Dynamic Scaling in an Aggregating 2D Lennard-Jones System

The evolution of a 2D Lennard-Jones system, quenched from the fluid to below the triple point, is simulated by molecular dynamics. We show that the structure factor obeys the scaling relation $S\left({q/q}_m\right(t\left)\right)\sim q_m\left(t{)}^{{-d}_f}\tilde{S}\right(q/{\tilde{q}}_m)$. Here $q_m$ is the location of the low angle peak in $S\left(q\right)$, $d_f=1.85\mathrm{}\pm 0.05$ is a fractal dimension, and $\tilde{S}(q/{\tilde{q}}_m)$ is a time-independent characteristic function which peaks at ${\tilde{q}}_m$. The quenching process is thermodynamically similar to the formation of a gel from a sol. Hence the relation suggests that a characteristic fractal dimension of even a dense gel can be derived from measurements of the time evolution of $S\left(q\right)$.