The theta condition for linear polymer chains in continuous space and three dimensions

Configurational properties of isolated flexible linear chains of lengths in the range 72⩽N⩽576 have been investigated close to the theta regime by continuous space simulations using a configurational bias Monte Carlo algorithm. The polymer model consisted of beads interacting through a nontruncated Lennard-Jones potential and connected by a Gaussian distribution of link vectors. We use two criteria in order to characterize departures from ideal behavior at finite N, first the ratio of the mean squared end-to-end distance and the mean squared radius of gyration, and second the end-to-end vector distribution. Both the criteria lead, within the statistical errors, to the same prediction for the theta temperature as N→∞; the ratio criterion gives kBTθrat/ε=4.167±0.035 and the distribution criterion gives kBTθdis/ε=4.184±0.035, in close agreement with previous estimates for the same model. Deviations from ideal behavior were found to be independent of whether the finite number of beads constitute a whole chain or merely an inner part of a much larger chain. The N-dependencies of several configurational properties including the moments of the end-to-end distribution and the asphericity have been examined at the N→∞ theta temperature. Nonideal effects are manifest in different ways dependent on the property being considered. For instance the radius of gyration shows a slight contraction effect which diminishes with increasing chain length and which shows remarkable quantitative agreement with the prediction of tricritical renormalization group theory, while the end-to-end distribution shows slight expansion effects. It is suggested that each property emphasizes nonideal effects in slightly different ways.