By Monte Carlo simulations of a variant of the bond-fluctuation model without topological constraints, we examine the center-of-mass (COM) dynamics of polymer melts in d = 3 dimensions. Our analysis focuses on the COM displacement correlation function

$C_\mathrm{N}(t) \approx \partial _t^2 h_\mathrm{N}(t)/2$
CN(t)≈∂t2hN(t)/2⁠, measuring the curvature of the COM mean-square displacement hN(t). We demonstrate that CN(t) ≈ −(RN/TN)2(ρ*/ρ) f(x = t/TN) with N being the chain length (16 ⩽ N ⩽ 8192), RN ∼ N1/2 is the typical chain size, TN ∼ N2 is the longest chain relaxation time, ρ is the monomer density,
$\rho ^*\approx N/R_\mathrm{N}^d$
ρ*≈N/RNd is the self-density, and f(x) is a universal function decaying asymptotically as f(x) ∼ x−ω with ω = (d + 2) × α, where α = 1/4 for x ≪ 1 and α = 1/2 for x ≫ 1. We argue that the algebraic decay NCN(t) ∼ −t−5/4 for t ≪ TN results from an interplay of chain connectivity and melt incompressibility giving rise to the correlated motion of chains and subchains.

Topics
Molecular dynamics, Lattice models, Physical quantities, Newtonian mechanics, Materials, Finite difference methods, Monte Carlo methods, Cage effect, Polymers
© 2011 American Institute of Physics.
2011
American Institute of Physics
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