The rate of escape of an ideal bead-spring polymer in a symmetric double-well potential is calculated using transition state theory (TST) and the results compared with direct dynamical simulations. The minimum energy path of the transitions becomes flat and the dynamics diffusive for long polymers making the Kramers-Langer estimate poor. However, TST with dynamical corrections based on short time trajectories started at the transition state gives rate constant estimates that agree within a factor of two with the molecular dynamics simulations over a wide range of bead coupling constants and polymer lengths. The computational effort required by the TST approach does not depend on the escape rate and is much smaller than that required by molecular dynamics simulations.
The rate of escape of polymers from a two-dimensionally confining potential well has been evaluated using self-avoiding as well as ideal chain representations of varying length, up to 80 beads. Long timescale Langevin trajectories were calculated using the path integral hyperdynamics method to evaluate the escape rate. A minimum is found in the rate for self-avoiding polymers of intermediate length while the escape rate decreases monotonically with polymer length for ideal polymers. The increase in the rate for long, self-avoiding polymers is ascribed to crowding in the potential well which re…
We study escape dynamics of a double-stranded DNA (dsDNA) through an idealized double nanopore (DNP) geometry subject to two equal and opposite forces (tug-of-war) using Brownian dynamics (BD) simulation. In addition to the geometrical restrictions imposed on the cocaptured dsDNA segment in between the pores, the presence of tug-of-war forces at each pore results in a variation of the local chain stiffness for the segment of the chain in between the pores which increases the overall stiffness of the chain. We use BD simulation results to understand how the intrinsic chain stiffness and the TOW…
Transport of tracer particles through mesh-like environments such as biological hydrogels and polymer matrices is ubiquitous in nature. These tracers could be passive, such as colloids or active (self-propelled), such as synthetic nanomotors or bacteria. Computer simulations in principle should be extremely useful in exploring the mechanism of active (self-propelled) transport of tracer particles through the mesh-like environments. Therefore, we construct a polymer network on a diamond lattice and use computer simulations to investigate the dynamics of spherical self-propelled particles inside…
Brownian escape is key to a wealth of physico-chemical processes, including polymer folding, and information storage. The frequency of thermally activated energy barrier crossings is assumed to generally decrease exponentially with increasing barrier height. Here, we show experimentally that higher, fine-tuned barrier profiles result in significantly enhanced escape rates in breach of the intuition relying on the above scaling law, and address in theory the corresponding conditions for maximum speed-up. Importantly, our barriers end on the same energy on which they start. For overdamped dynami…
Reply to Comment on "Why is the DNA Transition First Order?" and "Griffiths Singularities in Unbinding of Strongly Disordered Polymers" by M. Ya. Azbel
它表明，在评论中提出的各种索赔M。Ya. Azbel（物理学/0403106）在两个出版物物理。91，055502（2003）和Phys. Rev. Lett. 85，4988（2000）无效。这是对这两份文件要点的误解造成的。
The recrossing correction to the transition state theory estimate of a thermal rate can be difficult to calculate when the energy barrier is flat. This problem arises, for example, in polymer escape if the polymer is long enough to stretch between the initial and final state energy wells while the polymer beads undergo diffusive motion back and forth over the barrier. We present an efficient method for evaluating the correction factor by constructing a sequence of hyperplanes starting at the transition state and calculating the probability that the system advances from one hyperplane to anothe…
We investigate the binding transition of two flexible polymers grafted to a steric surface with closeby end points. While free polymers show a discontinuous transition, grafting to a steric flat surface leads to a continuous binding transition. This is supported by results from Metropolis and parallel multicanonical simulations. A combination of canonical and microcanonical analyses reveals that the change in transition order can be understood in terms of the reduced translational entropy of the unbound high-temperature phase upon grafting.
While the dynamics of a fully flexible polymer ejecting a capsid through a nanopore has been extensively studied, the ejection dynamics of semiflexible polymers has not been properly characterized. Here we report results from simulations of ejection dynamics of semiflexible polymers ejecting from spherical capsids. Ejections start from strongly confined polymer conformations of constant initial monomer density. We find that, unlike for fully flexible polymers, for semiflexible polymers the force measured at the pore does not show a direct relation to the instantaneous ejection velocity. The cu…
We investigate local phase transitions of the solvent in the neighborhood of a solvophobic polymer chain which is induced by a change of the polymer-solvent repulsion and the solvent pressure in the bulk solution. We describe the polymer in solution by the Edwards model, where the conditional partition function of the polymer chain at a fixed radius of gyration is described by a mean-field theory. The contributions of the polymer-solvent and the solvent-solvent interactions to the total free energy are described within the mean-field approximation. We obtain the total free energy of the soluti…
Effect of small additive molecules on the structural relaxation of polymer melts is investigated via molecular dynamics simulations. At a constant external pressure and a fixed number concentration of added molecules, the variation of particle diameter leads to a non-monotonic change of the relaxation dynamics of the polymer melt. For non-entangled chains, this effect is rationalized in terms of an enhanced added-particle-dynamics which competes with a weaker coupling strength upon decreasing the particle size. Interestingly, cooling simulations reveal a non-monotonic effect on the glass trans…
Polymers adopt extended coil and compact globule states according to the balance between entropy and interaction energies. The transition of a polymer between an extended coil state and compact globule state can be induced by changing thermodynamic force such as temperature to alter the energy/entropy balance. Previously, this transition was theoretically studied by taking into account the excluded-volume interaction between monomers of a polymer chain using the partition function. For binary mixtures of a long polymer and short polymers, the coil-globule transition can be induced by changing …
Systematic Microcanonical Analyses of Polymer Adsorption Transitions
在详细的微正则分析的状态密度得到广泛的multicanonical Monte Carlo计算机模拟，我们调查的热性能的构象转变吸附聚合物的经验附近有吸引力的基板。对于短链和强表面吸引力，微正则熵原来是一个凸函数的能量在过渡区，表明表面熵效应是相关的。虽然已知是一个连续过渡的热力学极限的无限长链，非接枝有限长度的聚合物的吸附过渡，从而表现出一个明确的签名的一阶样的过渡，与共存相的吸附和解吸的构象。微正则熵凸性的另一个显著结果是，随着能量的增加，跃迁伴随着微正则温度的降低。由于这是一个典型的物理效应，它可能不会被忽略在有限系统中的合作宏观状态转换的分析。
We analyze the conformational dynamics and statistical properties of an active polymer model. The polymer is described as a freely-jointed bead-rod chain subject to stochastic active force dipoles that act on the suspending solvent where they drive long-ranged fluid flows. Using Langevin simulations of isolated chains in unconfined domains, we show how the coupling of active flows with polymer conformations leads to emergent dynamics. Systems with contractile dipoles behave similarly to passive Brownian chains with enhanced fluctuations due to dipolar flows. In systems with extensile dipoles, …
We study conformations and dynamics of active star polymers. The analysis shows that active star polymers stretching behaviour is quite different from that of active linear chains. The visual inspection of conformations and bond-bond correlations reveal a better coordination for the alignment and coordination of bonds for the star polymers than for the linear counterparts. The architecture substantially affects the chain extension transition at high values of active force. The scaling laws for the shape factor and the arm asphericity ratio established for the passive star polymers coincide wit…
Associative polymers with sticker-and-spacer architectures undergo phase transitions that combine phase separation and bond percolation. Here, we generalize mean-field models for bond percolation and extract effective sticker interaction strengths from experimental data for specific proteins. We use graph-based Monte Carlo simulations to evaluate effects ignored by mean-field models. These include bond cooperativity defined as changes to strengths of new bonds (physical crosslinks) given the presence of a prior bond. We find that bond cooperativity fundamentally alters phase behavior, especial…
Adsorption transition of a self-avoiding polymer chain onto a rigid rod
本工作的主题是一个长的灵活的自避免聚合物链到一个刚性细棒的吸附转变。该杆由半径为R的圆柱体表示，该圆柱体具有对链单体的短程吸引表面势。一般的标度结果是通过使用重整化群的论点，结合现有的结果与弯曲边界的量子场论[McAvity and Osborn 1993 Nucl.Phys.B394，728]。相关的临界指数确定和估计使用几何参数。
We consider the phase diagram of self-avoiding walks (SAW) on the simple cubic lattice subject to surface and bulk interactions, modeling an adsorbing surface and variable solvent quality for a polymer in dilute solution, respectively. We simulate SAWs at specific interaction strengths to focus on locating certain transitions and their critical behavior. By collating these new results with previous results we sketch the complete phase diagram and show how the adsorption transition is affected by changing the bulk interaction strength. This expands on recent work considering how adsorption is a…
We perform numerical simulations of an active fully flexible self-avoiding polymer as a function of the quality of the embedding solvent described in terms of an effective monomer-monomer interaction. Specifically, by extracting the Flory exponent of the active polymer under different conditions, we are able to pin down the location of the coil-globule transition for different strength of the active forces. Remarkably, we find that a simple rescaling of the temperature is capable of qualitatively capture the dependence of the $Θ$-point of the polymer with the amplitude of the active fluctuatio…
By means of Metropolis Monte Carlo simulations of a coarse-grained model for flexible polymers, we investigate how the integrated autocorrelation times of different energetic and structural quantities depend on the temperature. We show that, due to critical slowing down, an extremal autocorrelation time can also be considered as an indicator for the collapse transition that helps to locate the transition point. This is particularly useful for finite systems, where response quantities such as the specific heat do not necessarily exhibit clear indications for pronounced thermal activity.
