Developments in Wang-Landau simulations of a simple continuous homopolymer

Seaton, Daniel T.; Mitchell, SJ; Landau, D. P.

doi:10.1590/s0103-97332008000100009

Cited by 20 publications

(14 citation statements)

References 19 publications

(34 reference statements)

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“…8 The transitions of single untethered polymer chains have been investigated intensively with a variety of offlattice polymer models. 30,31,44,45,46,47,48,49,50,51 Except for the shortest chains and the most short-ranged interactions, the heat capacity as a function of temperature shows two prominent features; a peak at higher temperatures that indicates the transition from disordered coil conformations to disordered globule conformations, and a peak at low temperatures that indicates the transition from a liquid-like disordered globule to a solid-like ordered globule. Typically, the peak associated with the order-disorder transition, which is sometimes referred to as the "freezing" transition, sharpens with increasing chain length and is accompanied by a bimodal probability distribution as expected for a discontinuous transition.…”

Section: Chain Collapse For a Hard Surfacementioning

confidence: 99%

Transitions of tethered polymer chains: A simulation study with the bond fluctuation lattice model

Luettmer-Strathmann

Rampf

Paul

et al. 2008

The Journal of Chemical Physics

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A polymer chain tethered to a surface may be compact or extended, adsorbed or desorbed, depending on interactions with the surface and the surrounding solvent. This leads to a rich phase diagram with a variety of transitions. To investigate these transitions we have performed Monte Carlo simulations of a bond fluctuation model with Wang-Landau and umbrella sampling algorithms in a two-dimensional state space. The simulations' density-of-states results have been evaluated for interaction parameters spanning the range from good- to poor-solvent conditions and from repulsive to strongly attractive surfaces. In this work, we describe the simulation method and present results for the overall phase behavior and for some of the transitions. For adsorption in good solvent, we compare with Metropolis Monte Carlo data for the same model and find good agreement between the results. For the collapse transition, which occurs when the solvent quality changes from good to poor, we consider two situations corresponding to three-dimensional (hard surface) and two-dimensional (very attractive surface) chain conformations, respectively. For the hard surface, we compare tethered chains with free chains and find very similar behavior for both types of chains. For the very attractive surface, we find the two-dimensional chain collapse to be a two-step transition with the same sequence of transitions that is observed for three-dimensional chains: a coil-globule transition that changes the overall chain size is followed by a local rearrangement of chain segments.

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Section: Chain Collapse For a Hard Surfacementioning

confidence: 99%

Transitions of tethered polymer chains: A simulation study with the bond fluctuation lattice model

Luettmer-Strathmann

Rampf

Paul

et al. 2008

The Journal of Chemical Physics

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“…In the microcanonical analysis, the temperature is defined via the curvature of the caloric entropy curve and thus all transition signals in the microcanonical entropy can be directly associated with a transition temperature.After introducing the method, we apply it to liquidsolid and solid-solid transitions occurring for elastic, flexible polymers, which have been under debate for quite some time. In contrast to the rather well-understood coil-globule collapse transition, the formation of highly compact crystalline, amorphous, or glasslike structures intricately depends on the precise relation of intrinsic energy and length scales in the system [4][5][6][7][8][9].In recent work, the microcanonical analysis has successfully been applied in aggregation studies of coarsegrained polymer and peptide models, where a nucleation process was found to be an energetically ordered hierarchy of individual structural subphase transitions [10]. Caloric approaches have also been used to investigate the folding behavior of proteins [11][12][13][14][15] and the structural phases of polymers with stiff bonds [8], as well as polymer adsorption transitions [16][17][18].…”

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confidence: 99%

Microcanonical entropy inflection points: Key to systematic understanding of transitions in finite systems

et al. 2011

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We introduce a systematic classification method for the analogs of phase transitions in finite systems. This completely general analysis, which is applicable to any physical system and extends towards the thermodynamic limit, is based on the microcanonical entropy and its energetic derivative, the inverse caloric temperature. Inflection points of this quantity signal cooperative activity and thus serve as distinct indicators of transitions. We demonstrate the power of this method through application to the long-standing problem of liquid-solid transitions in elastic, flexible homopolymers.PACS numbers: 05.20. Gg,36.40.Ei,82.60.Nh Structure formation processes are typically accompanied by nucleation transitions, where crystalline shapes form out of a liquid or vapor phase. Thus, nucleation is governed by finite-size and surface effects. For small physical systems, it is difficult to understand thermodynamic transitions of this type, as they strongly depend on system size.Cooperativity refers to collective changes in a statistically significant fraction of the degrees of freedom in a system, which transforms the system into a new macrostate. In the thermodynamic limit of an infinitely large system, the ensemble of macrostates sharing similar thermodynamic properties would be called a "phase" and the transformation a "phase transition". The description of such a transformation in a finite system is more subtle, as it cannot be described in the traditional Ehrenfest scheme of singularities in response quantities. However, statistical physics and thus thermodynamics are also valid for systems with no thermodynamic limit. Examples include the structure formation in small atomic clusters and all biomolecules. This is particularly striking for proteins, i.e., heterogeneous linear chains of amino acids. The fact that the individual biological function is connected with the geometrical shape of the molecule makes it necessary to discriminate unfolded (non-functional) and folded (functional) states. Although these systems are finite, they undergo a structural transition by passing a single (or more) free-energy barrier(s). Since these finite-system transitions exhibit strong similarities compared to phase transitions, we extend the terminology once defined in the thermodynamic limit to all systems exhibiting cooperative behavior.In this paper, we introduce a commonly applicable and simple method for the identification and classification of cooperative behavior in systems of arbitrary size by means of microcanonical thermodynamics [1]. It also includes the precise and straightforward analysis of the finite-size effects, which are important to a general understanding of the onset of phase transitions. This is in contrast to canonical approaches, where detailed information is lost by averaging out thermal fluctuations. Re-gaining information about finite-size effects in canonical schemes, e.g., by the investigation of the distribution of Lee-Yang zeros in the complex temperature plane [2] or by inverse Laplace transform [3...

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“…We employ a coarse-grained off-lattice model for a single elastic flexible homopolymer [17][18][19][20][21] consisting of N = 13 monomers [22]. All monomers interact pairwise via a LennardJones (LJ) potential V pp LJ (r) = 4 pp [(σ/r) 12 − (σ/r) 6 ],…”

Section: A Compound Polymer-membrane Modelmentioning

confidence: 99%

Thermodynamics of polymer adsorption to a flexible membrane

2011

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We analyze the structural behavior of a single polymer chain grafted to an attractive, flexible surface. Our model is composed of a coarse-grained bead-and-spring polymer and a tethered membrane. By means of extensive parallel tempering Monte Carlo simulations it is shown that the system exhibits a rich phase behavior ranging from highly ordered, compact to extended random coil structures, and from desorbed to completely adsorbed or even partially embedded conformations. These findings are summarized in a pseudophase diagram indicating the predominant class of conformations as a function of the external parameters temperature and polymer-membrane interaction strength. By comparison with adsorption to a stiff membrane surface it is shown that the flexibility of the membrane gives rise to qualitatively new behavior such as stretching of adsorbed conformations.

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Developments in Wang-Landau simulations of a simple continuous homopolymer

Cited by 20 publications

References 19 publications

Transitions of tethered polymer chains: A simulation study with the bond fluctuation lattice model

Transitions of tethered polymer chains: A simulation study with the bond fluctuation lattice model

Microcanonical entropy inflection points: Key to systematic understanding of transitions in finite systems

Thermodynamics of polymer adsorption to a flexible membrane

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