Scaling in three-dimensional linear and ring polymers

Bead size effects on the excluded volume of linear and ring polymers are investigated by 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→∞ where ν is the critical exponent for the mean dimensions of an isolated polymer chain.