Long Range Bond-Bond Correlations in Dense Polymer Solutions

Abstract

The scaling of the bond-bond correlation function P1(s) along linear polymer chains is investigated with respect to the curvilinear distance, s, along the flexible chain and the monomer density, ρ, via Monte Carlo and molecular dynamics simulations. Surprisingly, the correlations in dense three dimensional solutions are found to decay with a power law P1(s) ∼ s −ω with ω = 3/2 and the exponential behavior commonly assumed is clearly ruled out for long chains. In semidilute solutions, the density dependent scaling of P1(s) ≈ g −ω 0 (s/g) −ω with ω0 = 2 − 2ν = 0.824 (ν = 0.588 being Flory's exponent) is set by the number of monomers g(ρ) contained in an excluded volume blob of size ξ. Our computational findings compare well with simple scaling arguments and perturbation calculation. The power-law behavior is due to self-interactions of chains caused by the chain connectivity and the incompressibility of the melt. This study suggests a careful reexamination of the operational definitions used for the experimental determination of the persistence length.PACS numbers: 05.40. Fb, 05.10.Ln, 61.25.Hq In this Letter we study the correlations of the directions of bonds along polymer chains in semidilute solutions and melts [1,2,3]. We focus on flexible monodisperse chains of N monomers (cf. Fig. 1) under good solvent conditions in three dimensions (d = 3) where both the bond length l and the excluded volume screening length ξ [2, 4] are always much smaller than the chain end-to-end distance R e . In principle, once the bond-bond correlations are computed all other conformational single chain properties can be derived. Importantly, being the (second) derivative of the spatial distances along the chains, they allow us to probe directly -without trivial ideal contributions -the non-gaussian corrections proposed recently [5]. As we shall see, these corrections are crucial to make the description of dense polymer systems, first proposed by Flory [3] and later corroborated by Edwards [2, 4], fully self-consistent.The bond-bond correlation function P 1 (s) is generally believed to decrease exponentially [3]. This belief is based on the few simple single chain models which have been solved rigorously [3,6] and on the assumption that all long range interactions are negligible on distances larger than ξ due to the screening mechanism described by Edwards [2,4]. Hence, only correlations along the backbone of the chains are expected to matter and it is then straightforward to work out that an exponential cut-off is inevitable due to the multiplicative loss of any information transferred recursively along the chain [3].We demonstrate here that this assumption is in fact incorrect and that unexpected long range correlations remain. They are responsible for a scale free power law regime with P 1 (s) = c a (ρ)s −ω for g(ρ) ≪ s ≪ N (g(ρ) being the number of monomers per blob at monomer density ρ) characterized by an exponent ω > 1 and a density dependent amplitude. Our simulation results are pre- sented first and discussed together wi...

Intramolecular long-range correlations in polymer melts: The segmental size distribution and its moments

“…Recently, Flory's hypothesis has been challenged both theoretically [11,12,13,14,15] and numerically for threedimensional solutions [16,17,18,19,20] and ultrathin films [21,22]. These studies suggest that intra-and interchain excluded volume forces do not fully compensate each other on intermediate length scales, leading to long-range intrachain correlations.…”

“…(1). Elaborating and clarifying various points already presented briefly elsewhere [18,19,20], we focus here on melts of long and flexible polymers. Using two well-studied coarse-grained polymer models [23] various intrachain properties are investigated numerically as functions of s and compared with predictions from first-order perturbation theory.…”

Polymer chain generation for coarse-grained models using radical-like polymerization

“…The structure of a polymer melt can be characterized by a wide variety of static or dynamic interchain and intrachain correlation functions [1,5,8,9,10,11] which are more or less sensitive to the artifacts introduced by the preparation procedure and which equilibrate on different time scales. One may note that for fully flexible chains simulated in our model (only FENE + LJ interactions), i.e.…”

Distance Dependence of Angular Correlations in Dense Polymer Solutions

“…This result has been rationalized by means of scaling arguments and perturbation calculations which demonstrate the systematic swelling of the chain segments. 5,7,[11][12][13] The gist of the calculation is that the effective interactions between the monomers of a chain are only partially screened and represented (to leading order) by an effective potential in momentum spacẽ The bold vertical arrows represent the bond vectors (eq 10), dashed lines the effective monomer interactionsṽ(k) and thin lines the Fourier-Laplace transformed Gaussian propagators G(k, t) with the Laplace variable t being conjugated to the curvilinear distance s. The inserted wavevector q is conjugated to the distance r between both bonds in real space. Angular correlations in ring polymers are described by diagram (0).…”