The mean dimensions of multichain polymer systems are predicted to follow a scaling relation with scaling variable X=ldv-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) l2v 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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physical and Theoretical Chemistry