Monte Carlo simulation of tetrahedral chains, 4. Size and shape of linear and star‐branched polymers

Abstract

AbstractLinear and star‐branched chains with F = 4 − 12 arms and N = 125 − 7685 segments covering points of a tetrahedral lattice were generated by use of a pivot algorithm. For large N, the acceptance fractions f̄ of attempted moves may be described by a power law f̄ = A · (N − 1)−α. Clearly, the factor A decreases with increasing functionality F, but the exponent α is independent of the number of arms and equal to the value obtained for linear chains, α ≈ 0,1. Due to the influence of the hard‐core (centre) of the star, the acceptance fraction f̄ for small N is lower than predicted by the scaling law, yielding a stronger dependence on F than for large chains. Meansquare dimensions, i. e. mean‐square radius of gyration, mean‐square end‐to‐end distance and mean‐square centre‐to‐end distance obey a power law dependence on chain‐length (N − 1), the exponent being ≈ 1,184 for 245 ≤ N ≤ 7685 in all cases; alternatively, the (quadratic) dimensions may be described by a corrected scaling law (N − 1)2v · (C0 + C1 · (N − 1)−Δ) with v = 0,588 and Δ ≈ 0,5 as proposed by renormalization group theory for linear chains. The shape asymmetry of star‐branched polymers (with the same total number of segments each) decreases with increasing number of arms, but is still appreciable for F = 12, the highest number of arms examined.