A concerted rotation algorithm for atomistic Monte Carlo simulation of polymer melts and glasses

Dodd, Lawrence R.; Boone, Travis; Theodorou, Doros N.

doi:10.1080/00268979300100641

Cited by 286 publications

(352 citation statements)

References 29 publications

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“…More conventional MC algorithms which can be used to equilibrate polymer melts include reptation moves (generalized slithering snake algorithms), 5 configuration bias algorithms, [6][7][8] and concerted rotation algorithms. [8][9][10] Being relatively local, these methods work best for moderate chain lengths and densities. The complete equilibration of very long chain melts still requires long runs.…”

Section: Introductionmentioning

confidence: 99%

Equilibration of long chain polymer melts in computer simulations

Auhl

Everaers

Grest

et al. 2003

The Journal of Chemical Physics

527

737

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Several methods for preparing well equilibrated melts of long chains polymers are studied. We show that the standard method in which one starts with an ensemble of chains with the correct end-to-end distance arranged randomly in the simulation cell and introduces the excluded volume rapidly, leads to deformation on short length scales. This deformation is strongest for long chains and relaxes only after the chains have moved their own size. Two methods are shown to overcome this local deformation of the chains. One method is to first pre-pack the Gaussian chains, which reduces the density fluctuations in the system, followed by a gradual introduction of the excluded volume. The second method is a double-pivot algorithm in which new bonds are formed across a pair of chains, creating two new chains each substantially different from the original. We demonstrate the effectiveness of these methods for a linear bead spring polymer model with both zero and nonzero bending stiffness, however the methods are applicable to more complex architectures such as branched and star polymer.

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Section: Introductionmentioning

confidence: 99%

Equilibration of long chain polymer melts in computer simulations

Auhl

Everaers

Grest

et al. 2003

The Journal of Chemical Physics

527

737

View full text Add to dashboard Cite

show abstract

“…The main factor for the success of MC in polymer modelling is the development, over the years, of highly sophisticated algorithms which are able to sample very efficiently the phase space of polymeric systems at varied levels of chemical detail. For example in atomistic simulations such localized moves include, among others, the configurational bias (CB) (de Pablo et al, 1992a(de Pablo et al, , 1992bLaso et al, 1992;Siepmann and Frenkel, 1992) and the concerted rotation (ConRot) (Dodd et al, 1993) algorithms. Full-scale, robust equilibration even for very long chains is ensured through the application of advanced, chain-connectivity-altering moves: the end-bridging (EB) (Mavrantzas et al, 1999;Pant and Theodorou, 1995) and the double-bridging (DB) (Karayiannis et al, 2002a(Karayiannis et al, , 2002b.…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

Foteinopoulou

Karayiannis

Laso

2015

Chemical Engineering Science

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HIGHLIGHTS• Identification of the maximally random jammed state for polymer packings.• Molecular simulation of the phase transition in hard-sphere chains.• Molecular modelling of the effect of confinement in densely-packed athermal polymers.• Numerical calculation of the topological constraints in polymeric systems.• First-principles calculation of the scaling regimes in flexible polymers. ABSTRACTWe review the main results from extensive Monte Carlo (MC) simulations on athermal polymer packings in the bulk and under confinement. By employing the simplest possible model of excluded volume, macromolecules are represented as freely-jointed chains of hard spheres of uniform size. Simulations are carried out in a wide concentration range: from very dilute up to very high volume fractions, reaching the maximally random jammed (MRJ) state. We study how factors like chain length, volume fraction and flexibility of bond lengths affect the structure, shape and size of polymers, their packing efficiency and their phase behaviour (disorder-order transition). In addition, we observe how these properties are affected by confinement realized by fiat, impenetrable walls in one dimension. Finally, by mapping the parent polymer chains to primitive paths through direct geometrical algorithms, we analyse the characteristics of the entanglement network as a function of packing density.

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“…However, it has recently been questioned whether this bound is tight [5,8,24]. Algorithms are available to compute the values of f −1 when n = 3, for instance the elegant analytical method developed in [5], but they only return the values of f −1 for given poses of T .…”

Section: Introductionmentioning

confidence: 99%

On the structure of the inverse kinematics map of a fragment of protein backbone

2007

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Loop closure in proteins requires computing the values of the inverse kinematics (IK) map for a backbone fragment with 2n ≥ 6 torsional degrees of freedom (dofs). It occurs in a variety of contexts, e.g., structure determination from electron-density maps, loop insertion in homology-based structure prediction, backbone tweaking for protein energy minimization, and study of protein mobility in folded states. The first part of this paper analyzes the global structure of the IK map for a fragment of protein backbone with 6 torsional dofs and a slightly idealized kinematic model, called the canonical model. This model, which assumes that every two consecutive torsional bonds C α -C and N-C α are exactly parallel, makes it possible to separately compute the inverse orientation map and the inverse position map. The singularities of both maps and their images, the critical sets, respectively decompose SO(3) and R 3 into open regions where the number of IK solutions is constant. This decomposition leads to a constructive proof of the existence of a region in R 3 × SO(3) where the IK of the 6-dof fragment has 16 solutions. The second part of this paper extends this analysis to study fragments with more than 6 torsional dofs. It describes an efficient recursive algorithm to sample IK solutions for such fragments, by identifying the feasible range of each successive torsional dof. A numerical homotopy algorithm is then used to deform the IK solutions for a canonical fragment into solutions for a non-canonical fragment. Computational results for fragments ranging from 8 to 30 dofs are presented.

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A concerted rotation algorithm for atomistic Monte Carlo simulation of polymer melts and glasses

Cited by 286 publications

References 29 publications

Equilibration of long chain polymer melts in computer simulations

Equilibration of long chain polymer melts in computer simulations

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

On the structure of the inverse kinematics map of a fragment of protein backbone

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