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 understanding and process modeling of flow-induced crystallization in polymer melts.
We propose a theoretical approach to quantitatively account for the role of entanglement in the nucleation of polymer melts, which is the unique feature of polymer differentiated from small molecules. By performing molecular dynamics simulations, we obtain the nucleation barriers of polymer systems with different entanglement densities, which exhibits an opposite trend compared to the prediction of the classic nucleation theory (CNT). To amend the deficiency of the CNT in polymer crystallization, we introduce the entanglement free energy to reflect the role of entanglement in polymer nucleatio…
Mixtures of ideal polymers with hard spheres whose diameters are smaller than the radius of gyration of the polymer, exhibit extensive immiscibility. The interfacial tension between demixed phases of these mixtures is estimated, as is the barrier to nucleation. The barrier is found to scale linearly with the radius of the polymer, causing it to become large for large polymers. Thus for large polymers nucleation is suppressed and phase separation proceeds via spinodal decomposition, as it does in polymer blends.
It is shown that the intrinsic stress in solvent cast polymer coatings plays a key role in the nucleation of holes in the film. Nucleation is important because it is meanwhile clear that heterogeneous nucleation is the only relevant rupture mechanism for the technologically relevant thickness regime well above 100 nm. The most striking feature is that in contrast to what has been widely believed, the number density of holes scales not algebraically, but exponentially with the film thickness.
Kinetic barriers cause polymers to crystallize incompletely, into nanoscale lamellae interleaved with amorphous regions. As a result, crystalline polymers are full of crystal-melt interfaces, which dominate their physical properties. The longstanding theoretical challenge to understand these interfaces has new relevance, because of accumulating evidence that polymer crystals often nucleate via a metastable, partially ordered "rotator" phase. To test this idea requires a theory of the bulk and interfacial free energies of the critical nucleus. We present a new approach to the crystal-melt inter…
The investigation of freezing transitions of single polymers is computationally demanding, since surface effects dominate the nucleation process. In recent studies we have systematically shown that the freezing properties of flexible, elastic polymers depend on the precise chain length. Performing multicanonical Monte Carlo simulations, we faced several computational challenges in connection with liquid-solid and solid-solid transitions. For this reason, we developed novel methods and update strategies to overcome the arising problems. We introduce novel Monte Carlo moves and two extensions to…
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…
Starting from a protein solution which is metastable with respect to the crystalline phase, the effect of adding semidilute non-adsorbing polymer is considered. It is found to increase the chemical potential of the protein by a few tenths of kT, which may be enough to lower the barrier to nucleation of the crystalline phase by enough to allow crystallisation. It is also shown that assuming that the polymer induces a pairwise additive attraction leads to qualitatively incorrect results.
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…
We present a molecular dynamics simulation study of crystal nucleation from undercooled melts of n-alkanes, and we identify the molecular mechanism of homogeneous crystal nucleation under quiescent conditions and under shear flow. We compare results for n-eicosane(C20) and n-pentacontahectane(C150), i.e. one system below the entanglement length and one above. Under quiescent conditions, we observe that entanglement does not have an effect on the nucleation mechanism. For both chain lengths, the chains first align and then straighten locally. Then the local density increases and finally positio…
The crystallisation of entangled polymers from their melt is investigated using computer simulation with a coarse-grained model. Using hybrid Monte Carlo simulations enables us to probe the behaviour of long polymer chains. We identify solid-like beads with a centrosymmetry local order parameter and compute the nucleation free-energy barrier at relatively high supercooling with adaptive-bias windowed umbrella sampling. Our results demonstrate that the critical nucleus sizes and the heights of free-energy barriers do not significantly depend on the molecular weight of the polymer; however, the …
This paper reviews the research work on the liquid crystalline (LC) polymer vesicles (polymersomes), where the thermotropic nematic and smectic phases are displayed in the lyotropic bilayer polymer membrane. LC polymersomes possess the properties of both liquid crystals and polymers, the two essential soft matters. LC polymersomes offer, on the one hand, novel examples of the interplay between orientational order and the curved geometry of a two dimensional membrane. Spherical, ellipsoidal and tetrahedral vesicles are discussed. On the other hand, LC polymersomes enable novel design of stimuli…
Spatial distributions are presented that quantitatively capture how polymer properties (e.g., segment alignment, density, and potential energy) vary with distance from nascent polymer crystals (nuclei) in prototypical polyethylene melts. It is revealed that the spatial extent of nuclei and their interfaces is metric-dependent as is the extent to which nucleus interiors are solid-like. As distance from a nucleus increases, some properties, such as density, decay to melt-like behavior more rapidly than polymer segment alignment, indicating that a polymer nucleus resides in a nematic-like droplet…
The quasi--equilibrium approximation is employed as a systematic tool for solving the problem of deriving constitutive equations from kinetic models of liquid--crystalline polymers. It is demonstrated how kinetic models of liquid--crystalline polymers can be approximated in a systematic way, how canonical distribution functions can be derived from the maximum entropy principle and how constitutive equations are derived therefrom. The numerical implementation of the constitutive equations based on the intrinsic dual structure of the quasi--equilibrium manifold thus derived is developed and illu…
We present a self-consistent method for deriving moment equations for kinetic models of polymer dynamics. The Doi model [M. Doi, J.Polymer. Sci., Polym. Phys. Ed. 19, 229 (1981)] of liquid-crystalline polymers with the Onsager excluded-volume potential is considered as an example. To lowest order, this method amounts to a simple effective potential different from the Maier-Saupe form. Analytical results are presented which indicate that this effective potential provides a better approximation to the Onsager potential than the Maier-Saupe potential. Corrections to the effective potential are ob…
We calculate statistical properties of amorphous polymer chains between crystalline lamellae by self-consistent field model simulations. In our model, an amorphous subchain is modelled as a polymer chain of which ends are grafted onto the crystal-amorphous interfaces. The crystal-amorphous interfaces are expressed as impenetrable surfaces. We incorporate the interaction between segments to satisfy the incompressible condition for the segment density field. The simulation results show that amorphous polymer chains feel thin potential layers, which are mainly repulsive, near the crystal-amorphou…
Phase separation of sequence-disordered liquid crystalline polymers, a promising class of technological and biological relevance, is studied by field theory, and thermodynamic mechanisms responsible for orientational ordering observed in experiments, are discussed. The theory developed predicts that chemical disorder marginally affects the nematic/isotropic biphasic coexistence width, but strongly impacts ordering; above a critical chemical disorder threshold orientational ordering is precluded.
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…
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…
DNA renaturation is the recombination of two complementary single strands to form a double helix. It is experimentally known that renaturation proceeds through the formation of a double stranded nucleus of several base pairs (the rate limiting step) followed by a much faster zippering. We consider a lattice polymer model undergoing Rouse dynamics and focus on the nucleation of two diffusing strands. We study numerically the dependence of various nucleation rates on the strand lengths and on an additional local nucleation barrier. When the local barrier is sufficiently high, all renaturation ra…
The influence of the molecular structure of the nematic liquid crystal (NLC) on the photoalignment process at the NLC -- polymer interface has been investigated experimentally. NLCs having exclusively phenyl-, or cyclohexane rings in the rigid core, as well as NLCs containing both phenyl and cyclohexane groups have been considered. Substantial differences have been found in the photoalignment process depending on the molecular structure of the NLC, supporting the assumption that the polymer -- NLC interface should be regarded as a coupled system, where the two components mutually influence eac…
We investigate nonlinear rheology of dilute liquid crystalline polymer solutions under time dependent two-directional shear flow. We analyze the Smoluchowski equation, which describes the dynamics of the orientation of a liquid crystalline polymer, by employing technique of the full counting statistics. In the adiabatic limit, we derive the expression for time integrated currents generated by a Berry-like curvature. Using this expression, it is shown that the expectation values of the time-integrated angular velocity of a liquid crystalline polymer and the time-integrated stress tensor are gen…
The thermodynamics of strongly anisotropic crystalline surfaces is analogous to that of a binary mixture exhibiting phase separation. On a metastable planar surface, formation of stable orientations requires a nucleation process, in which the energy associated with the presence of corners must be considered. In this context, a nucleation event corresponds to the formation of a critical shape for the crystalline surface before the system enters the growth regime. We first derive the Euler-Lagrange equation for crystal surface nucleation, in two dimensions, and show that the saddle-point conditi…
We model a melt of monodisperse side-chain liquid crystalline polymers as a melt of comb copolymers in which the side groups are rod-coil diblock copolymers. We consider both excluded volume and Maier-Saupe interactions. The first acts among any pair of segments while the latter acts only between rods. Using a free energy functional calculated from this microscopic model, we study the spinodal stability of the isotropic phase against density and orientational fluctuations. The phase diagram obtained in this way predicts nematic and smectic instabilities as well as the existence of microphases …
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,…
Metastable states in first-order phase-transitions have been traditionally described by classical nucleation theory (CNT). However, recently an increasing number of systems displaying such a transition have not been successfully modelled by CNT. The delayed crystallization of phospholipids upon super-cooling is an interesting case, since the extended timescales allow access into the dynamics. Herein, we demonstrate the controllable behavior of the long-lived metastable liquid-crystalline phase of dilauroyl-phosphatidylethanolamine (DLPE), arranged in multi-lamellar vesicles, and the ensuing co…
We studied the dynamics of isotropic-nematic transitions in liquid crystalline polymers by integrating time-dependent Ginzburg-Landau equations. In a concentrated solution of rodlike polymers, the rotational diffusion constant Dr of the polymer is severely suppressed by the geometrical constraints of the surrounding polymers, so that the rodlike molecules diffuse only along their rod directions. In the early stage of phase transition, the rodlike polymers with nearly parallel orientations assemble to form a nematic polydomain. This polydomain pattern with characteristic length l, grows with se…
We address the crystallization of monodisperse hard spheres in terms of the properties of finite- size crystalline clusters. By means of large scale event-driven Molecular Dynamics simulations, we study systems at different packing fractions ϕ ranging from weakly supersaturated state points to glassy ones, covering different nucleation regimes. We find that such regimes also result in different properties of the crystalline clusters: compact clusters are formed in the classical-nucleation-theory regime (ϕ \leq 0.54), while a crossover to fractal, ramified clusters is encountered upon increasin…
We study the nucleation of crystalline cluster phases in the generalized exponential model with exponent n=4. Due to the finite value of this pair potential for zero separation, at high densities the system forms cluster crystals with multiply occupied lattice sites. Here, we investigate the microscopic mechanisms that lead to the formation of cluster crystals from a supercooled liquid in the low-temperature region of the phase diagram. Using molecular dynamics and umbrella sampling, we calculate the free energy as a function of the size of the largest crystalline nucleus in the system, and co…
The results obtained from molecular dynamics simulations of the friction at an interface between polymer melts and weakly attractive crystalline surfaces are reported. We consider a coarse-grained bead-spring model of linear chains with adjustable intrinsic stiffness. The structure and relaxation dynamics of polymer chains near interfaces are quantified by the radius of gyration and decay of the time autocorrelation function of the first normal mode. We found that the friction coefficient at small slip velocities exhibits a distinct maximum which appears due to shear-induced alignment of semif…
We report a novel multi-scale simulation methodology to quantitatively predict the thermodynamic behaviour of polymer mixtures, that exhibit phases with broken orientational symmetry. Our system consists of a binary mixture of oligomers and rod-like mesogens. Using coarse-grained molecular dynamics (CGMD) simulations we infer the topology of the temperature-dependent free energy landscape from the probability distributions of excess volume fraction of the components. The mixture exhibits nematic and smectic phases as a function of two temperature scales, the nematic-isotropic temperature $T_{N…
We present a computer simulation study on crystal nucleation and growth in supersaturated suspensions of mono-disperse hard spheres induced by a triangular lattice substrate. The main result is that compressed substrates are wet by the crystalline phase (the crystalline phase directly appears without any induction time), while for stretched substrates we observe heterogeneous nucleation. The shapes of the nucleated crystallites fluctuate strongly. In the case of homogeneous nucleation amorphous precursors have been observed (Phys. Rev. Lett. {\bf 105}(2):025701 (2010)). For heterogeneous nucle…
We present a Monte Carlo study of the surface anchoring of a nematic fluid on swollen layers of grafted liquid crystalline chain molecules. The liquid crystalline particles are modeled by soft repulsive ellipsoids, and the chains are made of the same particles. An appropriately modified version of the configurational bias Monte Carlo algorithm is introduced, which removes and redistributes chain bonds rather than whole monomers. With this algorithm, a wide range of grafting densities could be studied. The substrate is chosen such that it favors a planar orientation (parallel to the surface). D…
With computer simulations of the hard sphere model, we examine in detail the microscopic pathway connecting the metastable melt to the emergence of crystalline clusters. In particular we will show that the nucleation of the solid phase does not follow a two-step mechanism, where crystals form inside dense precursor regions. On the contrary, we will show that nucleation is driven by fluctuations of orientational order, and not by the density fluctuations. By considering the development of the pair-excess entropy inside crystalline nuclei, we confirm that orientational order precedes positional …
We investigate the influence of a shear flow on the process of nucleation. Mesoscopic nonequilibrium thermodynamics is used to derive the Fokker-Planck equation governing the evolution of the cluster size distribution in a metastable phase subjected to a stationary flow. The presence of the flow manifests itself in the expression for the effective diffusion coefficient of a cluster and introduces modifications in the nucleation rate. The implications of these results in condensation and polymer crystallization are discussed.
Modeling the Dielectric Relaxation in Semicrystalline Polymers -- Understanding the Role of the Interphase between the Amorphous and Crystalline Domains
The nucleation of crystals from the liquid melt is often characterized by a competition between different crystalline structures or polymorphs, and can result in nuclei with heterogeneous compositions. These mixed-phase nuclei can display nontrivial spatial arrangements, such as layered and onion-like structures, whose composition varies according to the radial distance, and which so far have been explained on the basis of bulk and surface free-energy differences between the competing phases. Here we extend the generality of these non-classical nucleation processes, showing that layered and on…
In the shear flow of liquid crystalline polymers (LCPs) the nematic director orientation can align with the flow direction for some materials, but continuously tumble in others. The nematic dumbbell (ND) model was originally developed to describe the rheology of flow-aligning semi-flexible LCPs, and flow-aligning LCPs are the focus in this paper. In the shear flow of monodomain LCPs it is usually assumed that the spatial distribution of the velocity is uniform. This is in contrast to polymer solutions, where highly non-uniform spatial velocity profiles have been observed in experiments. We ana…
A self-consistent-field theory (SCFT) in the grand canonical ensemble formulation is used to study transitions in a helix-coil multiblock copolymer globule. The helices are modeled as stiff rods. In addition to the established coil-globule transition we show for the first time that, even without explicit rod-rod alignment interaction, the system undergoes a transition to a nematic liquid-crystalline (LC) globular state. The LC-globule formation is driven by the hydrophobic helical segment attraction and the anisotropy of the globule surface energy. The full phase diagram of the copolymer was c…
From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability to understand and control the mechanisms guiding such processes across various scales has important application to research in materials science, finance, medicine, and energetics. Here we present a numerical study of anomalous diffusion of light through a semi-crystalline polymer structure where transport is guided by random disorder and nonlocal interactions. The numerical technique examines diffusion properties i…
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 …
A coarse-grained model for solutions of polymers in supercritical fluids is introduced and applied to the system of hexadecane and carbon dioxide as a representative example. Fitting parameters of the model to the gas-liquid critical point properties of the pure systems, and allowing for a suitably chosen parameter that describes the deviation from the Lorentz-Berthelot mixing rule, we model the liquid-gas and fluid-fluid unmixing transitions of this system over a wide range of temperatures and pressures in reasonable agreement with experiment. Interfaces between the polymer-rich phase and the…
Empirical potential structure refinement (EPSR) simulations are performed on total neutron scattering data from powder samples of polytetrafluoroethylene (PTFE) and polychlorotrifluoroethylene (PCTFE), both at 300K. For PTFE a number of Bragg peaks are visible in the scattering data and these are found to be consistent with a lattice spacing $a(=b)=5.69(1)$Å with a dihedral angle along the (helical) chain of 166$^\circ$ which gives a repeat distance along the chain (c-axis) of $\sim$19.6Å. The positions of the Bragg peaks are well reproduced by this model, although there is a mismatch in the a…
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.
We describe the large-scale collective behavior of solutions of polar biofilaments and both stationary and mobile crosslinkers. Both mobile and stationary crosslinkers induce filament alignment promoting either polar or nematic order. In addition, mobile crosslinkers, such as clusters of motor proteins, exchange forces and torques among the filaments and render the homogeneous states unstable via filament bundling. We start from a Smoluchowski equation for rigid filaments in solutions, where pairwise crosslink-mediated interactions among the filaments yield translational and rotational current…
The nucleation process of polyethylene under quiescent and shear flow conditions are comparatively studied with all_atom molecular dynamical simulations. At both conditions, nucleation are demonstrated to be two_step processes, which, however, proceed via different intermediate orders. Quiescent nucleation is assisted by local structure order coupling conformational and local rotational symmetric orderings, while flow_induced nucleation is promoted by density fluctuation, which is a coupling effect of conformational and orientation orderings. Flow drives the transformation from flexible chains…
A study of methodological nature demonstrates the efficiency of a probation test allowing for the intrinsic character of a rheological constitutive law to be assessed. Such a law is considered here for Semi-Crystalline Polymers exhibiting necking and for large deformation. In the framework of a $(\dotσ, σ, \dot\varepsilon, \varepsilon)$ behavior's law, tensile experiments conducted at an imposed constant strain rate $\dot\varepsilon_0$ bring true stress responses from which constitutive (material) parameters can be identified from Model-Based Metrology concepts. The same experiment repeated at…
