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We use the bond fluctuation model (BFM) to study the pore-blockade times of a translocating polymer of length N in two dimensions, in the absence of external forces on the polymer (i.e., unbiased translocation) and hydrodynamic interactions (i.e., the polymer is a Rouse polymer), through a narrow pore. Earlier studies using the BFM concluded that the pore-blockade time scales with polymer length as τd∼Nβ, with β=1+2ν, whereas some recent studies using different polymer models produce results consistent with β=2+ν, originally predicted by us. Here ν is the Flory exponent of the polymer; ν=0.75 in 2D. In this paper we show that for the BFM if the simulations are extended to longer polymers, the purported scaling τd∼N1+2ν ceases to hold. We characterize the finite-size effects, and study the mobility of individual monomers in the BFM. In particular, we find that in the BFM, in the vicinity of the pore the individual monomeric mobilities are heavily suppressed in the direction perpendicular to the membrane. After a modification of the BFM which counters this suppression (but possibly introduces other artifacts in the dynamics), the apparent exponent β increases significantly. Our conclusion is that BFM simulations do not rule out our theoretical prediction for unbiased translocation, namely, β=2+ν. [ABSTRACT FROM AUTHOR]

This paper investigates the conformational and scaling properties of long linear polymer chains. These investigations are done with the aid of Monte Carlo (MC) and molecular dynamics (MD) simulations. Chain lengths that comprise several orders of magnitude to reduce errors of finite size scaling, including the effect of solvent quality, ranging from the athermal limit over the θ-transition to the collapsed state of chains are investigated. Also the effect of polydispersity on linear chains is included which is an important issue in the real fabrication of polymers. A detailed account of the hybrid MD and MC simulation model and the exploited numerical methods is given. Many results of chain properties in the extrapolated limit of infinite chain lengths are documented and universal properties of the chains within their universality class are given. An example of the difference between scaling exponents observed in actual solvents and those observed in the extremes of “good solvents” and “θ-solvents” in simulations is provided by comparing simulation results with experimental data on low density polyethylene. This paper is concluded with an outlook on the extension of this study to branched chain systems of many different branching types. [ABSTRACT FROM AUTHOR]

Morphology of symmetric ABCD tetrablock quaterpolymers in melt was studied by the Monte Carlo (MC) simulation, where the volume fractions of the block chains, f, kept the relationships of fA = fD and fB = fC, and the volume fraction of the two mid-blocks φ was defined as φ = fB + fC. Previous self-consistent field theory for ABCD reported morphological change including several structures; however, the scope was limited within a two-dimensional system. To the contrary, in this paper, MC simulations were carried out in three dimensions with changing the φ value finely, which resulted in finding a tetracontinuous structure in the range of 0.625 ⩽ φ ⩽ 0.75. Moreover the tetracontinuous structure has been found to be the gyroid structure, and the mean curvature of the B/C interface is nearly zero. We concluded that the B/C interface must be the Schoen gyroid surface, one of three-dimensional periodic minimal surfaces. The geometrical nature of the A/B interface should be equivalent to that of the C/D interface, and they stand as level surfaces to the Schoen gyroid surface. [ABSTRACT FROM AUTHOR]

In this paper, we construct an effective model for the dynamics of an excluded-volume chain under confinement by extending the formalism of Rouse modes. We make specific predictions about the behavior of the modes for a single polymer confined to a tube. The results are tested against Monte Carlo simulations using the bond-fluctuation algorithm which uses a lattice representation of the polymer chain with excluded-volume effects. [ABSTRACT FROM AUTHOR]

Molecular mechanisms of crystal growth and homogeneous nucleation from the melt of polyethylene-like linear polymer are investigated by molecular dynamics simulations. The present paper is aimed at extending our previous work with respect to the system size and the boundary condition, thereby enabling detailed studies on the structures of sufficiently large lamellae and fully equilibrated melt. Lamellae of uniform thickness but with marked tapered edges are found to grow at constant velocity from the substrate. Three-dimensional shape of the growing lamellae exhibits peculiar undulation at the growth front, the origin of which is suggested to be the inhomogeneous thickness distribution within the lamellae. Trajectories of chains crystallizing onto the growth front reveal an unexpected pathway for chain folding, where a partially attached chain stem forms a new fold by plunging its head back into a neighboring stem position through slithering snake motions of the chain. Detailed statistics of folds and cilia show that the folds are rather neat and mostly make re-entries into the nearest or the second or third nearest neighboring stem positions, whereas the cilia are generally short but with a small number of longer cilia forming thick amorphous layers. Structure of supercooled melt investigated versus temperature reveals that, at moderate degree of supercooling, the overall chain conformation remains Gaussian random coil but the persistent length of chains increases monotonically with increasing supercooling. Exceptions are at the largest supercooling where homogeneous nucleation takes place; usual melt structure becomes rapidly unstable and emerges many crystallites of random orientations. During early 10–20 ns after the quench, density of melt, radius of gyration of chains, and fraction of kinked bonds show marked alterations. These structural changes are highly cooperative and are considered simply due to the emergence of many embryonic crystals in the melt. Conformations of the chains forming nuclei are also traced to reveal that the homogeneous nuclei are fringed micelle like aggregates of chains, but the chains as a whole have folded conformations, which are similar to those reported in previous simulations on a single polyethylene in a vacuum. [ABSTRACT FROM AUTHOR]

We present a computer simulation model of polymer melts representing each chain as one single particle. Besides the position coordinate of each particle, we introduce a parameter nij for each pair of particles i and j within a specified distance from each other. These numbers, called entanglement numbers, describe the deviation of the system of ignored coordinates from its equilibrium state for the given configuration of the centers of mass of the polymers. The deviations of the entanglement numbers from their equilibrium values give rise to transient forces, which, together with the conservative forces derived from the potential of mean force, govern the displacements of the particles. We have applied our model to a melt of C800H1602 chains at 450 K and have found good agreement with experiments and more detailed simulations. Properties addressed in this paper are radial distribution functions, dynamic structure factors, and linear as well as nonlinear rheological properties. [ABSTRACT FROM AUTHOR]

It is the purpose of this paper to establish a bottom-up multiscale approach for dendronized polymers. Based on our understanding of the phenomenology of an atomistic model for this class of polymers, we introduce a “Janus chain” (JC) model which adds a vectorial degree of freedom (Janus vector)—related to the sectorial amphiphilicity—to each segment of the linear backbone of a (classical) uncharged, semiflexible, and multibead chain representation of a polymer. The JC features induced polymeric curvature and ultimately triggers complexation. JC parameters related to the topology and chemical details are obtained from the atomistic level. Available experimental observations including the formation of superstructures and double helical conformations are well reproduced by the JC model. JC is efficiently solved via Brownian dynamics simulation and can be seen as a member of a universality class which is one (two) level(s) above the magnetic (semiflexible) chain model. It therefore should allow to model not only dendronized polymers but also structures belonging to the same class—exhibiting induced (or spontaneous) curvature—such as single stranded DNA and actin filaments. [ABSTRACT FROM AUTHOR]

This paper is aimed to develop a Brownian dynamics simulation method for strongly confined semiflexible polymers where numerical simulation plays an indispensable role in complementing theory and experiments. A wormlike chain under strong confinement is modeled as a string of virtual spherical beads connected by inextensible rods with length varying according to the confinement intensity of the chain measured by the Odijk deflection length. The model takes hydrodynamic interactions into account. The geometrical constraints associated with the inextensible rods are realized by the so-called linear constraint solver. The model parameters are studied by quantitatively comparing the simulated properties of a double-stranded DNA chain with available experimental data and theoretical predictions. [ABSTRACT FROM AUTHOR]

It has been suggested that, due to topological constraints, rings in the melt may assume a more compact shape than Gaussian chains. In this paper, we exploit the availability of narrow fractions of perdeuterated linear and cyclic polydimethylsiloxane (PDMS) and, through the analysis of the small angle neutron scattering (SANS) profiles, demonstrate the difference in scattering properties of linear and cyclic PDMS molecules. As expected for Gaussian chains, for the H/D linear PDMS samples, log-log plots of the scattered intensity versus scattering vector Q display a Q(-2) dependence. However, for H/D cyclic blends, the scaling exponent is higher than 2, as predicted by computer simulations reported in the literature. We show that cyclic molecules in bulk display the characteristic maximum in plots of scattered intensity versus Q(-2) that is expected on the basis of Monte Carlo calculations and from the Casassa equation [E. F. Casassa, J. Polym. Sci. A 3, 605 (1965)]. It is also shown that, for rings, the Debye equation [P. Debye, J. Appl. Phys. 15, 338 (1944)] is no longer appropriate to describe the SANS profiles of H/D cyclic blends, at least up to Mw≈10 000. For these samples, the Casassa form factor gives a better representation of the SANS data and we show that this function which was developed for monodisperse cyclics is still adequate to describe our slightly polydisperse samples. Deviations from all above observations are noted for Mw>11 000 and are attributed to partial contamination of cyclic samples with linear chains. The failure of both the Debye and the Casassa form factors could be due to contamination of the cyclic fractions by linear polymers or to a real conformational change. [ABSTRACT FROM AUTHOR]

Using methods adapted from the simulation of suspension dynamics, we have developed a Brownian dynamics algorithm with multibody hydrodynamic interactions for simulating the dynamics of polymer molecules. The polymer molecule is modeled as a chain composed of a series of inextensible, rigid rods with constraints at each joint to ensure continuity of the chain. The linear and rotational velocities of each segment of the polymer chain are described by the slender-body theory of Batchelor [J. Fluid Mech. 44, 419 (1970)]. To include hydrodynamic interactions between the segments of the chain, the line distribution of forces on each segment is approximated by making a Legendre polynomial expansion of the disturbance velocity on the segment, where the first two terms of the expansion are retained in the calculation. Thus, the resulting linear force distribution is specified by a center of mass force, couple, and stresslet on each segment. This method for calculating the hydrodynamic interactions has been successfully used to simulate the dynamics of noncolloidal suspensions of rigid fibers [O. G. Harlen, R. R. Sundararajakumar, and D. L. Koch, J. Fluid Mech. 388, 355 (1999); J. E. Butler and E. S. G. Shaqfeh, J. Fluid Mech. 468, 204 (2002)]. The longest relaxation time and center of mass diffusivity are among the quantities calculated with the simulation technique. Comparisons are made for different levels of approximation of the hydrodynamic interactions, including multibody interactions, two-body interactions, and the “freely draining” case with no interactions. For the short polymer chains studied in this paper, the results indicate a difference in the apparent scaling of diffusivity with polymer length for the multibody versus two-body level of approximation for the hydrodynamic interactions.© 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Large scale molecular dynamics and grand canonical Monte Carlo simulation techniques are used to study the behavior of the interdiffusion of a solvent into an entangled polymer matrix as the state of the polymer changes from a melt to a glass. The weight gain by the polymer increases with time t as t1/2 in agreement with Fickian diffusion for all cases studied, although the diffusivity is found to be strongly concentration dependent especially as one approaches the glass transition temperature of the polymer. The diffusivity as a function of solvent concentration determined using the one-dimensional Fick’s model of the diffusion equation is compared to the diffusivity calculated using the Darken equation from simulations of equilibrated solvent-polymer solutions. The diffusivity calculated using these two different approaches are in good agreement. The behavior of the diffusivity strongly depends on the state of the polymer and is related to the shape of the solvent concentration profile.© 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present the results of numerical simulations of the irreversible aggregation process for self-avoiding flexible polymers in three dimensions. We have paid special attention to two experimentally interesting systems: telechelic ionomers and reverse micelles. The dynamics used in this paper to simulate the clustering process is based on Eden’s method. This dynamics was previously introduced by us for two-dimensional systems. We find a scaling relation between the radius of gyration of the cluster Rg, the chain length n and the number of chains N in the cluster in the form Rg∼nαNβ. The values of the exponents α and β calculated from the numerical simulations are somewhat lower than those predicted by Flory’s classical theory. We argue that the lower values of the exponents are possibly due to the finite size of the clusters and the presence of higher order interaction terms not considered in Flory’s theory. [ABSTRACT FROM AUTHOR]

By employing the Massieu formalism presented in the preceding paper, Monte Carlo methods and extrapolation techniques are combined to simulate polymers with chain-length polydispersity. Semigrand canonical and grand canonical ensembles supplemented by identity exchange moves and expanded-ensemble moves have been tailored to simulate both thermodynamic properties and the structure of various coarse-grained model systems. It is demonstrated that the proposed methods can be used to simulate systems with arbitrary molecular weight distribution (e.g., to match experimental data), bulk-pore partitioning of polymer solutions, and liquid–liquid equilibrium of polydisperse polymer melts. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We propose a novel path sampling method based on the Onsager-Machlup (OM) action by generalizing the multiscale enhanced sampling technique suggested by Moritsugu and co-workers [J. Chem. Phys. 133, 224105 (2010)]. The basic idea of this method is that the system we want to study (for example, some molecular system described by molecular mechanics) is coupled to a coarse-grained (CG) system, which can move more quickly and can be computed more efficiently than the original system. We simulate this combined system (original + CG system) using Langevin dynamics where different heat baths are coupled to the two systems. When the coupling is strong enough, the original system is guided by the CG system, and is able to sample the configuration and path space with more efficiency. We need to correct the bias caused by the coupling, however, by employing the Hamiltonian replica exchange, where we prepare many path replicas with different coupling strengths. As a result, an unbiased path ensemble for the original system can be found in the weakest coupling path ensemble. This strategy is easily implemented because a weight for a path calculated by the OM action is formally the same as the Boltzmann weight if we properly define the path 'Hamiltonian.' We apply this method to a model polymer with Asakura-Oosawa interaction, and compare the results with the conventional transition path sampling method. [ABSTRACT FROM AUTHOR]

We present a theoretical approach to scale the artificially fast dynamics of simulated coarse-grained polymer liquids down to its realistic value. As coarse graining affects entropy and dissipation, two factors enter the rescaling: inclusion of intramolecular vibrational degrees of freedom and rescaling of the friction coefficient. Because our approach is analytical, it is general and transferable. Translational and rotational diffusion of unentangled and entangled polyethylene melts, predicted from mesoscale simulations of coarse-grained polymer melts using our rescaling procedure, are in quantitative agreement with united-atom simulations and with experiments. [ABSTRACT FROM AUTHOR]

The scanning simulation method is applied to a model of polymer adsorption in which a single self-avoiding walk is terminally attached to an attracting impenetrable surface on a simple cubic lattice. Relatively long chains are studied, of up to 1000 steps, which enable us to obtain new estimates for the reciprocal transition temperature |ε|/kBTa=θa =0.291±0.001 (ε is the interaction energy of a monomer with the surface), the crossover exponent [lowercase_phi_synonym]=0.530±0.007 and the free energy exponents at Ta, γ1SB =1.304±0.006 and γ11SB =0.805±0.015. At T=∞ we obtain, γ1=0.687±0.005, γ11=-0.38±0.02, and the effective coordination number q=4.6839±0.0001, which are in good agreement with estimates obtained by other methods. At T>Ta we demonstrate the existence of strong correction to scaling for the perpendicular part of the mean-square end-to-end distance ⊥ and for the monomer concentration profile ρ(z) (z is the distance from the surface). At T=∞ the leading correction to scaling term for ⊥ is c/Nψ, where c≊-0.9 and ψ≊0.4 is close to 0.5 obtained for the random walk model in the preceding paper. This means that the asymptotic regime, in which these corrections become negligible, corresponds to a large polymer length that is not realized experimentally. Close enough to Ta we demonstrate for our lattice model the validity of various scaling forms predicted by Eisenriegler, Kremer, and Binder [J. Chem. Phys. 77, 6296 (1982)] for a continuum model on the basis of the n-vector model. [ABSTRACT FROM AUTHOR]

The adsorption transition and the structure of semiflexible adsorbed macromolecules are studied by a molecular dynamics simulation of a coarse-grained, bead-spring type model. Varying chain length N and stiffness κ (which is proportional to the persistence length ℓp in d = 3 dimensions) as well as the strength ϵwall of the adsorption potential, the adsorbed monomer fraction, orientational bond order parameter, and chain linear dimensions are studied. In the simulations, excluded volume interactions normally are included but can be "switched off," and thus, the influence of excluded volume (leading to deviations from predictions of the wormlike chain model) can be identified. It is shown that the variation in the adsorption threshold ϵ w a l l c r with ℓp is compatible with the predicted law ϵ w a l l c r ∝ ℓ p − 1 / 3 . In the vicinity of the adsorption threshold, the coils are still three-dimensional, and for large ℓp, the effect of the excluded volume is almost negligible, while for strongly adsorbed chains it is always felt. Near the transition, the decay length of orientational correlations along the chain contour increases gradually from ℓp to 2ℓp. While the latter value is expected for strictly two-dimensional chains from the Kratky–Porod model, this model is inaccurate for the description of lateral chain dimensions of long, strongly adsorbed, semiflexible polymers due to its neglect of excluded volume. The significance of these findings for the interpretation of pertinent experiments is briefly discussed. [ABSTRACT FROM AUTHOR]

The effective diffusivity in a polymer matrix modified with inclusions is usually calculated based on Kalnin-Kotomin's model [J. R. Kalnin, E. A. Kotomin, and J. Maier, J. Phys. Chem. Solids 63, 449-456 (2002)], which extends the well known Maxwell-Garnett formula. Kalnin-Kotomin's model correctly predicts effective diffusivity for stationary diffusion or for infinite media. In the present paper diffusion in composite media is studied for finite systems under transient conditions. The process of diffusion is modeled numerically and effective diffusion coefficient in the transient state is estimated, which, under certain conditions, is different from the predictions of the Kalnin-Kotomin's model. An analytical model is proposed to explain deviations of the transient effective coefficient of diffusion from the stationary case. [ABSTRACT FROM AUTHOR]

Polymers in confined porous environments are ubiquitous throughout biology, physics, materials science, and engineering. Several experiments have suggested that in some porous environments, chain dynamics can become extremely slow. While phenomenological explanations exist, the exact mechanisms for these slow dynamics have not been fully characterized. In this work, we initiate a joint simulation–theory study to investigate chain packing and dynamics in a static porous environment. The main theoretical concept is the free energy of the chain partitioning into several chambers of the porous environment. Both the theoretical results and Langevin dynamics simulations show that chain packing in each of the chambers is predominantly independent of chain length; it is determined by the maximal packing of segments in each chamber. Dynamically, short chains (compared to the chamber size) become trapped in a single chamber and dynamics become extremely slow, characteristic of an Ogston sieving-like behavior. For longer chains, on the other hand, a hierarchy of slow dynamics is observed due to entropic trapping, characterized by sub-diffusive behavior and a temporary plateau in the mean square displacement. Due to the slow nature of the dynamics, the inevitable long-time diffusive behavior of the chains is not captured by our simulations. Theoretically, the slow dynamics are understood in terms of a free energy barrier required to thread the chain from one chamber to the next. There is overall qualitative and quantitative agreement between simulations and theory. This work provides foundations for a better understanding of how chain dynamics are affected by porous environments. [ABSTRACT FROM AUTHOR]

We analyze the electroosmotic flow (EOF) of an electrolytic solution in a polymer coated capillary electrophoresis tube. The polymeric density, charge, thickness, and the capillary tube charge vary as a function of pH and produce a non-trivial modulation of the EOF, including a flow reversal at acid pH conditions. By means of a theoretical argument and numerical simulations, we recover the experimental curve for the EOF, providing a firm approach for predictive analysis of electroosmosis under different polymeric coating conditions. A proposed application of the approach is to determine the near-wall charge of the coating to be used for further quantitative analysis of the electroosmotic flow and mobility. [ABSTRACT FROM AUTHOR]

The second virial coefficient, A2, for trivial-ring polymers in dilute condition was estimated from a Metropolis Monte Carlo (MC) simulation, and the temperature dependence of A2 has been discussed with their Flory's scaling exponent, v, in Rg ∝ Nv, where Rg is radius of gyration of a polymer molecule. A limited but not too small number of polymer molecules were employed in the simulation, and the A2 values at various temperatures were calculated from the molecular density fluctuation in the solution. In the simulation, the topology of ring polymers was kept, since chain crossing was prohibited. The excluded volume effects can be screened by the attractive force between segments, which depends on the temperature, Tα, defined in the Metropolis MC method. Linear and trivial-ring polymers have the v value of 1/2 at Tα = 10.605 and 10.504. At Tα = 10.504, the excluded volume effects are screened by the attractive force generated between segments in a ring polymer, but the A2 value for ring polymers is positive. Thus, the temperature at A2 = 0 for a ring polymer is lower than that at v = 1/2, and this fact can be explained with the following two reasons. (a) Rg value for a ring polymer is much smaller than that for a linear polymer at the same temperature and molecular weight, where interpenetration of a ring polymer chain into neighboring chains is apparently less than a linear chain. (b) The conformation of trivial rings can be statistically described as a closed random walk at v = 1/2, but their topologies are kept, being produced topological constraints, which strongly relate not only to the long-distance interaction between segments in a molecule but also the inter-molecular interaction. [ABSTRACT FROM AUTHOR]

The statistical theory of polymers tethered around the inner surface of a cylindrical channel has traditionally employed the assumption that the equilibrium density of the polymers is independent of the azimuthal coordinate. However, simulations have shown that this rotational symmetry can be broken when there are attractive interactions between the polymers. We investigate the phases that emerge in these circumstances, and we quantify the effect of the symmetry assumption on the phase behavior of the system. In the absence of this assumption, one can observe large differences in the equilibrium densities between the rotationally symmetric case and the non-rotationally symmetric case. A simple analytical model is developed that illustrates the driving thermodynamic forces responsible for this symmetry breaking. Our results have implications for the current understanding of the behavior of polymers in cylindrical nanopores. [ABSTRACT FROM AUTHOR]

We investigate the aggregation transition of theta polymers in spherical confinement with multicanonical simulations. This allows for a systematic study of the effect of density on the aggregation transition temperature for up to 24 monodisperse polymers. Our results for solutions in the dilute regime show that polymers can be considered isolated for all temperatures larger than the aggregation temperature, which is shown to be a function of the density. The resulting competition between single-polymer collapse and aggregation yields the lower temperature bound of the isolated chain approximation. We provide entropic and energetic arguments to describe the density dependence and finite-size effects of the aggregation transition for monodisperse solutions in finite systems. This allows us to estimate the aggregation transition temperature of dilute systems in a spherical cavity, using a few simulations of small, sufficiently dilute polymer systems. [ABSTRACT FROM AUTHOR]

The isomorph theory provides an explanation for the so-called power law density scaling which has been observed in many molecular and polymeric glass formers, both experimentally and in simulations. Power law density scaling (relaxation times and transport coefficients being functions of ƿγs/T, where p is density, T is temperature, and γs is a material specific scaling exponent) is an approximation to a more general scaling predicted by the isomorph theory. Furthermore, the isomorph theory provides an explanation for Rosenfeld scaling (relaxation times and transport coefficients being functions of excess entropy) which has been observed in simulations of both molecular and polymeric systems. Doing molecular dynamics simulations of flexible Lennard-Jones chains (LJC) with rigid bonds, we here provide the first detailed test of the isomorph theory applied to flexible chain molecules. We confirm the existence of isomorphs, which are curves in the phase diagram along which the dynamics is invariant in the appropriate reduced units. This holds not only for the relaxation times but also for the full time dependence of the dynamics, including chain specific dynamics such as the end-to-end vector autocorrelation function and the relaxation of the Rouse modes. As predicted by the isomorph theory, jumps between different state points on the same isomorph happen instantaneously without any slow relaxation. Since the LJC is a simple coarse-grained model for alkanes and polymers, our results provide a possible explanation for why power-law density scaling is observed experimentally in alkanes and many polymeric systems. The theory provides an independent method of determining the scaling exponent, which is usually treated as an empirical scaling parameter. [ABSTRACT FROM AUTHOR]

Using both theoretical analysis and Langevin dynamics simulations in two dimensions, we investigate the dynamics of polymer translocation through a nanopore induced by different sizes of the mobile crowding agents, where the crowding agents have equal area fraction [lowercase_phi_synonym] and their diameters are σ and σb >= σ at cis and trans sides, respectively. The chain prefers moving to the side with bigger crowding agents as expected, however, we find the size difference between crowding agents plays a complicated role in the probability of polymer translocation from cis to trans side, the translocation time τ and its distribution, and the translocation exponent. In particular, with increasing σb, the translocation probability shows a maximum value and τ has a minimum value. These results can be interpreted by the effective driving force, which always increases with increasing [lowercase_phi_synonym] but has a maximum value with increasing σb. [ABSTRACT FROM AUTHOR]

Milestoning is a method used to calculate the kinetics of molecular processes occurring on timescales inaccessible to traditional molecular dynamics (MD) simulations. In the method, the phase space of the system is partitioned by milestones (hypersurfaces), trajectories are initialized on each milestone, and short MD simulations are performed to calculate transitions between neighboring milestones. Long trajectories of the system are then reconstructed with a semi-Markov process from the observed statistics of transition. The procedure is typically justified by the assumption that trajectories lose memory between crossing successive milestones. Here we present Milestoning with Coarse Memory (MCM), a generalization of Milestoning that relaxes the memory loss assumption of conventional Milestoning. In the method, milestones are defined and sample transitions are calculated in the standard Milestoning way. Then, after it is clear where trajectories sample milestones, the milestones are broken up into distinct neighborhoods (clusters), and each sample transition is associated with two clusters: the cluster containing the coordinates the trajectory was initialized in, and the cluster (on the terminal milestone) containing trajectory's final coordinates. Long trajectories of the system are then reconstructed with a semi-Markov process in an extended state space built from milestone and cluster indices. To test the method, we apply it to a process that is particularly ill suited for Milestoning: the dynamics of a polymer confined to a narrow cylinder. We show that Milestoning calculations of both the mean first passage time and the mean transit time of reversal-which occurs when the end-to-end vector reverses direction-are significantly improved when MCM is applied. Finally, we note the overhead of performing MCM on top of conventional Milestoning is negligible. [ABSTRACT FROM AUTHOR]

We perform two-dimensional Langevin dynamics simulations of electric-field driven polymer translocation through an attractive nanopore. We investigate the effect of the location of the attractive region using different pore patterns. This is found to have an impact on both the translocation time as a function of the chain length and on the polymer entry frequency. We qualitatively compare our results to available experimental data. [ABSTRACT FROM AUTHOR]

It has been established that entangled polymer dynamics can be reasonably described by single chain models such as tube and slip-link models. Although the entanglement effect is a result of hard-core interaction between chains, linkage between the single chain models and the real multi-chain system has not been established yet. In this study, we propose a multi-chain slip-spring model where bead-spring chains are dispersed in space and connected by slip-springs inspired by the single chain slip-spring model [A. E. Likhtman, Macromolecules 38, 6128 (2005)]. In this model the entanglement effect is replaced by the slip-springs, not by the hard-core interaction between beads so that this model is located in the niche between conventional multi-chain simulations and single chain models. The set of state variables are the position of beads and the connectivity (indices) of the slip-springs between beads. The dynamics of the system is described by the time evolution equation and stochastic transition dynamics for these variables. We propose a simple model which is based on the well-defined total free-energy and detailed balance condition. The free energy in our model contains a repulsive interaction between beads, which compensate the attractive interaction artificially generated by the slip-springs. The explicit expression of linear relaxation modulus is also derived by the linear response theory. We also propose a possible numerical scheme to perform simulations. Simulations reproduced expected bead number dependence in transitional regime between Rouse and entangled dynamics for the chain structure, the central bead diffusion, and the linear relaxation modulus. [ABSTRACT FROM AUTHOR]

We use a recently proposed metric, termed the point-to-set correlation functions, to probe the molecular weight dependence of the relevant static length scales in glass-forming oligomeric chain liquids of 4, 5, 8, and 10 repeat units. In agreement with the results for simple, monatomic fluids, we find that static length scales of the oligomers increase monotonically when the temperature is lowered towards the glass transition temperature of the fluid. More interestingly, the static length scale increases with increasing chain length. Within the bounds of error in our simulations, the static length scale appears to scale as the radius of gyration of the oligomer, but with a prefactor, which is much larger than unity and which grows with the temperature. The preceding behavior contrasts with the length scales extracted from the radial distribution function of the oligomer system, which is practically independent of the chain length. [ABSTRACT FROM AUTHOR]

We consider a coarse-grained model in which polymers under good-solvent conditions are represented by soft spheres whose radii, which should be identified with the polymer radii of gyrations, are allowed to fluctuate. The corresponding pair potential depends on the sphere radii. This model is a single-sphere version of the one proposed in Vettorel et al. [Soft Matter 6, 2282 (2010)], and it is sufficiently simple to allow us to determine all potentials accurately from full-monomer simulations of two isolated polymers (zero-density potentials). We find that in the dilute regime (which is the expected validity range of single-sphere coarse-grained models based on zero-density potentials) this model correctly reproduces the density dependence of the radius of gyration. However, for the thermodynamics and the intermolecular structure, the model is largely equivalent to the simpler one in which the sphere radii are fixed to the average value of the radius of gyration and radii-independent potentials are used: for the thermodynamics there is no advantage in considering a fluctuating sphere size. [ABSTRACT FROM AUTHOR]

Using Langevin dynamics simulations, we investigate the dynamics of polymer translocation into a circular nanocontainer through a nanopore under a driving force F. We observe that the translocation probability initially increases and then saturates with increasing F, independent of [lowercase_phi_synonym], which is the average density of the whole chain in the nanocontainer. The translocation time distribution undergoes a transition from a Gaussian distribution to an asymmetric distribution with increasing [lowercase_phi_synonym]. Moreover, we find a nonuniversal scaling exponent of the translocation time as chain length, depending on [lowercase_phi_synonym] and F. These results are interpreted by the conformation of the translocated chain in the nanocontainer and the time of an individual segment passing through the pore during translocation. [ABSTRACT FROM AUTHOR]

Through a detailed Langevin dynamics simulation study, the role of memory effects during unbiased translocation is explored. Tests are devised to uncover the presence of memory effects by directly measuring forward/backward-correlated motion as well as the associated change in the dynamics. Conducting these tests at low and high viscosities, a range of behaviours across different time scales is revealed: short-time forward correlations at all viscosities, quasi-static behaviour at low viscosity, and long-time backward correlations at high viscosity. By applying these tests at different portions of the translocation process, these memory effects are also shown to vary as translocation proceeds. Combining this information with standard measurements, a physical picture of unbiased translocation as the diffusion of a local minimum is proposed. [ABSTRACT FROM AUTHOR]

We propose an ellipsoid-chain model which may be routinely parameterized to capture large-scale properties of semiflexible, amphiphilic conjugated polymers in various solvent media. The model naturally utilizes the defect locations as pivotal centers connecting adjacent ellipsoids (each currently representing ten monomer units), and a variant umbrella-sampling scheme is employed to construct the potentials of mean force (PMF) for specific solvent media using atomistic dynamics data and simplex optimization. The performances, both efficacy and efficiency, of the model are thoroughly evaluated by comparing the simulation results on long, single-chain (i.e., 300-mer) structures with those from two existing, finer-grained models for a standard conjugated polymer (i.e., poly(2-methoxy-5-(2′-ethylhexyloxy)-1,4-phenylenevinylene) or MEH-PPV) in two distinct solvents (i.e., chloroform or toluene) as well as a hybrid, binary-solvent medium (i.e., chloroform/toluene = 1:1 in number density). The coarse-grained Monte Carlo (CGMC) simulation of the ellipsoid-chain model is shown to be the most efficient-about 300 times faster than the coarse-grained molecular dynamics (CGMD) simulation of the finest CG model that employs explicit solvents-in capturing elementary single-chain structures for both single-solvent media, and is a few times faster than the coarse-grained Langevin dynamics (CGLD) simulation of another implicit-solvent polymer model with a slightly greater coarse-graining level than in the CGMD simulation. For the binary-solvent system considered, however, both of the two implicit-solvent schemes (i.e., CGMC and CGLD) fail to capture the effects of conspicuous concentration fluctuations near the polymer-solvent interface, arising from a pronounced coupling between the solvent molecules and different parts of the polymer. Essential physical implications are elaborated on the success as well as the failure of the two implicit-solvent CG schemes under varying solvent conditions. Within the ellipsoid-chain model, the impact of synthesized defects on local segmental ordering as well as bulk chain conformation is also scrutinized, and essential consequences in practical applications discussed. In future perspectives, we remark on strategy that takes advantage of the coordination among various CG models and simulation schemes to warrant computational efficiency and accuracy, with the anticipated capability of simulating larger-scale, many-chain aggregate systems. [ABSTRACT FROM AUTHOR]

A comprehensive microscopic dynamical theory is presented for the description of quantum fluids as they transform into glasses. The theory is based on a quantum extension of mode-coupling theory. Novel effects are predicted, such as reentrant behavior of dynamical relaxation times. These predictions are supported by path integral ring polymer molecular dynamics simulations. The simulations provide detailed insight into the factors that govern slow dynamics in glassy quantum fluids. Connection to other recent work on both quantum glasses as well as quantum optimization problems is presented. [ABSTRACT FROM AUTHOR]

The transient-time correlation function (TTCF) method is used to calculate the nonlinear response of a homogeneous atomic fluid close to equilibrium. The TTCF response of the pressure tensor subjected to a time-independent planar mixed flow of shear and elongation is compared to directly averaged non-equilibrium molecular dynamics (NEMD) simulations. We discuss the consequence of noise in simulations with a small rate of deformation. The generalized viscosity for planar mixed flow is also calculated with TTCF. We find that for small rates of deformation, TTCF is far more efficient than direct averages of NEMD simulations. Therefore, TTCF can be applied to fluids with deformation rates which are much smaller than those commonly used in NEMD simulations. Ultimately, TTCF applied to molecular systems is amenable to direct comparison between NEMD simulations and experiments and so in principle can be used to study the rheology of polymer melts in industrial processes. [ABSTRACT FROM AUTHOR]

We present a numerical self-consistent field (SCF) method which describes freely jointed chains of spherical monomers applied to densely grafted polymer brushes. We discuss both the Flory-Huggins model and the Carnahan-Starling equation of state and show the latter being preferable within our model at polymer volume fractions above 10%. We compare the results of our numerical method with data from molecular dynamics (MD) simulations [G.-L. He, H. Merlitz, J.-U. Sommer, and C.-X. Wu, Macromolecules 40, 6721 (2007)] and analytical SCF calculations [P. M. Biesheuvel, W. M. de Vos, and V. M. Amoskov, Macromolecules 41, 6254 (2008)] and obtain close agreement between the density profiles up to high grafting densities. In contrast to prior numerical and analytical studies of densely grafted polymer brushes our method provides detailed information about chain configurations including fluctuation, depletion, and packing effects. Using our model we could study the recently discovered instability of densely grafted polymer brushes with respect to slight variations of individual chain lengths, driven by fluctuation effects [H. Merlitz, G.-L. He, C.-X. Wu, and J.-U. Sommer, Macromolecules 41, 5070 (2008)]. The obtained results are in very close agreement with corresponding MD simulations. [ABSTRACT FROM AUTHOR]

This work presents an immersed boundary method that allows fast Brownian dynamics simulation of solutions of polymer chains and other Brownian objects in complex geometries with fluctuating hydrodynamics. The approach is based on the general geometry Ewald-like method, which solves the Stokes equation with distributed regularized point forces in O(N) or O(NlogN) operations, where N is the number of point forces in the system. Time-integration is performed using a midpoint algorithm and Chebyshev polynomial approximation proposed by Fixman. This approach is applied to the dynamics of a genomic DNA molecule driven by flow through a nanofluidic slit with an array of nanopits on one wall of the slit. The dynamics of the DNA molecule was studied as a function of the Péclet number and chain length (the base case being λ-DNA). The transport characteristics of the hopping dynamics in this device differ at low and high Péclet number, and for long DNA, relative to the pit size, the dynamics is governed by the segments residing in the pit. By comparing with results that neglect them, hydrodynamic interactions are shown to play an important quantitative role in the hopping dynamics. [ABSTRACT FROM AUTHOR]

We have performed classical density functional theory calculations to study the behavior of mixed polymer brushes tethered to a planar surface. We assume no lateral segregation of the polymer at the grafting density studied and consider an implicit solvent. For a binary mixture of short and long athermal polymer chains, the short chain is compressed while the long chain is stretched compared with corresponding pure polymer chains at the same grafting density, which is consistent with simulation. This results from configurational entropy effects. Furthermore, we add a mean-field interaction for each polymer brush to simulate their different response towards a solvent. The long chain is forced to dislike the solvent more than the short chain. Through the interplay between the solvent effects and configurational entropy effects, a switch of the polymer brush surface (or outer) layer is found with increasing chain length of the long chain. The transition chain length (long chain) increases with increasing the solvent selectivity, and decreases with increasing the grafting density of the long chain. These results can provide guidance for the design of smart materials based on mixed polymer brushes. [ABSTRACT FROM AUTHOR]

Dissipative particle dynamics simulations were used to study the effects of mixing time, solute solubility, solute and diblock copolymer concentrations, and copolymer block length on the rapid coprecipitation of polymer-protected nanoparticles. The simulations were aimed at modeling Flash NanoPrecipitation, a process in which hydrophobic solutes and amphiphilic block copolymers are dissolved in a water-miscible organic solvent and then rapidly mixed with water to produce composite nanoparticles. A previously developed model by Spaeth et al. [J. Chem. Phys. 134, 164902 (2011)] was used. The model was parameterized to reproduce equilibrium and transport properties of the solvent, hydrophobic solute, and diblock copolymer. Anti-solvent mixing was modeled using time-dependent solvent-solute and solvent-copolymer interactions. We find that particle size increases with mixing time, due to the difference in solute and polymer solubilities. Increasing the solubility of the solute leads to larger nanoparticles for unfavorable solute-polymer interactions and to smaller nanoparticles for favorable solute-polymer interactions. A decrease in overall solute and polymer concentration produces smaller nanoparticles, because the difference in the diffusion coefficients of a single polymer and of larger clusters becomes more important to their relative rates of collisions under more dilute conditions. An increase in the solute-polymer ratio produces larger nanoparticles, since a collection of large particles has less surface area than a collection of small particles with the same total volume. An increase in the hydrophilic block length of the polymer leads to smaller nanoparticles, due to an enhanced ability of each polymer to shield the nanoparticle core. For unfavorable solute-polymer interactions, the nanoparticle size increases with hydrophobic block length. However, for favorable solute-polymer interactions, nanoparticle size exhibits a local minimum with respect to the hydrophobic block length. Our results provide insights on ways in which experimentally controllable parameters of the Flash NanoPrecipitation process can be used to influence aggregate size and composition during self-assembly. [ABSTRACT FROM AUTHOR]

The effect of crowded environment with static obstacles on the translocation of a three-dimensional self-avoiding polymer through a small pore is studied using dynamic Monte Carlo simulation. The translocation time τ is dependent on polymer-obstacle interaction and obstacle concentration. The influence of obstacles on the polymer translocation is explained qualitatively by the free energy landscape. There exists a special polymer-obstacle interaction at which the translocation time is roughly independent of the obstacle concentration at low obstacle concentration, and the strength of the special interaction is roughly independent of chain length N. Scaling relation τ ∼ N1.25 is observed for strong driving translocations. The diffusion property of polymer chain is also influenced by obstacles. Normal diffusion is only observed in dilute solution without obstacles or in a crowded environment with weak polymer-obstacle attraction. Otherwise, subdiffusion behavior of polymer is observed. [ABSTRACT FROM AUTHOR]

This article reports the first attempt to apply the relaxation mode analysis method to a simulation of a biomolecular system. In biomolecular systems, the principal component analysis is a well-known method for analyzing the static properties of fluctuations of structures obtained by a simulation and classifying the structures into some groups. On the other hand, the relaxation mode analysis has been used to analyze the dynamic properties of homopolymer systems. In this article, a long Monte Carlo simulation of Met-enkephalin in gas phase has been performed. The results are analyzed by the principal component analysis and relaxation mode analysis methods. We compare the results of both methods and show the effectiveness of the relaxation mode analysis. [ABSTRACT FROM AUTHOR]

The use of ring polymer molecular dynamics (RPMD) for the direct simulation of electron transfer (ET) reaction dynamics is analyzed in the context of Marcus theory, semiclassical instanton theory, and exact quantum dynamics approaches. For both fully atomistic and system-bath representations of condensed-phase ET, we demonstrate that RPMD accurately predicts both ET reaction rates and mechanisms throughout the normal and activationless regimes of the thermodynamic driving force. Analysis of the ensemble of reactive RPMD trajectories reveals the solvent reorganization mechanism for ET that is anticipated in the Marcus rate theory, and the accuracy of the RPMD rate calculation is understood in terms of its exact description of statistical fluctuations and its formal connection to semiclassical instanton theory for deep-tunneling processes. In the inverted regime of the thermodynamic driving force, neither RPMD nor a related formulation of semiclassical instanton theory capture the characteristic turnover in the reaction rate; comparison with exact quantum dynamics simulations reveals that these methods provide inadequate quantization of the real-time electronic-state dynamics in the inverted regime. [ABSTRACT FROM AUTHOR]

Collapsed polymers in solution represent an oft-overlooked area of polymer physics, however recent studies of biopolymers in the bloodstream have suggested that the physics of polymer globules are not only relevant but could potentially lead to powerful new ways to manipulate single molecules using fluid flows. In the present article, we investigate the behavior of a collapsed polymer globule under the influence of linear combinations of shear and elongational flows. We generalize the theory of globule-stretch transitions that has been developed for the specific case of simple shear and elongational flows to account for behavior in arbitrary flow fields. In particular, we find that the behavior of a globule in flow is well represented by a two-state model wherein the critical parameters are the transition probabilities to go from a collapsed to a stretched state Pg - s and vice versa Ps - g. The collapsed globule to stretch transition is described using a nucleation protrusion mechanism, and the reverse transition is described using either a tumbling or a relaxation mechanism. The magnitudes of Pg - s and Ps - g govern the state in which the polymer resides; for Pg - s ≈ 0 and Ps - g ≈ 1 the polymer is always collapsed, for Pg - s ≈ 0 and Ps - g ≈ 0 the polymer is stuck in either the collapsed or stretched state, for Pg - s ≈ 1 and Ps - g ≈ 0 the polymer is always stretched, and for Pg - s ≈ 1 and Ps - g ≈ 1 the polymer undergoes tumbling behavior. These transition probabilities are functions of the flow geometry, and we demonstrate that our theory quantitatively predicts globular polymer conformation in the case of mixed two-dimensional flows, regardless of orientation and representation, by comparing theoretical results to Brownian dynamics simulations. Generalization of the theory to arbitrary three-dimensional flows is discussed as is the incorporation of this theory into rheological equations. [ABSTRACT FROM AUTHOR]

Polaron dynamics in a system of two randomly coupled polymer chains is simulated using a nonadiabatic evolution method. The simulations are performed within the framework of the Su-Schrieffer-Heeger model modified to include disordered interchain interactions and an external electric field. By analysing the polaron velocity statistically, we find that the polaron motion is determined by the competition between the electric field and the disordered interchain interactions. Polaron dynamics are classified into two types, weak-coupling dynamics and strong-coupling dynamics. It is found that the strength of interchain interactions is the dominant factor controlling charge propagation in weak-coupling dynamics, whereas the effects of disorder are dominant in strong-coupling dynamics. The charge carriers tend to have higher mobility for stronger interchain coupling, and interchain coupling disorder can be favorable for charge transport depending on the coupling strength and the electric field. [ABSTRACT FROM AUTHOR]

The dynamics of a collapsing polymer under a temperature quench in dilute solution is investigated by dissipative particles dynamics. Hydrodynamic interactions and many-body interaction are preserved naturally by incorporating explicit solvent particles in this approach. Our simulation suggests a four-stage collapse pathway: localized clusters formation, cluster coarsening in situ, coarsening involving global backbone conformation change into a crumpled globule, and compaction of the globule. For all the quench depths and chain lengths used in our study, collapse proceeds without the chain getting trapped in a metastable 'sausage' configuration, as reported in some earlier studies. We obtain the time scales for each of the first three stages, as well as its scaling with the quench depths ξ and chain lengths N. The total collapse time scales as τc ∼ ξ-0.46 ± 0.04N0.98 ± 0.09, with the quench depth and degree of polymerization. [ABSTRACT FROM AUTHOR]

The influence of hydrodynamic screening near a surface on the dynamics of a single semiflexible polymer is studied by means of Brownian dynamics simulations and hydrodynamic mean field theory. The polymer motion is characterized in terms of the mean squared displacements of the end-monomers, the end-to-end vector, and the scalar end-to-end distance. In order to control hydrodynamic screening effects, the polymer is confined to a plane at a fixed separation from the wall. When gradually decreasing this separation, a crossover from Zimm-type towards Rouse (free-draining) polymer dynamics is induced. However, this crossover is rather slow and the free-draining limit is not completely reached-substantial deviations from Rouse-like dynamics are registered in both simulations and theory-even at distances of the polymer from the wall on the order of the monomer size. Remarkably, the effect of surface-induced screening of hydrodynamic interactions sensitively depends on the type of dynamic observable considered. For vectorial quantities such as the end-to-end vector, hydrodynamic interactions are important and therefore surface screening effects are sizeable. For a scalar quantity such as the end-to-end distance, on the other hand, hydrodynamic interactions are less important, but a pronounced dependence of dynamic scaling exponents on the persistence length to contour length ratio becomes noticeable. Our findings are discussed against the background of single-molecule experiments on f-actin [L. Le Goff et al., Phys. Rev. Lett. 89, 258101 (2002)]. [ABSTRACT FROM AUTHOR]

We examine the thermally induced fracture of an unstrained polymer chain of discrete segments coupled by an anharmonic potential by means of molecular dynamics simulation with a Langevin thermostat. Cases of both under- and over-damped dynamics are investigated, and a comparison with recent studies of bond scission in model polymers with harmonic interactions is performed. We find that the polymer degradation changes qualitatively between the inertial regime and that of heavily damped dynamics. The role of bond healing (recombination) is also studied and probability distributions for the recombination times and overstretched bond lengths are obtained. Our extensive simulations reveal many properties of the scission dynamics in agreement with the notion of random breakdown of independent bonds, e.g., the mean time of chain rupture, <τ> follows an Arrhenian behavior with temperature T, and depends on the number of bonds N in the polymer as <τ>∝N-1. In contrast, the rupture rates of the individual bonds along the polymer backbone indicate clearly the presence of self-induced inhomogeneity resulting from the interplay of thermal noise and nonlinearity. Eventually we examine the fragmentation kinetics during thermolysis. We demonstrate that both the probability distribution function of fragment sizes as well as the mean length of fragments at subsequent times t characterize degradation as predominantly a first order reaction. [ABSTRACT FROM AUTHOR]

For branched polymers, the curvilinear motion of the branch point along the backbone is a significant relaxation source but details of this motion have not been well understood. This study conducts multi-chain sliplink simulations to examine effects of the spatial fluctuation and curvilinear hopping of the branch point on the viscoelastic relaxation. The simulation is based on the primitive chain network model that allows the spatial fluctuations of sliplink and branch point and the chain sliding along the backbone according to the subchain tension, chemical potential gradients, drag force against medium, and random force. The sliplinks are created and/or disrupted through the motion of chain ends. The curvilinear hopping of the branch point along the backbone is allowed to occur when all sliplinks on a branched arm are lost. The simulations considering the fluctuation and the hopping of the branch point described well the viscoelastic data for symmetric and asymmetric star polymers with a parameter set common to the linear polymer. On the other hand, the simulations without the branch point motion predicted unreasonably slow relaxation for asymmetric star polymers. For asymmetric star polymers, further tests with and without the branch point hopping revealed that the hopping is much less important compared to the branch point fluctuation when the lengths of the short and long backbone arms are not very different and the waiting time for the branch point hopping (time for removal of all sliplinks on the short arm) is larger than the backbone relaxation time. Although this waiting time changes with the hopping condition, the above results suggest a significance of the branch point fluctuation in the actual relaxation of branch polymers. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations have been employed to study the formation of a physical gel by semiflexible polymer chains. The formation of a geometrically connected network of these chains is investigated as a function of temperature and rate of cooling. The stiffness of the molecules is controlled via a potential between beads separated by two bonds. As the temperature is lowered, a percolated homogeneous solution phase separates to form a high-density, non-percolated nematic fluid and a low-density gas phase. On further decreasing the temperature, the chains are dynamically arrested preventing the completion of the vapor-liquid (VL) phase separation. As a result, the chains are stuck in a three-dimensional network of nematic bundles forming a percolated gel. Apart from temperature, the rate of cooling also plays an important role in the formation of the gel. Cooling the system at a faster rate yields gel while slower rates result in complete VL phase separation. [ABSTRACT FROM AUTHOR]

Using analytical techniques and Langevin dynamics simulations, we investigate the dynamics of polymer translocation into a narrow channel of width R embedded in two dimensions, driven by a force proportional to the number of monomers in the channel. Such a setup mimics typical experimental situations in nano/microfluidics. During the translocation process if the monomers in the channel can sufficiently quickly assume steady state motion, we observe the scaling τ ∼ N/F of the translocation time τ with the driving force F per bead and the number N of monomers per chain. With smaller channel width R, steady state motion cannot be achieved, effecting a nonuniversal dependence of τ on N and F. From the simulations we also deduce the waiting time distributions under various conditions for the single segment passage through the channel entrance. For different chain lengths but the same driving force, the curves of the waiting time as a function of the translocation coordinate s feature a maximum located at identical smax, while with increasing the driving force or the channel width the value of smax decreases. [ABSTRACT FROM AUTHOR]