Shape distribution and correlation between size and shape of star-branched tetrahedral lattice chains in athermal and theta systems

Abstract

By means of Monte Carlo simulation, linear (F=2) and star-branched tetrahedral lattice chains with F=3–12 arms of length n=480 connected to a hard core consisting of MIN(5,F+1) segments (the total number of segments thus ranging from 963 to 5765) were produced for athermal and theta conditions. Nonreversal random walks (random walks without backfolding bonds) were generated as a reference. Several quantities (asphericity factor δ*, prolateness factor S*, and shape factors sfi*) characteristic of the instantaneous shape of molecules—being based on the orthogonal components of the squared radius of gyration taken along the principal axes of inertia—were computed. The probability distributions of these quantities were calculated and their interdependence as well as their correlation with quantities characteristic of the size of configurations was analyzed. Shape and size of star-branched chains for athermal as well as for theta conditions are highly correlated as earlier found for linear chains and random walk stars. The broadness of distribution functions decreases with increasing number of arms, but remains appreciably for F=12, the system with the largest functionality evaluated.