Internal viscosity of polymers and the role of solvent resistance

Manke, Charles W.; Williams, Michael C.

doi:10.1021/ma00152a042

Cited by 50 publications

(60 citation statements)

References 12 publications

(19 reference statements)

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“…51 The effective diffusion constant for the single variable (SSS) approximation of the mean first contact time is taken to be the relative diffusion constant of cystine Identifying D eff as the relative diffusion constant of the two end monomers is only rigorously true for freedraining chains [Eq. (22)]. Comparison of the pair correlation function φ(t) from simulation and a free-draining chain supports for this choice (see Fig.…”

Section: Free Diffusion Coefficientmentioning

confidence: 75%

“…The effective diffusion coefficient, derived here as a short time approximation, can also be obtained from the variational lower bound [Eq. (22)] as well as a "local equilibrium" approximation. 33 First, the diffusion matrix in the Smoluchowski equation [Eq.…”

Section: Discussionmentioning

confidence: 99%

“…(22). As a specific example, the Rouse chain (nearest neighbor connectivity) and uniform diagonal friction, D ij = D 0 δ ij has modes and relaxation rates…”

Section: Discussionmentioning

confidence: 99%

“…As shown in the Appendix, a short time approximation to the diffusion coefficient also leads to D eff given by Eq. (22) (14); even though the formal manipulations are similar to the variational derivation, it is not evident from the "local equilibrium" approximation that the SSS approximation with this D eff is actually a lower bound. The diffusion coefficient contained the WF approximation follows more naturally from the model through the time dependence of the pair correlation function φ(t).…”

Section: Gaussian Chainsmentioning

confidence: 99%

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Non-Gaussian dynamics from a simulation of a short peptide: Loop closure rates and effective diffusion coefficients

Portman

2003

The Journal of Chemical Physics

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Intrachain contact formation rates, fundamental to the dynamics of biopolymer self-organization such as protein folding, can be monitored in the laboratory through fluorescence quenching measurements. The common approximations for the intrachain contact rate given by the theory of Szabo, Schulten, and Schulten (SSS) [J. Chem. Phys. 72, 4350 (1980)] and Wilemski-Fixman (WF) [J. Chem. Phys. 60,878 (1973)] are shown to be complementary variational bounds: the SSS and WF approximations are lower and upper bounds, respectively, on the mean first contact times. As reported in the literature, the SSS approximation requires an effective diffusion coefficient 10 to 100 times smaller than expected to fit experimentally measured quenching rates. An all atom molecular dynamics simulation of an eleven residue peptide sequence in explicit water is analyzed to investigate the source of this surprising parameter value. The simulated diffusion limited contact time is approximately 6 ns for a reaction radius of 4Å for solvent viscosity corresponding to that of water at 298 K and 1 atm (η = 1.0 cP). In analytical work, the polymer is typically modeled by a Gaussian chain of effective monomers. Compared to Gaussian dynamics, the simulated end-to-end distance autocorrelation has a much slower relaxation. The long time behavior of the distance autocorrelation function can be approximated by a Gaussian model in which the monomer diffusion coefficient D0 is reduced to D0/6. This value of the diffusion coefficient brings the mean end-to-end contact time from analytical approximations and simulation into agreement in the sense that the SSS and WF approximations bracket the simulated mean first contact time. Attention to the non-Gaussian nature of the dynamics has direct implications for the development of improved analytical models.

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Section: Free Diffusion Coefficientmentioning

confidence: 75%

Section: Discussionmentioning

confidence: 99%

“…(22). As a specific example, the Rouse chain (nearest neighbor connectivity) and uniform diagonal friction, D ij = D 0 δ ij has modes and relaxation rates…”

Section: Discussionmentioning

confidence: 99%

Section: Gaussian Chainsmentioning

confidence: 99%

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Non-Gaussian dynamics from a simulation of a short peptide: Loop closure rates and effective diffusion coefficients

Portman

2003

The Journal of Chemical Physics

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“…However, if the internal friction is too high then the looping and reconfiguration dynamics become slow even in poor solvent. Among the polymer rheologists the notion of internal friction associated with a single polymer chain is more than twenty five years old [1][2][3][4]. Surprisingly it is only very recently that the topic has gained attention in the chemical and biophysics community.…”

mentioning

confidence: 99%

Reconfiguration dynamics in folded and intrinsically disordered protein with internal friction: Effect of solvent quality and denaturant

Samanta

Chakrabarti

2016

Physica A: Statistical Mechanics and its Applications

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Thermal fluctuation spectrum of flexoelectric viscoelastic semiflexible filaments and polymers: A line liquid crystal model

et al. 2022

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In this paper, we generalize the internal viscosity model developed by Professor Williams to semiflexible polymers, biofilaments, and worm‐like micelles, where molecular dissipation is generated by bending. Current models for viscoelasticity with internal viscosity in semiflexible polymers and filaments are based on generalizations of the worm‐like model, but they neglect potential electromechanical couplings such as flexoelectricity. In this paper, inspired by the early work of Professor Williams, we develop a model for worm‐like viscoelastic flexoelectric filaments based on the “line liquid crystal model”. The electroelastic free energy and entropy production are formulated and used to derive the shape equation for these filaments undergoing thermal fluctuations. The resulting time relaxation spectrum is a useful tool to characterize experimentally viscoelastic material parameters. We show that flexoelectricity or polarization‐induced bending softens the filaments. The predicted time relaxation spectrum shows that at longer wavelength modes, the filament behaves like a rigid rod in a viscous solvent, but at shorter wavelengths, it reaches a plateau defined by the bending time scale. The key effect of flexoelectricity is to shift the entire spectrum to higher values, slowing down the response. The model itself is validated using the worm‐like chain and the viscoelasticity of liquid crystals, and the predictions are shown to be in qualitative consistency with the data. Since filament flexoelectricity is associated with 1D sensor‐actuator functionalities, the presented model has many potential novel applications in reduced geometries.

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Internal viscosity of polymers and the role of solvent resistance

Cited by 50 publications

References 12 publications

Non-Gaussian dynamics from a simulation of a short peptide: Loop closure rates and effective diffusion coefficients

Non-Gaussian dynamics from a simulation of a short peptide: Loop closure rates and effective diffusion coefficients

Reconfiguration dynamics in folded and intrinsically disordered protein with internal friction: Effect of solvent quality and denaturant

Thermal fluctuation spectrum of flexoelectric viscoelastic semiflexible filaments and polymers: A line liquid crystal model

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