Ion transfer models

Among the dynamical properties the ones most frequently studied are the lateral diffusion coefficient for water motion parallel to the interface, re-orientational motion near the interface, and the residence time of water molecules near the interface. Occasionally the single particle dynamics is further analyzed on the basis of the spectral densities of motion. Benjamin studied the dynamics of ion transfer across liquid/liquid interfaces and calculated the parameters of a kinetic model for these processes [10]. Reaction rate constants for electron transfer reactions were also derived for electron transfer reactions [11-19]. More recently, systematic studies were performed concerning water and ion transport through cylindrical pores [20-24] and water mobility in disordered polymers [25,26]. 

In this chapter, we wiU review electrochemical electron transfer theory on metal electrodes, starting from the theories of Marcus [1956] and Hush [1958] and ending with the catalysis of bond-breaking reactions. On this route, we will explore the relation to ion transfer reactions, and also cover the earlier models for noncatalytic bond breaking. Obviously, this will be a tour de force, and many interesting side-issues win be left unexplored. However, we hope that the unifying view that we present, based on a framework of model Hamiltonians, will clarify the various aspects of this most important class of electrochemical reactions. 

Schmickler W. 1995. A unified model for electrochemical electron and ion transfer reactions. Chem Phys Lett 152-160. 

On the assumption that = 2, the theoretical values of the ion solvation energy were shown to agree well with the experimental values for univalent cations and anions in various solvents (e.g., 1,1- and 1,2-dichloroethane, tetrahydrofuran, 1,2-dimethoxyethane, ammonia, acetone, acetonitrile, nitromethane, 1-propanol, ethanol, methanol, and water). Abraham et al. [16,17] proposed an extended model in which the local solvent layer was further divided into two layers of different dielectric constants. The nonlocal electrostatic theory [9,11,12] was also presented, in which the permittivity of a medium was assumed to change continuously with the electric field around an ion. Combined with the above-mentioned Uhlig formula, it was successfully employed to elucidate the ion transfer energy at the nitrobenzene-water and 1,2-dichloroethane-water interfaces. 

Based on these measurements, a new model of the transfer of hydrophilic ions across the 0/W interface was proposed (see Fig. 8). In this model, the hydrophilic ion transfers from W to O with some water molecules associated with the ion. A typical example in Fig. 8 shows that a sodium ion transfers across the NB/W interface with four water molecules. In theoretical treatment of of such a hydrophilic ion, therefore, the transferring... 

Therefore the lattice-gas model has proved most useful for the study of those processes in which the ionic double layer plays a major role, and there are quite a few. So it has been used to investigate the interfacial capacity, electron and ion-transfer reactions, and even such complex processes as ion pairing and assisted ion transfer. Because of its simplicity we carmot expect this model to give quantitative results for particular systems, but it is ideally suited to qualitative investigations such as the prediction of trends and orders of magnitude for various effects. 

In the following we will review recent applications of the lattice-gas model to liquid-liquid interfaces. We will start by presenting the basics of the model and various ways of treating its statistical mechanics. Then we will present model calculations for interfacial properties and for electron- and ion-transfer reactions. It is one of the virtues of the lattice-gas model that it is sufficiently flexible to serve as a framework for practically all processes at these interfaces. 

Of course, the lattice gas is not the only simple model that has been proposed for liquid-liquid interfaces. So we will conclude this review by a survey of several other models, which have usually been devised for certain aspects such as the interfacial capacity or ion transfer. Some of these models give a similar view of the interface, while others are radically different. 

In the two bulk phases the potential of mean force is constant, but it may vary near the interface. The difference in the bulk values of the chemical part is the free energy of transfer of the ion, which in our model is —2mu (we assume u < 0). Let us consider the situation in which the ion-transfer reaction is in equilibrium, and the concentration of the transferring ion is the same in both phases the system is then at the standard equilibrium potential 0oo- In Ihis case the potential of mean force is the same in the bulk of both phases the chemical and the electrostatic parts must balance ... 

Unfortunately, at the present time the experimental results for ion-transfer reactions are contradictory, so that it is not possible to verify the predictions of this model. Also, this model is only valid if the rate is determined by the ion-transfer step, and not by transport, and if the concentration of the supporting electrolyte is sufficiently low so that the extension of the space-charge regions is less than the width X of the region where the two solvents mix. These conditions are not always fulfilled in experiments. 

The above model can be extended to assisted ion transfer, in which the ion forms a complex with a suitable ionophore. The various mechanisms for such reactions have been classified by Shao et al. [21] and reviewed by Girault [22]. Schmickler [23] has examined the case of transfer by interfacial complexation, which is marked by the following reaction sequence (see Fig. 14) The transferring ion moves from the bulk of solution 1 towards the interface with solution 2, in which it is poorly soluble. At the interface it reacts with an ionophore from solution 2, and then the complexed ion is transferred towards the bulk of solution 2. 

In the lattice-gas model, as treated in Section IV.D above, ion transfer is viewed as an activated process. In an alternative view it is considered as a transport governed by the Nernst-Planck or the Langevin equation. These two models are not necessarily contra-dictive for high ionic concentrations the space-charge regions and the interface have similar widths, and then the barrier for ion transfer may vanish. So the activated mechanism may operate at low and the transport mechanism at high ionic concentrations. 

Unfortunately the development of models is hindered by a lack of reliable experimental data. For example, the rates of ion-transfer reactions measured at different times and by different groups vary widely. Also, it has been suggested that the high interfacial capacities that are measured in certain systems are an experimental artifact [13]. While this is frustrating for the researcher who wants to decide between competing models, it can also be viewed as a sign that the electrochemistry of liquid-liquid interfaces is an active field, where fundamental issues are just being explored. 

The voltammograms at the microhole-supported ITIES were analyzed using the Tomes criterion [34], which predicts ii3/4 — iii/4l = 56.4/n mV (where n is the number of electrons transferred and E- i and 1/4 refer to the three-quarter and one-quarter potentials, respectively) for a reversible ET reaction. An attempt was made to use the deviations from the reversible behavior to estimate kinetic parameters using the method previously developed for UMEs [21,27]. However, the shape of measured voltammograms was imperfect, and the slope of the semilogarithmic plot observed was much lower than expected from the theory. It was concluded that voltammetry at micro-ITIES is not suitable for ET kinetic measurements because of insufficient accuracy and repeatability [16]. Those experiments may have been affected by reactions involving the supporting electrolytes, ion transfers, and interfacial precipitation. It is also possible that the data was at variance with the Butler-Volmer model because the overall reaction rate was only weakly potential-dependent [35] and/or limited by the precursor complex formation at the interface [33b]. 

Since the ion transfer is a rather fast process, the faradaic impedance Zj can be replaced by the Warburg impedance Zfy corresponding to the diffusion-controlled process. Provided that the Randles equivalent circuit represents the plausible model, the real Z and the imaginary Z" components of the complex impedance Z = Z —jZ " [/ = (—1) ] are given by [60]... 

This chapter is basically divided in two parts, namely, the study of surface pressure-molecular area (jr — A) isotherms of phospholipids at ITIES and their effect on ion transfer. In the first part, the emphasis is put on topics which have been left out from Ref [5], i.e., Langmuir film techniques and theoretical modeling of jr — isotherms, as well as on the latest progress in the field, especially on experiments that combine Langmuir techni-... 

The description of the ion transfer process is closely related to the structure of the electrical double layer at the ITIES [50]. The most widely used approach is the combination of the BV equation and the modified Verwey-Niessen (MVN) model. In the MVN model, the electrical double layer at the ITIES is composed of two diffuse layers and one ion-free or inner layer (Fig. 8). The positions delimiting the inner layer are denoted by X2 and X2, and represent the positions of closest approach of the transferring ion to the ITIES from the organic and aqueous side, respectively. The total Galvani potential drop across the interfacial region, AgCp = cj) — [Pg.545]

Various types of research are carried out on ITIESs nowadays. These studies are modeled on electrochemical techniques, theories, and systems. Studies of ion transfer across ITIESs are especially interesting and important because these are the only studies on ITIESs. Many complex ion transfers assisted by some chemical reactions have been studied, to say nothing of single ion transfers. In the world of nature, many types of ion transfer play important roles such as selective ion transfer through biological membranes. Therefore, there are quite a few studies that get ideas from those systems, while many interests from analytical applications motivate those too. Since the ion transfer at an ITIES is closely related with the fields of solvent extraction and ion-selective electrodes, these studies mainly deal with facilitated ion transfer by various kinds of ionophores. Since crown ethers as ionophores show interesting selectivity, a lot of derivatives are synthesized and their selectivities are evaluated in solvent extraction, ion-selective systems, etc. Of course electrochemical studies on ITIESs are also suitable for the systems of ion transfer facilitated by crown ethers and have thrown new light on the mechanisms of selectivity exhibited by crown ethers. 

The theory of such processes was developed in an important paper by Ruckenstein and Prieve (1973). Their treatment and the later treatment of Samec (Samec et al, 1986) for the case of ion transfer is essentially the same, and we now develop a simplified and unified model for both systems using the concepts of transition-state theory. 

However, a closer inspection of the experimental data reveals several differences. For ion-transfer reactions the transfer coefficient a can take on any value between zero and one, and varies with temperature in many cases. For outer-sphere electron-transfer reactions the transfer coefficient is always close to 1/2, and is independent of temperature. The behavior of electron-transfer reactions could be explained by the theory presented in Chapter 6, but this theory - at least in the form we have presented it - does not apply to ion transfer. It can, in fact, be extended into a model that encompasses both types of reactions [7], though not proton-transfer reactions, which are special because of the strong interaction of the proton with water and because of its small mass. 

While a treatment of this unified model for electron- and ion-transfer reactions is beyond the scope of this book, we can gain some insight into the nature of electrochemical reactions by looking at some of its results. In particular, this model makes it possible to calculate the potential-energy surface of a reaction. To understand the meaning of... 

In a recent upsurge of studies on electron transfer kinetics, importance was placed on the outer shell solvent continuum, and the solvent was replaced by an effective model potential or a continuum medium with an effective dielectric constant. Studies in which the electronic and molecular structure of the solvent molecules are explicitly considered are still very rare. No further modem quantum mechanical studies were made to advance the original molecular and quantum mechanical approach of Gurney on electron and proton (ion) transfer reactions at an electrode. 

In the early 1990s a few classical semimoleculai and molecular models of electron transfer reactions involving bond breaking appeared in the literature. A quantum mechanical treatment of a unified mr el of electrochemical electron and ion transfer reactions involving bond breaking was put forward by Schmickler using Anderson-Newns Hamiltonian formalism (see Section V.2). 

Following the early studies on the pure interface, chemical and electrochemical processes at the interface between two immiscible liquids have been studied using the molecular dynamics method. The most important processes for electrochemical research involve charge transfer reactions. Molecular dynamics computer simulations have been used to study the rate and the mechanism of ion transfer across the water/1,2-dichloroethane interface and of ion transfer across a simple model of a liquid/liquid interface, where a direct comparison of the rate with the prediction of simple diffusion models has been made. ° ° Charge transfer of several types has also been studied, including the calculations of free energy curves for electron transfer reactions at a model liquid/liquid... 

One of the surprising aspects of this and other studies using naked metal ions as models for electron-transfer catalysis are the many analogies found to known transition metal chemistry, either in the gas phase with naked ions or for complexes under more normal conditions. Clearly, such simple models as the beryllium cation cannot account for transition metal reactivity, but they do have the advantage that, because of their very simplicity, the reasons for their effects are relatively clear. The fact that Be can catalyze a given reaction does not necessarily mean that, for instance, a transition metal does not use d-orbitals to catalyze the same reaction but it does mean that d-orbitals are not a prerequi-... 

Using a simple electrostatic interaction-based model factored into reaction rate theory, the energy barrier for ion hopping was related to the cation hydration radius. The conductance versus water content behavior was suggested to involve (1) a change in the rate constant for the elementary ion transfer event and (2) a change in the membrane microstructure that affects conduction pathways. 

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