Perturbation Theory of Large-Particle Diffusion in Liquids

A theoretical study is performed to investigate the effect of the solvation structure on a large-particle diffusion in liquids. The solvation structure stands for the density distribution of solvent particles around the solute. In this thesis, considering the solvation effect, a theory of the translational mobility of a large solute is formulated in oneand two-component solvent systems. The diffusion coefficient is obtained from the drag coefficient through the Einstein relation. Furthermore, using the theory, the diffusion coefficients are calculated numerically to clarify the solvation effect. First, a theory of the translational mobility in a one-component solvent is formulated by perturbation expansions with respect to the size ratio of the solute and solvent particles. The expansion allows one to derive hydrodynamic equations and boundary conditions on the solute surface up to the first order. Solving the hydrodynamic equations with the boundary conditions, one obtains an analytical expression of the drag coefficient including higher order terms of the size ratio. The drag coefficient can be calculated from the density distribution function. Then, the numerical results of this theory are compared with those calculated by the non-perturbative theory and computer simulation. The numerical results are in good agreement with those of other theories when the size ratio of the solute and solvent particles is larger than 7. Next, a theory of the drag coefficient in a two-component solvent mixture is formulated by extending the perturbation theory for a one-component solvent system. The drag coefficient is calculated by solving the hydrodynamic equations and boundary conditions on the solute surface. The boundary condition depends on the solvation structure of a binary mixture. Then, to investigate the solvation effects on the diffusion coefficient, the perturbation theory is applied to a binary hard-sphere solvent system. The calculated results show that the diffusion coefficient approaches the value of the Stokes-Einstein relation with the stick boundary condition as adding the larger solvent spheres. The transition to the stick boundary condition is observed when the density of the larger solvent around the solute increases. As the solvent density increases, the velocity of the solvent around the solute approaches zero.