A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 22
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The glass membrane is our startingpoint because it offers a fairly complete view of the fundamentals as well as the usualcomplications found in practical devices.2.4.2 Glass ElectrodesThe ion-selective properties of glass/electrolyte interfaces were recognized early in the20th century, and glass electrodes have been used since then for measurements of pH andthe activities of alkali ions (24, 37, 46-55). Figure 2.4.1 depicts the construction of a typi-2.4 Selective Electrodes \ 75Ag wireExcess AgCIInternalfilling solution (0.1 MHCI)Thin glassmembraneFigure 2.4.1A typical glass electrode.cal device. To make measurements, the thin membrane is fully immersed in the test solution, and the potential of the electrode is registered with respect to a reference electrodesuch as an SCE.
Thus, the cell becomes,.1 M)/AgCl/Ag(2.4.3)Glass electrode'sinternal referenceSCEGlass electrodeThe properties of the test solution influence the overall potential difference of the cell attwo points. One of them is the liquid junction between the SCE and the test solution.From the considerations of Section 2.3.5, we can hope that the potential difference thereis small and constant.
The remaining contribution from the test solution comes from itseffect on the potential difference across the glass membrane. Since all of the other interfaces in the cell feature phases of constant composition, changes in the cell potential canbe wholly ascribed to the junction between the glass membrane and the test solution. Ifthat interface is selective toward a single species /, the cell potential isRT, „solnE = constant + ^p In a\(2.4.4)where the constant term is the sum of potential differences at all of the other interfaces.17The constant term is evaluated by "standardizing" the electrode, that is, by measuring Efor a cell in which the test solution is replaced by a standard solution having a known activity for species /,18Actually, the operation of the glass phase is rather complicated (24, 37, 46^48, 51).The bulk of the membrane, which might be about 50 jiim thick, is dry glass through whichcharge transport occurs exclusively by the mobile cations present in the glass.
Usually,these are alkali ions, such as Na + or Li + . Hydrogen ion from solution does not contributeto conduction in this region. The faces of the membrane in contact with solution differfrom the bulk, in that the silicate structure of the glass is hydrated. As shown in Figure2.4.2, the hydrated layers are thin. Interactions between the glass and the adjacent solution, which occur exclusively in the hydrated zone, are facilitated kinetically by theswelling that accompanies the hydration.17Equation 2.4.4 is derived from (2.4.2) by recognizing the test solution as phase a and the internal fillingsolution of the electrode as phase /3.
See also Figures 2.3.5 and 2.3.6.18By the phrase "activity for species Г we mean the concentration of / multiplied by the mean ionic activitycoefficient. See Section 2.3.4 for a commentary and references related to the concept of single-ion activities.76Chapter 2. Potentials and Thermodynamics of CellsHydrated layerTest solutionHydrated layerInternal filling solutionDry glass• 5 0 (im15-100 nmM-Figure 2.4.2 Schematic profile through a glass membrane.The membrane potentials appear because the silicate network has an affinity forcertain cations, which are adsorbed (probably at fixed anionic sites) within the structure.
This action creates a charge separation that alters the interfacial potential difference. That potential difference, in turn, alters the rates of adsorption anddesorption. Thus, the rates are gradually brought into balance by a mechanism resembling the one responsible for the establishment of junction potentials, as discussed above.Obviously, the glass membrane does not adhere to the simplified idea of a selectively permeable membrane.
In fact, it may not be at all permeable to some of the ions ofgreatest interest, such as H + . Thus, the transference number of such an ion cannot be unity throughout the membrane, and it may actually be zero in certain zones. Canwe still understand the observed selective response? The answer is yes, provided that theion of interest dominates charge transport in the interfacial regions of the membrane.Let us consider a model for the glass membrane like that shown in Figure 2.4.3.The glass will be considered as comprising three regions.
In the interfacial zones, m!and m", there is rapid attainment of equilibrium with constituents in solution, so thateach adsorbing cation has an activity reflecting its corresponding activity in the adjacent solution. The bulk of the glass is denoted by m, and we presume that conductionthere takes place by a single species, which is taken as N a + for the sake of this argument. The whole system therefore comprises five phases, and the overall difference inpotential across the membrane is the sum of four contributions from the junctions between the various zones:тттттта~ Ф ") + (ф " ~ Ф ) + (Ф - Ф ) + (Ф ' ~ Ф )Test solutionInternal filling solutionEquilibriumadsorptionEquilibriumadsorptionFigure 2.4.3 Model for treating the membrane potential across a glass barrier.(2.4.5)2.4 Selective Electrodes77The first and last terms are interfacial potential differences arising from an equilibrium balance of selective charge exchange across an interface.
This condition is known asDonnan equilibrium (24, 51). The magnitude of the resulting potential difference can beevaluated from electrochemical potentials. Suppose we have Na + and H + as interfaciallyactive ions. Then at the a/m' interface,МЙ+ = MH+M + = MNa+(2-4.6)(2-4.7)Expanding (2.4.6), we have/!$*+ + RT In я£+ 4- ¥фа = ySfii + ЯГ In ajgV + F<£m'(2.4.8)and rearrangement givesOa(фт'Om'-ф<*) = ^и+^H +a+ ^ in^ l(2.4.9)An equivalent treatment of the interface between (3 and m" givesOm" _(фР - фт") = ^ Н + р0/3М н +m"+ £ 1 in ^ | ±(2.4.10)Note that Дна+ = A%+, because both a and /3 are aqueous solutions. Similarly,Мн+ = Мн+-w h e n w e a d d (2.4.9) and (2.4.10) later in this development, these equivalencies will cause the terms involving fi° to disappear.The second and third components in (2.4.5) are junction potentials within the glassmembrane. In the specialized literature, they are called diffusion potentials, because theyarise from differential ionic diffusion in the manner discussed in Section 2.3.2.
The systems correspond to type 3 junctions as defined there.We can treat them through a variant of the Henderson equation, (2.3.39), which wasintroduced earlier in Section 2.3.4. The usual form of this equation is derived from(2.3.36) by neglecting activity effects and assuming linear concentration profiles throughthe junction. Here, we are interested only in univalent positive charge carriers; hence wecan specialize (2.3.39) for the interface between m and m! as(фт-фт)= ^ \where the concentrations have been replaced by activities.
Also, for the interface betweenm and m",^a+(фт" - фт) = Qjf- InWJJ+ # н +mNa+——(2.4.12)~r ^Na~*~ ^Na~^Now let us add the component potential differences, (2.4.9)-(2.4.12), as dictated by(2.4.5), to obtain the whole potential difference across the membrane: 19RT,Он+Дн+— —pr 1П+—рг ШF_m,тч(Donnan Term);~(Diffusion term)(2.4.13)( M N a + /« H +)«Sa+ + «H+19Note that the diffusion term here is the same as that which would be predicted by the Henderson equationfrom the compositions of m' and m" without considering m as a separate phase. Many treatments of thisproblem follow such an approach. We have added the phase m because the three-phase model for the membraneis more realistic with regard to the assumptions underlying the Henderson equation.78;Chapter 2.
Potentials and Thermodynamics of CellsSome important simplifications can be made in this result. First, we combine the twoterms in (2.4.13) and rearrange the parameters to giveF_RTFNow consider (2.4.6) and (2.4.7), which apply simultaneously. Their sum must also be true:Й а + + Й?+ = М§+ + Й?а+(2.4.15)This equation is a free energy balance for the ion-exchange reaction:++++rNa (a) + H (m') ^± H (a) + N a (m )(2.4.16)Since it does not involve net charge transfer, it is not sensitive to the interfacial potentialdifference [see Section 2.2.4(c)], and it has an equilibrium constant given byAn equivalent expression, involving the same numeric value of К#+ N a + , would apply tothe interface between phases /3 and m'.
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