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, both transition temperatures converge to the same $T^*$, i.e. infinitely long polymers collapse immediately into a solid state. We explain this by the observation that polymers crystallize in the Rampf {\it et al.} model into a non-trivial cubic crystal structure (the `A15' or `Cr$_3$Si' Frank-Kasper structure) which has many degenerate ground states and, as a consequence, Bloch walls. If one controlls the polymer growth such that only one ground state is populated and Bloch walls are completely avoided, the liquid-solid transition is a smooth cross-over without any sharp transition at all.
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…
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 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…
Large scale Molecular Dynamics simulations of sixty-five systems with N=80000 Lennard-Jones particles at two different supercooled liquid state points reveals, that the supercooled states contain spatially heterogeneous distributed subdomains of particles with significant higher bond-order than the mean bond-order in the supercooled liquid. The onset of crystallization starts in such an area with relative high six-ford bond-order for a supercooled state, but low bond-order for a fcc crystal. The critical nucleus of N \approx 70 particles is surrounded by many hundred of particles with relative…
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…
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…
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 …
Despite its fundamental and technological importance, a microscopic understanding of the crystallization process is still elusive. By computer simulations of the hard-sphere model we reveal the mechanism by which thermal fluctuations drive the transition from the supercooled liquid state to the crystal state. In particular we show that fluctuations in bond orientational order trigger the nucleation process, contrary to the common belief that the transition is initiated by density fluctuations. Moreover, the analysis of bond orientational fluctuations shows that these not only act as seeds of t…
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…
In the gelation theory it has been implicitly assumed that (I) a cyclic bond is a finite bond that returns to itself; (II) cyclic bonds distribute at random in network structures. In this paper these two assumptions are reexamined from a new point of view. The physical soundness of the assumptions is assessed through comparison with experimental observations.
The bond fluctuation model with a bond potential has been applied to investigation of the glass transition of linear chains and chains with a regular disposition of small branches. Cooling and subsequent heating curves are obtained for the chain energies and also for the mean acceptance probability of a bead jump. In order to mimic different trends to vitrification, a factor B gauging the strength of the bond potential with respect to the long-range potential (i.e. the intramolecular or intermolecular potential between indirectly bonded beads) has been introduced. (A higher value of B leads to…
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…
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…
Polymer self-adhesion due to the interdiffusion of macromolecules has been an active area of research for several decades [70, 43, 62, 42, 72, 73, 41]. Here, we report a new phenomenon of sub-Tg, solid-state, plasticity-induced bonding; where amorphous polymeric films were bonded together in a period of time on the order of a second in the solid-state at ambient temperatures nearly 60 K below their glass transition temperature (Tg) by subjecting them to active plastic deformation. Despite the glassy regime, the bulk plastic deformation triggered the requisite molecular mobility of the polymer …
We study the transition of a granular packing from liquid to solid bonding in the course of drying. The particles are initially wetted by a liquid brine and the cohesion of the packing is ensured by capillary forces, but the crystallization of the solute transforms the liquid bonds into partially cemented bonds. This transition is evidenced experimentally by measuring the compressive strength of the samples at regular intervals of times. Our experimental data reveal three regimes: 1) Up to a critical degree of saturation, no solid bonds are formed and the cohesion remains practically constant;…
The lattice cluster theory (LCT) for strongly interacting, self-assembling telechelic polymers provides a theoretical tool that enables establishing the connections between important microscopic molecular details of self-assembling polymers and their bulk thermodynamics. The original LCT for self-assembly of telechelic polymers considers a model of fully flexible linear chains [J. Dudowicz and K. F. Freed, J. Chem. Phys. \textbf{136}, 064902 (2012)], while our recent work introduces a significant improvement to the LCT by including a description of chain semiflexibility for the bonds within ea…
Sacrificial bonds and hidden length (SBHL) in structural molecules provide a mechanism for energy dissipation at the nanoscale. It is hypothesized that their presence leads to greater fracture toughness than what is observed in materials without such features. Here, we investigate this hypothesis using a simplified model of a mineralized collagen fibril sliding on a polymeric interface with SBHL systems. A 1D coarse-grained nonlinear spring-mass system is used to model the fibril. Rate-and-displacement constitutive equations are used to describe the mechanical properties of the polymeric syste…
We study the effect of physical confinement on the capillary infiltration of polymers into cylindrical nanopores using molecular dynamics simulations. In particular, we probe whether the critical contact angle above which capillary rise infiltration ceases to occur changes for long chain polymers, possibly due to loss of conformation entropy induced by chain confinement. Surprisingly, the critical contact angle does not strongly depend on the length of polymer chains and stays constant for large N. A free energy model is developed to show that the critical angle for infiltration depends strong…
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…
The scaling of the bond-bond correlation function $C(s)$ along linear polymer chains is investigated with respect to the curvilinear distance, $s$, along the flexible chain and the monomer density, $ρ$, via Monte Carlo and molecular dynamics simulations. % Surprisingly, the correlations in dense three dimensional solutions are found to decay with a power law $C(s) \sim s^{-ω}$ with $ω=3/2$ and the exponential behavior commonly assumed is clearly ruled out for long chains. % In semidilute solutions, the density dependent scaling of $C(s) \approx g^{-ω_0} (s/g)^{-ω}$ with $ω_0=2-2ν=0.824$ ($ν=0.…
We perform simulations to compute the effective potential between the centers-of-mass of two polymers with reversible bonds. We investigate the influence of the topology of the unbonded precursor (linear or ring) and the specific sequence of the reactive groups (from purely random to periodic), establishing that both have a strong impact on the effective potential. When the reactive sites of both polymers are chemically orthogonal so that only intramolecular bonds are possible, the interactions become more repulsive the closer to periodic the sequence is. The opposite effect is found if both p…
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…
We examine the thermally-induced fracture of an unstrained polymer chain of discrete segments coupled by an anharmonic potential by means of Molecular Dynamics simulation with a Langevin thermostat. Cases of both under- and over-damped dynamics are investigated, and a comparison with recent studies of bond scission in model polymers with harmonic interactions is performed. We find that the polymer degradation changes qualitatively between the inertial regime and that of heavily damped dynamics. The role of bond healing (recombination) is also studied and probability distributions for the recom…
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…
Molecular Dynamics simulations of crystallization in a supercooled liquid of Lennard-Jones particles with different range of attractions shows that the inclusion of the attractive forces from the first, second and third coordination shell increases the trend to crystallize systematic. The bond-order $Q_6$ in the supercooled liquid is heterogeneously distributed with clusters of particles with relative high bond-order for a supercooled liquid, and a systematic increase of the extent of heterogeneity with increasing range of attractions. The onset of crystallization appears in such a cluster, wh…
The free energy landscape responsible for crystallization can be complex even for relatively simple systems like hard sphere and charged stabilized colloids. In this work, using hard-core repulsive Yukawa model, which is known to show complex phase behavior consisting of fluid, FCC and BCC phases, we studied the interplay between the free energy landscape and polymorph selection during crystallization. When the stability of the BCC phase with respect to the fluid phase is gradually increased by changing the temperature and pressure at a fixed fluid-FCC stability, the final phase formed by crys…
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…
The breakage of a polymer chain of segments, coupled by anharmonic bonds with applied constant external tensile force is studied by means of Molecular Dynamics simulation. We show that the mean life time of the chain becomes progressively independent of the number of bonds as the pulling force grows. The latter affects also the rupture rates of individual bonds along the polymer backbone manifesting the essential role of inertial effects in the fragmentation process. The role of local defects, temperature and friction in the scission kinetics is also examined.
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…
By means of Langevin dynamics simulations, we investigate the gel formation of randomly functionalized polymers in solution, with the ability to form both intra- and intermolecular reversible bonds. Under highly dilute conditions, these polymers form soft nano-objects (so-called single-chain nanoparticles, SCNPs), resulting from the purely intramolecular cross-linking of the reactive functional groups. Here we show that the competition between intra- and intermolecular bonds at finite concentration is governed by a delicate balance of various entropic contributions and leads to a density depen…
