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 journalArticle

    Abstract

    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
    Volume79
    Issue number7
    StatePublished - 1983

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    Polymers
    scaling
    Scaling laws
    polymers
    scaling laws
    exponents
    continuums
    simulation

    ASJC Scopus subject areas

    • Atomic and Molecular Physics, and Optics

    Cite this

    Bishop, M., Kalos, M. H., Sokal, A. D., & Frisch, H. L. (1983). Scaling in multichain polymer systems in two and three dimensions. The Journal of chemical physics, 79(7), 3496-3499.

    Scaling in multichain polymer systems in two and three dimensions. / Bishop, Marvin; Kalos, M. H.; Sokal, Alan D.; Frisch, H. L.

    In: The Journal of chemical physics, Vol. 79, No. 7, 1983, p. 3496-3499.

    Research output: Contribution to journalArticle

    Bishop, M, Kalos, MH, Sokal, AD & Frisch, HL 1983, 'Scaling in multichain polymer systems in two and three dimensions', The Journal of chemical physics, vol. 79, no. 7, pp. 3496-3499.
    Bishop M, Kalos MH, Sokal AD, Frisch HL. Scaling in multichain polymer systems in two and three dimensions. The Journal of chemical physics. 1983;79(7):3496-3499.
    Bishop, Marvin ; Kalos, M. H. ; Sokal, Alan D. ; Frisch, H. L. / Scaling in multichain polymer systems in two and three dimensions. In: The Journal of chemical physics. 1983 ; Vol. 79, No. 7. pp. 3496-3499.
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    abstract = "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.",
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