Soft ellipsoid model for Gaussian polymer chains

Eurich, Frank; Maass, Philipp

doi:10.1063/1.1337043

Cited by 56 publications

(67 citation statements)

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“…The close analogy between polymers and random walks has inspired many mathematical and statistical mechanical studies to analyze sizes and shapes of random walks [30][31][32][33][34][35][36][37][38][39][40][41][42][43]. Such studies validate Kuhn's insight and reveal broad distributions of radius of gyration and shape, as characterized by the eigenvalues of the gyration tensor.…”

Section: Introductionmentioning

confidence: 54%

Polymer crowding and shape distributions in polymer-nanoparticle mixtures

Lim

Denton

2014

The Journal of Chemical Physics

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Macromolecular crowding can influence polymer shapes, which is important for understanding the thermodynamic stability of polymer solutions and the structure and function of biopolymers (proteins, RNA, DNA) under confinement. We explore the influence of nanoparticle crowding on polymer shapes via Monte Carlo simulations and free-volume theory of a coarse-grained model of polymer-nanoparticle mixtures. Exploiting the geometry of random walks, we model polymer coils as effective penetrable ellipsoids, whose shapes fluctuate according to the probability distributions of the eigenvalues of the gyration tensor. Accounting for the entropic cost of a nanoparticle penetrating a larger polymer coil, we compute the crowding-induced shift in the shape distributions, radius of gyration, and asphericity of ideal polymers in a theta solvent. With increased nanoparticle crowding, we find that polymers become more compact (smaller, more spherical), in agreement with predictions of free-volume theory. Our approach can be easily extended to nonideal polymers in good solvents and used to model conformations of biopolymers in crowded environments.

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Section: Introductionmentioning

confidence: 54%

Polymer crowding and shape distributions in polymer-nanoparticle mixtures

Lim

Denton

2014

The Journal of Chemical Physics

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“…Since the results presented here challenge an important concept of polymer physics, they should hopefully be useful for a broad range of theoretical approaches which commonly assume the validity of the Gaussian chain model down to molecular scales [47,48,49]. This study shows that a polymer in dense solutions should not be viewed as one soft sphere (or ellipsoid) [50,51,52], but as a hierarchy of nested segmental correlation holes of all sizes aligned and correlated along the chain backbone ( Fig. 2 (b)).…”

Section: Discussionmentioning

confidence: 99%

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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“…One way to overcome this problem is through "multiscale modeling," where a set of simulations is performed at different levels of coarse-graining of the original system and in a subsequent step, information from different length scales is combined to provide the complete physical picture [7]. With such an approach, however, the challenge is not only to find the appropriate computational technique for each length scale simulated, but also to know (i ) the proper effective potential acting between coarse-grained units needed to carry out the simulations [8,9,10,11], and (ii ) the proper procedure for combining information from different scales of modeling once simulation data is acquired.…”

Section: Introductionmentioning

confidence: 99%

Theoretical coarse-graining approach to bridge length scales in diblock copolymer liquids

Sambriski

Guenza

2007

Phys. Rev. E

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A microscopic theory for coarse graining diblock copolymers into dumbbells of interacting soft colloidal particles has been developed, based on the solution of liquid-state integral equations. The Ornstein-Zernike equation is solved to provide a mesoscopic description of the diblock copolymer system at the level of block centers of mass, and at the level of polymer centers of mass. Analytical forms of the total correlation functions for block-block, block-monomer, and center-of-mass pairs are obtained for a liquid of structurally symmetric diblock copolymers as a function of temperature, density, chain length, and chain composition. The theory correctly predicts thermodynamicallydriven segregation of diblocks into microdomains as a function of temperature (chi parameter). The coarse-grained description contains contributions from density and concentration fluctuations, with the latter becoming dominant as temperature decreases. Numerical calculations for the block coarse-grained total correlation functions, as a function of the proximity of the system to its phase transition, are presented. Comparison with united atom molecular dynamics simulations are carried out in the athermal regime, where simulations and theory quantitatively agree with no need of adjustable parameters.

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Soft ellipsoid model for Gaussian polymer chains

Cited by 56 publications

References 23 publications

Polymer crowding and shape distributions in polymer-nanoparticle mixtures

Polymer crowding and shape distributions in polymer-nanoparticle mixtures

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

Theoretical coarse-graining approach to bridge length scales in diblock copolymer liquids

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