Kinetics of collapse for a flexible coil

de Gennes, P.G.

doi:10.1051/jphyslet:019850046014063900

Cited by 226 publications

(274 citation statements)

References 11 publications

Supporting

Mentioning

255

Contrasting

Order By: Relevance

“…The second step is to calculate the characteristic time associated with the various stages in the proposed route. A simple method for calculating the characteristic times was proposed by de Gennes [11]. It focuses on a volume element of solvent containing a single chain and coupled to a thermal reservoir that maintains a temperature T .…”

Section: Some General Considerations; Entropy Production Methodsmentioning

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%

See 1 more Smart Citation

Early stages of homopolymer collapse

2000

View full text Add to dashboard Cite

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.

show abstract

Section: Some General Considerations; Entropy Production Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Early stages of homopolymer collapse

2000

View full text Add to dashboard Cite

show abstract

“…According to theories based on phenomenological models, 11,12 the rate of chain collapse may be related to the nature of the polymer and solvent by Eq. ͑2͒.…”

Section: Discussionmentioning

confidence: 99%

“…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%

“…Equation ͑2͒ gives the characteristic time for the first stage in a two-stage collapse. 11,12 The characteristic time in the second stage depends on N 3 and may be much longer than that in the first stage. The results of the above experiments on the chain collapse process are not compatible with the theoretical prediction of two-stage collapse.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Nakamura

Sasaki

Nakata

2003

The Journal of Chemical Physics

View full text Add to dashboard Cite

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.

show abstract

Polymer association in poor solvents: from monomolecular micelles to clusters of chains and phase separation

Raos

Allegra

1999

Macromol. Theory Simul.

View full text Add to dashboard Cite

SUMMARY: We report some recent results obtained in our laboratory on the poor-solvent behavior of macromolecules. We first discuss the globular collapse of short chains that, unlike long ones, may form compact ordered states. We then address the collapse of random AB copolymers, which may provide significant clues to understanding biophysical issues such as the protein folding problem or the DNA arrangement in a living cell. Afterwards, we turn to the many-chain problem of homopolymer aggregation into polymolecular micelles or clusters of chains and eventually phase separation. The unifying feature of our approach consists in the self-consistent free-energy minimization with inclusion of intra-and inter-molecular interactions, whenever they are required, that enables us to describe the chain conformation in detail. General introductionThe collapse of a polymer chain to the globular state in poor solvents has received a wide interest both as a natural extension of the study of long-range a interactions beyond the good-solvent conditions 1,2) , and as a possible key to understand complex biophysical phenomena, in particular the native state of globular proteins or the conformation of DNA in a living cell 1) . Furthermore, it is a prerequisite for a description of coil aggregation leading to the formation of polymolecular micelles and eventually precipitation. While the general features of the collapse of long homopolymer chains (i. e., formed by identical repeat units) are relatively well understood 1, 3-7) , this is not so for short chains, in particular with reference to their local conformation. Most approaches are instead mainly focused on the overall features of the resulting globule. Therefore, in this Feature Article we discuss some recent theoretical results obtained in our laboratory on the poor-solvent behavior which stress the importance of the intramolecular degrees of freedom.Coil collapse is usually compared to the condensation of a vapor to the liquid phase. However, it was suggested 1, 3) that a slim chain may undergo other transitions to some "ordered" state, somehow akin to the formation of a crystal, or at least of a liquid crystal with nematic order. This indeed turns out to be the case for short chains 8) , as we shall report in the present paper. Also, the process of aggregation and precipitation confronts us with open issues, concerning for example the coil conformation near the critical point. Thus, we shall also address many-chain systems. Homopolymers are clearly a poor model for proteins, that may be regarded as copolymers with very specific monomer sequences (the aminoacid residues). Therefore, later efforts were directed to the study of appropriate copolymers [9][10][11][12][13][14][15][16] . For instance, simulation studies usually considered chains formed by unlike units, whereas other approaches took for simplicity AB copolymers consisting of hydrophobic and hydrophilic units only. Accordingly, we shall also report our recent work on the collapse of random copolymers formed by two di...

show abstract

Kinetics of collapse for a flexible coil

Cited by 226 publications

References 11 publications

Early stages of homopolymer collapse

Early stages of homopolymer collapse

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

Polymer association in poor solvents: from monomolecular micelles to clusters of chains and phase separation

Contact Info

Product

Resources

About