The effect of the spatial nonlocality of the Kirkwood g-factor on the determination of the long wavelength dielectric functions in dipolar fluids

The Kirkwood g-factor that determines the long wavelength dielectric constant of a simple, isotropic, translationally invariant dipolar fluid is given by an integral of a dipole-dipole correlation function over a spherical region of a nonzero radius R(K) chosen such that any further increase in the radius leads to no change in the value of the integral, thereby defining a Kirkwood correlation length R(K). For radii less than the correlation length the integral defines a radius dependent (nonlocal) Kirkwood g-factor, implying a nonlocal dielectric function. The nonlocal nature of these quantities has important consequences for the determination of the long wavelength dielectric function from dipole fluctuations via the Kirkwood-Fro?hlich connection. The dipole-dipole correlation function (the volume dipole auto-correlation function) commonly used in this determination involves particles residing solely within a sphere of radius R, unlike the correct correlation function which involves either a single particle with those particles in a spherical volume of radius R(K) or those particles in a spherical volume of radius R with those residing within a spherical volume of radius R+R(K). A procedure is suggested for extracting the infinite system dipole-dipole correlation function from results of simulations performed on finite spherical samples. Using some results reported in the recent literature, relative to the accurate correlation function the commonly used correlation function ranges from 27% too small for a sphere having a radius comparable to the Kirkwood correlation length to 4% too small at a radius of seven times that correlation length. As a result, the apparent dielectric constants, as determined by the conventional procedure of using the fluctuations of the sum of dipoles in a finite fixed volume, are also too small. This suggests that a dielectric constant extracted from computer simulations using a total dipole-total dipole correlation function in a given volume with other geometries and/or boundary conditions will result in similar errors.     

Dielectric Relaxation Study of Chloro Group with Associative Liquids. II. 1,2-Dichloroethane with Methanol, Ethanol, and 1-Propanol

Frequency spectra of the complex permittivity for 1,2-dichloroethane–alcohol binary mixtures have been determined over the frequency range 10 MHz to 20 GHz at 15, 25, 35, and 45°C, using the time-domain reflectometry (TDR) technique, for 11 compositions of each 1,2 dichloroethane–alcohol system. The alcohols used in the study were methanol, ethanol, and 1-propanol. The relaxation in these systems can be described by a single relaxation time using the Debye model. The static dielectric constant, relaxation time, the corresponding excess dielectric properties, Kirkwood correlation factor, and Bruggeman factor of the mixtures have been determined. The static dielectric constants for the mixtures have been fitted with the modified Bruggeman model.     

Measurement and modelling of static dielectric constants of aqueous solutions of methanol,ethanol and acetic acid at T = 293.15 K and 91.3 kPa

Static dielectric constants of aqueous solutions of methanol, ethanol and acetic acid at T = 293.15 K and 91.3 kPa were measured at weak electromagnetic field (≪0.001 V) and (≪60 Hz). The static dielectric measurements have been achieved by using the new set up presented in the previous work based on a low-pass filter. From the experimental data, excess dielectric constants, ɛ^E have been calculated and reported. An empirical polynomial equation was used for correlating the data of the dielectric constants for the aqueous solutions. In addition, the measured static dielectric constants data have been calculated on the basis of the empirical modification of the Kirkwood theory for multicomponent systems. According to the average absolute deviations obtained between experimental and calculated data, the calculated dielectric constants of aqueous solutions studied in this work are generally in good agreement with the experimental data.     

Temperature-Dependent Dielectric Relaxation of 2-Ethoxyethanol, Ethanol, and 1-Propanol in Dimethylformamide Solution Using the Time-Domain Technique

Complex reflection coefficients for 2-ethoxyethanol–dimethylformamide (DMF), ethanol–DMF, and 1-propanol–DMF mixtures at several temperatures from 20 to 50° and the frequency range 10 MHz to 10 GHz were determined by time-domain spectroscopy in reflection mode. Fourier transforms and least-squares fitting were used to obtain complex permittivity, static dielectric constant, and relaxation time. The excess dielectric parameters, Kirkwood correlation factors, and thermodynamic properties for the binary mixtures were also determined. The static dielectric constant for the mixtures was fitted well with the modified Bruggeman model.     

Simulations of high-dielectric Stockmayer fluids in hyperspherical geometry

The static dielectric properties of Stockmayer fluids are investigated in the hyperspherical geometry, S(3). Different methods of obtaining the static dielectric constant ε(r) are compared. Tested methods include the evaluation of the Kirkwood factor, fluctuations of the total dipole moment, and a two-center potential correlation formula to obtain the dielectric constant through effective interactions. With no coupling to the "surrounding," the different methods give consistent estimates of the dielectric constant. Adding a coupling to the surrounding gives large size dependencies and the two-center potential correlation formula breaks down. For low dipole moments, there is a good agreement in the dielectric constant with previous studies.     

Elastic, dielectric and optical constants of 4'-pentyl-4-cyanobiphenyl

4'-n-Pentyl-4-cyanobiphenyl (5CB) is a room temperature nematic liquid crystal with a high positive dielectric anisotropy and a high chemical stability. Many experimental results concerning the elastic and dielectric constants of 5CB are available in the literature, although there is often no satisfactory agreement between the experimental data obtained by different groups, especially as far as the dielectric constants are concerned. Furthermore, no detailed investigation of the temperature dependence of the elastic and dielectric constants close to the nematic-isotropic transition temperature T_NI has yet been reported. In this paper, we report the measurement of the elastic and dielectric constants of 5CB, and the temperature behaviour close to T_NI has been investigated in detail. The experiment consists in the measurement of the director deformation induced by an electric field using simultaneously both a dielectric and an optical method. The simultaneous use of these two methods provides an indirect check on the reliability of the measurements. Special attention has been devoted to control possible sources of uncertainty. In particular, the effects of finite anchoring energy and of finite pretilt angle have been considered. The temperature dependence of the anisotropy of the refractive indices is also obtained in the experiment.     

Static Dielectric Constants and Kirkwood Correlation Factor of the Binary Mixtures of N-Methylformamide with Formamide,N,N-Dimethylformamide and N,N-Dimethylacetamide

Static dielectric constant values of the binary mixtures of N-methylformamide with formamide, N,N-dimethylformamide and N,N-dimethylacetamide have been measured in the whole composition range at 303 K. The Kirkwood correlation factor values of the amide–amide mixtures were determined from the measured values of the static dielectric constant and high-frequency limit dielectric constant. The evaluated values of the excess dielectric constant and deviation in the Kirkwood correlation factor infer that deviations of their mixture values occur from the mole-fraction mixture law. Results confirm that there are strong hydrogen-bond interactions between unlike molecules of amide–amide mixtures and that 1:1 complexes are formed.     

Dielectric relaxation of Tripropylene glycol–water mixture using time domain reflectometry

The complex permittivity spectra of tripropylene glycol and water solutions have been obtained by time domain reflectometry (TDR) technique in the frequency range from 10 MHz to 30 GHz and the temperature range 20°C–05°C. The dielectric relaxation parameters such as static dielectric constant and relaxation time were obtained by using the non-linear least square fit method. The intermolecular hydrogen bonding of tripropylene glycol–water has been discussed using the Kirkwood correlation factor and thermodynamic parameters. The activation energy decreases with increase in water content in the mixture as expected in the Arrhenius behaviour. The dielectric constant for mixtures has been fitted to the Bruggeman mixture formula in the non-linear case.     

Dielectric Relaxation and Thermodynamic Studies of Binary Mixtures of 2-Nitrotoluene with Primary and Secondary Alcohols at Different Temperatures

The dielectric complex spectra of 2-nitrotoluene with primary or secondary alcohol binary mixtures were studied over the frequency range of 10 MHz to 20 GHz for the whole solute mole fraction range at four different temperatures. An unusual suppression phenomenon was observed in the real and imaginary parts of the mixture complex spectrum, which are smaller than those for the pure alcohols, at low solute concentrations. The dielectric constant and dielectric relaxation time values were obtained by fitting the complex dielectric spectrum data to the single Debye model using a non-linear least squares method. The dielectric constant of mixtures decrease with the increasing mole fraction of 2NT in both the primary alcohols and secondary alcohols; the dielectric relaxation time decreases for all the five binary systems. Using the dielectric data, derived dielectric parameters, namely: the excess dielectric constant, excess inverse relaxation time, effective Kirkwood correlation factor, molar activation enthalpy and molar activation entropy, were calculated. The non-linear variation of permittivity (?₀) reveals the change in size and shape of hetero-molecular complex due to intermolecular H-bond interaction. The negative variation of the excess permittivity constant confirms that the dipoles form multimer structures with anti-parallel ordering of unlike dipoles. The molar activation enthalpy was found to be higher at 0.2 mol fraction of 2NT for primary alcohol binary system. To confirm the molecular function group interaction, a FT-IR spectroscopy study was carried out at 298 K. The FT-IR analysis confirmed the formation of hydrogen bonds between the hydrogen atom of hydroxyl groups of the alcohols and the oxygen atom of nitro groups of 2NT in the binary mixtures.     

Polarographic study of mixed-ligand complex stability constants and kinetic parameters of reduction of Cr(III)-ethylenediamine-succinate system

Stability constants of the binary species Cr(III)-ethylenediamine, Cr(III)-succinate and mixed-ligand complex Cr(III)-ethylenediamine-succinate have been determined polarographically by the method of Sundaresan and Sundaram at 30±0.2°C at a constant ionic strength [μ = 0.6 M (NH₄ClO₄]. The values of the stability constants obtained by this method are compared with those reported in the literature. The positive values of the mixing constants for the mixed-ligand complexes indicate that the mixed-ligand complexes are more stable than simple binary complexes. The reduction of the simple and mixed complexes is irreversible at a dropping mercury electrode: therefore, kinetic parameters like the standard rate constant, transfer coefficient and activation energy have also been calculated.     

Kinetic study of thermal Z to E isomerization reactions of azobenzene and 4-dimethylamino-4'-nitroazobenzene in ionic liquids [1-R-3-methylimidazolium bis(trifluoromethylsulfonyl)imide with R = butyl, pentyl, and hexyl

Thermal Z to E isomerization reactions of azobenzene and 4-dimethylamino-4'-nitroazobenzene were examined in three ionic liquids of general formula 1-R-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (R = butyl, pentyl, and hexyl). The first-order rate constants and activation energies for the reactions of azobenzene measured in these ionic liquids were consistent with those measured in ordinary organic solvents, which indicated that the slow isomerization through the inversion mechanism with a nonpolar transition state was little influenced by the solvent properties, such as the viscosity and dielectric constant, of ionic liquids. On the other hand, the rate constants and the corresponding frequency factors of the Arrhenius plot were significantly reduced for the isomerization of 4-dimethylamino-4'-nitroazobenzene in ionic liquids compared with those for the isomerization in ordinary organic molecular solvents with similar dielectric properties. Although these ionic liquids are viscous, the apparent viscosity dependence of the rate constant could not be explained either by the Kramers-Grote-Hynes model or by the Agmon-Hopfield model for solution reactions. It is proposed that the positive and the negative charge centers of a highly polar rotational transition state are stabilized by the surrounding anions and cations, respectively, and that the ions must be rearranged so as to form highly ordered solvation shells around the charge centers of the reactant in the transition state. This requirement for the orderly solvation in the transition state results in unusually small frequency factors of 10(4)-10(7) s(-1).     

Elastic,dielectric and optical constants of 4'-pentyl-4-cyanobiphenyl

4'-n-Pentyl-4-cyanobiphenyl (5CB) is a room temperature nematic liquid crystal with a high positive dielectric anisotropy and a high chemical stability. Many experimental results concerning the elastic and dielectric constants of 5CB are available in the literature, although there is often no satisfactory agreement between the experimental data obtained by different groups, especially as far as the dielectric constants are concerned. Furthermore, no detailed investigation of the temperature dependence of the elastic and dielectric constants close to the nematic-isotropic transition temperature T _NI has yet been reported. In this paper, we report the measurement of the elastic and dielectric constants of 5CB, and the temperature behaviour close to T _NI has been investigated in detail. The experiment consists in the measurement of the director deformation induced by an electric field using simultaneously both a dielectric and an optical method. The simultaneous use of these two methods provides an indirect check on the reliability of the measurements. Special attention has been devoted to control possible sources of uncertainty. In particular, the effects of finite anchoring energy and of finite pretilt angle have been considered. The temperature dependence of the anisotropy of the refractive indices is also obtained in the experiment.     

Determination of affinity constants and response factors of the noncovalent dimer of gramicidin by electrospray ionization mass spectrometry and mathematical modeling

The dimerization of gramicidin, a 15-residue membrane peptide, in solution can be viewed as a model for protein-protein interactions. We reported previously that the dimer can be observed when electrosprayed from organic solvents and that the abundances of the dimer depends on the dielectric constant of the solvent. Here, we report an effort to determine an affinity constant for the dimerization of gramicidin by using gas-phase abundance. Two issues affecting the determination are the electrospray-induced dissociation of the dimer and discrimination in the electrospray of the dimer compared with the monomer. Other methods developed for the purpose of determining affinity from mass spectral abundance do not address the dissociation of the complex in the gas phase or can not be applied for cases of low affinity constant, K(a). We present a mathematical model that uses the ratio of the signal intensities of the dimer and the monomer during a titration. The model also incorporates the dissociation and an electrospray ionization-response factor of the dimer for extracting the affinity constant for the dimerization of gramicidin. The dimerization constants from the new method agree within a factor of two with values reported in the literature.     

Formation of photo-functional spiroxazine monolayers and their dielectric constant determination using surface plasmon resonance

Spiroxazine are of considerable interest as photochromic materials because of their application. On the other hand, surface plasmon resonance (SPR) is a well-known optical method for measuring optical constants of thin film. In this study, photochromic materials were used as self-assembled monolayers (SAMs) of newly synthesized spiroxazine derivatives. We used Fresnel equation (four-layer model) to determine the precise dielectric constant () of the photochromic monolayers. Structure changes of spiroxazine derivatives under UV-light irradiation resulted in the change of optical constants, the dielectric constant and thickness. The obtained results indicated that the ring opening of photochromic spiroxazine can lead to the decrease in the dielectric constant and thickness.     

Acetonitrile + nitromethane: An example of ideal solvent mixtures

Densities, viscosities, static dielectric constants and refractive indices of acetonitrile + nitromethane mixtures in the temperature range between 5 and 45°C are reported. Density and viscosity data, analyzed in terms of molar excess volumes and molar excess fluidities, show a weak interactions field between acetonitrile and nitromethane molecules. Lorentz-Lorenz molar refractivities and Kirkwood correlation factors, obtained from refractive indices and dielectric constants data, respectively, indicate that such weak interactions can be atributed to an antiparallel alignment between neighboring dipoles of unlike solvent molecules. Such specific features do not significantly perturb the local structures of the pure components so that acetonitrile + nitromethane mixtures can be considered, in a first approximation, one of the few ideal solvent mixtures for which the physical properties can be determined by applying the additivity rules to the pure components.     

The pressure dependence of the dielectric constant and density of acetonitrile at three temperatures

The static dielectric constant of liquid acetonitrile is reported at 10, 25, and 40°C and at pressures up to 3 kbar. Densities of pure acetonitrile were measured where needed in order to analyze the dielectric measurements using the Kirkwood-Fröhlich equation. The Kirkwood correlation factorg _K was found to be less than unity with a positive temperature but negative pressure coefficient, suggesting an increasing anticorrelation of dipoles with decreased temperature and increased pressure. Theg _K factors are analyzed by a dipole pair-bonding model as outlined by Dannhauser and Flueckinger in which the lowg _K values are attributed to the presence of dimers consisting of completely anticorrelated dipoles. The implication of this model on other measurements, especially MNR relaxation studies, is examined.     

Dielectric spectroscopy and electrophoretic mobility measurements interpreted with the standard electrokinetic model

We report results from complementary electrokinetic measurements-dielectric relaxation and electrophoretic mobility-undertaken to test the applicability of the standard electrokinetic theory with a model system. Dielectric spectra were obtained at frequencies between 1 kHz and 40 MHz with a new, two-electrode cell design [Hollingsworth and Saville, J. Colloid Interface Sci. 257 (2003) 65-76]; mobility data were acquired with an electrophoretic light scattering instrument. Data from the two-electrode cell were collected at different electrode separations and interpreted with newly developed procedures to remove the influence of electrode polarization. Methodology A employs extrapolation to infinite electrode separation to compute the dielectric constant and conductivity as functions of frequency. The contributions from suspended particles are reported in terms of dielectric constant and conductivity increments. Methodology B uses a theoretical model of electrode polarization and the standard electrokinetic model in a nonlinear regression scheme. Results are presented in several forms: frequency-dependent dielectric constant and conductivity increments, frequency-dependent dielectric constants and conductivities, and the complex dipole coefficient. It is shown that the standard model provides a consistent methodology for interpreting particle behavior; zeta-potentials inferred from mobility and dielectric relaxation agree to within experimental error. Moreover, the cell design and interpretation are straightforward and provide relatively simple ways to obtain complementary measurements over a wide frequency range. The results unambiguously show that electrokinetic character of this dispersion follows the standard model.     

Application of principal component-wavelet neural network in spectrophotometric determination of acidity constants of 4-(2-thiazolylazo)-resorcinol

The acidity constants of 4-(2-thiazolylazo)-resorcinol (TAR) were determined by the principal component-wavelet neural network (WNN). Biprotic acid mass balance equations, the distribution functions and the corresponding spectral profiles which were generated by a Gaussian model, have been considered to simulate all required absorbance-pH data. The simulated absorption-pH data matrix was used as training set whereas the TAR absorption-pH data was used as the test set of WNN model. The obtained acidity constants were in good agreement with the reported values of acidity constants in the literature and with those calculated by DATAN software. Artificial neural network (ANN) model has been also employed in this study and the results of WNN were compared with those obtained by ANN. It was found that WNN gives faster convergence and slightly better accuracy.