Modeling Diffusion of Adsorbed Polymer with Explicit Solvent

Computer simulations of a polymer chain of length $N$ strongly adsorbed at the solid-liquid interface in the presence of explicit solvent are used to delineate the factors affecting the $N$ dependence of the polymer lateral diffusion coefficient, $D_{\parallel }$. We find that surface roughness has a large influence, and $D_{\parallel }$ scales as $D_{\parallel }\sim N^{-x}$, with $x\approx 3/4$ and $x\approx 1$ for ideal smooth and corrugated surfaces, respectively. The first result is consistent with the hydrodynamics of a “particle” of radius of gyration $R_G\sim N^{\nu }$ ($\nu =0.75$) translating parallel to a planar interface, while the second implies that the friction of the adsorbed chains dominates. These results are discussed in the context of recent measurements.

Figure 1

Dependence of $D_{\parallel }$ on lateral size of the simulation cell ($L$) and distance between walls ($M$) for smooth surfaces. (a) $D_{\parallel }$ is plotted linearly against $L$ for $M=13\sigma$ and $N=80$. (b)  $D_{\parallel }$ as a function of $N$ for $L=24\sigma$ and $M=13$, 16.5, 20, $26\sigma$.

Figure 2

Analysis of near-surface solvent diffusion for smooth surfaces. (a) $D_{\mathrm{solvent}\parallel }$ is plotted against $1/L^2$. (b) $Z(t)/Z(0)$ vs time for $M=13\sigma$ and for $L$ values as indicated (c) $Z(t)/Z(0)$ vs time for $L=13\sigma$ and for $M$ values as indicated.

Figure 3

$D_{\mathrm{mutual}\parallel }$ plotted vs $N$. (a) smooth surfaces. The data are consistent with the power-law slope $-0.75$. The symbols refer to different system sizes as noted in the figure: the first two numbers are $L$ and the last $M$. (b) Same as (a) except that the surfaces are corrugated (squares) or smooth with no-slip imposed by a Maxwell demon (circles). Lines through the points are drawn with power-law slope $-1.0$. (c) Same as (b) except that the relaxation time of the polymer chain is plotted.