Free Volume Concept Research Articles

A Review of Particle Packing Models and Their Applications to Characterize Properties of Sand-Silt Mixtures

This paper reviews particle packing models and explores their application in geotechnical engineering, specifically for sand-silt mixtures. The review covers key models, including limiting case, linear, and non-linear packing models, focusing on their mathematical structures, physical principles, assumptions, and limitations through the concept of excess free volume. The application of particle packing models in geotechnical engineering is explored in characterizing the properties of sand-silt mixtures, offering insights into maximum, minimum, and critical void ratios and inter-granular void ratio, and the prediction of mechanical properties.

Doped holes and/or electrons induced superconductivity domes explained with the free volume concept

The conductivity equation developed in our previous work without any restrictions to specific materials is employed to explore how superconductivity transition temperature Tc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{c}$$\\end{document} changes with the doped hole or electron concentrations based on the free volume concept. The predicted relationship is used to fit experimental data available in the literature and a good agreement with observations is achieved. Our findings may provide an alternative explanation for doping-induced domes and/or double domes with a-dip phenomena observed among many superconductors.

Pressure-induced superconductivity domes described with a theoretical equation based on the free volume concept

A generic conductivity equation developed in our previous work is borrowed to explore how superconductivity transition temperature changes with external high pressure. The volume-pressure relationship revealed in the literature is utilized to estimate the pressure-dependent free volume based on our free volume equation. Pressure-induced single and double superconductivity domes are predicted with the obtained equation. It is also used to fit experimental data available in the literature. A good agreement with experimental observations is obtained. Our equation can fit nonlinear and polynomial relationships as well. The findings provide a theoretical foundation for pressure-induced phenomena among many superconductors.

Dislocation phenomena described with free volume concept and Eyring's rate process theory.

Dislocation phenomena in solids under simple shear stress are theoretically addressed with the free volume concept and Eyring's rate process theory for obtaining a generic and unified description. The obtained equations do not have any restrictions to specific materials and are compared with various theories and empirical equations like the Hall-Petch and its inverse forms. Moreover, our equations are used to fit experimental data of mechanical properties and dislocation density against grain sizes available in the literature. A good agreement with observations is achieved, indicating that our theoretical framework is sound. Our findings provide a theoretical foundation for the very common dislocation phenomena observed among many solid materials including pure metals, metallic alloys, ceramics, and even geological scale entities, potentially clearing out many inconsistencies and puzzles in the literature.

The empty world - a view from the free volume concept and Eyring's rate process theory.

The many-body problem is a common issue, irrespective of the scale of entities under consideration. From electrons to atoms, small molecules like simple inorganic or organic structures, large molecules like proteins or polymers, nanometer- or micrometer-sized particles, granular matter, and even galaxies, the precise determination or estimation of geometrical locations and momentum energy of individual entities, and interaction forces between these millions of entities, is impossible but unfortunately important for understanding the collective physical properties like mechanical and electrical characteristics of the whole system. Despite foreseeable difficulties and complexities, attempts to estimate "interparticle" forces have never stopped using traditional Newtonian models, quantum mechanical approaches, and density functional theory. In this review, a simple approach integrating the free volume and Eyring's rate process theory is summarized and its application across a wide range of scales from electrons to the universe is presented in a unified manner. The focus is on comparisons between theoretical predictions and experimental results.

Enhanced diffusion in thin-film Cu-Zr nanoglasses

Tracer measurements with both radioactive, 55Fe, as well as natural, mainly 56Fe, isotopes are used to investigate Fe diffusion in a Cu-Zr nanoglass in comparison to their diffusion rates in a homogeneous amorphous counterpart. The columnar-structured nanoglass and the homogeneous amorphous films are synthesized using radio-frequency magnetron sputtering. Ion beam sputtering (with the 55Fe radioisotope) and time-of-flight secondary ion mass spectroscopy (with natural Fe) are used for the diffusion experiments. Remarkably, faster Fe diffusion is observed in the columnar nanoglasses, supporting the concept of glass–glass interfaces. The relative diffusion enhancement is explained within the excess free volume concept that is supported by structural investigations using transmission electron microscopy. For the first time, the relaxation dynamics in a nanoglass as well as in a homogeneous thin-film glass of identical composition are evaluated via time-dependent diffusion measurements.

Changes in the Structure of Amorphous Alloys under Deformation by High-Pressure Torsion and Multiple Rolling.

X-ray diffraction and scanning electron microscopy were used to study changes in the structure of amorphous alloys under deformation by high-pressure torsion and multiple rolling. The change in mean nearest neighbor distance (the radius of the first coordination sphere) under deformation was determined. During deformation, shear bands are formed in amorphous alloys, which are regions of lower density compared to the surrounding undeformed amorphous matrix. Shear bands are zones of increased free volume, in which crystallization processes are facilitated. The change in the proportion of free volume under deformation of various types was estimated. The formation of shear bands leads to the appearance of steps on the surface of the samples. The number of shear bands and the surface morphology of deformed amorphous alloys were determined by the type of deformation and the physical properties of the material. The results obtained are discussed within the concept of free volume in the amorphous phase.

Effect of pre-straining on the structure and nano-mechanical properties of a CuZrAl bulk metallic glass

Pre-straining was carried out on a CuZrAl bulk metallic glass (BMG), in order to understand the physical correlation between its structural heterogeneity and nano-mechanical performance. As the pre-strain increases, the studied glass remains its amorphous structure whereas the degree of local order firstly decreases and then increases, yielding a minimum value at 10 % pre-strain, and the Helmholtz activation energy (ΔF*), shear transformation zone (STZ) volume, number of atoms in the STZ (N), and the nanohardness value exhibits a similar trend. The variation in the structure and thus mechanical performance induced by pre-straining has been interpreted from the viewpoint of free volume concept. The results obtained here can be beneficial for tailoring the structure and the corresponding mechanical properties of BMGs.

Accelerated relaxation behavior during water desorption in the mechano-sorptive creep of wood: modeling and analysis based on the free volume concept and Kohlausch–Williams–Watts function

Abstract The accelerated creep behavior during water desorption of wood was modeled on the Kohlausch–Williams–Watts (KWW) function and free volume concept. Assuming that the water desorption rate dmc/dln t $\text{dmc/dln\,t}$ is involved in the creation of a new free volume, the net creep compliance during desorption J du(t) was obtained as ln J du ( t ) = β c ln t − β c ( ln τ c 0 + k f dmc / d ln t ) + ln J c ∞ $\mathrm{ln} {J}_{\text{du}}\left(t\right)={\beta }_{\text{c}} \mathrm{ln} t-{\beta }_{\text{c}}\left(\mathrm{ln} {\tau }_{\text{c}0}+{k}_{\text{f}}\,\text{dmc}/\text{d}\mathrm{ln} t\right)+\mathrm{ln} {J}_{\text{c}\infty }$ where β c, τ c0 and J c∞ are the stretching parameter, characteristic time of the relaxation, and long-time asymptote compliance at a constant moisture content (mc) equal to the initial mc of the accelerated creep, respectively, and k f is the coefficient of the water desorption rate. These parameters were determined by simulation using experimental data and literature results and were found to be reasonable. The simulation results agreed well with the experimental ones. This verifies the validity of the model and its derived equations.

Theoretical exploration of external pressure impact on superconducting transition temperatures

An external pressure could raise superconducting transition temperatures Tc, which has been experimentally observed but hasn’t been understood systematically. Utilizing superconducting transition temperature equations obtained with Eyring’s rate process theory and free volume concept in our previous work, we have explored how an externally applied pressure could change Tc in this article, under an assumption that the pressure P could change the free volume available for electrons in a system. The electron traveling distance and/or inter-particle spacing between electrons could have a linear, power law, and exponential relationships with pressures, borrowed from the relationship between viscosity and the free volume of molecules for glass liquids. Predicted relationships between Tc and pressures can be used to explain currently observed experimental phenomena such as Tc linearly increasing with pressures, initially slowly increasing and then suddenly jumping to a very high level, or showing skewed saw tooth relationships, etc. Our findings may provide an alternative simple theoretical approach to understand pressure induced superconductivity phenomena, further clearing doubts on many seemingly unrelated experimental observations.

Local-Average Free Volume Correlates with Dynamics in Glass Formers.

Glass formers exhibit a pronounced slowdown in dynamics, accompanied by progressive heterogeneity as they approach the glass transition. There is intense debate over whether the dramatic slowdown is caused by dynamical heterogeneity and whether the enhanced dynamical heterogeneity originates from structural causes. However, the connection between dynamical heterogeneity and the spatial distribution of the single-particle free volume (a purely static structural quantity) was found to be rather weak, which raises the question of whether dynamic heterogeneity has a purely structural origin. Here, by introducing the concept of local-average free volume, we present numerical evidence that long-time dynamic heterogeneity shows significantly enhanced correlation with the average local free volume over a length scale of a few neighboring shells. Our results resolve the long-standing controversy about whether free volume plays an important role in particle rearrangements associated with the activated hopping relaxation. The concept of "local average" can be applied to other local structural descriptors to better correlate with dynamic heterogeneity in glass-forming liquids.

Reversible linear-compression behavior of free volume in a metallic glass

Free volume is one of the key structural concepts widely used to describe various glass phenomena. However, free volume is challenging to be rigorously defined in glass structures and directly determined by experiments. Here, we employed metallic glass as a simple glass model system and studied the structural evolution of an as-spun (hyperquenched) and another thermally annealed metallic glass with different amounts of free volume by in situ high-pressure synchrotron x-ray diffraction. Therefore, the effect of free volume on the compression behavior of metallic glasses can be clarified by comparing the two samples at identical experimental conditions. We find that a higher amount of free volume causes both lower density and bulk modulus as expected at ambient conditions. Surprisingly, during compression, the decrease of free volume has a constant rate up to $\ensuremath{\sim}30\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$ and appears to be mostly reversible upon decompression without obvious permanent densification after pressure release. These results suggest an elastic process in metallic glasses under pressure. Implications of these results for the structural models based on the free-volume concept are discussed. The typically assumed glass structural model with isolated domains of ``liquidlike'' (free-volume rich) region embedded in a solidlike (free-volume poor) matrix seems unlikely. Instead, a more ``homogeneous'' model over a wide range of length scales such as a nested fractal network of liquid- and solidlike regions seems more consistent with the experimental observation.

Quantized conductance and superconductivity of twisted graphene and other 2D crystals explained with the Eyring’s rate process theory and free volume concept

Theoretical treatment originally intended to address proton transporting through a 2D (two dimensional) crystal like graphene and hexagonal boron nitride has been borrowed to examine conductivity and superconductivity of single layer, bilayer, trilaye, even multilayer graphene or other 2D crystals. The theory was developed based on the Eyring’s rate process theory and free volume concept under an assumption that protons behave exactly same as electrons, thus obtained equations should hold for electron conduction through a 2D crystal, too. These equations show that at high temperature regions conductivity should be scaled as σ=ν1e2h, similar to fractional/integral quantum Hall effect; while at low temperature regions conductivity should be scaled as σ=ν22eh, similar to Josephson junction effect. At high temperature regions, the parameter α, related to electron packing structure and critical to superconductivity, is canceled out and not present in derived equations, indicating that no superconductivity occurs in high temperature regions. While in low temperature regions, superconductivity should appear at temperature about 5 K or even higher, depending on electron packing structures. The fractional parameter f that can vary from fully close status with f=0 or full open status with f=1 should be controlled by the twisted angles. Our equations predict that superconductivity and insulating states are closely adjacent to each other; ”on” and ”off” superconductivity can be observed periodically when twisted angles are precisely varied from one direction to another. The volume ratio of conduction electrons to the conductive area and thickness play a critical role in superconductivity, implying that varying the area and/or thickness could have similar impact as twisted angle does. Our findings shed new lights on conductivity of stacked graphene or other 2D crystals.

A Thermodynamic-Consistent Model for the Thermo-Chemo-Mechanical Couplings in Amorphous Shape-Memory Polymers

Chemically-responsive amorphous shape-memory polymers (SMPs) can transit from the temporary shape to the permanent shape in responsive to solvents. This effect has been reported in various polymer-solvent systems. However, limited attention has been paid to the constitutive modeling of this behavior. In this work, we develop a fully thermo-chemo-mechanical coupled thermodynamic framework for the chemically-responsive amorphous SMPs. The framework shows that the entropy, the chemical potential and the stress can be directly obtained if the Helmholtz free energy density is defined. Based on the entropy inequality, the evolution equation for the viscous strain, the temperature and the number of solvent molecules are also derived. We also provide an explicit form of Helmholtz free energy density as an example. In addition, based on the free volume concept, the dependence of viscosity and diffusivity on the temperature and solvent concentration is defined. The theoretical framework can potentially advance the fundamental understanding of chemically-responsive shape-memory effect. Meanwhile, it can also be used to describe other important physical processes such as the diffusion of solvents in glassy polymers.

Enhanced Free Surface Mobility Facilitates the Release of Free-Volume Holes in Thin-Film Polymer Glasses

The concept of free volume underpins the variations in polymer dynamics. Annihilation of free-volume holes through diffusion to surfaces has been proposed to determine the vitrification of the conf...

Revisiting Ionic Liquid Structure-Property Relationship: A Critical Analysis.

In the last few years, ionic liquids (ILs) have been the focus of extensive studies concerning the relationship between structure and properties and how this impacts their application. Despite a large number of studies, several topics remain controversial or not fully answered, such as: the existence of ion pairs, the concept of free volume and the effect of water and its implications in the modulation of ILs physicochemical properties. In this paper, we present a critical review of state-of-the-art literature regarding structure–property relationship of ILs, we re-examine analytical theories on the structure–property correlations and present new perspectives based on the existing data. The interrelation between transport properties (viscosity, diffusion, conductivity) of IL structure and free volume are analysed and discussed at a molecular level. In addition, we demonstrate how the analysis of microscopic features (particularly using NMR-derived data) can be used to explain and predict macroscopic properties, reaching new perspectives on the properties and application of ILs.

Influence of hydrostatic pressure on rheological properties of polymer melts—A review

Rheological properties of polymer melts are significantly dependent on molecular structure and external parameters. While numerous experimental data of the dependence of the rheological behavior on stress, shear rate, and temperature are available in the literature, much less is known on the effect of hydrostatic pressure. This article reviews the knowledge about the pressure dependence of rheological properties of polymer melts. The different experimental devices for measurements under pressure are described, and the methods of determining the pressure coefficients of viscosity are critically analyzed. Very few investigations of the pressure dependence of viscoelastic properties are addressed. A comparison of the pressure coefficients of commercial polymers obtained by various authors from viscosity measurements with different methods shows the deficits in getting exact data. It can be said, however, that the pressure coefficients increase in the order of high density polyethylene, linear low-density polyethylene, low-density polyethylene, polypropylene, and polystyrene. For amorphous polymers and, particularly, for polystyrene, it is shown how the pressure coefficients decrease with growing temperature. For polyolefins, this dependency is less significant. The free volume concept is discussed with respect to an interpretation of the experimental findings. Results of using the hole fraction theory for describing the pressure dependence of viscosity are presented and critically assessed.

Nonempirical Free Volume Viscosity Model for Alkane Lubricants under Severe Pressures.

Viscosities η and diffusion coefficients D_{s} of linear and branched alkanes at pressure 0<P<0.7 GPa and temperature T=500-600 K are calculated from molecular dynamics simulations. Combining Stokes-Einstein, free volume, and random walk concepts results in an accurate viscosity model for the considered P and T. All model parameters (hydrodynamic radius, random walk step size, and step frequency) are extracted from equilibrium molecular dynamics via microscopic ensemble averages rendering η(P,T) aparameter-free predictor for lubrication simulations.

Pressure effects on local atomic structure of Ni15Co15Al70 metallic glasses

Molecular dynamics simulations are used to study the pressure effects on the local atomic structure of Ni15Co15Al70 metallic glasses. Interatomic interactions are modeled by the semi-empirical embedded atom method. The effects of pressure were systematically investigated through a variety of local structural analysis methods, such as bond angle distribution, structure factor, Voronoi tessellation and total and partial coordination numbers. Via the Went-Abraham parameter, our numerical results show an increase of the glass transition temperature Tg with increasing pressure. In the same context, Voronoi tessellation and coordination number analyses indicate that the local structure of glassy Ni15Co15Al70 is obviously influenced by the applied pressure, and the degree of local fivefold symmetry in the quenched systems decreases when the pressure increases. Lastly, we also investigated other parameters of structural disorder in amorphous alloys Ni15Co15Al70, including the concept of free volume and the atomic-level stresses. Implications of these findings are discussed.

On the prediction of temperature-dependent viscosity of multicomponent liquid alloys

The simulation of casting processes demands accurate information on thermophysical properties for selected alloys to properly feed the mathematical models. One of such properties is the viscosity of pure liquid metals and alloys, which can be either found in the literature as experimental data or to be calculated by theoretical models. Nevertheless, a considerable discrepancy between experimental data and simulated results is frequently observed for some pure metals, as high as twice the experimental measured values. Several models can be found in the literature, such as those in the form of Arrhenius-type equations, which depend on the availability of experimental data with a view to permitting the apparent activation energy and the pre-exponential constant parameters to be determined. Furthermore, models based on Andrade’s equation and its extensions, to deal with the apparent activation energy and the free volume concepts, are generally dependent only on thermodynamic data, that is, molar weight, molar volume, Gibbs energy of viscous flow activation, Gibbs energy and enthalpy of formation, and the molar fractions of the alloy components. In this paper, an extension of Takahira’s model for pure liquid metals is proposed, which permits to deal with the viscosity of liquid multicomponent alloys. Comparisons are made among simulations provided by an Arrhenius-type equation, Kaptay’s and Takahira’s models for pure metals, as well as among an Arrhenius-type equation, Kaptay’s model and the present approach for multicomponent alloys. The simulated results are plotted against experimental viscosity data from the literature for pure liquid metals (Al, Cu, Si and Mg) and for ternary and quaternary commercial Al-based alloys. The proposed approach for multicomponent alloys is shown to agree well with the experimental scatters and with Kaptay’s model for all examined cases.