Polymer dynamics in repton model at large fields

Kolomeisky, Anatoly B.; Drzewiński, Andrzej

doi:10.1063/1.1687321

Cited by 8 publications

(11 citation statements)

References 31 publications

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“…The repton model is extensively discussed and illustrated in the literature [5,6]. Duke has extended the repton model to study gel electrophoresis [7], by adding an electric field which acts on the charged reptons; also this model has been studied extensively [6,8,9]. A highly efficient simulation approach of the repton model was developed based on bit-operations [8]; the present work uses this approach as well.…”

Section: Introduction: Polymer Reptation and The Repton Modelmentioning

confidence: 99%

Structural modes of a polymer in the repton model

Barkema

Panja

Leeuwen

2011

The Journal of Chemical Physics

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Using extensive computer simulations, the behavior of the structural modes-more precisely, the eigenmodes of a phantom Rouse polymer-are characterized for a polymer in the three-dimensional repton model and are used to study the polymer dynamics at time scales well before the tube renewal. Although these modes are not the eigenmodes for a polymer in the repton model, we show that numerically the modes maintain a high degree of statistical independence. The correlations in the mode amplitudes decay exponentially with ( p/N ) 2 A(t), in which p is the mode number, N is the polymer length, and A(t) is a single function shared by all modes. In time, the quantity A(t) causes an exponential decay for the mode amplitude correlation functions for times <1; a stretched exponential with an exponent 1/2 between times 1 and τ R ∼ N 2 , the time-scale for diffusion of tagged reptons along the contour of the polymer; and again an exponential decay for times t > τ R . Having assumed statistical independence and the validity of a single function A(t) for all modes, we compute the temporal behavior of three structural quantities: the vectorial distance between the positions of the middle monomer and the center-of-mass, the end-to-end vector, and the vector connecting two nearby reptons around the middle of the polymer. Furthermore, we study the mean-squared displacement of the center-of-mass and the middle repton, and their relation with the temporal behavior of the modes.

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Section: Introduction: Polymer Reptation and The Repton Modelmentioning

confidence: 99%

Structural modes of a polymer in the repton model

Barkema

Panja

Leeuwen

2011

The Journal of Chemical Physics

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“…We have recently studied polymers using the Rubinstein-Duke (RD) model in timedependent periodic potentials [28]. The RD model [29] is a good prototype of a complex molecule since the size of a linear polymer can be easily varied, it is strongly correlated, and the model has been actively studied for two decades [30][31][32][33][34][35][36]. There has also been in-terest towards polymers as Brownian motors recently [5,6,37].…”

Section: Introductionmentioning

confidence: 99%

Characteristics of the polymer transport in ratchet systems

Kauttonen

Merikoski

2010

Phys. Rev. E

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Molecules with complex internal structure in time-dependent periodic potentials are studied by using short Rubinstein-Duke model polymers as an example. We extend our earlier work on transport in stochastically varying potentials to cover also deterministic potential switching mechanisms, energetic efficiency, and nonuniform charge distributions. We also use currents in the nonequilibrium steady state to identify the dominating mechanisms that lead to polymer transportation and analyze the evolution of the macroscopic state ͑e.g., total and head-to-head lengths͒ of the polymers. Several numerical methods are used to solve the master equations and nonlinear optimization problems. The dominating transport mechanisms are found via graph optimization methods. The results show that small changes in the molecule structure and the environment variables can lead to large increases of the drift. The drift and the coherence can be amplified by using deterministic flashing potentials and customized polymer charge distributions. Identifying the dominating transport mechanism by graph analysis tools is found to give insight in how the molecule is transported by the ratchet effect.

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“…2(e)-(f) for N = 11 and N = 12. The situation is analogous with reptating polymers in large fields, for which a large field limit for the velocity can be derived for the Rubinstein-Duke model, having the form v ∝ exp (−EN) [35]. Similar behavior can also be expected for the ME model.…”

Section: The Limit Of Very Large Fieldsmentioning

confidence: 66%

“…Therefore the escape probability of such configurations approaches zero as the field increases. These configurations are typically called trap configurations, and they also appear for other models [35]. For the axis-directed field this means variations of U-shapes and for the diagonal field, trap configurations are V-shaped.…”

Section: The Limit Of Very Large Fieldsmentioning

confidence: 99%

Single-layer metal-on-metal islands driven by strong time-dependent forces

Kauttonen

Merikoski²

2012

Phys. Rev. E

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Non-linear transport properties of single-layer metal-on-metal islands driven with strong static and time-dependent forces are studied. We apply a semi-empirical lattice model and use master equation and kinetic Monte Carlo simulation methods to compute observables such as the velocity and the diffusion coefficient. Two types of time-dependent driving are considered: a pulsed rotated field and an alternating field with a zero net force (electrophoretic ratchet). Small islands up to 12 atoms were studied in detail with the master equation method and larger ones with simulations.Results are presented mainly for a parametrization of Cu on Cu(001) surface, which has been the main system of interest in several previous studies. The main results are that the pulsed field can increase the current in both diagonal and axis direction when compared to static field, and there exists a current inversion in the electrophoretic ratchet. Both of these phenomena are a consequence of the coupling of the internal dynamics of the island with its transport. In addition to the previously discovered "magic size" effect for islands in equilibrium, a strong odd-even effect was found for islands driven far out of equilibrium. Master equation computations revealed nonmonotonous behavior for the leading relaxation constant and effective Arrhenius parameters. Using cycle optimization methods, typical island transport mechanisms are identified for small islands.

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Polymer dynamics in repton model at large fields

Cited by 8 publications

References 31 publications

Structural modes of a polymer in the repton model

Structural modes of a polymer in the repton model

Characteristics of the polymer transport in ratchet systems

Single-layer metal-on-metal islands driven by strong time-dependent forces

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