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=ldν−1 ρ, where l is the number of statistical segments on the chain, ρ is the segment density, d is the dimension, and ν is the critical exponent for the mean dimensions of an isolated polymer chain. The scaling laws are 〈R2〉≊A(X) l2ν for l→ ∞ with X bounded, and 〈R2〉≊B(ρ) l for l→ ∞ with X → ∞. Moreover, the critical amplitudes behave as A(X)∼X−(2ν−1)/(dν−1) as X → ∞ and B(ρ)∼ρ−(2ν−1)/(dν−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.