Brownian Motion of Lattice-Model Polymer Chains

Abstract

The dynamical behavior of lattice‐model polymer chains is studied by assuming the Markoff nature of the motion of chain elements. In accord with the Monte Carlo calculations of Verdier, the autocorrelation function obtained for the square of the end‐to‐end distance of a simple‐cubic‐lattice‐model chain is in close agreement with that for a spring‐bead‐model chain. The diffusion equation for the lattice‐model chain is also exactly similar to that for the spring‐bead‐model chain. The diffusion constant for a lattice element is found to be ${\mathrm{pl}}^2\text{\hspace{0.17em}/\hspace{0.17em}3}$ and the equivalent spring constant to be ${\text{3kT\hspace{0.17em}/\hspace{0.17em}l}}^2$ . Here, $l$ is the lattice constant, $p$ is the probability that a given chain element moves to its adjacent lattice points in unit time, and $\mathrm{kT}$ has the usual meaning.