Debye liquid electrolytes

The local compostion model is developed as a symmetric model, based on pure solvent and hypothetical pure completely-dissociated liquid electrolyte. This model is then normalized by infinite dilution activity coefficients in order to obtain an unsymmetric local composition model. Finally the unsymmetric Debye-Huckel and local composition expressions are added to yield the excess Gibbs energy expression proposed in this study. 

The Debye-Huckel concept fails very soon (see Fig. 19) and probably earlier than in liquid electrolytes (at latest for 1 ). Also... 

Solid electrolytes are not usually solutions of a conducting solute in a solvent matrix. Liquid electrolyte solutions are often sufficiently dilute (1-10 millimolar) to be described by the textbook theories of Debye-Hiickel or Onsager and oppositely charged ions are sufficiently dispersed for interaction between anions and cations to be minimized. By contrast, molten salts are very concentrated (typically 2-20 molar), ion-ion interactions are pronounced, and alternative theories such as that of Fuoss [105] are required. Polymer electrolytes typically have [repeat unit] [cation] ratios, n, in the range 8 to 30, corresponding to 0.7 to 2.5 molar for PEOn LiC104 [106], and ion clustering is an important feature of their behaviour. To account for both the ion-polymer and ion-cluster interactions, Ratner and Nitzan have developed dynamic percolation theory [107]. 

An important quantity in solid and liquid electrolytes is the Debye length Ld, given by... 

VOINOV You said the Debye length you calculate in the case of solid electrolyte is smaller than atomic dimension and consequently diffuse layer effects are irrelevant- Presumably, you use for this calculation the Debye length formula developed for the case of aqueous electrolytes. As you have stressed, in many solid electrolytes, only one species can migrate and in that case the solution of Poisson s equation is not the same as in the case of liquid electrolytes. As long as you do not have this solution and have shown it can be approximated by an exponential, and that this exponential is the same as in the case of liquid electrolytes, it seems to me difficult to calculate a Debye length in solid electrolytes. 

Debye length in solid electrolytes. The Debye length Id describes the shielding of an electric field by the charge carriers. The electrostatic potential drops to 1/e of its value within Id- In contrast to diluted media with small concentrations of ions, such as liquid electrolytes, solid electrolytes have very small Debye lengths. 

Lidiard has shown that the Debye-Huckel theory for liquid electrolytes can be applied to the case of charged defects in ionic solids. The activity coefficient for a defect i can be written ... 

The jump relaxation model of Punke is a concept of wide validity [410]. In certain aspects it may be compared to the Debye-Falkenhagen theory [411] of liquid electrolytes. The interaction of the point defects expresses itself in a relatively flat defect potential , that is superimposed on the lattice potential, as shown in Fig. 6.34. 

CRUZ (7) equation for gE of binary electrolyte solution which incorporates a DEBYE - HUCKEL term, a BORN - DEBYE - MAC. AULAY contribution for electric work, and NRTL equation, can be used to represent the vapor-liquid equilibria of volatile electrolyte in the whole range of concentration. 

Very few generalized computer-based techniques for calculating chemical equilibria in electrolyte systems have been reported. Crerar (47) describes a method for calculating multicomponent equilibria based on equilibrium constants and activity coefficients estimated from the Debye Huckel equation. It is not clear, however, if this technique has beep applied in general to the solubility of minerals and solids. A second generalized approach has been developed by OIL Systems, Inc. (48). It also operates on specified equilibrium constants and incorporates activity coefficient corrections for ions, non-electrolytes and water. This technique has been applied to a variety of electrolyte equilibrium problems including vapor-liquid equilibria and solubility of solids. 

The disjoining pressure vs. thickness isotherms of thin liquid films (TFB) were measured between hexadecane droplets stabilized by 0.1 wt% of -casein. The profiles obey classical electrostatic behavior. Figure 2.20a shows the experimentally obtained rt(/i) isotherm (dots) and the best fit using electrostatic standard equations. The Debye length was calculated from the electrolyte concentration using Eq. (2.11). The only free parameter was the surface potential, which was found to be —30 mV. It agrees fairly well with the surface potential deduced from electrophoretic measurements for jS-casein-covered particles (—30 to —36 mV). 

What are the correct values of the potentials In the metal the potential is the same everywhere and therefore 99 has one clearly defined value. In the electrolyte, the potential close to the surface depends on the distance. Directly at the surface it is different from the potential one Debye length away from it. Only at a large distance away from the surface is the potential constant. In contrast to the electric potential, the electroc/zmz caZpotential is the same everywhere in the liquid phase assuming that the system is in equilibrium. For this reason we use the potential and chemical potential far away from the interface. 

For charged particles, the net charge contained by the solvent must balance that carried by the particles. Suppose, in addition to these counterions, there is a concentration Ub of a symmetric electrolyte, where is the number of ion pairs per unit volume of suspension the concentration of ion pairs in the liquid phase is = nb/(l—0). The inverse square Debye length from both contributions then works out to be (Russel et al. 1989)... 

For low pressures (a few atmospheres and lower) we can apply the ideal gas model for gases and ideal mixture models for liquids. This formulation is very common in reactor technology. In some cases at higher pressures, the pressure effect on the gas phase is important. A suitable model for these systems is to use an EOS for the gas phase, and an ideal mixture model for liquids. However, in most situations at low pressures the liquid phase is more non-ideal than the gas phases. Then we will rather apply the ideal gas law for the gas phase, and excess properties for liquid mixtures. For polar mixtures at low to moderate pressures we may apply a suitable EOS for gas phases, and excess properties for liquid mixtures. All common models for excess properties are independent of pressure, and cannot be used at higher pressures. The pressure effect on the ideal (model part of the) mixture can be taken into account by the well known Poynting factor. At very high pressures we may apply proper EOS formulations for both gas and liquid mixtures, as the EOS formulations in principle are valid for all pressures. For non-volatile electrol3d es, we have to apply a suitable EOS for gas phases and excess properties for liquid mixtures. For such liquid systems a separate term is often added in the basic model to account for the effects of ions. For very dilute solutions the Debye-Htickel law may hold. For many electrolyte systems we can apply the ideal gas law for the gas phase, as the accuracy reflected by the liquid phase models is low. 

The orientation and induction interactions are electrostatic effects, so they are not subjected to electromagnetic retardation. Instead, they are subject to Debye screening due to the presence of electrolyte ions in the liquid phases. Thus, for the interaction across an electrolyte solution the screened Hamaker constant is given by the expression " ... 

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