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Register a new userA finite excluded volume bond-fluctuation model: Static properties of dense polymer melts revisited
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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 $P(s) si m g^0s^{-3/2}$.
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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.
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.
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. %
The effect of excluded volume interactions on the structure of a polymer in shear flow is investigated by Brownian Dynamics simulations for chains with size $30leq Nleq 300$. The main results concern the structure factor $S({bf q})$ of chains of N=300 Kuhn segments, observed at a reduced shear rate $beta=dot{gamma}tau=3.2$, where $dot{gamma}$ is the bare shear rate and $tau$ is the longest relaxation time of the chain. At low q, where anisotropic global deformation is probed, the chain form factor is shown to match the form factor of the continuous Rouse model under shear at the same reduced shear rate, computed here for the first time in a wide range of wave vectors. At high q, the chain structure factor evolves towards the isotropic equilibrium power law $q^{-1/ u}$ typical of self-avoiding walk statistics. The matching between excluded volume and ideal chains at small q, and the excluded volume power law behavior at large q are observed for ${bf q}$ orthogonal to the main elongation axis but not yet for ${bf q}$ along the elongation direction itself, as a result of interferences with finite extensibility effects. Our simulations support the existence of anisotropic shear blobs for polymers in good solvent under shear flow for $beta>1$ provided chains are sufficiently long.
We present an effective and simple multiscale method for equilibrating Kremer Grest model polymer melts of varying stiffness. In our approach, we progressively equilibrate the melt structure above the tube scale, inside the tube and finally at the monomeric scale. We make use of models designed to be computationally effective at each scale. Density fluctuations in the melt structure above the tube scale are minimized through a Monte Carlo simulated annealing of a lattice polymer model. Subsequently the melt structure below the tube scale is equilibrated via the Rouse dynamics of a force-capped Kremer-Grest model that allows chains to partially interpenetrate. Finally the Kremer-Grest force field is introduced to freeze the topological state and enforce correct monomer packing. We generate $15$ melts of $500$ chains of $10.000$ beads for varying chain stiffness as well as a number of melts with $1.000$ chains of $15.000$ monomers. To validate the equilibration process we study the time evolution of bulk, collective and single-chain observables at the monomeric, mesoscopic and macroscopic length scales. Extension of the present method to longer, branched or polydisperse chains and/or larger system sizes is straight forward.
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