Dielectric constant variation with concentration

Fig. 18. Variation of the dielectric constant e with binder concentration C for polyester syntactic foams with PVC microspheres Original polyester dielectric constants (1) 2.0, (2) 2.2, (3) 2.4, and (4) 2.6 521...

The exponential term is the ratio of the electrostatic to thermal energy, with a the distance at which the ions can be considered paired, k is Boltzmann s constant, and e is the average dielectric constant of the solvent ave- The ion size parameter a is a constant with temperature showing little variation with solvent. The variation of Ki does depend on the variation of the dielectric constant(s) with temperature. Once the values for a, e(T), m(T), and /x (orientation) are known for a given solute/solvent system, the current as a function of temperature and concentration may be considered determined. Experimental and calculated results for the system tetra-iso- pentyl ammonium bromide in a mixed solvent containing compounds of alkoxy benzylidine-p-amine phenyl esters (APAPA family) re shown in Fig. 5. 

The variations of dielectric constant and of the tangent of the dielectric-loss angle with time provide information on the mobility and concentration of charge carriers, the dissociation of defect clusters, the occurrence of phase transitions and the formation of solid solutions. Techniques and the interpretation of results for sodium azide are described by Ellis and Hall [372]. 

The marked changes in the carbonyl IR bands accompanying the solvent variation from tetrahydrofuran to MeCN coincide with the pronounced differences in colour of the solutions. For example, the charge-transfer salt Q+ Co(CO)F is coloured intensely violet in tetrahydrofuran but imperceptibly orange in MeCN at the same concentration. The quantitative effects of such a solvatochromism are indicated by (a) the shifts in the absorption maxima and (b) the diminution in the absorbances at ACT. The concomitant bathochromic shift and hyperchromic increase in the charge-transfer bands follow the sizeable decrease in solvent polarity from acetonitrile to tetrahydrofuran as evaluated by the dielectric constants D = 37.5 and 7.6, respectively (Reichardt, 1988). The same but even more pronounced trend is apparent in passing from butyronitrile, dichloromethane to diethyl ether with D = 26, 9.1 and 4.3, respectively. The marked variation in ACT with solvent polarity parallels the behaviour of the carbonyl IR bands vide supra), and the solvatochromism is thus readily ascribed to the same displacement of the CIP equilibrium (13) and its associated charge-transfer band. As such, the reversible equilibrium between CIP and SSIP is described by (14), where the dissociation constant Kcip applies to a... 

In ether the propagation rate for polyisoprenyllithium (0.03 litre per mole sec) is even lower than in tetrahydrofuran (93). The propagation rate is first order in polyisoprenyllithium in the concentration range IQ-4 to 5 X 10-s molar but above this range the observed order decreases. The authors assumed that the polyisoprenyllithium was extensively dissociated to free ions and that the rate constant derived refers to the free carbanion. From the variation of rate with concentration of polyisoprenyllithium a dissociation constant of 2.5 X 10 a was derived for the dissociation to free ions. This value is too high by a factor of about 10s over that expected in a solvent of dielectric constant about four. It seems more reasonable to assume that the major species present is the... 

The bulk capacitance is (besides geometric parameters) determined by the bulk dielectric constant e, like the mobility, s is usually quite insensitive with respect to P, C, and—unlike the mobility—also to T. Only at high carrier concentrations (e.g., formation of polar associates) or in special compounds (e.g., ferroelectrica) strong variations are to be expected. 

The first theoretical description of the double layers assumed that the ions interact via a mean potential, which obeys the Poisson equation.2 Such a simple theory is clearly only approximate and sometimes predicts ionic concentrations in the vicinity of the surface that exceed the available volume.3 There were a number of attempts to improve the model, by accounting for the variation of the dielectric constant in the vicinity of the surface,4 for the volume-exclusion effects of the ions,5 or for additional interactions between ions and surfaces, due to the screened image force potential,6 to the van der Waals interactions of the ions7 with the system, or to the change in hydration energy when an ion approaches the interface.8... 

Equivalent Conductance Minima.—Provided the dielectric constant of the medium is greater than about 30, the conductance behavior in that medium is usually similar to that of electrolytes in water the differences are not fundamental and are generally differences of degree only. With solvents of low dielectric constant, however, the equivalent conductances often exhibit distinct abnormalities. It is frequently found, for example, that with decreasing concentration, the equivalent conductance decreases instead of increasing at a certain concentration, however, the value passes through a minimum and the subsequent variation is normal. In other cases, e.g., potassium iodide in liquid sulfur dioxide and tetra-... 

In addition to solubility and cryoscopic studies, the association of solute molecules may be investigated by the variation of the dielectric constant with concentration. If the solution is non-polar, the value of the dipole moment calculated from the value of the dielectric constant at infinite dilution, obtained by extrapolation, may be close to the value obtained in the gaseous phase. If this be so, there are no anomalous solvent effects, but cases exist where this is not so and such behaviour may be explained by two theories. The first assumes that association of solute molecules persists at low concentrations and may be illustrated with reference to the curious variation of polarization of ethyl alcohol in hexane solution. As the concentration is increased, the polarization falls, passes through a minimum, rises to a maximutn value and then falls to the value for the polarization of pure ethyl alcohol. In dilute solution the molecules are evidently associated in such a way that the dipole moment is decreased, this may occur through the formation of quadrupoles by means of hydrogen bonds, viz... 

In solvents of moderate dielectric constant (e.g. THF, D 7.6 at room temperature) the polymerization systems show measurable conductance. It is clear that the concentration of free ions cannot be large, since conventional inorganic salts are not highly dissociated in such solvents. Figure 3 shows the variation of equivalent conductance with concentration for polystyrylsodium (two ended, Na CH(Ph)CH2. (CHPhCH2 ) q-CH2CH(Ph)"Na" ) in THF at 20°C. A varies as [C] - as expected if the degree of dissociation to free ions is low. A dissociation constant of... 

The polymerization of lactams initiated with carboxylic acids has been found to be first order with respect to the lactam [10, 194, 200]. However, the order of reaction with respect to the initiating acid, eqn. (100), varied from 0.5 for caprolactam [194, 196] to 0.8 for capryllactam [200]. The deviation of the apparent order of reaction from unity can be due to variation in the activity coefficients of the reacting species which are affected by the dielectric constant of the medium [197]. The different polarity and basicity of caprolactam and capryllactam is one of the reasons for the different apparent order of reaction with respect to the initiator concentration. 

It has to be pointed out, however, that the values of K, K2 and K3 depend on the initial concentration of water [2, 3, 5, 12, 221, 225, 232, 234, 235] (Figs. 29 and 30) even when the formation of cyclic oligomers is taken into account [15]. Giori and Hayes [14] demonstrated that the variation of the equilibrium constants with changing initial composition is due to the variation of the activity coefficient of water. Substitution of the water activity for the molar concentration in eqn. (132) yields much lower but fairly constant values of K2 (Fig. 30). Besides this, the variation of the dielectric constant with changing water content will affect the degree of ionization of end groups and, consequently, the proportion of the catalysed and uncatalysed reactions (115)—(117). 

Equation (3) is presumably a quantitative representation of the variation of / within a wide range of concentrations. The fact still remains, however, that the equation has no exact significance, since factors A and B depend upon the dielectric constant, and the third constant is not really a constant. Bjerrum maintains furthermore that association of ions must be reckoned with. 

In the case of charged surfaces, Henderson and Lozada-Cassou pointed out that the physical origin of the hydration repulsion can be attributed to the presence of a layer of lower dielectric constant, e, in the vicinity of the interface. It was demonstrated that the DLVO theory complemented with such a layer correctly predicts the dependence of hydration repulsion on the electrolyte concentration. A further extension of this approach was given by Basu and Sharma, who incorporated the effect of the variation of e in the theory of electrostatic disjoining pressure. Their model provides quantitative agreement with the experimental data at low electrolyte concentration and pH, and qualitative agreement at higher electrolyte concentration and pH. 

Numerous models predict the activity coefficient of individual ions in solution. The one by Debye and Hiickel [8] considers only electrostatic (columbic) interactions between cations and anions in a dilute solution of a single, completely dissociated salt. It is assumed that ion-ion interactions (as opposed to other phenomena such as ion-solvent interactions, ion solvation effects, and variations in the solvent dielectric constant with salt concentration) cause the ion activity coefficients to deviate from 1.0. From a practical point, only the Debye-Hiickel activity coefficient relationship is needed, along with some knowledge of the theory s shortcomings, which restrict its application. For a dilute electrolytic solution containing a binary salt (i.e., a salt with one type each of cation and anion species), the ion activity coefficient from Debye-Hiickel theory is given by... 

Capacitance Methods. Capacitance methods have been used to measure solids concentration in slurry pipelines (79). This method requires the dielectric constant of the solids and the carrying fluid to be significantly different. Sand-water slurry is a good example to use the capacitance method. In this case, the dielectric constant for water is 80, whereas that of the sand particles is 5. The method relies on the variation of the dielectric constant of the mixture, Em, with the solids concentration, C. For homogeneous slurries of spherical particles at low solids concentration, Maxwell s correlation can be used to predict the dielectric constant of the mixture. However, several investigators assumed that the relationship of the dielectric constant of the mixture and solids concentration was linear, as follows ... 

In solvents of low dielectric constant, ion association occurs. The appearance of ion pairs A B and ion triplets A B A and B A B results in a very rapid variation of conductivity with concentration. 

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