Relaxation Mode Analysis of a Single Polymer Chain in a Melt

Katsumi Hagita, Hiroshi Takano

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30 Citations (Scopus)


Relaxation modes and rates of a polymer chain in a melt are studied by Monte Carlo simulations of the bond fluctuation model, where only the excluded volume interaction is taken into account. Polymer chains, each of which consists of N segments, are located on an L × L × L simple cubic lattice under periodic boundary conditions, where each segment occupies 2 × 2 × 2 unit cells. The results for N = 32, 48, 64, 96, 128, 192, 256, 384 and 512 at the volume fraction φ ≃ 0.5 are reported, where L = 128 for N ≤ 256 and L = 192 for N ≥ 384. The relaxation modes and rates are estimated by solving generalized eigenvalue problems for the equilibrium time correlation matrices Ci,j(t) = 1/3 〈R̄i(t) · R̄j(0)〉 of the coarse-grained relative positions R̄i of segments of a polymer chain defined by R̄ i = 1/n ∑k=1n R(i-1)n+k, where Rk denotes the position of the kth segment relative to the center of mass of the polymer chain. The apparent exponent z which describes the N-dependence of the slowest relaxation rate λ1 as λ1 ∝ N-z increases beyond three as N increases. From the data for N = 256, 384 and 512, the apparent exponent is estimated to be z ≃ 3.5. The behavior of the pth slowest relaxation rate λp for a fixed value of N is consistent with the prediction of the reptation theory λp ∝ p2. The first and second slowest relaxation modes show the Rouse-like behavior.

Original languageEnglish
Pages (from-to)673-676
Number of pages4
JournalJournal of the Physical Society of Japan
Issue number3
Publication statusPublished - 2002 Mar 1


  • Bond fluctuation model
  • Lattice model
  • Melt
  • Monte Carlo simulations
  • Polymer chain
  • Relaxation modes
  • Relaxation rates
  • Reptation

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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