Scaling in multichain polymer systems in two and three dimensions

Marvin Bishop, M. H. Kalos, Alan D. Sokal, H. L. Frisch

    Research output: Contribution to journalArticlepeer-review


    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.

    Original languageEnglish (US)
    Pages (from-to)3496-3499
    Number of pages4
    JournalThe Journal of Chemical Physics
    Issue number7
    StatePublished - 1983

    ASJC Scopus subject areas

    • General Physics and Astronomy
    • Physical and Theoretical Chemistry


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