Polymeric Glass-forming Liquids Research Articles

Understanding Relaxation in the Kob-Andersen Liquid Based on Entropy, String, Shoving, Localization, and Parabolic Models.

We assess the validity of a range of models of glass formation based on molecular dynamics simulation results of the Kob-Andersen (KA) model system under a wide range of constant volume and constant pressure conditions. These models include the Adam-Gibbs model emphasizing configurational entropy, the string model emphasizing collective particle exchange motion, the shoving model emphasizing material elasticity, the localization model emphasizing dynamical free volume, and parabolic models based on the ideas of dynamic facilitation and, alternatively, the hypothesis that glass formation involves an avoided critical point. We demonstrate that these seemingly disparate models all provide a reasonable description of structural relaxation and diffusion data for the KA model system under all simulation conditions considered. Hence, the present study points to some unity in our understanding of the relationship between leading models of glass formation, supporting inferences drawn from previous studies of polymeric glass-forming liquids.

Influence of Density and Pressure on Glass Formation in the Kob-Andersen Model.

We systematically study glass formation in the well-known Kob-Andersen model over a wide range of densities and pressures as a basis for judging the "universality" of glass formation through a comparison to a recent systematic study of model polymeric glass-forming liquids. Our purpose is to establish general characteristics of glass formation, to identify new relations, and to discern which properties of glass-forming liquids are material-specific and which are "universal." To this end, we analyze a number of characteristic properties of glass formation, such as the structural relaxation time, self-diffusion coefficient, viscosity, characteristic temperatures, and fragility. We also consider a suite of properties presumably related to dynamic heterogeneity in an attempt to better understand its relation to structural relaxation. We demonstrate that the glassy dynamics in the Kob-Andersen model exhibit many of the essential trends observed in polymeric glass-forming liquids, pointing to a remarkable "universality" of many aspects of glass formation.

Molecular Dynamics Investigation of the Pressure Dependence of Glass Formation in a Charged Polymer Melt

Most commodity polymers are derived from petroleum raw materials, and correspondingly, these materials are normally uncharged and nonpolar, attributes that make this class of material relatively insoluble in water and relatively slow to breakdown in the environment. Natural and synthetic charged polymer materials often do not exhibit these drawbacks, thereby offering the potential for being more sustainable. As with all polymer materials, properties related to glass formation play a central role in the design and characterization of materials. Here, we investigate the influence of a crucial processing variable, the pressure P, on the glass formation of a coarse-grained charged polymer melt using molecular dynamics simulation. We find that the temperature (T) dependence of the thermodynamics and segmental dynamics under variable P conditions largely resemble the trends observed before for uncharged polymer liquids. In particular, we are able to organize all our segmental relaxation data as functions of both T and P in terms of the conventional phenomenology for uncharged polymer melts, namely, the Vogel–Fulcher–Tammannn temperature dependence of the structural relaxation time τα and a pressure analog of this equation, etc. Moreover, we can quantitatively describe all our simulation data for both charged and uncharged polymer melts with the string model of glass formation. Importantly, our results indicate that the main effect of charge on the dynamics of polymeric glass-forming liquids is to “renormalize” the cohesive interaction strength. This opens the possibility of applying theories of neutral polymer melts to describe the glass formation of synthetic and natural charged polymer melts, ionic fluids, and possibly even polar polymer melts, once an accounting is made for how charge modifies the effective cohesive interaction strength.

Data-Driven Identification and Analysis of the Glass Transition in Polymer Melts.

Understanding the nature of glass transition, as well as the precise estimation of the glass transition temperature for polymeric materials, remains open questions in both experimental and theoretical polymer sciences. We propose a data-driven approach, which utilizes the high-resolution details accessible through the molecular dynamics simulation and considers the structural information on individual chains. It clearly identifies the glass transition temperature of polymer melts of weakly semiflexible chains. By combining principal component analysis and clustering, we identify the glass transition temperature in the asymptotic limit even from relatively short time trajectories, which just reach into the Rouse-like monomer displacement regime. We demonstrate that fluctuations captured by the principal component analysis reflect the change in a chain's behavior: from conformational rearrangement above to small fluctuations below the glass transition temperature. Our approach is straightforward to apply and should be applicable to other polymeric glass-forming liquids.

Temperature Dependence of Structural Relaxation in Glass-Forming Liquids and Polymers.

Understanding the microscopic mechanism of the transition of glass remains one of the most challenging topics in Condensed Matter Physics. What controls the sharp slowing down of molecular motion upon approaching the glass transition temperature Tg, whether there is an underlying thermodynamic transition at some finite temperature below Tg, what the role of cooperativity and heterogeneity are, and many other questions continue to be topics of active discussions. This review focuses on the mechanisms that control the steepness of the temperature dependence of structural relaxation (fragility) in glass-forming liquids. We present a brief overview of the basic theoretical models and their experimental tests, analyzing their predictions for fragility and emphasizing the successes and failures of the models. Special attention is focused on the connection of fast dynamics on picosecond time scales to the behavior of structural relaxation on much longer time scales. A separate section discusses the specific case of polymeric glass-forming liquids, which usually have extremely high fragility. We emphasize the apparent difference between the glass transitions in polymers and small molecules. We also discuss the possible role of quantum effects in the glass transition of light molecules and highlight the recent discovery of the unusually low fragility of water. At the end, we formulate the major challenges and questions remaining in this field.

Melt Properties and String Model Description of Glass Formation in Graft Polymers of Different Side-Chain Lengths

Graft polymers have attracted growing interest due to their unique properties, but a fundamental understanding of their glass formation remains to be established. We perform extensive molecular dynamics simulations of a coarse-grained bead–spring polymer model to investigate the influence of side-chain length on the glass formation of general classes of graft polymers having a fixed reduced molecular mass, which are classified based on the relative rigidities of the backbone and side chains. We first examine the basic properties of the graft polymers in a melt to understand their conformational and structural properties. Our analysis indicates that the overall average size and shape of our model graft polymers exhibit a nonmonotonic dependence on the side-chain length, while the side chains undergo a smooth transition from rod-like to coiled chain conformations near a side-chain length of 10 statistical segments. We then utilize the string model to understand the structural relaxation of graft polymers in the low-temperature non-Arrhenius regime─a model that takes the average string length as a key quantity in the description of the dynamics of glass-forming liquids, along with the high-temperature activation free energy. We find the string model to be capable of quantitatively describing the structural relaxation time over the range of temperatures considered in our model graft polymers. The string model also allows us to discuss issues related to the energetic parameters of high temperature activation, and our analysis indicates that the entropic contribution to the high-temperature activation free energy is not generally negligible for polymeric glass-forming liquids, in contrast to the assumption in the entropy theory of glass formation. We expect our work to motivate further studies of the glass formation of graft polymers based on the models in which the fluid entropy and collective motion are of central importance.

Equation of State and Entropy Theory Approach to Thermodynamic Scaling in Polymeric Glass-Forming Liquids

We show that thermodynamic scaling can be derived by combining the Murnaghan equation of state (EOS) with the generalized entropy theory (GET) of glass formation. In our theory, thermodynamic scaling arises in the non-Arrhenius relaxation regime as a scaling property of the fluid configurational entropy density $s_c$, normalized by its value $s_c^*$ at the onset temperature $T_A$ of glass formation, $s_c / s_c^*$, so that a constant value of $TV^{\gamma}$ corresponds to a \textit{reduced isoentropic} fluid condition. Molecular dynamics simulations on a coarse-grained polymer melt are utilized to confirm that the predicted thermodynamic scaling of $\tau_{\alpha}$ by the GET holds both above and below $T_A$ and to test whether the extent $L$ of stringlike collective motion, normalized its value $L_A$ at $T_A$, also obeys thermodynamic scaling, as required for consistency with thermodynamic scaling. While the predicted thermodynamic scaling of both $\tau_{\alpha}$ and $L/ L_A$ is confirmed by simulation, we find that the isothermal compressibility $\kappa_T$ and the long wavelength limit $S(0)$ of the static structure factor do not exhibit thermodynamic scaling, an observation that would appear to eliminate some proposed models of glass formation emphasizing fluid `structure' over configurational entropy. It is found, however, that by defining a low temperature hyperuniform reference state, we may define a compressibility relative to this condition, $\delta \kappa_T$, a transformed dimensionless variable that exhibits thermodynamic scaling and which can be directly related to $s_c / s_c^*$. Further, the Murnaghan EOS allows us to interpret $\gamma$ as a measure of intrinsic anharmonicity of intermolecular interactions that may be directly determined from the pressure derivative of the material bulk modulus.

Polymer Glass Formation: Role of Activation Free Energy, Configurational Entropy, and Collective Motion

We provide a perspective on polymer glass formation, with an emphasis on models in which the fluid entropy and collective particle motion dominate the theoretical description and data analysis. The entropy theory of glass formation has its origins in experimental observations relating to correlations between the fluid entropy and liquid dynamics going back nearly a century ago, and it has entered a new phase in recent years. We first discuss the dynamics of liquids in the high-temperature Arrhenius regime, where transition state theory is formally applicable. We then summarize the evolution of the entropy theory from a qualitative framework for organizing and interpreting temperature-dependent viscosity data by Kauzmann to the formulation of a hypothetical “ideal thermodynamic glass transition” by Gibbs and DiMarzio, followed by seminal measurements linking entropy and relaxation by Bestul and Chang and the Adam–Gibbs (AG) model of glass formation rationalizing the observations of Bestul and Chang. These developments laid the groundwork for the generalized entropy theory (GET), which merges an improved lattice model of polymer thermodynamics accounting for molecular structural details and enabling the analytic calculation of the configurational entropy with the AG model, giving rise to a highly predictive model of the segmental structural relaxation time of polymeric glass-forming liquids. The development of the GET has occurred in parallel with the string model of glass formation in which concrete realizations of the cooperatively rearranging regions are identified and quantified for a wide range of polymeric and other glass-forming materials. The string model has shown that many of the assumptions of AG are well supported by simulations, while others are certainly not, giving rise to an entropy theory of glass formation that is largely in accord with the GET. As the GET and string models continue to be refined, these models progressively grow into a more unified framework, and this Perspective reviews the present status of development of this promising approach to the dynamics of polymeric glass-forming liquids.

What does the instantaneous normal mode spectrum tell us about dynamical heterogeneity in glass-forming fluids?

We examine the instantaneous normal mode spectrum of model metallic and polymeric glass-forming liquids. We focus on the localized modes in the unstable part of the spectrum [unstable localized (UL) modes] and find that the particles making the dominant contribution to the participation ratio form clusters that grow upon cooling in a fashion similar to the dynamical heterogeneity in glass-forming fluids, i.e., highly mobile (or immobile) particles form clusters that grow upon cooling; however, a comparison of the UL mode clusters to the mobile and immobile particle clusters indicates that they are distinct entities. We also show that the cluster size provides an alternate method to distinguish localized and delocalized modes, offering a significant practical advantage over the finite-size scaling approach. We examine the trajectories of particles contributing most to the UL modes and find that they have a slightly enhanced mobility compared to the average, and we determine a characteristic time quantifying the persistence time of this excess mobility. This time scale is proportional to the structural relaxation time τα of the fluid, consistent with a prediction by Zwanzig [Phys. Rev. 156, 190 (1967)] for the lifetime of collective excitations in cooled liquids. Evidently, these collective excitations serve to facilitate relaxation but do not actually participate in the motion associated with barrier crossing events governing activated transport. They also serve as a possible concrete realization of the "facilitation" clusters postulated in previous modeling of glass-forming liquids.

Universal nature of dynamic heterogeneity in glass-forming liquids: A comparative study of metallic and polymeric glass-forming liquids.

Glass-formation is a ubiquitous phenomenon that is often observed in a broad class of materials ranging from biological matter to commonly encountered synthetic polymer, as well as metallic and inorganic glass-forming (GF) materials. Despite the many regularities in the dynamical properties of GF materials, the structural origin of the universal dynamical properties of these materials has not yet been identified. Recent simulations of coarse-grained polymeric GF liquids have indicated the coexistence of clusters of mobile and immobile particles that appear to be directly linked, respectively, to the rate of molecular diffusion and structural relaxation. The present work examines the extent to which these distinct types of "dynamic heterogeneity" (DH) arise in metallic GF liquids (Cu-Zr, Ni-Nb, and Pd-Si alloys) having a vastly different molecular structure and chemistry. We first identified mobile and immobile particles and their transient clusters and found the DH in the metallic alloys to be remarkably similar in form to polymeric GF liquids, confirming the "universality" of the DH phenomenon. Furthermore, the lifetime of the mobile particle clusters was found to be directly related to the rate of diffusion in these materials, while the lifetime of immobile particles was found to be proportional to the structural relaxation time, providing some insight into the origin of decoupling in GF liquids. An examination of particles having a locally preferred atomic packing, and clusters of such particles, suggests that there is no one-to-one relation between these populations of particles so that an understanding of the origin of DH in terms of static fluid structure remains elusive.

Influence of Branching on the Configurational and Dynamical Properties of Entangled Polymer Melts.

We probe the influence of branching on the configurational, packing, and density correlation function properties of polymer melts of linear and star polymers, with emphasis on molecular masses larger than the entanglement molecular mass of linear chains. In particular, we calculate the conformational properties of these polymers, such as the hydrodynamic radius , packing length p, pair correlation function , and polymer center of mass self-diffusion coefficient, D, with the use of coarse-grained molecular dynamics simulations. Our simulation results reproduce the phenomenology of simulated linear and branched polymers, and we attempt to understand our observations based on a combination of hydrodynamic and thermodynamic modeling. We introduce a model of “entanglement” phenomenon in high molecular mass polymers that assumes polymers can viewed in a coarse-grained sense as “soft” particles and, correspondingly, we model the emergence of heterogeneous dynamics in polymeric glass-forming liquids to occur in a fashion similar to glass-forming liquids in which the molecules have soft repulsive interactions. Based on this novel perspective of polymer melt dynamics, we propose a functional form for D that can describe our simulation results for both star and linear polymers, covering both the unentangled to entangled polymer melt regimes.

Influence of Branching on the Configurational and Dynamical Properties of Entangled Polymer Melts

We probe the influence of branching on the configurational, packing, and density correlation function properties of polymer melts of linear and star polymers, with emphasis on molecular masses larger than the entanglement molecular mass of linear chains. In particular, we calculate the conformational properties of these polymers, such as the hydrodynamic radius R h , packing length p, pair correlation function g ( r ) , and polymer center of mass self-diffusion coefficient, D, with the use of coarse-grained molecular dynamics simulations. Our simulation results reproduce the phenomenology of simulated linear and branched polymers, and we attempt to understand our observations based on a combination of hydrodynamic and thermodynamic modeling. We introduce a model of “entanglement” phenomenon in high molecular mass polymers that assumes polymers can viewed in a coarse-grained sense as “soft” particles and, correspondingly, we model the emergence of heterogeneous dynamics in polymeric glass-forming liquids to occur in a fashion similar to glass-forming liquids in which the molecules have soft repulsive interactions. Based on this novel perspective of polymer melt dynamics, we propose a functional form for D that can describe our simulation results for both star and linear polymers, covering both the unentangled to entangled polymer melt regimes.

Advances in the generalized entropy theory of glass-formation in polymer melts.

The generalized entropy theory (GET) of polymeric glass-forming liquids is reformulated into a computationally simpler and more natural formalism than the original version of this theory. The new theoretical framework greatly facilitates establishing essential trends in the dependence of the segmental relaxation time τ, fragility, characteristic temperatures of glass-formation, etc., on the combined influences of monomer molecular structure, chain rigidity, and cohesive interaction strength. Special attention is placed on the estimating the parameters of the phenomenological Vogel-Fulcher-Tammann relations for describing segmental relaxation in diverse liquids in the low temperature range of glass-formation, Tg > T > Tc (or Tg < T < Tg + 100 K), where Tg and Tc are, respectively, the glass transition temperature and the crossover temperature separating the high and low temperature regimes of glass-formation. Finally, we discuss how the molecular energetic interaction parameters of the GET can be estimated from experimental data. Illustrative calculations are performed for the stiffness factor σ and the cohesive energy density u as a first step in this direction.

Application of the entropy theory of glass formation to poly(α-olefins)

The entropy theory of glass formation, which has previously been developed to describe general classes of polymeric glass-forming liquids, is extended here to model the thermodynamic and dynamic properties of poly(alpha-olefins). By combining this thermodynamic theory with the Adam-Gibbs model (which relates the configurational entropy to the rate of structural relaxation), we provide systematic computations for all four characteristic temperatures (T(A), T(c), T(g), T(0)), governing the position and breadth of the glass transition, and the fragility parameters (D,m) describing the strength of the temperature dependence of the structural relaxation time, where T(A) is the temperature below which the relaxation is non-Arrhenius, T(c) is the crossover or empirical mode-coupling temperature, T(g) is the glass transition temperature, and T(0) is the temperature at which the extrapolated relaxation time diverges. These temperatures and fragility parameters are evaluated as a function of molar mass, pressure, and the length n of the alpha-olefin side chains. The nearest neighbor interaction energy and local chain rigidities are found to strongly influence the four characteristic temperatures and the low temperature fragility. We also observe an "internal plasticization" of the poly(alpha-olefins) wherein the fragility decreases as the number n of "flexible" side group units increases. Our computations provide solid support for a pressure counterpart of the Vogel-Fulcher-Tammann relation. The entropy theory of glass formation predicts systematic changes in fragility with chain stiffness, cohesive energy, polymerization index, and side chain length, and qualitative trends in these parameters are discussed.

Fragility of Glass-Forming Polymer Liquids

The fragility of polymeric glass-forming liquids is calculated as a function of molecular structural parameters from a generalized entropy theory of polymer glass-formation that combines the Adam-Gibbs (AG) model for the rate of structural relaxation with the lattice cluster theory (LCT) for polymer melt thermodynamics. Our generalized entropy theory predicts the existence of distinct high and low temperature regimes of glass-formation that are separated by a thermodynamically well-defined crossover temperature T(I) at which the product of the configurational entropy and the temperature has an inflection point. Since the predicted temperature dependence of the configurational entropy and structural relaxation time are quite different in these temperature regimes, we introduce separate definitions of fragility for each regime. Experimentally established trends in the fragility of polymer melts with respect to variations in polymer microstructure and pressure are interpreted within our theory in terms of the accompanying changes in the chain packing efficiency.

Cooperative rearranging regions in polymeric materials: Relationship with the fragility of glass-forming liquids

From measurements performed on different polymeric glass-forming liquids using differential scanning calorimetry (DSC), we determined the values of the fragility index m according to the concept proposed by Angell. We calculated the average size of a cooperative rearranging region (CRR) at the glass transition i.e. z( T g), according to the definition proposed by Solunov. This quantity is linked to the Kauzmann temperature which was determined from dielectric spectroscopy or viscosimetry measurements performed on different samples including three-dimensional polymeric networks and linear polymer families with variable lateral chain lengths. By using our experimental data and others collected in the literature in order to scan a large domain of fragility values, we show that the fragility index m, characterising the glass-forming liquid, can be correlated to z( T g) which characterises the glass formed.