Free Volume Model Research Articles

A free-volume model for the rheology of undercooled ZrTiCuNiBe liquid

Abstract A self-consistent model based on creation and annihilation of free volume during steady flow is presented. The model successfully simulates the experimental shear-rate dependent viscosity of undercooled Zr 41.25 Ti 13.75 Cu 12.5 Ni 10 Be 22.5 liquid. The model solution is well approximated by an analytic function, which appears identical to the Johnson–Segalman formulation for viscoelastic fluids.

Nanoporosity as quantum positron traps

Abstract Two-semiempirical positron stationary quantum models are developed for the study of nanoporosity in a wide range of solid porous materials. The cubic and conic well potentials are considered and their geometric parameters are related to the Positron Annihilation LifeTime Spectroscopy measurements (PALS). A new resonance lifetime phenomenon is found, which enables to propose a technique to trap positrons in such sites. The free volume equations of these new models were then compared to the well-known and widely utilized Spherical Free Volume Model (SFVM) and we found remarkable differences. A strong variation of the free volume size–positron lifetime relation with the geometry involved is observed and a remarkable dependence of the electron layer thickness parameter Δ R with the hole-shape under study and with the nature of the material considered. The mathematical functions appearing in the conic case are the superposition of Bessel functions of the first kind and trigonometric functions in the cubic case. Generalized free volume diagrams were drawn and a geometrical representation of the diverse cases considered was obtained.

A model for cylindrical nanoporosity based on single positron annihilation

A semiempirical positron stationary Quantum Model was developed to study nanoporosity in solid porous materials, such as silica gels. The cylindrical well potential is considered and its geometric parameters are related to the Positron Annihilation LifeTime Spectroscopy measurements (PALS). An alternative novel method to determine free volume sizes in solid materials was developed. The free volume equations of this new model were then compared to the well-known and widely utilized Spherical Free Volume Model (SFVM) and remarkable differences were found. A strong variation of the free volume size-positron lifetime relation with the geometry involved is observed as well as a strong dependence on the electron layer thickness parameter ΔR with the nature of the material.

Scaling of the supercooled dynamics and its relation to the pressure dependences of the dynamic crossover and the fragility of glass formers

Master curves of the relaxation time, tau, or viscosity, eta, versus T^-1V^-x, where T is temperature, V the specific volume, and x a material constant, are used to deduce the effect of pressure on the dynamic crossover and the fragility. The crossover is determined from the change in slope of derivative plots of the relaxation times or viscosities. We confirm our previous findings that the value of tau or eta at the crossover is independent of both T and P; that is, the dynamic crossover is associated with a characteristic value of the relaxation time. Previous determinations were limited to liquids having crossovers occurring at large values of tau (> 10 microsec), whereas by interpolating within T^-1V^-x space, we extend the analysis to smaller values of the crossover time. Using the superpositioned data, the dynamic crossover can be observed in isochoric data, where it is found that the relaxation time at the crossover for constant volume is equivalent to the value obtained under (the more usual) condition of constant pressure. Similarly, from the scaling analysis, isobaric relaxation times at high pressure are deduced from experimental measurements at atmospheric pressure. We find for all glass-formers studied, that the fragility (normalized temperature dependence of tau or eta) is a decreasing function of pressure. This conclusion is less subject to uncertainties in the measurements than published determinations of the pressure coefficient of fragility. Finally, we show that an empirical function, having the form of the Cohen-Grest relation but without connection to any free volume model, parameterizes the master curves, and accurately describes the data over all measured conditions.

Defect-assisted conductivity in organic ionic plastic crystals

In order to determine the role of defects (vacancies and extended lattice defects) in the conductivity mechanism of a well studied organic ionic plastic crystal electrolyte, conductivity and mean defect volumes were measured. The ionic conductivity of the salt showed a characteristic phase dependence. Defect volumes, as measured by positron annihilation lifetime spectroscopy, showed increasing rates of expansion with increasing rotational disorder. The dependence of ionic conductivity on defect volume was observed to be phase dependent. Increases in mean defect volume size below approximately 100 cm(3) mol(-1) did not always facilitate ionic conductivity. It was shown that the material undergoes a solid-solid phase transition to the most disordered phase (a plastic crystalline phase with the highest conductivity) when the mean defect volume becomes larger than the molar volume of either the rotating anionic or cationic species. Conductivity in this phase had the strongest dependence on defect volume. Critical volumes calculated from the free volume model of Cohen and Turnbull were unrealistically large.

Dynamic Viscosity Modeling of Methane + n-Decane and Methane + Toluene Mixtures : Comparative Study of Some Representative Models

Viscosity measurements of well-defined mixtures are useful in order to evaluate existing viscosity models. Recently, an extensive experimental study of the viscosity at pressures up to 140 MPa has been carried out for the binary systems methane + n-decane and methane + toluene, between 293.15 and 373.15 K and for several methane compositions. Although very far from real petroleum fluids, these mixtures are interesting in order to study the potential of extending various models to the simulation of complex fluids with asymmetrical components (light/heavy hydrocarbon). These data (575 data points) have been discussed in the framework of recent representative models (hard sphere scheme, friction theory, and free volume model) and with mixing laws and two empirical models (particularly the LBC model which is commonly used in petroleum engineering, and the self-referencing model). This comparative study shows that the average absolute deviation of the models is between 3.8 and 49.8%, and the maximum deviation is between 11.6 and 78.4%, depending on the considered model.

Conductivity, viscosity and volumetric behavior of molten hydrates of M3 + and M2+ ions

Conductivity, density and viscosity of molten hydrated salts consisting of M 3 + (Al 3 + and Fe 3 + ) and M 2 + (Ca 2 + , Cd 2 + , Mg 2 + and Zn 2 + ) ions were measured over a wide composition range and at temperatures ranging between 273.2 to 363.2 K. Representative data for FeCl 3 .6H 2 O + MgCl 2 .6H 2 O is taken for the discussion purposes. A change in hydration envelope of the cations and the competition of anions for hydration are considered to be the main factors for deviations from the ideal behavior in volumetric properties-composition isotherms. Temperature dependence of conductivity (A) and viscosity (η) was found to be non-Arrhenian; curvature in In (A, η) vs T - 1 curves indicate an increase in activation energy with decrease in temperature. The data were expressed using VTF equation, Free Volume Model (FVM) and Configurational Entropy Model (CEM) of liquid transport. The calculated values of zero mobility temperature, T o , exhibited a random variation with composition. The plot of In (Λ, η) vs (V - V o ) - 1 were linear indicating the applicability of Doolittle equation. A parallelism between V o and (V) T o vs composition indicate that free volume theory is applicable to describe the behavior of liquid transport in these system over the available temperature range. Composition dependence of the coefficients of VTF and Doolittle equations do not exhibit a systematic trend as expected from FVM and CEM. However, the standard deviations from the computer data fittings reveal that CEM formulations represent the data more closely to experimental values. Applicability of environmental relaxation model (ERM) of liquid transport was also examined. Constancy of C o , the limiting activation energy, for conductivity and viscosity is attributed for small temperature range available in this study. The e o values obtained in this study matches closely to the reported values for the similar systems. Though, ERM successfully predicts the temperature variations of transport properties, it is general observation that the parameters of ERM evaluated from a short range temperature data may not be useful to predict the behavior over wide range of temperatures.

Development of a unified framework for calculating molecular weight distribution in diffusion controlled free radical bulk homo-polymerization

In the present work, two different approaches to model diffusion controlled free radical polymerization, namely the free volume model and the entanglement theory are compared. These approaches are applied to methyl methacrylate bulk polymerization in a batch reactor to calculate the conversion, total radical concentration, the number and weight average molecular weights as well as the entire molecular weight distribution as a function of the polymerization time and the process conditions. All the diffusion-controlled phenomena were taken into account, including gel, glass and cage effects as well as residual termination. The molecular weight distribution is calculated by direct numerical integration of a large system of non-linear ordinary differential equations describing the conservation of the mass of macromolecular species in the batch reactor. Model predictions are in good agreement with available experimental data for conversion, number and weight average molecular weights as well as the entire molecular weight distribution, thus justifying the ability of these models to describe the main issues of the diffusion-controlled free radical polymerization.

Simplified Bulk Experiments and Hygrothermal Nonlinear Viscoelasticity

Bulk and shear linear viscoelastic functions were simultaneously determined using confined compression experiments on an epoxy primer, one component of a concrete/fiber-reinforced polymer composite bond line. The results were validated with data from separately conducted bulk creep compliance experiments. The transition region of the bulk modulus was as wide as those of the tensile and shear relaxation moduli. Thermal and hygral expansions were measured and used to calibrate a hybrid nonlinear viscoelastic constitutive model which represented the hygrothermal nonlinear viscoelastic response of the material. This model was a combination of Schapery’s (Further Development of a Thermodynamic Constitutive Theory: Stress Formulation, AA {&} ES Report (69–2), 1969a, Purdue University, West Lafayette; Schapery, R.A., ‘On the characterization of nolinear viscoelastic materials’, Polym. Eng. Sci. 9 1969b, 295–310.) and Popelar’s (K., ‘Multiaxial nonlinear viscoelastic characterization and modeling of a structural adhesive’, J. Eng. Mater. Technol. Trans. ASME 119, 1997, 205–210.) shear modified free volume model, which was calibrated ramp using torsion and tension experiments at various temperature and humidity levels. Using free volume concepts to accomplish time shifting as a function of strain, temperature and humidity levels did not create the extent of the softening behavior that was observed in the experiments, particularly at high humidity levels. The vertical shifting concepts of Schapery were required to capture the extraordinarily strong hygral effect.

Viscoelastic Characterization of Polymers Under Multiaxial Compression

A novel experimental configuration—a confined compression loading scheme—was used for the characterization of viscoelastic constitutive behavior of polymers. In this paper we present a brief description of the configuration, discuss its applicability to the determination of viscoelastic constitutive response, and examine the precautions needed for specimen preparation. The configuration is then utilized in the simultaneous determination of the bulk and shear relaxation response of polymethylmethrylate (PMMA) and polycarbonate (PC). Time–temperature superposition is utilized to obtain master curves of the bulk and shear moduli. Issues related to the interconversion between these moduli and the uniaxial relaxation modulus are also discussed. It is found that the effect of the confinement is to retard the rate of relaxation of the polymers; this is discussed in the framework of a free-volume model of viscoelastic material behavior.

Strain-Induced Changes of Free Volume Measured by Positron Lifetime Spectroscopy in Ultrahigh Molecular Weight Polyethylene

Positron lifetime spectroscopy and wide-angle X-ray scattering have been applied to investigate the structural changes induced by tensile deformation in ultrahigh molecular weight linear polyethylene. The results reveal a correlation between the crystallinity, the positron annihilation characteristics, and the strain of the polymer. The probability of positronium formation increases and the crystallinity of the material decreases with increasing tensile strain. The size distribution of the free-volume holes, where positronium atoms form, is determined from their lifetime distribution. The positron lifetime measurements are interpreted in terms of a free-volume approach assuming that the free volume associated with each liquidlike cell of the amorphous phase is divided into free-volume holes whose size distribution is given by a normal frequency function. The cumulative distribution functions determined from the positron annihilation measurements agrees with those predicted by the free-volume model. This indicates that the positrons contributing to the lifetime component associated with orthopositronium annihilation really probe the free volume in the amorphous phase of the polymer. The experiments evidence free-volume changes induced by tensile strain which are unrecoverable after relieving the stress.

Comparative study of viscosity models on the ternary system methylcyclohexane + cis-decalin + 2,2,4,4,6,8,8-heptamethylnonane up to 100 MPa

Recently, a comprehensive experimental study of the viscosity up to 100 MPa has been carried out on the ternary system composed of methylcyclohexane, cis-decalin, and 2,2,4,4,6,8,8-heptamethylnonane in order to provide data for asymmetrical hydrocarbon mixtures. Although not as complex as real petroleum fluids, the studied system is of interest for the evaluation of viscosity models for their potential application to the simulation of complex fluids with an asymmetrical molecular distribution. The measured data (1554 points) have been used in an extensive evaluation of the performance of seven different viscosity models applicable to hydrocarbon fluids. These models range from empirical correlations, such as the self-referencing model and the commonly used LBC model in petroleum engineering, to recent approaches with a physical and theoretical background, such as the hard-sphere scheme, the free-volume model, and the friction theory. This comparative study shows that the evaluated models, except the LBC model, can represent the viscosity of the ternary system within an acceptable uncertainty for most engineering applications. However, the extension to real reservoir fluids may be more appropriate for some of the models, such as the free volume and the friction theory, since these models are not limited to liquids and dense fluids, but are also applicable to gases, which is a required feature within the oil industry.

Influence of the number of CH 2CH 2O groups on the viscosity of polyethylene glycol dimethyl ethers at high pressure

This work reports new measurements of the viscosity of liquid diethylene glycol dimethylether (DEGDME) upto 100 MPa at eight temperatures ranging from 293.15 to 353.15 K. The measurements at atmospheric pressure have been performed with an Ubbelohde-type glass capillary tube viscometer with an uncertainty of ±1%. At pressures upto 100 MPa the viscosity was determined with a falling body viscometer with an uncertainty of ±2%. Using previous polyalkylene glycol dimethylether viscosity and density data (Triethylene glycol dimethyl ether and tetraethylene glycol dimethyl ether) obtained at the laboratory, present measurements were used to study the dependence of the viscosity and of the molecular parameters of hard-sphere scheme and free-volume model on the number of CH 2CH 2O groups.

Characterization of free volume changes associated with shear band formation in Zr- and Cu-based bulk metallic glasses

The free volume model for flow in metallic glasses predicts a significant increase in free volume at the onset of plastic deformation. The details of these structural changes are unclear, however, particularly during strain localization in shear bands. In this study, the free volume changes associated with inhomogeneous plastic deformation of a Cu-based bulk metallic glass were examined using positron annihilation spectroscopy (PAS). PAS results indicated that there was a distribution of free volume site sizes in both the as-quenched and rolled glasses, and that the concentration of larger sites increased with deformation. Differential scanning calorimetry was also used to observe the glass transition behaviors of Cu- and Zr-based glasses after rolling and annealing. Annealing resulted in an increase in the height of the endothermic glass transition peak, consistent with structural relaxation relative to the as-quenched material. Deformation resulted in both a lower endothermic peak height and an earlier and deeper exothermic peak associated with structural relaxation, indicating a more disordered structure with more free volume.

Interplay of surface and confinement effects on the molecular relaxation dynamics of nanoconfined poly(methyl methacrylate) chains.

The thermally stimulated current (TSC) signatures of the primary (alpha) transition and its precursor, the Johary-Goldstein (beta) relaxation, are used to probe effects of nanoconfinement on the dielectric relaxation dynamics of poly(methyl methacrylate) (PMMA) radically polymerised in situ 50 angstroms mean pore size silica-gel. Nanoconfinement leads to a broadened and low-temperature-shifted beta band (peaking at Tbeta, with deltaTbeta = T(conf.)beta - T(bulk)beta = -15 degrees C for a heating rate of 5 deg/min), signifying the occurrence of faster relaxing moieties compared to the bulk-like PMMA film. Furthermore, both TSCs and differential scanning calorimetry (DSC) estimate a rise of the glass transition temperature for the confined phase ([Formula: see text]= +13 degrees C) and an increased width for the corresponding transition signals, relative to the signals in the bulk. Simple free-volume and entropy models seem inadequate to provide a collective description of the above perturbations. The observation of a spatial heterogeneity regarding the relaxation dynamics is discussed in terms of the presence of a motional gradient, with less mobile segments near the interface and more mobile segments in the core, and the interplay of adsorption ( e.g., strong physical interactions that slow down molecular mobilities) and confinement effects ( e.g., lower entanglements concentration and local density fluctuations that provide regions of increased free space). The results suggest that in the case of high-molecular-weight polymers confined in small-pore systems, adsorption effects have considerable bearing on the glass transition phenomenon whereas confinement primarily influences side-chains' rotational mobilities. The confinement effect is expected to dominate over adsorption for PMMA phases occluded in higher pore sizes and silanised walls.

Volume and temperature as control parameters for the dielectric α relaxation of polymers and molecular glass formers

Methods of analysing the dielectric α relaxation and equation-of-state data for supercooled glass-forming materials, to determine the relative contribution of volume and temperature, are illustrated using measurements on poly[(o-cresyl glycidyl ether)–co-formaldehyde] (PCGE). The ratio E V /E P = 0.66 of apparent activation energies and the ratio |α τ |/α P = 1.7, of the thermal expansivities, evaluated at τ = 1 s and P = 0.1 MPa respectively, reveal that for PCGE the volume and temperature both exert a substantial influence on the relaxation times. In this regard, PCGE is similar to other polymers and non-associated molecular liquids for which such analyses have been carried out. This means that the underlying bases of both free-volume and thermal activation models are not correct. The exceptional behaviour is that of hydrogen-bonded liquids, such as polyalcohols, for which competing effects minimize the sensitivity to pressure, whereby temperature becomes the dominant control variable.

Ion beam-induced anisotropic plastic deformation of silicon microstructures

Amorphous silicon micropillars show anisotropic plastic shape changes upon irradiation with 30 MeV Cu ions. The transverse plastic strain rate is (2.5±0.2)×10−17 cm2/ion at 77 K, which is about one order of magnitude less than that of silica glass. In contrast, crystalline silicon pillars, irradiated under the same conditions, do not exhibit anisotropic deformation. A viscoelastic and free volume model is used to qualitatively describe the data. By irradiating partially amorphous structures a variety of silicon microshapes can be fabricated.

Simultaneous free-volume modeling of the self-diffusion coefficient and dynamic viscosity at high pressure.

In this work, a simultaneous modeling of the self-diffusion coefficient and the dynamic viscosity is presented. In the microstructural theory these two quantities are governed by the same friction coefficient related to the mobility of the molecule. A recent free-volume model, already successfully applied to dynamic viscosity, has been considered and generalized. In this generalized model the compound is characterized by only four parameters. But if the quadratic length is known, the number of adjustable parameters is three. The compounds considered in this work are benzene, carbon tetrachloride, chlorotrifluoromethane, cyclohexane, methylcyclohexane, and tetramethylsilane. For these pure compounds we have found in the literature several data for both the self-diffusion and the dynamic viscosity in large viscosity, diffusion, temperature, and pressure intervals (up to around 500 MPa for methylcyclohexane and tetramethylsilane). The average absolute deviation obtained by the modeling is generally less than 3% for the viscosity and 5% for the self-diffusion.

Lateral Diffusion of the Reconstituted Dialkyl Viologen Monolayer at the Air/Water Interface Studied with Electrochemistry

The reconstituted dialkyl viologen monolayer at the air/water interface was studied as a model system of the biomembrane for the study of lateral diffusion of the electroactive viologen moiety because lateral diffusion of biomembrane molecules has key functions for the life phenomena. The shortest alkyl chain of 1,1‘-didodecyl-4,4‘-bipyridium dibromide (C12VC12) could not form the stable monolayer in the subphase of NaCl and NaBr aqueous solutions and also does not show any distinct phase transitions because it is partially soluble in the aqueous phase. For 1,1‘-ditetradecyl-4,4‘-bipyridium dibromide (C14VC14) and 1,1‘-dihexadecyl-4,4‘-bipyridium dibromide (C16VC16) molecules, the stable monolayer was obtained at the air/water interface, and this was identified with pressure−area isotherms and directly observed at Brewster angle microscopy (BAM) images. The changing orientation of alkyl chain of the viologenes was detected by surface potential measurements with moving barrier. Finally, the lateral diffusion of the viologen moiety of dialkyl viologenes at the air/water interface was successfully determined with electrochemical techniques using a microband electrode. The linear decrease of the diffusion constant of viologen molecules with decreasing mean molecular area and increasing alkyl chain length of viologenes at the air/water interface is explained by the decreasing free volume of the moving headgroup. This is well explained by the modified Cohen−Turnbull free volume model.

Analysis of the swelling behaviour of chemically modified softwood: A novel approach

Volume changes due to modification with acetic and hexanoic anhydride are due to the volume occupied by the reagent and an associated void volume. The void volume is larger in hexanoic anhydride modified wood. Less weight of water per gm of unmodified wood was accommodated by acetic anhydride modified wood than by hexanoic modified wood, at equivalent WPG. A non-linear relationship was found between weight of water per gm of unmodified Corsican pine wood and bulking, whereas a linear relationship would be predicted. However, this takes no account of void volume. When the value of void volume is deducted from the bulking a linear relationship was indeed obtained with acetic anhydride, but not with hexanoic anhydride modified Corsican pine. It seems therefore that the free volume model offers a reasonable explanation of the differences in swelling recorded for Corsican pine sapwood modifying to varying wpg’s with acetic anhydride.