非均匀介质球颗粒的等效介电常量

从求解拉普拉斯方程的边值问题出发,讨论了非均匀介质球颗粒的等效介电常量,给出了多种介质组成的多壳层介质球颗粒的等效介电常量的一般递推公式,推导了壳层的介电常量随半径连续变化的梯度介质球的等效介电常量的微分方程．并以壳层的介电常量为幂函数为例,得到了梯度壳层介质球的等效介电常量．     

Dielectric behaviour of ketone-amine binary mixtures at microwave frequencies

Values of dielectric constant (ε′) and loss factor (ε″) have been experimentally determined for binary liquid mixtures of ethyl methyl ketone+ethylenediamine and methyl isobutyl ketone+ethylenediamine at 9.44 GHz microwave frequencies at 30°C. The values ofε′ andε″ have been used to evaluate the molar polarization, apparent polarization and the excess permittivities. Excess refractive index, viscosity and activation energy of viscous flow have also been estimated. These parameters have been used to explain the formation of 1:1 complexes for both the systems.     

Molecular dynamics results for the radial distribution functions of highly asymmetric hard sphere mixtures

Molecular dynamics (MD) results for the radial distribution functions of mixtures of large and small hard spheres are reported for size ratios whose (large/small) values are 1, 2.5, 5, 7.5, and 10 in the region where the concentration of the large spheres is very small. The MD contact values of these functions are compared with formulae due to Boublik, Mansoori, Carnahan, Starling, Leland, Grundke, and Henderson, Viduna and Smith, Henderson, Trokhymchuk, Woodcock, and Chan, as well as new formulae that are considered here. The new formulae give good agreement for the large–small contact values and reasonably good agreement for the large–large contact values. The Viduna–Smith formula is satisfactory for the small–small contact value and quite reasonable for the small–large contact value. Undoubtedly, further improvements are possible. These results give insight into what may be called the colloidal limit, where the size ratio is exceedingly large while the concentration of the large spheres is exceedingly small, and into the passage to this limit.     

Explicit solution of the mean spherical model for ions and dipoles

It is shown that the solution of the mean spherical approximation for the ion-dipole mixtures obtained by Blum, Adelman, and Deutch has an explicit closed form solution which is one of the roots of a cubic equation.     

Heat capacities of the dipolar Yukawa model polar fluid

The Stockmayer fluid is often used to describe a polar fluid. The dipolar Yukawa (DY) fluid is also a useful model for such fluids and is convenient for theoretical applications. Here we use the mean spherical approximation (MSA) and perturbation theory (PT) to study the heat capacities of the DY fluid model of a polar fluid and compare these results with Monte Carlo simulations for this model polar fluid. We find that the DY fluid shows the same features as the Stockmayer fluid does; demonstrating the utility of the DY fluid and further finding that the MSA and PT approaches give reasonably accurate results for the heat capacity.     

A solution of the multiple-binding mean spherical approximation for ionic mixtures

The mean spherical approximation (MSA) for an arbitrary mixture of charged hard spheres with saturating bonds is solved in the Wertheim formalism. Any number of bonds is allowed. It is shown that the general solution is given in terms of a screening MSA-like parameter ^T , a cross-interaction parameter that will depend on the binding association equations, the set of binding association fractions, and an additional algebraic equation. The equation for ^T is given for the general case. The equation for , however, depends strongly on the particular closure that is used to compute the contact pair correlation function. The full solution requires, as in the dimer case recently solved by Blum and Bernard, solvingm+2 equations and additionally the inversion of a matrix of size [(–1)m] for a system withm components and bonds. We recall that when =1, only dimers are allowed; for =2, only linear chains are formed: and when 3, branching of the polymers occurs. It can be shown that the excess entropy for the polymer case is as before,S ^MSA=( ^T )³/3 + sticky terms, where the sticky terms depend on the model and will be given in future work.     

Contact values of highly asymmetric hard sphere mixtures from Fundamental Measure Density Functional Theory

The White Bear version of Fundamental Measure Theory (FMT-WB) has been tested in binary mixtures of hard spheres in the vicinity of the colloidal limit, where the size ratio of the two species is exceedingly large and the large sphere mole fraction is infinitely low. Contact values of large–large sphere radial distribution functions have been calculated and compared with molecular dynamics simulations and previously proposed theoretical formulas. In contrast to the failure of BMCSL (Boublik, Mansoori, Carnahan, Starling, Leland equation of state) predictions, FMT-WB gives good agreement with simulation for a range of species size ratios and mole fractions. The performance of BMCSL is qualitatively related to one of its model parameters, which could indicate the reliability of the BMCSL result. Our results confirm the accuracy of FMT-WB in the colloidal limit for the first time and suggest that BMCSL contact values must be applied carefully to account for chain connectivity when studying certain cases with classical Density Functional Theories.     

Frequency-independent rules for the dielectric susceptibility derived from two forms of self-similar dynamical behavior of dipolar systems

This paper provides the frequency domain analysis of the probabilistic representation of the cluster model for dielectric relaxation in dipolar systems. It is proved that the restriction (0.1) experimentally found for both the powerlaw coefficientsn andm is the necassary and sufficient condition to obtain the low- and high-frequency power-law behavior. Consequently, in both frequency regions the Kramers-Krönig-compatible frequency-independent rules are fulfilled. Moreover, in contrast to the empirical functions proposed to fit the experimental data, the dielectric susceptibility derived from the stochastioc considerations does cover the full range of the observed dielectric responses.     

Chain length effect on dynamical structure of poly (vinyl pyrrolidone)-polar solvent mixtures in dilute solution of dioxane studied by microwave dielectric relaxation measurement

Dielectric relaxation study of the binary mixtures of poly(vinyl pyrrolidone) (PVP) (Mw=24000, 40000 and 360000 g mol⁻¹) with ethyl alcohol (EA) and poly(ethylene glycol)s (PEGs) (Mw=200 and 400 g mol⁻¹) in dilute solutions of dioxane were carried out at 10.1 GHz and 35°C. The relaxation time of PVP-EA mixtures was interpreted by the consideration of a wait-and-switch model in the local structure of self-associated ethyl alcohol molecules and also the PVP chain length as a geometric constraint for the reorientational motion of ethyl alcohol molecules. The formation of complexes and effect of PVP chain length on the molecular dynamics, chain flexibility and stretching of PEG molecules in PVP-PEG mixtures were explored from the comparative values of dielectric relaxation time. Further, relaxation time values in dioxane and benzene solvent confirm the viscosity independent molecular dynamics in PVP-EA mixtures but the values vary significantly with the non-polar solvent environment.     

Adsorption of dipolar hard spheres onto a smooth,hard wall in the presence of an electric field

Integral equations have been solved for the density profile of dipolar hard spheres against a hard, smooth wall in the presence of an electric field. This density profile was examined as a function of the bulk medium's temperature and density with different field strengths and field directions. It was found to depend primarily upon the competitive interactions of the field with the monolayer particles and the first outer shell with the monolayer particles.Supported by the ARGC.     

Normal modes and quality factors of spherical dielectric resonators: I — shielded dielectric sphere

Electromagnetic theoretic analysis of shielded homogeneous and isotropic dielectric spheres has been made. Characteristic equations for the TE and TM modes have been derived. Dielectric spheres of radii of the order of μm size are found suitable for the optical frequency region whereas for the microwave region radii of the order of mm size are found suitable. Parameters suitable for their application in the optical and microwave frequency ranges have been used to compute the frequencies corresponding to the normal modes for the TE and TM modes. Expressions for the quality factors for realistic resonators, i.e., for a dielectric sphere with a non-zero conductivity and a metal shield with a finite conductivity have also been derived for the TE and TM modes. Computations of the quality factors have been made for resonators with parameters suitable for the optical and the microwave regions.     

Investigations of polymer dynamics in nanoporous media by field cycling NMR relaxometry and the dipolar correlation effect

The chain dynamics of short-chain perfluoropolyether melts confined in Vycor nanoporous media has been characterized by field cycling nuclear magnetic resonance relaxometry and the dipolar correlation effect. The slowdown of motions under confinement, leading to larger residual dipolar couplings, has been probed by looking at the quotient of stimulated and primary echoes. Using field cycling relaxometry, it has been shown that there is strong evidence of reptation-like motion, even for such short-chain polymers as shown by the frequency and molecular weight dependences of the spin-lattice relaxation time.     

Orientational structure of dipolar hard spheres near a hard neutral wall

Spherical boundaries are used in a Monte Carlo simulation to calculate the angular structure of dipolar hard spheres near a neutral hard wall.     

Further property of Lennard-Jones fluid: Thermal conductivity

In this paper, we calculate the thermal conductivity of noble gases, methane, and three noble gas mixtures including He+Kr, He+Xe, and Kr+Xe assuming they obey Lennard-Jones (LJ) (12-6) model potential. One of the required quantities to calculate the thermal conductivity of these systems is the pair correlation function. Therefore, we solve numerically the Ornstein-Zernike (OZ) integral equation using the mean spherical approximation (MSA) to obtain the pair correlation functions. We use these functions to obtain the thermal conductivity, then compare our results with the available data. According to the results obtained from the present work for pure and mixtures of LJ fluids reveals that the integral equations method is suitable for predicting the thermal conductivity of this class of fluid.     

Evolution of solid state systems containing mutually coupled dipolar and quadrupole spins: perturbation treatment

Perturbation approach to time evolution of multi-spin systems containing quadrupole and dipolar spins has been presented and discussed. The treatment comprises polarization transfer effects, field-dependent relaxation processes of dipolar as well as quadrupole spins and combined results of both of them. Complete theories dealing with various aspects of the spin dynamic processes have been proposed. Because of an educational character of this paper, relevant assumptions, limitations and even particular steps of the proposed treatments have been discussed in detail. Special emphasis is put on understanding of validity regimes of the perturbation treatment, depending on relative strengths of spin interactions and timescales of relevant motional processes affecting them. Motional regimes required for spins to be involved in essentially different evolution pathways like polarization transfers or relaxation have been illustrated by experimental examples.     

Universal cubic equation of state and contact values of the radial distribution functions for multi-component additive hard-sphere mixtures

A universal cubic equation of state (UC EOS) is proposed based on a modification of the virial Percus-Yevick (PY) integral equation EOS for hard-sphere fluid. The UC EOS is extended to multi-component hard-sphere mixtures based on a modification of Lebowitz solution of PY equation for hard-sphere mixtures. And expressions of the radial distribution functions at contact (RDFC) are improved with the form as simple as the original one. The numerical results for the compressibility factor and RDFC are in good agreement with the simulation results. The average errors of the compressibility factor relative to MC data are 3.40%, 1.84% and 0.92% for CP3P, BMCSL equations and UC EOS, respectively. The UC EOS is a unique cubic one with satisfactory precision among many EOSs in the literature both for pure and mixture fluids of hard spheres.     

Mean spherical model for hard ions and dipoles: Thermodynamics and correlation functions

The solution of the mean spherical model of a mixture of equal-size hard ions and dipoles is reinvestigated. Simple expressions for the coefficients of the Laplace transform of the pair correlation function and the other thermodynamic properties are given.Supported by DOE through the Center of Environment and Energy Research of the University of Puerto Rico and NSF Grant CH 77-14611.     

Solution of the mean spherical approximation for hard ions and dipoles of arbitrary size

The general solution of the mean spherical approximation (MSA) for an arbitrary mixture of hard spherical ions and dipoles, in which the ions can be of different size, is found. This solution is given in terms of three parameters that are calculated by solving an algebraic equation. Two of these parameters are scaling parameters required to satisfy the general symmetry of the pair correlation functions, and are similar to the one introduced in the solution of the MSA for an ionic mixture in earlier work. For equal size and low ionic concentration, we get a rather explicit solution of the MSA, which is formally similar to the Waisman-Lebowitz solution of the restricted primitive model, but with a concentration-dependent dielectric constant.Supported in part through NSF grant 77-04597.     

The structure of strongly dipolar hard sphere fluids with extended dipoles by Monte Carlo simulations

We have investigated the structural change of dipolar hard sphere fluid while we change the dipole from an idealised point dipole (pDHS fluid) to a physically more realistic extended dipole (eDHS fluid) by increasing the distance d of the two point charges ±q while keeping the dipole moment μ = qd fixed. We discuss our results on the basis of the first- and second-rank orientational order parameters, angular distribution functions, chain-length distributions, and snapshots. At a low density, we have found chain formation with longer chains as the distance d is increased. At a high density, we have found phase transition from an orientationally ordered ferroelectric nematic phase (at low d) into an isotropic liquid containing chains (at large d).