Scaling in multichain polymer systems in two and three dimensions

The mean dimensions of multichain polymer systems are predicted to follow a scaling relation with scaling variable X=l^dv-1 ρ, where l is the number of statistical segments on the chain, ρ is the segment density, d is the dimension, and v is the critical exponent for the mean dimensions of an isolated polymer chain. The scaling laws are 〈R²〉≈A(X) l^2v for l→∞ with X bounded, and 〈R ²〉≈B(ρ)l for l→_∞ with X→_∞. Moreover, the critical amplitudes behave as A(X)∼X^{-(2v-1)/(dv-1)} as X→_∞ and B(ρ)∼ρ^{-(2v-1)/(dv-1)} as ρ→0. Simulations of both continuum and lattice systems are reanalyzed and found to be consistent with these scaling relations. Previous naive use of short-chain data has led to misleading results.