We investigate the viscoelastic properties of entangled networks of semiflexible polymers. At intermediate time scales the elastic response of these networks to shear deformation is described by the plateau modulus $G$. Different scaling laws with polymer concentration $c$ have been proposed based on the assumption that the deformation field is affine on all length scales. We develop a numerical approach that allows to calculate the modulus via free energy changes for both affine and non-affine deformations. The non-affine deformation field is obtained by a free energy minimization. Our findings allow for a confirmation of a power law $G \propto c^{7/5} l_p^{-1/5}$ with polymer concentration $c$ and persistence length $l_p$ and furthermore quantify the systematic deviations due to the affinity assumption.
The non-equilibrium structural and dynamical properties of semiflexible polymers confined to two dimensions are investigated by molecular dynamics simulations. Three different scenarios are considered: The force-extension relation of tethered polymers, the relaxation of an initially stretched semiflexible polymer, and semiflexible polymers under shear flow. We find quantitative agreement with theoretical predictions for the force-extension relation and the time dependence of the entropically contracting polymer. The semiflexible polymers under shear flow exhibit significant conformational chan…
We present the statistical-mechanical theory of semiflexible polymers based on the connection between the Kratky-Porod model and the quantum rigid rotator in an external homogeneous field, and treatment of the latter using the quantum mechanical propagator method. The expressions and relations existing for flexible polymers can be generalized to semiflexible ones, if one replaces the Fourier-Laplace transform of the end-to-end polymer distance, $1/(k^{2}/3+p)$, through the matrix $\tilde{P}(k,p)=(I+ikDM)^{-1}D$, where $D$ and $M$ are related to the spectrum of the quantum rigid rotator, and co…
We present using simple scaling arguments and one step replica symmetry breaking a theory for the localization of semiflexible polymers in a quenched random environment. In contrast to completely flexible polymers, localization of semiflexible polymers depends not only on the details of the disorder but also on the ease with which polymers can bend. The interplay of these two effects can lead to the delocalization of a localized polymer with an increase in either the disorder density or the stiffness. Our theory provides a general criterion for the delocalization of polymers with varying degre…
We consider the motion of semiflexible polymers in double-well potentials. We calculate shape, energy, and effective diffusion constant of kink excitations, and in particular their dependence on the bending rigidity of the semiflexible polymer. For symmetric potentials, the kink motion is purely diffusive whereas kink motion becomes directed in the presence of a driving force on the polymer. We determine the average velocity of the semiflexible polymer based on the kink dynamics. The Kramers escape over the potential barriers proceeds by nucleation and diffusive motion of kink-antikink pairs, …
The conformational states of a semiflexible polymer enclosed in a volume $V:=\ell^{3}$ are studied as stochastic realizations of paths using the stochastic curvature approach developed in [Rev. E 100, 012503 (2019)], in the regime whenever $3\ell/\ell_ {p}> 1$, where $\ell_{p}$ is the persistence length. The cases of a semiflexible polymer enclosed in a cube and sphere are considered. In these cases, we explore the Spakowitz-Wang type polymer shape transition, where the critical persistence length distinguishes between an oscillating and a monotonic phase at the level of the mean-square end-to…
The phase behaviour of a single large semiflexible polymer immersed in a suspension of spherical particles is studied. All interactions are simple excluded volume interactions and the diameter of the spherical particles is an order of magnitude larger than the diameter of the polymer. The spherical particles induce a quite long ranged depletion attraction between the segments of the polymer and this induces a continuous coil-globule transition in the polymer. This behaviour gives an indication of the condensing effect of macromolecular crowding on DNA.
We consider the adsorption of a semiflexible polymer chain onto interfaces and surfaces by using the differential equation of the distribution function $G(R,L)$ of the end-to-end distance $R$, which is associated with the moment expansion of the latter. We present the results of the approximative treatment consisting of taking into account the 2nd and 4th moments in the differential equation for $G(R,L)$. The essential features of adsorption of the semiflexible polymer are: {\it i}) the existence of a new local length scale, which results in two-exponential decay of the monomer density of adso…
We demonstrate that a semiflexible bundle of wormlike chains exhibits a state-dependent bending stiffness that alters fundamentally its scaling behavior with respect to the standard wormlike chain. We explore the equilibrium conformational and mechanical behavior of wormlike bundles in isolation, in crosslinked networks, and in solution.
We analyze static properties of a strongly confined semiflexible polymer, i.e. either trapped in a closed space or compressed by external forces, in an athermal solvent. Like a flexible polymer case, we can resort to an analogy with the semidilute solution, but a complication due to the additional length scale arising from the chain rigidity results in more diverse behaviours depending on system parameters. For each regime, scaling forms of the excess free energy of the confinement are derived. Effects of the confinement geometry and the solvent quality are briefly discussed.
We develop a scaling theory to describe dynamic fluctuations of a semiflexible polymer and find several distinct regimes. We performed simulations to characterize the longitudinal and transverse dynamics; using ensemble averaging for a range of different degrees of coarse-graining we avoid the problems of slow equilibration often encountered in simulations. We find that the longitudinal fluctuations of a semiflexible object scales as t^7/8. These fluctuations are correlated over a length which varies as t^1/8. Our results are pertinent to the interpretation of high frequency microrheology expe…
In this paper, we present a new approach to the Kratky-Porod Model (KP) of semiflexible polymers. Our solution to the model is based on the definition of a generating function which we use to study the statistical mechanics of semiflexible polymer chains. Specifically, we derive mathematical expressions for the characteristic function, the polymer propagator and the mean square end-to-end distance from the generating function. These expressions are valid for polymers with any number of segments and degree of rigidity. Furthermore, they capture the limits of fully flexible and stiff polymers ex…
The mean square end-to-end distance of a N-step polymer on a Bethe lattice is calculated. We consider semiflexible polymers placed on isotropic and anisotropic lattices. The distance on the Cayley tree is defined by embedding the tree on a sufficiently high dimensional Euclidean space considering that every bend of the polymer defines a direction orthogonal to all the previous ones. In the isotropic case, the result obtained for the mean square end-to-end distance turns out to be identical to the one obtained for ideal chains without immediate returns on an hypercubic lattice with the same coo…
Here, we provide an overview of theoretical approaches to semiflexible polymers and their networks. Such semiflexible polymers have large bending rigidities that can compete with the entropic tendency of a chain to crumple up into a random coil. Many studies on semiflexible polymers and their assemblies have been motivated by their importance in biology. Indeed, crosslinked networks of semiflexible polymers form a major structural component of tissue and living cells. Reconstituted networks of such biopolymers have emerged as a new class of biological soft matter systems with remarkable materi…
We show using Brownian dynamics simulations and theory how the shear relaxation modulus G(t) of dilute solutions of relatively stiff semiflexible polymers differs qualitatively from that of rigid rods. For chains shorter than their persistence length, G(t) exhibits three time regimes: At very early times, when the longitudinal deformation is affine, G(t) \sim t^{-3/4}. Over a broad intermediate regime, during which the chain length relaxes, G(t) \sim t^{-5/4}. At long times, $G(t) mimics that of rigid rods. A model of the polymer as an effectively extensible rod with a frequency dependent elas…
We present a theoretical analysis of a simple model of the depinning of an anchored semiflexible polymer from a fixed planar substrate in (1+1) dimensions. We consider a polymer with a discrete sequence of pinning sites along its contour. Using the scaling properties of the conformational distribution function in the stiff limit and applying the necklace model of phase transitions in quasi-one-dimensional systems, we obtain a melting criterion in terms of the persistence length, the spacing between pinning sites, a microscopic effective length which characterizes a bond, and the bond energy. T…
The dynamic structure factor of semiflexible polymers in solution is derived from the wormlike chain model. Special attention is paid to the rigid constraint of an inextensible contour and to the hydrodynamic interactions. For the cases of dilute and semidilute solutions exact expressions for the initial slope are obtained. When the hydrodynamic interaction is treated on the level of a renormalized friction coefficient, the decay of the structure factor due to the structural relaxation obeys a stretched exponential law in agreement with experiments on actin. We show how the characteristic para…
We study the thermodynamic properties of a semiflexible polymer confined inside strips of widths L<=9 defined on a square lattice. The polymer is modeled as a self-avoiding walk and a short range interaction between the monomers and the walls is included through an energy e associated to each monomer placed on one of the walls. Also, an additional energy is associated to each elementary bend of the walk. The free energy of the model is obtained exactly through a transfer matrix formalism. The profile of the monomer density and the force on the walls are obtained. We notice that as the bending …
The conformations of semiflexible (bio)polymers are studied in flow through geometrically structured microchannels. Using mesoscale hydrodynamics simulations, we show that the polymer undergoes a rod-to-helix transition as it moves from the narrow high-velocity region into the wide low-velocity region of the channel. The transient helix formation is the result of a non-equilibrium and non-stationary buckling transition of the semiflexible polymer, which is subjected to a compressive force originating from the fluid-velocity variation in the channel. The helix properties depend on the diameter …
The entropic force exerted by the Brownian fluctuations of a grafted semiflexible polymer upon a rigid smooth wall are calculated both analytically and by Monte Carlo simulations. Such forces are thought to play an important role for several cellular phenomena, in particular, the physics of actin-polymerization-driven cell motility and movement of bacteria like Listeria. In the stiff limit, where the persistence length of the polymer is larger than its contour length, we find that the entropic force shows scaling behavior. We identify the characteristic length scales and the explicit form of t…
We review the physical properties of macromolecular networks, consisting of semiflexible polymers such as actin. We start by giving a theoretical analysis of the conformational statistics and mechanical response of single filaments. Experimentally relevant quantities such as the end-to-end distribution function and the force-extension relation are discussed. The results are used to analyze the elastic modulus of an entangled solution of such objects. We also discuss the short time and long time (terminal regime) dynamics and compare our results with recent dynamic light scattering and viscoela…
Recently many important biopolymers have been found to possess intrinsic curvature. Tubulin protofilaments in animal cells, FtsZ filaments in bacteria and double stranded DNA are examples. We examine how intrinsic curvature influence the conformational statistics of such polymers. We give exact results for the tangent-tangent spatial correlation function C(r) = t(s).t(s + r), both in two and three dimensions. Contrary to expectation, C(r) does not show any oscillatory behavior, rather decays exponentially and the effective persistence length has strong length dependence for short polymers. We …
A {\it new} formula for the force vs extension relation is derived from the discrete version of the so called {\it worm like chain} model. This formula correctly fits some recent experimental data on polymer stretching and some numerical simulations with pairwise repulsive potentials. For a more realistic Lennard-Jones potential the agreement with simulations is found to be good when the temperature is above the $θ$ temperature. For lower temperatures a plateau emerges, as predicted by some recent experimental and theoretical results, and our formula gives good results only in the high force r…
Spherical confinement can act either stabilizing or destabilizing on the collapsed state of a semi-flexible polymer. General free-energy arguments suggest that the order of the unconstrained collapse transition is the distinguishing factor: First order implies stabilization, second order causes destabilization. We confirm this conjecture by Monte Carlo simulations of a coarse-grained model for semiflexible polymers whose chain stiffness tunes the transition order. The resulting physical picture is potentially relevant for other systems under strong confinement such as proteins and DNA.
We present a model for semiflexible polymers in Hamiltonian formulation which interpolates between a Rouse chain and worm-like chain. Both models are realized as limits for the parameters. The model parameters can also be chosen to match the experimental force-extension curve for double-stranded DNA. Near the ground state of the Hamiltonian, the eigenvalues for the longitudinal (stretching) and the transversal (bending) modes of a chain with N springs, indexed by p, scale as lambda_lp ~ (p/N)^2 and lambda_tp ~ p^2(p-1)^2/N^4 respectively for small p. We also show that the associated decay time…
Conformations of a single semiflexible polymer chain dissolved in a low molecular weight liquid crystalline solvents (nematogens) are examined by using a mean field theory. We takes into account a stiffness and partial orientational ordering of the polymer. As a result of an anisotropic coupling between the polymer and nematogen, we predict a discontinuous (or continuous) phase transition from a condensed-rodlike conformation to a swollen-one of the polymer chain, depending on the stiffness of the polymer. We also discuss the effects of the nematic interaction between polymer segments.
The non-equilibrium structural and dynamical properties of a semiflexible polymer confined in a cylindrical microchannel and exposed to a Poiseuille flow is studied by mesoscale hydrodynamic simulations. For a polymer with a length half of its persistence length, large variations in orientation and conformations are found as a function of radial distance and flow strength. In particular, the polymer exhibits U-shaped conformations near the channel center. Hydrodynamic interactions lead to strong cross-streamline migration. Outward migration is governed by the polymer orientation and the corres…
Semiflexible polymers form central structures in biological material. Modeling approaches usually neglect influences of polymer-specific molecular features aiming to describe semiflexible polymers universally. Here, we investigate the influence of molecular details on networks assembled from filamentous actin, intermediate filaments, and synthetic DNA nanotubes. In contrast to prevalent theoretical assumptions, we find that bulk properties are affected by various inter-filament interactions. We present evidence that these interactions can be merged into a single parameter in the frame of the g…
Exact solutions for the elastic and thermodynamic properties for the wormlike chain model are elaborated in terms of Mathieu functions. The smearing of the classical Euler buckling instability for clamped polymers is analyzed for the force-extension relation. Interestingly, at strong compression forces the thermal fluctuations lead to larger elongations than for the elastic rod. The susceptibility defined as the derivative of the force-extension relation displays a prominent maximum at a force that approaches the critical Euler buckling force as the persistence length is increased. We also eva…
Kinetics of conformational change of a semiflexible polymer under mechanical external field were investigated with Langevin dynamics simulations. It is found that a semiflexible polymer exhibits large hysteresis in mechanical folding/unfolding cycle even with a slow operation, whereas in a flexible polymer, the hysteresis almost disappears at a sufficiently slow operation. This suggests that the essential features of the structural transition of a semiflexible polymer should be interpreted at least on a two-dimensional phase space. The appearance of such large hysteresis is discussed in relati…
Linear Viscoelasticity of Semiflexible Polymers with Hydrodynamic Interactions
IITB-Monash Research Academy, Indian Institute of Technology Bombay（印度理工学院孟买分校 IITB-莫纳什研究院）；Department of Chemical Engineering, Indian Institute of Technology Bombay（印度理工学院孟买分校化学工程系）；Department of Chemical and Biological Engineering, Monash University（莫纳什大学化学与生物工程系）
The statistical mechanics of a ribbon polymer made up of two semiflexible chains is studied using both analytical techniques and simulation. The system is found to have a crossover transition at some finite temperature, from a type of short range order to a fundamentally different sort of short range order. In the high temperature regime, the 2-point correlation functions of the object are identical to worm-like chains, while in the low temperature regime they are different due to a twist structure. The crossover happens when the persistence length of individual strands becomes comparable to t…
Employing Monte Carlo simulations of semiflexible polymer rings in weak spherical confinement a conformational transition to figure eight shaped, writhed configurations is discovered and quantified.
The folding transition of single, long semiflexible polymers was studied with special emphasis on the chain length effect using Monte Carlo simulations. While a relatively short chain (10-25 Kuhn segments) undergoes a large discrete transiton between swollen coil and compact toroid conformations, a long chain (50 Kuhn segments) exhibits an intrachain segregated state between the disordered coil and ordered toroid.
We elucidate the elastic behavior of a wormlike chain in 3D under compression and provide exact solutions for the experimentally accessible force-extension relation in terms of generalized spheroidal wave functions. In striking contrast to the classical Euler buckling instability, the force-extension relation of a clamped semiflexible polymer exhibits a smooth crossover from an almost stretched to a buckled configuration. In particular, the associated susceptibility, which measures the strength of the response of the polymer to the applied force, displays a prominent peak in the vicinity of th…
Molecular Dynamics (MD) simulations are presented for a coarse-grained bead-spring model of ring polymer brushes under compression. Flexible polymer brushes are always disordered during compression, whereas semiflexible brushes tend to be ordered under sufficiently strong compression. Besides, the polymer monomer density of semiflexible polymer brush is very high near the polymer brush surface, inducing a peak value of free energy near the polymer brush surface. Therefore, by compressing nanoparticles (NPs) in semiflexible ring brush system, NPs tend to exhibit a closely packed single layer st…
We employ the recently introduced generalized microcanonical inflection point method for the statistical analysis of phase transitions in flexible and semiflexible polymers and study the impact of the bending stiffness upon the character and order of transitions between random-coil, globules, and pseudocrystalline conformations. The high-accuracy estimates of the microcanonical entropy and its derivatives required for this study were obtained by extensive replica-exchange Monte Carlo simulations. We observe that the transition behavior into the compact phases changes qualitatively with increas…
Semiflexible polymer models are widely used as a paradigm to understand structural phases in biomolecules including folding of proteins. Since stable knots are not so common in real proteins, the existence of stable knots in semiflexible polymers has not been explored much. Here, via extensive replica exchange Monte Carlo simulation we investigate the same for a bead-stick and a bead-spring homopolymer model that covers the whole range from flexible to stiff. We establish the fact that the presence of stable knotted phases in the phase diagram is dependent on the ratio $r_b/r_{\rm{min}}$ where…
We discuss the adsorption of semiflexible polymers to a planar attractive wall and focus on the questions of the adsorption threshold for polymers of {\it finite} length and their loop and tail distributions using both Monte-Carlo simulations and analytical arguments. For the adsorption threshold, we find three regimes: (i) a flexible or Gaussian regime if the persistence length is smaller than the adsorption potential range, (ii) a semiflexible regime if the persistence length is larger than the potential range, and (iii) for finite polymers, a novel crossover to a rigid rod regime if the def…
We study the dynamical properties of semiflexible polymers with a recently introduced bead-spring model. We focus on double-stranded DNA. The two parameters of the model, $T^*$ and $ν$, are chosen to match its experimental force-extension curve. The bead-spring Hamiltonian is approximated in the first order by the Hessian that is quadratic in the bead positions. The eigenmodels of the Hessian provide the longitudinal (stretching) and transverse (bending) eigenmodes of the polymer, and the corresponding eigenvalues match well with the established phenomenology of semiflexible polymers. Using th…
By large-scale Monte Carlo simulations of semiflexible polymers in $d=2$ dimensions the applicability of the Kratky-Porod model is tested. This model is widely used as "standard model" for describing conformations and force versus extension curves of stiff polymers. It is shown that semiflexible polymers in $d=2$ show a crossover from hard rods to self-avoiding walks, the intermediate Gaussian regime (implied by the Kratky-Porod model) is completely absent. Hence the latter can also describe force versus extension curves only if the contour length is only a few times larger than the persistenc…
We consider an inextensible, semiflexible polymer or worm-like chain which is confined in the transverse direction by a parabolic potential and subject to a longitudinal force at the ends, so that the polymer is stretched out and backfolding is negligible. Simple analytic expressions for the partition function, valid in this regime, are obtained for chains of arbitrary length with a variety of boundary conditions at the ends. The spatial distribution of the end points or radial distribution function is also analyzed.
The nematic ordering in semiflexible polymers with contour length $L$ exceeding their persistence length $\ell_p$ is described by a confinement of the polymers in a cylinder of radius $r_{eff}$ much larger than the radius $r_ρ$, expected from the respective concentration of the solution. Large scale Molecular Dynamics simulations combined with Density Functional Theory are used to locate the Isotropic-Nematic ($I-N$)-transition and to validate this cylindrical confinement. Anomalous fluctuations, due to chain deflections from neighboring chains in the nematic phase are proposed. Considering de…
We use the worm-like chain model to analytically calculate the linear response of a grafted semiflexible polymer to a uniform force field. The result is a function of the bending stiffness, the temperature, the total contour length, and the orientation of the field with respect to that of the grafted end. We also study the linear response of a worm-like chain with a periodic alternating sequence of positive and negative charges. This can be considered as a model for a polyampholyte with intrinsic bending siffness and negligible intramolecular interactions. We show how the finite intrinsic pers…
We study the conformational properties of polymers in presence of extended columnar defects of parallel orientation. Two classes of macromolecules are considered: the so-called partially directed polymers with preferred orientation along direction of the external stretching field and semiflexible polymers. We are working within the frames of lattice models: partially directed self-avoiding walks (PDSAWs) and biased self-avoiding walks (BSAWs). Our numerical analysis of PDSAWs reveals, that competition between the stretching field and anisotropy caused by presence of extended defects leads to e…
The properties of semiflexible polymers tethered by one end to an impenetrable wall and exposed to oscillatory shear flow are investigated by mesoscale simulations. A polymer, confined in two dimensions, is described by a linear bead-spring chain, and fluid interactions are incorporated by the Brownian multiparticle collision dynamics approach. At small strains, the polymers follow the applied flow field. However, at high strain, we find a strongly nonlinear response, with major conformational changes. Polymers are stretched along the flow direction and exhibit U-shaped conformations while fol…
Binary mixtures of semiflexible polymers with the same chain length but different persistence lengths separate into two coexisting different nematic phases when the osmotic pressure of the lyotropic solution is varied. Molecular Dynamics simulations and Density Functional Theory predict phase diagrams either with a triple point, where the isotropic phase coexists with two nematic phases, or a critical point of unmixing within the nematic mixture. The difference in locally preferred bond angles between the constituents drives this unmixing without any attractive interactions between monomers.
Using molecular dynamics simulations of a tangent-soft-sphere bead-spring polymer model, we examine the degree to which semiflexible polymer melts solidify at isostaticity. Flexible and stiff chains crystallize when they are isostatic as defined by appropriate degree-of-freedom-counting arguments. Semiflexible chains also solidify when isostatic if a generalized isostaticity criterion that accounts for the slow freezing out of configurational freedom as chain stiffness increases is employed. The dependence of the average coordination number at solidification $Z(T_s)$ on chains' characteristic …
We study the adsorption of semiflexible polymers such as polyelectrolytes or DNA on planar and curved substrates, e.g., spheres or washboard substrates via short-range potentials using extensive Monte-Carlo simulations, scaling arguments, and analytical transfer matrix techniques. We show that the adsorption threshold of stiff or semiflexible polymers on a planar substrate can be controlled by polymer stiffness: adsorption requires the highest potential strength if the persistence length of the polymer matches the range of the adsorption potential. On curved substrates, i.e., an adsorbing sphe…
We investigate wrinkling of two-dimensional random and triangular semiflexible polymer networks under shear. Both types of semiflexible networks exhibit wrinkling above a small critical shear angle, which scales with an exponent of the bending modulus between 1.9 and 2.0. Random networks exhibit hysteresis at the wrinkling threshold. Wrinkling lowers the total elastic energy by up to 20% and strongly affects the elastic properties of all semiflexible networks such as the crossover between bending and stretching dominated behavior. In random networks, we also find evidence for metastable wrinkl…
Generic interactions e.g. the Coulomb or other long ranged radially symmetric repulsive interactions between monomers of bead-spring model of a semi-flexible polymer induce instabilities in a initially straight polymer chain to form long lived helical structures. This mechanism can explain the spontaneous emergence of helices in stiff (bio-)polymers as effective charge of the chain increases. The helix formation is independent of the chemistry and torsional potentials are not used. So this method can be used to synthesize helical springs at length scales of nm-10$μ$.
The nonequilibrium dynamical behavior and structure formation of end-functionalized semiflexible polymer suspensions under flow are investigated by mesoscale hydrodynamic simulations. The hybrid simulation approach combines the multiparticle collision dynamics method for the fluid, which accounts for hydrodynamic interactions, with molecular dynamics simulations for the semiflexible polymers. In equilibrium, various kinds of scaffold-like network structures are observed, depending on polymer flexibility and end-attraction strength. We investigate the flow behavior of the polymer networks under…
A number of strange results have been reported for the twist elasticity of a semiflexible filament, actin. In particular dynamic and static methods for determining the torsional twist modulus give very different results. I show here that internal losses (friction) in a semiflexible filament could be an important cause of dissipation and that the interpretation of dynamic experiments should be made in terms of a storage and loss modulus for actin proteins.
The flow behavior of a semiflexible polymer in microchannels is studied using Multiparticle Collision Dynamics (MPC), a particle-based hydrodynamic simulation technique. Conformations, distributions, and radial cross-streamline migration are investigated for various bending rigidities, with persistence lengths Lp in the range 0.5 < Lp/Lr < 30. The flow behavior is governed by the competition between a hydrodynamic lift force and steric wall-repulsion, which lead to migration away from the wall, and a locally varying flow-induced orientation, which drives polymer away from the channel center an…
We analyse the nature of the confinement of an infinitely long (and finite) linear semiflexible homo-polymer chain confined in between two geometrical constraints (A&B) under good solvent condition in two dimensions. The constraints are stair shaped impenetrable lines. A lattice model of fully directed self avoiding walk is used to list information of walks of the confined chain and the exact enumeration technique is used for the canonical ensemble of conformations of the confined chain to discuss equilibrium statistics of the chain. We obtain the probability of polymerization of the confined …
We study the translocation of a semiflexible polymer through extended pores with patterned stickiness, using Langevin dynamics simulations. We find that the consequence of pore patterning on the translocation time dynamics is dramatic and depends strongly on the interplay of polymer stiffness and pore-polymer interactions. For heterogeneous polymers with periodically varying stiffness along their lengths, we find that variation of the block size of the sequences and the orientation, results in large variations in the translocation time distributions. We show how this fact may be utilized to de…
We explore the effect of an attractive interaction between parallel-aligned polymers, which are perpendicularly grafted on a substrate. Such an attractive interaction could be due to, e.g., reversible cross-links. The competition between permanent grafting favoring a homogeneous state of the polymer brush and the attraction, which tends to induce in-plane collapse of the aligned polymers, gives rise to an instability of the homogeneous phase to a bundled state. In this latter state the in-plane translational symmetry is spontaneously broken and the density is modulated with a finite wavelength…
We develop a theory describing density profile of the semi-flexible polymers absorbed onto a planar surface. The theoretical analysis consists of two parts. As a first part, we calculate a density profile of the adsorbed polymers by developing an extension of the Bethe-Peierls approximation to the case of nonhomogeneous systems. This approach relies on the combination of the single chain adsorption theory and the lattice version of the self-consistent field theory. Semi-flexibility of a chain is described by incorporating a finite coordination number of the lattice into the consideration, in t…
Motivated by the structure of networks of cross-linked cytoskeletal biopolymers, we study the orientationally ordered phases in two-dimensional networks of randomly cross-linked semiflexible polymers. We consider permanent cross-links which prescribe a finite angle and treat them as quenched disorder in a semi-microscopic replica field theory. Starting from a fluid of un-cross-linked polymers and small polymer clusters (sol) and increasing the cross-link density, a continuous gelation transition occurs. In the resulting gel, the semiflexible chains either display long range orientational order…
