Monte Carlo study of lattice polymer dynamics

Lax, M.; Brender, Chava

doi:10.1063/1.435048

Cited by 44 publications

(9 citation statements)

References 9 publications

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“…Various dynamical MC methods have also been developed to study a single polymer chain (see e.g. Verdier and Stockmayer 1962, Wall and Mandel 1975, Lax and Brender 1977, but these methods also introduce statistical bias, depending on the dynamic processes chosen to allow the chain to evolve (Hilhorst and Deutsch 1975). Even the latest work we are aware of (Kremer et a1 1981) simulated chains with N S lo2, though in a continuum.…”

Section: Constant-fugacity Monte Carlo Methodsmentioning

confidence: 99%

Position-space renormalisation group for isolated polymer chains

Redner¹,

Reynolds²

1981

J. Phys. A: Math. Gen.

100

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We develop a cell position-space renormalisation group (PSRG) with which we study the scaling properties of isolated polymer chains. We model a chain by a self-avoiding walk constrained to a lattice. For rescaling factors b S 6, we calculate recursion relations analytically on the square lattice with several different choices for the PSRG weight function. We also calculate implicit cell-to-cell transformations in which a cell of size b is rescaled to a cell of size b'. The results of these PSRGS improve both as b increases and as b/b'+ 1. In addition, we construct a true infinitesimal PSRG transformation, which appears to become exact as the dimensionality d approaches 1; we obtain the closed-form expression for the correlation length exponent, U = (dl) / (d In d). The Flory formula deviates from this already at first order in (d-1). We also develop a constant-fugacity Monte Carlo method which enables us to simulate-in an unbiased way within the grand canonical ensemble-chains of up to lo3 bonds. With this method, we extend the PSRG to larger cells (b s 150) on the square lattice. Our numerical method provides high statistical accuracy for all cell sizes. However, in the range of b we study, the asymptotic behaviour of our results appears to depend on the choice of weight function. One weight function provides smooth behaviour as a function of b, and with it we extrapolate to find U = 0.756* 0.004. Further work is required to resolve the apparent anomalies in the results based on the other weight functions.

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Section: Constant-fugacity Monte Carlo Methodsmentioning

confidence: 99%

Position-space renormalisation group for isolated polymer chains

Redner¹,

Reynolds²

1981

J. Phys. A: Math. Gen.

100

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“…The kink jumps and end rotation moves (used here) originally described by Verdier and Stockmayer [17] are sufficient for simulating the equilibrium configuration of the chain, but do not accurately replicate folding dynamics. When dynamics are in question, a third crankshaft move should be added to the chain relaxation algorithm [23]. The three dimensional configuration of the chain is monitored (and validated against experimental data) by root-mean-square (RMS) chain end-to-end distance.…”

Section: Introductionmentioning

confidence: 99%

Multi-scale modeling to predict ligand presentation within RGD nanopatterned hydrogels

et al. 2006

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“…Computer models of polymer chain dynamics have been developed over the past 30 years by Verdier, Stockmayer, and Kranbuehl1-24 and others. [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] In these models, a number of monomer units sufficient to constitute a statistical segment in a random-coil chain is represented by a "bead", a structureless unit connected to its neighboring beads along the chain by "sticks" of fixed length. The lattice chain model has been especially useful because it is readily amenable to the introduction of hard-core excluded volume interactions.…”

Section: Introductionmentioning

confidence: 99%