Monte Carlo simulation studies of ring polymers at athermal and theta conditions

By use of an intramolecular criterion, i.e., the direct proportionality between mean square dimension and chain length, theta conditions for linear chains and ring shaped polymers are evaluated for several types of cubic lattice chains (simple cubic, body centered cubic, and face centered cubic). The properties of the rings are evaluated for the same thermodynamic conditions under which they are prepared thus allowing for a natural amount of knots which have been identified by use of Alexander polynomials. For the limit of infinite chain lengths the same theta parameter is found for linear chains and rings. On the contrary, a significant theta point depression occurs due to an additional excluded volume effect if unknots are exclusively regarded. Parameters characteristic of the shape of rings and chains under theta conditions extrapolated to infinite chain length fairly well coincide with respective data for random walks. Mean square dimensions (characteristic of the size) of theta systems are slightly in excess as compared to nonreversal random walks due to the necessity of avoiding overlaps on a local scale. Furthermore athermal systems are studied as well for comparison; mean square dimensions are described by use of scaling relations with proper short chain corrections, shape parameters are given in the limit of infinite chain length.