Dynamical eigenmodes of star and tadpole polymers

Keesman, Rick; Barkema, G. T.; Panja, Debabrata

doi:10.1088/1742-5468/2013/02/p02021

Cited by 6 publications

(6 citation statements)

References 7 publications

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“…Our results for anomalous diffusion is consistent with a pattern that the dynamics of magnetisation at the critical temperature in spin models is anomalous [21][22][23]. Importantly, the anomalous diffusion is described by the Generalised Langevin Equation (GLE) [22,23] (and bears strong resemblance to anomalous diffusion in polymeric and membrane systems under a variety of circumstances [3,5,12,[24][25][26][27][28][29][30][31][32][33][34][35][36][37]), which we verify in Sec. IV.…”

Section: Introductionsupporting

confidence: 88%

“…In line with our previous works on the Ising and φ 4 model with Glauber dynamics [22,23] and in polymeric systems [3,[24][25][26], the relation of the restoring force f (t) and the "velocity" of magnetisationṀ l (t) can be expressed as…”

Section: A Generalized Langevin Equation For the Line Magnetisationsupporting

confidence: 67%

“…For the form (2) to hold, the Hessian must be independent of {r α }, which restricts the class of such Hamiltonians only to harmonic ones (i.e., H is quadratic in {q i }). Classic examples of such systems are the bead-spring models of linear polymeric systems [1,2], their extensions to star and tadpole polymers [3], polymeric membranes [4,5], 2D cytoskeleton of cells [6][7][8] and graphite oxide sheets [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

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Approximate dynamical eigenmodes of the Ising model with local spin-exchange moves

2019

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We establish that the Fourier modes of the magnetisation serve as the dynamical eigenmodes for the two-dimensional Ising model at the critical temperature with local spin-exchange moves, i.e., Kawasaki dynamics. We obtain the dynamical scaling properties for these modes, and use them to calculate the time evolution of two dynamical quantities for the system, namely the autocorrelation function and the mean-square deviation of the line magnetisations. At intermediate times 1 t L zc , where z c = 4 − η = 15/4 is the dynamical critical exponent of the model, we find that the line magnetisation undergoes anomalous diffusion. Following our recent work on anomalous diffusion in spin models, we demonstrate that the Generalized Langevin Equation (GLE) with a memory kernel consistently describes the anomalous diffusion, verifying the corresponding fluctuation-dissipation theorem with the calculation of the force autocorrelation function.

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Section: Introductionsupporting

confidence: 88%

Section: A Generalized Langevin Equation For the Line Magnetisationsupporting

confidence: 67%

Section: Introductionmentioning

confidence: 99%

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Approximate dynamical eigenmodes of the Ising model with local spin-exchange moves

2019

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“…While a broader class of polymers (dubbed “topological”) has been studied in dilute conditions, , in this Letter, we focus on entangled, semidilute concentrations and report the first molecular dynamics simulation (Figure D) of tadpole-shaped polymers in this regime. Our main finding is that we observe a dynamical transition in which systems of tadpoles with long enough tails and heads display a markedly slower dynamics than a corresponding system of linear chains with equal mass.…”

mentioning

confidence: 99%

“…In conclusion, we have investigated the dynamics of entangled systems of tadpole-shaped polymers, as the simplest example of a broader family of “chimeric” polymers formed by the combination of unknotted and unlinked loops and branches (Figure A). While similar architectures had been investigated in the dilute regime, , here we design entangled systems with the aim of understanding how to achieve a fine control over threading topological constraints and, in turn, over the rheology of the bulk.…”

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confidence: 99%

Threading-Induced Dynamical Transition in Tadpole-Shaped Polymers

et al. 2020

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The relationship between polymer topology and bulk rheology remains a key question in soft matter physics. Architecture-specific constraints (or threadings) are thought to control the dynamics of ring polymers in ring–linear blends, which thus affects the viscosity to range between that of the pure rings and a value larger, but still comparable to, that of the pure linear melt. Here we consider qualitatively different systems of linear and ring polymers, fused together in “chimeric” architectures. The simplest example of this family is a “tadpole”-shaped polymer, a single ring fused to the end of a single linear chain. We show that polymers with this architecture display a threading-induced dynamical transition that substantially slows chain relaxation. Our findings shed light on how threadings control dynamics and may inform design principles for chimeric polymers with topologically tunable bulk rheological properties.

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Theory of mobility of inhomogeneous-polymer-grafted particles

Tian

Chen

et al. 2023

The Journal of Chemical Physics

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We develop a theory for the motion of a particle grafted with inhomogeneous bead-spring Rouse chains via the generalized Langevin equation (GLE), where individual grafted polymers are allowed to take different bead friction coefficients, spring constants, and chain lengths. An exact solution of the memory kernel K(t) is obtained for the particle in the time (t) domain in the GLE, which depends only on the relaxation of the grafted chains. The t-dependent mean square displacement g(t) of the polymer-grafted particle is then derived as a function of the friction coefficient γ0 of the bare particle and K(t). Our theory offers a direct way to quantify the contributions of the grafted chain relaxation to the mobility of the particle in terms of K(t). This powerful feature enables us to clarify the effect on g(t) of dynamical coupling between the particle and grafted chains, leading to the identification of a relaxation time of fundamental importance in polymer-grafted particles, namely, the particle relaxation time. This timescale quantifies the competition between the contributions of the solvent and grafted chains to the friction of the grafted particle and separates g(t) into the particle- and chain-dominated regimes. The monomer relaxation time and the grafted chain relaxation time further divide the chain-dominated regime of g(t) into subdiffusive and diffusive regimes. Analysis of the asymptotic behaviors of K(t) and g(t) provides a clear physical picture of the mobility of the particle in different dynamical regimes, shedding light on the complex dynamics of polymer-grafted particles.

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Dynamical eigenmodes of star and tadpole polymers

Cited by 6 publications

References 7 publications

Approximate dynamical eigenmodes of the Ising model with local spin-exchange moves

Approximate dynamical eigenmodes of the Ising model with local spin-exchange moves

Threading-Induced Dynamical Transition in Tadpole-Shaped Polymers

Theory of mobility of inhomogeneous-polymer-grafted particles

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