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(q/qₘ(t))~qₘ(t)^-df ̃ \~S(q/ ̃ \~qₘ). Here qₘ is the location of the low angle peak in $S(q)$, df0ex0ex=0ex0ex1.85±0.05 is a fractal dimension, and ̃ \~S(q/ ̃ \~qₘ) is a time-independent characteristic function which peaks at ̃ \~qₘ. 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 $S(q)$.