Free Volume Theory Research Articles

Characterize the high-temperature steady-state rheological behavior and Arrhenius activation of PEEK via strain rate jump tensile tests

Polyetheretherketone (PEEK) is a high-performance thermoplastic polymer with diverse industrial applications, such as aerospace, automotive, electronics, and medical devices. However, systematic research on its high-temperature rheological characteristics is inadequate. In this study, strain rate jump tensile tests were introduced to examine the steady-state rheology phenomena and strain rate sensitivity of PEEK at four different temperatures and nine different strain rates. Theoretical analysis based on the free volume theory and the Arrhenius law was also carried out to further analyze the transition of PEEK from Newtonian flow to non-Newtonian flow. Results indicate that PEEK materials exhibit a transition from Newtonian flow to non-Newtonian flow similar to metal materials at high temperatures. The transition point from Newtonian flow to non-Newtonian flow is marked by the emergence of steady-state rheology and its characteristic stress. Theoretical analysis demonstrates that the transition of PEEK is in accordance with the Arrhenius low. Moreover, its apparent activation energy (1.42 eV) is significantly lower than that of metal materials (5.28 eV), indicating a lower energy barrier and an easier transition. The strain rate sensitivity index correlates negatively with rising temperatures, especially at lower rates. This study enhances understanding of PEEK's rheological characteristics at high temperatures, aiding the development and application of high-performance thermoplastic materials.

A cooperative relaxation model with two physical parameters for investigating the temperature and cure dependence of relaxation mechanisms in resins

Modeling the relaxation properties of resin matrix during cure plays an important role in predicting process-induced residual stresses and final distortions of resin-based composites. This paper develops a physical characterization model, which explains the temperature and cure-degree dependence of relaxation behaviors in terms of the size of cooperatively rearranging region, and special emphasis is placed on investigating the general physical mechanism of cure degree affecting the relaxation properties. In this model, the relaxation time is governed by a modified Adam-Gibbs equation, which is extended here to include the cure dependence. In addition, the relaxation modulus is modeled in a chemo-rheologically simple manner (CSM) based on the free volume theory. Material characterization is carried out using experimental data of two typical resins. It is shown that two cure-dependent model parameters, i.e., the smallest size of the cooperatively rearranging region and the glass transition temperature, are sufficient in accounting for the effect of cure on the relaxation modulus, and could provide a physical explanation of the influence of cure on relaxation behaviors. Furthermore, the proposed model is numerically realized by incorporating ABAQUS with UMAT subroutine, and its validity in predicting the residual stresses and final distortion of composites is also numerically verified by comparing with the results available in literature.

Degradation mechanism for epoxy resins under combined electric, thermal and compressive stresses

Epoxy resins are widely used in equipment such as ultra-high voltage dry-type bushings, which are subjected to severe electric, thermal, and compressive stresses. Some physical mechanisms have already been proposed to explain the degradations generated by these different stresses, however their effects have not yet been quantified.. The degradation characteristics of epoxy resin under combined stresses of 8 kV/mm, 40 °C-120 °C, and 0–60 MPa were investigated in experiments. The results showed that the degradation characteristics turned significantly with the increase of compressive stress. With the increase in compressive stress, initially the partial discharge initiation voltage, tree initiation voltage and time to breakdown increased, and fractal dimension decreased. While the compressive stress exceeded the turning point, the characteristics were reversed. It can be suggested that opposing mechanisms exist. The free volume and phase field theories dominate at lower and higher stresses, respectively. A novel degradation model of the epoxy resin was proposed based on the theories above. When the compressive stress was low, the reduction of free volume played a dominant role in slowing down the degradation. When the compressive stress was high, the partial energy density concentration accelerated the degradation and played a dominant role. The molecular dynamics and finite element simulation of degradation process stress was carried out and proved consistent with experiments. It confirmed the proposed degradation model reliable and valid.

A novel approach for the atomic scale characterization of Li-ion battery components probed by positron annihilation lifetime spectroscopy

Recent research has focused on solid polymer electrolytes (SPEs) as the best liquid electrolyte replacements. Poly(ethylene oxide) (PEO) is the most frequent one because of its fast segmental movements in the free volume which controls lithium-ion transport between electrodes. Therefore, PEO-based copolymer electrolytes that can be tailored for mechanical strength and ionic conductivity are often studied. The most popular material is PEO chains containing PMMA because PEO transports ions, and PMMA has good mechanical properties. Further investigations on PEO-based solid polymer electrolytes (SPEs) have shown that chain designs with more nonlinear branches prevent crystallinity and maintain fast segmental dynamics. For this purpose, we worked on PEO-grafted-PMMA copolymers in which the free volume probed by positron annihilation lifetime spectroscopy considerably affects the structure-ionic conductivity relationship. Finally, we investigated the free volume theory of ionic condcutivity using Yahsi-Ulutas-Tav (YUT) theory.

Free volume theory of self-diffusion in zeolites: Molecular simulation and experiment

Neutron scattering and molecular dynamics are used to unravel the microscopic mechanisms that govern methane diffusion in MFI zeolite (silicalite-1). First, using neutron scattering for silicalite-1 loaded with different methane amounts, we analyze the experimental dynamic structure factor S(q,ω) in terms of molecular rotations and translations. While the rotational diffusion is found to be nearly independent of the zeolite loading, the translational diffusivity drastically decreases with the adsorbed amount. To gain insights into the diffusion mechanisms, trajectories obtained using molecular dynamics simulations are analyzed by determining mean square displacements 〈Δr2(t)〉 and incoherent scattering functions F(q,t). We also determine how anisotropy affects diffusion by considering independently the x, y and z directions. While the activation energy for diffusion is found to be weakly dependent on methane loading, the self-diffusivity decreases as the loading increases. Both the experimental and molecular simulation results suggest that steric repulsion between confined molecules – which increases as the loading increases – drastically affects diffusion. Using a free volume theory, we provide a simple formalism to predict consistently diffusion in the internal porous network of MFI zeolite. To demonstrate the applicability of this simple yet robust framework, we show that the free volume theory accurately captures diffusion in each direction of space but also when the size of the adsorbate molecule is arbitrarily increased.

Understanding the influence of sodium chloride concentration on ion diffusion in charged polymers

Previous observations made on sulfonated polysulfones equilibrated with solutions of increasing salinity, where salt diffusion coefficients increase concurrently with reductions in water content driven by osmotic de-swelling, are currently unexplained. To further explain the molecular underpinnings of these observations, we characterized the influence of external salt solution concentration on the average salt and ion diffusion properties of two sulfonated polymers: a model cross-linked material (XLAMPS) and a series of sulfonated polysulfones (HQ:BP – XX). Analysis of the average salt and co- and counter-ion diffusion coefficients in these polymers suggest that the increase in charge screening (of electrostatic interactions between anionic sulfonate groups and co-ions) that occurs with increasing salinity affects the salt diffusion coefficients of sulfonated polysulfone in a manner that is different from what would be expected based on changes in water content alone and from what was observed for XLAMPS. Free volume theory describes the influence of these electrostatic effects on salt diffusion using a parameter related to the characteristic free volume element size necessary for diffusion. The results and analysis suggest that charge screening reduces the characteristic free volume element size necessary for diffusion in sulfonated polysulfone, which provides an explanation for the observed increase in average salt diffusion coefficients with increased salinity.

Viscosity of Polyelectrolytes: Influence of Counterion and Solvent Type.

We study the viscosity of polystyrenesulfonate with sodium and tetrabutylammonium counterions in aqueous and organic solvent media. We find that at low concentrations the Fuoss law (ηsp ∼ c1/2) is approximately obeyed, but at higher concentrations, an exponential dependence on the polymer volume fraction sets in. These findings are discussed in terms of Fujita's free volume theory.

Diffusion mechanism explorations on the sustainable warm mix asphalt and synchronous rejuvenated SBS-modified asphalt binder using the free volume theory

The blending degree, dominated by the diffusion process between virgin and rejuvenated asphalt, profoundly affects the performance of recycled mixtures. However, research on the blending degree in Warm Mix Asphalt (WMA) containing Styrene-Butadiene-Styrene-modified asphalt (SBSMA) mixtures remains relatively underexplored despite its significant impact on pavement performance. To this concern, a predictive model for characterizing the diffusion behavior of the WMA modified SBSMA and synchronous rejuvenated SBSMA was developed based on the free volume theory, which was validated by the pulsed field gradient nuclear magnetic resonance test. Based on the predicted diffusion coefficients, the influences of WMA additives, rejuvenator types, and temperatures on diffusion behavior were systematically investigated. Results indicated that the diffusion coefficients were affected by the interaction of WMA additives, rejuvenator types, and temperatures. The presence of the WMA additive and the increase in diffusion temperature were able to improve the blending degree by increasing the diffusion coefficient. Rebalancing the unstable colloidal structure of SBSMA can enhance the diffusion coefficient of the WMA modified SBSMA twice than that of untreated one. After further reconstruction of small SBS fragments into the triblock copolymers, the blending between the WMA modified SBSMA and synchronous rejuvenated SBSMA was completed in the form of mutual diffusion, showing the highest diffusion coefficients (10−7).

Extreme dependence of dynamics on concentration in highly crowded polyelectrolyte solutions.

Charge-carrying species, such as polyelectrolytes, are vital to natural and synthetic processes that rely on their dynamic behavior. Through single-particle tracking techniques, the diffusivity of individual polyelectrolyte chains and overall system viscosity are determined for concentrated polylysine solutions. These studies show scaling dependences of D ~ c-6.1 and η ~ c7.2, much stronger than theoretical predictions, drawing the applicability of power law fits into question. Similar trends are observed in concentrated solutions prepared at various pH and counterion conditions. These hindered system dynamics appear universal to polyelectrolyte systems and are attributed to the large effective excluded volumes of polyelectrolyte chains inducing glassy dynamics. The framework of the Vrentas-Duda free-volume theory is used to compare polyelectrolyte and neutral systems. Supported by this theory, excluding counterion mass from total polymer mass results in all environmental conditions collapsing onto a common trendline. These results are applicable to crowded biological systems, such as intracellular environments where protein mobility is strongly inhibited.

A model on the coupling between cyclic fatigue and microstructure evolution in a metallic glass

Establishing the intrinsic correlation between microstructural heterogeneity and mechanical properties is a challenging issue of metallic glasses. The ratchet behavior was examined in a Zr-based metallic glass under cyclic tensile loading well below the yield point, particularly near the glass transition temperature. It is found that strain evolution during cyclic loading shows heightened sensitivity to temperature and stress rate. Also, creep behavior mirrors the ratchet strain induced by cyclic loading. The proposed constitutive model, integrating the Burgers model with defect concentration based on free volume theory, effectively describes strain evolution during cyclic loading near glass transition temperature. Both macroscopic and microscopic perspectives are included in this model. The results verify that metallic glasses exhibit significant viscous characteristics, displaying noticeable creep deformation under low stress rates and amplitudes, which contributes to ratchet behavior. The fitted parameters show that plastic viscosity decreases with temperature and increases with stress rate, corroborating the decrease of tensile yield stress with temperature increasing; also, the fitted relaxation time increases with loading frequency, reflecting evolution of defect concentration. Structural relaxation competes favorably against stress-driven rejuvenation throughout the cyclic process, suggesting potential in tuning metallic glasses properties through innovation thermos-mechanical processing techniques.

Modeling self‐diffusion coefficients of ionic liquids using ePC‐SAFT and FVT combined with Einstein relation

AbstractThe electrolyte perturbed‐chain statistical associating fluids theory (ePC‐SAFT) coupled with free volume theory (FVT) was combined with Einstein relation, that is, ePC‐SAFT‐FVT‐E, to describe self‐diffusion coefficients (SDCs) of ionic liquids (ILs). In modeling, ePC‐SAFT was used to calculate density, while FVT parameters, determined from viscosity data, were utilized to calculate the summation of ionic SDCs through the Einstein relation with one parameter. Two strategies were employed to determine this parameter: fitting experimental data for each IL or estimating a universal parameter from van der Waals volume. Comparative analysis reveals good agreement with experimental data, with average absolute relative deviations (ARDs) of 8.14% (strategy 1) and 10.29% (strategy 2). Subsequently, cationic and anionic SDCs were reliably determined from the summation of ionic SDCs, with average ARDs of 10.80% and 10.21%, respectively. This study indicates the ePC‐SAFT‐FVT‐E model, employing viscosity‐derived parameters and three universal parameters, reliably predicts SDCs of ILs in wide temperature and pressure ranges.

Density and Viscosity Analysis of 3-Methyl-3-pentanol and C3–C6 1-Alkanols: Employing Free Volume Theory for Viscosity Insights

Density and Viscosity Analysis of 3-Methyl-3-pentanol and C3–C6 1-Alkanols: Employing Free Volume Theory for Viscosity Insights

Investigating the Density and Viscosity of 3-Ethyl-3-Pentanol and Short-Chain 1-Alkanol: A Free Volume Theory Approach

Investigating the Density and Viscosity of 3-Ethyl-3-Pentanol and Short-Chain 1-Alkanol: A Free Volume Theory Approach

Modified Free-Volume Theory for the Viscosity Modeling of Ionic Liquids and Deep Eutectic Solvents

Modified Free-Volume Theory for the Viscosity Modeling of Ionic Liquids and Deep Eutectic Solvents

Kinetics model of crystal nucleation and growth in supercooled water for designing ice-templating soft matter scaffold

Ice-templating technology has recently attracted extensive attention to achieve programed structure-property relationships in porous soft matter scaffolds. However, there is a huge gap existed between theoretical understanding and practical applications of nucleation kinetics and growth of ice crystals in supercooled water. This paper establishes a nucleation kinetics model of crystal growth in supercooled water, for designing ice-templating soft matter scaffolds with programmable structure-property relationship. A phase transition model was firstly formulated to characterize liquid-liquid phase transition of supercooled water, based on a two-state model and free-volume theory. Effects of diffusion coefficient and density of the supercooled water on ice nucleation kinetics and crystal growth were investigated, based on the classic nucleation theory. Analytical results showed excellent agreement with experimental data, with correlation indices of R2=90.7 % for diffusion coefficients and R2=94.0 % for densities, respectively. The model predicted a nucleation rate of 31.7 m−3∙s−1 at 200 K and peak nucleation rate and crystal growth rates appearing at 183 K and 227 K. Constitutive relationships among mechanical behaviors, ice nucleus radius, nucleation ratio, and crystallization growth rate, were developed for the ice-templating scaffolds, based on the affine model theory and verified with finite element analysis results (R2= 99.9 %) and experimental results (R2 = 95.8 %). Finally, the prediction results using the proposed model were further verified using the experimental data reported in the literature. This study provides a new methodology to describe the nucleation kinetics and growth of ice crystals in supercooled water and programmable structure-property relationships in ice-templating soft matter scaffolds.

Deciphering non-elastic deformation in amorphous alloy: Simultaneous aging-induced ordering and rejuvenation-induced disordering

The mechanical and physical properties of amorphous alloys depend on their time, temperature, and stress history. Due to their out-of-thermodynamic-equilibrium nature, describing the nonelastic deformation while considering the evolution of the structural state poses a significant challenge. We address this challenge by incorporating a parameter for structural state changes into a conventional deformation theory. This allows us to account for aging-induced ordering and deformation-induced disordering in the description of the mechanical deformation. In the apparent elastic regime (small strain), aging dominates while disorder caused by deformation can be disregarded. In this context, we have also made modifications to the widely used stretched exponential function, incorporating in-situ aging during deformation. This modification successfully describes the stress relaxation behavior under small deformation conditions and provides insights into parameter evolution in this process. Under large deformation conditions, both aging and deformation induced rejuvenation effects on the structural state must be considered simultaneously. By analyzing the evolution of defect concentration during this process, we describe relevant experimental results within the framework of the free volume theory, effectively separating the contributions of aging and rejuvenation to the structural state during the deformation process.

An entropy trap model of thermodynamic anomalies for dual-amorphous water undergoing liquid-liquid phase transition

Water displays numerous anomalously thermodynamic behaviors. However, the working principles behind these anomalies are not well understood, and the liquid-liquid phase transition (LLPT) is often regarded as the potential reason. In this study, we developed an entropy trap model to characterize the thermodynamic LLPT in dual-amorphous water, i.e. having both low-density and high-density liquid water. From the Adam-Gibbs model and free-volume theory, thermodynamic behaviors of water have been described using the proposed model, in which the constitutive relationships among density, heat capacity, thermal expansivity and glass transition temperature have been formulated. Moreover, the glass transition and its connection to thermodynamic behaviors were also investigated for dual-amorphous water. Finally, experimental data reported in the literature were used to verify effectiveness of the proposed model. This study is expected to provide a physical insight into the anomalous thermodynamics of dual-amorphous water undergoing the LLPT.

Free volume theory explains the unusual behavior of viscosity in a non-confluent tissue during morphogenesis.

A recent experiment on zebrafish blastoderm morphogenesis showed that the viscosity (η) of a non-confluent embryonic tissue grows sharply until a critical cell packing fraction (ϕS). The increase in η up to ϕS is similar to the behavior observed in several glass-forming materials, which suggests that the cell dynamics is sluggish or glass-like. Surprisingly, η is a constant above ϕS. To determine the mechanism of this unusual dependence of η on ϕ, we performed extensive simulations using an agent-based model of a dense non-confluent two-dimensional tissue. We show that polydispersity in the cell size, and the propensity of the cells to deform, results in the saturation of the available free area per cell beyond a critical packing fraction. Saturation in the free space not only explains the viscosity plateau above ϕS but also provides a relationship between equilibrium geometrical packing to the dramatic increase in the relaxation dynamics.

Free volume theory explains the unusual behavior of viscosity in a non-confluent tissue during morphogenesis

A recent experiment on zebrafish blastoderm morphogenesis showed that the viscosity (η) of a non-confluent embryonic tissue grows sharply until a critical cell packing fraction (ϕS). The increase in η up to ϕS is similar to the behavior observed in several glass-forming materials, which suggests that the cell dynamics is sluggish or glass-like. Surprisingly, η is a constant above ϕS. To determine the mechanism of this unusual dependence of η on ϕ, we performed extensive simulations using an agent-based model of a dense non-confluent two-dimensional tissue. We show that polydispersity in the cell size, and the propensity of the cells to deform, results in the saturation of the available free area per cell beyond a critical packing fraction. Saturation in the free space not only explains the viscosity plateau above ϕS but also provides a relationship between equilibrium geometrical packing to the dramatic increase in the relaxation dynamics.

On De Gennes narrowing of fluids confined at the molecular scale in nanoporous materials.

Beyond well-documented confinement and surface effects arising from the large internal surface and severely confining porosity of nanoporous hosts, the transport of nanoconfined fluids remains puzzling in many aspects. With striking examples such as memory, i.e., non-viscous effects, intermittent dynamics, and surface barriers, the dynamics of fluids in nanoconfinement challenge classical formalisms (e.g., random walk, viscous/advective transport)-especially for molecular pore sizes. In this context, while molecular frameworks such as intermittent Brownian motion, free volume theory, and surface diffusion are available to describe the self-diffusion of a molecularly confined fluid, a microscopic theory for collective diffusion (i.e., permeability), which characterizes the flow induced by a thermodynamic gradient, is lacking. Here, to fill this knowledge gap, we invoke the concept of "De Gennes narrowing," which relates the wavevector-dependent collective diffusivity D0(q) to the fluid structure factor S(q). First, using molecular simulation for a simple yet representative fluid confined in a prototypical solid (zeolite), we unravel an essential coupling between the wavevector-dependent collective diffusivity and the structural ordering imposed on the fluid by the crystalline nanoporous host. Second, despite this complex interplay with marked Bragg peaks in the fluid structure, the fluid collective dynamics is shown to be accurately described through De Gennes narrowing. Moreover, in contrast to the bulk fluid, the departure from De Gennes narrowing for the confined fluid in the macroscopic limit remains small as the fluid/solid interactions in severe confinement screen collective effects and, hence, weaken the wavevector dependence of collective transport.