The Monte Carlo method in statistical calculations of macromolecules

Kron, A.K.

doi:10.1016/0032-3950(65)90209-1

Cited by 62 publications

(32 citation statements)

References 4 publications

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“…Although easy to implement, these algorithms suffer a very serious drawback: as shown by Madras and Sokal [6], any local algorithm is not ergodic and simulations span only an exponentially small part of the phase space. A different algorithm was inspired by an attempt to model the true dynamics of the polymer in the solvent: the reptation algorithm [7][8][9][10]. However, it was soon realized [8,9] that it is not ergodic because of the possibility of configurations with trapped endpoints.…”

Section: Introductionmentioning

confidence: 99%

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Caracciolo

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Ferraro

et al. 2000

Journal of Statistical Physics

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Section: Introductionmentioning

confidence: 99%

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Caracciolo

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Ferraro

et al. 2000

Journal of Statistical Physics

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confidence: 99%

“…The large system sizes used allow us to suppress finite box-size effects for systems with large chains. Using a mix of local, slithering snake [27,28,29], and double-bridging [17,23,30, 31] MC moves we were able to equilibrate dense systems with chain lengths up to N = 8192.Equilibration and sampling of high-molecular BFM melts. Standard BFM implementations [26,32,33] use local MC jumps to the 6 closest lattice sites to prevent the crossing of chains and conserve therefore the chain topology.…”

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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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“…The slowing down of the singlechain motion by the combination of interfaces and slip-links increases the ordering time by 30%. Mimicking a tightly entangled copolymer melt via the slithering-snake algorithm [170,171], we observe an increase of the ordering time by a factor of almost 9. Thus, while the sequence of morphologies remains unaltered by the single-chain dynamics in this example, the time scale of ordering is strongly affected.…”

Section: Eo /(N K B T )mentioning

confidence: 97%

Studying Amphiphilic Self-assembly with Soft Coarse-Grained Models

2011

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Highly coarse-grained models for investigating the self-assembly of lipids and copolymer materials are discussed. Soft interactions between segments that represent many atoms naturally arise in the course of systematic coarse-graining, and they are necessary for modeling fluctuation effects whose strengths is dictated by a large invariant degree of polymerization. The soft non-bonded interactions of the coarse-grained models are related to the excess free-energy functional of an equivalent field-theoretic description. The connection between the particle-based model and the field-theoretic description helps to identify the physical significance of the model interactions. Non-bonded interactions, which describe the complex phase behavior of compressible mixtures or include local fluid-like packing effects of the coarse-grained segments, can be systematically constructed based on liquid-state theory or classical density functional theory. Details of the computational implementation and limitations of soft coarse-grained models are discussed. Two computational techniques-field-theoretic force-matching and umbrella sampling-are devised for computing a free-energy functional from a particle-based description. They can be employed to (i) derive the non-bonded free-energy functional of a soft coarse-grained model from a more detailed computational model or to (ii) derive a field-theoretic description from a particle-based model. Moreover, different strategies for accurately calculating free energies of self-assembled systems are described and selected applications presented.

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The Monte Carlo method in statistical calculations of macromolecules

Cited by 62 publications

References 4 publications

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

Studying Amphiphilic Self-assembly with Soft Coarse-Grained Models

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