Excluded-volume expansion of polymer chains: A Monte Carlo study of the scaling properties

Results are presented of Monte Carlo simulations of continuum-model polymer chains which results confirm the idea that for long chains the degree of expansion due to excluded volume depends on the interaction range $\sigma$, on $N$, the number of links, and on the link size $a$ through a single variable $z\propto {\left(\frac{\sigma }{a}\right)}^3\sqrt{N}$. The expansion factor $\psi \mathrm{}\left(z\right)\mathrm{}$ is very close in form to that found by Lax, Barrett, and Domb for lattice models of a polymer. For $z\ge 2$, $\psi \mathrm{}\left(z\right)\mathrm{}$ follows a power law predicted by Flory. For finite chains there are corrections to $\psi \mathrm{}\left(z\right)\mathrm{}$ which depend on $N$ and on the form of the interaction.