Dielectric properties of a mixture of dipolar hard spheres

A theory for the dielectric constant, ε, of a fluid mixture of dipolar hard spheres is formulated by generalizing the methods developed by Ramshaw and Wertheim for the pure fluid case. The resulting expression for ε depends on the pair distribution functions, g _αβ(r ₁, θ₁, r ₂, θ₂) for a dipolar mixture. Due to the unavailability of exact representations for these dipolar pair distribution functions, the results of the mean spherical approximation are employed in the formalism developed. Numerical results are given for ε as calculated from the pair distribution functions for a spherical volume of macroscopic dimensions. The compositional dependence of the ε obtained in this way for a specific mixture is compared with the corresponding properties of the well established theories of Clausius-Mossotti-Debye and Onsager. In addition, the relative importance of the dipole moment and size of the hard sphere parameters in determining ε for a dipolar mixture (the correlative behaviour of which is described by the mean spherical approximation) is evaluated. It is found that the differences in hard core diameters can be largely ignored, in that ε for an ‘effective’ single component fluid can be given to within 2–5 per cent relative error (at worst) of the mean spherical approximation's result. Such an ‘effective pure fluid’ is described as having the same polarization content as the actual mixture being considered. Thereby, the properties of the effective fluid are determined by the quantity y = 4πβ(m ₁ ² ρ₁ + m ₂ ² ρ₂)/9 where m_i and ρ _i are the dipole moment and number density of component i in the binary mixture, with β = (kT)^-1.     

Corresponding states principle for newtonian viscosities-temperature effects

In the first part of the paper a superposition method for the polymer solution zero shear rate viscosity η_o as a function of concentration c is reviewed. The method was successful in numerous systems, but it partially failed in four, the worst case being polyisobutene in isooctane, where data were available over the full concentration range and molecular weights (MW) ranged from 900 to 2.5 × 10⁶. It was postulated that the possible cause for this is either MW dependence of T_g which would result in a faster than expected increase in η_o for higher MW samples, or a difference in flow mechanism between the solutions at low and high concentration. In the second part, a new theory for the temperature effect on η_o is proposed. The theory permits linearization of η_o (T) results both for small molecules and for polymeric liquids. In systems where a transition occurs, the linearized plot shows a sharp break. The theory was extended to the concentration dependence of the polymer solution viscosity.

It permits linearization of η_o (c) data, compensates for the MW dependence of T_g, and allows detection of transition points. The theory was tested on solutions of polyisobutene and polydimethyl-siloxane. In both cases, the data were superimposed on a single master curve.     

“Magic Relation” Between the Structures of Coexisting Phases at a First-Order Phase Transition in a Hard Sphere System

In the statistical geometry of a hard sphere system of any number of dimensions, V _o and S _o, the so-called available space and the area of the interface between the available and unavailable space, respectively, can be used as surrogates for chemical potential and pressure. It is shown exactly that, if a first-order transition occurs, the relation dV _o/dS _o=–/2D, where is the diameter of a sphere and D is the dimensionality of the system, must hold for densities in the phase coexistence region. This relation is remarkable in that –/2D is the ratio of the volume to the surface area of a sphere. Also, it is shown that it is possible for the system to have two successive first-order transitions, but that the occurrence of a continuous transition (even in two dimensions) is unlikely. It is argued that this unlikelihood is substantially strengthened by the absence of temperature (except as a trivial factor) as a variable in hard-sphere systems. This suggests that the findings of the KTHNY theory, recent simulations, and colloid experiments (specialized to sticky hard disks) can be extended to true hard disks. The fundamental physics underlying the magic relation is yet to be exposed. The author continues to search for the underlying reason and hopes that the present paper will stimulate others to join the search.     

Study of gold nanocluster sputtering under 38-keV Au ion bombardment by a classical molecular dynamics method

The computer simulation of the interaction of 38-keV Au₁ ions with isolated spherical Au _N nanoclusters of diameters 2.6 and 18 nm is performed in the framework of the classical molecular dynamics (MD) method. The distribution of the absorbed energy ε per one atom of the irradiated cluster and the sputtering yields are analyzed for different ratios of the nanocluster diameter D to the average projective range R _p of the bombarding ion. It is established that the small values of the absorbed energy (ε ? ε_max = E/N) are most probable for D < R _p, and either small (ε ? ε_max) or the maximum possible (ε ～ ε_max) values are mainly realized for D ≤ R _p. It is shown that the total sputtering yield depends weakly on the impact parameter. It is demonstrated for the first time that the irradiated cluster, as a whole, can be ejected by direct impact with a probability of approximately 6–13%. Such events are realized in the cases where the bombarding ion causes secondary cluster-atom emission in the dominant direction to a substrate, with the result that an unsputtered cluster fraction acquires momentum in the opposite direction. This recoil effect can be one of the mechanisms for desorption of nanoclusters deposited on the surface under ion (or cluster) bombardment.     

Excess molar volumes, viscosities, and refractive indices for binary and ternary mixtures of {cyclohexanone (1) + N,N-dimethylacetamide (2) + N,N-diethylethanolamine (3)} at (298.15, 308.15, and 318.15) K

Densities ρ, viscosities η, and refractive indices n_D, of the binary and ternary mixtures formed by cyclohexanone + N,N-dimethylacetamide + N,N-diethylethanolamine were measured at (298.15, 308.15, and 318.15) K for the liquid region and at ambient pressure for the whole composition ranges. The excess molar volumes V_m^E, viscosity deviations Δη, and refractive index deviations Δn_D, were calculated from experimental densities and refractive indices. The excess molar volumes are positive over the mole fraction range for binary mixtures of cyclohexanone(1) + N,N-dimethylacetamide (2) and N,N-dimethylactamide (2) + N,N-diethylethanolamine (3) and increase with increasing temperatures from (298.15 to 318.15) K. The excess molar volumes of cyclohexanone (1) + N,N-diethylethanolamine (3) are S-shaped dependence on composition with negative values in the N,N-diethylethanolamine rich-region and positive values at the opposite extreme and increase with increasing temperatures from (298.15 to 318.15) K. The excess molar volumes are positive over the whole mole fraction ranges for the ternary mixtures at all temperatures. Viscosity deviations are negative over the mole fraction range for all binary and ternary mixtures and decrease with increasing temperatures from (298.15 to 318.15) K. Refractive index deviations are negative over the mole fraction range for all binary and ternary mixtures and increase with increasing temperatures from (298.15 to 318.15) K. The experimental data of constitute were correlated as a function of the mole fraction by using the Redlich–Kister equation for binary and , Cibulka, Jasinski and Malanowski , Singe et al., Pintos et al., Calvo et al., Kohler, and Jacob–Fitzner for ternary mixture, respectively. McAllister^'s three body, Hind, and Nissan–Grunberg models were used for correlating the kinematic and dynamic viscosity of binary mixtures. The experimental data of the constitute binaries are analyzed to discuss the nature and strength of intermolecular interactions in these mixtures.     

Depletion effects and gelation in a binary hard-sphere fluid

A study of the binary hard-sphere fluid with size ratio [sgrave]_B/[sgrave]_A = 0.1 is reported. Molecular dynamics and Monte Carlo simulations have been carried out over the mole fraction (x _A) range 0.002-0.1 and over the high density range where several recent authors have predicted a thermodynamic demising transition on the basis of integral equations. In this region, there is no evidence of such first-order thermodynamic phase separation, or two fluid phases. The effect of the depletion force, arising from the entropic exclusion of B spheres from between two A spheres, as x _B is increased at constant packing fraction y _A, is to cause a large increase in the partial pressure of A and the radial distribution function of A at contact, a reduction on the mobility of A, and eventually, at a sufficient x _B, the gelation of component A to an open, low coordination, amorphous structure. This gelation transition of A shows discontinuities similar to a glass transition; it can be traced back to the hard sphere glass formation as x _B approaches zero. Thermodynamic properties are reported over the range studied, and used to evaluate the predictions of current theories and the accuracy of equations of state. The Boublik—Mansoori—Carnahan—Starling—Leland equation is found to be remarkably accurate in this region, over the whole fluid range, but shows systematic deviations at high packing densities.     

Equations of state for the hard disk fluids

By using the published accurate new virial coefficients B₁₁～B₁₄ for the hard disk fluids [C. Zhang and B.M. Pettitt, Mol. Phys., 2014, 112, 1427], we here propose a new updated version of Tian-Gui-Mulero equation of state [J.X. Tian, Y.X. Gui and A. Mulero, Phys. Chem. Chem. Phys., 2010, 12, 13597]. Compared with other proposals, the new version stands strongly to be the only which can reproduce the known virial coefficients B₂～B₁₃ at the same time that can describe the relation of the compressibility factor versus the packing fraction for the hard disk fluids with high accuracy.     

A model for viscosity coefficients of gases with potentials differing in form

A recent theory of non-conformal interactions has been very succesful in providing effective spherical potentials for the pressure of more than 40 real gases and many of their binary mixtures. Here, this theory is applied to deal with low-density viscosity coefficients. In its simplest form, the approximate non-conformal (ANC) theory introduces, besides the usual corresponding states parameters-energy ? and distance r_m-a softness parameter s to account for the form of a particular potential function. We investigate the effects of the potential form on the temperature behaviour of the viscosisty coefficient η. It is shown that the softer potentials, with wider attractive wells, have larger viscosities and an explicit expression for η (T, ?, r_m, s) is obtained. The ANC potentials are tested in their capacity to reproduce the temperature dependence of η for the heavier noble gases (Ar, Kr and Xe), diatomics (H₂, N₂, O₂ and CI₂) and a dozen small polyatomics. It is found that the ANC model η (T, ?, r_m, s), with only three substance-dependent parameters, reproduces experimental 7 data within their estimated error.     

Influences of initial velocity, diameter and Reynolds number on a circular turbulent air/air jet

This paper assesses the suitability of the inflow Reynolds number defined by Re_o ≡ U_oD/ν (here U_o and D are respectively the initial jet velocity and diameter while ν is kinematic viscosity) for a round air/air jet. Specifically an experimental investigation is performed for the influences of U_o, D and Re_o on the mean-velocity decay and spread coefficients (K_u, K_r) in the far field of a circular air jet into air from a smoothly contracting nozzle. Present measurements agree well with those previously obtained under similar inflow conditions. The relations K_u ∝ U_o and K_r ∝ 1/U_o for U_o < 5 m/s appear to work, while each coefficient approaches asymptotically to a constant for U_o > 6 m/s, regardless of the magnitudes of Re_o and D. It is revealed that Re_o may not be an appropriate dimensionless parameter to characterize the entire flow of a free air/air jet. This paper is the first paper that has challenged the suitability of Re_o for turbulent free jets.     

The pressure of a hard sphere fluid on a curved surface

Utilizing the integral equation approach to the hard sphere fluid system developed in the preceding paper, the hard sphere-hard wall interaction is studied. For the case of a flat wall, perturbation solutions of the integral equation valid to second and third order in the packing fraction,y, are derived. For a surface of arbitrary curvature, an equation of state valid to second order in the packing fraction is also derived. When applied to very small cavities, it is found that the pressure at high densities is significantly higher than it would be for a flat wall.     

In-medium properties of nucleon resonances

Recent experimental results for the in-medium properties of nucleon resonances are discussed. The experiments were done with the TAPS detector at the tagged photon beam of the MAMI accelerator in Mainz. Measured was the photoproduction of mesons (final states π⁰X, ηX, 2π⁰X and π⁰π^±X) from the nuclei ¹²C, ⁴⁰Ca, ⁹³Nb and ²⁰⁸Pb up to the second resonance region. The results were analyzed in view of the in-medium properties of the P₃₃(1232), the D₁₃(1520), and the S₁₁(1535) resonances.     

Permeability of mixed soft and hard granular material: Hydrogels as drainage modifiers

We measure the flow of water through mixed packings of glass spheres and soft swellable hydrogel grains, at constant sample volume. Permeability values are obtained at constant sample volume and at porosities smaller than random close packing, for different glass bead diameters D and for variable gel grain diameter d, as controlled by the salinity of the water. The gel content is also varied. We find that the permeability decays exponentially in n(D/d ) ^b , where n = N _gel/N _glass is the gel to glass bead number ratio and b is approximately 3. Therefore, flow properties are determined by the volume fraction of gel beads. A simple model based on the porosity of overlapping spheres is used to account for these observations.     

Phase coexistence and interface structure of a two-component Lennard-Jones fluid in porous media: application of Born—Green—Yvon equation

The Born-Green-Yvon equation with smoothed density approximation is used to calculate the liquid-liquid density profiles of a symmetric Lennard-Jones fluid in a hard sphere disordered matrix. The phase diagrams are evaluated for model systems characterized by different matrix densities and compared with the results of theoretical predictions and the Monte Carlo simulations of Gordon, P. A., and Glandt, E. D., 1996, J. chem. Phys., 105, 4257. It was found that increasing the matrix packing fraction reduces the magnitude of the miscibility gap and smooths the density profiles between two coexisting phases.     

Influence of isotopic substitution on the diffusion and thermal diffusion coefficient of binary liquids

The mutual mass diffusion coefficient (D) and the thermal diffusion coefficient ( D _T) of the liquids acetone, benzene, benzene-d ₁, benzene-d ₃, benzene-d ₅, benzene-d ₆, benzene- ¹³C₆, n-hexane, toluene, 1, 2, 3, 4-tetrahydronaphtalene, isobutylbenzene, and 1, 6-dibromohexane in protonated and perdeuterated cyclohexane have been measured with a transient holographic grating technique at a temperature of 25 ^°C. The mass diffusion coefficient shows a pronounced concentration dependence. Perdeuteration of cyclohexane only leads to marginal changes of the mass diffusion coefficient. The Stokes-Einstein equation describes the limiting tracer diffusion coefficients well if the solute molecule is smaller than the solvent. It is not capable to describe the small isotope effect of a few percent. On the other hand, the isotope effect, which is independent of concentration, is in agreement with the Enskog theory, that does not provide the absolute value of the mass diffusion coefficient of the liquid mixtures. The thermal diffusion coefficient of all the binary mixtures shows a moderate and almost linear concentration dependence. Its isotope effect, which is the change of D _T upon deuteration of cyclohexane, varies with mole fraction. The thermophoretic force acting on any tracer molecule in cyclohexane changes by the same amount when cyclohexane is perdeuterated, irrespective of the magnitude of the thermophoretic force before deuteration. This change of the thermophoretic force is equal but of opposite sign to the difference between the thermophoretic forces acting on cyclohexane and perdeuterated cyclohexane as tracers in any of the above liquids.     

Incorporation of deep centres in VPE GaAs

The incorporation of deep levels in high purity vapour phase epitaxy (VPE) GaAs is studied as a function of the crystal growth conditions. Two deep levels, at 0.4 eV and 0.75 eV above the valence band, are investigated using photocapacitance. It is shown that their concentrations are always equal and vary together as a function of the AsCl₃ mole fractionX. Two regimes are observed, respectively, characterized by different variations of the total deep level concentrationN _T:N _TαX for lowX, andN _TαX⁻² for highX. In this last range,N _T andN _D are found to vary similarly. This work has been supported by the DRME.     

Pressure and temperature dependence of the structure of liquid Sn up to 5.3 GPa and 1373 K

Pressure and temperature dependence of the structure of liquid Sn has been measured up to 5.3?GPa and 1373?K using multi-angle energy-dispersive X-ray diffraction in Paris–Edinburgh cell. Under nearly isobar condition at ～1?GPa, liquid Sn displays a normal behavior with gradual structural changes with temperature up to 1373?K. Under isothermal compressions at 850 and 1373?K, however, the structure factors of liquid Sn both show a turn-over at ～3?GPa in the height of the first diffraction peak. According to the hard sphere cluster model, the structure of liquid Sn may be viewed as two different types of clusters. Below ～3?GPa, it is shown that the packing fraction of the dominant cluster (occupying ～0.94 fraction) changes with compression, while above ～3?GPa, the packing fractions and the hard sphere diameters of both clusters start to influence the structure, causing significant changes with increasing pressure. Our results suggest that the compression behavior of liquid Sn changes from localized densification only in one cluster below ～3?GPa to homogeneous structural changes in both clusters above ～3?GPa.     

Theoretical optimization of metalp–n silicon Schottky barrier solar cell

The theoretical optimization of the design parametersN _A ,N _D andW _P has been done for efficient operation of Au-p-n Si solar cell including thermionic field emission, dependence of lifetime and mobility on impurity concentrations, dependence of absorption coefficient on wavelength, variation of barrier height and hence the optimum thickness ofp region with illumination. The optimized design parametersN _D =5×10²⁰ m⁻³,N _A =3×10²⁴ m⁻³ andW _P =11.8 nm yield efficiencyη=17.1% (AM0) andη=19.6% (AM1). These are reduced to 14.9% and 17.1% respectively if the metal layer series resistance and transmittance with ZnS antireflection coating are included. A practical value ofW _P =97.0 nm gives an efficiency of 12.2% (AM1).