Investigating thermodynamic properties of liquid-solid transitions of flexible homopolymers with elastic bonds by means of multicanonical Monte Carlo simulations, we find crystalline conformations that resemble ground-state structures of Lennard-Jones clusters. This allows us to set up a structural classification scheme for finite-length flexible polymers and their freezing mechanism in analogy to atomic cluster formation. Crystals of polymers with "magic length" turn out to be perfectly icosahedral.
In this paper, we report dynamic Monte Carlo simulation results on the crystallization of crystalline/crystalline (A/B) symmetric binary polymer blend, wherein the melting temperature of A-polymer is higher than B-polymer. Crystallization of A-polymer precedes the crystallization of B-polymer upon cooling from a homogeneous melt. The morphological development is controlled by the interplay between crystallization and macrophase separation. With increasing segregation strength, smaller and thinner crystals form with lesser crystallinity. During the process, A-polymer crystallizes first followed…
Polymer blends offer an exciting material for various potential applications due to their tunable properties by varying constituting components and their relative composition. Our simulation results unravel an intrinsic relationship between the phase behavior and crystallization characteristics with the relative composition of A- and B-polymer in the system. We report simulation results for non-isothermal and isothermal crystallization with weak and strong segregation strength to elucidate the composition dependent crystallization behavior. With increasing composition of low melting B-polymer,…
I develop a kinetic mechanism to explain chain folding in polymer crystallization which is based on the competition between the formation of stems, which is due to frequent occupations of trans states along the chains in the supercooled polymer melt, and the random coil structure of the polymer chains. Setting equal the average formation time of stems of length $% d_l$ with the Rouse time of a piece of polymer of the same arc length $d_l$ yields a lower bound for the thickness of stems and bundles. The estimated lamellar thickness is inversely proportional to the supercooling. The present appr…
We study the possibility of the spinodal decomposition in the induction period of the polymer crystallization. This phenomenon was first reported in an X-ray scattering experiment, and has still been controversial due to various experiments and theories that support or deny the phenomenon. In this article, we explain the condition for the spinodal decomposition to occur in polymer melts by deriving a Ginzburg-Landau model of the free energy as a functional of the density and the orientation of the segments, where we introduce the excluded volume and the nematic interactions through a combinati…
We report Monte Carlo simulations of a lattice-polymer model that can account for both polymer crystallization and liquid-liquid demixing in solutions of semiflexible homopolymers. In our model, neighboring polymer segments can have isotropic interactions that affect demixing, and anisotropic interactions that are responsible for freezing. However, our simulations show that the isotropic interactions also have a noticeable effect on the freezing curve, as do the anisotropic interactions on demixing. As the relative strength of the isotropic interactions is reduced, the liquid-liquid demixing t…
Based on classical nucleation theory, we propose a couple of theoretical models for the nucleation of polymer crystallization, i.e. one for a single chain system (Model S) and the other for a multi-chain system (Model M). In these models, we assume that the nucleus is composed of tails, loops and a cylindrical ordered region, and we evaluate the conformation entropy explicitly by introducing a transfer matrix. Using these two models, we evaluate the occurrence probability of critical nucleus as a function of the polymer chain stiffness. We found that the critical nucleus in Model M is easier t…
Molecular process of crystallization from an oriented amorphous state was reproduced by molecular dynamics simulation for a realistic polyethylene model. Initial oriented amorphous state was obtained by uniaxial drawing an isotropic glassy state at 100 K. By the temperature jump from 100 K to 330 K, there occurred the crystallization into the fiber structure, during the process of which we observed the developments of various order parameters. The real space image and its Fourier transform revealed that a hexagonally ordered domain was initially formed, and then highly ordered crystalline stat…
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…
While the $Θ$-collapse of single long polymers in bad solvents is usually a continuous (tri-critical) phase transition, there are exceptions where it is preempted by a discontinuous crystallization (liquid $\leftrightarrow$ solid) transition. For a version of the bond-fluctuation model (a model where monomers are represented as $2\times 2\times 2$ cubes, and bonds can have lengths between 2 and $\sqrt{10}$) it was recently shown by F. Rampf {\it et al.} that there exist distinct collapse and crystallization transitions for long but {\it finite} chains. But as the chain length goes to infinity,…
Effect of Pre-Shear and Dispersity on Crystallization of a Model Polymer with Soft Pair Interactions using Molecular Dynamics Simulations
University of Illinois, Urbana–Champaign（伊利诺伊大学厄巴纳-香槟分校）；The Grainger College of Engineering, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校格雷恩格工程学院）
Recent experiments in some polymer melts quenched below the melting temperature have reported spinodal kinetics in small-angle X ray scattering before the emergence of crystalline structure. To explain these observations we propose that the coupling between density and chain conformation induces a liquid-liquid binodal within the equilibrium liquid--crystalline solid coexistence region. A simple phenomenological theory is developed to illustrate this idea, and several experimentally testable consequences are discussed. Shear is shown to enhance the kinetic role of the hidden binodal.
In the present work, crystallization in melts and poor-solvent solutions of semiflexible polymers with different concentration was studied by means of dissipative particle dynamics simulation technique. We use a coarse-grained polymer model trying to catch general principles of crystallization in such systems on large time and length scales. We observe the crystallization process starting from an initial randomly prepared system with different polymer volume fractions in a poor solvent. Because the solvent is very poor, the macrophase polymer-solvent separation takes place very fast and is acc…
We prepared a buoyancy matched binary mixture of polydisperse polystyrene microgel spheres of size ratio 0.785 and at a volume fraction of 0.567 just below the kinetic glass transition. In line with theoretical expectations, a eutectic phase behavior was observed, but only a minor fraction of the samples crystallized at all. By adding a short non-adsorbing polymer we enforce inter-species fractionation into coexisting pure component crystals, which in turn also shows signs of intra-species fractionation. We show that in formerly inaccessible regions of the phase diagram binary hard sphere phys…
Crystallization within the discrete spheres of a block copolymer mesophase was studied by time-resolved x-ray scattering. The cubic packing of microdomains, established by self-assembly in the melt, is preserved throughout crystallization by strong interblock segregation even though the amorphous matrix block is well above its glass transition temperature. Homogeneous nucleation within each sphere yields isothermal crystallizations which follow first-order kinetics, contrasting with the sigmoidal kinetics normally exhibited in the quiescent crystallization of bulk polymers.
We have studied the structure and free energy landscape of a semi-flexible lattice-polymer in the presence of a surface. At low temperatures coexistence of two-dimensional integer-folded crystals is observed. As the temperature is increased there is a transition from these crystalline configurations to a disordered coil adsorbed onto the surface. The polymer then gradually develops three-dimensional character at higher temperatures. We compute the free energy as a function of increasing crystallinity and compare with the free energy profiles assumed by the Lauritizen-Hoffman surface nucleation…
We develop a simple coarse-grained bead-spring polymer model exhibiting competing crystallization and glass transitions. For quench rates slower than the critical nucleation rate $|\dot{T}|_{crit}$, systems exhibit a first-order crystallization transition below a critical temperature $T=T_{cryst}$. Such systems form close-packed crystallites of FCC and/or HCP order, separated by domain walls, twin defects, and an amorphous interphase. The size of amorphous regions grows continuously as the quench rate $|\dot{T}|$ increases, producing nearly amorphous structure for $|\dot{T}|>|\dot{T}|_{crit}$.…
The present contribution focuses on the thermodynamically consistent mechanical modeling of the strain-induced crystallization in unfilled polymers. This phenomenon is of particular importance for the mechanical properties of polymers as well as for their manufacturing and the application. The model developed uses the principle of the minimum of dissipation potential and assumes two internal variables: the deformations due to crystallization and the regularity of the network. In addition to the dissipation potential necessary for the derivation of evolution equations, the well-established Arru…
We map out the solid-state morphologies formed by model soft-pearl-necklace polymers as a function of bending stiffness $k_b$ spanning the range from fully flexible to rodlike chains. The ratio of Kuhn length to bead diameter ($l_K/r_0$) increases monotonically with increasing $k_b$ and yields a one-parameter model that relates chain shape to bulk morphology and yields insights into the packing of anisotropic particles. In the flexible limit, monomers occupy the sites of close-packed crystallites while chains retain random-walk-like order. In the rodlike limit, nematic chain ordering typical o…
By means of multicanonical computer simulations, we investigate thermodynamic properties of the aggregation of interacting semiflexible polymers. We analyze a mesoscopic bead-stick model, where nonbonded monomers interact via Lennard-Jones forces. Aggregation turns out to be a process, in which the constituents experience strong structural fluctuations, similar to peptides in coupled folding-binding cluster formation processes. In contrast to a recently studied related proteinlike hydrophobic-polar heteropolymer model, aggregation and crystallization are separate processes for a homopolymer wi…
We present a kinetic model of crystal growth of polymers of finite molecular weight. Experiments help to classify polymer crystallization broadly into two kinetic regimes. One is observed in melts or in high molar mass polymer solutions and is dominated by nucleation control with $G \sim \exp(1/T ΔT)$, where $G$ is the growth rate and $ΔT$ is the super-cooling. The other is observed in low molar mass solutions (as well as for small molecules) and is diffusion controlled with $G \sim ΔT$, for small $ΔT$. Our model unifies these two regimes in a single formalism. The model accounts for the accum…
Colloidal interactions in nematic liquid crystals can be described as interactions between elastic multipoles that depend on particle shape, topology, chirality, boundary conditions and induced topological defects. Here, we describe a nematic colloidal system consisting of mesostructures of gold capable of inducing elastic multipoles of different order. Elastic monopoles are formed by relatively large asymmetric mesoflower particles, for which gravity and elastic torque balancing yields monopole-type interactions. High-order multipoles are instead formed by smaller mesoflowers with a myriad of…
Through a combination of rheological characterization and temperature-variable imaging methods, a novel gelation pathway in dilute solutions of a semiconducting polymer to achieve interconnected, crystalline networks with hierarchical porosity is reported. Upon rapid cooling, solutions of regioregular poly(3-hexylthiophene) (RR-P3HT) in ortho-dichlorobenzene formed thermoreversible gels. Temperature-variable confocal microscopy revealed cooling-induced structural rearrangement to progress through viscoelastic phase separation. The phase separation process arrested prematurely during the format…
The work introduces a 3D cellular automaton model for the spatial and crystallographic prediction of spherulite growth phenomena in polymers at the mesoscopic scale. The automaton is discrete in time, real space, and orientation space. The kinetics is formulated according to the Hoffman-Lauritzen secondary surface nucleation and growth theory for spherulite expansion. It is used to calculate the switching probability of each grid point as a function of its previous state and the state of the neighboring grid points. The actual switching decision is made by evaluating the local switching probab…
Going beyond the classical Gaussian approximation of Einstein's fluctuation theory, Ruppeiner gave it a Riemannian geometric structure with an entropic metric. This yielded a fundamental quantity - the Riemannian curvature, which was used to extract information on the nature of interactions between molecules in fluids, ideal gases and other open systems. In this article, we examine the implications of this curvature in a non-equilibrium thermodynamic system where relaxation is sufficiently slow so as not to invalidate the local equilibrium hypothesis. The non-equilibrium system comprises of a …
We solve a two dimensional model for polymer chain folding in the presence of mechanical pulling force ($f$) exactly using equilibrium statistical mechanics. Using analytically derived expression for the partition function we determine the phase diagram for the model in the $f$-temperature ($T$) plane. A square root singularity in the susceptibility indicates a second order phase transition from a folded to an unfolded state at a critical force ($f_c$) in the thermodynamic limit of infinitely long polymer chain. Surprisingly, the temperature dependence of $f_c$ shows a reentrant phase transiti…
While proteins have been treated as particles with a spherically symmetric interaction, of course in reality the situation is rather more complex. A simple step towards higher complexity is to treat the proteins as non--spherical particles and that is the approach we pursue here. We investigate the phase behavior of enhanced green fluorescent protein (eGFP) under the addition of a non--adsorbing polymer, polyethylene glycol (PEG). From small angle x-ray scattering we infer that the eGFP undergoes dimerization and we treat the dimers as spherocylinders with aspect ratio $L/D-1 = 1.05$. Despite …
We perform molecular-dynamics simulations for polymer melts of the coarse-grained polyvinyl alcohol model that crystallizes upon slow cooling. To establish the properties of its high temperature liquid state as a reference point, we characterize in detail the structural features of equilibrated polymer melts with chain lengths $5\le N \le 1000$ at a temperature slightly above their crystallization temperature. We find that the conformations of sufficiently long polymers with $N >50$ obey essentially the Flory's ideality hypothesis. The chain length dependence of the end-to-end distance and the…
Spin coating is an out-of-equilibrium technique for producing polymer films and colloidal crystals quickly and reproducibly. In this review, we present an overview of theoretical and experimental studies of the spin coating of colloidal suspensions. The dynamics of the spin coating process is discussed first, and we present insights from both theory and experiment. A key difference between spin coating with polymer solutions and with monodisperse colloidal suspensions is the emergence of long range (centimeter scale) orientational correlations in the latter. We discuss experiments in different…
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.
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 …
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…
We examine nonequilibrium features of collapse behavior in model polymers with competing crystallization and glass transitions using extensive molecular dynamics simulations. By comparing to "colloidal" systems with no covalent bonds but the same non-bonded interactions, we find three principal results: (i) Tangent-sphere polymers and colloids, in the equilibrium-crystallite phase, have nearly identical static properties when the temperature T is scaled by the crystallization temperature T_{cryst}; (ii) Qualitative features of nonequilibrium relaxation below T_{cryst}, measured by the evolutio…
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…
We analyze the crystallization and collapse transition of a simple model for flexible polymer chains on simple cubic and face-centered cubic lattices by means of sophisticated chain-growth methods. In contrast to bond-fluctuation polymer models in certain parameter ranges, where these two conformational transitions were found to merge in the thermodynamic limit, we conclude from our results that the two transitions remain well-separated in the limit of infinite chain lengths. The reason for this qualitatively distinct behavior is presumably due to the ultrashort attractive interaction range in…
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 that nascent polymer crystals (i.e., nuclei) are anisotropic entities, with neither spherical nor cylindrical geometry, in contrast to previous assumptions. In fact, cylindrical, spherical, and other high symmetry geometries are thermodynamically unfavorable. Moreover, post-critical transitions are necessary to achieve the lamellae that ultimately arise during the crystallization of semicrystalline polymers. We also highlight how inaccurate treatments of polymer nucleation can lead to substantial errors (e.g., orders of magnitude discrepancies in predicted nucleation rates). The…
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…
We combine computer simulations and scaling arguments to develop a unified view of polymer entanglement based on the primitive path analysis (PPA) of the microscopic topological state. Our results agree with experimentally measured plateau moduli for three different polymer classes over a wide rangeof reduced polymer densities: (i) semi-dilute theta solutions of synthetic polymers, (ii) the corresponding dense melts above the glass transition or crystallization temperature, and (iii) solutions of semi-flexible (bio)polymers such as f-actin or suspensions of rodlike viruses. Together these syst…
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. …
Syndiotactic polystyrene (sPS) exhibits complex polymorphic behavior upon crystallization. Computational modeling of polymer crystallization has remained a challenging task because the relevant processes are slow on the molecular time scale. We report herein a detailed characterization of sPS-crystal polymorphism by means of coarse-grained (CG) and atomistic (AA) modeling. The CG model, parametrized in the melt, shows remarkable transferability properties in the crystalline phase. Not only is the transition temperature in good agreement with atomistic simulations, it stabilizes the main $α$ an…
Force versus extension curves measure entropic elasticity of single polymer chain in force spectroscopy experiments. A Worm-like Chain model is used to describe force extension experiments with an intrinsic chain parameter called persistence length, which is a measure of local bending flexibility. For flexible polymers, there is a discrepancy in estimates of persistence length in various force regimes. For instance, Atomic Force Microscopy (AFM) based pulling experiments report anomaly low values which are also inconsistent with magnetic tweezers experiments. To understand this, we investigate…
We report on the crystallization kinetics in an entropically attractive colloidal system using a combination of time resolved scattering methods and microscopy. Hard sphere particles are polystyrene microgels swollen in a good solvent (radius a=380nm, starting volume fraction 0.534) with the short ranged attractions induced by the presence of short polymer chains (radius of gyration rg = 3nm, starting volume fraction 0.0224). After crystallization, stacking faulted face centred cubic crystals coexist with about 5% of melt remaining in the grain boundaries. From the Bragg scattering signal we i…
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…
The present contribution deals with the thermomechanical modeling of the strain-induced crystallization in unfilled polymers. This phenomenon significantly influences mechanical and thermal properties of polymers and has to be taken into consideration when planning manufacturing processes as well as applications of the final product. In order to simultaneously capture both kinds of effects, the model proposed starts by introducing a triple decomposition of the deformation gradient and furthermore uses thermodynamic framework for material modeling based on the Coleman--Noll procedure and minimu…
The relation between elasticity and yielding is investigated in a model polymer solid by Molecular-Dynamics simulations. By changing the bending stiffness of the chain and the bond length, semicrystalline and disordered glassy polymers - both with bond disorder - as well as nematic glassy polymers with bond ordering are obtained. It is found that in systems with bond disorder the ratio Ty/G between the shear yield strength Ty and the shear modulus G is close to the universal value of the atomic metallic glasses. The increase of the local nematic order in glasses leads to the increase of the sh…
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 examine how the distribution of contour lengths and the high-stretch stiffening of individual chain segments affect the macroscopic shear modulus of flexible polymer gels, using a 2D numerical model, in which polymer segments form a triangular network and disorder is introduced by varying their contour lengths. We show that in the relevant parameter range: (i) the non-affine contribution to the shear modulus is negligible, i.e. the Born approximation is satisfactory; (ii) the shear modulus is dominated by the contribution originating from equilibrium chain tensions. Moreover, mechanical equ…
We study phase separation and transient gelation in a mixture consisting of polydisperse colloids and non-adsorbing polymers, where the ratio of the average size of the polymer to that of the colloid is approximately 0.063. Unlike what has been reported previously for mixtures with somewhat lower colloid polydispersity, the addition of polymers does not expand the fluid-solid coexistence region. Instead, we find a region of fluid-solid coexistence which has an approximately constant width but an unexpected re-entrant shape. We detect the presence of a metastable gas-liquid binodal, which gives…
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…
