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The microscopic model of semi-crystalline polymer in high-elastic state is proposed. The model is based on the assumption that, below the melting temperature, the semi-crystalline polymer comprises crystal nuclei connected by stretched chain segments (SCS) with random configuration of monomers. The key factor that stalls the phase transition below the melting temperature is the tension of the SCS. External stress applied to the polymer also shifts the equilibrium and causes unfolding of the nuclei, which enables large reversible deformation of the polymer without loss of integrity. The simple 1D model predicts plateau in stress-strain curve of high-elastic polymer above the yield stress, which agrees with experimental observations. The model prediction for the temperature dependence of polytetrafluoroethylene (PTFE) yield stress in high-elastic state is in satisfactory agreement with experiment.
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Machine learning (ML) and artificial intelligence (AI) have the remarkable ability to classify, recognize, and characterize complex patterns and trends in large data sets. Here, we adopt a subclass of machine learning methods viz., deep learnings and develop a general-purpose AI tool - dPOLY for analyzing molecular dynamics trajectory and predicting phases and phase transitions in polymers. An unsupervised deep neural network is used within this framework to map a molecular dynamics trajectory undergoing thermophysical treatment such as cooling, heating, drying, or compression to a lower dimension. A supervised deep neural network is subsequently developed based on the lower dimensional data to characterize the phases and phase transition. As a proof of concept, we employ this framework to study coil to globule transition of a model polymer system. We conduct coarse-grained molecular dynamics simulations to collect molecular dynamics trajectories of a single polymer chain over a wide range of temperatures and use dPOLY framework to predict polymer phases. The dPOLY framework accurately predicts the critical temperatures for the coil to globule transition for a wide range of polymer sizes. This method is generic and can be extended to capture various other phase transitions and dynamical crossovers in polymers and other soft materials.
We show that the structural properties and phase behavior of a self-avoiding polymer chain on adhesive substrate, subject to pulling at the chain end, can be obtained by means of a Grand Canonical Ensemble (GCE) approach. We derive analytical expressions for the mean length of the basic structural units of adsorbed polymer, such as loops and tails, in terms of the adhesive potential and detachment force, and determine values of the universal exponents which govern their probability distributions. Most notably, the hitherto controversial value of the critical adsorption exponent $phi$ is found to depend essentially on the interaction between different loops. The chain detachment transition turns out to be of the first order, albeit dichotomic, i.e., no coexistence of different phase states exists. These novel theoretical predictions and the suggested phase diagram of the adsorption-desorption transformation under external pulling force are verified by means of extensive Monte Carlo simulations.
The two-dimensional (zero magnetic field) Ising model is known to undergo a second order para-ferromagnetic phase transition, which is accompanied by a correlated percolation transition for the Fortuin-Kasteleyn (FK) clusters. In this paper we uncover that there exists also a second temperature $T_{text{eb}}<T_c$ at which the elastic backbone of FK clusters undergoes a second order phase transition to a dense phase. The corresponding universality class, which is characterized by determining various percolation exponents, is shown to be completely different from directed percolation, proposing a new anisotropic universality class with $beta=0.54pm 0.02$, $ u_{||}=1.86pm 0.01$, $ u_{perp}=1.21pm 0.04$ and $d_f=1.53pm 0.03$. All tested hyper-scaling relations are shown to be valid.
The phase diagram of star polymer solutions in a good solvent is obtained over a wide range of densities and arm numbers by Monte Carlo simulations. The effective interaction between the stars is modeled by an ultrasoft pair potential which is logarithmic in the core-core distance. Among the stable phases are a fluid as well as body-centered cubic, face-centered cubic, body-centered orthogonal, and diamond crystals. In a limited range of arm numbers, reentrant melting and reentrant freezing transitions occur for increasing density.
We present a Brownian dynamics model of driven polymer translocation, in which non-equilibrium memory effects arising from tension propagation (TP) along the cis side subchain are incorporated as a time-dependent friction. To solve the effective friction, we develop a finite chain length TP formalism, expanding on the work of Sakaue [Sakaue, PRE 76, 021803 (2007)]. The model, solved numerically, yields results in excellent agreement with molecular dynamics simulations in a wide range of parameters. Our results show that non-equilibrium TP along the cis side subchain dominates the dynamics of driven translocation. In addition, the model explains the different scaling of translocation time w.r.t chain length observed both in experiments and simulations as a combined effect of finite chain length and pore-polymer interactions.
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