Institute of Theoretical Physics, University of Warsaw, Hoza 69, 00-681 Warsaw, Poland.
J Chem Phys. 2010 Feb 21;132(7):074704. doi: 10.1063/1.3305328.
As a first step toward the interpretation of dynamic light scattering with evanescent illumination from suspensions of interacting spheres, in order to probe their near wall dynamics, we develop a theory for the initial slope of the intensity autocorrelation function. An expression for the first cumulant is derived that is valid for arbitrary concentrations, which generalizes a well-known expression for the short-time, wave-vector dependent collective diffusion coefficient in bulk to the case where a wall is present. Explicit expressions and numerical results for the various contributions to the initial slope are obtained within a leading order virial expansion. The dependence of the initial slope on the components of the wave vector parallel and perpendicular to the wall, as well as the dependence on the evanescent-light penetration depth are discussed. For the hydrodynamic interactions between colloids and between the wall, which are essential for a correct description of the near-interface dynamics, we include both far-field and lubrication contributions. Lubrication contributions are essential to capture the dynamics as probed in experiments with small penetration depths. Simulations have been performed to verify the theory and to estimate the extent of the concentration range where the virial expansion is valid. The computer algorithm developed for this purpose will also be of future importance for the interpretation of experiments and to develop an understanding of near-interface dynamics, at high colloid concentrations.
作为对用消逝场照明悬浮液中相互作用球体的动态光散射进行解释的第一步，以便探测其近壁动力学，我们为强度自相关函数的初始斜率开发了一种理论。推导出了第一个累积量的表达式，该表达式对于任意浓度都是有效的，它将在体相中原有的、依赖于短时间和波矢的集体扩散系数的著名表达式推广到存在壁的情况。在主要的 virial 展开下，获得了初始斜率的各个贡献的显式表达式和数值结果。讨论了初始斜率对平行于壁和面外的波矢分量的依赖性，以及对消逝光穿透深度的依赖性。对于胶体之间以及胶体与壁之间的流体动力学相互作用，这对于正确描述近界面动力学至关重要，我们同时包括了远场和润滑贡献。润滑贡献对于捕捉用小穿透深度进行实验探测的动力学是必不可少的。已经进行了模拟以验证理论，并估计了 virial 展开有效的浓度范围。为此目的开发的计算机算法对于解释实验和理解高胶体浓度下的近界面动力学也将具有重要意义。
