing SAXS
Method
[J.Prass,D. Muter, P. Fratzl and O. Paris, APL 95,083121 (2009)]
Estimation of strain in this study:
Estimations of strain in existing SAXS method:
[G.Y. Gor and A.V. Neimark Langmuir 26(16), 13021-13027 (2010)]
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APS_presentation_Mayur
- 1. X-ray Scattering Study of Capillary Condensation in Mesoporous Silica Mayur Sundararajan and Gang Chen Department of Physics and Astronomy Ohio University Athens OH
- 2. MCM-41 (Mobil Crystalline Material) Hexagonal pore arrangementMesopores 2 - 5nm MCM-41 Porewall Nanoporous materials – Surface effects such as adsorption, surface tension, adhesion, cohesion are dominant. – Capillary condensation phenomenon Nanoporous materials with pore size (2-50 nm) are classified as mesoporous material, Ex. Mesoporous Silica. Mesopores Porewall Amorphous Silica Ordered pores Disordered pores
- 3. Capillary Condensation and Capillary Action 0% 100%Relative Vapor Pressure Capillary condensation •Pc-capillary pressure •rm- mean radius of the meniscus •α-contact angle •ϒ-liquid surface tension 2ϒLV cosθ rm Pc = = hρg Laplace Pressure r = 1nm Pc =140 MPah = 14km Greater pressure than the bottom of Mariana Trench
- 4. Objectives • Develop a new wide angle x-ray scattering (WAXS) method to measure the Poisson’s ratio and Young’s Modulus of nanoporous materials by using the capillary condensation phenomenon. • Existing small angle x-ray scattering (SAXS) methods, Prass, et. al(2009) & Gor et. al(2010) , assumes the Poisson’s ratio of the bulk to calculate this Young’s modulus. 4
- 5. Experimental Method •X-ray scattering technique (SAXSess & Synchrotron source) SAXS (Existing method) WAXS (Newly developed method) •Gas sorption technique(Micromeritics TRISTAR II) Pore width Pore volume Pore size distribution Pore area The Relative Vapor Pressure(RH) of the sample chamber was varied from 100% to 0% (desorption) in steps of 5% at 1 atm, and the data was collected for each step. 5 SAXSess experiment Samples: MCM-41(AS) As synthesised MCM-41(AN) Annealed at 650C for 2 hours WAXS (10-50°) SAXS (0.1-10°) Relative humidity generator Imaging plate Humidity chamber Micromeritics TRISTAR II Ref: www.micromeritics.com
- 6. Stresses on the pore wall due to capillary action Stress Direction Stress Stress term Normal(X-Y Plane) σx,σy Tangential(Z direction) σz • Surface Tension • Laplace Pressure 6 Tangentialcomponentϒlv PL y z x Normal component ϒlv 2RTln P P0 ) ) V r + γLV RT ln P P0 ) ) V r - γLV
- 7. Effective strain in each direction Silica scaffold is isotropic Modulus E = Stress (σ) Strain (ε) By substituting the derived stresses σx σy σz we determined strain as, Transverse strain Longitudinal strain Poisson’s ratio ν = RT ln P P0 ) ) EV (2 - 3ν) E r εx = + γLV εy = εx RT ln P P0 ) ) EV (1 - 4ν) E r εz = - γLV (1 + 2ν)
- 8. X-ray Scattering Data SAXS WAXS Scattering angle 1° - 10° Probes structures at nm Scattering angle > 10° Probes structures at atomic scales FSDP – First Sharp Diffraction Peak d10 60° Inter-pore distance Pore wall Pore 0.165 0.170 0.175 0.180 0.185 0.190 0.195 0.0 0.5 1.0 1.5 Intensity(arb.units) q(Å-1 ) RH-95 RH-72 RH-50 Strain SAXS 8 Figure 9 WAXS 1.5 1.6 1.7 1.8 0.016 0.018 0.020 Intensity(arb.units) q(Å-1 ) RH-95 RH-72 RH-50 FSDP p(0) p(RH) - 1ε =
- 9. SAXS Data Analysis This strain is in x-y direction and corresponds to inter-pore distance. -2.50 -2.25 -2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25 0.00 -0.003 -0.002 -0.001 0.000 0.001 0.002 0.003 0.004 Strain_SAXS ln(RH) Equation y = a + b*x Weight No Weighting Residual Sum of Squares 9.32953E-8 Pearson's r 0.99864 Adj. R-Square 0.99695 Value Standard Error Strain_SAXS Intercept 0.00415 8.23879E-5 Slope 0.00921 1.69818E-4 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 intensity(arb.units) RH Tension Compression Bragg’s Peak position vs ln(RH) 9 Intensity vs RH RT ln P P0 ) ) EV (2 - 3ν) γLV E r εx = + (2 - 3ν) E RT Vln P P0 ) ) εx (Slope)SAXS ==
- 10. WAXS Data Analysis -2.50 -2.25 -2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25 0.00 -0.004 -0.003 -0.002 -0.001 0.000 Strain_WAXS ln(RH) Equation y = a + b*x Weight No Weighting Residual Sum of Squares 5.31695E-7 Pearson's r 0.97963 Adj. R-Square 0.95464 Value Standard Error Strain_WAXS Intercept 1.35433E-4 1.96682E-4 Slope 0.00559 4.05401E-4 Compression Only ! WAXS strain corresponds to average strain in all the directions. 10 FSDP peak position vs ln(RH) Strain and intensity plot 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Intensity_SAXS Strain_WAXS RH Intensity(arb.units) -0.004 -0.003 -0.002 -0.001 0.000 Strain_WAXS RT ln P P0 ) ) 3EV (5 - 10ν) 3E r εavg = + γLV (1 - 2ν) (5 - 10ν) 3E RT Vln P) ) εavg (Slope)WAXS == P0
- 11. 11 Poisson’s ratio and Young’s Modulus of the material can be found by comparing the slopes obtained in SAXS and WAXS method: Determination of Poisson’s Ratio and Elastic Modulus Sample Poisson’s Ratio ESAXS/WAXS (GPa) MCM41-AS 0.3±0.02 16.2±1.1 MCM41-AN 0.27±0.02 25.6±1.9 ν for Steel ~ 0.3 ν for Silica - 0.17 (2 - 3ν) E RT Vln P P0 ) ) εx (Slope)SAXS == (5 - 10ν) 3E RT Vln P) ) εavg (Slope)WAXS == P0
- 12. Conclusion • New WAXS technique was successfully developed and it offers wider range of application. • Poisson’s ratio and Elastic modulus were calculated by employing the two methods. • Annealing increases the strength of MCM-41 significantly. • Poisson’s ratio in nanomaterial is different from the bulk. 12
- 13. Thank You 13
- 14. Additions to the Existing SAXS Method [J.Prass,D. Muter, P. Fratzl and O. Paris, APL 95,083121 (2009)] Estimation of strain in this study: Estimations of strain in existing SAXS method: [G.Y. Gor and A.V. Neimark Langmuir 26(16), 13021-13027 (2010)] 14
- 15. Samples Surface Area (m2/g) Pore width (nm) Pore wall thickness(nm) Poisson’s Ratio ESAXS/WAXS (GPa) MCM-41(AS) 1082.2 2.4 1.5 0.3±0.02 16.2±1.1 MCM-41(AN) 1132 2.6 1.6 0.27±0.02 25.6±1.9 Summary of the Results Gas-sorption method SAXS/WAXS method
- 16. Porous Material Characterization: Techniques Gas sorption SANS Small Angle X-ray Scattering SEM TEMMercury Porosimtery Technique •Surface area •Pore width •Pore area •Pore size distribution Strain due to the capillary action Wide Angle X-ray Scattering 16 Figure 10
- 17. Capillary Condensation, Capillary action and Kelvin Equation p Po ln RT 2VMϒLVcosα rm = Kelvin Equation P/P0 -Relative Vapor pressure of the gas P/P0 is Relative Humidity(RH) for water rm- mean radius of the meniscus α-contact angle ϒ LV -liquid surface tension Figure5 Beginningof Capillary Evaporation Beginningof Capillary condensation Isotherm Volumeadsorbed(cm2/g) Relative Humidity 0% 100% Relative Humidity Capillary condensation Figure4 Figure 3:Capillaryaction Ref: www.diracdelta.co.uk •Pc-capillary pressure •rm- mean radius of the meniscus •α-contact angle •ϒ-liquid surface tension 2ϒLV cosα rm Pc = = hρg Laplace Pressure
- 18. Effective strain in each direction Silica scaffold is isotropic, so Modulus E = Stress (σ) Strain (ε) By substituting the stresses σx σy σz we determined, ν - Poisson’s ratio E - Elastic modulus
- 19. Stresses on the pore wall due to capillary action Stress Direction Stress Stress term Normal(X-Y Plane) σx,σy Tangential(Z direction) σz (1+cosθ)ϒlv/ r1 PL y z x Stress (σ) depends on surface tension and laplace pressure Laplace pressure PL using Kelvin equation 19 Figure 8: Stresses on the pore (1+cosθ)ϒlv/ r1
- 20. Samples Surface Area (m2/g) Pore width (nm) Pore wall thickness(nm) Poisson’s Ratio ESAXS/WAXS (GPa) MCM-41(AS) 1082.2 2.4 1.5 0.3±0.02 16.2±1.1 MCM-41(AN) 1132 2.6 1.6 0.27±0.02 25.6±1.9 Summary of the Results Gas-sorption method SAXS/WAXS method ν for Steel ~ 0.3 ν for Silica - 0.17