Relaxation Mode Analysis of a Single Polymer Chain in a Melt

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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 C_<i,j>(t)=1/3(R_i(t)・R_j(O)) of the coarse-grained relative positions R_i of segments of a polymer chain defined by R_i=1/n？^n_<k=1>R_<(i-1)n+k>, where R_k 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 λ_1 as λ_1 α 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 λ_p for a fixed value of N is consistent with the prediction of the reptation theory λ_p α p^2. The first and second slowest relaxation modes show the Rouse-like behavior.
社団法人日本物理学会の論文
2002-03-15