Crossover approach to scaling behavior in dilute polymer solutions: theory and simulation

L. Lue, S. B. Kiselev

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9 Citations (Scopus)


We develop a crossover theory for dilute polymer solutions, analogous to crossover theories for critical phenomena in simple fluids. In this theory, a critical degree of polymerization N∗ is found, which plays a similar role as the Ginzburg number in second-order phase transitions. To test the predictions of this theory, we perform Monte Carlo simulations of polymer chains composed of rigidly bonded hard spheres of various diameters and chain lengths. Various properties of these chains were analyzed, including the end-to-end distance distribution and mean-square radius of gyration. We find that the approach to the asymptotic scaling regime displays two types of crossover behavior, depending on the value of the model parameter ū, which is a measure of the strength of the monomer-monomer excluded volume interaction: (i) ū<1 and (ii) ū>1. In case (i), the system exhibits crossover from a Gaussian chain to the Kuhnian chain, as the degree of polymerization increases. In case (ii), the system exhibits crossover from the rigid rod to a Kuhnian chain. Our crossover theory is found to work well for polymers with ū>1 only near the asymptotic scaling regime. However, for ū<1, the theory works well in all regimes.
Original languageEnglish
Pages (from-to)2684-2691
Number of pages7
JournalJournal of Chemical Physics
Issue number5
Publication statusPublished - 1 Feb 1999


  • conformational space renormalization
  • self-avoiding walks
  • Monte-Carlo simulation
  • excluded-volume
  • dimensional regularization
  • 2-parameter theory
  • pivot algorithm
  • 3 dimensions
  • chain
  • lattice


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