Electroneutral combinations

If several ( ) charged species i equilibrate across the phase boundary, the set of Eqns. (4.116) has to be solved simultaneously for i = 1,2,..This does not lead to an over-determination of Atpb but ensures that the chemical potentials of the electroneutral combinations of the ions (= neutral components of the system) are constant across the interface. The electric structure (space charge) of interfaces will be discussed later. 

Electroneutral combinations are often favored by enthalpic against entropic contributions, however with noticeable exceptions. Thus, crown ether 18-C-6 complexes with e.g. free amines in methanol show stability constants around lgK= 2.5 0.1, quite independent of the amine structure, but very sizeable differences in AH, ranging from 1 or 2 kJ/mol for secondary or tertiary amines to 30 kJ/mol for primary amines with surprisingly favorable entropic TAS values of up to 13 kJ/mol. Protonated amines show increased lg K values of up to 4.4, mainly due to enthalpic advantages, and not. as one might expect for the more polar combinations, due to entropic effects, although these are also sizeable.[38]... 

The r.h.s. s only contain measurable variables. The ionic components of charge and or are obtainable except for a constant, by Integration of the Esln-Markov coefficient with respect to a°, see 13.4.16). Here, no single ionic excesses are counted but sums of electroneutral combinations, including the negative adsorption of electrolyte,, see 13.4.8). Therefore, dy is also... 

Table B-4, Table B-5, Table B-6 and Table B-7 contain the selected specific ion interaction coefficients used in this review, according to the specific ion interaction theory described. Table B-4 contains cation interaction coefficients with Cl", CIO" andNOj, Table B-5 anion interaction coefficients with Li, Na" (or NH ) and K, and Table B-7 neutral species—electroneutral combination of ions. The coefficients have the units of kgmof and are valid for 298.15 K and 1 bar. The species are ordered by charge and appear, within each charge class, in standard order of arrangement, cf. Section II. 1.8.

Table B-7 SIT interaction coefficient z(j,k) kg mol for neutral species,/ with k, electroneutral combination of ions.

Let us consider now the case when a solution contains a mixture of two anionic (or cationic) surfactants (for example, homologues RiX and R2X with a eommon eounterion X ) with addition of inorganic electrolyte XY. In such systems the counterion concentration is given by the sum of concentrations of RiX, R2X and XY. For simplicity, the saturation adsorptions of the two homologues will be taken as equal, i.e., o)ix= o)2x=2too. After consideration of the surface-to-bulk distribution of both electroneutral combinations of ions, the surface layer equation of state for the Frumkin-type non-ideality of a mixture of two ionic surfactants can be written in a form similar to Eq. (2.35), where it is assumed that l/tO, = Corresponding... 

As in the binary system, 0, =Xj, but for the ionic solutes 0, =2x] and 02=2xj. In Eq. (3.32) the factor 2 can be omitted when the molar area of the ions toi is introduced instead of (B. After consideration of the surface-to-bulk distribution of both electroneutral combinations of ions, we arrive at the equation for the adsorption isotherm of the two surfactants RiX and R2X, respectively... 

All mixture data in Figure 3.69 merge to a single curve for R R" when plotted as a function of the ionic product of the three electroneutral combinations. In such mixtures, the adsorption is represented almost completely by the equimolar composition R"R", which has a very high surface activity, without any noticeable contribution of Na R" and R Br" over the entire range of mixing ratios [89]. Thus one can describe the surface tensions of the mixtures by Eq. (3.1) combined with an isotherm equation for R R ... 

For small periodic surface perturbations as it is the case in longitudinal wave experiments Bonfillon and Langevin [104] derived a respective solution. Joos et al. [105] demonstrated that the kinetic problem becomes extremely simple for solutions of mixed anionic and cationic surfactants, and the adsorption of the resulting electroneutral combination of the two molecules is governed by the simple diffusion model [106, 107]. 

You should be aware of one important difference between the electrochemical potential and the chemical potential. The chemical potential describes the free energy of inserting one particle into a particular place or phase, subject to any appropriate constraint. Constraints are introduced explicitly. In contrast, the electrochemical potential always carries an implicit constraint with it overall electroneutrality must be obeyed. This is a very strong constraint. You can never insert a single ion in a volume of macroscopic dimensions because that would violate electroneutrality. You can insert only an electroneutral combination of ions. 

A thorough theoretical investigation was made of the dynamic surface properties of mixed anionic-cationic surfactant solutions [50]. This study is more general than previous studies [51], which considered both ionic species to diffuse as an electroneutral combination, because it includes cases where the anionic and cationic surfactants can diffuse to the surface at different rates and will affect the diffusion of their inorganic counterions as well. 

When the diffusion time has comparable magnitude with the time of formation of the electric double layer, the quasiequilibrium model is not applicable. Lucassen et al. [Ill] and Joos et al. [112] established that mixtures of anionic and cationic surfactants diffuse as a electroneutral combination in the case of small periodic fluctuations of the surface area consequently, this process is ruled by the simple diffusion equation. The e/ec ro-diffusion problem was solved by Bonfillon et al. [113] for a similar case of small periodic surface corrugations related to the capillary-wave methods of dynamic surface-tension measurement. 

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