We analyze the freezing 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 the lattice models considered here.
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…
Freezing of polymer solutions has been extensively investigated from many aspects, especially the complex pattern formation. The cell/dendrite micro-structures are believed to be in the type of diffusion-induced M-S instability. However, the presence of polymer as an impurity in water is significantly different from that of small ions. The quantitative transient investigation on directional freezing of polymer solutions remains lack due to some challenges. For the first time, we observed the planar instability behaviors during unidirectional freezing of a polymer solution together with a typic…
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…
Nafion is a perfluorosulfonated polymer, widely used in Proton Exchange Membrane Fuel Cells. This polymer adopts a complex structural organisation resulting from the microsegregation between hydrophobic backbones and hydrophilic sulfonic acid groups. Upon hydration appear water-filled channels and cavities, in which are released the acidic protons to form a solution of hydronium ions in water embedded in the polymer matrix. Below 273 K, a phenomenon of water sorption/desorption occurs, whose origin is still an open question. Performing neutron diffraction, we monitored the quantity of ice form…
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…
Polymer-Regulated Freezing of Water Droplets Revealed by Synchrotron X-ray Imaging and Raman Spectroscopy
Ulsan National Institute of Science and Technology (UNIST)（蔚山科学技术院）；Korea Polar Research Institute (KOPRI)（韩国极地研究所）；Pohang Accelerator Laboratory, Pohang University of Science and Technology (POSTECH)（浦项科技大学波项加速器实验室）；UNIST Research Center for Soft and Living Matter, Ulsan National Institute of Science and Technology (UNIST)（蔚山科学技术院软体与生命物质研究中心）
We report the results of Monte Carlo simulations investigating the effect of a spherical confinement within a simple model for a flexible homopolymer. We use the parallel tempering method combined with multi-histogram reweighting analysis and multicanonical simulations to investigate thermodynamical observables over a broad range of temperatures, which enables us to describe the behavior of the polymer and to locate the freezing and collapse transitions. We find a strong effect of the spherical confinement on the location of the collapse transition, whereas the freezing transition is hardly ef…
We investigate numerically the dynamical behaviour of a polymer chain collapsing in a dilute solution. The rate of collapse is measured with and without the presence of hydrodynamic interactions. We find that hydrodynamic interactions both accelerate polymer collapse and alter the folding pathway.
The nature of the globule-coil transition of surface-confined polymers has been an issue of debate. Here this 2D collapse transition is studied through a partially directed lattice model. In the general case of polymers with positive bending stiffness ($Δ>0$), the collapse transition is {\em first-order}; it becomes {\em second-order} only in the limiting case of zero bending stiffness ($Δ\equiv 0$). These analytical results are confirmed by Monte Carlo simulations. We also suggest some possible future experiments.
We investigate the behavior of hydrated sulfonated polysulfones over a range of ion contents through differential scanning calorimetry (DSC), Fourier transform infrared spectroscopy (FTIR), and molecular dynamics (MD) simulations. Experimental evidence shows that at comparable ion contents, the spacing between the ionic groups along the polymer backbone can significantly impact the amount of melting water present in the polymer. When we only consider water molecules that can hydrogen bond to four neighboring water molecules as the melting water, the MD simulation results are found to agree wit…
Smart polymers are a modern class of polymeric materials that often exhibit unpredictable behavior in mixtures of solvents. One such phenomenon is co-non-solvency. Co-non-solvency occurs when two (perfectly) miscible and competing good solvents, for a given polymer, are mixed together. As a result, the same polymer collapses into a compact globule within intermediate mixing ratios. More interestingly, polymer collapses when the solvent quality remains good and even gets increasingly better by the addition of the better cosolvent. This is a puzzling phenomenon that is driven by strong local con…
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.
It has been revealed by mean-field theories and computer simulations that the nature of the collapse transition of a polymer is influenced by its bending stiffness $ε_{\rm b}$. In two dimensions, a recent analytical work demonstrated that the collapse transition of a partially directed lattice polymer is always first-order as long as $ε_{\rm b}$ is positive [H. Zhou {\em et al.}, Phys. Rev. Lett. {\bf 97}, 158302 (2006)]. Here we employ Monte Carlo simulation to investigate systematically the effect of bending stiffness on the static properties of a 2D lattice polymer. The system's phase-diagr…
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,…
We study the elastic properties of a rigid filament in a bath of self-propelled particles. We find that while fully flexible filaments swell monotonically upon increasing the strength of the propelling force, rigid filaments soften for moderate activities, collapse into metastable hairpins for intermediate strengths, and eventually re-expand when the strength of the activity of the surrounding fluid is large. This collapse and re-expansion of the filament with the bath activity is reminiscent of the behavior observed in polyelectrolytes in the presence of different concentrations of multivalen…
We study the kinetics of the isotropic-smectic phase transition in a colloidal rod/polymer mixture by visualizing individual smectic layers. First, we show that the bulk isotropic-smectic phase transition is preceded by a surface freezing transition in which a quasi two-dimensional smectic phase wets the isotropic-nematic interface. Next, we identify a two step kinetic pathway for the formation of a bulk smectic phase. In the first step a metastable isotropic-nematic interface is formed. This interface is wetted by the surface induced smectic phase. In the subsequent step, smectic layers nucle…
We investigate, using numerical simulations, the conformations of isolated active ring polymers. We find that the their behaviour depends crucially on their size: short rings ($N \lesssim$ 100) are swelled whereas longer rings ($N \gtrsim$ 200) collapse, at sufficiently high activity. By investigating the non-equilibrium process leading to the steady state, we find a universal route driving both outcomes; we highlight the central role of steric interactions, at variance with linear chains, and of topology conservation. We further show that the collapsed rings are arrested by looking at differe…
Collapse of the polymer chain upon the sharp decrease of solvent quality is studied. During collapse, any pair of polymer units appearing in a sufficiently close vicinity in space has the possibility with a certain probability to form an irreversible crosslink, thereby preventing the interpenetration of chain material between the forming clusters. Globular structures having different spatial chain packing at various scales are obtained by computer simulations. It is shown that the dependence of probability of contact between two monomers in space , where s is a distance between monomers along …
We develop a new quantitative molecular theory of liquid-phase dipolar polymer gels. We model monomer units of the polymer network as a couple of charged sites separated by a fluctuating distance. For the first time, within the random phase approximation, we have obtained an analytical expression for the electrostatic free energy of the dipolar gel. Depending on the coupling parameter of dipole-dipole interactions and the ratio of the dipole length to the subchain Kuhn length, we describe the gel collapse induced by electrostatic interactions in the good solvent regime as a first-order phase t…
Conformational transitions of flexible molecules, especially those driven by hydrophobic effects, tend to be hindered by desolvation barriers. For such transitions, it is thus important to characterize and understand the interplay between solvation and conformation. Using specialized molecular simulations, here we perform such a characterization for a hydrophobic polymer solvated in water. We find that an external potential, which unfavorably perturbs the polymer hydration waters, can trigger a coil-to-globule or collapse transition, and that the relative stabilities of the collapsed and exten…
We have discovered unusual behavior of polymer coils in a binary solvent (nitroethane+isooctane) near the critical temperature of demixing. The exceptionally close refractive indices of the solvent components make the critical opalescence relatively weak, thus enabling us to simultaneously observe the Brownian motion of the polymer coils and the diverging correlation length of the critical fluctuations. The polymer coils exhibit a collapse-reswelling-expansion-collapse transition upon approaching the critical temperature. While the first stage (collapse-reswelling) can be explained by the theo…
We probe, using the Surface Forces Apparatus, the thermal response of poly(N-isopropylacrylamide) (PNIPAM) brushes of various grafting densities, grown from plasma-activated mica by means of surface-initiated polymerization. We thus show that dense thermoresponsive brushes collapse gradually as temperature is increased, and that grafting density greatly affects their ability to swell: the swelling ratio of the brushes, which characterizes the thickness variation between the swollen and the collapsed state, is found to decrease from $\sim 7$ to $\sim 3$ as the number of grafted chains per unit …
The collapse and swelling behavior of a generic homopolymer is studied using implicit-solvent, explicit-cosolvent Langevin dynamics computer simulations for varying interaction strengths. The systematic investigation reveals that polymer swelling is maximal if both monomer-monomer and monomer-cosolute interactions are weakly attractive. In the most swollen state the cosolute density inside the coil is remarkably bulk-like and homogenous. Highly attractive monomer-cosolute interactions, however, are found to induce a collapse of the chain which, in contrast to the collapsed case induced by pure…
We present a simple analytical theory of flexible polymer chain dissolved in a good solvent, carrying permanent freely oriented dipoles on the monomers. We take into account the dipole correlations within the random phase approximation (RPA), as well as a dielectric heterogeneity in the internal polymer volume relative to the bulk solution. We demonstrate that the dipole correlations of monomers can be taken into account as pairwise ones only when the polymer chain is in a coil conformation. In this case the dipole correlations manifest themselves through the Keesom interactions of the permane…
We consider a binary mixture of colloid and polymer particles with positions on a simple cubic lattice. Colloids exclude both colloids and polymers from nearest neighbor sites. Polymers are treated as effective particles that are mutually non-interacting, but exclude colloids from neighboring sites; this is a discrete version of the (continuum) Asakura-Oosawa-Vrij model. Two alternative density functionals are proposed and compared in detail. The first is based on multi-occupancy in the zero-dimensional limit of the bare model, analogous to the corresponding continuum theory that reproduces th…
Dynamics of various biological filaments can be understood within the framework of active polymer models. Here we consider a bead-spring model for a flexible polymer chain in which the active interaction among the beads is introduced via an alignment rule adapted from the Vicsek model. Following a quench from the high-temperature coil phase to a low-temperature state point, we study the coarsening kinetics via molecular dynamics (MD) simulations using the Langevin thermostat. For the passive polymer case the low-temperature equilibrium state is a compact globule. Results from our MD simulation…
The presence of ordered structures such as helices in collapsed states of polymer chains is still an open question challenging physics and biology. In this work, we present a potential model for polymer chains with monomers that are not strictly attractive, but that can make adhesive contacts with other monomers. We find that the chain develop helical order during the process of collapsing from an initially stretched conformation. It seems in this case that the adhesive contacts help the polymer chain to stay trapped in the helix state.
Using molecular dynamics simulations of a tangent-soft-sphere bead-spring polymer model, we examine the degree to which semiflexible polymer melts solidify at isostaticity. Flexible and stiff chains crystallize when they are isostatic as defined by appropriate degree-of-freedom-counting arguments. Semiflexible chains also solidify when isostatic if a generalized isostaticity criterion that accounts for the slow freezing out of configurational freedom as chain stiffness increases is employed. The dependence of the average coordination number at solidification $Z(T_s)$ on chains' characteristic …
We investigate the dynamics and the pathways of the collapse of a single, semiflexible polymer in a poor solvent via 3-D Brownian Dynamics simulations. Earlier work indicates that the condensation of semiflexible polymers generically proceeds via a cascade through metastable racquet-shaped, long-lived intermediates towards the stable torus state. We investigate the rate of decay of uncollapsed states, analyze the preferential pathways of condensation, and describe likelihood and lifespan of the different metastable states. The simulation are performed with a bead-stiff spring model with exclud…
Molecular dynamics simulations are used to investigate the conformations of a single polymer chain, represented by the Kremer-Grest bead-spring model, in a solution with a Lennard-Jones liquid as the solvent when the interaction strength between the polymer and solvent is varied. Results show that when the polymer-solvent interaction is unfavorable, the chain collapses as one would expect in a poor solvent. For more attractive polymer-solvent interactions, the solvent quality improves and the chain is increasingly solvated and exhibits ideal and then swollen conformations. However, as the poly…
We report dynamic Monte Carlo simulation on conformational transition of H-shaped branched polymers by varying main chain (backbone) and side chain (branch) length. H-shaped polymers in comparison with equivalent linear polymers exhibit a depression of theta temperature accompanying with smaller chain dimensions. We observed that the effect of branches on backbone dimension is more pronounced than the reverse, and is attributed to the conformational heterogeneity prevails within the molecule. With increase in branch length, backbone is slightly stretched out in coil and globule state. However,…
We investigate the internal structure of a polymer during collapse from an expanded coil to a compact globule. Collapse is more probable in local regions of high curvature, so a smoothing of the fractal polymer structure occurs that proceeds systematically from the shortest to the longest length scales. A proposed universal scaling relationship is tested by comparison with Monte Carlo simulations. We speculate that the universal form applies to various fractal systems with local processes that promote smoothness over time. The results complement earlier work showing that on the macroscale poly…
Conformational properties of star-shaped polymer aggregates that carry attractive end-groups, called telechelic star polymers, are investigated by simulation and analytical variational theory. We focus on the case of low telechelic star polymer functionalities, $f \leq 5$, a condition which allows aggregation of all attractive monomers on one site. We establish the functionality- and polymerization-number dependence of the transition temperature from the "star burst'' to the "water melon" macroparticle structure. Extensions to telechelic stars featuring partially collapsed configurations are a…
Molecular process of polymer collapse was reproduced by isothermal molecular dynamics simulation. The initial polymer chains were obtained by mean of random walks in continuum space. Two potential models were considered to represent short range interactions between monomers. Various structural properties during the collapse of the polymer were measured and different collapse pathways were observed. For low temperatures, we have obtained a spontaneous collapse to helical states.
The universality of the swelling of the radius of gyration of a homopolymer relative to its value in the $θ$ state, independent of polymer-solvent chemistry, in the crossover regime between $θ$ and athermal solvent conditions, is well known. Here we study, by Brownian dynamics, a polymer model where a subset of monomers is labelled as "stickers". The mutual interaction of the stickers is more attractive than those of the other ("backbone") monomers, and has the additional important characteristic of "functionality" $φ$, i.e., the maximum number of stickers that can locally bind to a given stic…
We study the Brownian dynamics of flexible and semiflexible polymer chains densely grafted on a flat substrate, upon rapid quenching of the system when the quality of solvent becomes poor and chains attempt collapse into a globular state. The collapse process of such a polymer brush differs from individual chains, both in its kinetics and its structural morphology. We find that the resulting collapsed brush does not form a homogeneous dense layer, in spite of all chain monomers equally attracting each other via a model Lennard-Jones potential. Instead, a very distinct inhomogeneous density dis…
The rupture of a polymer chain maintained at temperature $T$ under fixed tension is prototypical to a wide array of systems failing under constant external strain and random perturbations. Past research focused on analytic and numerical studies of the mean rate of collapse of such a chain. Surprisingly, an analytic calculation of the probability distribution function (PDF) of collapse rates appears to be lacking. Since rare events of rapid collapse can be important and even catastrophic, we present here a theory of this distribution, with a stress on its tail of fast rates. We show that the ta…
Recently it has been shown that a two-dimensional model of self-attracting polymers based on attracting segments with the addition of stiffness displays three phases: a swollen phase, a globular, liquid-like phase, and an anisotropic crystal-like phase. Here, we consider the attracting segment model in three dimensions with the addition of stiffness. While we again identify a swollen and two distinct collapsed phases, we find that both collapsed phases are anisotropic, so that there is no phase in which the polymer resembles a disordered liquid drop. Moreover all the phase transitions are firs…
We have used computer simulation to study the collapse of a hydrophobic chain in water. We find that the mechanism of collapse is much like that of a first order phase transition. The evaporation of water in the vicinity of the polymer provides the driving force for collapse, and the rate limiting step is the nucleation of a sufficiently large vapor bubble. The study is made possible through the application of transition path sampling and a coarse grained treatment of liquid water. Relevance of our findings to understanding the folding and assembly of proteins is discussed.
Recent emerging interest in experiments of single-polymer dynamics urge computational physicists to revive their understandings, particularly in the nonequilibrium context. Here we briefly discuss the currently evolving approaches of investigating the evolution dynamics of homopolymer collapse in computer simulations. Primary focus of these approaches is to understand various dynamic scaling laws related to coarsening and aging during the collapse in space dimension $d=3$, using tools popular in nonequilibrium coarsening dynamics of particle or spin systems. In addition to providing an overvie…
We study numerically a lattice model of semiflexible homopolymers with nearest neighbor attraction and energetic preference for straight joints between bonded monomers. For this we use a new algorithm, the "Pruned-Enriched Rosenbluth Method" (PERM). It is very efficient both for relatively open configurations at high temperatures and for compact and frozen-in low-T states. This allows us to study in detail the phase diagram as a function of nn-attraction epsilon and stiffness x. It shows a theta-collapse line with a transition from open coils to molten compact globules (large epsilon) and a fr…
In earlier work we provided the first evidence that the collapse, or coil-globule, transition of an isolated polymer in solution can be seen in a four-dimensional model. Here we investigate, via Monte Carlo simulations, the canonical lattice model of polymer collapse, namely interacting self-avoiding walks, to show that it not only has a distinct collapse transition at finite temperature but that for any finite polymer length this collapse has many characteristics of a rounded first-order phase transition. However, we also show that there exists a `$θ$-point' where the polymer behaves in a sim…
The rapid collapse of a polymer, due to external forces or changes in solvent, yields a long-lived `crumpled globule.' The conjectured fractal structure shaped by hierarchical collapse dynamics has proved difficult to establish, even with large simulations. To unravel this puzzle, we study a coarse-grained model of in-falling spherical blobs that coalesce upon contact. Distances between pairs of monomers are assigned upon their initial coalescence, and do not `equilibrate' subsequently. Surprisingly, the model reproduces quantitatively the dependence of distance on segment length, suggesting t…
Shear responsive surfaces offer potential advances in a number of applications. Surface functionalisation using polymer brushes is one route to such properties, particularly in the case of entangled polymers. We report on neutron reflectometry measurements of polymer brushes in entangled polymer solutions performed under controlled shear, as well as coarse-grained computer simulations corresponding to these interfaces. Here we show a reversible and reproducible collapse of the brushes, increasing with the shear rate. Using two brushes of greatly different chain lengths and grafting densities, …
Single partially confined collapsed polymers are studied in two dimensions. They are described by self-avoiding random walks with nearest-neighbour attractions below the $Θ$-point, on the surface of an infinitely long cylinder. For the simulations we employ the pruned-enriched-Rosenbluth method (PERM). The same model had previously been studied for free polymers (infinite lattice, no boundaries) and for polymers on finite lattices with periodic boundary conditions. We verify the previous estimates of bulk densities, bulk free energies, and surface tensions. We find that the free energy of a po…
Critical fluctuations are known to induce a collapse of polymer chains in a mixed solvent upon approaching its liquid-liquid critical point, as originally predicted by Brochard and de Gennes. Recently, we have found that closer to the critical point this collapse is followed by a reswelling of the polymer coils well beyond the original dimensions, a phenomenon not predicted by the theory of Brochard and de Gennes. We submit that upon approaching the critical temperature more closely, the correlation length of the critical fluctuations inside the polymer coils can no longer further increase due…
The elastic interactions between objects embedded in a nematic liquid crystal are usually caused by the average distorsion-rather than by the fluctuations-of the nematic orientational field. We argue that for sufficiently small particles, the nematic-mediated interaction originates purely from the fluctuations of the nematic director. This Casimir interaction decays as d^(-6), d being the distance between the particles, and it dominates van der Waals interactions close to the isotropic-to-nematic transition. Considering the nematic as a polymer solvent, we show that the onset of this Casimir i…
We investigate a lattice model of polymers where the nearest-neighbour monomer-monomer interaction strengths differ according to whether the local configurations have so-called ``hydrogen-like'' formations or not. If the interaction strengths are all the same then the classical $θ$-point collapse transition occurs on lowering the temperature, and the polymer enters the isotropic liquid-drop phase known as the collapsed globule. On the other hand, strongly favouring the hydrogen-like interactions give rise to an anisotropic folded (solid-like) phase on lowering the temperature. We use Monte Car…
We enumerate all minimal energy packings (MEPs) for small single linear and ring polymers composed of spherical monomers with contact attractions and hard-core repulsions, and compare them to corresponding results for monomer packings. We define and identify ``dividing surfaces" in polymer packings, which reduce the number of arrangements that satisfy hard-sphere and covalent bond constraints. Compared to monomer MEPs, polymer MEPs favor intermediate structural symmetry over high and low symmetries. We also examine the packing-preparation dependence for longer single chains using molecular dyn…
The experimentally observed swelling and collapse response of weakly charged polymers to the addition of specific salts displays quite convoluted behavior that is not easy to categorize. Here we use a minimalistic implicit solvent / explicit salt simulation model with a focus on ion-specific interactions between ions and a single weakly charged polyelectrolyte to qualitatively explain the observed effects. In particular, we demonstrate ion-specific screening and bridging effects cause collapse at low salt concentrations whereas the same strong ion-specific direct interactions drive re-entrant …
There have been separate studies of the polymer collapse transition, where the collapse was induced by two different types of attraction. In each case, the configurations of the polymer were given by the same subset of random walks being self-avoiding trails on the square lattice. Numerical evidence shows that when interacting via nearest-neighbour contacts, this transition is different from the collapse transition in square-lattice trails interacting via multiply visited sites. While both transitions are second-order, when interacting via nearest-neighbour contacts, the transition is relative…
