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

Abstract

Chains embedded in the tetrahedral lattice have been produced by means of Monte Carlo simulation for athermal and for theta conditions. Nonreversal random walks (random walks without backfolding bonds) have been generated as a reference. Probability distributions of an asphericity factor δ*, of a prolatness factor S*, and of shape factors sfi* have been evaluated, the quantities being based on the orthogonal components of the squared radius of gyration taken along the principal axes of inertia. In addition, the correlation between δ* and other shape descriptors as well as between δ* and quantities characteristic of the size of configurations have been evaluated. In accordance with existing literature, the distributions H(δ*) and H(S*) are found to be very broad. The distributions H(sf1*) of the small and H(sf3*) of the large shape factor (sf1*⩽sf2*⩽sf3*, sf1*+sf2*+sf3*=1) are clearly distinct from each other, while the distribution of sf2* overlaps with that of sf1* and (slightly) with H(sf3*). Distributions of theta chains (“unperturbed” polymer) coincide fairly well with respective distributions of nonreversal random walks (which in turn are nearly identical to those of (off-lattice) random walks. As a matter of course, other shape descriptors are directly correlated with the asphericity factor δ*. Actually, for all systems evaluated, the global size of configurations is strongly correlated with δ* as well: The larger the asymmetry the larger are the dimensions of the configuration under consideration.