Dynamics of the solvent around a solute: Generalized Langevin theory

The generalized Langevin theory for a solution has been derived as the infinite dilution limit of the theory for a two component mixture. Following a similar formalism, the mode coupling approximations of the memory kernel have been also obtained. We have applied this method for one component bulk liquid of Lennard-Jones spheres and proved this approximation theoretically. The analysis of the space and time pair correlation proposed by Van Hove has been carried out as a function of solute particle sizes. It is found that the size of the solute particle is deeply related to the relaxation process of the solvation structure characterized around a solute particle at equilibrium. We have also investigated the relation between the different thermodynamic environments and relaxation process. From these studies, we have obtained the useful information about the rapidity of the relaxation of the solvation structure around a solute at equilibrium.

Figure 1

Comparison of $F\left(q,t\right)$ for each components vs $\text{log}\left(t\right)$ at $q^{\ast }=6.81$, which is a first peak of the static structure factor. Solid, dashed, and dashed-dotted lines denote $F_{\text{uv}}\left(q,t\right)$, $F_{\text{uu}}\left(q,t\right)$, and $F_{\text{vv}}\left(q,t\right)$, respectively. Circle line provides the function which subtracts $F_{\text{uu}}\left(q,t\right)$ from $F_{\text{vv}}\left(q,t\right)$.

Figure 2

$F_{\text{uv}}\left(q,t\right)$ of Ar at $t^{\ast }=1.4$. Solid, dashed, and dashed-dotted lines denote the plots of the GLE/MCT, Vineyard approximation, and molecular dynamics, respectively.

Figure 3

$F_{\text{uv}}\left(q,t\right)$ at the first peak of each $S_{\text{uv}}\left(q\right)$ vs time. All curves are normalized by $S_{\text{uv}}\left(q\right)$. Solid, dashed, and dashed-dotted lines denote the cases of solutes A, B, and C, respectively.

Figure 4

$F_{\text{uu}}\left(q,t\right)$ at the first peak of each $S_{\text{uv}}\left(q\right)$ vs time. Solid, dashed, and dashed-dotted lines denote the cases of solutes A, B, and C, respectively.

Figure 5

Radial distribution function (RDF) $g\left(r\right)$ for solute and solvent. Solid line, RDF for solute A and argon; dashed line, RDF for solute B and argon; dashed-dotted line, RDF for solute C and argon.

Figure 6

Solid, dashed, and dashed-dotted lines provide the functions for solutes A, B, and C, respectively. (a) Van Hove function for single solute, $G_{\text{uu}}\left(r,t\right)$, at $t^{\ast }=1.4$. (b) Solute-solvent Van Hove function, $G_{\text{uv}}\left(r,t\right)$, at $t^{\ast }=1.4$. (c) $G_{\text{uu}}\left(r,t\right)$ at $t^{\ast }=2.8$. (d) $G_{\text{uv}}\left(r,t\right)$ at $t^{\ast }=2.8$. (e) $G_{\text{uu}}\left(r,t\right)$ at $t^{\ast }=5.6$. (f) $G_{\text{uv}}\left(r,t\right)$ at $t^{\ast }=5.6$.