Large deviations of Rouse polymer chain: First passage problem

Cao, Jiashun; Zhu, Jian; Wang, Zuowei; Likhtman, Alexei E.

doi:10.1063/1.4936130

Cited by 15 publications

(56 citation statements)

References 25 publications

(29 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[72] for a fBM in a parabolic potential as well as in Ref. [15] in the case of a Rouse polymer chain. As demonstrated in Fig.…”

Section: First-passage Timementioning

confidence: 78%

See 1 more Smart Citation

First-passage dynamics of linear stochastic interface models: numerical simulations and entropic repulsion effect

Groß¹

2018

J. Stat. Mech.

View full text Add to dashboard Cite

A fluctuating interfacial profile in one dimension is studied via Langevin simulations of the Edwards-Wilkinson equation with non-conserved noise and the Mullins-Herring equation with conserved noise. The profile is subject to either periodic or Dirichlet (no-flux) boundary conditions. We determine the noise-driven time-evolution of the profile between an initially flat configuration and the instant at which the profile reaches a given height M for the first time. The shape of the averaged profile agrees well with the prediction of weak-noise theory (WNT), which describes the most-likely trajectory to a fixed first-passage time. Furthermore, in agreement with WNT, on average the profile approaches the height M algebraically in time, with an exponent that is essentially independent of the boundary conditions. However, the actual value of the dynamic exponent turns out to be significantly smaller than predicted by WNT. This "renormalization" of the exponent is explained in terms of the entropic repulsion exerted by the impenetrable boundary on the fluctuations of the profile around its most-likely path. The entropic repulsion mechanism is analyzed in detail for a single (fractional) Brownian walker, which describes the anomalous diffusion of a tagged monomer of the interface as it approaches the absorbing boundary. The present study sheds light on the accuracy and the limitations of the weak-noise approximation for the description of the full first-passage dynamics.

show abstract

“…[72] for a fBM in a parabolic potential as well as in Ref. [15] in the case of a Rouse polymer chain. As demonstrated in Fig.…”

Section: First-passage Timementioning

confidence: 78%

“…(1.9)], analytical solutions of the first-passage problem are technically difficult and are available only in certain limits (see, e.g., Refs. [11][12][13][14][15][16]). The first-passage dynamics of the profile is thus addressed here via numerical simulation of Eqs.…”

Section: Introductionmentioning

confidence: 99%

First-passage dynamics of linear stochastic interface models: numerical simulations and entropic repulsion effect

Groß¹

2018

J. Stat. Mech.

View full text Add to dashboard Cite

show abstract

“…[16][17][18][19][20] Recently we have shown by simulations and theoretical calculations that if the star arm is represented by a Rouse chain with more beads, the mean FP time of the chain extension or retraction gets faster than that predicted by the single-bead models. 21 More accurate description of arm retraction dynamics should be achieved by solving a multi-dimensional Kramer's problem even for the cases without CR.…”

Section: Introductionmentioning

confidence: 99%

Microscopic Picture of Constraint Release Effects in Entangled Star Polymer Melts

Cao

Wang

2016

Macromolecules

Self Cite

View full text Add to dashboard Cite

The constraint release (CR) effect in entangled branched polymers is generally described by the widely accepted Dynamic Tube Dilation (DTD) theory based on the tube model, which predicts the stress relaxation function reasonably well, but not the dielectric or arm end-to-end vector relaxation. The microscopic picture of entanglement dynamics even in the simple case of star polymers is still not fully resolved. In this * To whom correspondence should be addressed entanglements sitting on a target star arm, only those destroyed by the arm free end dominate the arm end-to-end vector relaxation, while the constraint release events produce an accelerated drift of the mean positions of these specific entanglements towards the arm-end, which is an essential mechanism for understanding the relaxation of star polymers in concentrated solutions or melts. Our findings call for an examination of the microscopic foundation of conventional DTD picture and inspire the development of quantitative theories with consideration of more microscopic details.

show abstract

“…The development of such theories requires the analytical solution of the multi-dimensional FP problem of arm retraction. 18 On the other hand, the coarse-grained slip-link or slip-spring (SS) simulation models have demonstrated strong potential in describing dynamics and rheology of entangled polymers. [19][20][21][22][23][24][25][26][27][28] For example, the single-chain slip-spring model developed by Likhtman 25 can provide simulation results on multiple experimentally measurable observables, such as neutron spin echo, linear rheology, dielectric relaxation and diffusion.…”

Section: Introductionmentioning

confidence: 99%

“…To our knowledge the only reported work on applying the transition path sampling methods to study entanglement dynamics is the FFS simulation of Rouse chains in the regime relevant to arm retraction dynamics. 18 We will mainly focus on the systems without constraint release for the following reasons: 1) It is relatively convenient to implement the FFS method and find an appropriate reaction coordinate in the non-CR systems; 2) The terminal relaxation times in the systems without CR are much longer than those with CR, allowing us to test the computational efficiency and limit of the combined method; 3) Reliable simulation data on the FP times of arm retractions without CR are highly desired for examining analytical solutions of the multiple-dimensional Kramers problem 18 ; 4) The extension of the method developed in the non-CR case to the CR case is fairly straightforward, as will be shown in Section V. With an optimized selection of the reaction coordinate, which is the index of the monomer that the innermost slip-link sits on, we first validate the proposed simulation method by producing simulation results on the terminal relaxation times τ d of mildly entangled star arms up to 8 entanglements in good agreement with those obtained from SS model simulations. The FFS simulations are then extended to longer arms with lengths up to 16 entanglements and so reach τ d values about 6 decades beyond that accessible by brute force simulations (from 6 × 10 6 to 3 × 10 12 SS unit time).…”

Section: Introductionmentioning

confidence: 99%

Arm retraction dynamics of entangled star polymers: A forward flux sampling method study

Zhu

Likhtman

Wang

2017

The Journal of Chemical Physics

Self Cite

View full text Add to dashboard Cite

The study of dynamics and rheology of well-entangled branched polymers remains a challenge for computer simulations due to the exponentially growing terminal relaxation times of these polymers with increasing molecular weights. We present an efficient simulation algorithm for studying the arm retraction dynamics of entangled star polymers by combining the coarse-grained slip-spring (SS) model with the forward flux sampling (FFS) method. This algorithm is first applied to simulate symmetric star polymers in the absence of constraint release (CR). The reaction coordinate for the FFS method is determined by finding good agreement of the simulation results on the terminal relaxation times of mildly entangled stars with those obtained from direct shooting SS model simulations with the relative difference between them less than 5%. The FFS simulations are then carried out for strongly entangled stars with arm lengths up to 16 entanglements that are far beyond the accessibility of brute force simulations in the non-CR condition. Apart from the terminal relaxation times, the same method can also be applied to generate the relaxation spectra of all entanglements along the arms which are desired for the development of quantitative theories of entangled branched polymers. Furthermore, we propose a numerical route to construct the experimentally measurable relaxation correlation functions by effectively linking the data stored at each interface during the FFS runs. The obtained star arm end-to-end vector relaxation functions Φ(t) and the stress relaxation function G(t) are found to be in reasonably good agreement with standard SS simulation results in the terminal regime. Finally, we demonstrate that this simulation method can be conveniently extended to study the arm-retraction problem in entangled star polymer melts with CR by modifying the definition of the reaction coordinate, while the computational efficiency will depend on the particular slip-spring or slip-link model employed.

show abstract

Large deviations of Rouse polymer chain: First passage problem

Cited by 15 publications

References 25 publications

First-passage dynamics of linear stochastic interface models: numerical simulations and entropic repulsion effect

First-passage dynamics of linear stochastic interface models: numerical simulations and entropic repulsion effect

Microscopic Picture of Constraint Release Effects in Entangled Star Polymer Melts

Arm retraction dynamics of entangled star polymers: A forward flux sampling method study

Contact Info

Product

Resources

About