I. Relaxation of Concentration Fluctuations in Entangled Polymer Mixtures

Semenov, A. N.

doi:10.1007/978-94-011-5480-2_5

Cited by 4 publications

(4 citation statements)

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“…Our work is part of a broader attempt to describe systematically the effects of correlated density fluctuations in dense polymer systems, both for static [12,13,44,45] and dynamical [29,35,46] properties. An important unresolved question is for instance whether the predicted long-range repulsive forces of van der Waals type ("Anti-Casimir effect") [13,45] are observable, for instance in the oscillatory decay of the standard density pair-correlation function of dense polymer solutions.…”

Section: Discussionmentioning

confidence: 99%

“…Before dynamical measurements are performed the original order of beads must then be restored. )Interestingly, a significantly larger slithering snake attempt frequency would not be useful since the relaxation time of slithering snakes without or only few local moves increases exponentially with mass [29,34] due to the correlated motion of snakes [35]. In order to obtain an efficient free snake diffusion (with a chain length independent curvilinear diffusion 28,29]) it is important to relax density fluctuations rapidly by local dynamical pathways.…”

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confidence: 99%

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

et al. 2007

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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) ≈ s/ρR 3 (s) ≈ c e / √ s when connecting two segments together where s denotes the curvilinear length of a segment, R(s) its typical size, c e ≈ 1/ρb 3 e the "swelling coefficient", b e the effective bond length and ρ 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 b e and the swelling coefficient c e of asymptotically long chains. At striking variance to the short-range decay suggested by Flory's 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. PACS numbers: 61.25.Hq,64.60.Ak,05.40.Fb * Electronic address: jwittmer@ics.u-strasbg.fr † URL: http://www-ics.u-strasbg.fr/~etsp/welcome.php 1 I. FLORY'S IDEALITY HYPOTHESIS REVISITEDA cornerstone of polymer physics. Polymer melts are dense disordered systems consisting of macromolecular chains [1]. Theories that predict properties of chains in a melt or concentrated solutions generally start from the "Flory ideality hypothesis" formulated already in the 1940s by Flory [2,3,4]. This cornerstone of polymer physics states that chain conformations correspond to "ideal" random walks on length scales much larger than the monomer diameter [1,4,5,6]. The commonly accepted justification of this mean-field result is that intrachain and interchain excluded volume forces compensate each other if many chains strongly overlap which is the case for three-dimensional melts [5]. Since these systems are essentially incompressible, density fluctuations are known to be small. Hence, all correlations are supposed to be short-ranged as has been systematically discussed first by Edwards who developed the essential statistical mechanical tools [6,7,8,9, 10] also used in this paper.One immediate consequence of Flory's hypothesis is that the mean-squared size of chain segments of curvilinear length s = m − n (with 1 ≤ n < m < N) should scale as R Both equations are expected to hold as long as the moment is not too high for a given segment length and the finite-extensibility of the polymer strand remains irrelevant [6].Deviations caused by the segmental correlation hole effect. 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 2 that intra-and interchain excluded volume forces do not fully compensate each other on intermediate length scales, l...

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Section: Discussionmentioning

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

et al. 2007

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“…Semenov argues that intuitive arguments can be given which support either one of these two, contradictory results. 19 The "fast diffusion idea", according to Semenov, is based on the notion that the fast chain component would be capable of rapidly diffusing into a matrix of the slower chain component. The faster component would thus drive the process of mixing, and thereby relax any compositional fluctuations, dominating collective diffusion.…”

Section: Analytical Resultsmentioning

confidence: 99%

“…Semenov argues that intuitive arguments can be given which support either one of these two, contradictory results . The “fast diffusion idea”, according to Semenov, is based on the notion that the fast chain component would be capable of rapidly diffusing into a matrix of the slower chain component.…”

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confidence: 99%

Describing the Relaxation Spectrum of Entangled Homopolymer Blends with the Dynamic Random-Phase Approximation

Lumma

Mochrie

2001

Macromolecules

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Detailed calculations of the intermediate scattering function of entangled, binary homopolymer blends are presented. The calculations are based on the reptation model of polymer dynamics and employ the dynamic random-phase approximation for inferring collective blend behavior from single-chain characteristics. The relaxation spectra found here for blendsincluding the relaxation rates and amplitudes of higher-order modesare contrasted with those for melts and are given for the entire range of length scales from the diffusive to the nondiffusive regime of polymer dynamics. Analytical limits of the intermediate scattering function are successfully compared to numerical results. The dominance of higher-order relaxation modes in specific, experimentally feasible, asymmetric blend systems is indicated, and the possibility of significant deviations of the expected time−correlation functions from a single-exponential decay is noted.

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Scale-Free Static and Dynamical Correlations in Melts of Monodisperse and Flory-Distributed Homopolymers

Wittmer

Cavallo

Xu³

et al. 2011

J Stat Phys

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It has been assumed untill very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length ξ 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 ≫ ξ . 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.

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I. Relaxation of Concentration Fluctuations in Entangled Polymer Mixtures

Cited by 4 publications

References 16 publications

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

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

Describing the Relaxation Spectrum of Entangled Homopolymer Blends with the Dynamic Random-Phase Approximation

Scale-Free Static and Dynamical Correlations in Melts of Monodisperse and Flory-Distributed Homopolymers

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