Generalized entropy theory of glass-formation in fully flexible polymer melts

Generalized entropy theory investigation of the relatively high segmental fragility of many glass-forming polymers

We utilize the generalized entropy theory (GET) of glass formation to address one of the most singular and least understood properties of polymer glass-forming liquids in comparison to atomic and small molecule liquids-the often relatively high fragility of the polymer dynamics on a segmental scale, ms. Based on this highly predictive framework of both the thermodynamics and segmental dynamics in terms of molecular structure, polymer backbone and side-group rigidities, and intermolecular interaction strength, we first analyze the relation between ms and the ratio, , where Sc is the configurational entropy density of the polymer fluid, equals Sc at the onset temperature TA for non-Arrhenius relaxation, and Tg is the glass transition temperature at which the structural relaxation time τα equals 100 s. While the reduced activation energy estimated from an Arrhenius plot (i.e., differential activation energy) normalized by kBTg is determined to be not equal to the actual activation energy, we do find that an apparently general nonlinear relation between ms and holds to a good approximation for a large class of polymer models, . The predicted ranges of ms and are consistent with experimental estimates for high molecular-mass polymer, oligomeric, small molecule, and atomic glass-forming liquids. In particular, relatively high values of ms are found for polymers having complex monomer structures and significant chain stiffness. The variation of ms with molecular mass, chain stiffness, and intermolecular interaction strength can be traced to the variation of , which is shown to provide a measure of packing frustration defined in terms of the dimensionless thermal expansion coefficient and isothermal compressibility. The often relatively high fragility and large extent of cooperative motion are found in the GET to derive from the often relatively large packing frustration in this class of polymer glass-forming liquids. Finally, we also develop a tentative model of the "dynamical segmental relaxation time" based on the GET, in which the polymers on a coarse-grained scale are modeled as strings of structureless "beads", as assumed in the Rouse and reptation models of polymer dynamics.

Confinement effect of inter-arm interactions on glass formation in star polymer melts

We utilized molecular dynamic simulation to investigate the glass formation of star polymer melts in which the topological complexity is varied by altering the number of star arms (f). Emphasis was placed on how the "confinement effect" of repulsive inter-arm interactions within star polymers influences the thermodynamics and dynamics of star polymer melts. All the characteristic temperatures of glass formation were found to progressively increase with increasing f, but unexpectedly the fragility parameter KVFT was found to decrease with increasing f. As previously observed, stars having more than 5 or 6 arms adopt an average particle-like structure that is more contracted relative to the linear polymer size having the same mass and exhibit a strong tendency for intermolecular and intramolecular segregation. We systematically analyzed how varying f alters collective particle motion, dynamic heterogeneity, the decoupling exponent ζ phenomenologically linking the slow β- and α-relaxation times, and the thermodynamic scaling index γt. Consistent with our hypothesis that the segmental dynamics of many-arm star melts and thin supported polymer films should exhibit similar trends arising from the common feature of high local segmental confinement, we found that ζ increases considerably with increasing f, as found in supported polymer films with decreasing thickness. Furthermore, increasing f led to greatly enhanced elastic heterogeneity, and this phenomenon correlates strongly with changes in ζ and γt. Our observations should be helpful in building a more rational theoretical framework for understanding how molecular topology and geometrical confinement influence the dynamics of glass-forming materials more broadly.

Systematic Coarse-graining of Epoxy Resins with Machine Learning-Informed Energy Renormalization

A persistent challenge in predictive molecular modeling of thermoset polymers is to capture the effects of chemical composition and degree of crosslinking (DC) on dynamical and mechanical properties with high computational efficiency. We established a new coarse-graining (CG) approach that combines the energy renormalization method with Gaussian process surrogate models of the molecular dynamics simulations. This allows a machine-learning informed functional calibration of DC-dependent CG force field parameters. Taking versatile epoxy resins consisting of Bisphenol A diglycidyl ether combined with curing agent of either 4,4-Diaminodicyclohexylmethane or polyoxypropylene diamines, we demonstrated excellent agreement between all-atom and CG predictions for density, Debye-Waller factor, Young's modulus and yield stress at any DC. We further introduce a surrogate model enabled simplification of the functional forms of 14 non-bonded calibration parameters by quantifying the uncertainty of a candidate set of high-dimensional/flexible calibration functions. The framework established provides an efficient methodology for chemistry-specific, large-scale investigations of the dynamics and mechanics of epoxy resins.

Glass transition and dynamics of semiflexible polymer brushes

The glass transition and dynamics of densely grafted semiflexible polymer brushes are studied by molecular dynamics simulation. The glass transition temperature (T_g) increases with the polymer rigidity. The local glass transition temperature (T_g,local) is estimated from the temperature-dependent dynamics of individual segments including the lateral position fluctuation and lateral mean square displacement. Different from the flexible polymer brush, T_g,local of semiflexible polymer brushes is roughly independent of the segment height. Our simulation reveals that the glass transition is in synchronism with an abrupt change of the chain conformation in semiflexible polymer brushes. When the temperature drops to near T_g, the semiflexible polymer chains elongate, tilt, and become more ordered. Moreover, enhanced segmental dynamics is observed at temperatures just above T_g for the semiflexible polymer brushes.

Dynamic heterogeneity, cooperative motion, and Johari-Goldstein β -relaxation in a metallic glass-forming material exhibiting a fragile-to-strong transition

We investigate the Johari-Goldstein (JG)β -relaxation process in a model metallic glass-forming (GF) material (Al 90 Sm 10 ), previously studied extensively by both frequency-dependent mechanical measurements and simulation studies devoted to equilibrium properties, by molecular dynamics simulations based on validated and optimized interatomic potentials with the primary aim of better understanding the nature of this universal relaxation process from a dynamic heterogeneity (DH) perspective. The present relatively low temperature and long-time simulations reveal a direct correspondence between the JGβ -relaxation timeτ J G and the lifetime of the mobile particle clustersτ M , defined as in previous DH studies, a relationship dual to the corresponding previously observed relationship between theα -relaxation timeτ α and the lifetime of immobile particle clustersτ I M . Moreover, we find that the average diffusion coefficient D nearly coincides withD A l of the smaller atomic species (Al) and that the 'hopping time' associated with D coincides withτ J G to within numerical uncertainty, both trends being in accord with experimental studies. This indicates that the JGβ -relaxation is dominated by the smaller atomic species and the observation of a direct relation between this relaxation process and rate of molecular diffusion in GF materials at low temperatures where the JGβ -relaxation becomes the prevalent mode of structural relaxation. As an unanticipated aspect of our study, we find thatAl 90 Sm 10 exhibits fragile-to-strong (FS) glass formation, as found in many other metallic GF liquids, but this fact does not greatly alter the geometrical nature of DH in this material and the relation of DH to dynamical properties. On the other hand, the temperature dependence of the DH and dynamical properties, such as the structural relaxation time, can be significantly altered from 'ordinary' GF liquids.

Configurational entropy of glass-forming liquids

The configurational entropy is one of the most important thermodynamic quantities characterizing supercooled liquids approaching the glass transition. Despite decades of experimental, theoretical, and computational investigation, a widely accepted definition of the configurational entropy is missing, its quantitative characterization remains fraught with difficulties, misconceptions, and paradoxes, and its physical relevance is vividly debated. Motivated by recent computational progress, we offer a pedagogical perspective on the configurational entropy in glass-forming liquids. We first explain why the configurational entropy has become a key quantity to describe glassy materials, from early empirical observations to modern theoretical treatments. We explain why practical measurements necessarily require approximations that make its physical interpretation delicate. We then demonstrate that computer simulations have become an invaluable tool to obtain precise, nonambiguous, and experimentally relevant measurements of the configurational entropy. We describe a panel of available computational tools, offering for each method a critical discussion. This perspective should be useful to both experimentalists and theoreticians interested in glassy materials and complex systems.

Zero-temperature glass transition in two dimensions

Liquids cooled towards the glass transition temperature transform into amorphous solids that have a wide range of applications. While the nature of this transformation is understood rigorously in the mean-field limit of infinite spatial dimensions, the problem remains wide open in physical dimensions. Nontrivial finite-dimensional fluctuations are hard to control analytically, and experiments fail to provide conclusive evidence regarding the nature of the glass transition. Here, we develop Monte Carlo methods for two-dimensional glass-forming liquids that allow us to access equilibrium states at sufficiently low temperatures to directly probe the glass transition in a regime inaccessible to experiments. We find that the liquid state terminates at a thermodynamic glass transition which occurs at zero temperature and is associated with an entropy crisis and a diverging static correlation length. Our results thus demonstrate that a thermodynamic glass transition can occur in finite dimensional glass-formers.

Energy renormalization for coarse-graining polymers having different segmental structures

Multiscale coarse-grained (CG) modeling of soft materials, such as polymers, is currently an art form because CG models normally have significantly altered dynamics and thermodynamic properties compared to their atomistic counterparts. We address this problem by exploiting concepts derived from the generalized entropy theory (GET), emphasizing the central role of configurational entropy s c in the dynamics of complex fluids. Our energy renormalization (ER) method involves varying the cohesive interaction strength in the CG models in such a way that dynamic properties related to s c are preserved. We test this ER method by applying it to coarse-graining polymer melts (i.e., polybutadiene, polystyrene, and polycarbonate), representing polymer materials having a relatively low, intermediate, and high degree of glass "fragility". We find that the ER method allows the dynamics of the atomistic polymer models to be faithfully described to a good approximation by CG models over a wide temperature range.

Tuning the Relaxation of Nanopatterned Polymer Films with Polymer-Grafted Nanoparticles: Observation of Entropy-Enthalpy Compensation

Polymer films provide a versatile platform in which complex functional relief patterns can be thermally imprinted with a resolution down to few nanometers. However, a practical limitation of this method is the tendency for the imprinted patterns to relax ("slump"), leading to loss of pattern fidelity over time. While increasing temperature above glass transition temperature ( Tg) accelerates the slumping kinetics of neat films, we find that the addition of polymer-grafted nanoparticles (PGNP) can greatly enhance the thermal stability of these patterns. Specifically, increasing the concentration of poly(methyl methacrylate) (PMMA) grafted titanium dioxide (TiO2) nanoparticles in the composite films slows down film relaxation dynamics, leading to enhanced pattern stability for the temperature range that we investigated. Interestingly, slumping relaxation time is found to obey an entropy-enthalpy compensation (EEC) relationship with varying PGNP concentration, similar to recently observed relaxation of strain-induced wrinkling in glassy polymer films having variable film thickness. The compensation temperature,  Tcomp was found to be in the vicintity of the bulk  Tg of PMMA. Our results suggest a common origin of EEC relaxation in patterned polymer thin films and  nanocomposites.

Energy-Renormalization for Achieving Temperature Transferable Coarse-Graining of Polymer Dynamics

The bottom-up prediction of the properties of polymeric materials based on molecular dynamics simulation is a major challenge in soft matter physics. Coarse-grained (CG) models are often employed to access greater spatiotemporal scales required for many applications, but these models normally experience significantly altered thermodynamics and highly accelerated dynamics due to the reduced number of degrees of freedom upon coarse-graining. While CG models can be calibrated to meet certain properties at particular state points, there is unfortunately no temperature transferable and chemically specific coarse-graining method that allows for modeling of polymer dynamics over a wide temperature range. Here, we pragmatically address this problem by "correcting" for deviations in activation free energies that occur upon coarse-graining the dynamics of a model polymeric material (polystyrene). In particular, we propose a new strategy based on concepts drawn from the Adam-Gibbs (AG) theory of glass formation. Namely we renormalize the cohesive interaction strength and effective interaction length-scale parameters to modify the activation free energy. We show that this energy-renormalization method for CG modeling allows accurate prediction of atomistic dynamics over the Arrhenius regime, the non-Arrhenius regime of glass formation, and even the non-equilibrium glassy regime, thus allowing for the predictive modeling of dynamic properties of polymer over the entire range of glass formation. Our work provides a practical scheme for establishing temperature transferable coarse-grained models for predicting and designing the properties of polymeric materials.