We investigate configuration dynamics of a flexible polymer chain in a bath of active particles with dynamic chirality, i.e., particles rotate with a deterministic angular velocity $ω$ besides self-propulsion,by Langevin dynamics simulations in two dimensional space. Particular attentions are paid to how the gyration radius $R_{g}$ changes with the propulsion velocity $v_{0}$,angular velocity $ω$ and chain length. We find that in a chiral bath with a typical nonzero $ω$, the chain first collapses into a small compact cluster and swells again with increasing $v_{0}$, in quite contrast to the case for a normal achiral bath $(ω=0)$ wherein a flexible chain swells with increasing $v_{0}$. More interestingly, the polymer can even form a closed ring if the chain length is large enough,which may oscillate with the cluster if $v_{0}$ is large. Consequently, the gyration radius $R_{g}$ shows nontrivial non-monotonic dependences on $v_{0}$, i.e., it undergoes a minimum for relatively short chains, and two minima with a maximum in between for longer chains. Our analysis shows that such interesting phenomena are mainly due to the competition between two roles played by the chiral active bath: while the persistence motion due to particle activity tends to stretch the chain, the circular motion of the particle may lead to an effective osmotic pressure that tends to collapse the chain. In addition, the size of the circular motion $R_{0}=v_{0}/ω$ shows an important role in that the compact clusters and closed-rings are both observed at nearly the same values of $R_{0}$ for different $ω$.
The configurations taken by polymers embedded in out-of-equilibrium baths may have broad effects in a variety of biological systems. As such, they have attracted considerable interest, particularly in simulation studies. Here we analyze the distribution of configurations taken by a passive flexible chain in a bath of hard, self-propelled, vibrated disks and systematically compare it to that of the same flexible chain in a bath of hard, thermal-like, vibrated disks. We demonstrate experimentally that the mean length and mean radius of gyration of both chains obey Flory's Law. However, the Kuhn …
We investigate modifications of a stochastic polymer picture through a shift in the boundary between the system and an external environment. A conventional bead-and-spring model serving as the coarse-graining model is given by the Langevin equation for all the monomers subject to white noise. However, stochastic motion for only a tagged monomer is observed to occur in the presence of colored noise. The qualitative change in the observations arises from the boundary shift decided by the observer. The Langevin dynamics analyses interpret the colored noise as the emergence of the polymeric elasti…
We describe method to discuss thermodynamics of a defected semi-flexible homo-polymer chain in the two and three dimensions using fully directed self-avoiding walk lattice model. The defects are located along a line and these defects are not in the thermal equilibrium with the monomers of the semi-flexible polymer chain; i. e. we consider the case of defected semi-flexible polymer chain in the present manuscript for the case of quenched defects. There are m defects on the conformations of the N monomers long semi-flexible polymer chain and we exactly count the number of Q realizations of the d…
Investigating thermodynamic properties of liquid-solid transitions of flexible homopolymers with elastic bonds by means of multicanonical Monte Carlo simulations, we find crystalline conformations that resemble ground-state structures of Lennard-Jones clusters. This allows us to set up a structural classification scheme for finite-length flexible polymers and their freezing mechanism in analogy to atomic cluster formation. Crystals of polymers with "magic length" turn out to be perfectly icosahedral.
In this topical review, we give an overview of the structure and dynamics of a single polymer chain in active baths, Gaussian or non-Gaussian. The review begins with the discussion of single flexible or semiflexible linear polymer chains subjected to two noises, thermal and active. The active noise has either Gaussian or non-Gaussian distribution but has a memory, accounting for the persistent motion of the active bath particles. This finite persistence makes the reconfiguration dynamics of the chain slow as compared to the purely thermal case and the chain swells. The active noise also result…
The generalized entropy theory (GET) offers many insights into how molecular parameters influence polymer glass-formation. Given the fact that chain rigidity often plays a critical role in understanding the glass-formation of polymer materials, the GET was originally developed based on models of semiflexible chains. Consequently, all previous calculations within the GET considered polymers with some degree of chain rigidity. Motivated by unexpected results from computer simulations of fully flexible polymer melts concerning the dependence of thermodynamic and dynamic properties on the cohesive…
We study the driven translocation of a flexible polymer through an interacting conical pore using Langevin dynamics simulations. We find that, for a fixed value of externally applied force and pore polymer interaction strength, the mean residence time of monomers inside the pore shows non-monotonic variations with pore apex angle $α$. We explain this behavior using a free energy argument by explicitly accounting for pore-polymer interactions and external drive. Our theoretical observations are corroborated by the simulation results of the mean translocation times as the pore-polymer interactio…
The conformational properties of a semi-flexible polymer chain, anchored at one end in a uniform force field, are studied in a simple two-dimensional model. Recursion relations are derived for the partition function and then iterated numerically. We calculate the angular fluctuations of the polymer about the direction of the force field and the average polymer configuration as functions of the bending rigidity, chain length, chain orientation at the anchoring point, and field strength.
Nano-scale confinement of polymer in cone-shaped geometries occurs in many experimental situations. A flexible polymer confined in a cone-shaped nano-channel is studied theoretically and using molecular dynamics simulations. Distribution of the monomers inside the channel, configuration of the confined polymer, entropic force acting on the polymer, and their dependence on the channel and the polymer parameters are investigated. The theory and the simulation results are in very good agreement. The entropic force on the polymer that results from the asymmetric shape of the channel is measured in…
A simple analytic theory for mixtures of hard spheres and larger polymers with excluded volume interactions is developed. The mixture is shown to exhibit extensive immiscibility. For large polymers with strong excluded volume interactions, the density of monomers at the critical point for demixing decreases as one over the square root of the length of the polymer, while the density of spheres tends to a constant. This is very different to the behaviour of mixtures of hard spheres and ideal polymers, these mixtures although even less miscible than those with polymers with excluded volume intera…
In this work we present the general phase behavior of short tubelike flexible polymers. The geometric thickness constraint is implemented through the concept of the global radius of curvature. We use sophisticated Monte Carlo sampling methods to simulate small bead-stick polymer models with Lennard-Jones interaction among non-bonded monomers. We analyze energetic fluctuations and structural quantities to classify conformational pseudophases. We find that the tube thickness influences the thermodynamic behavior of simple tubelike polymers significantly, i.e., for given temperature, the formatio…
The characterization of the interactions between two fully flexible self-avoiding polymers is one of the classic and most important problems in polymer physics. In this paper we measure these interactions in the presence of active fluctuations. We introduce activity into the problem using two of the most popular models in this field. One where activity is effectively embedded into the monomers' dynamics, and the other where passive polymers fluctuate in an explicit bath of active particles. We establish the conditions under which the interaction between active polymers can be mapped into the c…
In a contact density chain-growth study we investigate the solubility-temperature pseudo-phase diagram of a lattice polymer in a cavity with an attractive surface. In addition to the main phases of adsorbed and desorbed conformations we find numerous subphases of collapsed and expanded structures.
The equilibrium structure and dynamics of a single polymer chain in a thermal solvent is by now well-understood in terms of scaling laws. Here we consider a polymer in a bacterial bath, i.e. in a solvent consisting of active particles which bring in nonequilibrium fluctuations. Using computer simulations of a self-avoiding polymer chain in two dimensions which is exposed to a dilute bath of active particles, we show that the Flory-scaling exponent is unaffected by the bath activity provided the chain is very long. Conversely, for shorter chains, there is a nontrivial coupling between the bacte…
The validity of the affine assumption in model flexible polymer networks is explored. To this end, the displacements of fluorescent tracer beads embedded in polyacrylamide gels are quantified by confocal microscopy under shear deformation, and the deviations of these displacements from affine responses are recorded. Non-affinity within the gels is quantified as a function of polymer chain density and cross-link concentration. Observations are in qualitative agreement with current theories of polymer network non-affinity. The measured degree of non-affinity in the polyacrylamide gels suggests t…
We study the elastic properties of a rigid filament in a bath of self-propelled particles. We find that while fully flexible filaments swell monotonically upon increasing the strength of the propelling force, rigid filaments soften for moderate activities, collapse into metastable hairpins for intermediate strengths, and eventually re-expand when the strength of the activity of the surrounding fluid is large. This collapse and re-expansion of the filament with the bath activity is reminiscent of the behavior observed in polyelectrolytes in the presence of different concentrations of multivalen…
We consider a fully directed self-avoiding walk model on a cubic lattice to mimic the conformations of an infinitely long confined flexible polymer chain; and the confinement condition is achieved by two parallel athermal plates. The confined polymer system is under good solvent condition and we revisit this problem to solve the real polymer's model for any length of chain and also for any separation in between the plates. The equilibrium statistics of the confined polymer chain is derived using an analytical calculations based on the generating function technique. The force of the confinement…
We investigate the propagation of a suddenly applied tension along a thermally excited semi-flexible polymer using analytical approximations, scaling arguments and numerical simulation. This problem is inherently non-linear. We find sub-diffusive propagation with a dynamical exponent of 1/4. By generalizing the internal elasticity, we show that tense strings exhibit qualitatively different tension profiles and propagation with an exponent of 1/2.
We analyze the freezing and collapse transition of a simple model for flexible polymer chains on simple cubic and face-centered cubic lattices by means of sophisticated chain-growth methods. In contrast to bond-fluctuation polymer models in certain parameter ranges, where these two conformational transitions were found to merge in the thermodynamic limit, we conclude from our results that the two transitions remain well-separated in the limit of infinite chain lengths. The reason for this qualitatively distinct behavior is presumably due to the ultrashort attractive interaction range in the la…
We study the nonequilibrium kinetics during the coil-globule transition of a flexible polymer chain with active beads after a quench from good to poor solvent condition using molecular dynamics simulation. Activity for each bead is introduced via the well-known Vicsek-like alignment rule due to which the velocity of a bead tries to align towards the average direction of its neighbors. We investigate the role of quenching temperature with varying activity during collapse of this polymer. We find that although for lower activities the kinetics remains qualitatively similar for different temperat…
A simple model of a polymer with long rigid segments which interact via excluded volume repulsions and short ranged attractions is proposed. The coil-globule transition of this model polymer is strongly first order, the globule is crystalline and the coil which coexists with the globule is swollen. A virial expansion truncated at low order is shown to provide a very poor approximation to the free energy and so a cell theory is used to calculate the free energy of the globule.
We analyze the crystallization and collapse transition of a simple model for flexible polymer chains on simple cubic and face-centered cubic lattices by means of sophisticated chain-growth methods. In contrast to bond-fluctuation polymer models in certain parameter ranges, where these two conformational transitions were found to merge in the thermodynamic limit, we conclude from our results that the two transitions remain well-separated in the limit of infinite chain lengths. The reason for this qualitatively distinct behavior is presumably due to the ultrashort attractive interaction range in…
The nature of the globule-coil transition of surface-confined polymers has been an issue of debate. Here this 2D collapse transition is studied through a partially directed lattice model. In the general case of polymers with positive bending stiffness ($Δ>0$), the collapse transition is {\em first-order}; it becomes {\em second-order} only in the limiting case of zero bending stiffness ($Δ\equiv 0$). These analytical results are confirmed by Monte Carlo simulations. We also suggest some possible future experiments.
Using field theoretic approach, we study equilibrium shape deformation of a vesicle induced by the presence of enclosed flexible polymers, which is a simple model of drug delivery system or endocytosis. To evaluate the total free energy of this system, it is necessary to calculate the bending elastic energy of the membrane, the conformation entropy of the polymers and their interactions. For this purpose, we combine phase field theory for the membrane and self-consistent field theory for the polymers. Simulations on this coupled model system for axiosymmetric shapes show a shape deformation of…
We directly visualize single polymers with persistence lengths ranging from $\ell_p=0.05$ to 16 $μ$m, dissolved in the nematic phase of rod-like {\it fd} virus. Polymers with sufficiently large persistence length undergo a coil-rod transition at the isotropic-nematic transition of the background solvent. We quantitatively analyze the transverse fluctuations of semi-flexible polymers and show that at long wavelengths they are driven by the fluctuating nematic background. We extract both the Odijk deflection length and the elastic constant of the background nematic phase from the data.
The de Gennes' blob model is extensively used in different problems of polymer physics. This model is theoretically applicable when the number of monomers inside each blob is large enough. For confined flexible polymers, this requires the confining geometry to be much larger than the monomer size. In this manuscript, the opposite limit of polymer in nano-slits with one to several monomers width is studied, using molecular dynamics simulations. Extension of the polymer inside nanoslits, confinement force on the plates, and the effective spring constant of the confined polymer are investigated. …
Entropy-driven directed translocation of a flexible polymer through a cone-shaped channel is studied theoretically and using computer simulation. For a given length of the channel, the effective force of entropic origin acting on the polymer is calculated as a function of the apex angle of the channel. It is found that the translocation time is a non-monotonic function of the apex angle. By increasing the apex angle from zero, the translocation time shows a minimum and then a maximum. Also, it is found that regardless of the value of the apex angle, the translocation time is a uniformly decrea…
We report the results of Monte Carlo simulations investigating the effect of a spherical confinement within a simple model for a flexible homopolymer. We use the parallel tempering method combined with multi-histogram reweighting analysis and multicanonical simulations to investigate thermodynamical observables over a broad range of temperatures, which enables us to describe the behavior of the polymer and to locate the freezing and collapse transitions. We find a strong effect of the spherical confinement on the location of the collapse transition, whereas the freezing transition is hardly ef…
Using a coarse-grained bead-spring model for semi-flexible macromolecules forming a polymer brush, structure and dynamics of the polymers is investigated, varying chain stiffness and grafting density. The anchoring condition for the grafted chains is chosen such that their first bonds are oriented along the normal to the substrate plane. Compression of such a semi-flexible brush by a planar piston is observed to be a two-stage process: for small compressions the chains contract by "buckling" deformation whereas for larger compression the chains exhibit a collective (almost uniform) bending def…
Generalized-ensemble simulations enable the study of complex adsorption scenarios of a coarse-grained model polymer near an attractive nanostring, representing an ultrathin nanowire. We perform canonical and microcanonical statistical analyses to investigate structural transitions of the polymer and discuss their dependence on the temperature and on model parameters such as effective wire thickness and attraction strength. The result is a complete hyperphase diagram of the polymer phases, whose locations and stability are influenced by the effective material properties of the nanowire and the …
We study equilibrium statistics of single semi-flexible polymer chain in the presence of defects. The defects are lying along a line in the two and three dimensions and the monomers are interacting with the onsite potential of the defects. A fully directed self-avoiding walk model is used in two and three dimensions to describe thermo-dynamical behaviour of the chain in the presence of m defects. We have found that the number of conformations of the semiflexible polymer chain may be controlled by means of introduction of such defects so that a particular fraction of the chain conformations may…
We examine how the distribution of contour lengths and the high-stretch stiffening of individual chain segments affect the macroscopic shear modulus of flexible polymer gels, using a 2D numerical model, in which polymer segments form a triangular network and disorder is introduced by varying their contour lengths. We show that in the relevant parameter range: (i) the non-affine contribution to the shear modulus is negligible, i.e. the Born approximation is satisfactory; (ii) the shear modulus is dominated by the contribution originating from equilibrium chain tensions. Moreover, mechanical equ…
We derive scaling relations for the extension statistics and the confinement free energy for a semi-flexible polymer confined to a channel with a rectangular cross-section. Our motivation are recent numerical results [Gupta {\em et al.}, JCP {\bf 140} (2014) 214901] indicating that extensional fluctuations are quite different in rectangular channels compared to square channels. Our results are of direct relevance for interpreting current experiments on DNA molecules confined to nano-channels, as many experiments are performed for rectangular channels with large aspect ratios while theoretical …
In this work we investigate structural properties of native states of a simple model for short flexible homopolymers, where the steric influence of monomeric side chains is effectively introduced by a thickness constraint. This geometric constraint is implemented through the concept of the global radius of curvature and affects the conformational topology of ground-state structures. A systematic analysis allows for a thickness-dependent classification of the dominant ground-state topologies. It turns out that helical structures, strands, rings, and coils are natural, intrinsic geometries of su…
Structural changes in giant DNA induced by the addition of the flexible polymer PEG were examined by the method of single-DNA observation. In dilute DNA conditions, individual DNA assumes a compact state via a discrete coil-globule transition, whereas in concentrated solution, DNA molecules exhibit an extended conformation via macroscopic phase segregation. The long axis length of the stretched state in DNA is about 1000 times larger than that of the compact state. Phase segregation at high DNA concentrations occurs at lower PEG concentrations than the compaction at low DNA concentrations. The…
The phase behaviour of two-component bottle-brush polymers with fully flexible backbones under poor solvent conditions is studied via molecular-dynamics simulations, using a coarse-grained bead-spring model and side chains of up to $N=40$ effective monomers. We consider a symmetric model where side chains of type A and B are grafted alternately onto a flexible backbone. The aim of this study to explore the phase behaviour of two-component bottle-brushes depending on parameters, such as as the grafting density $σ$, the backbone length $N_b$, the side-chain length $N$, and the temperature $T$. B…
We use molecular simulations to study jamming of a crumpled bead-spring model polymer in a finite container and compare to jamming of repulsive spheres. After proper constraint counting, the onset of rigidity is seen to occur isostatically as in the case of repulsive spheres. Despite this commonality, the presence of the curved container wall and polymer backbone bonds introduce new mechanical properties. Notably, these include additional bands in the vibrational density of states that reflect the material structure as well as oscillations in local contact number and density near the wall but …
Understanding the role of self-propulsion on the conformational properties of active filamentous objects has relevance in biology. In this context, we consider a flexible bead-spring model polymer for which along with both attractive and repulsive interactions among the non-bonded monomers, activity for each bead works along its intrinsic direction of self-propulsion. We study its kinetics in the overdamped limit, following a quench from good to poor solvent condition. We observe that with low activities, though the kinetic pathways remain similar, the scaling exponent for the relaxation time …
The conformational and dynamical properties of active polymers in solution are determined by the nature of the activity, and the behavior of polymers with self-propelled, active Brownian particle-type monomers differs qualitatively from that of polymers with monomers driven externally by colored noise forces. We present simulation and theoretical results for polymers in solution in the presence of external active noise. In simulations, a semiflexible bead-spring chain is considered, in analytical calculations, a continuous linear wormlike chain. Activity is taken into account by independent mo…
We report molecular dynamics simulations of the segregation of two overlapping chains in cylindrical confinement. We find that the entropic repulsion between the chains can be sufficiently strong to cause segregation on a time scale that is short compared to the one for diffusion. This result implies that entropic driving forces are sufficiently strong to cause rapid bacterial chromosome segregation.
Experimental observations and computer simulations have recently revealed universal aspects of polymer solution behaviour that were previously unknown. This progress has been made possible due to developments in experimental methodologies and simulation techniques, and the formulation of scaling arguments that have identified the proper scaling variables with which to achieve data collapse, both for equilibrium and nonequilibrium properties. In this review, these advances in our understanding of universal polymer solution behaviour are discussed, along with a brief overview of prior experiment…
We review recent progress on the theory of dynamics of polymer translocation through a nanopore based on the iso-flux tension propagation (IFTP) theory. We investigate both pore-driven translocation of flexible and a semi-flexible polymers, and the end-pulled case of flexible chains by means of the IFTP theory and extensive molecular dynamics (MD) simulations. The validity of the IFTP theory can be quantified by the waiting time distributions of the monomers which reveal the details of the dynamics of the translocation process. The IFTP theory allows a parameter-free description of the translo…
Conformations of a single-component bottle-brush polymer with a fully flexible backbone under poor solvent conditions are studied by molecular-dynamics simulations, using a coarse-grained bead-spring model with side chains of up to N=40 effective monomers. By variation of the solvent quality and the grafting density $σ$ with which side chains are grafted onto the flexible backbone, we study for backbone lengths of up to $N_b=100$ the crossover from the brush/coil regime to the dense collapsed state. At lower temperatures, where collapsed chains with a constant monomer density are observed, the…
We study analytically a model of a two dimensional, partially directed, flexible or semiflexible polymer, attached to an attractive wall which is perpendicular to the preferred direction. In addition, the polymer is stretched by an externally applied force. We find that the wall has a dramatic effect on the polymer. For wall attraction smaller than the non-sequential nearest neighbor attraction, the fraction of monomers at the wall is zero and the model is the same as that of a polymer without a wall. However, for greater than, the fraction of monomers at the wall undergoes a first order trans…
We have mapped the physics of a system of semi-flexible inextensible polymers onto a complex Ginzburg-Landau field theory using techniques of functional integration. It is shown in the limit of low number density of monomers in a melt of semi-flexible, inextensible polymers, kept apart by an excluded volume interaction, the radius of gyration scales as N^{nu}, where N is the chain length, and nu = 1, in contrast to the value of nu ~ 0.6 for flexible polymer melts. Using Renormalization Group arguments, we show that the system exhibits an infra-red stable fixed point which can be identified as …
We consider random walk model of a semi-flexible polymer chain on a square and a cubic lattice to enumerate conformations of the polymer chain in two and three dimensions, respectively. The bending energy of the chain is assumed as the key factor which controls the minimum average length of the chain in between two successive bends in the chain; and the average length of the chains per unit bend is defined as the persistence length of the polymer chain. It has been found that the minimum energy required to bend the chain is expressed in the form of simple relation which includes space dimensio…
