Entire Range Of Volume Fraction Research Articles

Structure and short-time diffusion of concentrated suspensions consisting of silicone-stabilised PMMA particles: a quantitative analysis taking polydispersity effects into account.

We characterise structure and dynamics of concentrated suspensions of silicone-stabilised PMMA particles immersed in index-matching decalin-tetralin mixtures by means of static and quasielastic light scattering experiments. These particles can reproducibly be prepared via a comparatively easy route and are thus promising model systems with hard-sphere interaction. We demonstrate the hard-sphere behaviour of dense suspensions of these systems rigorously taking polydispersity effects into account. Structure factors S(Q) can in the entire range of volume fractions with liquid-like structure quantitatively be modelled using a multi-component Percus-Yevick ansatz regarding the particle size distribution and the form factor assuming a core-shell model with a scattering length density gradient in the PMMA core. Herewith, hydrodynamic functions H(Q) are in the whole accessible Q-range beyond the second maximum of H(Q) quantitatively modelled using a rescaled δγ-approach for all investigated volume fractions. With these data, previously provided characterisation of dilute systems is extended: the excellent agreement of structural and dynamic properties with theoretical predictions for hard spheres demonstrates the suitability of these particles as a model system for hard spheres.

Static Dielectric Constants, Densities, Refractive Indices and Related Properties of Binary Mixtures at Various Temperatures Under Atmospheric Pressure

Experimental dielectric constants at (293.15, 298.15, 303.15) K, densities and refractive indices at 293.15 K are reported for water- ethanol and water- n-butanol binary mixture systems over the entire volume fraction range and atmospheric pressure. From the experimental dielectric data, the excess dielectric constant, effective Kirkwood correlation factor, Bruggeman factor and from density and refractive index data various parameters and their excess properties like excess density, excess refractive index, excess molar polarization, and excess molar volume were estimated and reported in the study. The static dielectric constant of the studied binary mixtures decreases with increase in temperature and volume fraction of the solutes. The density values are decreasing and refractive indices are increasing with increasing volume fraction of ethanol and n-butanol in water. Excess molar volumes values of ethanol and n-butanol are negative over the entire volume fraction range shows the presence of intermolecular interaction and hydrogen bonding in both the binary mixtures.

Design of isotropic porous plates for use in hierarchical plate-lattices

This work deals with the elastic and plastic properties of two-dimensional periodic metamaterials. Design maps are developed to ensure their isotropic elastic response while attaining the theoretical stiffness limits. Numerical simulations of two different topologies - triangular and round hole staggered patterns - are performed to analyze their large deformation response for relative densities ranging from 0.1 to 0.9. The investigations show that the strength of triangular perforated plates is profoundly dependent on the unit cells’ direction concerning the axial loading; 0 and 30 degrees have the lowest and highest yield strength over the entire range of volume fractions. In contrast, the round hole staggered patterns exhibit an almost uniform yield strength in all directions. The yield strength of the circular patterns is significantly lower at low- and intermediate-density ranges; whereas they outperform the triangular ones at relative densities higher than 0.6. Additionally, validation experiments are performed on specimens of 0.3 relative density that have been extracted from DP980 steel sheets using micro waterjet cutting, showing good agreement in terms of force-displacement response and surface strain fields. A foam-like structure is built from periodic sheets and the scaling of the elastic properties of the resulting hierarchical 3D metamaterial are discussed.

Combinatorial structural-analytical models for the prediction of the mechanical behaviour of isotropic porous pure metals

This work provides insight on the prediction of the mechanical behaviour of isotropic porous pure metals using empirical and structural-analytical models and proposes two new combinatorial structural-analytical models for the estimation of the mechanical properties. Porous metals such as foams are advanced engineering materials and therefore the prediction of their properties for their optimisation is beneficial. Nevertheless, the estimation of their mechanical behaviour generally relies on semi-empirical models, which are limited to specific materials (i.e. type of metal + type of internal structure + individual property) and for which empirical constants need to be determined. Among the available structural-analytical models, which were developed to estimate mathematically equivalent thermophysical properties, the Symmetric and Interconnected Skeleton Structural (SISS) model gives the best prediction over a broad range of volume fraction of pores (i.e. 0.4–1.0) but always significantly overestimates the elongation to failure. This study presents the derivation of new combinatorial structural-analytical models that are able to rapidly and accurately predict the Young modulus plus ultimate tensile strength and the elongation to failure, respectively, across the entire range of volume fraction of pores. These models have physical bases, are not time- and computing-intensive (thus rapid and low cost), and have reasonable accuracy for materials whose microstructure is uncertain.

Explicit estimates versus numerical bounds for the electrical conductivity of dispersions with dissimilar particle shape and distribution

An effective-medium theory for the electrical conductivity of Ohmic dispersions taking explicit account of particle shape and spatial distribution independently is available from the work of Ponte Castañeda and Willis [J Mech Phys Solids 43:1919–1951, 1996]. When both shape and distribution take particular “ellipsoidal” forms, the theory provides analytically explicit estimates. The purpose of the present work is to evaluate the predictive capabilities of these estimates when dispersions exhibit dissimilar particle shape and distribution. To this end, comparisons are made with numerical bounds for coated ellipsoid assemblages computed via the finite element method. It is found that estimates and bounds exhibit good agreement for the entire range of volume fractions, aspect ratios, and conductivity contrasts considered, including those limiting values corresponding to an isotropic distribution of circular cracks. The fact that the explicit estimates lie systematically within the numerical bounds hints at their possible realizability beyond the class of isotropic dispersions.

On the permeability of colloidal gels

We reexamine and refine analytical theories for permeability in colloidal networks, with particular focus on constants and identification of approximations. The new theories are compared against numerical simulations of Stokes flow through the networks and reveal nearly quantitative power-law predictions for both pore size and permeability at low volume fractions, with systematic deviations observed only at high volume fractions. Comparison with two previously published experimental data sets yields mixed results: in one case, very good agreement is found, while in the other, only the scaling is correctly predicted. In fractal gel networks, the permeability is commonly modeled as a power-law function of volume fraction, with the fractal dimension of the network determining the power-law exponent. To quantitatively probe the influence of gel structure on permeability, we investigate this relation in structures generated by diffusion-limited cluster aggregation (DLCA) and reaction-limited cluster aggregation (RLCA) and, for contrast, non-overlapping uniform random dispersions of particles. Geometric analyses are used to determine network pore size distributions, fractal dimensions, and percolation characteristics. High-fidelity simulations of the slow viscous flow of Newtonian fluids are used to obtain first-principles-based velocity and fields and hence network permeabilities. Interestingly, the effective pore size that determines permeability is found to be somewhat larger than that measured by a method based on the insertion of spherical probes. Empirical inclusion of a fractal dimension dependence on volume fraction is found to yield quantitative results for permeabilities over the entire volume fraction range studied, in both DLCA and RLCA materials.

Dynamic viscosity of colloidal silica suspensions at low and high volume fractions

A comprehensive study was carried out on the dynamic viscosity of X30 silica dispersions at both high and low volume fractions of colloidal silica particles at various electrolyte ionic strength and pH values. Booth and Ruiz-Reina and Carrique theoretical models (R-R&C) were compared in predicting the primary electroviscous effect (PEE) for viscosity at low volume fractions. To this respect the colloidal dispersion was well characterised with regards to electrolyte properties such as the Debye length, κ−1, calculated from the ionic strength, and zeta potential, ζ, calculated from the electrophoretic mobility using the full numerical model by O’Brien and White (O’B&W). R-R&C hard sphere model (which is a modified version of Simha hard sphere model that includes a boundary condition by Happel on the outer radius of the cell) and the semi-empirical Krieger-Dougherty (K-D) models were fitted to the experimental data at high volume fractions. At both low and high volume fractions the viscosity increased with pH and decreased with ionic strength. At low volume fractions both theoretical models significantly underestimated the experimental dynamic viscosities obtained in this work. This could be attributed to the fuzzy structures for silica particles in aqueous conditions reported previously in the literature, where a significantly larger electroviscous parameter, p, was obtained experimentally for silica particles. The experimental electroviscous parameter, pexp, in this work was found to be roughly an order of magnitude up to 26 times larger than that predicted by Booth and around 5 ± 1 times larger than the predicted p by R-R&C model allowing the introduction of a correction factor in the PEE coefficient obtained from R-R&C model enabling good prediction for X30 silica dispersions by the latter model. The significant improvement of the electroviscous effect predictions by R-R&C model compared to Booth model may be attributed to the limitations invalidating the Booth model at the electrolyte conditions in this study. At high volume fractions, the R-R&C hard sphere cell model, gave a much better fit to the experimental data compared to the K-D model, which also had the advantage of being only dependent on a coefficient that linearly relates an effective volume fraction postulated for the fuzzy silica particles to the experimental. The K-D model however, depends on the intrinsic viscosity, [η], which requires the calculation of the experimental slope of the dynamic viscosity against volume fraction in the dilute limit, and also on a maximum packing fraction as a fitting parameter. Due to the effect of the fuzzy structures on the viscosity, the latter effective volume fraction ϕeff was calculated using two approaches: (i) as a fitting parameter by fitting the R-R&C hard sphere model to the experimental viscosity data over the entire volume fraction range, and (ii) by fitting only the linear part of the experimental viscosity at low volume fractions, It is concluded that the R-R&C hard sphere model with the effective volume fraction accounting for the fuzzy structures fits reasonably well the full range of experimental results at low and high volume fractions. When the model was used with the Adamczyk effective volume fraction (i.e., considering only the dilute region in the fitting procedure), the predictions became worse at high volume fractions where significant deviations from the experimental results were found upon the increase of pH.

Modelling compressible dense and dilute two-phase flows

Many two-phase flow situations, from engineering science to astrophysics, deal with transition from dense (high concentration of the condensed phase) to dilute concentration (low concentration of the same phase), covering the entire range of volume fractions. Some models are now well accepted at the two limits, but none are able to cover accurately the entire range, in particular regarding waves propagation. In the present work, an alternative to the Baer and Nunziato (BN) model [Baer, M. R. and Nunziato, J. W., “A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials,” Int. J. Multiphase Flow 12(6), 861 (1986)], initially designed for dense flows, is built. The corresponding model is hyperbolic and thermodynamically consistent. Contrarily to the BN model that involves 6 wave speeds, the new formulation involves 4 waves only, in agreement with the Marble model [Marble, F. E., “Dynamics of a gas containing small solid particles,” Combustion and Propulsion (5th AGARD Colloquium) (Pergamon Press, 1963), Vol. 175] based on pressureless Euler equations for the dispersed phase, a well-accepted model for low particle volume concentrations. In the new model, the presence of pressure in the momentum equation of the particles and consideration of volume fractions in the two phases render the model valid for large particle concentrations. A symmetric version of the new model is derived as well for liquids containing gas bubbles. This model version involves 4 characteristic wave speeds as well, but with different velocities. Last, the two sub-models with 4 waves are combined in a unique formulation, valid for the full range of volume fractions. It involves the same 6 wave speeds as the BN model, but at a given point of space, 4 waves only emerge, depending on the local volume fractions. The non-linear pressure waves propagate only in the phase with dominant volume fraction. The new model is tested numerically on various test problems ranging from separated phases in a shock tube to shock–particle cloud interaction. Its predictions are compared to BN and Marble models as well as against experimental data showing clear improvements.

Effective permittivity of nanocomposites from 3D charge transport simulations

ABSTRACTThe effective permittivity and stored energy in nanocomposites incorporating dielectric and conducting nanofillers are computed by simulating bipolar charge injection, transport, attachment, and recombination through amorphous polymer using a self‐consistent 3D particle‐in‐cell model with nanofillers treated as extensions to the classical electrical double layer. Effective permittivities computed using an energy conserving scheme is shown to have excellent agreement with the Lichtenecker, Bruggeman, and Maxwell‐Garnett mixing rules especially at low volume fraction, low permittivity contrast, and small Clausius‐Mossotti factor, and lie well within the Wiener bounds. The energy conserving scheme with Maxwell‐Garnett E field interpolation combines the best of the Maxwell‐Garnett and fundamental Lichtenecker rules and results in broad validity over the entire volume fraction range. Computed stored energies show monotonic increase with dielectric fillers and a peak at 25 vol % for conducting fillers, attributed to the competing effects of higher energy with increasing E field modification and lower energy with decreasing binder volume. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 43300.

Analytical expressions for effective thermal conductivity of composite materials with inclusions of square cross-section

Thermal conductivity of composite materials with periodically distributed cylindrical inclusions of square cross-section is investigated. Analytical interpolation formula for the effective thermal conductivity in transversal direction valid in the entire range of volume fraction of inclusions and value of their thermal conductivity is derived. The methods of asymptotic homogenization, boundary shape perturbation and asymptotically equivalent functions are used. Asymptotic expansions of the effective thermal conductivity in limiting cases of size of inclusions and their thermal conductivity are obtained. The analytical expressions are evaluated numerically and compared to other models. It is shown that the discrepancy between these results is very low in all cases.

Analysis of the effective conductivity of composite materials in the entire range of volume fractions of inclusions up to the percolation threshold

The analytical interpolation formulas for the effective electrical conductivity of fiber-reinforced and particulate composites for any volume fractions of inclusions are derived in the present paper. The Garnett formulas are used for a limiting case of small volume fractions of inclusions. And the formulas based on the Shklovskii–De Gennes model are adopted for a limiting case of large volume fractions of inclusions approaching the percolation threshold. The derivation is based on application of the method of asymptotically equivalent functions. This approach presents a natural generalization of the two-point Padé approximants to the case, when in one of the limits the interpolated function cannot be represented in the form of power series. The application of this interpolation technique made it possible to derive the formulas for the effective conductivity of fiber-reinforced and particulate composites with very high volume fractions of inclusions, up to the percolation threshold. The numerical results are compared with the known asymptotic expressions, and also with the existing exact expressions in some limiting cases, for example, in the case of statistically equivalent arrangement of the constituent materials. Comparison with the experimental data confirms the satisfactory accuracy of the obtained analytical results.

Cooperative and synergistic solvent effects in SET‐LRP of MA

AbstractSET‐LRP requires a combination of ligand and solvent that mediates the disproportionation of Cu(I)X into Cu(0) activator, and Cu(II) deactivator. The solvent also modulates the kinetics of the reaction. More polar solvents, including mixtures of water and organic solvents enhance the rate of polymerization in accord with the Dimroth‐Reichardt parameter. Here, it is demonstrated that a similar effect is observed in binary mixtures of organic solvents, wherein the addition of a more polar solvent to a less polar solvent provides a linear increase in the apparent rate constant of propagation, k. However, this linear relationship does not hold for the entire range of volume fraction for binary mixtures when ethylene carbonate (EC) or MeOH are one of the two components. Results herein, suggest that the kinetics of SET‐LRP in these solvent mixtures is cooperatively and synergistically determined by polarity, degree of disproportionation, and also by another parameter related to the ability of the solvent to stabilize colloidal Cu(0) and determine its particle size. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5591–5605, 2009

Diffusion in Cytoplasm: Effects of Excluded Volume Due to Internal Membranes and Cytoskeletal Structures

The intricate geometry of cytoskeletal networks and internal membranes causes the space available for diffusion in cytoplasm to be convoluted, thereby affecting macromolecule diffusivity. We present a first systematic computational study of this effect by approximating intracellular structures as mixtures of random overlapping obstacles of various shapes. Effective diffusion coefficients are computed using a fast homogenization technique. It is found that a simple two-parameter power law provides a remarkably accurate description of effective diffusion over the entire range of volume fractions and for any given composition of structures. This universality allows for fast computation of diffusion coefficients, once the obstacle shapes and volume fractions are specified. We demonstrate that the excluded volume effect alone can account for a four-to-sixfold reduction in diffusive transport in cells, relative to diffusion in vitro. The study lays the foundation for an accurate coarse-grain formulation that would account for cytoplasm heterogeneity on a micron scale and binding of tracers to intracellular structures.

Prediction of Effective Permittivity of Diphasic Dielectrics as a Function of Frequency

An analytical model based on an equivalent impedance circuit for effective permittivity of a composite dielectric as a function of frequency with complex-shaped inclusions is presented. The geometry of the capacitor containing this composite dielectric is discretized into partial impedance elements, the total equivalent impedance is calculated, and the effective permittivity of the composite dielectric is obtained from this equivalent impedance. An example application using this method is given for an individual cell of a diphasic dielectric consisting of a high-permittivity spherical inclusion enclosed in a low-permittivity parallelepiped. The capacitance and resistance for individual discretized elements in the composite cell are modeled as a function of an inclusion radius. The proposed approach is then extended to a periodic three-dimensional structure comprised of multiple individual cells. The equivalent impedance model is valid for both static and alternating applied electric fields, over the entire range of volume fraction of inclusions. The equivalent impedance model has a few advantages over existing effective medium theories, including no limitations on the shape of inclusions or their separation distance.

Excess molar volumes and ultrasonic studies of N-methyl-2-pyrrolidone with ketones at T=303.15K

Excess molar volumes (VE) and ultrasonic studies at T = 303.15 K and atmospheric pressure have been measured over the whole composition range for the binary mixtures of N-methyl-2-pyrrolidone (NMP) with ketones. The ketones studied in the present investigation include methyl ethyl ketone (MEK), diethylketone (DEK), methyl propyl ketone (MPK), methyl isobutyl ketone (MIBK), and cyclohexanone (CH). The VE values were measured using a dilatometer and were negative over the entire mole fraction range for NMP with MEK, DEK, MPK, and MIBK and were positive for NMP with CH. The ultrasonic sound velocities for the above systems were measured with a single crystal interferometer at a frequency of 3 MHz. The sound velocity (u) results have been used to calculate isentropic compressibility (Ks) and deviation in isentropic compressibility (ΔKs) over the entire range of volume fraction. The sound velocity results have been predicted in terms of free length theory (FLT), collision factor theory (CFT), and Nomoto relation. The results reveal that all the theories gave a satisfactory estimate of the sound velocity. The deviation values of the isentropic compressibilities (ΔKs) were negative over the entire range of volume fraction in all the binary liquid mixtures except in the binary system NMP with CH, where we observed positive ΔKs values. The results are interpreted on possible molecular interactions between components.

Excess molar volumes and ultrasonic studies of dimethylsulphoxide with ketones at T = 303.15 K

Excess molar volumes ( V E) and ultrasonic sound velocities at T = 303.15 K and ambient pressure have been measured as a function of composition for the binary liquid mixtures of dimethylsulphoxide (DMSO) with ketones. The ketones studied in the present investigation include ethyl methyl ketone (EMK), diethylketone (DEK), methyl propyl ketone (MPK), methyl isobutyl ketone (MIBK), and cyclohexanone (CH). The V E values were measured using a dilatometer and were positive over the entire mole fraction range for all systems except in the binary system DMSO with EMK where the V E exhibits an inversion in sign. The experimental V E values have been correlated using Redlich–Kister and Hwang et al. equations. The ultrasonic sound velocities for the above systems have been measured with a single crystal interferometer at a frequency of 3 MHz. The sound velocity ( u) data have been used to calculate isentropic compressibility ( K s) and deviation in isentropic compressibility (Δ K s) over the entire range of volume fraction. The sound velocity data have been predicted in terms of free length theory (FLT), collision factor theory (CFT), and Nomoto relation. The results reveal that all the theories gave a satisfactory estimate of the sound velocity. The deviations in values of isentropic compressibility (Δ K s) were negative over the entire range of volume fraction in all the binary liquid mixtures. The results are interpreted with respect to possible molecular interactions between components.

Yielding Behavior of Thermo-reversible Colloidal Gels

The breakdown of structure in gelled suspensions due to the application of an external stress results in flow. Here we explore the onset of flow by investigating the onset of nonlinear behavior in the elastic moduli of a widely studied class of thermo-reversible gels over a range of volume fractions. We employ the system composed of octadecyl-coated silica particles (radius = 24 nm) suspended in decalin that displays a transition from a liquid to a gel below a volume-fraction-dependent gel temperature, Tgel. The perturbative yield stress at which the gel modulus drops to 90% of its value in the linear viscoelastic limit is found to increase monotonically with volume fraction and decreasing temperature. The recently proposed activated barrier-hopping theory of Schweizer and co-workers1,2 presents a framework to capture the impact of external forces on the mechanical properties of structurally arrested systems. By characterizing particle interactions with a Yukawa potential and employing the resultant static structure factor as input into the activated barrier-hopping theory, we make predictions for how the elastic modulus evolves with the applied stress. Comparisons of these calculations with experiments reveal that the theory does an excellent job of quantitatively capturing the perturbative yield stresses over the entire range of volume fractions and temperatures explored in the study. The match of predictions with experimental results suggests that the theory not only captures particle localization but also how this localization is modulated in the presence of an external stress.

Density and Speed of Sound of Binary Mixtures of N-Methylacetamide with Ethyl Acetate, Ethyl Chloroacetate, and Ethyl Cyanoacetate in the Temperature Interval (303.15 to 318.15) K

The excess isentropic compressibilities are computed by measuring the density and speed of sound of binary mixtures of N-methylacetamide with ethyl acetate, ethyl chloroacetate, and ethyl cyanoacetate over the entire range of volume fraction in the temperature range of (303.15 to 318.15) K. The experimental results are fitted to a Redlich−Kister type polynomial equation. Estimated coefficients and standard deviation values are also presented.

Volumetric, Ultrasonic and Transport Properties of Binary Liquid Mixtures Containing Dimethyl Formamide at 303.15 K

AbstractExcess volumes (VE), ultrasonic velocities (u), isentropic compressibility (ΔKs) and viscosities (η) for the binary mixtures of dimethyl formamide (DMF) with 1,2‐dichlorobenzene, 1,3‐dichlorobenzene, 1,2,4‐trichlorobenzene, o‐chlorotoluene, m‐chlorotoluene, p‐chlorotoluene, o‐nitrotoluene and m‐nitrotoluene at 303.15 K were studied. Excess volume data exhibit an inversion in sign for the mixtures of dimethyl formamide with 1,2‐ and 1,3‐dichlorobenzenes and the property is completely positive over the entire composition range for the mixtures of dimethyl formamide with 1,2,4‐trichlorobenzene, o‐nitrotoluene and m‐nitrotoluene. On the other hand, the quantity is negative for the mixtures of dimethyl formamide with chlorotoluenes. Isentropic compressibility (Ks) has been computed for the same systems from precise sound velocity and density data. Further, deviation of isentropic compressibility (ΔKs) from ideal behavior was also calculated. ΔKs values are negative over the entire volume fraction range in all the binary mixtures. The experimental sound velocity data were analysed in terms of Free Length Theory (FLT) and Collision Factor Theory (CFT). The viscosity data were analysed on the basis of corresponding state approach. The measured data were discussed on the basis of intermolecular interactions between unlike molecules.

Mechanisms of steady-shear rheology in polymer-nanoparticle composites

We use coarse-grained computer simulations to delineate the mechanisms governing the steady-shear rheology of polymer-nanoparticle composites. Our studies specifically focus on the regimes where the particle sizes and the interparticle distances become comparable to the polymer sizes and where the interactions between polymer and particles become relevant in influencing the dynamical characteristics. Our results suggest the shear rheology of the composite is very similar to that of colloidal suspensions in a simple fluid when polymer rheology, the particle-induced changes in the polymer rheology and the polymer slip effects are accounted. At dilute and semidilute nanoparticle concentrations, the composite shear rheology is shown to be dominated by the shear thinning of the polymer chains which in turn is modified by the presence of the particles. For higher particle loads, the polymeric contribution to the rheology becomes much less important and the shear rheology is dominated by the particles stresses. Using our results we suggest how a simple empirical model can be constructed for the shear rheology of the composite over the entire range of volume fractions. Our results and mechanistic explanations are in very good agreement with associated experimental observations.