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.
Following Florys ideality hypothesis the chemical potential of a test chain of length $n$ immersed into a dense solution of chemically identical polymers of length distribution P(N) is extensive in $n$. We argue that an additional contribution $delta
mu_c(n) sim +1/rhosqrt{n}$ arises ($rho$ being the monomer density) for all $P(N)$ if $n ll <N>$ which can be traced back to the overall incompressibility of the solution leading to a long-range repulsion between monomers. Focusing on Flory distributed melts we obtain $delta mu_c(n) approx (1- 2 n/<N>) / rho sqrt{n}$ for $n ll <N>^2$, hence, $delta mu_c(n) approx - 1/rho sqrt{n}$ if $n$ is similar to the typical length of the bath $<N>$. Similar results are obtained for monodisperse solutions. Our perturbation calculations are checked numerically by analyzing the annealed length distribution P(N) of linear equilibrium polymers generated by Monte Carlo simulation of the bond-fluctuation model. As predicted we find, e.g., the non-exponentiality parameter $K_p equiv 1 - <N^>/p!<N>^p$ to decay as $K_p approx 1 / sqrt{<N>}$ for all moments $p$ of the distribution.
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 $N$.
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 $P(s) si m g^0s^{-3/2}$.
Following the Flory ideality hypothesis intrachain and interchain excluded volume interactions are supposed to compensate each other in dense polymer systems. Multi-chain effects should thus be neglected and polymer conformations may be understood fr
om simple phantom chain models. Here we provide evidence against this phantom chain, mean-field picture. We analyze numerically and theoretically the static correlation function of the Rouse modes. Our numerical results are obtained from computer simulations of two coarse-grained polymer models for which the strength of the monomer repulsion can be varied, from full excluded volume (`hard monomers) to no excluded volume (`phantom chains). For nonvanishing excluded volume we find the simulated correlation function of the Rouse modes to deviate markedly from the predictions of phantom chain models. This demonstrates that there are nonnegligible correlations along the chains in a melt. These correlations can be taken into account by perturbation theory. Our simulation results are in good agreement with these new theoretical predictions.
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.
