The microscopic model of semi-crystalline polymer in high-elastic state is proposed. The model is based on the assumption that, below the melting temperature, the semi-crystalline polymer comprises crystal nuclei connected by stretched chain segments (SCS) with random configuration of monomers. The key factor that stalls the phase transition below the melting temperature is the tension of the SCS. External stress applied to the polymer also shifts the equilibrium and causes unfolding of the nuclei, which enables large reversible deformation of the polymer without loss of integrity. The simple 1D model predicts plateau in stress-strain curve of high-elastic polymer above the yield stress, which agrees with experimental observations. The model prediction for the temperature dependence of polytetrafluoroethylene (PTFE) yield stress in high-elastic state is in satisfactory agreement with experiment.
To predict flow behavior of entangled polymer melt, we have developed multiscale simulation composed of Lagrangian fluid particle simulation and coarse-grained polymer dynamics simulation. We have introduced a particle deformation in the Lagrangian fluid particle simulation to describe elongation flow at a local point. The particle deformation is obtained to be consistent with the local polymer deformation.
We perform thorough molecular-dynamics simulations to compare elasticity and yielding of atomic crystals and model semicrystalline polymers, the latter characterized by very similar positional ordering with respect to atomic crystals and considerable bond disorder. We find that the elastic modulus, the shear yield strength and the critical yield strain of semicrystalline polymers are higher than (modulus and yield strength), or comparable to (critical strain), the corresponding ones of atomic crystals. The findings suggest that the bond disorder suppresses dislocation-mediated plasticity in po…
Investigating thermodynamic properties of liquid-solid transitions of flexible homopolymers with elastic bonds by means of multicanonical Monte Carlo simulations, we find crystalline conformations that resemble ground-state structures of Lennard-Jones clusters. This allows us to set up a structural classification scheme for finite-length flexible polymers and their freezing mechanism in analogy to atomic cluster formation. Crystals of polymers with "magic length" turn out to be perfectly icosahedral.
We explore the elastic behavior of a wormlike chain under compression in terms of exact solutions for the associated probability densities. Strikingly, the probability density for the end-to-end distance projected along the applied force exhibits a bimodal shape in the vicinity of the critical Euler buckling force of an elastic rod, reminiscent of the smeared discontinuous phase transition of a finite system. These two modes reflect the almost stretched and the S-shaped configuration of a clamped polymer induced by the compression. Moreover, we find a bimodal shape of the probability density f…
We study the elasticity of cross-linked networks of thermally fluctuating stiff polymers. As compared to their purely mechanical counterparts, it is shown that these thermal networks have a qualitatively different elastic response. By accounting for the entropic origin of the single-polymer elasticity, the networks acquire a strong susceptibility to polydispersity and structural randomness that is completely absent in athermal models. In extensive numerical studies we systematically vary the architecture of the networks and identify a wealth of phenomena that clearly show the strong dependence…
A thermodynamically related model is developed for describing elastic rubber-like behavior of amorphous and crystallizing polymers and demonstrated on example of simple extension. Both the “entropic” and “energetic” motions of polymer chains that contribute in macroscopic elastic deformation are taken into account. The model displays a continuous transition from entropy to energetic elasticity, without common singularity caused by finite extensibility of polymer chains. A multi-scale molecular approach, based on recent literature concepts has been employed for evaluatio…
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…
We demonstrate a novel route of spatially organizing the colloid arrangements on the polymer-grafted substrate by use of self-consistent field and density functional theories. We find that grafting of polymers onto a substrate can effectively control spatial dispersions of deposited colloids as a result of the balance between colloidal settling force and entropically elastic force of brushes, and colloids can form unexpected ordered structures on a grafting substrate. The depositing process of colloidal particles onto the elastic "soft" substrate includes two steps: brush-mediated one-dimensio…
Rod-shaped colloids with attractive tips can form linear aggregates that may subsequently undergo hierarchical self-assembly into nematic fluids. Inspired by recent modelling efforts on chromonic liquid crystals, composed of discotic building blocks, we formulate a second-virial theory for reversible supramolecular rods. Unlike chromonics, these systems are capable of forming stable nematic phases in the high-temperature, monomeric limit in the absence of polymerization. Changing the tip potential from attractive to repulsive thus enables a smooth crossover from a monomeric to a polymeric nema…
The entropy of a polymer confined in a curved surface and the elastic free energy of a membrane consisting of polymers are obtained by scaling analysis. It is found that the elastic free energy of the membrane has the form of the in-plane strain energy plus Helfrich's curvature energy [Z. Naturforsch. C \textbf{28}, 693 (1973)]. The elastic constants in the free energy are obtained by discussing two simplified models: one is the polymer membrane without in-plane strains and asymmetry between its two sides, which is the counterpart of quantum mechanics in curved surface [Jensen and Koppe, Ann. …
We analyse the elastic energy of an intercalated smectic where orientationally ordered polymers with an average orientation varying from layer to layer are intercalated between smectic planes. The lowest order terms in the coupling between polymer director and smectic layer curvature are added to the smectic elastic energy. Integration over the smectic degrees of freedom leaves an effective polymer twist energy that has to be included into the total polymer elastic energy leading to a fluctuational renormalization of the intercalated polymer twist modulus. If the polymers are chiral this in it…
In this work we use molecular simulations to examine methods of controlling mechanical properties of polymeric glass materials such as elastic moduli, mechanical heterogeneity as well as their glass transition temperature. We study filled and unfilled polymers and examine the effect of particle size, volume fraction and polymer-particle interactions. We identify a relationship between mobility and dynamic heterogeneity with elastic moduli and glass transition temperature.
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…
We employ a first principles, force-level approach to self-consistently construct the anharmonic tube confinement field for entangled fluids of rigid needles and for primitive-path (PP) level chains in two limiting situations where chain stretching is assumed to either completely relax or remain unrelaxed. The influence of shear and extensional deformation and polymer orientation is determined in a nonlinear elastic limit where dissipative relaxation processes are intentionally neglected. For needles and PP-level chains, a Gaussian analysis of transverse polymer dynamical fluctuations predicts…
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 elastic response in polymeric gels is studied by means of a percolation dynamic model. By numerical simulations the fluctuations in the gyration radius and in the center of mass motion of the percolating cluster are determined. Their scaling behaviour at the gelation threshold gives a critical exponent for the elastic modulus $f \sim 2.5 \pm 0.1$ in agreement with the prediction $f = d ν$.
Short fiber reinforced polymer composites have found extensive industrial and engineering applications owing to their unique combination of low cost, relatively easy processing and superior mechanical properties compared to their parent polymers. In this study, a coarse grained (CG) model of cross linked carbon nanotube (CNT) reinforced polymer matrix composites is developed. A characteristic feature of the CG model is the ability to capture the interactions between polymer chains, and nanotubes and polymer matrix. The dependence of the elastic properties of the composites on the mole fraction…
Semiflexible polymers such as filamentous actin play a vital role in the mechanical behavior of cells, yet the basic properties of cross-linked F-actin networks remain poorly understood. To address this issue, we have performed numerical studies of the linear response of homogeneous and isotropic two-dimensional networks subject to an applied strain at zero temperature. The elastic moduli are found to vanish for network densities at a rigidity percolation threshold. For higher densities, two regimes are observed: one in which the deformation is predominantly affine and the filaments stretch an…
We present a theory for the elasticity of cross-linked stiff polymer networks. Stiff polymers, unlike their flexible counterparts, are highly anisotropic elastic objects. Similar to mechanical beams stiff polymers easily deform in bending, while they are much stiffer with respect to tensile forces (``stretching''). Unlike in previous approaches, where network elasticity is derived from the stretching mode, our theory properly accounts for the soft bending response. A self-consistent effective medium approach is used to calculate the macroscopic elastic moduli starting from a microscopic charac…
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…
We study a model of "elastic" lattice polymer in which a fixed number of monomers $m$ is hosted by a self-avoiding walk with fluctuating length $l$. We show that the stored length density $ρ_m = 1 - <l>/m$ scales asymptotically for large $m$ as $ρ_m=ρ_\infty(1-θ/m + ...)$, where $θ$ is the polymer entropic exponent, so that $θ$ can be determined from the analysis of $ρ_m$. We perform simulations for elastic lattice polymer loops with various sizes and knots, in which we measure $ρ_m$. The resulting estimates support the hypothesis that the exponent $θ$ is determined only by the number of prime…
We have performed accurate dynamic light-scattering measurements near critical demixing points of solutions of polystyrene in cyclohexane with polymer molecular weight ranging from 200,000 to 11.4 million. Two dynamic modes have been observed, ''slow'' and ''fast'', that result from a coupling between diffusive relaxation of critical fluctuations of the concentration and visco-elastic relaxation associated with the entanglement network of the polymer chains. The coupling with the visco-elastic mode causes an additional slowdown of the critical mode on top of the uncoupled diffusion mode. By im…
We report extensive numerical simulations of different models of 2D polymer rings with internal elasticity. We monitor the dynamical behavior of the rings as a function of the packing fraction, to address the effects of particle deformation on the collective response of the system. In particular, we compare three different models: (i) a recently investigated model [Gnan \& Zaccarelli, Nat. Phys. 15, 683 (2019)], where an inner hertzian field providing the internal elasticity acts on the monomers of the ring, (ii) the same model where the effect of such a field on the center of mass is balanced…
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 investigate solid-solid and solid-liquid transitions of elastic flexible off-lattice polymers with Lennard-Jones monomer-monomer interaction and anharmonic springs by means of sophisticated variants of multicanonical Monte Carlo methods. We find that the low-temperature behavior depends strongly and non-monotonically on the system size and exhibits broad similarities to unbound atomic clusters. Particular emphasis is dedicated to the classification of icosahedral and non-icosahedral low-energy polymer morphologies.
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…
Homogeneous polymer solutions are well-known to exhibit viscoelastic flow instabilities: purely elastic when inertia is negligible, inertio-elastic otherwise. Recently, shear-banding wormlike micelles solutions were also discovered to follow a similar phenomenology. In the shear-banding regime, inertia is usually negligible so only purely elastic flows have been reported. Here, we investigate a non-shear-banding solution where inertia becomes significant, leading to flow patterns akin to the inertio-elastic regime of dilute polymer solutions. We show that the instability follows a supercritica…
We explore the transport features of a single flexible polymer chain that walks on a periodic ratchet potential coupled with spatially varying temperature. At steady state the polymer exhibits a fast unidirectional motion where the intensity of its current rectification depends strongly on its elastic strength and size. Analytic and numerical analysis reveal that the steady state transport of the polymer can be controlled by attenuating the strength of the elastic constant. Furthermore, the stall force at which the chain current vanishes is independent of the chain length and coupling strength…
Recent experiments have demonstrated that the nonlinear elasticity of in vitro networks of the biopolymer actin is dramatically altered in the presence of a flexible cross-linker such as the abundant cytoskeletal protein filamin. The basic principles of such networks remain poorly understood. Here we describe an effective medium theory of flexibly cross-linked stiff polymer networks. We argue that the response of the cross-links can be fully attributed to entropic stiffening, while softening due to domain unfolding can be ignored. The network is modeled as a collection of randomly oriented rod…
The excess low-frequency vibrational spectrum, called boson peak, and non-affine elastic response are the most important particularities of glasses. Herein, the vibrational and mechanical properties of polymeric glasses are examined by using coarse-grained molecular dynamics simulations, with particular attention to the effects of the bending rigidity of the polymer chains. As the rigidity increases, the system undergoes a glass transition at a higher temperature (under a constant pressure), which decreases the density of the glass phase. The elastic moduli, which are controlled by the decreas…
We study the thermodynamics of binary mixtures with the volume fraction of the minority component less than the amount required to form a flat interface and show that the surface tension dominated equilibrium phase of the mixture forms a single macroscopic droplet. Elastic interactions in gel-polymer mixtures stabilize a phase with multiple droplets. Using a mean-field free energy we compute the droplet size as a function of the interfacial tension, Flory parameter, and elastic moduli of the gel. Our results illustrate the role of elastic interactions in dictating the phase behavior of biopoly…
When liquid droplets nucleate and grow in a polymer network, compressive stresses can significantly increase their internal pressure, reaching values that far exceed the Laplace pressure. When droplets have grown in a polymer network with a stiffness gradient, droplets in relatively stiff regions of the network tend to dissolve, favoring growth of droplets in softer regions. Here, we show that this elastic ripening can be strong enough to reverse the direction of Ostwald ripening: large droplets can shrink to feed the growth of smaller ones. To numerically model these experiments, we generaliz…
When subjected to sufficiently strong velocity gradients, solutions of long, flexible polymers exhibit flow instabilities and chaotic motion, often referred to as elastic turbulence. Its mechanism differs from the familiar, inertia-driven turbulence in Newtonian fluids, and is poorly understood. Here, we demonstrate that the dynamics of purely elastic pressure-driven channel flows of dilute polymer solutions are organised by exact coherent structures that take the form of two-dimensional travelling waves. Our results demonstrate that no linear instability is required to sustain such travelling…
We introduce and implement a Monte Carlo scheme to study the equilibrium statistics of polymers in the globular phase. It is based on a model of "interacting elastic lattice polymers" and allows a sufficiently good sampling of long and compact configurations, an essential prerequisite to study the scaling behaviour of free energies. By simulating interacting self-avoiding rings at several temperatures in the collapsed phase, we estimate both the bulk and the surface free energy. Moreover from the corresponding estimate of the entropic exponent $α-2$ we provide evidence that, unlike for swollen…
Amorphous materials exhibit peculiar mechanical and vibrational properties, including non-affine elastic responses and excess vibrational states, i.e., the so-called boson peak. For polymer glasses, these properties are considered to be affected by the bending rigidity of the constituent polymer chains. In our recent work [Tomoshige, et al., Sci. Rep. 9 19514 (2019)], we have revealed simple relationships between the variations of vibrational properties and the global elastic properties: the response of the boson peak scales only with that of the global shear modulus. This observation suggests…
We study the dependence of the fracture surface energy on the pulling velocity for nano-porous polypropylene (PP) sheets to find two components: the static and dynamic ones. We show that these terms can be interpreted respectively as plastoelastic and viscoelastic components, as has been shown for soft polyethylene (PE) foams in a previous work. Considering significant differences in the pore size, volume fraction and Young's modulus of the present PP and previous PE sheets, the present results suggest a universal physical mechanism for fracture of porous polymer sheets. The simple physical in…
Stretching response of polymer chains under external force is crucial in understanding polymer dynamics under equilibrium and non-equilibrium conditions. Here we measure the elastic response of poly(ethylene glycol) using a lock-in based amplitude modulation-AFM with sub-angstrom amplitude in both low and high frequency regime. Appropriate analysis that takes into account the cantilever geometry and hydrodynamic loading effects of oscillating cantilever in liquid, relates X signal of lock-in amplifier linearly to stiffness.Stiffness data extracted from X signal was compared with stiffness from…
Conducting polymers have wide technological applications in sensors, actuators, electric and optical devices, solar cells etc. To improve their operational performance, mechanical, thermal, electrical and optical properties, such polymers are doped with carbon allotrope nanofillers. Functionality of the novel nanocomposite polymers may be stipulated by size characteristics of nanoparticles and the polymer, different physical effects like charge transfer in such objects etc. We characterize and analyze structure, elastic, electric properties and of novel polymer nanocomposites, isotactic polypr…
Evaporating droplets of polymer or colloid solution may produce a glassy crust at the liquid-vapour interface, which subsequently deforms as an elastic shell. For sessile droplets, the known radial outward flow of solvent is expected to generate crusts that are thicker near the pinned contact line than the apex. Here we investigate, by non-linear quasi-static simulation and scaling analysis, the deformation mode and stability properties of elastic caps with a non-uniform thickness profile. By suitably scaling the mean thickness and the contact angle between crust and substrate, we find data co…
In this paper we derive the general equilibrium equations of a polymer chain with a noncircular cross section by the variation of the free energy functional. From the equilibrium equation of the elastic ribbon we derive analytically the equilibrium conformations both of the helical ribbons and the twisted ribbons. We find that the pitch angle of the helical ribbons depends on the ratio of the torsional rigidity to the bending one. For the twisted ribbons, the rotation rate depends on the spontaneous torsion, which is determined by the elastic properties of the polymers. Our results for helical…
An elastic rod model for semi-flexible polymers is presented. Theory for a continuum rod is reviewed, and it is shown that a popular discretised model used in numerical simulations gives the correct continuum limit. Correlation functions relating to both bending and twisting of the rod are derived for both continuous and discrete cases, and results are compared with numerical simulations. Finally, two possible implementations of the discretised model in the multi-purpose molecular dynamics software package LAMMPS are described.
We perform a direct numerical simulation (DNS) of the forced, incompressible two-dimensional Navier-Stokes equation coupled with the FENE-P equations for the polymer-conformation tensor. The forcing is such that, without polymers and at low Reynolds numbers $\mbox{Re}$, the film attains a steady state that is a square lattice of vortices and anti-vortices. We find that, as we increase the Weissenberg number $\mbox{Wi}$, a sequence of nonequilibrium phase transitions transforms this lattice, first to spatially distorted, but temporally steady, crystals and then to a sequence of crystals that os…
Nanoscale polymeric thin films are widely used in diverse applications such as energy devices, flexible electronics and biosensors, where a satisfactory mechanical performance is of vital importance to realize their full functionality. It has been evidenced that the elastic properties of polymer films are often strongly affected by their thickness; however, the underlying mechanism of this phenomenon, especially a thorough understanding at the microscopic level, has yet to be achieved. Here we established a coarse-grained molecular dynamics (CGMD) based computational framework, combining with …
Effective and fast convergence toward an equilibrium state for long-chain polymer melts is realized by a hybrid method coupling molecular dynamics and the elastic continuum. The required simulation time to achieve the equilibrium state is reduced drastically compared with conventional equilibration methods. The polymers move on a wide range of the energy landscape due to large-scale fluctuation generated by the elastic continuum. A variety of chain structures is generated in the polymer melt which results in the fast convergence to the equilibrium state.
Speed of sound waves in gases and liquids is governed by medium compressibility. There exists another type of non-dispersive waves which speed depends on stress instead of medium elasticity. A well-known example is the Alfven wave propagating, with a speed determined by a magnetic tension, in plasma permeated by a magnetic field. Later, an elastic analog of the Alfven waves has been predicted in a flow of dilute polymer solution, where elastic stress engendered by polymer stretching determines the elastic wave speed. Here, we present quantitative evidence of elastic Alfven waves observed in el…
For the estimation of transition points of finite elastic, flexible polymers with chain lengths from $13$ to $309$ monomers, we compare systematically transition temperatures obtained by the Fisher partition function zeros approach with recent results from microcanonical inflection-point analysis. These methods rely on accurate numerical estimates of the density of states, which have been obtained by advanced multicanonical Monte Carlo sampling techniques. Both the Fisher zeros method and microcanonical inflection-point analysis yield very similar results and enable the unique identification o…
The importance of nonlinearities in material constitutive relations has long been appreciated in the continuum mechanics of macroscopic rods. Although the moment (torque) response to bending is almost universally linear for small deflection angles, many rod systems exhibit a high-curvature softening. The signature behavior of these rod systems is a kinking transition in which the bending is localized. Recent DNA cyclization experiments by Cloutier and Widom have offered evidence that the linear-elastic bending theory fails to describe the high-curvature mechanics of DNA. Motivated by this rece…
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 study the elastic deformations in a cross-linked polymer network film triggered by the binding of submicron particles with a sticky surface, mimicking the interactions of viral pathogens with thin films of stimulus-responsive polymeric materials such as hydrogels. From extensive Langevin Dynamics simulations we quantify how far the network deformations propagate depending on the elasticity parameters of the network and the adhesion strength of the particles. We examine the dynamics of the collective area shrinkage of the network and obtain some simple relations for the associated characteri…
