Configurational statistics of a disordered polymer chain

Obukhov, S P

doi:10.1088/0305-4470/19/17/028

Cited by 60 publications

(46 citation statements)

References 6 publications

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“…Even the equilibrium properties of these polymers at infinite dilution are rather poorly understood at the minute, though some researches are beginning to be published in the theoretical and experimental literature. [27][28][29][30][31] In this chapter we present preliminary results of our study of equilibrium, dynamics and kinetics near the collapselike transition of random copolymers. We consider a model of a random copolymer consisting of only two different monomer types randomly distributed along the chain.…”

Section: Random Copolymers: Equilibrium and Kineticsmentioning

confidence: 99%

Kinetics at the collapse transition of homopolymers and random copolymers

Kuznetsov

Timoshenko

Dawson

1995

The Journal of Chemical Physics

127

156

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We describe the results of Monte Carlo simulations for kinetics at the collapse transition of a homopolymer in a lattice model. We find the kinetic laws corresponding to the three kinetic stages of the process: R g 2 (t)ϭR g 2 (0)ϪAt 7/11 at the early stage corresponding to formation and growth of locally collapsed clusters, the coarsening stage is characterized by growth of clusters according to the law S ϰ t 1/2 , where S is the average number of Kuhn units per cluster, and the final relaxation stage is described by the law R g 2 (t)ϭR g 2 (ϱ)ϩA 1 (1) e Ϫt/ 1(1) with 1 (1) ϰ N 2 . We also present preliminary results on the equilibrium properties and ''collapse'' transition of a random copolymer. The transition curve is determined as a function of hydrophobic bead concentration n a . We discuss the different collapsed copolymer states as a function of the composition. At low hydrophilicity we believe the critical value of the interaction parameter is governed by the law c (n a ) ϰ n a Ϫ2/3 . In the kinetics we see unusual phenomena such as the appearance of a metastable long-lived states with few clusters and nontrivial loop structure.

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Section: Random Copolymers: Equilibrium and Kineticsmentioning

confidence: 99%

Kinetics at the collapse transition of homopolymers and random copolymers

Kuznetsov

Timoshenko

Dawson

1995

The Journal of Chemical Physics

127

156

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“…In statics such models have been solved using replica theory, see [1,[3][4][5][6]8,9], and it is to be anticipated that the method of path integrals [13] would have to be used for solving the dynamics, as in e.g. [7].…”

Section: Discussionmentioning

confidence: 99%

Solvable lattice gas models of random heteropolymers at finite density: II. Dynamics and transitions to compact states

Chakravorty

Mourik²,

Coolen³

2001

The European Physical Journal E

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In this paper we analyse both the dynamics and the high density physics of the infinite dimensional lattice gas model for random heteropolymers recently introduced in [1]. Restricting ourselves to site-disordered heteropolymers, we derive exact closed deterministic evolution equations for a suitable set of dynamic order parameters (in the thermodynamic limit), and use these to study the dynamics of the system for different choices of the monomer polarity parameters. We also study the equilibrium properties of the system in the high density limit, which leads to a phase diagram exhibiting transitions between swollen states, compact states, and regions with partial compactification. Our results find excellent verification in numerical simulations, and have a natural and appealing interpretation in terms of real heteropolymers.PACS. 61.41.+e Polymers, elastomers and plastics -75.10.Nr Spin-glass and other random models

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“…We have studied a simple lattice gas model for random hetero-polymers in ∞-dimensions, the finite dimensional analogues of which had been studied using various approaches [11][12][13][14][15][16][17][18][19][20]. The simplicity and transparency of the model has allowed us to formulate an exact solution in terms of true order parameters for discrete disorder, and in terms of self-averaging mesoscopic variables for continuous disorder.…”

Section: Discussionmentioning

confidence: 99%

“…In the present paper we consider the three most commonly used interaction types: -In the random hydrophobic/hydrophilic model (RHM) [11][12][13][14] a label λ i is assigned to each monomer (with λ i > 0 for hydrophilic and λ i < 0 for hydrophobic monomers), and…”

Section: Model Definitionsmentioning

confidence: 99%

“…When the average charge is 0 (λ 0 = 0), we expect the monomers to group together into boxes such that the total charge in each box goes to zero, because the energy is exactly the sum of the squares of the local charges λ r (11). When λ 0 = 0 (take λ 0 > 0 without loss of generality), however, there is a total charge Nλ 0 , a total negative charge Nλ n , and we define A by…”

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Solvable lattice gas models of random hetero-polymers at finite density: I. Statics

Mourik

2000

The European Physical Journal E

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We introduce ∞-dimensional lattice gas versions of three common models of random heteropolymers, in which both the polymer density and the density of the polymer-solvent mixture are finite. These solvable models give valuable insight into the problems related to the (quenched) average over the randomness in statistical mechanical models of proteins, without having to deal with the hard geometrical constraints occurring in finite-dimensional models. Our exact solution, which is specific to the ∞-dimensional case, is compared to the results obtained by a saddle-point analysis and by the grand ensemble approach, both of which can also be applied to models of finite dimension. We find, somewhat surprisingly, that the saddle-point analysis can lead to qualitatively incorrect results.PACS. 61.41.+e Polymers, elastomers, and plastics -75.10.Nr Spin-glass and other random models

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Configurational statistics of a disordered polymer chain

Cited by 60 publications

References 6 publications

Kinetics at the collapse transition of homopolymers and random copolymers

Kinetics at the collapse transition of homopolymers and random copolymers

Solvable lattice gas models of random heteropolymers at finite density: II. Dynamics and transitions to compact states

Solvable lattice gas models of random hetero-polymers at finite density: I. Statics

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