Microscopic Mechanism for Self-Diffusion and Relative Diffusion in Simple Liquids

Graphical displays of computer‐generated data simulating the microscopic dynamics of a two‐dimensional dense fluid of Lennard‐Jones disks indicate that the microscopic mechanism for diffusion in simple liquids may be largely cooperative in nature. The cooperative effects are important for processes involving the relative motion of two particles, such as the relative diffusion of solute molecules separated by short distances in a liquid, or electromagnetic absorption or scattering in which the dipole moment or polarizability tensor varies with the interparticle separation. The statistical time‐correlation functions describing self‐diffusion in the model fluid are found to behave in a manner consistent with existing theoretical treatments of diffusion in simple liquids. The anomalous long‐time behavior of the velocity autocorrelation function seen by Alder and Wainwright is discussed. It leads to a divergent diffusion coefficient in two‐dimensional fluids. It appears not to have a strong effect on our results in the important kinetic regime ${\text{(t\hspace{0.17em}≤\hspace{0.17em}10}}^{\text{−11}}\sec )$ . Relative diffusion of particles separated by distances of 1 to 3 diam is found to proceed more slowly than predicted by theories that neglect correlations in the motions of neighboring particles. The time‐displaced distribution function $G_{\text{2,s}}[{\mathbf{r}}_{12}\mathrm{(\tau ),}{\mathbf{r}}_{12}\text{(0)]}$ describing this relative motion is more complex than the ordinary Van Hove function $G_d{\mathrm{[r}}_2{\mathrm{(\tau )\hspace{0.17em}-\hspace{0.17em}r}}_1\text{(0)]}$ . The Smoluchowski equation describing $G_{\text{2,s}}$ is shown to be a consistent description only if the relative diffusion coefficient at close separations is depressed about 40% below the singlet value.