Evanescent wave dynamic light scattering by optically anisotropic Brownian particles

Hydrodynamic interactions are an important feature of any soft matter or colloidal system. The long-ranged disturbances of flow field caused by the presence of suspended particles are known to strongly affect the macroscopic transport coefficients of a suspension. In a system bounded by a planar no-slip wall, friction experienced by the colloids is additionally enhanced, leading to a general slow-down of near-wall dynamics. The presence of a flat interface introduces additional anisotropy into the system, distinguishing the directions parallel and normal to the wall. Thus, the colloidal diffusive motion becomes anisotropic, with the diffusivity dependent on the wall-particle distance. Since many technological, chemical, and biological processes occur in a confined system, it is of vital importance to assess the effect of hydrodynamic interactions on the colloidal motion. Along with the theoretical description, relevant experimental techniques have to be developed to study near-wall dynamics of sub-micron particles. An example of an experimental technique giving insight into near-wall diffusion in colloidal suspensions is evanescent wave dynamic light scattering (EWDLS). In such experiments, light is scattered by colloidal particles diffusing in the presence of a wall and the scattered light intensity time auto-correlation function is measured in order to trace near-wall dynamics of a suspension. The evanescent wave which enters the sample decays as exp(-\kappa z/2) with the distance z from the wall, and restricts the scattering volume to a region characterized by the penetration depth \kappa^{-1}. By changing the scattering vector q, the system is probed on different length scales. Compared to standard Dynamic Light Scattering, EWDLS has some inherent features, combining the effects of non-uniform illumination of the sample, and the hindrance of particles’ diffusivity near a hard boundary. The optical anisotropy of the particles couples to the hydrodynamic anisotropy due to the presence of the wall and the non-spherical shape of the colloids. Since both effects have a pronounced impact on the relaxation of the scattered electric field correlation function, the interpretation of experimental data is much more involved in this case. The Thesis is devoted to the development of a proper theoretical framework for the analysis of EWDLS correlation functions, focusing particularly on their initial decay rate, called the first cumulant. We focus on a dilute suspension, in which the system is fully characterised by single-particle properties, and study the first cumulant for optically anisotropic, axially symmetric particles. Using the Smoluchowski equation formalism, we derive exact theoretical expressions for the first cumulant of the experimentally measured correlation functions and relate it to the diffusive properties of the system. Performing EWDLS experiments for the special case of anisotropic spherical colloids, and employing measurements with differently polarized light (in the VV and VH geometry), we are able to trace both the translational and rotational diffusion of spherical colloids near a wall. Moreover, the EWDLS set-up allows independent variation of the components of the scattering vector parallel and perpendicular to the wall, hence allowing to extract the diffusion coefficients of particles in these directions and to investigate the anisotropy of their motion in more detail. Our theoretical predictions for spherical particles are favourably compared to experimental findings, and to Brownian Dynamics simulations. As a next step, we analyse theoretically and numerically the resulting expressions for non-spherical axisymmetric colloids, such as rods or discs. Using the multipole expansion method to investigate hydrodynamic interactions of such particles with a wall, we develop analytical formulae for the correction to the single-particle bulk mobility tensor due to the presence of a nearby wall, and study its dependence on the distance and orientation of the particle with respect to the boundary. With both scattering and hydrodynamic effects taken into account, we develop precise software which allows for the calculation of the first cumulant in arbitrary experimental conditions. We further explore the dependence of the first cumulant on the scattering vector and the penetration depth in a chosen experimental alignment. Our findings lead to practical approximations for the interpretation of EWDLS by axisymmetric particles, thus opening the way to study more complex systems using this technique.