The pivot algorithm and polygons: results on the FCC lattice

Rensburg, E J Janse van; Whittington, S G; Madras, Neal

doi:10.1088/0305-4470/23/9/021

Cited by 31 publications

(8 citation statements)

References 33 publications

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“…16,27 The pivot algorithm has been used on this lattice before. 28 In that case, the lattice was termed the fcc lattice, using the more common name for this lattice, and was used to study polygons or cyclic polymers.…”

Section: Methodsmentioning

confidence: 99%

Rotational isomeric state chains on a high coordination lattice: Dynamic Monte Carlo algorithm details

Clancy

Mattice

2000

The Journal of Chemical Physics

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A high coordination lattice model for simulating coarse-grained rotational isomeric state ͑RIS͒ chains has been under development recently. Initially, the model was developed for chains with symmetric torsional potential energy functions, E()ϭϪE(). A single-bead move Monte Carlo algorithm was used and found to be effective in simulating polyethylene chains. A modification was subsequently developed to allow for the simulation of chains with an asymmetric torsional potential, E() ϪE(). The single-bead move Monte Carlo ͑MC͒ algorithm employed previously was found to be ineffective following this modification. Similar kinetic effects have been seen previously with single-bead MC moves on the cubic lattice, which lead to the Hilhorst-Deutch modification ͑two-bead crankshaft MC move͒ of the Verdier-Stockmayer ͑single-bead move MC͒ algorithm. A reptation MC move applied to this model appears problematic. A multiple-bead MC move is developed using the pivot algorithm formalism in order to avoid the lattice model specific kinetic effect seen with only single-bead MC moves. This allows for the effective simulation of vinyl polymers with asymmetric torsional potentials such as polypropylene and polyvinyl chloride. Polypropylene ͑PP͒ and poly͑vinyl chloride͒ ͑PVC͒ chains of varying stereochemical structure are simulated. The chains are found to relax with reasonable efficiency. Polypropylene and polyvinyl chloride chains are reverse mapped back to the fully atomistic description. The solubility parameters of the reverse-mapped atomistic structures are found to agree reasonably well with experimental values.

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Section: Methodsmentioning

confidence: 99%

Rotational isomeric state chains on a high coordination lattice: Dynamic Monte Carlo algorithm details

Clancy

Mattice

2000

The Journal of Chemical Physics

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“…On the other hand, the pivot algorithm [37][38][39] , where one part of an (already existing) chain is moved around a randomly selected bond, has proved most valuable not only for studying very long (linear) chains 49,81) due to large acceptance fractions and small (integral) autocorrelation times of global properties, but also for polygons 82) . A linear chain may be regarded as a star molecule having two arms.…”

Section: Motivation For the Present Investigationmentioning

confidence: 99%

Monte Carlo simulation studies of the size and shape of linear and star-branched polymers embedded in the tetrahedral lattice

Zifferer¹

1999

Macromol. Theory Simul.

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SUMMARY: In recent years the author investigated the size and shape of linear and star-branched model chains as a function of functionality (number of arms) F and chain length (total number of beads) N for several lattice and off-lattice random walk models as well as for self-avoiding random walks (embedded in the tetrahedral lattice) subjected to various thermodynamic conditions. Not only mean values -characteristic quantities averaged over a large number of configurations of given length, functionality and thermodynamic conditions -have been computed, but also distributions of shape parameters, and the correlation operative between size and shape has been explored. The present feature article in principle summarizes these results, however, the data given in part are recomputed for still larger sample sizes and chain-lengths as in the underlying papers. In addition to stars with F = 4, 8 and 12 arms, so far unpublished investigations on stars with F = 3, F = 6 and F = 10 arms are presented and discussed.

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“…The algorithm for the Monte Carlo simulation of the discrete model consists of two basic moves [21,22]: a single particle flip and a global flip. In the single particle flip, a particle is picked at random and reflected about the straight line joining its two neighbours (see Fig.…”

Section: A Monte Carlo Simulationsmentioning

confidence: 99%

Phase transitions in pressurized semiflexible polymer rings

2008

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We propose and study a model for the equilibrium statistical mechanics of a pressurized semiflexible polymer ring in two dimensions. The Hamiltonian has a term which couples to the algebraic or signed area of the ring and a term which accounts for bending (semiflexibility). The model allows for self-intersections. Using a combination of Monte Carlo simulations, Flory-type scaling theory, mean-field approximations, and lattice enumeration techniques, we obtain a phase diagram in which collapsed and inflated phases are separated by a continuous transition. The scaling properties of the averaged area as a function of the number of units of the ring are derived. For large pressures, the asymptotic behavior of the area is calculated for both continuum and lattice versions of the model. For small pressures, the area is obtained through a known mapping onto the quantum mechanical problem of an electron moving in a magnetic field. The simulation data agree well with the analytic and mean-field results.

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The pivot algorithm and polygons: results on the FCC lattice

Cited by 31 publications

References 33 publications

Rotational isomeric state chains on a high coordination lattice: Dynamic Monte Carlo algorithm details

Rotational isomeric state chains on a high coordination lattice: Dynamic Monte Carlo algorithm details

Monte Carlo simulation studies of the size and shape of linear and star-branched polymers embedded in the tetrahedral lattice

Phase transitions in pressurized semiflexible polymer rings

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