Scaling in two-dimensional linear and ring polymers

Bead size effects on the excluded volume of two-dimensional linear and ring polymers are investigated with Brownian dynamics. It is found that the mean dimensions of the chains follow a scaling relation with scaling variable X=N(σ/l)d/φ, where N is the number of units on the chain, σ is the size of the unit, l is the link length, d is the dimension, and φ is the crossover exponent. The scaling law is 〈R2〉/〈R2〉0 or 〈S2〉/〈S2〉0∼X2ν−1 for X→∞. Here ν is the critical exponent for the mean dimensions of an isolated polymer chain and the subscript 0 denotes the nonexcluded volume case.