The Monte Carlo method of calculating volume effects in linear polymer chains

Kron, A.K.; Ptitsyn, Oleg B.

doi:10.1016/0032-3950(64)90513-1

Cited by 3 publications

(1 citation statement)

References 8 publications

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“…In this work, we introduce fast lattice Monte Carlo (FLMC) simulations where multiple occupancy of lattice sites is allowed with a proper Boltzmann weight. While this idea was used in the early single-chain simulations of variable excluded-volume effects 9 and in the Domb-Joyce model 10 proposed for single-chain systems, we demonstrate here its great advantages for multi-chain systems, and further compare our FLMC results with the corresponding lattice self-consistent field (LSCF) calculations based on the same Hamiltonian.…”

Section: Introductionmentioning

confidence: 78%

Studying soft matter with “soft” potentials: fast lattice Monte Carlo simulations and corresponding lattice self-consistent field calculations

Wang

2009

Soft Matter

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The basic idea of fast Monte Carlo (MC) simulations is to perform particle-based MC simulations with the excluded-volume interactions modeled by "soft" repulsive potentials that allow particle overlapping. This gives much faster system relaxation and better sampling of the configurational space than conventional molecular simulations with "hard" repulsions that prevent particle overlapping. Here we present fast lattice MC (FLMC) simulations for confined homopolymers, where multiple occupancy of lattice sites is allowed with a proper Boltzmann weight and thus the evaluation of nearest-neighbor interactions can also be avoided. When compared with the corresponding lattice field theories based on the same Hamiltonian, FLMC simulations further provide a powerful means for unambiguously and quantitatively revealing the correlation/fluctuation effects. PACS numbers: 05.10.Ln, 61.25.H-, 64.60.DeSignificant advances have been made in the past three decades in applying conventional, "particle-based" molecular simulation techniques (e.g., Monte Carlo (MC) and molecular dynamics simulations) to the study of polymeric systems. Even with coarse-grained models where each segment represents several to tens of repeat units of real polymers, however, conventional molecular simulations of multi-chain systems are still hindered by "hard" excluded-volume interactions and, for off-lattice simulations, expensive pair-potential calculations. The former is implemented in off-lattice simulations commonly by either hard-sphere repulsion or the harsh Lennard-Jones repulsion, and in lattice simulations by the self-and mutual-avoiding walk (SMAW). While such hard-core repulsions are needed to produce realistic dynamics, they greatly reduce the chain relaxation towards equilibrium configurations as well as the efficiency of sampling the configurational space. On the other hand, the pair-potential calculations are expensive for dense polymeric systems, and lattice simulations are in general much faster and thus widely used.The basic idea of fast MC simulations is to perform particle-based MC simulations with the excluded-volume interactions modeled by "soft" repulsive potentials that allow particle overlapping (i.e., by soft particles whose interaction energy u(r) is finite when they overlap). This avoids the hard repulsions (i.e., u(r → 0) → ∞ as in the Lennard-Jones potential) used in conventional molecular simulations, thus allowing much faster chain relaxation and better sampling of the configurational space. Such coarse-grained models are particularly suitable for the study of equilibrium properties of soft matter such as polymers. It turns out that soft potentials are commonly used in polymer field theories (e.g., the widely applied self-consistent field (SCF) theory with great * Electronic address: q.wang@colostate.edu success for many polymeric systems)[1], where individual polymer segments are modeled as volumeless points with the excluded-volume interactions described by either the Helfand compressibility [2] or the incompressibility...

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Section: Introductionmentioning

confidence: 78%

Studying soft matter with “soft” potentials: fast lattice Monte Carlo simulations and corresponding lattice self-consistent field calculations

Wang

2009

Soft Matter

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Monte‐carlo‐rechnungen an makromolekülmodellen. 2. Mitt.: Quadratischer mittelwert des trägheitsradius und expansionskoeffizient

Bruns

1970

Makromol. Chem.

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ZUSAMMENFASSUNG :Fur zwei gitterfreie Modelle wurden mit Hilfe der Monte-Carlo-Rechnung unter Beriicksichtigung des ,,ausgeschlossenen Volumens'& Zufallsketten erzeugt, die als vereinfachtes Bild h e a r e r Polymermolekiile dienen konnen. Die Ketten bestanden aus maximal etwa 100 Struktureinheiten. Die Abhangigkeit des mittleren Quadrats des Tragheitsradius von der Bindungszahl wurde bestimmt und dafur fur n > 15 3 = 0,229 n1~237 bzw. 9 = 0,185 n1,250 gefunden. Das Verhaltnis @/? nahert sich asymptotisch einem Wert von ca. 6,s.Sechs aus der Literatur bekannte Beziehungen zwischen dem Expansionskoeffizienten c( und dem Wechselwirkungsparameter z wurden getestet. Fur den untersuchten Bereich erwiesen sich die Naherung von FIXMAN, die allerdings modifiziert werden muate, und die von JAMES als die besten. Letztere besitzt jedoch den Nachteil, daD ihre Anwendung fur langere Ketten problematisch ist, wahrend die Gleichung nach FIXMAN, wie Untersuchungen an Gittermodellen gezeigt haben, auch dort giiltig ist. Die GroDe des ,,ausgeschlossenen Volumens" und des Verhaltnisses von der Segmentzahl zur Zahl der Struktureinheiten wurde anhand der Ergebnisse diskutiert. S, U' M M A R Y :Two nonlattice non-intersecting random walks have been used as a model for the linear polymer chain with excluded volume. The chains consisted of -100 structural units a t most. The dependence of the mean-square radius of gyration on the number of structural units has been investi dted and the relations 9 = 0,229 n1,237 and 9 = 0,185 111,250 have been found for n > 1 Z F h e ratio @/? approaches asymptotically a value of 6,s. Six known relations between the expansion coefficient 9c and the segment interaction parameter z have been teste_d.lFor the range investigated the approximation of FIXMAN, which had to be slightly modified, and that of JAMES were the best of them. The latter, however, has the disadvantage of being problematic in its applicability to long chains, while the equation of FIXMAN is also valid in this range as shown by investigations of lattice models. The size of the excluded volume and the ratio of the number of segments to the number of structural units has been discussed in view of the results.

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Calculation of volume effects in macromolecules by means of a Monte Carlo method: Non-self-intersecting chains on a cubic lattice

Kron

Ptitsyn

1967

Polymer Science U.S.S.R.

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The Monte Carlo method of calculating volume effects in linear polymer chains

Cited by 3 publications

References 8 publications

Studying soft matter with “soft” potentials: fast lattice Monte Carlo simulations and corresponding lattice self-consistent field calculations

Studying soft matter with “soft” potentials: fast lattice Monte Carlo simulations and corresponding lattice self-consistent field calculations

Monte‐carlo‐rechnungen an makromolekülmodellen. 2. Mitt.: Quadratischer mittelwert des trägheitsradius und expansionskoeffizient

Calculation of volume effects in macromolecules by means of a Monte Carlo method: Non-self-intersecting chains on a cubic lattice

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