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Register a new userNote: Scale-free center-of-mass displacement correlations in polymer films without topological constraints and momentum conservation
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Added by
Patrycja Poli\\'nska
Publication date
2011
fields
Physics
and research's language is
English
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We present here computational work on the center-of-mass displacements in thin polymer films of finite width without topological constraints and without momentum conservation obtained using a well-known lattice Monte Carlo algorithm with chain lengths ranging up to N=8192. Computing directly the center-of-mass displacement correlation function C_N(t) allows to make manifest the existence of scale-free colored forces acting on a reference chain. As suggested by the scaling arguments put forward in a recent work on three-dimensional melts, we obtain a negative algebraic decay C_N(t) sim -1/(Nt) for times t << T_N with T_N being the chain relaxation time. This implies a logarithmic correction to the related center-of-mass mean square-displacement h_N(t) as has been checked directly.
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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 $CN(t) approx partial_t^2 MSDcmN(t)/2$, measuring the curvature of the COM mean-square displacement $MSDcmN(t)$. We demonstrate that $CN(t) approx -(RN/TN)^2 (rhostar/rho) f(x=t/TN)$ with $N$ being the chain length ($16 le N le 8192$), $RNsim N^{1/2}$ the typical chain size, $TNsim N^2$ the longest chain relaxation time, $rho$ the monomer density, $rhostar approx N/RN^d$ the self-density and $f(x)$ a universal function decaying asymptotically as $f(x) sim x^{-omega}$ with $omega = (d+2) times alpha$ where $alpha = 1/4$ for $x ll 1$ and $alpha = 1/2$ for $x gg 1$. We argue that the algebraic decay $N CN(t) sim - t^{-5/4}$ for $t ll TN$ results from an interplay of chain connectivity and melt incompressibility giving rise to the correlated motion of chains and subchains.
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The spatial correlations of entangled polymer dynamics are examined by molecular dynamics simulations and neutron spin-echo spectroscopy. Due to the soft nature of topological constraints, the initial spatial decays of intermediate scattering functions of entangled chains are, to the first approximation, surprisingly similar to those of an unentangled system in the functional forms. However, entanglements reveal themselves as a long tail in the reciprocal-space correlations, implying a weak but persistent dynamic localization in real space. Comparison with a number of existing theoretical models of entangled polymers suggests that they cannot fully describe the spatial correlations revealed by simulations and experiments. In particular, the strict one-dimensional diffusion idea of the original tube model is shown to be flawed. The dynamic spatial correlation analysis demonstrated in this work provides a useful tool for interrogating the dynamics of entangled polymers. Lastly, the failure of the investigated models to even qualitatively predict the spatial correlations of collective single-chain density fluctuations points to a possible critical role of incompressibility in polymer melt dynamics.
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