The meaning of the "universal" WLF parameters of glass-forming polymer liquids

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.

Competing Effects of Molecular Additives and Cross-Link Density on the Segmental Dynamics and Mechanical Properties of Cross-Linked Polymers

The introduction of molecular additives into thermosets often results in changes in their dynamics and mechanical properties that can have significant ramifications for diverse applications of this broad class of materials such as coatings, high-performance composites, etc. Currently, there is limited fundamental understanding of how such additives influence glass formation in these materials, a problem of broader significance in glass-forming materials. To address this fundamental problem, here, we employ a simplified coarse-grained (CG) model of a polymer network as a model of thermoset materials and then introduce a polymer additive having the same inherent rigidity and polymer-polymer interaction strength as the cross-linked polymer matrix. This energetically "neutral" or "self-plasticizing" additive model gives rise to non-trivial changes in the dynamics of glass formation and provides an important theoretical reference point for the technologically more important case of interacting additives. Based on this rather idealized model, we systematically explore the combined effect of varying the additive mass percentage (m) and cross-link density (c) on the segmental relaxation dynamics and mechanical properties of a model thermoset material with additives. We find that increasing the additive mass percentage m progressively decreases both the glass-transition temperature Tg and the fragility of glass formation, a trend opposite to increasing c so that these thermoset variables clearly have a competing effect on glass formation in these model materials. Moreover, basic mechanical properties (i.e., bulk, shear, and tensile moduli) likewise exhibit a competitive variation with the increase of m and c, which are strongly correlated with the Debye-Waller parameter ⟨u2⟩, a measure of material stiffness at a molecular scale. Our findings prove beneficial in the development of structure-property relationships for the cross-linked polymers, which could help guide the design of such network materials with tailored physical properties.

Temperature and Frequency Dependence of the Dynamic Viscoelastic Properties of Silicone Rubber

Temperature-frequency sweep tests were performed on silicone rubber to investigate the dynamic viscoelastic properties. The test results show that the viscoelasticity of silicone rubber presents significant temperature dependence and frequency dependence. The dynamic viscoelastic test curves at different temperatures can be shifted along the logarithmic frequency coordinate axis to construct smooth master curves at the reference temperature of 20 °C, covering a frequency range of 10 decades, which indicates thermorheological simplicity on a macro level and frequency temperature equivalence of the silicone rubber material in the experimental temperature range. The van Gurp-Palmen plot and Cole-Cole plot for the test data at various temperatures merge into a common curve, which further validates thermorheological simplicity. The temperature dependent shift factors of silicone rubber material were well characterized by the Williams-Landel-Ferry equation. Moreover, the fractional-order differential Kelvin (FDK) model, the fractional-order differential Zener (FDZ) model, and the improved fractional-order differential Zener (iFDZ) model were used to model the asymmetric loss factor master curve. The result shows that the iFDZ model is in good agreement with the test results, indicating that this model is suitable for describing the asymmetry of dynamic viscoelastic properties of silicone rubber.

Mechanism Study of Ultrasonic Vibration-Assisted Microgroove Forming of Precise Hot-Pressed Optical Glass

Microgroove structures with helical pitches in a wavelength level are increasingly required in optical areas. However, conventional manufacturing techniques generate relatively high stresses during pressing, resulting in poor precision when forming microgrooves. This paper reports on the mechanism of the ultrasonic vibration-assisted microgroove forming of precise hot-pressed optical glass. A finite element (FE) thermocompression model of the viscoelastic material was developed and the entire forming process was numerically simulated using coupled thermal-structural analysis. The analysis of several process parameters was carried out using orthogonal experiments, from which the optimum combination of parameters was selected. The glass thermoforming process is also assisted by ultrasonic vibration. The thermal and mechanical effects of vibration improved material flow and optimized forming results. The average maximum stress in the glass during the forming process was only 3.04 × 10^-3 Mpa, while the maximum stress in the hot-pressing stage without ultrasound was 1.648 Mpa. The stress results showed that the material-forming stress is significantly reduced.

Energetic and Structural Characterizations of the PET-Water Interface as a Key Step in Understanding Its Depolymerization

We report molecular simulations of the interaction between poly(ethylene terephthalate) (PET) surfaces and water molecules with a short-term goal to better evaluate the different energy contributions governing the enzymatic degradation of amorphous PET. After checking that the glass transition temperature, density, entanglement mass, and mechanical properties of an amorphous PET are well reproduced by our molecular model, we extend the study to the extraction of a monomer from the bulk surface in different environments, i.e., water, vacuum, dodecane, and ethylene glycol. We complete this energetic characterization by the calculation of the work of adhesion of PET surfaces with water and dodecane molecules and by the determination of the contact angle of water droplets. These calculations are compared with experiments and should help us to better understand the enzymatic degradation of PET from both the thermodynamic and molecular viewpoints.

Prediction Formula Describing Viscoelasticity of Unvulcanized Rubber Compound Based on Time-Temperature Equivalent Superposition Principle

Fitting unvulcanized rubber compound’s (URC) dynamic viscoelasticity prediction formula and then constructing its mechanical constitutive model are of great significance for studying defect mechanisms in rubber products. However, it is difficult to measure the dynamic viscoelasticity of unvulcanized rubber at high and low frequencies due to its rapid relaxation property. This paper presents a convenient method to measure the dynamic viscoelasticity of unvulcanized rubber. The data of different temperatures at a fixed frequency are measured by dynamic thermomechanical analysis, and the master curve of unvulcanized rubber is obtained by using the time-temperature equivalent superposition principle, which is used to predict the modulus and stress at different temperatures as a function of frequency. The predicted moduli are in good agreement with experimental data when the strain is less than 10% and the applicable temperature range of the Williams–Landel–Ferry (WLF) equation, which indicates that the proposed method is a feasible way to study the dynamic viscoelasticity of unvulcanized rubber at different temperatures.

Decoupling Ion Transport and Matrix Dynamics to Make High Performance Solid Polymer Electrolytes

Transport of ions through solid polymeric electrolytes (SPEs) involves a complicated interplay of ion solvation, ion-ion interactions, ion-polymer interactions, and free volume. Nonetheless, prevailing viewpoints on the subject promote a significantly simplified picture, likening ion transport in a polymer to that in an unstructured fluid at low solute concentrations. Although this idealized liquid transport model has been successful in guiding the design of homogeneous electrolytes, structured electrolytes provide a promising alternate route to achieve high ionic conductivity and selectivity. In this perspective, we begin by describing the physical origins of the idealized liquid transport mechanism and then proceed to examine known cases of decoupling between the matrix dynamics and ionic transport in SPEs. Specifically we discuss conditions for "decoupled" mobility that include a highly polar electrolyte environment, a percolated path of free volume elements (either through structured or unstructured channels), high ion concentrations, and labile ion-electrolyte interactions. Finally, we proceed to reflect on the potential of these mechanisms to promote multivalent ion conductivity and the need for research into the interfacial properties of solid polymer electrolytes as well as their performance at elevated potentials.

Molecular Simulations of Thermomechanical Properties of Epoxy-Amine Resins

All-atom molecular dynamics (MD) simulations were performed with the CHARMM force field to characterize various epoxy resins, such as aliphatic and bisphenol-based resins. A multistep cross-linking algorithm was established, and key properties such as density, glass temperature, and elastic modulus were calculated. A quantitative comparison was made and was proven to be in good agreement with experimental data, with average absolute deviations between experiments and molecular simulation comprised between 2% and 12%. Additional findings on structure-property relationships were highlighted such as the effect of the cross-linking rate and oligomerization of the resin.

Understanding the role of cross-link density in the segmental dynamics and elastic properties of cross-linked thermosets

Cross-linking is known to play a pivotal role in the relaxation dynamics and mechanical properties of thermoset polymers, which are commonly used in structural applications because of their light weight and inherently strong nature. Here, we employ a coarse-grained (CG) polymer model to systematically explore the effect of cross-link density on basic thermodynamic properties as well as corresponding changes in the segmental dynamics and elastic properties of these network materials upon approaching their glass transition temperatures (T_g). Increasing the cross-link density unsurprisingly leads to a significant slowing down of the segmental dynamics, and the fragility K of glass formation shifts in lockstep with T_g, as often found in linear polymer melts when the polymer mass is varied. As a consequence, the segmental relaxation time τ_α becomes almost a universal function of reduced temperature, (T - T_g)/T_g, a phenomenon that underlies the applicability of the "universal" Williams-Landel-Ferry (WLF) relation to many polymer materials. We also test a mathematical model of the temperature dependence of the linear elastic moduli based on a simple rigidity percolation theory and quantify the fluctuations in the local stiffness of the network material. The moduli and distribution of the local stiffness likewise exhibit a universal scaling behavior for materials having different cross-link densities but fixed (T - T_g)/T_g. Evidently, T_g dominates both τ_α and the mechanical properties of our model cross-linked polymer materials. Our work provides physical insights into how the cross-link density affects glass formation, aiding in the design of cross-linked thermosets and other structurally complex glass-forming materials.

Prediction model of residual stress during precision glass molding of optical lenses

Precision glass molding (PGM) is an important processing technology for aspheric lenses that has the advantages of low complexity, high precision, and short processing time. The key problem in the PGM process is to accurately predict the residual stress of aspheric lenses. In this paper, we examine the residual stress relaxation model for aspheric lenses, including a creep experiment of D-K9 glass, calculating shear relaxation function, and predicting residual stress of aspheric lenses with the finite element method. Validations of the proposed model are conducted for three different process parameters, including molding temperature, molding pressure, and molding rate. The experimental and simulation results show that the errors of the residual stresses of the three process parameters are within 0.358 Mpa, which proves the validity of the model. The model can be used to predict the residual stress of the optical glass lens fabricated by PGM and analyze the processing parameters.

Polyimide/Ionic Liquid Composite Membranes for Middle and High Temperature Fuel Cell Application: Water Sorption Behavior and Proton Conductivity

Four water insoluble room-temperature protic ionic liquids (PILs) based on the N-alkylimidazolium cation with the alkyl chain length from 1 to 4 and bis(trifluoromethylsulfonyl)imide anion were synthesized and their chemical structure was confirmed by the 1H NMR and 19F NMR analysis. PILs were revealed to be thermally stable up to 360 and 400 °C. At the same time, the proton conductivity of PILs was found to be dependent mostly on the temperature and, to a less extent, on the type of the cation, i.e., the increase of the conductivity from ~3 × 10-4 S/cm at 25 °C to 2 × 10-2 S/cm at 150 °C was observed. The water vapour sorption capacity of PILs was evaluated as a function of relative humidity and the influence of the alkyl chain length on the phase behaviour in the PIL-water system was discussed. The composite polyimide/PILs membranes were prepared by the PIL immobilization in the porous polymer (Matrimid® 5218) film. The composite membranes showed a high level of proton conductivity (~10-3 S/cm) at elevated temperatures (up to 160 °C). The obtained results reveal that the elaborated composite polyimide/PIL membranes are promising candidates for the application as proton exchange membrane at middle and high temperatures.

A simple mean-field model of glassy dynamics and glass transition

We propose a phenomenological model to describe the equilibrium dynamic behavior of amorphous glassy materials. It is assumed that a material can be represented by a lattice of cooperatively re-arranging regions (CRRs), with each CRR having two states, the low-temperature "solid" and the high-temperature "liquid". At low temperatures, the material exhibits two characteristic relaxation times, corresponding to the slow large-scale motion between the "solid" CRRs (α-relaxation) and the faster local motion within individual CRRs (β-relaxation). At high temperatures, the α- and β-relaxation times merge, as observed experimentally and suggested by the "Coupling Model" framework. Our new approach is labeled "Two-state, two (time)scale model" or TS2. It is shown that the TS2 treatment can successfully describe the "two-Arrhenius" relaxation time behavior described in several recent experiments. We also apply TS2 to describe the pressure- and molecular-weight dependence of the glass transition temperature in bulk polymers, as well as its dependence on film thickness in thin films.

The Effects of Asphalt Migration on the Dynamic Modulus of Asphalt Mixture

Asphalt migration is one of the significant detrimental effects on asphalt pavement performance. In order to simulate the state after the occurrence of asphalt migration amid asphalt pavement layers and further investigate the effects of asphalt migration on the dynamic modulus of asphalt mixture, samples with different asphalt contents layers were firstly separated into the upper and lower half portions and then compacted together. By conducting the dynamic modulus test with the Superpave Simple Performance Tester (SPT), the variation laws of the dynamic modulus (|E*|) and the phase angle (δ) at different testing temperatures and loading frequencies were analyzed in this paper. Further, the dynamic modulus and the stiffness parameter (|E*|/sinδ) at the loading frequency of 10 Hz and testing temperature of 50 °C were illustrated. Simultaneously, the master curves of the dynamic modulus and phase angle of asphalt mixtures under different testing conditions were constructed to better investigate the effects of asphalt migration on the dynamic modulus by means of Williams–Landel–Ferry (WLF) equation and Sigmoidal function. Results show that, after the asphalt migration, the dynamic modulus of asphalt mixtures increase with the increasing loading frequency while they decrease with the increasing testing temperature; the dynamic modulus and the stiffness parameter are the highest when asphalt mixtures have the optimum asphalt content layers, and then decrease with the incremental difference of asphalt content in the upper and lower half portions. Besides this, different from the master curves of dynamic modulus, the master curves of phase angle firstly increase with the increase of loading frequency to the highest point and then decrease with the further increase of loading frequency and are not as smooth as that of dynamic modulus. It can be concluded that the asphalt migration has compromised the mixture’s mechanical structure, and the more asphalt migrates, the weaker the mechanical properties of asphalt mixture will be. Additionally, based on the shift factors and master curves in the time–temperature superposition principle (TTSP), the effects of asphalt migration on the dynamic modulus and the variation laws of the dynamic modulus of asphalt mixture after the occurrence of asphalt migration can be better construed at the quantitative level.

Temperature Dependence of Rate Processes Beyond Arrhenius and Eyring: Activation and Transitivity

Advances in the understanding of the dependence of reaction rates from temperature, as motivated from progress in experiments and theoretical tools (e. g., molecular dynamics), are needed for the modeling of extreme environmental conditions (e.g., in astrochemistry and in the chemistry of plasmas). While investigating statistical mechanics perspectives (Aquilanti et al., 2017b, 2018), the concept of transitivity was introduced as a measure for the propensity for a reaction to occur. The Transitivity plot is here defined as the reciprocal of the apparent activation energy vs. reciprocal absolute temperature. Since the transitivity function regulates transit in physicochemical transformations, not necessarily involving reference to transition-state hypothesis of Eyring, an extended version is here proposed to cope with general types of transformations. The transitivity plot permits a representation where deviations from Arrhenius behavior are given a geometrical meaning and make explicit a positive or negative linear dependence of transitivity for sub- and super-Arrhenius cases, respectively. To first-order in reciprocal temperature, the transitivity function models deviations from linearity in Arrhenius plots as originally proposed by Aquilanti and Mundim: when deviations are increasingly larger, other phenomenological formulas, such as Vogel-Fulcher-Tammann, Nakamura-Takayanagi-Sato, and Aquilanti-Sanches-Coutinho-Carvalho are here rediscussed from the transitivity concept perspective and with in a general context. Emphasized is the interest of introducing into this context modifications to a very successful tool of theoretical kinetics, Eyring's Transition-State Theory: considering the behavior of the transitivity function at low temperatures, in order to describe deviation from Arrhenius behavior under the quantum tunneling regime, a "d-TST" formulation was previously introduced (Carvalho-Silva et al., 2017). In this paper, a special attention is dedicated to a derivation of the temperature dependence of viscosity, making explicit reference to feature of the transitivity function, which in this case generally exhibits a super-Arrhenius behavior. This is of relevance also for advantages of using the transitivity function for diffusion-controlled phenomena.