Generalized Entropy Theory of Glass Formation in Polymer Melts with Specific Interactions

Abstract

Chemical structure has been long recognized to greatly influence polymer glass formation, but a general molecular theory that predicts how chemical structure determines the properties of glass-forming polymers has been slow to develop. While the generalized entropy theory (GET) explains the influence of various molecular details on polymer glass formation, the application of the GET has heretofore been limited to the use of the simplest polymer model in which all united atom groups within the monomers of a species interact with a common monomer averaged van der Waals energy. However, energetic heterogeneities are ubiquitous within the monomers of real polymers, and their implications for polymer glass formation remain to be investigated theoretically. This paper uses an extension of the GET to explore the influence of energetic heterogeneities within monomers upon the nature of polymer glass formation. This extension of the GET is achieved by combining the Adam−Gibbs theory relating the structural relaxation time to the configurational entropy with a recent significant extension of the lattice cluster theory for polymer melts with specific interactions, in particular, for melts where three distinct van der Waals interaction energies are required to describe the energetic heterogeneities within monomers. The present paper focuses on establishing general trends for the variation of characteristic properties of glass formation, such as the isobaric fragility parameter m P and the glass transition temperature T g , with molecular details, such as the specific interactions and chain stiffness. Our computations confirm that the previously used model with monomer averaged interactions correctly captures general trends in the variation of m P and T g with various molecular parameters. More importantly, adjustment of the energetic heterogeneities within monomers alone are shown to provide an efficient mechanism for tailoring the properties of glass-forming polymers. The variations of polymer properties along iso-fragility and iso-T g lines are illustrated as important design tools for exhibiting the combined influence of specific interactions and chain stiffness. INTRODUCTIONDespite the fact that polymeric materials readily form glasses upon cooling, a general theory for the nature of polymer glass formation and for the properties of polymer glasses remains elusive. Numerous studies demonstrate that molecular characteristics, such as chain stiffness, monomer structure, and the chemical structures of the backbone and side groups, profoundly affect polymer glass formation. 1−12 Hence, understanding of the relation between material properties and these molecular details offers the potential to control polymer glass formation in a systematic manner. In particular, recent experiments 2 indicate that both the glass transition temperature T g and the fragility parameter m, where m measures the sensitivity of the structural relaxation time or viscosity to temperature changes, can be greatly tuned by modifying the chemical structu...

Glass Transition Phenomenon for Conjugated Polymers

“…For example, the analytical generalized entropy theory (GET) developed by Freed and co-workers has shown great success in describing the glass formation of polymer melts as functions of molecular parameters, including monomer structure, cohesive interaction strength, chain rigidity, plasticization, etc. [63,[289][290][291][292][293][294][295][296][297][298][299] In addition, Schweizer and co-workers have successfully developed and applied the elastically collective nonlinear Langevin equation (ECNLE) to investigate the dynamics for different polymeric systems including polymer melts and thin films. [300][301][302][303][304][305] Moreover, for polymer thin films, a faster relaxation process near the free surface has been reported by simulations.…”

“…Apart from utilizing the experimental techniques, extensive efforts have been made to investigate the glass transition phenomena in polymers, both in bulk and under confinement, with simulation and theory. For example, the analytical generalized entropy theory (GET) developed by Freed and co‐workers has shown great success in describing the glass formation of polymer melts as functions of molecular parameters, including monomer structure, cohesive interaction strength, chain rigidity, plasticization, etc . In addition, Schweizer and co‐workers have successfully developed and applied the elastically collective nonlinear Langevin equation (ECNLE) to investigate the dynamics for different polymeric systems including polymer melts and thin films .…”

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

“…7(b) indicates that the growth of T x with ǫ becomes somewhat non-linear as E b increases, a result that is also revealed in previous calculations within the GET. [5][6][7][8][9] While this non-linear behavior is more pronounced for T g and T 0 than for T A and T c , we find that the dependence of all characteristic temperatures on ǫ for E b /k B = 800 K can be described by the simple empirical relation, T x = (u x + v x ǫ)/(1 + w x ǫ), where the fitting parameters u x , v x , and w x are provided in the caption of Fig. 7.…”

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

“…Because the LCT 137,138 is a powerful theoretical framework for addressing the thermodynamics of a vast array of polymer systems, a number of important problems relevant to polymer glass formation can be investigated by the GET. 19 For instance, the GET has been demonstrated to quantitatively describe the characteristic properties of poly(α-olefins), 174 to clarify the meaning of activation volume of polymer liquids, 175 to elucidate the influence of cohesive energy and chain stiffness on polymer glass formation, 172,176,177 and to better understand a variety of phenomena related to polymer glass formation, such as plasticization and antiplasticization of polymer melts by molecular additives, 168 density-temperature scaling of the segmental dynamics of polymer melts, 178 two glass transitions in miscible polymer blends, 169 and the interpretation of the 'universal' WLF parameters of polymer liquids 92 and the related observation that the structural relaxation time depends nearly universally on T − T g in related families of GF liquids. 179 The LCT has also been extended to model polymers with specific interactions 138,177 where cohesive interaction strengths are different between united-atom groups and telechelic polymers [180][181][182] where associative groups at the chain ends have strong interactions, enabling predictions of glass formation in these polymer systems when combined with the AG model.…”