Langevin dynamics simulations of polymer translocation through nanopores

We investigate the dynamics of polymer translocation through a nanopore using two-dimensional Langevin dynamics simulations. In the absence of an external driving force, we consider a polymer which is initially placed in the middle of the pore and study the escape time tau(e) required for the polymer to completely exit the pore on either side. The distribution of the escape times is wide and has a long tail. We find that tau(e) scales with the chain length N as tau(e) approximately N(1+2nu), where nu is the Flory exponent. For driven translocation, we concentrate on the influence of the friction coefficient xi, the driving force E, and the length of the chain N on the translocation time tau, which is defined as the time duration between the first monomer entering the pore and the last monomer leaving the pore. For strong driving forces, the distribution of translocation times is symmetric and narrow without a long tail and tau approximately E(-1). The influence of xi depends on the ratio between the driving and frictional forces. For intermediate xi, we find a crossover scaling for tau with N from tau approximately N(2nu) for relatively short chains to tau approximately N(1+nu) for longer chains. However, for higher xi, only tau approximately N(1+nu) is observed even for short chains, and there is no crossover behavior. This result can be explained by the fact that increasing xi increases the Rouse relaxation time of the chain, in which case even relatively short chains have no time to relax during translocation. Our results are in good agreement with previous simulations based on the fluctuating bond lattice model of polymers at intermediate friction values, but reveal additional features of dependency on friction.     

Stiffness and excluded volume effects on conformation and dynamics of polymers: A simulation study

This work investigates the effects of the excluded volume and especially those of the chain stiffness on the structural and dynamical properties of a model polymer chain.The theoretical framework is the same as in the recent works by Steinhauser et al.,where a Rouse approach is adopted.Our model differs in that our chains have a finite average bending angle.As in the works by Steinhauser et al.,Langevin dynamic simulations were performed without hydrodynamic interactions.Whereas this doesn’t impact the static properties we obtain,it also allows us to compare our results on dynamic properties to those predicted by Rouse theory,where hydrodynamic interactions are also neglected.Our results show that the structural properties are very sensitive to the chain stiffness,whereas the dynamic scaling laws remain the same as those by Rouse theory,with the prefactor depending on the persistence length.     

Polymer translocation in solid-state nanopores: dependence of scaling behavior on pore dimensions and applied voltage

We investigate unforced and forced translocation of a Rouse polymer (in the absence of hydrodynamic interactions) through a silicon nitride nanopore by three-dimensional Langevin dynamics simulations, as a function of pore dimensions and applied voltage. Our nanopore model consists of an atomistically detailed nanopore constructed using the crystal structure of β-Si(3)N(4). We also use realistic parameters in our simulation models rather than traditional dimensionless quantities. When the polymer length is much larger than the pore length, we find the translocation time versus chain length scales as τ ～ N(2+ν) for the unforced case and as τ ～ N((1+2ν)/(1+ν)) for the forced case. Our results agree with theoretical predictions which indicate that memory effects and tension on the polymer chain play an important role during the translocation process. We also find that the scaling exponents are highly dependent on the applied voltage (force). When the length of the polymer is on the order of the length of the pore, we do not find a continuous scaling law, but rather scaling exponents that increase as the length of the polymer increases. Finally, we investigate the scaling behavior of translocation time versus applied voltage for different polymer and pore lengths. For long pores, we obtain the theoretical scaling law of τ ～ 1/V(α), where α ? 1 for all voltages and polymer lengths. For short pores, we find that α decreases for very large voltages and/or small polymer lengths, indicating that the value of α = 1 is not universal. The results of our simulations are discussed in the context of experimental measurements made under different conditions and with differing pore geometries.     

End-monomer Dynamics in Semiflexible Polymers

Spurred by an experimental controversy in the literature, we investigate the end-monomer dynamics of semiflexible polymers through Brownian hydrodynamic simulations and dynamic mean-field theory. Precise experimental observations over the last few years of end-monomer dynamics in the diffusion of double-stranded DNA have given conflicting results: one study indicated an unexpected Rouse-like scaling of the mean squared displacement (MSD) ?r(2)(t)? ~ t(1/2) at intermediate times, corresponding to fluctuations at length scales larger than the persistence length but smaller than the coil size; another study claimed the more conventional Zimm scaling ?r(2)(t)? ~ t(2/3) in the same time range. Using hydrodynamic simulations, analytical and scaling theories, we find a novel intermediate dynamical regime where the effective local exponent of the end-monomer MSD, α(t) = d log?r(2)(t)?/d log t, drops below the Zimm value of 2/3 for sufficiently long chains. The deviation from the Zimm prediction increases with chain length, though it does not reach the Rouse limit of 1/2. The qualitative features of this intermediate regime, found in simulations and in an improved mean-field theory for semiflexible polymers, in particular the variation of α(t) with chain and persistence lengths, can be reproduced through a heuristic scaling argument. Anomalously low values of the effective exponent α are explained by hydrodynamic effects related to the slow crossover from dynamics on length scales smaller than the persistence length to dynamics on larger length scales.     

Dynamics of polymers in a particle-based mesoscopic solvent

We study the dynamics of flexible polymer chains in solution by combining multiparticle-collision dynamics (MPCD), a mesoscale simulation method, and molecular-dynamics simulations. Polymers with and without excluded-volume interactions are considered. With an appropriate choice of the collision time step for the MPCD solvent, hydrodynamic interactions build up properly. For the center-of-mass diffusion coefficient, scaling with respect to polymer length is found to hold already for rather short chains. The center-of-mass velocity autocorrelation function displays a long-time tail which decays algebraically as (Dt)(-3/2) as a function of time t, where D is the diffusion coefficient. The analysis of the intramolecular dynamics in terms of Rouse modes yields excellent agreement between simulation data and results of the Zimm model for the mode-number dependence of the mode-amplitude correlation functions.     

Dissipative particle dynamics simulations of polymer melts. I. Building potential of mean force for polyethylene and cis-polybutadiene

We present the derivation of coarse-grained force fields for two types of polymers, polyethylene (PE), and cis-polybutadiene (cis-PB), using the concept of potential of mean force. Coarse-grained force fields were obtained from microscopic simulations for several coarse-graining levels, i.e., different number of monomers lambda per mesoscopic unit called "bead." These force fields are then used in dissipative particle dynamics (DPD) simulations to study structural and dynamical properties of polymer melts of PE and cis-PB. The radial distribution functions g(R), the end-to-end distance R0, the end-to-end vector relaxation time tau, and the chain center of mass self-diffusion D(CM), are computed for different chain lengths at different coarse-graining factor lambda. Scaling laws typical of the Rouse regime are obtained for both polymers for chain lengths ranging from 6 to 50 beads. It is found that the end-to-end distance R0 obtained from DPD simulations agree well with values obtained from both microscopic simulations and experiments. The dependence of the friction coefficient used in DPD simulations versus the coarse-graining level is discussed in view of the overall scaling of the dynamical properties.     

Monte Carlo simulations of stress relaxation of entanglement-free Fraenkel chains. I. Linear polymer viscoelasticity

Shear stress relaxation modulus GS(t) curves of entanglement-free Fraenkel chains have been calculated using Monte Carlo simulations based on the Langevin equation, carrying out both in the equilibrium state and following the application of a step shear deformation. While the fluctuation-dissipation theorem is perfectly demonstrated in the Rouse-chain model, a quasiversion of the fluctuation-dissipation theorem is observed in the Fraenkel-chain model. In both types of simulations on the Fraenkel-chain model, two distinct modes of dynamics emerge in GS(t), giving a line shape similar to that typically observed experimentally. Analyses show that the fast mode arises from the segment-tension fluctuations or reflects the relaxation of the segment tension created by segments being stretched by the applied step strain-an energetic-interactions-driven process-while the slow mode arises from the fluctuations in segmental orientation or represents the randomization of the segmental-orientation anisotropy induced by the step deformation-an entropy-driven process. Furthermore, it is demonstrated that the slow mode is well described by the Rouse theory in all aspects: the magnitude of modulus, the line shape of the relaxation curve, and the number-of-beads (N) dependence of the relaxation times. In other words, one Fraenkel segment substituting for one Rouse segment, it has been shown that the entropic-force constant on each segment is not a required element to give rise to the Rouse modes of motion, which describe the relaxation modulus of an entanglement-free polymer over the long-time region very well. This conclusion provides an explanation resolving a long-standing fundamental paradox in the success of Rouse-segment-based molecular theories for polymer viscoelasticity-namely, the paradox between the Rouse segment size being of the same order of magnitude as that of the Kuhn segment (each Fraenkel segment with a large force constant HF can be regarded as basically equivalent to a Kuhn segment) and the meaning of the Rouse segment as defined in the Rouse-chain model. The general agreement observed in the comparison of the simulation and experimental results indicates that the Fraenkel-chain model, while being still relatively simple, has captured the key element in energetic interactions--the rigidity on the segment--in a polymer system.     

Interchain coupled chain dynamics of poly(ethylene oxide) in blends with poly(methyl methacrylate): coupling model analysis

Quasielastic neutron scattering and molecular dynamics simulation data from poly(ethylene oxide) (PEO)/poly(methyl methacrylate) (PMMA) blends found that for short times the self-dynamics of PEO chain follows the Rouse model, but at longer times past t(c) = 1-2 ns it becomes slower and departs from the Rouse model in dependences on time, momentum transfer, and temperature. To explain the anomalies, others had proposed the random Rouse model (RRM) in which each monomer has different mobility taken from a broad log-normal distribution. Despite the success of the RRM, Diddens et al. [Eur. Phys. Lett. 95, 56003 (2011)] extracted the distribution of friction coefficients from the MD simulations of a PEO/PMMA blend and found that the distribution is much narrower than expected from the RRM. We propose a simpler alternative explanation of the data by utilizing alone the observed crossover of PEO chain dynamics at t(c). The present problem is just a special case of a general property of relaxation in interacting systems, which is the crossover from independent relaxation to coupled many-body relaxation at some t(c) determined by the interaction potential and intermolecular coupling/constraints. The generality is brought out vividly by pointing out that the crossover also had been observed by neutron scattering from entangled chains relaxation in monodisperse homopolymers, and from the segmental α-relaxation of PEO in blends with PMMA. The properties of all the relaxation processes in connection with the crossover are similar, despite the length scales of the relaxation in these systems are widely different.     

Semi-bottom-up coarse graining of water based on microscopic simulations

The generalized dissipative particle dynamics (DPD) equation derived from the generalized Langevin equation under Markovian approximations is used to simulate coarse-grained (CG) water cells. The mean force and the friction coefficients in the radial and transverse directions needed for DPD equation are obtained directly from the all atomistic molecular dynamics (AAMD) simulations. But the dissipative friction forces are overestimated in the Markovian approximation, which results in wrong dynamic properties for the CG water in the DPD simulations. To account for the non-Markovian dynamics, a rescaling factor is introduced to the friction coefficients. The value of the factor is estimated by matching the diffusivity of water. With this semi-bottom-up mapping method, the radial distribution function, the diffusion constant, and the viscosity of the coarse-grained water system computed with DPD simulations are all in good agreement with AAMD results. It bridges the microscopic level and mesoscopic level with consistent length and time scales.     

Confinement and viscoelastic effects on chain closure dynamics

Chemical reactions inside cells are typically subject to the effects both of the cell's confining surfaces and of the viscoelastic behavior of its contents. In this paper, we show how the outcome of one particular reaction of relevance to cellular biochemistry--the diffusion-limited cyclization of long chain polymers--is influenced by such confinement and crowding effects. More specifically, starting from the Rouse model of polymer dynamics, and invoking the Wilemski-Fixman approximation, we determine the scaling relationship between the mean closure time t(c) of a flexible chain (no excluded volume or hydrodynamic interactions) and the length N of its contour under the following separate conditions: (a) confinement of the chain to a sphere of radius d and (b) modulation of its dynamics by colored Gaussian noise. Among other results, we find that in case (a) when d is much smaller than the size of the chain, t(c) ~ Nd(2), and that in case (b), t(c) ~ N(2/(2-2H)), H being a number between 1/2 and 1 that characterizes the decay of the noise correlations. H is not known a priori, but values of about 0.7 have been used in the successful characterization of protein conformational dynamics. At this value of H (selected for purposes of illustration), t(c) ~ N(3.4), the high scaling exponent reflecting the slow relaxation of the chain in a viscoelastic medium.     

Mass accommodation mechanism of water through monolayer films at water∕vapor interface

The mass transfer dynamics at water∕vapor interface through monolayer films was theoretically investigated by a combination of molecular dynamics and Langevin dynamics simulations. The rare events of mass accommodation are sampled by the Langevin simulation with sufficient statistical accuracy, on the basis of the free energy and friction profiles obtained by the molecular dynamics simulation. The free energy profiles exhibit a barrier in the long-chain monolayers, and the mechanism of the barrier is elucidated in relation to the "water finger" formation. The present Langevin simulation well described the remarkable dependence of the mass accommodation coefficient on the chain length and surface density. The transition state theory for the barrier passage remarkably overestimates the mass accommodation coefficient, and the Kramers or Grote-Hynes theory may not be appropriate, due to large variation of the friction in the entrance channel and∕or broad barrier.     

Why does the rouse model fairly describe the dynamic characteristics of polymer melts at molecular masses below critical mass?

Generalization of the Rouse model without any use of the postulates concerning the Gaussian distribution of the vector connecting the ends of segments is advanced. In the initial (in general, nonlinear) Langevin equations, self-averaging over continuous fragments of a macromolecule naturally defines a linear term for the tagged chain, and this term differs from the entropy term of the classical Rouse model only by the numerical coefficient. According to the inertia-free approximation, the initial decay rates of correlation functions for the normal modes are described by the Rouse model independently of the character of fluctuations of the vector connecting the ends of the Kuhn segment. This statement is valid for any moment if the initial Langevin equations are treated in terms of the approximation of dynamic self-consistency. Simulation of the Fraenkel chains by the method of Brownian dynamics shows that decay of autocorrelation functions of shortwave normal modes is fairly described by the linearized equations for a given model of a chain and that the Rouse equation can be used for the long-wave modes. The results of this study make it possible to explain a marked difference between the lengths of the Kuhn and Rouse segments that is estimated from static and dynamic experiments.     

Modeling real dynamics in the coarse-grained representation of condensed phase systems

This work presents a systematic multiscale methodology to provide a more faithful representation of real dynamics in coarse-grained molecular simulation models. The theoretical formalism is based on the recently developed multiscale coarse-graining (MS-CG) method [S. Izvekov and G. A. Voth, J. Phys. Chem. B. 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] and relies on the generalized Langevin equation approach and its simpler Langevin equation limit. The friction coefficients are determined in multiscale fashion from the underlying all-atom molecular dynamics simulations using force-velocity and velocity-velocity correlation functions for the coarse-grained sites. The diffusion properties in the resulting CG Brownian dynamics simulations are shown to be quite accurate. The time dependence of the velocity autocorrelation function is also well-reproduced relative to the all-atom model if sufficient resolution of the CG sites is implemented.     

Self-affine roughness influence on the friction coefficient for rubbers onto solid surfaces

In this paper we investigate the influence of self-affine roughness on the friction coefficient mu(f) of a rubber body under incomplete contact onto a solid surface. The roughness is characterized by the rms amplitude w, the correlation length xi, and the roughness exponent H. It is shown that with increasing surface roughening at short and/or long length scales (decreasing H and/or increasing ratio w/xi, respectively), the maximum of the friction coefficient mu(f) shifts to lower sliding velocities. The latter occurs only for conditions of incomplete contact for small contact length scales lambda (xi).     

Equilibrium conformational dynamics of a polymer in a solvent

Molecular dynamics simulations were used to study the conformational dynamics of a bead-spring model polymer in an explicit solvent under good solvent conditions. The dynamics of the polymer chain were investigated using an analysis of the time autocorrelation functions of the Rouse coordinates of the polymer chain. We have investigated the variation of the correlation functions with polymer chain length N, solvent density rho, and system size. The measured initial decay rates gamma(p) of the correlation functions were compared with the predictions from a theory of polymer dynamics which uses the Oseen tensor to describe hydrodynamic interactions between monomers. Over the range of chain lengths considered (N = 30-60 monomers), the predicted scaling of gamma(p) proportional to N(-3nu) was observed at high rho, where nu is the polymer scaling exponent. The predicted gamma(p) are generally higher than the measured values. This discrepancy increases with decreasing rho, as a result in the breakdown in the conditions required for the Oseen approximation. The agreement between theory and simulation at high rho improves considerably if the theoretical expression for gamma(p) is modified to avoid sum-to-integral approximations, and if the values of (R(p)2), which are used in the theory, are taken directly from the simulation rather than being calculated using approximate scaling relations. The observed finite-size scaling of gamma(p) is not quantitatively consistent with the theoretical predictions.     

Local and chain dynamics in miscible polymer blends: A Monte Carlo simulation study

Local chain structure and local environment play an important role in the dynamics of polymer chains in miscible blends. In general, the friction coefficients that describe the segmental dynamics of the two components in a blend differ from each other and from those of the pure melts. In this work, we investigate polymer blend dynamics with Monte Carlo simulations of a generalized bond fluctuation model, where differences in the interaction energies between nonbonded nearest neighbors distinguish the two components of a blend. Simulations employing only local moves and respecting a no bond crossing condition were carried out for blends with a range of compositions, densities, and chain lengths. The blends investigated here have long time dynamics in the crossover region between Rouse and entangled behavior. In order to investigate the scaling of the self-diffusion coefficients, characteristic chain lengths N(c) are calculated from the packing length of the chains. These are combined with a local mobility mu determined from the acceptance rate and the effective bond length to yield characteristic self-diffusion coefficients D(c)=muN(c). We find that the data for both melts and blends collapse onto a common line in a graph of reduced diffusion coefficients DD(c) as a function of reduced chain length NN(c). The composition dependence of dynamic properties is investigated in detail for melts and blends with chains of length N=20 at three different densities. For these blends, we calculate friction coefficients from the local mobilities and consider their composition and pressure dependence. The friction coefficients determined in this way show many of the characteristics observed in experiments on miscible blends.     

Dynamic evolution in coarse-grained molecular dynamics simulations of polyethylene melts

We test a coarse-grained model assigned based on united atom simulations of C50 polyethylene to seven chain lengths ranging from C76 to C300. The prior model accurately reproduced static and dynamic properties. For the dynamics, the coarse-grained time evolution was scaled by a constant value [t=alphatCG] predictable based on the difference in intermolecular interactions. In this contribution, we show that both static and dynamic observables have continued accuracy when using the C50 coarse-grained force field for chains representing up to 300 united atoms. Pair distribution functions for the longer chain systems are unaltered, and the chain dimensions present the expected N0.5 scaling. To assess dynamic properties, we compare diffusion coefficients to experimental values and united atom simulations, assign the entanglement length using various methods, examine the applicability of the Rouse model as a function of N, and compare tube diameters extracted using a primitive path analysis to experimental values. These results show that the coarse-grained model accurately reproduces dynamic properties over a range of chain lengths, including systems that are entangled.     

Dynamics of fluids near the consolute critical point: a molecular-dynamics study of the Widom-Rowlinson mixture

Molecular-dynamics simulations are presented for the dynamic behavior of the Widom-Rowlinson mixture [B. Widom, and J. S. Rowlinson, J. Chem. Phys. 52, 1670 (1970)] at its critical point. This model consists of two components where like species do not interact and unlike species interact via a hard-core potential. Critical exponents are obtained from a finite-size scaling analysis. The self-diffusion coefficient shows no anomalous behavior near the critical point. The shear viscosity and thermal conductivity show no divergent behavior for the system sizes considered, although there is a significant critical enhancement. The mutual diffusion coefficient, D(AB), vanishes as D(AB) approximately xi(-1.26 +/- 0.08), where xi is the correlation length. This is different from the renormalization-group (D(AB) approximately xi(-1.065)) mode coupling theory (D(AB) approximately xi(-1)) predictions. The theories and simulations can be reconciled if we assume that logarithmic corrections to scaling are important.     

Dissipative dynamics within the electronic friction approach: the femtosecond laser desorption of H2/D2 from Ru(0001)

An electronic friction approach based on Langevin dynamics is used to describe the multidimensional (six-dimensional) dynamics of femtosecond laser induced desorption of H(2) and D(2) from a H(D)-covered Ru(0001) surface. The paper extends previous reduced-dimensional models, using a similar approach. In the present treatment forces and frictional coefficients are calculated from periodic density functional theory (DFT) and essentially parameter-free, while the action of femtosecond laser pulses on the metal surface is treated by using the two-temperature model. Our calculations shed light on the performance and validity of various adiabatic, non-adiabatic, and Arrhenius/Kramers type kinetic models to describe hot-electron mediated photoreactions at metal surfaces. The multidimensional frictional dynamics are able to reproduce and explain known experimental facts, such as strong isotope effects, scaling of properties with laser fluence, and non-equipartitioning of vibrational, rotational, and translational energies of desorbing species. Further, detailed predictions regarding translations are made, and the question for the controllability of photoreactions at surfaces with the help of vibrational preexcitation is addressed.     

Multiple time scale dynamics of distance fluctuations in a semiflexible polymer: a one-dimensional generalized Langevin equation treatment

Time-dependent fluctuations in the distance x(t) between two segments along a polymer are one measure of its overall conformational dynamics. The dynamics of x(t), modeled as the coordinate of a particle moving in a one-dimensional potential well in thermal contact with a reservoir, is treated with a generalized Langevin equation whose memory kernel K(t) can be calculated from the time-correlation function of distance fluctuations C(t) identical with x(0)x(t). We compute C(t) for a semiflexible continuum model of the polymer and use it to determine K(t) via the GLE. The calculations demonstrate that C(t) is well approximated by a Mittag-Leffler function and K(t) by a power-law decay on time scales of several decades. Both functions depend on a number of parameters characterizing the polymer, including chain length, degree of stiffness, and the number of intervening residues between the two segments. The calculations are compared with the recent observation of a nonexponential C(t) and a power law K(t) in the conformational dynamics within single molecule proteins [Min et al., Phys. Rev. Lett. 94, 198302 (2005)].