Diffusion potential solution

Reference electrodes are used in the measurement of potential [see the explanation to Eq. (2-1)]. A reference electrode is usually a metal/metal ion electrode. The electrolyte surrounding it is in electrolytically conducting contact via a diaphragm with the medium in which the object to be measured is situated. In most cases concentrated or saturated salt solutions are present in reference electrodes so that ions diffuse through the diaphragm into the medium. As a consequence, a diffusion potential arises at the diaphragm that is not taken into account in Eq. (2-1) and represents an error in the potential measurement. It is important that diffusion potentials be as small as possible or the same in the comparison of potential values. Table 3-1 provides information on reference electrodes. 

The error due to diffusion potentials is small with similar electrolyte solutions (cj = C2) and with ions of equal mobility (/ Iq) as in Eq. (3-4). This is the basis for the common use of electrolytic conductors (salt bridge) with saturated solutions of KCl or NH4NO3. The /-values in Table 2-2 are only applicable for dilute solutions. For concentrated solutions, Eq. (2-14) has to be used. 

Greater deviations which are occasionally observed between two reference electrodes in a medium are mostly due to stray electric fields or colloid chemical dielectric polarization effects of solid constituents of the medium (e.g., sand [3]) (see Section 3.3.1). Major changes in composition (e.g., in soils) do not lead to noticeable differences of diffusion potentials with reference electrodes in concentrated salt solutions. On the other hand, with simple metal electrodes which are sometimes used as probes for potential controlled rectifiers, certain changes are to be expected through the medium. In these cases the concern is not with reference electrodes, in principle, but metals that have a rest potential which is as constant as possible in the medium concerned. This is usually more constant the more active the metal is, which is the case, for example, for zinc but not stainless steel. 

In addition, the temperature dependence of the diffusion potentials and the temperature dependence of the reference electrode potential itself must be considered. Also, the temperature dependence of the solubility of metal salts is important in Eq. (2-29). For these reasons reference electrodes with constant salt concentration are sometimes preferred to those with saturated solutions. For practical reasons, reference electrodes are often situated outside the system under investigation at room temperature and connected with the medium via a salt bridge in which pressure and temperature differences can be neglected. This is the case for all data on potentials given in this handbook unless otherwise stated. 

When paint films are immersed in water or solutions of electrolytes they acquire a charge. The existence of this charge is based on the following evidence. In a junction between two solutions of potassium chloride, 0 -1 N and 0 01 N, there will be no diffusion potential, because the transport numbers of both the and the Cl" ions are almost 0-5. If the solutions are separated by a membrane equally permeable to both ions, there will still be no diffusion potential, but if the membrane is more permeable to one ion than to the other a diffusion potential will arise it can be calculated from the Nernst equation that when the membrane is permeable to only one ion, the potential will have the value of 56 mV. 

It is easy to measure the potential of this system and it has been found that membranes of polystyrene, linseed oil and a tung oil varnish yielded diffusion potentials of 43-53 mV, the dilute solution being always positive to the concentrated. Similar results have been obtained with films of nitrocellulose, cellulose acetate , alkyd resin and polyvinyl chloride . 

Note that a number of complicating factors have been left out for clarity For instance, in the EMF equation, activities instead of concentrations should be used. Activities are related to concentrations by a multiplicative activity coefficient that itself is sensitive to the concentrations of all ions in the solution. The reference electrode necessary to close the circuit also generates a (diffusion) potential that is a complex function of activities and ion mobilities. Furthermore, the slope S of the electrode function is an experimentally determined parameter subject to error. The essential point, though, is that the DVM-clipped voltages appear in the exponent and that cheap equipment extracts a heavy price in terms of accuracy and precision (viz. quantization noise such an instrument typically displays the result in a 1 mV, 0.1 mV, 0.01 mV, or 0.001 mV format a two-decimal instrument clips a 345.678. .. mV result to 345.67 mV, that is it does not round up ... 78 to ... 8 ). 

The ionic concentration gradients in the transition layer constitute the reason for development of the diffusion component E of electric field strength (the component arising from the difference in diffusion or mobihties between the individual ions). The diffusion potential between the solutions, 9 = - / can be calculated... 

When both solutions are binary and identical in nature and differ only by their concentration and the component E of the held strength is given by Eq. (4.18), the diffusion potential 9 can be expressed by Eq. (4.19). An equation of this type was derived by Walther Nemst in 1888. Like other equations resting on Eick s law (4.1), this equation, is approximate and becomes less exact with increasing concentration. For the more general case of multicomponent solutions, the Henderson equation (1907),... 

TABLE 5.1 Diffusion Potentials Caiculated for Interfaces Between Aqueous Solutions of Different Composition from Eq. (5.2) or (5.3), and Simiiar Potentials Determined Experimentally (cp = — /( )... 

Aqueous solutions of the salts KCl and NH4NO3 are of interest inasmuch as here the mobilities (and also the diffusion coefficients) of the anion and cation are very similar. The higher the concentration of these salts, the larger is the contribution of their ions to transition-layer composition and, as can be seen from Table 5.1, the lower the diffusion potentials will be at interfaces with other solutions. This situation is often used for a drastic reduction of diffusion potentials in cells with transference. To this end one interposes between the two solutions a third solution, usually saturated KCl solution (which is about 4.2mol/L) ... 

In laboratory practice salt bridges are often used to connect the vessels holding the two solutions. The reduction of the overall diffusion potential is particularly marked... 

We shall write (p) and (q) for the membrane surface layers adjacent to solutions (a) and (p), respectively. Using the equations reported in Section 5.3, we can calculate the ionic concentrations in these layers as well as the potential differences and between the phases. According to Eq. (5.1), the expression for the total membrane potential additionally contains the diffusion potential within the membrane itself, where equilibrium is lacking. Its value can be found with the equations of Section 5.2 when the values of and have first been calculated. 

The trends of behavior described above are found in solutions containing an excess of foreign electrolyte, which by definition is not involved in the electrode reaction. Without this excess of foreign electrolyte, additional effects arise that are most distinct in binary solutions. An appreciable diffusion potential q) arises in the diffusion layer because of the gradient of overall electrolyte concentration that is present there. Moreover, the conductivity of the solution will decrease and an additional ohmic potential drop will arise when an electrolyte ion is the reactant and the overall concentration decreases. Both of these potential differences are associated with the diffusion layer in the solution, and strictly speaking, are not a part of electrode polarization. But in polarization measurements, the potential of the electrode usually is defined relative to a point in the solution which, although not far from the electrode, is outside the diffusion layer. Hence, in addition to the true polarization AE, the overall potential drop across the diffusion layer, 9 = 9 + 9ohm is included in the measured value of polarization, AE. ... 

The equation obtained can be used when the electrode potential can be varied independent of solution composition (i.e., when the electrode is ideally polarizable). For practical calculations we must change from the Galvani potentials, which cannot be determined experimentally, to the values of electrode potential that can be measured E = ( q + const (where the constant depends on the reference electrode chosen and on the diffusion potential between the working solution and the solution of the reference electrode). When a constant reference electrode is used and the working solutions are sufficiently dilute so that the diffusion potential will remain practically constant when their concentration is varied, dE (i(po and... 

Because of solubility changes, the saturated calomel RE has a large temperature coefficient (0.65 mV/K). Its main advantages are ease of preparation (an excess of KCl is added to the solution) and low values of diffusion potential at interfaces with other solutions (see Section 5.2). The potentials of calomel REs can be reproduced to 0.1 mV. These electrodes are very convenient for measurements in neutral solutions (particularly chloride solutions). 

As briefly mentioned in the previous section, PCS provides quantitative information on the lifetime of the non-radiative state for molecules in solution in the time range from sub-microseconds to seconds. This method can, potentially, be applied to the characterization of the photophysical properties of quantum dots freely diffusing in solution with higher temporal resolution than the previous SPD. 

An ion-selective electrode contains a semipermeable membrane in contact with a reference solution on one side and a sample solution on the other side. The membrane will be permeable to either cations or anions and the transport of counter ions will be restricted by the membrane, and thus a separation of charge occurs at the interface. This is the Donnan potential (Fig. 5 a) and contains the analytically useful information. A concentration gradient will promote diffusion of ions within the membrane. If the ionic mobilities vary greatly, a charge separation occurs (Fig. 5 b) giving rise to what is called a diffusion potential. 

In such cells, aqueous solutions contain electrolytes with a common cation. The EMF of this cell is equal to the difference of distribution potentials of both electrolytes and to the diffusion potential in the organic phase. Under appropriate conditions the EMF depends only on the difference of distribution potentials. It should be noted that cells of this type can also contain many and various ions in both phases. 

The foregoing text highlights the fact that at the interface between electrolytic solutions of different concentrations (or between two different electrolytes at the same concentration) there originates a liquid junction potential (also known as diffusion potential). The reason for this potential lies in the fact that the rates of diffusion of ions are a function of their type and of their concentration. For example, in the case of a junction between two concentrations of a binary electrolyte (e.g., NaOH, HC1), the two different types of ion diffuse at different rates from the stronger to the weaker solution. Hence, there arises an excess of ions of one type, and a deficit of ions of the other type on opposite sides of the liquid junction. The resultant uneven distribution of electric charges constitutes a potential difference between the two solutions, and this acts in such a way as to retard the faster ion and to accelerate the slower. In this way an equilibrium is soon reached, and a steady potential difference is set up across the boundary between the solutions. Once the steady potential difference is attained, no further net charge transfer occurs across the liquid junction and the different types of ion diffuse at the same rate. 

A permeable membrane, which merely serves to prevent rapid mixing of components within solutions on both sides of the membrane in principle, no potential occurs unless a diffusion potential occurs. 

In coulometry these exchange membranes are often used to prevent the electrolyte around the counter electrode from entering the titration compartment (see coulometry, Section 3.5). However, with membrane electrodes the ion-exchange activity is confined to the membrane surfaces in direct contact with the solutions on both sides, whilst the internal region must remain impermeable to the solution and its ions, which excludes a diffusion potential nevertheless, the material must facilitate some ionic charge transport internally in order to permit measurement of the total potential across the membrane. The specific way in which all these requirements are fulfilled in practice depends on the type of membrane electrode under consideration. 

We assume that between the membrane phase (n) and the solutions (S and S0) no diffusion potentials occur, i.e., the potential differences (n/S) and 0(n/So) are merely caused by ion-exchange activity. Further, all phases are considered to be homogeneous so that is constant within the membrane and also pi = plQ within the solutions. Let us at first consider the simple system of selective indication of an univalent anion A in the presence of an interfering univalent anion B. Here we obtain the following exchange equilibrium ... 

Here, x is the coordinate normal to the diaphragm, so that d — q—p. The liquid junction potential A0L is the diffusion potential difference between solutions 2 and 1. The liquid junction potential can be calculated for more complex systems than that leading to Eq. (2.5.31) by several methods. A general calculation of the integral in Eq. (2.5.30) is not possible and thus assumptions must be made for the dependence of the ion concentration on x in the liquid junction. The approximate calculation of L. J. Henderson is... 

In potentiometric measurements the simplest approach to the liquid-junction problem is to use a reference electrode containing a saturated solution of potassium chloride, for example the saturated calomel electrode (p. 177). The effect of the diffusion potential is completely suppressed if the solutions in contact contain the same indifferent electrolyte in a sufficient... 

A similar situation occurs in tracer diffusion. This type of diffusion occurs for different abundances of an isotope in a component of the electrolyte at various sites in the solution, although the overall concentration of the electrolyte is identical at all points. Since the labelled and the original ions have the same diffusion coefficient, diffusion of the individual isotopes proceeds without formation of the diffusion potential gradient, so that the diffusion can again be described by the simple form of Fick s law. 

One potential solution to the problem of filter-restricted diffusion of a solute is to use a filter with larger pores. However, there are practical limitations to how porous a filter one can use and still support the monolayer. In some cases, if the pores are too large (e.g., >1-3 pm diameter), the cell can actually migrate through the filter and begin to grow on the basolateral side of the membrane. This results in a poorly defined monolayer and should be avoided whenever possible. 

PBP model considers the membrane potential as a sum of the potentials formed at the membrane-solution interfaces (phase boundary potentials), and generally neglects any diffusion potential within the membrane ... 

Oxidative UPD involves the oxidation of species to form an atomic layer where the precursor contains the element in a negative oxidation state. A classic example is the formation of oxide layers on Pt and Au, where water is oxidized to form atomic layers of oxygen. Halide adsorption can be thought of similarly, where a species such as I oxidatively adsorbs on a metal surface as the halide atom. In that case, a bulk film is not formed at more positive potentials, but the diatomic is generated and diffuses into solution. With respect to compound formation, oxidative UPD from a sulfide solution is a good example ... 

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