Kinetics of a homopolymer collapse: Beyond the Rouse–Zimm scaling

Klushin, Leonid I.

doi:10.1063/1.476229

Cited by 53 publications

(76 citation statements)

References 13 publications

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“…The dissipation in this case is attributed to the Stokes drag force on the pearls. Most recently the problem was re-examined by Klushin [13]. In this model the driving free energy is the transfer free energy to the dense phase and the dissipation is due to the Stokes drag force.…”

Section: Discussionmentioning

confidence: 99%

“…Theoretical studies have utilized a variety of approaches in focusing on different aspects of the problem. Langevin models [8][9][10], phenomenological models [11][12][13] and computer simulations [14][15][16][17][18][19][20] have been used to consider the kinetics of collapse in the absence of topological constraints. Other studies have focused on the role of internal entanglements [21,22] or the competition with chain-chain aggregation [23,24].…”

Section: Introductionmentioning

confidence: 99%

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Early stages of homopolymer collapse

2000

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Interest in the protein folding problem has motivated a wide range of theoretical and experimental studies of the kinetics of the collapse of flexible homopolymers. In this Paper a phenomenological model is proposed for the kinetics of the early stages of homopolymer collapse following a quench from temperatures above to below the θ temperature. In the first stage, nascent droplets of the dense phase are formed, with little effect on the configurations of the bridges that join them. The droplets then grow by accreting monomers from the bridges, thus causing the bridges to stretch. During these two stages the overall dimensions of the chain decrease only weakly. Further growth of the droplets is accomplished by the shortening of the bridges, which causes the shrinking of the overall dimensions of the chain. The characteristic times of the three stages respectively scale as N 0 , N 1/5 and N 6/5 , where N is the degree of polymerization of the chain.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Early stages of homopolymer collapse

2000

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“…(Otherwise, addition time scales and regimes would enter the problem. [4,13,14]) The system evolves dynamically according to microscopic equations of motion of chain segments. The segments are straightened arrays of globules, and further straightening streamlines them at larger length scales.…”

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confidence: 99%

“…[5] Attempts made to incorporate the capillary instability in the description of the collapse of a polymer chain, [12,13] however, have so far resulted in no universally accepted theoretical description, particularly in prediction of how the time for collapse scales with chain length. The purpose of this paper is to present a theory based on a new idea for the mechanism of the collapse transition, and to support this theory by comparing directly to results of large-scale molecular dynamics simulations.…”

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confidence: 99%

Collapse dynamics of a polymer chain: Theory and simulation

2002

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We present a scaling theory describing the collapse of a homopolymer chain in poor solvent. At time t after the beginning of the collapse, the original Gaussian chain of length N is streamlined to form N/g segments of length R(t), each containing g ∼ t monomers. These segments are statistical quantities representing cylinders of length R ∼ t 1/2 and diameter d ∼ t 1/4 , but structured out of stretched arrays of spherical globules. This prescription incorporates the capillary instability. We compare the time-dependent structure factor derived for our theory with that obtained from ultra-large-scale molecular dynamics simulation with explicit solvent. This is the first time such a detailed comparison of theoretical and simulation predictions of collapsing chain structure has been attempted. The favorable agreement between the theoretical and computed structure factors supports the picture of the coarse-graining process during polymer collapse. 64.60.Ak,64.60.Fr,61.25.Hq,83.10.Nn The collapse transition of a single polymer molecule is for several reasons an interesting physical problem. [1,2,3,4,5,6,7,8,9] Understanding the collapse transition is foremost a precursor to understanding protein folding, [10] and how other biomolecules react to changes in environment. Furthermore, a better physical picture of the collapse transition will enhance the ability of nanoscale micromanipulation techniques to provide a way to experimentally approach many such problems. [9,11] The earliest consistent theoretical picture of the collapse transition stems from de Gennes.[1] In this scenario, when the temperature is shifted by ∆T from θ conditions, a Gaussian coil starts to aggregate, resulting in a uniformly dense sausage-like shape. As time goes on, the minimization of interfacial area drives this sausagelike shape to thicken and shorten until, at the final stage, a globule is formed. More recent work has shown that such uniform sausage-like shapes are highly unstable in solvents due to the capillary instability, which selects for "pearl-necklace" structures over uniform sausages.[5] Attempts made to incorporate the capillary instability in the description of the collapse of a polymer chain, [12,13] however, have so far resulted in no universally accepted theoretical description, particularly in prediction of how the time for collapse scales with chain length. The purpose of this paper is to present a theory based on a new idea for the mechanism of the collapse transition, and to support this theory by comparing directly to results of large-scale molecular dynamics simulations.Consider a Gaussian coil representing a polymer in θ solvent. We may think of this coil as a Gaussian fractal, created by a heirarchical scheme, demonstrated in the right side of Fig. 1. We subject this system to an instantaneous drop in temperature, which quenches the system rapidly into poor solvent conditions. This effectively introduces monomer-monomer attraction. We assume this quench is so deep that the initial nucleation of the first globules of t...

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“…The kinetics of chain collapse has been studied on the basis of phenomenological models [11][12][13][14][15] and by computer simulations. 16 -19 de Gennes first studied a mechanism of chain collapse and derived the characteristic time 0 as 11…”

Section: Introductionmentioning

confidence: 99%

Solvent effect on single-chain collapse of poly(methyl methacrylate) in tert-butyl alcohol

Nakamura

Sasaki

Nakata

2003

The Journal of Chemical Physics

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Kinetic and static properties of the coil-globule transition of poly͑methyl methacrylate͒ ͑PMMA͒ in pure tert-butyl alcohol were determined by static light scattering and compared with those of PMMA in the mixed solvent tert-butyl alcoholϩwater͑2.5 vol %͒ in order to examine the effect of water on the chain collapse. The measurements were carried out for the molecular weight M ϫ10 Ϫ6 ϭ4.1 and 12.2 in the concentration range of 0.6ϫ10 Ϫ4 -2.6ϫ10 Ϫ4 g/cm 3 , and the mean-square radius of gyration ͗s 2 ͘ was determined as a function of the time after an abrupt decrease of temperature.PMMA chains collapsed to equilibrium globules within 90 min after quenching for M ϭ1.22 ϫ10 7 and within 30 min for M ϭ4.1ϫ10 6 . Chain aggregation due to phase separation became noticeable after the collapse of the chain because of an increase of observed molecular weight. For PMMA in the mixed solvent tert-butyl alcoholϩwater͑2.5 vol %͒, the chain collapse process has been observed for periods from hours to weeks depending on the molecular weight and temperature, and the chain aggregation was negligibly small in the chain collapse process. The expansion factor ␣ 2 ϭ͗s 2 ͘/͗s 2 ͘ 0 obtained for fully collapsed chains in pure tert-butyl alcohol was represented by the theoretical prediction ␣ 3 Ϫ␣ϪC(␣ Ϫ3 Ϫ1)ϭB(1Ϫ /T)M 1/2 with the coefficients of Bϭ0.0179 and Cϭ0.054. For PMMA in the mixed solvent, the coil-globule transition curve has been expressed by the same equation with Bϭ0.0164 and Cϭ0.049, close to the above values. The small amount of water in the mixed solvent caused a drastic slowdown in the chain-collapse rate but had little effect on the coil-globule transition curve.

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Kinetics of a homopolymer collapse: Beyond the Rouse–Zimm scaling

Cited by 53 publications

References 13 publications

Early stages of homopolymer collapse

Early stages of homopolymer collapse

Collapse dynamics of a polymer chain: Theory and simulation

Solvent effect on single-chain collapse of poly(methyl methacrylate) in tert-butyl alcohol

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