On the definition of the excess permittivity of a fluid mixture

It is shown that under the assumption of no intermolecular interaction, the permittivity of a homogeneous linear and isotropic fluid mixture is the sum of the individual permittivities weighted with the mole fractions of the components. For definiteness, a proof is given for gasses under standard temperature and pressure; it is, however, easy to generalize it to other conditions, as well as to liquids, as long as the assumption of no intermolecular interaction is retained. Also, although the proof is given for a binary mixture, it is a simple exercise to extend it to any multicomponent mixture.     

The Kirkwood-Buff theory of solutions and the local composition of liquid mixtures

The present paper is devoted to the local composition of liquid mixtures calculated in the framework of the Kirkwood-Buff theory of solutions. A new method is suggested to calculate the excess (or deficit) number of various molecules around a selected (central) molecule in binary and multicomponent liquid mixtures in terms of measurable macroscopic thermodynamic quantities, such as the derivatives of the chemical potentials with respect to concentrations, the isothermal compressibility, and the partial molar volumes. This method accounts for an inaccessible volume due to the presence of a central molecule and is applied to binary and ternary mixtures. For the ideal binary mixture it is shown that because of the difference in the volumes of the pure components there is an excess (or deficit) number of different molecules around a central molecule. The excess (or deficit) becomes zero when the components of the ideal binary mixture have the same volume. The new method is also applied to methanol + water and 2-propanol + water mixtures. In the case of the 2-propanol + water mixture, the new method, in contrast to the other ones, indicates that clusters dominated by 2-propanol disappear at high alcohol mole fractions, in agreement with experimental observations. Finally, it is shown that the application of the new procedure to the ternary mixture water/protein/cosolvent at infinite dilution of the protein led to almost the same results as the methods involving a reference state.     

Kirkwood correlation factors in liquid mixtures from an extended Onsager-Kirkwood-Fröhlich equation

Two approaches for applying the Onsager-Kirkwood-Fr?hlich equation to liquid mixtures are revisited at the light of recent developments leading to the estimation of relative permittivities and refractive indices of thermodynamically ideal liquid mixtures. From the one-liquid approach, the squared permanent dipole moment of the mixture molecular-equivalent species M is demonstrated to be a mole-fraction average of squared permanent dipole moments of the components. An expression is obtained for calculating the ideal Kirkwood correlation factor of M at any composition by using only pure-constituent properties. From the two-liquid approach (B?ttcher's equation), equations are obtained to describe the dependence on composition of the Kirkwood correlation factor of both components in the ideal mixture, even in mixtures of Onsager liquids. This dependency is tentatively ascribed to London dispersion forces acting between unlike molecules. It is demonstrated that B?ttcher's equation can only be applied to mixtures where the relative permittivity of each component is larger than the squared refractive index of the other component. From the interplay of one- and two-liquid approaches, the ideal Kirkwood correlation factor of M and of both constituents are inter-related. Thermodynamic expressions are given for the calculation of excess Kirkwood correlation factors. In the case where permanent dipole moments are unknown, the ratio excess/ideal, termed the relative excess Kirkwood correlation factor for components and species M can still be evaluated. These ratios are related to more conventional excess properties. Density, relative permittivity and refractive index data are reported for binary mixtures of 2,2,2-trifluoroethanol with mono-, di-, tri- or tetra-glyme over the whole composition range at 288 K and 298 K. For these systems, ideal, excess and relative excess and Kirkwood correlation factors are calculated and discussed. In particular, by regarding Kirkwood correlation factors as a measure of order/molecular organisation in liquid mixtures, it is found that the formation of ideal mixtures entails a decrease of order which, for the present binary systems, is almost cancelled out upon passage to the corresponding real mixtures. It is concluded that the present formulation permits to estimate Kirkwood correlation factors of each constituent of liquid mixtures and thereby to draw information on their molecular organisation.     

A new approach for prediction of the permittivity of mixtures

Working on a mesoscopic scale, a new cubic expression for the effective permittivity of mixtures as a function of the mean permittivity fluctuation is established. Using previous methods for calculating this mean value, the effective permitivity of a mixture can thereby be written as a function of the fractional volumes of its components and their pure permittivities. A comparison with experimental results for (tetraglyme  + n -nonane) near the consolute point with some other known expressions for mixtures are presented.     

DMF水溶液的等效介电常数特异性

在288、298和313 K三个温度和2.45 GHz频率下利用微扰谐振腔法测量N,N-二甲基甲酰胺(DMF)、水(H2O)及其混合溶液的等效介电常数过程中, 发现了混合溶液介电损耗虚部大于其中任一组分的介电损耗虚部的特异现象. 理论计算表明, 出现这种特异现象的原因是DMF 和水混合后其高频摩擦项引起的. 这就意味着在混合溶液中, 新的等效介电常数计算公式中必需引入氢键贡献来解释这种特异现象.     

Interpretation of the difference between the work of separation determined by the separation potential and the thermodynamically estimated work of isobaric-isothermal mixing

The previously described scheme of a symmetrical cascade consisting of two equivalent sections and several steps of equilibrium (quasi-static) separation of components of an ideal gas solution was used to calculate gas mixture pressures at cascade stages. It was shown that, at equal concentrations of fractions feeding steps, pressures of mixing fractions were different. The difference between the work of separation determined using the separation potential and the thermodynamically estimated work of mixing is interpreted as a consequence of an increase in entropy during fraction mixing in the corresponding units of a symmetrical cascade. Original Russian Text ? V.P. Chizhkov, V.N. Boitsov, 2009, published in Zhurnal Fizicheskoi Khimii, 2009, Vol. 83, No. 2, pp. 370–374.     

Radiothermoluminescence of <Emphasis Type="Italic">n</Emphasis>-eicosane mixtures with <Emphasis Type="Italic">n</Emphasis>-tetracosane: Effect of mixture composition

Radiothermoluminescence (RTL) curves of mixtures of C20 and C24 n-alkanes have been deconvoluted into the curves of crystalline and disordered regions, and their change depending on the mixture composition has been analyzed. The shape of the total RTL curve of the mixture regardless of the its composition is fundamentally different from that shape of the sum of the curves of the individual components taken in the relevant ratios. The difference becomes noticeable at as low a C20 amount in the mixture as 2% and is manifested in the disappearance of the intense RTL peaks of the individual components and appearance of new intense peaks in temperature intervals other than those of the RTL peaks of the components. It has been shown that these changes correlate with changes of the crystalline structure of the mixture: a new crystalline structure other than the structure of any of the individual components emerges and the mixture becomes amorphous. High selectivity of charge trapping in disordered regions of the mixture has been revealed: the contribution of RTL of the disordered regions to the total curve is many times higher than their volume fraction in the mixture. This selectivity might be due to an increase in concentration of defects in the unordered regions of the mixture in comparison with their concentration in the pure alkanes. These defects are traps for electrons that are accessible to acceptors introduced into the mixture.     

Effect of stagnant-layer conductivity on the electric permittivity of concentrated colloidal suspensions

A long-lasting experience in the electrokinetics of suspensions has shown that the so-called standard model may be partly in error in explaining experimental data. In this model, the stagnant layer is considered nonconducting (Ksigmai=0), and only the diffuse layer contributes to the total surface conductivity (Ksigma=Ksigmad). In the present work, the authors analyze the consequences of assuming a nonzero stagnant layer conductivity on the permittivity of concentrated suspensions. Using a cell model to account for the particle-particle interactions, and a well established ion adsorption isotherm on the inner region of the double layer, the authors find the frequency-dependent electric permittivity of suspensions of spherical particles with volume fractions of solids up to above 40%. It is demonstrated that the addition of Ksigmai significantly increases the contributions of the double layer to the polarization of the suspension: the alpha or concentration polarization at low (kilohertz) frequencies, and the Maxwell-Wagner-O'Konski (associated with conductivity mismatch between particle and medium) one at intermediate (megahertz) frequencies. While checking for the possibility that the results obtained in conditions of Ksigmai not equal 0 could be reproduced assuming Ksigmai=0 and raising Ksigmad to reach identical total Ksigma, it is found that this is approximately possible in the calculation of the permittivity. Interestingly, this does not occur in the case of electrophoretic mobility, where the situations Ksigma=Ksigmad and Ksigma=Ksigmad+Ksigmai (for equal Ksigma) can be distinguished for all frequencies. This points to the importance of using more than one electrokinetic technique to properly evaluate not only the zeta potential but other transport properties of concentrated suspensions, particularly Ksigmai.     

Relative permittivity increments for {xCH3OH + (1 − x)CH3OCH2(CH2OCH2)3CH2OCH3} fromT = 283.15 K toT = 323.15 K

Relative permittivities of { CH₃OH  +  CH₃OCH₂(CH₂OCH₂)₃CH₂OCH₃(2,5,8,11,14-pentaoxapentadecane, tegdme)} at temperatures from 283.15 K to 323.15 K and atmospheric pressure, were measured over the whole composition range. Experimental relative permittivities were fitted by a polynomial function in mole fraction. Values of relative permittivity were measured using a HP4284A precision LCR Meter together with the measuring cell HP16452A at 1 MHz. Relative permittivity increments were determined from experimental data and fitted to a variable-degree polynomial function. Different theoretical models were used to predict the permittivity of this mixture. The predictions are better when the volume change on mixing is considered.     

Distinctive features of radiothermoluminescence curves of alkanes

Radiothermoluminescence (RTL) curves of alkanes have a special character: each curve is specific to a particular alkane and thus can be used for identifying it. The RTL curve of a mechanical mixture of two alkanes quantitatively coincides with the sum of the curves for the individual components of the mixture. The additivity property is lost for the mixtures prepared from a melt or chloroform solution. The loss is due to the change of the crystalline state of the mixture. An X-ray study shows that the X-ray diffractogram of such a mixture does not coincide with the sum of diffractograms of the individual components (even the crystal lattice type changes).     

Space charge characterization of MgO by coupling cavity resonator and mirror method

Charge trapping occurs at defects or insulator interfaces which have different permittivities and different conductivities. It has been observed that, after X-ray irradiation, magnesium oxide (MgO) accumulates charge when it is bombarded by electrons with sufficiently high energies. In this work we investigate the effect of an electromagnetic field on the permittivity of a charged insulator (MgO). Using two complementary techniques: the perturbation of a cavity resonator and the mirror method, one can determine the dielectric permittivity and trapped charge. Details of the experiments and the methods of charge determination are given.     

Experimental problems in Raman spectroscopy applied to pigment identification in mixtures

Raman spectroscopy provides useful information to detect and identify pictorial materials in artworks, although some problems are involved when the identification of individual pigments in mixtures is treated. With the hypothesis of the Principle of superposition, the mixture spectrum should be the direct sum of each pondered individual spectrum. In this work, we will show several mixtures where it can be noticed that the mixture spectrum is not qualitatively proportional to the sum of pondered individual spectra. Also there were some cases where the bands of one of the pigments could not be detected in the mixture spectrum. This non-linear behaviour could be attributed to specific proprieties of each material that are revealed when they interact with each other. We conjecture that, for instance, the different reflectances or the wavelength of the laser source could be determinant factors of the obtained results. In this paper an experimental method has been designed in order to characterize the quantitative behaviour of the Raman bands corresponding to each pigment in a mixture. Adequate coefficients are defined and calculated to facilitate the study of the spectral contribution of the different components of a mixture.     

钛酸铅/聚[偏氟乙烯(70)-三氟乙烯(30)]复合物的非线性介电性质

用自建的非线性介电测试装置研究了陶瓷相被极化 (B1 )以及陶瓷相和共聚物相都被极化 (B2 )的钛酸铅 /聚 [偏氟乙烯 ( 70 ) 三氟乙烯 ( 3 0 ) ](PT/P[VDF( 70 ) TrFE( 3 0 ) ]) 0 3型铁电复合物厚片在不同测试场强下的非线性介电系数 .对于PT含量 >0 3的复合物 ,介电系数ε1随场强的升高明显增大 .在 <0 1时 ,可用Maxwell Garnett方程拟合实验结果 .Bruggeman方程适合于低电场 ( <1MV/m)下复合物介电系数的预测 .通过Lz 的变化 ,用Yamada模型可拟合不同场强下复合物介电系数随的变化关系 .二阶非线性介电系数ε2 随的升高而增大 ,B2的ε2 大于B1 ,说明B2具有较高的剩余极化 .三阶非线性介电系数ε3 随场强的升高而减小 ,且高值的复合物具有较大的ε3 .两相都被极化试样的ε3 小于仅陶瓷相被极化的试样 .     

A study of molecular mobility and relaxation properties of epoxy-allyl polymers during formation of interpenetrating polymer networks under conditions of the phase separation of the networks

Molecular mobility and relaxation properties of epoxy-allyl polymers (EAPs) and features of the formation of interpenetrating polymer networks under conditions of the phase separation of the network have been studied. The presence of the extensive interphase zone between the individual epoxy and allyl component networks has been established. The segregation degree has been calculated taking into account the volume fractions of the components of the polymer mixture. The interrelation between the features of the structure of the obtained EAP with a high level of adhesion and deformation-strength characteristics of polymers in glassy and highly elastic states has been demonstrated.     

Adsorption Equilibrium of Binary Mixtures in Zeolites and State of Adsorbed Phase

The criterion of ideal behavior of a mixture of a few molecules within a separate zeolite cavity is formulated on the basis of the statistical thermodynamics. The criterion determines the dependence of the Helmholtz free energy, internal energy, and entropy of a molecular aggregate on the ratio of the number of molecules of components 1 and 2. The similarity between this criterion and the criterion of ideal behavior for bulk solutions is shown. Expressions of excess thermodynamic functions of the molecular mixture in a cavity are obtained. The negative magnitude of these excess functions is proposed to be due to rearrangement of molecules under influence of energetic heterogeneity. The calculation procedure of the excess functions has been demonstrated for the system CO₂-C₂ H₆-zeolite NaX, the information of both isotherms and isosteric adsorption heats being used simultaneously. The approach offered allows the state of adsorbed mixture in a separate cavity to be analyzed from pure-component and multicomponent experimental data.     

A new gas chromatographic methodology for the estimation of the composition of binary gas mixtures

The relatively new technique of reversed-flow gas chromatography (RFGC) is used to determine the diffusion coefficients of pure gases into gas mixtures (D(mix)(exp)). The pure gases are CO and CO(2), and the mixtures consist of H(2) and He in various volume percentage compositions. A linear regression analysis of D(mix)(exp) of CO and CO(2) in various mixtures of H(2) and He against the percentage composition (X(H2) or X(He)) of the mixtures at different temperatures results in an empirical equation relating D(mix)(exp) to the corresponding theoretical values of the diffusion coefficients of CO and CO(2) in the pure gases H(2) and He, as they are calculated from the Fuller-Schettler-Giddings equation. The empirical equation shows that the diffusion coefficient of an analyte gas in a gas mixture is the partial sum of its diffusion coefficients in the component gases, therefore making possible the determination of the mole fractions of the components of the mixture. The found percentage volume compositions are very close to those determined independently by routine gas chromatography, indicating that the proposed RFGC methodology could be successfully applied to the accurate determination of the volume composition of binary gas mixtures.     

Dielectric analysis of sheep erythrocyte ghost. Examination of applicability of dielectric mixture equations

The purpose of this study is to confirm the applicability of dielectric mixture equations in dielectric analysis of biological cell suspensions. Two dielectric mixture equations, the Pauly-Schwan (P-S) equation and the Hanai-Asami-Koizumi (H-A-K) equation were tested using sheep erythrocyte ghosts whose internal solution is identical with the external solution. Dielectric measurements were carried out for the ghost suspensions over a frequency range 10 kHz to 100 MHz; a single dielectric relaxation was found between 100 kHz and 10 MHz. From the dielectric relaxation, the conductivity and permittivity of the ghost interior and the capacitance of the cell membrane were calculated following the P-S and H-A-K equations. When the H-A-K equation was employed (and as expected from the property of the ghosts), the estimated internal conductivity was in good agreement with the external conductivity at volume fractions up to about 0.7. With the P-S equation, on the other hand, the same results as above were obtained but only at low volume fractions below about 0.3. In addition, the H-A-K equation provided a better simulation for the observed relaxation curves than did the P-S equation, especially at high volume fractions. It is, therefore, concluded that the H-A-K equation is applicable to a wider range of volume fraction than is the P-S equation.     

Analyzing nonexponential kinetics with multiple population-period transient spectroscopy (MUPPETS)

A new multidimensional spectroscopy (MUPPETS) was recently introduced (van Veldhoven, E.; et al. ChemPhysChem 2007, 8, 1761) that distinguishes between nonexponential relaxations that are due to heterogeneous dynamics and those that are due to homogeneous dynamics. This paper develops methods for the quantitative analysis of MUPPETS data and demonstrates the ability of this experiment to decompose a complex decay into its components. These methods have been applied to MUPPETS data on the ground-state recovery of auramine in methanol and on a mixture of auramine and coumarin 102 in methanol. The auramine is found to have two kinetically different components, even though the decay times are too similar to be distinguished in a one-dimensional experiment. The dynamics of each component are derived from the MUPPETS data in a model-free procedure in particular without assuming that the individual decays are exponential or that they have similar shapes. In fact, the component decays are each found to be nonexponential and to have different decay shapes. We suggest that the two components are due to ion-paired and nonpaired molecules. The effect of rotation on MUPPETS with all parallel polarizations is analyzed. The nonexponentiality in ground-state recovery signals due to the combination of rotation and population decay is shown to behave as a nearly ideal homogeneous nonexponentiality. This prediction is confirmed in a mixture of auramine and coumarin. MUPPETS allows the decay from the fast relaxing auramine to be removed from the mixture, leaving only the rotation/population decay of the coumarin.     

Azeotropic phenomena in a dilute solution of lithium hydride in lithium at liquid-vapor phase equilibrium

A Li-LiH-type system under liquid-vapor phase equilibrium conditions was considered. Liquid is a binary infinitely dilute solution of lithium hydride in lithium, and the coexisting vapor phase is a multi-component chemically reacting ideal mixture of gas components. The phenomenon of the existence of azeotropy in such systems, earlier unknown, was established. The concentration of the components was expressed in the atomic fractions of hydrogen in both phases. The temperature and concentration boundaries of the azeotropic zone were found. The trends revealed are of importance for applications.