Shape Characterization Using Dynamic & Static Light Scattering
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The document presents a comprehensive overview of light scattering techniques used for characterizing the shape and size of colloidal particles, particularly focusing on dynamic and static light scattering (DLS/SLS). It discusses the advantages of DLS, such as its speed and non-destructive nature, and elaborates on methods to obtain detailed shape information using depolarized configurations. Key findings include the ability to derive translational and rotational diffusion coefficients, which further allow for the characterization of anisotropic particles like the tobacco mosaic virus and magnetic nanoparticles.
Shape Characterization Using Dynamic & Static Light Scattering
- 1. Company presentation Shape Characterization Using Dynamic & Static Light Scattering Andrea Vaccaro PhD, CTO LS Instruments AG
- 2. In SLS/DLS, a laser beam is sent through a colloidal sample, the average scattered intensity and the auto/cross correlation of the resulting scattered light are computed. Why choose DLS as a characterization method? • Fast • Simple measurements with easy sample preparation • In-situ, non-destructive approach Measuring particle size reliably 2 Static and Dynamic Light Scattering (SLS/DLS) 𝜽
- 3. 3 SLS The measured intensity can be divided up into contributions from within particles (intraparticle) and between particles (interparticle): I(q) ≈ c ∙ Mw ∙ V² ∙ P(q) ∙ S(q) The Radius of Gyration can be determined from the so-called Guinier Plot: Slope = Ln (I) Guinier regime 𝐪𝟐
- 4. DLS 4 Intensity fluctuation s I t <I > 𝜽 𝐷 Diffusion Coefficient 𝑅h= 𝑘𝐵 𝑇 6 𝜋𝜂 𝐷 Stokes- Einstein Relation Particle Size Intensity correlation function g 2 (t)-1 τ Correlato r
- 5. Structural Information from DLS/SLS: Coil to Globule Transition 5 Sun S. et al., J. Chem. Phys. 73, 5971 (1980) 𝑅h 𝑅𝑔 Temperature
- 6. Shape from DLS/SLS 6 Can we get detailed shape and size information from SLS/DLS?
- 7. 7 Depolarized Static and Dynamic Light Scattering (D-SLS/D-DLS) » In D-SLS /D-DLS we add a polarizer at detection before the detector » Depending on the orientation of the polarizer, vertical or horizontal we can measure in two different configurations, VV and VH » In D-SLS /D-DLS gives access to advanced shape and size information
- 8. Decorrelation for Anisotropic Particles 8 Diffusion Translational Diffusion 𝑫𝑻 Rotational Diffusion 𝑫𝑹 For anisotropic particles, the diffusion mechanism is more complex as it involves translations and rotations
- 9. D-DLS in VV Configuration 9 Intensity fluctuation s 𝑰𝑽𝑽 t <I > Intensity correlation function (t)-1 τ Correlato r 𝑫𝑻 , 𝑫𝑹 R. Nixon-Luke, G. Bryant, Part. Part. Syst. Charact. 2019, 36, 1800388.
- 10. D-DLS in VV Configuration: The Tobacco Mosaic Virus 10 For small scattering angles, : 𝒈𝟐 𝑽𝑽 −1≅ 𝛽𝑆0 (𝜽 ) exp(− 𝑫𝑻 𝑞2 𝝉 ) log 𝒈𝟐 𝑽𝑽 −1 𝛽 ≅ 𝐴− 𝑫𝑻 𝑞 2 𝝉 log 𝒈 𝟐 𝑽𝑽 −1 𝛽 𝝉 For small scattering angles, the logarithmic plot of the correlation function is linear and yields the translational diffusion coefficient, − 𝑫𝑻 𝑞2 Wada A. et al., J. Chem. Phys. 55, 1798 (1971) Tobacco Virus
- 11. D-DLS in VV Configuration: The Tobacco Mosaic Virus 11 log 𝒈 𝟐 𝑽𝑽 −1 𝛽 𝝉 For large : 𝒈𝟐 𝑽𝑽 −1 𝛽 𝑆2 exp (−( 𝑫𝑻 𝑞 2 +6 𝑫 𝑹)𝝉 ) log 𝒈𝟐 𝑽𝑽 −1 𝛽 ≅ 𝐵 −(𝑫𝑻 𝑞 2 +6 𝑫 𝑹)𝝉 −(𝑫𝑻 𝑞 2 +6 𝑫𝑹) For large the logarithmic plot of the correlation function is linear and yields the rotational diffusion coefficient, Wada A. et al., J. Chem. Phys. 55, 1798 (1971)
- 12. Shape and Size from Diffusion Coefficients For an axisymmetric particle of major size, , minor size, , and anisotropy factor 𝑫𝑻 , 𝑫𝑹 Microhydrodynami cs 𝑳,𝒅,𝒑 For rodlike particles, such as Tobacco Mosaic Virus: 𝑫 𝑹= 1 3 𝑘𝑇 (ln 𝒑 𝑪 𝑹) 𝜋 𝜂0 𝑳 3 𝑫𝑻 = 1 3 𝑘𝑇 (ln 𝒑 𝑪𝑻 ) 𝜋 𝜂0 𝑳 𝑪𝑻 =0.312+ 0.565 𝒑 + 0.100 𝒑 𝟐 𝑪𝑹=−0.662+ 0.917 𝒑 − 0.050 𝒑 𝟐 Ortega A.; Garc a ı́ de la Torre J., J. Chem. Phys. 119, 9914–9919 (2003) Shape and Size 𝑳 𝒅
- 13. Takeaways » In VV Configuration at low angles DLS provides access to the translational diffusion of anisotropic particles » At large angles and large lag times, knowing the translational diffusion coefficient, we can obtain the rotational diffusion coefficient » From translational and rotational diffusion coefficients we can obtain size and shape parameters of anisotropic particles » The procedure is complicated by the fact that in general correlation functions display an angle-dependent double decay
- 14. D-DLS in VH Configuration 14 Intensity fluctuation s 𝑰𝑽 𝑯 t <I > Intensity correlation function (t)-1 τ Correlato r 𝑫𝑻 , 𝑫𝑹 𝑔2 𝑽 𝑯 =1+ 𝛽 exp (−2 (𝑫𝑻 𝑞 2 + 6 𝑫𝑹 )𝝉) Simpler single exponential decay R. Nixon-Luke, G. Bryant, Part. Part. Syst. Charact. 2019, 36, 1800388. Decay Rate
- 15. D-DLS in VH Configuration 15 𝜞 ≡ 𝑞2 𝑫𝑻 +6 𝑫 𝑹 » In VH configuration we obtain a simpler single exponential decay » Plotting the decay rate vs we obtain the translational diffusion coefficient from the slope and the rotational diffusion coefficient from the intercept of the linear plot » The procedure is simpler than in the VV configuration case Decay Rate: 𝟔 𝑫𝑹 𝑫𝑻 𝒒𝟐 𝜞
- 16. D-DLS in VH Configuration: Magnetic Nanoparticles with Tunable Shape Anisotropy 16 » Anisotropic Magnetic NPs characterized by TEM and D- DLS » The two techniques agree thus confirming the validity of D- DLS Martchenko I. et al., J. Chem. Phys. B 115(49), 14838-14845 (2011)
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