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Register a new userLong Range Bond-Bond Correlations in Dense Polymer Solutions
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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. %
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Angular correlations in dense solutions and melts of flexible polymer chains are investigated with respect to the distance $r$ between the bonds by comparing quantitative predictions of perturbation calculations with numerical data obtained by Monte Carlo simulation of the bond-fluctuation model. We consider both monodisperse systems and grand-canonical (Flory-distributed) equilibrium polymers. Density effects are discussed as well as finite chain length corrections. The intrachain bond-bond correlation function $P(r)$ is shown to decay as $P(r) sim 1/r^3$ for $xi ll r ll r^*$ with $xi$ being the screening length of the density fluctuations and $r^* sim N^{1/3}$ a novel length scale increasing slowly with (mean) chain length $N$.
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.
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 $P(s) si m g^0s^{-3/2}$.
Presenting theoretical arguments and numerical results we demonstrate long-range intrachain correlations in concentrated solutions and melts of long flexible polymers which cause a systematic swelling of short chain segments. They can be traced back to the incompressibility of the melt leading to an effective repulsion $u(s) approx s/rho R^3(s) approx ce/sqrt{s}$ when connecting two segments together where $s$ denotes the curvilinear length of a segment, $R(s)$ its typical size, $ce approx 1/rho be^3$ the ``swelling coefficient, $be$ the effective bond length and $rho$ the monomer density. The relative deviation of the segmental size distribution from the ideal Gaussian chain behavior is found to be proportional to $u(s)$. The analysis of different moments of this distribution allows for a precise determination of the effective bond length $be$ and the swelling coefficient $ce$ of asymptotically long chains. At striking variance to the short-range decay suggested by Florys ideality hypothesis the bond-bond correlation function of two bonds separated by $s$ monomers along the chain is found to decay algebraically as $1/s^{3/2}$. Effects of finite chain length are considered briefly.
The core-core structure factor of dense star polymer solutions in a good solvent is shown theoretically to exhibit an unusual behaviour above the overlap concentration. Unlike usual liquids, these solutions display a structure factor whose first peak decreases by increasing density while the second peak grows. The scenario repeats itself with the subsequent peaks as the density is further enhanced. For low enough arm numbers $f$ ($f leq 32$), various different considerations lead to the conclusion that the system remains fluid at all concentrations.
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