Integral equation approximations for fluids of hard spheres with dipoles and quadrupoles

The LHNC, QHNC and mean spherical approximations are solved for fluids of hard spheres with dipoles and linear quadrupoles. The theories are evaluated by comparison with new Monte Carlo results. The dielectric constant is found to decrease rapidly with increasing quadrupole moment.     

Density and dielectric constant of dense argon and krypton mixtures

The density and the dielectric constant of three dense argon-krypton mixtures have been measured at 25°C and up to 8000 bar. For density measurements a constant volume method is used. The dielectric constant is determined by a capacitance measurement. The polarizability of the three mixtures is studied as a function of density.     

Quantum theory of polarizable quadrupolar fluids. I

Using the path integral representation of quantum theory, we construct a simple quantum mechanical model for a polarizable quadrupolar molecule, which represents a generalization of the dipolar Drude model and which takes full account of molecular quadrupoles, both permanent and induced. We consider the predictions of the model in the condensed phase within a class of linear theories which include as examples the mean spherical approximation and the linear hypernetted chain equation. We analyse both the pair correlation function of the model fluid and the renormalized, frequency dependent electrical properties of the molecule in the condensed phase; a simple practical method of calculating the latter quantities is described. The physical implications of the model are discussed and it is pointed out that a number of non-trivial predictions result from the model, including the predicted appearance of a collision-induced electronic dipolar absorption band. We discuss the relationship of the model here presented to the classical Yvon-Kirkwood model of polarization, and discuss a possible extension to the case of polarizable dipolar-quadrupolar fluids.     

The dielectric constant of polarizable fluids from the renormalized perturbation theory

A perturbation theoretical equation for the dielectric constant of polarizable dipolar fluids is proposed. For the fluctuation of the dipole moment, namely for the Kirkwood g-factor, a formula is given on the basis of Wertheim's renormalized perturbation theory. Using this formula, a series expansion for ?(p) is suggested on the basis of the Kirkwood equation, which gives an implicit function for ? as a function of ¶. The same series expansion can be derived from the Clausius-Mosotti equation—thus it proves to be independent of the boundary conditions. The resulting equation gives excellent results for the dielectric constant of the polarizable Stockmayer fluid producing good agreement with computer simulation data. The series expansion gives better results than the Kirkwood equation itself.     

Dielectric Measurements as a Function of Temperature of Sodium‐Lithium Phosphate Glasses Evaluated at 10 MHz and 9 GHz

Dielectric constant measurements can be performed at temperatures greater than room temperature; some techniques are shown in this work. The dielectric constant of phosphate glasses, measured in the X‐band microwave range, was determined using a microwave setup assembled to measure the shift in the standing wave pattern produced by the insertion of the sample inside the waveguide. The glass system 50P₂O₅ · 25Li₂O · 25Na₂O was chosen in this work due to its lower melting point and lower transition temperature (T_g) values. The dielectric constant of the glass studied in this work increases in the temperature range 25–330°C, as shown by the results at radio and microwave frequencies. The method of standing wave shift was applied, and it is shown to be a useful tool to estimate the T_g of glasses. This assumption was confirmed by differential thermal analysis technique. Measurements were compared to that at 10 MHz by impedancimetric methods.     

Some dielectric properties of monoclinic lysozyme crystals

The frequency dependences of the dielectric loss tangent and the magnitude of the impedance for monoclinic lysozyme single crystals and the solution used for preparing the crystals were investigated. The measurements were performed in the frequency range 1–10⁷ Hz under exposure of the crystals at a temperature of 25°C, cooling to ?20°C, and subsequent heating. The analysis of the experimental dielectric properties of the crystals demonstrated that drying of the crystals at room temperature in air initially led to the removal of “free” water with the content approximately equal to 65% of the total content. Further drying resulted in the removal of “bound” water. The solvent contained in the crystals (～26 wt %) was frozen at a constant temperature of approximately ?6.5°C. The permittivity of the dehydrated crystal at high frequencies was considerably higher than that of ice.     

Monte Carlo simulation of liquid neopentane

Monte Carlo simulations are reported for liquid neopentane at 25°C and 0·592 g cm^-3 using three different potential models. These results are compared with X-ray diffraction data and simulations for other tetrahedral molecules.     

Theory of polar fluids. I

We examine a classical fluid composed of molecules which contain a polarizable electric dipole with finite permanent moment. The long-ranged dipolar and the short-ranged interactions are treated on a different footing by expanding relative to a reference system characterized by the absence of electrostatic interactions. Extensions of graph theoretical techniques developed in an earlier paper are used to analyse the pair distribution function and the dielectric constant. Reduction of the number of graphs and their complexity is effected by introducing renormalizations of the permanent moment and the polarizability. The analysis leads to the definition of a new function w(12), which is free of terms dependent on the shape of the sample. For polar, polarizable molecules the direct correlation function lacks translational invariance; its role as a basic quantity is ceded to w(12). The pair distribution function and the dielectric constant ε are expressed in terms of w(12) and two closely related functions. Attention is drawn to an unsolved problem in dielectric theory, and an alternative formula for ε is presented in the form of a conjecture. An approximation for ε is formulated for the case in which the short-ranged non-dipolar interactions are independent of the molecular orientations. A simplified version is solved analytically.     

Hydrogen bond studies

The deuteron magnetic resonance spectra from partially deuterated single crystals of NaHC₂O₄. H₂O have been studied. The quadrupole coupling tensors for stationary deuterons are determined at about 25°C. The quadrupole coupling constants and the assymmetry parameters η of the tensors for the two deuterons in the water molecule are, 235·2 ± 1·9 and 228·5 ± 1·6 kHz, and 0·09 ± 0·01 and 0·13 ± 0·01, respectively. The principal axes corresponding to the largest components both deviate by 0·9 ± 0·5° from their respective O-H directions. For one of the tensors this angular displacement is in the plane of the H₂O molecule and towards the other O-H direction. The displacement for the other tensor is out of the plane of the H₂O molecule.     

Structural study of aqueous solutions of tetrahydrofuran and acetone mixtures using dielectric relaxation technique

The complex permittivity, static dielectric constant and relaxation time for tetrahydrofuran-water and acetone-water mixtures have been determined at 0°, 10°, 25° and 35°C using time domain reflectometry technique (TDR). The behaviour of relaxation time of the mixture shows a maxima for the mixture with 30% of water by volume. This suggests that the tendency to form cluster between water and solute molecule is maximum for this mixture. The excess permittivity for both tetrahydrofuran-water mixture and acetone-water mixtures, are found to be negative. The Kirkwood correlation factor has been determined at various concentrations of water. Static dielectric constant for the mixtures have been fitted well with the modified Bruggeman model. The values of the Bruggeman parametera for tetrahydrofuran is found to be more than the corresponding value for acetone.     

The properties of some derivative autocorrelation functions computed with the atom-atom potential

High-resolution quasi-elastic neutron-scattering measurements have been made on two nematogens: DMBCA with a nematic range 108 to 119°C, and 5CB and a tail-deuteriated sample (D5CB), having a nematic range 22·6 to 35·1°C.

Results on 5CB in the crystal phase at ～18°C showed no significant quasielastic broadening, which means that any random motions of the alkyl chain are slower than about 5 × 10⁹ rad s^-1. Measurements were made at a single temperature in the nematic phases on specimens aligned in a magnetic field of 0·25T; for DMBCA with scattering vector Q⊥n (n is the nematic director) and for 5CB and D5CB with Q⊥n and Q∥n and also on the isotropic liquid phase of D5CB at 45°C. Analysis of the coherent scattering from nematic D5CB at Q = 1·2 Å^-1 and 25°C gave an order parameter <P ₂>=0·55, close to the simple mean field value for this temperature. The coherent scattering from DMBCA is too weak to allow this experiment to be performed.

The most remarkable qualitative feature of the results is the close similarity of the scattering law S(Q, ω) for D5CB (and 5CB) with Q⊥n and Q∥n. Analysis of the results in all cases was made using values for the translational diffusion constants measured previously. Corrections for multiple scattering are shown to be important and a single simple model has been devised which fits the line shapes of all the results for D5CB in nematic (Q⊥n and Q∥n) and isotropic liquid phases and DMBCA. The model involves uniaxial rotational diffusion about the long molecular axis m coupled to a displacement along the rotation axis giving a net rotation in a plane whose normal makes an angle ∝ relative to the direction m. Values for the rotational diffusion constant D _rd ns^-1 are as follows: D5CB, 25°C, 6 (∝ ～ 50°); 45°C, 10. DMBCA, 112°C, 16, (all ±10–15 per cent).

The results for D5CB and 5CB are so similar that no additional detailed model fitting was attempted for the fully hydrogenous sample and it is concluded that while the motion of the alkyl tails is freer, the time scale of the motions is not more than about a factor of 2 faster than that of the molecular cores.     

Characterization of nanostructured ceramics prepared by both high energy ball milling and fast firing sintering processes

High-energy ball milling technique was successfully applied to calcinated lead zirconate titanate (PZT 60/40) powders. After 20?h of ball milling, large PZT particles were completely broken down, reducing its initial size in three orders of magnitude. Experimental results show a huge sinterability enhancement of the PZT powders by using this technique, achieving its maximum sintering rate at ～800°C. Relatively low densities (～91%) were achieved in stoichiometric samples, while in 3% lead excess samples sintered at 950°C for 30, 45, 60, 90 and 120?min using a fast firing process and a post-annealing treatment at 800°C for 4 h, densities of ～97% of the theoretical were achieved. PZT nanostructured ceramics prepared under optimized processing conditions (60?h of powder milling, 950°C of sintering temperature, 60?min of sintering time and a post-annealing process at 800°C during 4?h) show high dielectric constant (ε′) values (900) and low dielectric loss (tan?δ) at room temperature and a ferroelectric-paraelectric transition temperature at 375°C.     

Die optischen Konstanten des Kaliums und die Theorie von Drude

The results of new measurements of the optical constantsn andk of the alkali metal K, performed in ultrahigh vacuum on mirrorlike surfaces free of any contamination and distortion in the wavelength region from 0·365 μ to 2 μ at temperatures between ?183° C and +85° C were compared with the predictions of the Drude-theory. This permits the following main conclusions:

1. 1.
   The relation forn ²-k ²≡ε (real part of the metal's dielectric constant) derived by Drude proves to be valid; therefore, the total polarisation 4πNα (α=polarizability) of the metal remains small compared with 1 and the interband absorption has no influence on it.     
   
   

Messung der komplexen Dielektrizitätskonstanten von Seignette-Salz bei 10 GHz in Abhängigkeit von der Temperatur

We determined the complex dielectric constant of Rochelle Salt at 9.61·10⁹ Hz and its temperature dependence using a microwave interferometer. In thex-direction of the crystal which becomes its ferroelectric axis between ?18°C and +24°C, the real part of the dielectric constant shows distinct minima at the transition points according to our measurements. We find agreement with results ofJäckle but discrepancies to older measurements. Neither the humidity of the surrounding atmosphere nor the position of the sample in the growing crystal proved to have an effect. In they- andz-directions, we observed no anomaly of the dielectric constant.     

Dielectric behaviour of anisotropic ionic crystals

In the case of cubic ionic crystals Havinga has shown that the temperature variation of dielectric constant could be described in terms of volume and temperature effects. By extending his formalism to anisotropic, ionic crystals it has been shown that unlike in cubic ionic crystals where the volume effect consists of a change in the number per unit volume of the polarizable particles and their polarizability with volume, in the case of anisotropic ionic crystals, in addition to these, a variation in the anisotropy of polarizability due to uneven thermal expansion also has to be taken into account. This method of analysis has been examined by taking rutile as an example.     

Dielectric studies on binary polar mixtures of propanoic acid with esters

It is interesting to see the nature of intermolecular interactions between associative and non-associative polar liquids. Binary polar–polar liquid mixtures of ethyl acetate, ethyl benzoate, ethyl acrylate, ethyl butyrate, n-butyl acetate and benzyl benzoate, each with propanoic acid were subjected to dielectric studies at temperatures 25 °C, 35 °C and 45 °C. Static permittivity (ε_o) and dielectric constant at high frequency (ε_∞) were found through dielectric measurements for different concentrations of each system. The Bruggeman dielectric factor, Kirkwood correlation factor and the excess permittivity were determined. Deviations from the linearity of various models suggest molecular association through hydrogen bonding between the polar–polar constituents of the mixtures. The formation of cyclic and linear α-multimers in the above systems were identified. The results and their temperature dependence were interpreted accordingly.     

Structure Characterization of HSQ Films for Low Dielectrics Using D5 as Sacrificial Porous Materials

Low-density materials, commercially available hydrogensilsesquioxane （HSQ） offer a low dielectric constant. HSQ films can be obtained by spin on deposition （SOD）. In this work, low-dielectric-constant HSQ films are prepared by using D5 （decamethylcyclopentasiloxane） as sacrificiaJ porous materials. The dielectric constant of silica films significantly changes from 3.0 to 2.4. We report the structural aspects of the films in relation to their composition after annealed at 300℃, 400℃, and 500℃ for 1.5h in nitrogen ambient and annealed at 400℃ for 1.5h in vacuum. Si-OH appears after annealed at 400℃ for 1.5h in vacuum. The results indicate that the proper condition is in nitrogen ambient. Intensity of the Sill peak increases with the increasing temperature. Fourier transform infrared spectroscopy is used to identify the network structure and cage structure of Si-O-Si bonds and other possible bonds. Dielectric constant k is significantly lowered by annealing at 350℃ for 1.5h in nitrogen ambient. The I-V and C-V measurements are used to determine the dielectric constant, the electric resistivity and the breakdown electric field.     

Dielectric constant of a highly polarizable atomic fluid: the clausius–mossotti versus the onsager relation

The relation between the dielectric constant and the particle polarizability for a polarizable liquid composed of Lennard-Jones particles carrying a saturable induced dipole is studied by computer simulations. It is shown that the widely accepted Clausius–Mossotti relation is only valid for low polarizabilities and fails for high polarizabilities. The results can be fitted accurately by an Onsager-like relation using an effective particle radius measured in the simulations which is larger than the equivalent hard-sphere radius defined conventionally. Furthermore, the orientational ordering transition found at high polarizabilities is shown to be of anti-ferroelectric type.     

Dielectric responses of composite films based on P(VDF-TrFE) copolymer with TGS inclusions

The dielectric characteristics of film samples of P(VDF-TrFE) + TGS composite in the frequency range of 10³–10⁷ Hz are studied. The values of the real and imaginary parts of the complex dielectric constant in the temperature range of–40 to 140°C, including the points of the polymer matrix’s transition to the glassy state when T_g ≈–25°C and the ferroelectric phase transition. An analysis of the ferroelectric crystal inclusion effect on the dielectric response of P(VDF-TrFE) copolymer matrix is carried out.