Route to calculate the length scale for the glass transition in polymers (original) (raw)
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A Novel Route to Calculate the Length Scale for the Glass Transition in Polymers
Arxiv preprint cond-mat/0612054, 2006
The occurrence of glass transition is believed to be associated to cooperative motion with a growing length scale with decreasing temperature. We provide a novel route to calculate the size of cooperatively rearranging regions CRR of glass-forming polymers combining the Adam-Gibbs theory of the glass transition with the self-concentration concept. To do so we explore the dynamics of glass-forming polymers in different environments. The material specific parameter α connecting the size of the CRR to the configurational entropy is obtained in this way. Thereby, the size of CRR can be precisely quantified in absolute values. This size results to be in the range 1 ÷ 3 nm at the glass transition temperature depending on the glass-forming polymer.
Macromolecules
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.
Collective dynamics of glass-forming polymers at intermediate length scales
EPJ Web of Conferences, 2015
Motivated by the proposition of a new theoretical ansatz [V.N. Novikov, K.S. Schweizer, A.P. Sokolov, J. Chem. Phys. 138, 164508 (2013)], we have revisited the question of the characterization of the collective response of polyisobutylene at intermediate length scales observed by neutron spin echo (NSE) experiments. The model, generalized for sublinear diffusion -as it is the case of glass-forming polymers-has been successfully applied by using the information on the total self-motions available from MD-simulations properly validated by direct comparison with experimental results. From the fits of the coherent NSE data, the collective time at Q → 0 has been extracted that agrees very well with compiled results from different experimental techniques directly accessing such relaxation time. We show that a unique temperature dependence governs both, the Q → 0 and Q → ∞ asymptotic characteristic times. The generalized model also gives account for the modulation of the apparent activation energy of the collective times with the static structure factor. It mainly results from changes of the short-range order at inter-molecular length scales. This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Journal of Non-Crystalline Solids, 2015
Understanding why the glass transition temperature (T g ) of polymers deviates substantially from the bulk with nanoscale confinement has been a 20-year mystery. Ever since the observation in the mid-1990s that the T g values of amorphous polymer thin films are different from their bulk values, efforts to understand this behavior have intensified, and the topic remains the subject of intense research and debate. This is due to the combined scientific and technological implications of size-dependent glassy properties. Here, we discuss an intriguing aspect of the glassy behavior of confined amorphous polymers. As experimentally assessed, the glass transition is a dynamic event mediated by segmental dynamics. Thus, it seems intuitive to expect that a change in T g due to confinement necessitates a corresponding change in molecular dynamics, and that such change in dynamics may be predicted based on our understanding of the glass transition. The aim of this perspectives article is to examine whether or not segmental dynamics change in accordance with the value of T g for confined polymers based on bulk rules. We highlight past and recent findings that have examined the relationship between T g and segmental dynamics of confined polymers. Within this context, the decoupling between these two aspects of the glass transition in confinement is emphasized. We discuss these results within the framework of our current understanding of the glass transition as well as efforts to resolve this decoupling. Finally, the anomalous decoupling between translational (diffusion) and rotational (segmental) motion taking place in the proximity of attractive interfaces in polymer thin films is discussed.
Journal of physics, 2019
An analysis of the methods for measuring the characteristic length of the cooperative molecular dynamics in glass-forming liquids is submitted. The equations and methods for measuring the size of the cooperatively rearranging regions in post Adam-Gibbs theories are compered, and it is proved that they give one and the same number, but with different interpretation for the relaxed molecular units. The interpretation that the rearranging units defined by Wunderlich are smallest structural units, named beads, is supported by the predicted "universal" value for the cooperatively rearranging range at the glass-transition temperature, as well as from a precise modeling for the relaxations by the generalized entropy theory. It has been found that the characteristic length estimated by random first order transition theory, as well as by the "four-point" dynamic susceptibility method, measured as the number of the bead's diameters coincide with the length of the cooperatively rearranging region in Adam-Gibbs theory extended at the molecular level.
Physical chemistry chemical physics : PCCP, 2015
Monte Carlo simulations performed on multiple polymer chains have produced accurate relaxation modulus Gs(t) curves which match the experimental G(t) curves of polystyrene reasonably well, over a wide temperature range around the glass transition region. The inter-segmental interactions, defined in terms of ε* (well depth) and σ (monomer size), exert a strong influence on the modulus, the length scale and the relaxation time scale of the system. Judicious selection of these interaction parameters has enabled us to create the whole range of temperature dependence of the thermorheological complexity, from ΔT = 40 °C to ΔT = 0 °C. Near the glass transition temperature, the development of nonergodicity vis-à-vis a crowding effect in the system emerges naturally from the analysis of the G(t) line shapes. The entropic slow mode is well described by the Rouse theory and the energetic fast mode shifts to longer time scales, revealing the generic behavior of the thermorheological complexity....
Influence of molecular-weight polydispersity on the glass transition of polymers
Physical review. E, Statistical, nonlinear, and soft matter physics, 2016
It is well known that the polymer glass transition temperature T_{g} is dependent on molecular weight, but the role of molecular-weight polydispersity on T_{g} is unclear. Using molecular-dynamics simulations, we clarify that for polymers with the same number-average molecular weight, the molecular-weight distribution profile (either in Schulz-Zimm form or in bimodal form) has very little influence on the glass transition temperature T_{g}, the average segment dynamics (monomer motion, bond orientation relaxation, and torsion transition), and the relaxation-time spectrum, which are related to the local nature of the glass transition. By analyzing monomer motions in different chains, we find that the motion distribution of monomers is altered by molecular-weight polydispersity. Molecular-weight polydispersity dramatically enhances the dynamic heterogeneity of monomer diffusive motions after breaking out of the "cage," but it has a weak influence on the dynamic heterogeneity...
Entropy theory of polymer glass formation revisited. I. General formulation
The Journal of Chemical Physics, 2006
A generalized entropy theory of glass formation is developed by merging the lattice cluster theory for the thermodynamics of semiflexible polymer melts at constant pressure with the Adam-Gibbs relation between the structural relaxation time and the configurational entropy. Since experimental studies have suggested that the relative rigidity of the chain backbone and the side groups is an essential parameter governing the nature of glass formation in polymers, we incorporate this rigidity disparity parameter, along with monomer structure, into our new theoretical description of the polymer fluid thermodynamics. Our entropy theory is compared with alternative theories that describe the rate of structural relaxation in glass-forming liquids in terms of an activated rate process.
Entropy Theory of Polymer Glass-Formation in Variable Spatial Dimension
Advances in Chemical Physics, 2016
We explore the nature of glass-formation in variable spatial dimensionality (d) based on the generalized entropy theory, a synthesis of the Adam-Gibbs model with direct computation of the configurational entropy of polymer fluids using an established statistical mechanical model. We find that structural relaxation in the fluid state asymptotically becomes Arrhenius in the d → ∞ limit and that the fluid transforms upon sufficient cooling above a critical dimension near d = 8 into a dense amorphous state with a finite positive residual configurational entropy. Direct computations of the isothermal compressibility and thermal expansion coefficient, taken to be physical measures of packing frustration, demonstrate that these fluid properties strongly correlate with the fragility of glass-formation.