We study theoretically the surface response of a semi-infinite viscoelastic polymer network using the two-fluid model. We focus on the overdamped limit and on the effect of the network's intrinsic length scales. We calculate the decay rate of slow surface fluctuations, and the surface displacement in response to a localized force. Deviations from the large-scale continuum response are found at length scales much larger than the network's mesh size. We discuss implications for surface scattering and microrheology. We provide closed-form expressions that can be used for surface microrheology -- the extraction of viscoelastic moduli and intrinsic length scales from the motions of tracer particles lying on the surface without doping the bulk material.
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 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…
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.
We present a novel generating function (GF) method for the self-condensing vinyl polymerization (SCVP) system with any initial distribution of preexisted polymers. Such a method was proven to be especially useful to investigate the semi-batch SCVP system allowing a sequence of feeding operations during the polymerization. Consequently, the number-, weight-, and z-average molecular weights as well as polydispersity index of hyperbranched polymers can be explicitly given, which are determined by predetermined feeding details and conversions in each polymerization step. These analytical results a…
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…
Rheo-optical measurements on Polyemethyl methacrylate (PMMA) and 4-Butoxycarbonylmethylurethane (4-BCMU) show that these synthetic random coil polymer chains compress in Couette flow at semi-dilute concentrations. All previous models of polymer flow behaviour have assumed that the chains extend. A new model of polymers in flow in semi-dilute solution is presented where the chains compress in accord with the experimental findings. The chains are modeled as simple blobs exposed to a linear shear gradient which results in a compressive hydrodynamic force on the chain. Equating the hydrodynamic an…
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…
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 study theoretically the entropic elasticity of a semi-flexible polymer, such as DNA, confined to two dimensions. Using the worm-like-chain model we obtain an exact analytical expression for the partition function of the polymer pulled at one end with a constant force. The force-extension relation for the polymer is computed in the long chain limit in terms of Mathieu characteristic functions. We also present applications to the interaction between a semi-flexible polymer and a nematic field, and derive the nematic order parameter and average extension of the polymer in a strong field.
The correlations between the segments of a semidilute polymer solution are found to induce correlations in the positions of small particles added to the solution. Small means a diameter much less than the polymer's correlation length. In the presence of polymer the particles behave as if they attracted each other. It is shown how the polymer's correlation length may be determined from a scattering experiment performed on the spheres.
In this work, we consider a semi-dilute solution of identical star-polymers, made of attached flexible long polymer chains of the same polymerization degree N. We first compute the effective pair-potential between star-polymers. Such a potential results from the excluded volume forces between monomers. We show that this potential is logarithmic, below some known characteristic distance, σ, depending on the number of attached chains per star-polymer, f, and volume fraction of polymers, φ0 . Beyond σ, the potential fails exponentially. Second, we investigate the structure and ther…
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 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…
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…
We image semi-flexible polymer networks under shear at the micrometer scale. By tracking embedded probe particles, we determine the local strain field, and directly measure its uniformity, or degree of affineness, on scales of 2-100 micron. The degree of nonaffine strain depends on polymer length and crosslink density, consistent with theoretical predictions. We also find a direct correspondence between the uniformity of the microscale strain and the nonlinear elasticity of the networks in the bulk.
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.
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.
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 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.
Understanding confined flows of complex fluids requires simultaneous access to the mechanical behaviour of the liquid and the boundary condition at the interfaces. Here, we use evanescent wave microscopy to investigate near-surface flows of semi-dilute, unentangled polyacrylamide solutions. By using both neutral and anionic polymers, we show that monomer charge plays a key role in confined polymer dynamics. For solutions in contact with glass, the neutral polymers display chain-sized adsorbed layers, while a shear-rate-dependent apparent slip length is observed for anionic polymer solutions. T…
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…
We develop a analytical and quantitative theory of the tube model concept for entangled networks of semiflexible polymers. The absolute value of the tube diameter L_perp is derived as a function of the polymers' persistence length l_p and mesh size xi of the network. To leading order we find L_\perp = 0.32 xi^{6/5} l_p^{-1/5}, which is consistent with known asymptotic scaling laws. Additionally, our theory provides corrections to scaling that account for finite polymer length effects and are dominated by the mesh size to polymer length ratio. We support our analytical studies by extensive comp…
We derive the Frank elastic constants for nematic solutions of semiflexible polymers. We plot these results as a function of the coarse-grained Maier-Saupe quadrupole aligning strength and polymer stiffness ranging from rigid to highly flexible. The derivation uses the random phase approximation and combines the exact results for the statistics of a worm-like-chain with polymer field theory using a spherical harmonic basis. The results are evaluated using a numerical inverse Laplace transform. We present the results in terms of microscopic features such as hairpins and polymer ends so the tren…
Actin is a filamentary protein which has many remarkable properties making it an ideal system for the study of the dynamics and mechanics of semi-flexible polymer solutions and gels; actin has a persistence length of over 10 microns and can polymerize to lengths of several tens of microns, this permits the use of video microscopy and other optical methods in the study polymer dynamics. Many associated proteins exist which can be used to regulate length or crosslink filaments. We discuss the dynamics and rheology of these solutions.
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 investigate the conformations of a semiflexible polymer confined to a square box. Results of Monte Carlo simulations show the existence of a shape transition when the persistence length of the polymer becomes comparable to the dimensions of box. An order parameter is introduced to quantify this behavior. A simple mean-field model is constructed to study the effect of the shape transition on the effective persistence length of the polymer.
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 …
A coarse-grained multi-blob description of polymer solutions is presented, based on soft, transferable effective interactions between bonded and non-bonded blobs. The number of blobs is chosen such that the blob density does not exceed their overlap threshold, allowing polymer concentrations to be explored deep into the semi-dilute regime. This quantitative multi-blob description is shown to preserve known scaling laws of polymer solutions and provides accurate estimates of amplitudes, while leading to orders of magnitude increase of simulation efficiency and allowing analytic calculations of …
We consider a long, semiflexible polymer, with persistence length $P$ and contour length $L$, fluctuating in a narrow cylindrical channel of diameter $D$. In the regime $D\ll P\ll L$ the free energy of confinement $ΔF$ and the length of the channel $R_\parallel$ occupied by the polymer are given by Odijk's relations $ΔF/R_\parallel=A_\circ k_BTP^{-1/3}D^{-2/3}$ and $R_\parallel=L[1-α_\circ(D/P)^{2/3}]$, where $A_\circ$ and $α_\circ$ are dimensionless amplitudes. Using a simulation algorithm inspired by PERM (Pruned Enriched Rosenbluth Method), which yields results for very long polymers, we de…
The Monte Carlo carbyne model is modified to investigate the glass transition of the semi-flexible entangled polymer chains. The stochastic bombardment between monomers are monitored by Metropolis algorithm with help of the consideration of hard potential while the mobility of monomers is governed by its mass, scattering rate and temperature. Our model is capable to show that the glass transition temperature reduces with decreasing film thickness and the formation of critical voids in the thinner polymer contributing to the glass transition that is much easier than the bulk polymer.
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…
Self-assembling, semi-flexible polymers are ubiquitous in biology and technology. However, there remain conflicting accounts of the equilibrium kinetics for such an important system. Here, by focusing on a dynamical description of a minimal model in an overdamped environment, I identify the correct kinetic scheme that describes the system at equilibrium in the limits of high bonding energy and dilute concentration.
Motivated by the organization of crosslinked cytoskeletal biopolymers, we present a semimicroscopic replica field theory for the formation of anisotropic random networks of semiflexible polymers. The networks are formed by introducing random permanent crosslinks which fix the orientations of the corresponding polymer segments to align with one another. Upon increasing the crosslink density, we obtain a continuous gelation transition from a fluid phase to a gel where a finite fraction of the system gets localized at random positions. For sufficiently stiff polymers, this positional localization…
We theoretically investigate the kinetics of the folding transition of a single semiflexible polymer. In the folding transition, the growth rate decrease with an increase in the number of monomers in a collapsed domain, suggesting that the main contribution to dissipation is from the motion of the domain. In the unfolding transition, dynamic scaling exponents, 1/8 and 1/4, were determined for disentanglement and relaxation steps, respectively. We performed Langevin dynamics simulations to test our theory. It is found that our theory is in good agreement with simulations. We also propose the ki…
We present a numerical solution of the Worm-Like Chain (WLC) model for semi-flexible polymers. We display graphs for the end-to-end distance distribution and the force-extension relation expected from the model. We predict the expected level of fluctuations around the mean value in force-extension curves. Our treatment analyses the entire range of polymer lengths and reproduces interesting qualitative features seen in recent computer simulations for polymers of intermediate length. These results can be tested against experiments on single molecules. This study is relevant to mechanical propert…
We have simulated the motion of a bead subjected to a constant force while embedded in a network of semiflexible polymers which can represent actin filaments. We find that the bead displacement obeys the power law x ~ t^alfa. After the initial stage characterized by the exponent alfa=0.75 we find a new regime with alfa=0.5. The response in this regime is linear in force and scales with the polymer concentration as c^(-1.4). We find that the polymers pile up ahead of the moving bead, while behind it the polymer density is reduced. We show that the force resisting the bead motion is due to steri…
We present a theoretical framework for the linear and nonlinear visco-elastic properties of reversibly crosslinked networks of semiflexible polymers. In contrast to affine models where network strain couples to the polymer end-to-end distance, in our model strain rather serves to locally distort the network structure. This induces bending modes in the polymer filaments, the properties of wich are slaved to the surrounding network structure. Specifically, we investigate the frequency-dependent linear rheology, in particular in combination with crosslink binding/unbinding processes. We also deve…
Networks of semiflexible or stiff polymers such as most biopolymers are known to deform inhomogeneously when sheared. The effects of such non-affine deformation have been shown to be much stronger than for flexible polymers. To date, our understanding of non-affinity in such systems is limited to simulations or specific 2D models of athermal fibers. Here, we present an effective medium theory (EMT) for non-affine deformation of semiflexible polymer and fiber networks, which is general to both 2D and 3D and in both thermal and athermal limits. The predictions of this model are in good agreement…
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…
The dynamic behavior of semi-dilute polymer solutions is governed by an interplay between solvent quality, concentration, molecular weight, and flow type. Semi-dilute solutions are characterized by large fluctuations in concentration, wherein polymer coils interpenetrate but may not be topologically entangled at equilibrium. In non-equilibrium flows, it is generally thought that polymer chains can self-entangle in semi-dilute solutions, thereby leading to entanglements in solutions that are nominally unentangled at equilibrium. Despite recent progress, we still lack a complete molecular-level …
The persistence length of macromolecules is one of their basic characteristics, describing their intrinsic local stiffness. However, it is difficult to extract this length from physical properties of the polymers, different recipes may give answers that disagree with each other. Monte Carlo simulations are used to elucidate this problem, giving a comparative discussion of two lattice models, the self-avoiding walk model extended by a bond bending energy, and bottle-brush polymers described by the bond fluctuation model. The conditions are discussed under which a description of such macromolecu…
While polymer solutions lack the mechanical stability only transiently cross-linked networks can fulfill the competing requirements of structural stability and maximal energy dissipation. Here, we show that transient cross-links entail local stress relaxation and energy dissipation in an intermediate elasticity dominated frequency regime. We quantify the mechanical response of a semi-flexible polymer network by experimentally tuning the off-rate of the transient cross-linker molecule and theoretically reproduce the measured frequency response by a model that is predicated on microscopic unbind…
The longitudinal response of single semiflexible polymers to sudden changes in externally applied forces is known to be controlled by the propagation and relaxation of backbone tension. Under many experimental circumstances, realized, e.g., in nano-fluidic devices or in polymeric networks or solutions, these polymers are effectively confined in a channel- or tube-like geometry. By means of heuristic scaling laws and rigorous analytical theory, we analyze the tension dynamics of confined semiflexible polymers for various generic experimental setups. It turns out that in contrast to the well-kno…
Shape enantiomerism in semi-rigid polymer liquid crystals
Laboratoire de Physique des Solides - UMR 8502, CNRS, Université Paris-Saclay（巴黎萨克雷大学固体物理实验室）；Institut Charles Sadron, Université de Strasbourg & CNRS（斯特拉斯堡大学夏尔·萨德龙研究所）
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…
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 …
We present a method to generate realistic, three-dimensional networks of crosslinked semiflexible polymers. The free energy of these networks is obtained from the force-extension characteristics of the individual polymers and their persistent directionality through the crosslinks. A Monte Carlo scheme is employed to obtain isotropic, homogeneous networks that minimize the free energy, and for which all of the relevant parameters can be varied: the persistence length, the contour length as well as the crosslinking length may be chosen at will. We also provide an initial survey of the mechanical…
It has long been known for elastomers that the velocity of crack propagation jumps as a function of strain. On the other hand, such a jump has not been reported in the literature for polymers which do not exhibit a rubbery plateau in the storage-modulus plot. Here, we report observation of jumps in crack propagation for semi-crystalline polymer sheets without the rubbery plateau, as a result of pulling the sheets at a constant speed. We discuss the advantages of this crack-propagation test under constant-speed stretching and provide physical interpretation of the velocity jump observed for non…
Conformations of partially or fully adsorbed semiflexible polymer chains are studied varying both contour length $L$, chain stiffness, $κ$, and the strength of the adsorption potential over a wide range. Molecular Dynamics simulations show that partially adsorbed chains (with "tails", surface attached "trains" and "loops") are not described by the Kratky-Porod wormlike chain model. The crossover of the persistence length from its three-dimensional value $(\ell_p)$ to the enhanced value in two dimensions $(2\ell_p)$ is analyzed, and excluded volume effects are identified for $L \gg \ell_p$. Con…
We study the viscoelasticity of surface polymer monolayers by measuring the dynamics of thermal concentration fluctuations with surface light scattering. For various systems of proteins and synthetic polymers we find a semi-dilute regime in which both the elastic and viscous components of the dilational modulus show power law dependencies on the concentration. Surprisingly there is a universal relationship between the exponents for the two components: the viscosity scales with a power double that of the elasticity. These results cannot be explained on the basis of theory developed for bulk sys…
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 findin…
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 investigate the statistical properties of a randomly branched 3--functional $N$--link polymer chain without excluded volume, whose one point is fixed at the distance $d$ from the impenetrable surface in a 3--dimensional space. Exactly solving the Dyson-type equation for the partition function $Z(N,d)=N^{-θ} e^{γN}$ in 3D, we find the "surface" critical exponent $θ={5/2}$, as well as the density profiles of 3--functional units and of dead ends. Our approach enables to compute also the pairwise correlation function of a randomly branched polymer in a 3D semi-space.
We study single-chain motion in semidilute solutions of polymers of length N = 1000 with excluded-volume and hydrodynamic interactions by a novel algorithm. The crossover length of the transition from Zimm (short lengths and times) to Rouse dynamics (larger scales) is proportional to the static screening length. The crossover time is the corresponding Zimm time. Our data indicate Zimm behavior at large lengths but short times. There is no hydrodynamic screening until the chains feel constraints, after which they resist the flow: "Incomplete screening" occurs in the time domain.
Using a combination of the replica-exchange Monte Carlo algorithm and the multicanonical method, we investigate the influence of bending stiffness on the conformational phases of a bead-stick homopolymer model and present the pseudo-phase diagram for the complete range of semi-flexible polymers, from flexible to stiff. Although a simple model, we observe a rich variety of conformational phases, reminiscent of conformations observed for synthetic polymers or biopolymers. Changing the internal bending stiffness, the model exhibits different pseudo phases like bent, hairpin or toroidal. In partic…
We study the statistical mechanics of double-stranded semi-flexible polymers using both analytical techniques and simulation. We find a 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. In the low temperature phase, the polymers develop a kink-rod structure which could clarify some recent puzzling experiments on actin.
We perform kinetic Monte Carlo simulations of flow-induced nucleation in polymer melts with an algorithm that is tractable even at low undercooling. The configuration of the non-crystallized chains under flow is computed with a recent non-linear tube model. Our simulations predict both enhanced nucleation and the growth of shish-like elongated nuclei for sufficiently fast flows. The simulations predict several experimental phenomena and theoretically justify a previously empirical result for the flow-enhanced nucleation rate. The simulations are highly pertinent to both the fundamental underst…
