In the present work, four series of simulations are analyzed: entangled model networks of a) mono-disperse or b) poly-disperse weight distribution between the crosslinks, c) non-entangled phantom model networks and d) non-entangled model networks with excluded volume interactions. Previous work on the average residual bond orientations (RBO) of model networks [1] is extended to describe the distribution of RBOs for the entangled networks of the present study. The phantom model can be used to describe the monomer fluctuations, average RBOs, and the distribution of RBOs in networks without entanglements and without excluded volume. Monomer fluctuations in networks with excluded volume but without entanglements can be described if the phantom model is corrected by the effect of the incompletely screened excluded volume. It is shown that parameters of the tube model can be determined from monomer fluctuations in polymer networks and from the RBO. A scaling of the RBO $\propto N^{-1/2}$ is observed in both mono-disperse and poly-disperse entangled networks, while for all networks without entanglements an RBO $\propto N^{-1}$ is found. The distribution of the RBO of entangled samples can be described by assuming a normal distribution of tube lengths that is broadened by local fluctuations in tube curvature. Both observables, monomer fluctuations and RBO, are in agreement with slip link or slip tube models [2] for networks and disagree with network models that do not allow a sliding motion of the monomers along a confining tube.
It is discussed that the kinetics observed by Shusterman et al. [Phys. Rev. Lett. 92, 048303] for long dsDNA is not the Rouse one and, in fact, the macromolecule behaves (approximately) as the Zimm polymer.
A coarse-graining strategy for dilute and semi-dilute solutions of interacting polymers, and of colloid polymer mixtures is briefly described. Monomer degrees of freedom are traced out to derive an effective, state dependent pair potential between the polymer centres of mass. The cross-over between good and poor solvent conditions is discussed within a scaling analysis. The method is extended to block copolymers represented as "necklaces" of soft "blobs", and its success is illustrated here in the case of a symmetric diblock copolymer which exhibits microphase separation.
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. …
We study the conformations of a self-avoiding polymer confined to a channel by computing the cross-sectional distributions of the positions of its monomers. By means of Monte-Carlo simulations for a self-avoiding, freely-jointed chain we determine how the cross-sectional distribution for a given monomer depends on its location in the polymer, and how strongly this distribution is affected by self avoidance. To this end we analyze how the frequency of intra-chain collisions between monomers depends on their spatial position in the channel and on their location within the polymer. We show that m…
We make use of the previously developed formalism for a monomer ensemble and include angular dependence of the segments of the polymer chains thus described. In particular we show how to deal with stiffness when the polymer chain is confined to certain regions. We investigate the stiffness from the perspectives of a differential equation, integral equations, or recursive relations for both continuum and lattice models. Exact analytical solutions are presented for two cases, whereas numerical results are shown for a third case.
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.
Recent advances in Generalized Ensemble simulations and microcanonical analysis allowed the investigation of structural transitions in polymer models over a broad range of local bending and torsion strengths. It is reasonable to argue that electrostatic interactions play a significant role in stabilizing and mediating structural transitions in polymers. We propose a bead-spring polymer model with randomly distributed charged monomers interacting via a screened Coulomb potential. By combining the Replica Exchange Wang-Landau (REWL) method with energy-dependent monomer updates, we constructed th…
We perform a thermodynamic analysis of the polymerization-induced phase separation in nanoparticle-monomer-polymer blends using a simple model recently proposed by V. V. Ginzburg (Macromolecules 2005, 38, 2362.). The model was adapted for ternary blends constituted by nanoparticles, a monomer and a linear polymer, where the relative fractions of polymer and monomer determine the conversion in the polymerization reaction. The analysis showed that phase separation can occur in the course of polymerization for a large range of values of the relevant parameters (interaction parameter, and polymer …
We present a simple analytical theory of flexible polymer chain dissolved in a good solvent, carrying permanent freely oriented dipoles on the monomers. We take into account the dipole correlations within the random phase approximation (RPA), as well as a dielectric heterogeneity in the internal polymer volume relative to the bulk solution. We demonstrate that the dipole correlations of monomers can be taken into account as pairwise ones only when the polymer chain is in a coil conformation. In this case the dipole correlations manifest themselves through the Keesom interactions of the permane…
We study the energy structure and the coherent transfer of an extra electron or hole along aperiodic polymers made of $N$ monomers, with fixed boundaries, using B-DNA as our prototype system. We use a Tight-Binding wire model, where a site is a monomer (e.g., in DNA, a base pair). We consider quasi-periodic (Fibonacci, Thue-Morse, Double-Period, Rudin-Shapiro) and fractal (Cantor Set, Asymmetric Cantor Set) polymers made of the same monomer (I polymers) or made of different monomers (D polymers). For all types of such polymers, we calculate the HOMO and LUMO eigenspectrum, the HOMO-LUMO gap an…
A coarse-grained model to describe the lateral structure of a one-component polymer brush is presented. In this model, a single polymer chain is described by just two coordinates, namely the position of the grafted monomer, and the monomer on the non-grafted end. Due to its simplicity, the lateral arrangement of large numbers of structural units, each unit containing hundreds of polymers, can be analyzed. We consider here the corresponding low-energy configurations. Provided the grafting density is large enough, the latter all feature hexagonal order, even when the grafted monomers are distrib…
The reaction of $AB_m$ monomers (m=2,3) with a multifunctional B_f-type polymer chain ("hypergrafting") is studied by coarse-grained molecular dynamics simulations. The $AB_m$ monomers are hypergrafted using the slow monomer addition strategy. Fully dendronized, i.e., perfectly branched polymers are also simulated for comparison. The degree of branching DB of the molecules obtained with the "hypergrafting" process critically depends on the rate with which monomers attach to inner monomers compared to terminal monomers. This ratio is more favorable if the $AB_m$ monomers have lower reactivity, …
A relationship between the measurable monomer-monomer structure factor, and the centre-of-mass (CM) structure factor of dilute or semi-dilute polymer solutions is derived from Ornstein-Zernike relations within the ``polymer reference interaction site model'' (PRISM) formalism, by considering the CM of each polymer as an auxiliary site and neglecting direct correlations between the latter and the CM and monomers of neighbouring polymers. The predictions agree well with Monte Carlo data for self-avoiding walk polymers, and are considerably more accurate than the predictions of simple factorizati…
The random walk of a bonded monomer in a polymer melt is anisotropic due to local order and bond connectivity. We investigate both effects by molecular-dynamics simulations on melts of fully-flexible linear chains ranging from dimers ($M=2$) up to entangled polymers ($M=200$). The corresponding atomic liquid is also considered as reference system. To disentangle the influence of the local geometry and the bond arrangements, and reveal their interplay, we define suitable measures of the anisotropy emphasising either the former or the latter aspect. Connectivity anisotropy, as measured by the co…
Chemical structure has been long recognized to greatly influence polymer glass formation, but a general molecular theory that predicts how chemical structure determines the properties of glass-forming polymers has been slow to develop. While the generalized entropy theory (GET) explains the influence of various molecular details on polymer glass formation, the application of the GET has heretofore been limited to the use of the simplest polymer model in which all united atom groups within the monomers of a species interact with a common monomer averaged van der Waals energy. However, energetic…
We analyze structural and conformational properties in a simulated bead-spring model of a non-entangled, supercooled polymer melt. We explore the statics of the model via various structure factors, involving not only the monomers, but also the center of mass (CM). We find that the conformation of the chains and the CM-CM structure factor, which is well described by a recently proposed approximation [Krakoviack et al., Europhys. Lett. 58, 53 (2002)], remain essentially unchanged on cooling toward the critical glass transition temperature of mode-coupling theory. Spatial correlations between mon…
Friction between ring-polymer brushes at melt densities sliding past each other are studied using extensive course-grained molecular dynamics simulations and scaling arguments, and the results are compared to the friction between linear-polymer brushes. We show that for a velocity range spanning over three decades, the frictional forces measured for ring-polymer brushes are half the corresponding friction in case of linear brushes. In the linear-force regime, the weak inter-digitation of two ring brushes compared to linear brushes also leads to a lower number of binary collisions between the m…
Configurational fluctuations of conducting polymers in solution can bring into proximity monomers which are distant from each other along the backbone. Electrons can hop between these monomers across the "bridges" so formed. We show how this can lead to (i) a collapse transition for metallic polymers, and (ii) to the observed dramatic efficiency of acceptor molecules for quenching fluorescence in semiconducting polymers.
We study the dynamics and conformation of polymers composed by active monomers. By means of Brownian dynamics simulations we show that when the direction of the self-propulsion of each monomer is aligned with the backbone, the polymer undergoes a coil-to-globule-like transition, highlighted by a marked change of the scaling exponent of the gyration radius. Concurrently, the diffusion coefficient of the center of mass of the polymer becomes essentially independent of the polymer size for sufficiently long polymers or large magnitudes of the self-propulsion. These effects are reduced when the se…
. We consider three dimensional model of the Gaussian polymer chain in the presence of defects to understand the formation of a polymer aggregate where the aggregate is induced by the defects. The defects are acting as an attractive centres of the monomers and it induces aggregation of the monomers of the chain around the defects. It has been shown using the analytical calculations that the formation of a polymer aggregates are favoured when the defects have extensions in all the possible three dimensions. We have also calculated relevant other thermo-dynamical parameters (i. e. the average nu…
We use the thread model for linear chains of interacting monomers, and the ``polymer reference interaction site model'' (PRISM) formalism to determine the monomer-monomer pair correlation function $h_{mm}(r)$ for dilute and semi-dilute polymer solutions, over a range of temperatures from very high (where the chains behave as self-avoiding walks) to below the $θ$ temperature, where phase separation sets in. An inversion procedure, based on the HNC integral equation, is used to extract the effective pair potential between ``average'' monomers on different chains. An accurate relation between $h_…
We describe a simple Monte Carlo simulation method to calculate the free-energy cost of localizing a single monomer of a polymer confined to a cavity. The localization position is chosen to be on the inside surface of the confining cavity. The method is applied to a freely-jointed hard-sphere polymer chain confined to cavities of spherical and cubic geometries. In the latter case we consider localization at a corner and at the center of a face of the confining cube. We consider cases of end-monomer localization both with and without tethering of the other end monomer to a point on the surface.…
Force-driven translocation of a macromolecule through a nanopore is investigated by taking into account the monomer-pore friction as well as the "crowding" of monomers on the {\it trans} - side of the membrane which counterbalance the driving force acting in the pore. The set of governing differential-algebraic equations for the translocation dynamics is derived and solved numerically. The analysis of this solution shows that the crowding of monomers on the trans side hardly affects the dynamics, but the monomer-pore friction can substantially slow down the translocation process. Moreover, the…
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…
Spurred by an experimental controversy in the literature, we investigate the end-monomer dynamics of semiflexible polymers through Brownian hydrodynamic simulations and dynamic mean-field theory. Precise experimental observations over the last few years of end-monomer dynamics in the diffusion of double-stranded DNA have given conflicting results: one study indicated an unexpected Rouse-like scaling of the mean squared displacement (MSD) r^2(t) ~ t^(1/2) at intermediate times, corresponding to fluctuations at length scales larger than the persistence length but smaller than the coil size; anot…
Using molecular dynamics simulation of a standard bead-spring model we investigate the density crossover scaling of strictly two-dimensional self-avoiding polymer chains focusing on properties related to the contact exponent set by the intrachain subchain size distribution. Irrespective of the density sufficiently long chains are found to consist of compact packings of blobs of fractal perimeter dimension dp = 5/4.
Monte Carlo(MC) simulations produce evidence that annealed copolymers incorporating two interconverting monomers, P and H, adsorb as homopolymers with an effective adsorption energy per monomer, $ε_{eff}$, that depends on the PH equilibrium constants in the bulk and at the surface. The cross-over exponent, $Φ,$ is unmodified. The MC results on the overall PH ratio, the PH ratio at the surface and in the bulk as well as the number of adsorbed monomers are in quantitative agreement with this hypothesis and the theoretically derived $ε_{eff}$. The evidence suggests that the form of surface potent…
Uni-Macro-FRPN: Full-Resolution and Cross-Scale Learning for Polymers
South China Advanced Institute for Soft Matter Science and Technology, School of Emergent Soft Matter, South China University of Technology（华南软物质科学与技术高等研究院， emergent soft matter 学院，华南理工大学）；Guangdong Provincial Key Laboratory of Functional and Intelligent Hybrid Materials and Devices, South China University of Technology（广东省功能性与智能型杂化材料器件重点实验室，华南理工大学）
We present an effective and simple multiscale method for equilibrating Kremer Grest model polymer melts of varying stiffness. In our approach, we progressively equilibrate the melt structure above the tube scale, inside the tube and finally at the monomeric scale. We make use of models designed to be computationally effective at each scale. Density fluctuations in the melt structure above the tube scale are minimized through a Monte Carlo simulated annealing of a lattice polymer model. Subsequently the melt structure below the tube scale is equilibrated via the Rouse dynamics of a force-capped…
We investigate mutual local chain order in systems of fully flexible polymer melts in a simple generic bead-spring model. The excluded-volume interaction together with the connectivity leads to local ordering effects which are independent of chain length between 25 and 700 monomers, i.e. in the Rouse as well as in the reptation regime. These ordering phenomena extend to a distance of about 3 to 4 monomer sizes and decay to zero afterwards.
The classical bond-fluctuation model (BFM) is an efficient lattice Monte Carlo algorithm for coarse-grained polymer chains where each monomer occupies exclusively a certain number of lattice sites. In this paper we propose a generalization of the BFM where we relax this constraint and allow the overlap of monomers subject to a finite energy penalty $\overlap$. This is done to vary systematically the dimensionless compressibility $g$ of the solution in order to investigate the influence of density fluctuations in dense polymer melts on various s tatic properties at constant overall monomer dens…
Advanced chain-growth computer simulation methodologies have been employed for a systematic statistical analysis of the critical behavior of a polymer adsorbing at a substrate. We use finitesize scaling techniques to investigate the solvent-quality dependence of critical exponents, critical temperature, and the structure of the phase diagram. Our study covers all solvent effects from the limit of super-self-avoiding walks, characterized by effective monomer-monomer repulsion, to poor solvent conditions that enable the formation of compact polymer structures. The results significantly benefit f…
A soft ellipsoid model for Gaussian polymer chains is studied, following an idea proposed by Murat and Kremer [J. Chem. Phys. 108, 4340 (1998)]. In this model chain molecules are mapped onto ellipsoids with certain shapes, and to each shape a monomer density is assigned. In the first part of the work, the probabilities for the shapes and the associated monomer densities are studied in detail for Gaussian chains. Both quantities are expressed in terms of simple approximate formulae. The free energy of a system composed of many ellipsoids is given by an intramolecular part accounting for the int…
The vibrational dynamics of a model polymer glass is studied by Molecular Dynamics simulations. The focus is on the "soft" monomers with high participation to the lower-frequency vibrational modes contributing to the thermodynamic anomalies of glasses. To better evidence their role, the threshold to qualify monomers as soft is made severe, allowing for the use of systems with limited size. A marked tendency of soft monomers to form quasi-local clusters involving up to 15 monomers is evidenced. Each chain contributes to a cluster up to about three monomers and a single cluster involves monomer …
We investigate conformations and dynamics of a polymer considering its monomers to be active Brownian particles. This active polymer shows very intriguing physical behavior which is absent in an active Rouse chain. The chain initially shrinks with active force, which starts swelling on further increase in force. The shrinkage followed by swelling is attributed purely to excluded-volume interactions among the monomers. In the swelling regime, chain shows a cross-over from the self-avoiding behavior to Rouse-behavior with scaling exponent $ν_a \simeq 1/2$ for end-to-end distance. The non-monoton…
The Rouse model can be regarded as the standard model to describe the dynamics of a short polymer chain under melt conditions. In this contribution, we explicitly check one of the fundamental assumptions of this model, namely that of a uniform friction coefficient for all monomers, on the basis of MD simulation data of a poly(ethylene oxide) (PEO) melt. This question immediately arises from the fact that in a real polymer melt the terminal monomers have on average more intermolecular neighbors than the central monomers, and one would expect that exactly these details affect the precise value o…
A comparative dynamic Monte Carlo simulation study of polydisperse living polymer brushes, created by surface initiated living polymerization, and conventional polymer monodisperse brush, comprising linear polymer chains, grafted to a planar substrate under good solvent conditions, is presented. The living brush is created by end-monomer (de)polymerization reaction after placing an array of initiators on a grafting plane in contact with a solution of initially non-bonded segments (monomers). At equilibrium, the monomer density profile ϕ(z) of the LPB is found to decline as ϕ(z) ~ z^{-α} with t…
Solutions of semiflexible polymers confined by repulsive planar walls are studied by density functional theory and Molecular Dynamics simulations, to clarify the competition between the chain alignment favored by the wall and the depletion caused by the monomer-wall repulsion. A coarse-grained bead-spring model with bond bending potential is studied, varying both the contour length and the persistence length of the polymers, as well as the monomer concentration in the solution (good solvent conditions are assumed throughout, and solvent molecules are not included explicitly). The profiles of m…
The Langevin Equation for cooperative dynamics represents the dynamics of polymer melts with chains of increasing degree of polymerization, covering the full range of behavior from the unentangled to the entangled regime. This equation describes the motion of a group of interpenetrating polymers that are interacting through an effective potential resulting from the many-body coupling of the inter polymer potential inside the macromolecular liquid. The confinement of the dynamics due to the presence of entanglements is accounted for by an effective inter-monomer potential which is zero until th…
We study the energy structure and the transfer of an extra electron or hole along periodic polymers made of $N$ monomers, with a repetition unit made of $P$ monomers, using a Tight-Binding wire model, where a site is a monomer (e.g., in DNA, a base pair), for $P$ even, and deal with two categories of such polymers: made of the same monomer (GC..., GGCC..., etc) and made of different monomers (GA..., GGAA..., etc). We calculate the HOMO and LUMO eigenspectra, density of states and HOMO-LUMO gap and find some limiting properties these categories possess, as $P$ increases. We further examine the …
The collapse and swelling behavior of a generic homopolymer is studied using implicit-solvent, explicit-cosolvent Langevin dynamics computer simulations for varying interaction strengths. The systematic investigation reveals that polymer swelling is maximal if both monomer-monomer and monomer-cosolute interactions are weakly attractive. In the most swollen state the cosolute density inside the coil is remarkably bulk-like and homogenous. Highly attractive monomer-cosolute interactions, however, are found to induce a collapse of the chain which, in contrast to the collapsed case induced by pure…
The dynamics of flexible polymers in dilute solution is usually described in terms of the pure Rouse or Zimm bead-spring models assuming continuous distribution of the internal relaxation modes. We show that this approach may lead to misleading interpretation of experimental data. The more correct description should come from the joint Rouse-Zimm (RZ) theory that contains the Rouse and Zimm models as limiting cases. The internal modes are discrete with respect to the mode number, and the type of the bead motion changes in the time from the Rouse to Zimm behavior. We demonstrate this interpreti…
Thermo-mechanical properties of polymer networks depend on functionality of the monomer precursors -- an association that is frequently exploited in materials science. We use molecular simulations to generate spatial networks from chemically different monomers with identical functionality and show that such networks have several universal graph-theoretical properties as well as near universal Young's modulus. The vitrification temperature is shown to be universal only up to a certain density of the network, as measured by the bond conversion. The latter observation is explained by the fact tha…
As a first step to understanding the role of molecular or chemical polydispersity in self-assembly, we put forward a coarse-grained model that describes the spontaneous formation of quasi-linear polymers in solutions containing two self-assembling species. Our theoretical framework is based on a two-component self-assembled Ising model in which the bidispersity is parameterized in terms of the strengths of the binding free energies that depend on the monomer species involved in the pairing interaction. Depending upon the relative values of the binding free energies involved, different morpholo…
We study bottlebrush macromolecules in a good solvent by small-angle neutron scattering (SANS), static light scattering (SLS), and dynamic light scattering (DLS). These polymers consist of a linear backbone to which long side chains are chemically grafted. The backbone contains about 1600 monomer units (weight average) and every second monomer unit carries side-chains with ca. 60 monomer units. The SLS- and SANS data extrapolated to infinite dilution lead to the form factor of the polymer that can be described in terms of a worm-like chain with a contour length of 380 nm and a persistence leng…
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 isothermal, isobaric spontaneous crystallization of a supercooled polymer melt is investigated by MD simulation of an ensemble of fully-flexible linear chains. Frustration is introduced via two incommensurate length scales set by the bond length and the position of the minimum of the non-bonding potential. Marked polymorphism with considerable bond disorder, distortions of both the local packing and the global monomer arrangements is observed. The analyses in terms of: i) orientational order parameters characterizing the global and the local order and ii) the angular distribution of the ne…
We examine the ejection of an initially strongly confined flexible polymer from a spherical capsid through a nanoscale pore. We use molecular dynamics for unprecedentedly high initial monomer densities. We show that the time for an individual monomer to eject grows exponentially with the number of ejected monomers. By measurements of the force at the pore we show this dependence to be a consequence of the excess free energy of the polymer due to confinement growing exponentially with the number of monomers initially inside the capsid. This growth relates closely to the divergence of mixing ene…
Single two dimensional polymers confined to a strip are studied by Monte Carlo simulations. They are described by N-step self-avoiding random walks on a square lattice between two parallel hard walls with distance 1 << D << N^ν(ν= 3/4 is the Flory exponent). For the simulations we employ the pruned-enriched-Rosenbluth method (PERM) with Markovian anticipation. We measure the densities of monomers and of end points as functions of the distance from the walls, the longitudinal extent of the chain, and the forces exerted on the walls. Their scaling with D and the universal ratio between force and…
We use the method of dimensional reduction to show that a branching polymer with excluded volume interaction confined between two flat plates has, in the thermodynamic limit, a confinement free energy and density profile that is the same as that of an ideal linear polymer with the same number of monomers and the same monomer-plate interaction potential. Condensation due to branching is exactly compensated by swelling due to excluded volume interaction.
The presence of ordered structures such as helices in collapsed states of polymer chains is still an open question challenging physics and biology. In this work, we present a potential model for polymer chains with monomers that are not strictly attractive, but that can make adhesive contacts with other monomers. We find that the chain develop helical order during the process of collapsing from an initially stretched conformation. It seems in this case that the adhesive contacts help the polymer chain to stay trapped in the helix state.
We perform, with the help of cloud computing resources, extensive Langevin simulations which provide free energy estimates for unbiased three dimensional polymer translocation. We employ the Jarzynski equality in its rigorous setting, to compute the variation of the free energy in single monomer translocation events. In our three-dimensional Langevin simulations, the excluded-volume and van der Waals interactions between beads (monomers and membrane atoms) are modeled through a repulsive Lennard-Jones (LJ) potential and consecutive monomers are subject to the Finite-Extension Nonlinear Elastic…
The self-consistent field (SCF) theory of dense polymer liquids assumes that short-range correlations are almost independent of how monomers are connected into polymers. Some limits of this idea are explored in the context of a perturbation theory for mixtures of structurally identical polymer species, A and B, in which the AB pair interaction differs slightly from the AA and BB interaction, and the difference is controlled by a parameter alpha Expanding the free energy to O(α) yields an excess free energy of the form alpha $z(N)ϕ_{A}ϕ_{B}$, in both lattice and continuum models, where z(N) is …
