The Wien Effect and lonic Association

Abstract

High field conductance is sensitively dependent on ion association, so that if one has available theoretical means to compute high field conductances, experimental measurements can be used to determine association constants. The authors have programmed for machine computation the Onsager-Kim strong electrolyte theory of the Wien effect, combined with the Onsager weak electrolyte theory in such a way as to account for the high field conductances of associated electrolytes. The computation is a considerable improvement over previous ones, being both more precise and much faster. Graphs are presented of a number of computed results, compared with experimental measurements, illustrating the way in which theory and measurement can be combined to obtain information about ion association. The majority of these calculations have not been attempted previously.Experimental measurements of the high field conductance quotient (Wien effect) have been found useful for studying ionic association in solutions ranging from those which one would characterize as involving strong electrolytes, through the middle ground where ionic association significantly alters the behavior of what would otherwise be regarded as strong electrolytes, to those of electrolytes which are sufficiently associated to be classified as weak. It is convenient to compare the experimental Wien effect measurements with computed theoretical results and to use the theory to derive estimates of ionic association in the solutions. Until recently, application of this approach has been hindered by the lack of a theory of the Wien effect for nonsymmetrical valence-type strong electrolytes and by the complexity and tediousness of the calculations required. The first of these impediments has been removed by the appearance of the Onsager-Kim theory (1) for the high field conductance of nonsymmetrical strong electrolytes. The authors have now programmed this theory for machine computation on the IBM 650 computer, have included in this program a correction for association utilizing the Onsager theory for weak electrolytes, and have also incorporated into the program a computation of the mean activity coefficient of the electrolyte under examination, at zero field, by the method developed by Poirier (2) based on the Mayer cluster theory of imperfect gases. The present authors have used this program to refine considerably an earlier calculation of Bailey and Patterson (3) and to show a number of possible ways to study ionic association, the results of these computations being presented in the sections which follow.

Volume change for the formation of magnesium sulfate ion pairs at various temperatures

“…Fisher45•46 has shown that these individual AV°'s yield a plot of RT log KA [where KA is calculated from eq 36] that is in excellent agreement with the experimental value (the slope gives 7.7 cm3/mol). From eq 38, we obtain AVa°= 0 + 0.052[3 + 14 to 18 + (14 to 18)/0.11] « 6.5 to 8.3 cm3/mol (39) using Kn = 1.0 and Km = 0.11. If the Kn = 1.97 and Km = 0.17 of Atkinson and Petrucci37 are used, we obtain °= 9.9 to 12.7 cm3/mol, which is 2.7 to 5.5 cm3/mol larger than the experimental value.…”

Quantification of Steady-State Ion Transport through Single Conical Nanopores and a Nonuniform Distribution of Surface Charges

“…The high applied electric field is believed to affect the distribution of those deprotonation sites and thus lead to nonuniform surface charge distribution. 20 This is analogous to the electron transfer reactions driven by the applied electric field in solution at a bipolar electrode, which consists of an isolated electrode on an insulating substrate (with no direct contact with external circuit). Therefore, a uniform SCD value at the substrate− solution interface defined in existing theoretical models might be inadequate to describe the experimental system.…”

“…The origin of the proposed SCD gradient is attributed to the applied electric field localized near the conical nanopore orifice. 20 Illustrated in Scheme 1, the SCD will decrease from a maximum value at the pore orifice to the bulk value of ca. −1 mC m −2 at a certain depth, where the electric field becomes negligible.…”

Field-dependent ion transport in disordered solid electrolytes

“…Apart from single-particle hopping models discussed below, phenomenological models were proposed taking into account (i) the interactions among the mobile ions and (ii) the interactions between mobile ions and the rigid matrix. Examples are Wien effect-type approaches 29 and Pool-Frenkel-type approaches. 20,21 When considering single-particle hopping models, it is instructive to start with a regular hopping model with ionic sites of identical energy and with barriers of identical height between the sites.…”