Noise Effects in Polymer Dynamics

Journal of Statistical Mechanics: Theory and Experiment, 2009

In this work we study the noise induced effects on the dynamics of short polymers crossing a potential barrier, in the presence of a metastable state. An improved version of the Rouse model for a flexible polymer has been adopted to mimic the molecular dynamics by taking into account both the interactions between adjacent monomers and introducing a Lennard-Jones potential between all beads. A bending recoil torque has also been included in our model. The polymer dynamics is simulated in a two-dimensional domain by numerically solving the Langevin equations of motion with a Gaussian uncorrelated noise. We find a nonmonotonic behaviour of the mean first passage time and the most probable translocation time, of the polymer centre of inertia, as a function of the polymer length at low noise intensity. We show how thermal fluctuations influence the motion of short polymers, by inducing two different regimes of translocation in the molecule transport dynamics. In this context, the role played by the length of the molecule in the translocation time is investigated.

Acta Physica Polonica Series B

In this paper, we examine the influence of a spatially correlated noise on a 2D polymer-like particle. The molecule is modeled with harmonic potential for bonds and angular interactions and a global Lennard-Jones potential. We present a method for generating a spatially correlated noise if the time and spatial terms in the correlation function factorize. The dynamics of polymer's shape transformation process is investigated by means of Fourier analysis. An increase in correlation length results in the environmentally induced stiffening of the chain.

Polymer Journal, 1974

Studies are made to examine the validity of the de-Gennes' theory of the stochastic motion of a polymer chain in the presence of fixed obstacles. The two-dimensional cases are treated. The topological requirement that the chain cannot intersect any of the obstacles is imposed on the stochastic motion. Observations are made on the diffusion coefficient of the center of mass, the relaxation time of the end-to-end vector and the mean-square displacement of a monomer, by varying the chain length and the concentration of the obstacles. The results are compared with those of de-Gennes' theory and Rouse's. It is found that de-Gennes' theory provides a reasonable explanation for the slow relaxation phenomena• under topological restrictions. Some minor revisions are made to obtain better agreement. It is found that, for the fast relaxation phenomena, the agreement is not good even if the concentration of the obstacles is sufficiently large. The condition for the applicability of the de-Gennes' theory is also discussed. The transition from the Rouse-type motion to the de-Gennes-type motion is observed and found to be rather diffuse.

2011

We consider the translocation of a one-dimensional polymer through a pore channel helped by a motor driven by a dichotomous noise with time exponential correlation. We are interested in the study of the translocation time, mean velocity and stall force of the system as a function of the mean driving frequency. We find a monotonous translocation time, in contrast with the mean velocity which shows a pronounced maximum at a given frequency. Interestingly, the stall force shows a nonmonotonic behavior with the presence of a minimum. The influence of the spring elastic constant to the mean translocation times and velocities is also presented.

Europhysics Letters (EPL), 2004

We use an off-lattice bead-spring model of a self-avoiding polymer chain immersed in a 3-dimensional quenched random medium to study chain dynamics by means of a Monte-Carlo (MC) simulation. The chain center of mass mean-squared displacement as a function of time reveals two crossovers which depend both on chain length N and on the degree of Gaussian disorder ∆. The first one from normal to anomalous diffusion regime is found at short time τ1 and observed to vanish rapidly as τ1 ∝ ∆ −11 with growing disorder. The second crossover back to normal diffusion, τ2, scales as τ2 ∝ N 2ν+1 f (N 2−3ν ∆) with f being some scaling function. The diffusion coefficient DN depends strongly on disorder and drops dramatically at a critical dispersion ∆c ∝ N −2+3ν of the disorder potential so that for ∆ > ∆c the chain center of mass is practically frozen. The time-dependent Rouse modes correlation function Cp(t) reveals a characteristic plateau at ∆ > ∆c which is the hallmark of a non-ergodic regime. These findings agree well with our recent theoretical predictions.

Acta Physica Polonica B, 2013

This paper provides additional insight into the effect of spontaneous unfolding of the model polymeric chain driven by spatially correlated noise, described in M. Majka, P.F. Góra, Phys. Rev. E86, 051122 (2012). We examine the statistical data on the linearized chain substructures to find that the global unfolding effect arises mainly from the cumulation of short, 2-segment-long fragments, scattered along the chain. This supports an alternative view of spatially correlated noise as both the source of disturbance and the conformation preserving factor.

Macromolecules, 1989

Dynamic properties of a self-avoiding walk chain, which performs Brownian motion between randomly distributed impenetrable fixed obstacles, have been investigated by Monte Carlo simulations. Analogous to the case of a random walk chain in random media, the chain dynamics is found to be slower than even reptation demonstrated by a stronger inverse dependence of the chain diffusion coefficient on chain length. This phenomenon is attributed to the slowing down of the chain due to the presence of bottlenecks in the random medium. The bottlenecks squeeze the chain and reduce the chain entropy setting up entropic barriers at random locations. A scaling analysis is adopted to account for the effects of such entropic barriers on chain diffusion. The simulation data are consistent with the predictions of the scaling arguments demonstrating that chain diffusion in random media is controlled by the entropic barriers of the media.

Physical Review E, 2012

The problem of a spatially correlated noise affecting a complex system is studied in this paper. We present a comprehensive analysis of a 2D model polymer chain, driven by the spatially correlated Gaussian noise, for which we have varied the amplitude and the correlation length. The chain model is based on a bead-spring approach, enriched with a global Lennard-Jones potential and angular interactions. We show that spatial correlations in the noise inhibit the chain geometry dynamics, enhancing the preservation of the polymer shape. This is supported by the analysis of correlation functions of both the module length and angles between neighboring modules, which have been measured for the noise amplitude ranging over 3 orders of magnitude. Moreover, we have observed the correlation length dependent beads motion synchronization, and the spontaneous polymer unfolding, resulting from an interplay between chain potentials and the spatially structured noise.

2017

In the presence of active noise, flexible and semiflexible polymers exhibit drastically different conformational and dynamical features compared to the case of thermal (white) noise only. For a non-Markovian exponentially correlated temporal noise (colored noise), flexible polymers swell with increasing noise strength, whereas semiflexible polymers shrink first and, for larger noise strengths, swell similar to flexible polymers. Thereby, a suitable treatment of the finite polymer contour length is essential. The finite contour length implies a strong dependence of the polymer relaxation times on the noise strengths. We discuss the conformational and dynamical aspects in terms of an analytical model, adopting the continuous Gaussian semiflexible polymer description. Moreover, results of computer simulations are shown and compared with analytical results.

Physical Review Letters, 2007

We present a neutron scattering investigation on a miscible blend of two polymers with greatly different glass-transition temperatures T g . Under such conditions, the nearly frozen high-T g component imposes a random environment on the mobile chain. The results demand the consideration of a distribution of heterogeneous mobilities in the material and demonstrate that the larger scale dynamics of the fast component is not determined by the average local environment alone. This distribution of mobilities can be mapped quantitatively on the spectrum of local relaxation rates measured at high momentum transfers.