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Register a new userScale-free center-of-mass displacement correlations in dense polymer solutions and melts without topological constraints and momentum conservation: A bond-fluctuation model study
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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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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.
The classical bond-fluctuation model (BFM) is an efficient lattice Monte Carlo algorithm for coarse-grained polymer chains where each monomer occupies exclusively a certain number of lattice sites. In this paper we propose a generalization of the BFM where we relax this constraint and allow the overlap of monomers subject to a finite energy penalty $overlap$. This is done to vary systematically the dimensionless compressibility $g$ of the solution in order to investigate the influence of density fluctuations in dense polymer melts on various s tatic properties at constant overall monomer density. The compressibility is obtained directly from the low-wavevector limit of the static structure fa ctor. We consider, e.g., the intrachain bond-bond correlation function, $P(s)$, of two bonds separated by $s$ monomers along the chain. It is shown that the excluded volume interactions are never fully screened for very long chains. If distances smaller than the thermal blob size are probed ($s ll g$) the chains are swollen acc ording to the classical Fixman expansion where, e.g., $P(s) sim g^{-1}s^{-1/2}$. More importantly, the polymers behave on larger distances ($s gg g$) like swollen chains of incompressible blobs with $P(s) si m g^0s^{-3/2}$.
The scaling of the bond-bond correlation function $C(s)$ along linear polymer chains is investigated with respect to the curvilinear distance, $s$, along the flexible chain and the monomer density, $rho$, via Monte Carlo and molecular dynamics simulations. % Surprisingly, the correlations in dense three dimensional solutions are found to decay with a power law $C(s) sim s^{-omega}$ with $omega=3/2$ and the exponential behavior commonly assumed is clearly ruled out for long chains. % In semidilute solutions, the density dependent scaling of $C(s) approx g^{-omega_0} (s/g)^{-omega}$ with $omega_0=2-2 u=0.824$ ($ u=0.588$ being Florys exponent) is set by the number of monomers $g(rho)$ contained in an excluded volume blob of size $xi$. % Our computational findings compare well with simple scaling arguments and perturbation calculation. The power-law behavior is due to self-interactions of chains on distances $s gg g$ caused by the connectivity of chains and the incompressibility of the melt. %
It has been assumed until very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length $xi$ characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances $r gg xi$. These correlations are scale-free and, surprisingly, do not depend explicitly on the compressibility of the solution. Both monodisperse and (essentially) Flory-distributed equilibrium polymers are considered.
We present a numerical study of the slip link model introduced by Likhtman for describing the dy- namics of dense polymer melts. After reviewing the technical aspects associated with the implemen- tation of the model, we extend previous work in several directions. The dependence of the relaxation modulus with the slip link density and the slip link stiffness is reported. Then the nonlinear rheolog- ical properties of the model, for a particular set of parameters, are explored. Finally, we introduce excluded volume interactions in a mean field such as manner in order to describe inhomogeneous systems, and we apply this description to a simple nanocomposite model. With this extension, the slip link model appears as a simple and generic model of a polymer melt, that can be used as an alternative to molecular dynamics for coarse grained simulations of complex polymeric systems.
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