Towards a solid state reference electrode

Sensors and Actuators B 44 (1997) 381 – 388

Towards a solid state reference electrode Kristin Eine a,*, Signe Kjelstrup b, Kalman Nagy a, Kristin Syverud a a

The Foundation for Scientific and Industrial Research, Norwegian Institute of Technology, Di6ision of SINTEF Chemistry, N-7034 Trondheim, Norway b Department of Physical Chemistry, Norwegian Uni6ersity of Science and Technology, Trondheim, N-7034 Trondheim, Norway Accepted 4 April 1997

Abstract The construction of a solid state reference electrode is presented. The solid state reference electrode has two membranes arranged in parallel. The membranes are anion and cation conducting, and both of them are in contact with the sample solution. Resistors with considerably larger resistance than that of the ion-exchange membranes are soldered onto each of the two electrode parts, to give the same amount of charge transferred in the parallel paths. The anion and cation conducting paths of the electrode then give contributions to the e.m.f. that cancel, and we show that the cell e.m.f. varies with the concentration of the ion reversible to the ion selective electrode (ISE) in a Nernstian way. As an example of the ISE we have studied a fluoride selective electrode. We have also tested materials for the anion and cation conducting parts of the reference electrode, and found that they behave close to what is predicted. The performance of the total reference electrode can be compared to a commercially available electrode. Procedures for further progress in the realization of the ideal reference electrode are discussed on the background of our theoretical development. © 1997 Published by Elsevier Science S.A. Keywords: Anion conducting membrane; Cation conducting membrane; Fluoride selective electrode; Solid state reference electrode

construction:

1. Introduction We have recently presented the general idea and a theoretical description of a new solid state reference electrode construction based on irreversible thermodynamics, which has potential advantages over common reference electrodes [1]. The purpose of the present article is to apply this theory to a specific use of the electrode; namely, for the cell which contains the reference electrode and a fluoride selective electrode. We shall first give the equations for this cell. In do doing we hope to present the general theory in a way that is more accessible to the reader. We shall also report on the progress made towards a realization of the reference electrode, and describe a few experiments performed for this purpose, including one with the cell referred to above (see also [2,3]). The importance of a new reference electrode can be understood by analysis of the most common reference electrode that is commercially available, namely the * Corresponding author. [email protected]

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Ag(s) AgCl(s) KCl(sat, aq) Porous plug

(a)

Several problems are encountered with this electrode, problems of a theoretical as well as of a practical nature. Contributions to the e.m.f. from the liquid junction across the porous plug are difficult to control because diffusion takes place continuously. These contributions are usually calculated using, for example, Henderson’s approximation of linear concentration profiles. Johnsen et al. [4] and Breer et al. [5] found significant deviations from linearity in the concentration profiles in the junction and non-Nernstian cell responses for certain conditions. For this reason, accurate concentration determinations of K + were not always possible with this reference electrode [6]. The reference electrode Eq. (a) will slightly alter the cell e.m.f. when the ionic strength in the sample solution changes [5]. Consequently, it is difficult to know whether the changes in the measured e.m.f. in an electrochemical cell originate from the reference electrode, or from the remaining part of the experimental cell. In the development of new electrodes it is important to

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know the origin and magnitude of the separate contributions to the cell e.m.f.. Otherwise it is difficult to know how to improve the electrodes. All solid state electrodes have several advantages over electrodes with internal filling solution, one of them being the minimization of the contribution from the liquid junction. Also, all solid state electrodes may be exposed to higher temperatures and pressures than the liquid filled electrodes, and they need not be used in an upright position. They are miniaturizable, do not need refilling with internal solution and can be prepared in various shapes and sizes. All solid state electrodes allow construction of micro-multisensors consisting of a reference electrode and several specific electrodes, and can easily be equipped with impedance transforming micro-electronics in the vicinity of the membrane [7,8]. These are crucial factors for in vivo monitoring, which is one of the major goals of current research in the field of ion selective electrodes (ISEs). There has been a considerable effort to develop solid state reference electrodes over the past years. These will not be reviewed here; for a short discussion see [1]. We have used an operationally defined electrochemical method [9] to define criteria for our electrode. The principles of this method are discussed briefly below as we apply the method to the cell of interest.

2. Principles

2.1. Criterion for a solid state reference electrode A general criterion for a reference electrode is zero net contribution to the cell e.m.f. from the electrode upon concentration changes in the electrolyte. We have seen already [1] that a structure that fulfils this criterion is a particular parallel coupling of a cation and an anion conducting membrane (c.m.). This electrode in a cell with a fluoride selective electrode, denoted NaF LaF3, can be given schematically as: B BY, CY(ss) Cation c.m. B BY, CY(ss) Anion c.m.

NaCl, NaF(aq) LaF3 (b)

Contact is made between the metals B, and B and the F-selective electrode are connected to the terminals of the potentiometer (see Fig. 1). The contact B BY, CY(ss) is a solid state contact where BY enters the electrode reaction. These materials are so far not specified. The sample solution is a mixture of NaCl (supporting electrolyte) and NaF. The cation conducting membrane can contain Na + and C + . The anion conducting membrane can contain Y − , Cl − and F − . Cell (b) has two parallel paths, I and II. Path I is described by: B BY, CY(ss) Cation c.m. NaCl, NaF LaF3

According to the formulation of irreversible thermodynamics by Førland et al. [11], it is possible to find the usual formulas for the e.m.f. of electrochemical cells by choosing the neutral electrolytes, not the ions, as the variables of the system. We then analyse the changes in composition of these thermodynamic components in each volume element i, and the change in Gibbs energy which follows from the compositional changes. These changes are related by the Nernst equation: DG(Q)=%i DGi (Q) = −EF

time and stability all depend on the existence of reversible contacts.

(I)

Path II is given by: B BY, CY(ss) Anion c.m. NaCl, NaF LaF3

(II)

In the following, we show how the contribution to the e.m.f. is zero from the reference electrode in the two parallel paths when the same number of faradays is going through each of the paths.

(1)

The local change in Gibbs energy is denoted by DGi (Q), because only those changes that are connected to transfer of charge (Q) contribute to the measured e.m.f. The sum of the local changes gives the total DG(Q) of the cell. E is the e.m.f. of the cell and F is Faraday’s constant. One of the basic precepts of irreversible thermodynamics is the assumption of local equilibrium. In order to use this theory, we must ensure that local equilibrium is established, in particular, at all interfaces. When local equilibrium exists in an electrochemical cell, the charge transfer process is reversible; that is, the process can be reversed by changing the direction of the electric current. Good electrode sensitivity, response

Fig. 1. Schematic drawing of the reference electrode separated by two paths. Path I represents the cation conducting part, path II represents the anion conducting part.

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2.2. Local equilibrium at the solid state interfaces B BY, CY(ss) Membrane

For the interface between the sample solution and the anion exchange membrane, there are two anion exchange reactions:

Reversibility of the reaction between the electronic conductor B and the adjacent ionic conductor requires the presence of a salt of the metal, say BY. The reversible reaction taking place at the interface B BY, CY(ss) is:

NaF(aq)+ PCl v NaCl(aq)+ PF

(7)

NaF(aq)+ PY v NaY(aq)+PF

(8)

B(s) + Y − v BY(ss) +e −

mPF − mNaF = mPCl − mNaCl

(9)

mPY − mNaY = mPCl − mNaCl

(10)

(2)

The salt CY hinders B + from entering the membrane and ions from the solution from taking part in the electrode reaction. The salt CY, together with BY, serves as a reservoir for cations (path I) or anions (path II) to be transported across the membranes. The stability and life-time of the electrode may be improved by adding CY. This is discussed further in Section 5. The membranes are equilibrated with BY and/or CY so that part of the membrane always contains the ions for which it is permselective. The equilibrium between CY(ss) and CR in a cation exchange membrane with fixed anionic sites, R − , are: mCY =mCR

(3)

where mCY is the chemical potential of CY. Similarly, for the equilibrium between CY(ss) and PY in the anion exchange membrane with fixed cationic sites, P + : mCY =mPY

(4)

where mPY is the chemical potential of PY. We assume that electroneutrality holds on times scales that are relevant for e.m.f. measurements [10]. Consider the left side of the membrane. During the e.m.f. measurement, electroneutrality is maintained in path I by transfer of cations from left to right across the membrane. In path II, which has the anion conducting membrane, the Y − ions consumed by reaction Eq. (2) are replaced by anion transport from right to left across the membrane.

2.3. Local equilibrium at the interfaces of anion or cation conducting membrane NaCl, NaF(aq)

The chemical potentials of Eq. (9) and Eq. (10) can be assumed to be unaltered during the e.m.f. measurement. The formulations Eq. (6), Eq. (9) and Eq. (10) of the equilibrium conditions will simplify the expression for the cell e.m.f. (see below).

2.4. Chemical potentials We use a definition of chemical potential of the salts in the sample solution which is described elsewhere [11]. For the purpose of discussing path I, we define the chemical potential of NaCl and NaF by: mNaX = m oNaX + RT ln aNaX = m oNaX + RT ln cNa + cX − yNaX −

(5)

(11)

where X does not discriminate between Cl and F − . The standard chemical potential of NaX is m oNaX and aNaX is the activity. The concentrations of Na + and X − are cNa + and cX − , respectively, and the activity coefficient of the salt is yNaX. The amount of NaX is everywhere given by the cNa + . The total concentration of the sodium salts in equivalents per liter is co, and the equivalent cation fraction of Na + is xNa + . This gives: cNa + = coxNa +

−

(12)

The equivalent anion fraction of X − is unity (xX − = 1). This gives: cX − = co

We shall find a useful formulation of the equilibrium condition for the membrane solution interface. Consider first the cation exchange membrane. At the solution interface we have the membrane components CR and NaR. With the present sample solution, the exchange equilibrium is: NaCl(aq)+ CR v CCl(aq) + NaR

These reactions give:

(13)

With this special notation, Eq. (12) and Eq. (13) can be introduced into Eq. (11) to give: mNaX = m oNaX + RT(2 ln co + ln xNa + yNaX)

(14)

The chemical potential of the cation membrane component is [11]: mNaR = m oNaR + RT ln xNaR fNaR

(15)

The establishment of the equilibrium in Eq. (5) does not depend on the charge transfer, when diffusion into and out of the membrane is relatively fast. At equilibrium, we have for the chemical potentials of Eq. (5):

Here fKR is the activity coefficient on a cation fraction basis where the membrane in the pure form denotes the standard state. For the processes of path II we define the chemical potential of the chloride NaCl similar to Eq. (14):

mCCl −mCR =mNaCl −mNaR

mNaCl = m oNaCl + RT(2 ln co + ln xCl − yNaCl)

(6)

(16)

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In order to maintain electroneutrality when F − is produced by the electrode reaction, transport of cations takes place across the membrane. The cations Na + and C + are transported across the membrane from left to right. The transference number of Na + is tNa + and of C + it is tC + . Consider, therefore, the transport processes taking place at the membrane-sample solution interface during charge transfer. The Gibbs energy can be expressed for the anion X − by: DGI,3(Q)= tC + (mCX − mCR)+ tNa + (mNaX − mNaR) Fig. 2. Reversible mass changes in path I.

The equivalent anion fraction of Cl − is xCl − , and the standard chemical potential of NaCl is m oNaCl. The chemical potential of NaF in the context of both paths I and II, mNaF, is defined as: mNaF =m oNaF + RT(ln co +ln cF − yNaF)

(17)

where cF − =xF − co and xF − is the equivalent anion fraction of F − .

(20)

There are changes in composition from one side of the membrane to the other. Provided that the chemical potential gradients are kept within the membrane, only a constant contribution to the Gibbs energy change will arise from transport between the part that contains CR and the parts that contain NaR [12]. The chemical potentials of the salts were defined above. With equilibrium across the membrane solution interface, we can apply Eq. (6). One of the differences in chemical potentials of Eq. (20) can then be substituted by the other. We do this and add the result to Eqs. (18) and (19). The result is the change in Gibbs energy for path I:

2.5. The e.m.f. of the cell with the solid state reference electrode and an ISE

DGI(Q)= (mNaX − mNaR)(tNa + + tC + )+ mNaF + constant (21)

We shall find the e.m.f. of cell (b) according to Eq. (1). We consider processes taking part in the cell when the same number of charges Q are passing path I and path II. The changes in Gibbs energy in paths I and II due to charge transfer, DGI(Q) and DGII(Q), will be calculated separately. This will be done by first analysing the mass changes upon transfer of 1 faraday of charge, Q= 1 F, for each path. The changes in Gibbs energy then follow from the corresponding chemical potentials of the components.

The constant of this equation contains the contributions from B, BY, LaF3 and the membrane interior. The sum of the cation transference numbers equals 1. There is no requirement on the value of the single transport numbers in the cation membrane. The total change in Gibbs energy for this path is therefore simply:

2.5.1. e.m.f. contributions from path I The mass changes that occur when 1 faraday is passing cell I are illustrated in Fig. 2. The electrode reactions govern the component changes in the left and right cell compartments. At the very left interface 1 mole of B is consumed and 1 mole of BY is formed according to Eq. (2). We have assumed that only C + conducts charge into the membrane, so that 1 mole of CY disappears and 1 mole of CR is formed (see Fig. 2). The Gibbs energy changes, which accompany these mass changes are: DGI,1(Q)= mB + mBY −mCY +mCR

(18)

The last two terms cancel at local equilibrium (see Eq. (3)). The change in Gibbs energy due to the electrode reaction of the ISE is: DGI,2(Q)= mNaF −mLaF3

(19)

DGI(Q)= mNaX − mNaR + mNaF + constant

(22)

By introducing Eqs. (14)–(18) into Eq. (22) we have the following expression for Gibbs energy change along path I: DGI(Q) x y = RT ln cF − yNaF + RT ln co + RT ln NaX NaX xNaR fNaR + constant

(23)

The constant contains now also the standard chemical potentials. The activity coefficients of the salts can be determined from experiments in many cases. We shall use that they are constant when cF − varies. The changes in Gibbs energy over the path containing the cation exchange membrane is then: DGI(Q)= RT ln cF − + RT ln co + constant

(24)

We see that DGI(Q) varies with co, but this variation will cancel a similar variation of DGII(Q) (see Eq. (28)).

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2.5.2. e.m.f. contributions from path II Consider the mass and energy changes in path II with the anion conducting membrane when 1 faraday is transferred from left to right in the inner circuit (see Fig. 3). The Gibbs energy changes which accompany the mass changes at the two interfaces to the left are:

1 [DGI(Q)+ DGII(Q)]= RT ln cF − + constant 2

DGII,1(Q)= − mB +mBY +mCY −mPY

Ecell = −

(25)

The last two terms cancel again (cf. Eq. (4)). The changes in Gibbs energy at the ISE are again: DGII,2(Q)= mNaF −mLaF3 −

(26) −

−

The anions, F , Cl and Y , which transport charge across the membrane from right to left, have the transference numbers tF − , tCl − and tY − . The Gibbs energy change by transport across the interface between the anion exchange membrane and the sample solution is: DGII,3(Q) = tF − (mPF − mNaF)+ tCl − (mPCl −mNaCl) +tY − (mPY −mNaY)

(27)

We use the same trick as for the path I; substitute all chemical potential differences by (mPCl −mNaCl) according to Eq. (9) and Eq. (10) and apply that the sum of transference numbers of anions equals 1. This gives: DGII(Q)= mPCl −mNaCl +mNaF +constant

(28)

By a similar set of assumptions as for path I, we have for path II: DGII(Q)= RT ln cF − −RT ln co +constant

(29)

We see that the variation in DGII(Q) with co, will cancel the variation of DGI(Q), Eq. (23).

2.5.3. Combination of the local contributions to e.m.f. While the electric potentials are not additive, the Gibbs energy changes are. The simplest way to find the e.m.f. of our cell is to add the Gibbs energy changes calculated for each parallel path and divide by the 2 faradays that have been passed in total.

385

(30)

We see that the salt concentration of the sample solution has disappeared in Eq. (29) as a variable. With a perfect ISE we have the e.m.f.: RT ln cF − − constant F

(31)

The cell potential is Nernstian as long as the conditions for its derivation are valid.

2.5.4. Comments on the choice of materials The separation of the two functions, electrode reaction and membrane transport, through the application of CY in addition to BY, may be advantageous in practice, as it introduces a flexibility in finding the best salt for the different purposes. While the presence of BY is required by the electrode reaction, the salt CY may be chosen mainly to prevent ions from the sample solution from participating in the charge transfer processes at the left side of the membranes. When transport of BY and CY occur over their constant chemical potential, these components do not contribute to the e.m.f. A constant chemical potential is obtained for pure solid phases, but a solid solution of BY and CY can also be used. The solubility of BY in CY must then be low, so that interdiffusion of B + (Y − ) in the cation (anion) membrane is negligible. Leakage of BY across the membrane, which can alter the chemical potential of CY on the left side of the membranes, can then be avoided. Low solubility of BY and CY in the membranes, and also low interdiffusion of the B + or Y − ions may also be a critical part of the electrode realization. A failure to meet this criterion will lead to a changing chemical potential for BY on the inside of the membrane. The part of the paths I and II which constitute the reference electrode form a galvanic cell [1]. This may produce a non-zero electric current in a short-circuited cell under unfortunate circumstances. Care must be taken in the choice of materials also to avoid this situation.

3. Experimental The suggested reference electrode was constructed and tested as follows.

3.1. Membrane composition and manufacture

Fig. 3. Reversible mass changes in path II.

As a first choice for anion and cation conducting membranes, we used standard electrode membrane materials [13] with selected additions. The cation and anion exchanging materials were embedded in a membrane matrix consisting of 23–27 wt% polyvinyl chlo-

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ride, 65–69 wt% softener [bis(2-ethylhexyl)sebacate], and 2 wt% lipophilic salt [potassium tetrakis(pchlorophenyl)borate] in the cation exchange membrane and tridodecylmethyl ammonium chloride in the anion exchange membrane. All components were p.a. grade from Fluka. Between 2 and 10 wt% anion or cation exchange material was used. We used poly[N-(4-vinylbenzyl)N,N-dimethylamine] as the anion exchange material and a copolymer of methacrylic acid and methyl methacrylate in a molar ratio of 1:1 as the cation exchange material. Polymers were synthesized in tetrahydrofuran (THF). All membrane components were mixed in THF and homogenized in an ultrasonic bath. The membrane resistance was measured with a Schlumberger s1 1260 impedance gain phase analyser to be in the range of 0.01–0.09 MV.

3.2. Electrode manufacture As components B(s) BY(s) in cell (a) we used Ag/ AgCl. A shielded copper wire was separated in two parts and a resistor of 10 MV soldered onto each of them. A difference in the membrane resistance does not affect the equal charge conductance of paths I and II with this size of resistor. AgCl(s) was formed on the silver by electrolysis of 0.1 M HCl (supra pure, Merck) (current density 1 mA cm − 2). The resulting wire was dipped several times in the respective anion and cation conducting membrane cocktails (see above). THF was allowed to evaporate for 24 h before use. Separate anion and cation conducting electrodes were also made according to this procedure, but without separating the copper wire into two parts and without any extra resistor.

3.3. Electrode testing The e.m.f. measurements were made at 20°C with a Keithley electrometer. Anion and cation conducting electrodes were tested against a calomel reference electrode (Radiometer). The electrolyte used was KNO3 in the range 10 − 4 – 10 − 1 M. The complete reference electrode was tested in cell (b). The performance of cell (b) was compared to the performance of an Orion F-combination electrode. This electrode consists of a fluoride selective electrode and a common liquid junction reference electrode. In both experiments 0.1 M NaCl was used as a supporting electrolyte, while NaF varied from 10 − 5 to 10 − 1 M. Liquid junction potentials in the calomel reference electrode and the Orion F-combination electrode were corrected according to the Henderson formalism and the activity coefficients were calculated according to Meier [14].

Fig. 4. Schematic drawing of the solid state reference electrode prepared at SINTEF.

4. Results The reference electrode was constructed as described above; a schematic illustration is given in Fig. 4. The tests of the anion and cation conducting parts of the reference electrode will be reported first. The e.m.f.s of the test cells were plotted versus ln cKNO3. The change in mV per tenfold change of concentration was 55.2 for the cell with the cation membrane and − 58.9 for the cell with the anion membrane. The linear range was between 10 − 3.5 and 10 − 1 M for both cells. In order to have ideal performance from these membranes in the reference electrode in cell (b), the two slopes should have the same value but with opposite signs (cf. Eq. (23) and Eq. (28)). They should also give the ideal Nernstian slope, which is 58.1 mV dec − 1 at 20°C. The experimental results for cell (b) are shown in Fig. 5. The e.m.f. as a function of ln cNaF gives a straight line between 10 − 5 and 10 − 1 M NaF. The slope of the line is − 57.8 mV dec − 1. The Orion F-combination electrode gave − 59.7 mV dec − 1 after correcting for the liquid junction contribution. For comparison, these results are plotted in the same figure.

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5. Discussion

387

5.2. A theoretical foundation amenable to experimental control

5.1. Performance of the reference electrode The performance of the new reference electrode must be seen on the background of the performance of the separate anion and cation conducting electrodes and on the studies of Orion combination electrode. The anion membrane electrode gave a slope which was closer to the ideal slope than did the cation membrane electrode. From the recorded difference between the two electrodes it can be predicted that the electrode will give a net negative contribution to the e.m.f. As long as the cation and anion membrane electrodes do not give the required equal but opposite slopes, a deviation from ideality must turn up in the completed reference electrode, and the slope −57.8 mV dec − 1 is in accordance with this. This slope will improve when membrane materials with more ideal selectivities have been found. We have also not included any second solid salt CY(s). According to the comments we have made on the material choices, there is good reason to believe that addition of a second solid salt to AgCl(s) will improve the performance of the system. In spite of the lack of ideal performance of the single parts of the electrode, we also tested their combination in a complete realization of the solid state reference electrode. While our electrode tested 0.3 mV dec − 1 away from the theoretical value, the commercial electrode was 1.6 mV dec − 1 away from this value. There are at present not enough data to say that one measuring cell is significantly better than the other. It is surprising, however, to see that our electrode performs so well, in spite of our knowledge of the less than perfect performance of the separate anion and cation conducting parts.

In the present work the electrochemical theory of Kjelstrup Ratkje and coworkers [1–4,11,14] was applied to design a solid state reference electrode. The theory uses operationally defined quantities only (i.e. quantities that can be measured). The concepts on which this theory is based, allow us to examine the different parts of the reference electrode separately. Accordingly, we are able to identify the origin of net contributions to the e.m.f. that may arise from the reference electrode. This is an advantage for the practical follow-up of the design. We have seen already how this feature has been applied to the anion and cation conducting paths of the electrode. Membranes should be tested for their selectivity before use in the electrode, i.e. by measuring transference numbers of the membrane. It was furthermore a requirement that the same (infinitesimally small) electric current was passing through each membrane. This criterion can be checked by measuring circuit impedances. Also, all interfaces can be checked for reversible performance—i.e. e.m.f. that changes sign upon the reversal of the electric current. In the derivation of Eq. (30) the activity coefficients were taken as constants. When the assumption is not valid, it can be corrected for. According to this, we shall proceed to measure new membrane materials in test cells I and II, interface impedances, and reversibility of contacts, before the combination of parts into the reference electrode. The shift of focus from the local electrostatic potential in the cell to the local Gibbs energy change, implies that Donnan potentials at the membrane solution interface or the diffusion potential across the membrane are not of interest. This is not the same as saying that these potentials are not there. We only found a way to circumvent the problems of their determination. In spite of the different premises used in the derivation of E in our method, and in the conventional method, the criteria formulated for the solid state electrode are the same.

6. Conclusions

Fig. 5. Linear range for an Orion F-selective electrode used versus two reference electrodes: (1) the reported solid state reference electrode, (2) the internal reference in an Orion F-combination electrode.

The performance of a solid state reference electrode together with a fluoride selective electrode is described theoretically. A first set of experiments which describe its performance is also given. The electrode avoids problems with the liquid junction [2–4], and has all the practical advantages of solid state electrodes; i.e. no internal filling solution, possibilities for miniaturization, and few restrictions on handling. More work is needed to find better materials for the electrode parts. The

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reference electrode still perform in a cell, at the same level as a commercial electrode system. It is hoped that the theory applied, and its practical implementation, can serve as a fruitful base for development of a series of multisensors that are solid, consisting of a reference electrode and one or more ISEs.

[14] P.C. Meier, Two-parameter Debye – Hu¨ckel approximation for the evalutaion of mean activity coefficients of 109 electrolytes, Anal. Chim. Acta 136 (1982) 363.

Biographies References [1] T. Førland, S. Kjelstrup, K. Nagy, K. Eine, Theory of a new solid state reference electrode, J. Electrochem. Soc. (submitted for publication). [2] K. Nagy, K. Eine, O. Aune, K. Syverud, Promising new solid state reference electrode, J. Electrochem. Soc. 144 (1) (1997) 1 – 2. [3] K. Nagy, T. Førland, K. Eine, All-solid state reference electrode, Patent application no. NO 951705, 1995. [4] E.E. Johnsen, S. Kjelstrup Ratkje, T. Førland, K.S. Førland, The liquid junction contribution to e.m.f., Z. Phys. Chem. 168 (1990) 101 – 114. [5] J. Breer, S. Kjelstrup Ratkje, G.F. Olsen, Control of liquid junctions: the system HCl–KCl, Z. Phys. Chem. 174 (1991) 179 – 198. [6] K. Syverud, S. Kjelstrup Ratkje, An operationally defined method for ion selective electrode studies: potassium selectivity of polyvinychloride membranes, Z. Phys. Chem. 185 (1994) 245 – 261. [7] T.A. Fjeldly, K. Nagy, B. Stark, Solid state differential potentiometric sensors, Sensors and Actuators 3 (1982/83) 111–118. [8] T.A. Fjeldy, K. Nagy, Fluoride electrodes with reversible solidstate contacts, J. Electrochem. Soc. 127 (1980) 1299–1303. [9] K.S. Førland, T. Førland, S. Kjelstrup Ratkje, Irreversible Thermodynamics. Theory and Applications, 2nd ed., Wiley, Chichester, 1992. [10] J.L. Jackson, Charge neutrality in the electrolytic solutions and the liquid potential, J. Phys. Chem. 78 (1974) 179–183. [11] T. Førland, Thermodynamic properties of systems of fused salts, in: B.R. Sundheim (Ed.), Fused Salts. McGraw-Hill, New York, 1962, pp. 63 – 164. [12] M. Ottøy, T. Førland, S. Kjelstrup Ratkje, S. Møller-Holst, Membrane transference numbers from a new emf method, J. Membr. Sci. 74 (1992) 1–8. [13] E. Lindner, E. Gra`f, Z. Niegreisz, K. To`th, E. Pungor, R.P. Buck, Responses of site-controlled, plasticized membrane electrodes, Anal. Chem. 60 (1988) 295–301.

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Signe Kjelstrup (previously Ratkje) is dr.ing. from 1974, dr.techn. from 1982, and professor of physical chemistry from 1985 at the Norwegian University of Science and Technology. She has written about 75 original articles mostly on coupled transport phenomena in electrochemistry. Together with Katrine Seip and Tormod Førland she has written a book on irreversible thermodynamics which also describes electrode behavior. Kristin Eine, MSc.Ing. 1992 in physical chemistry. She has been a research scientist at SINTEF Applied Chemistry since 1994, working mostly on development of solid state reference and ion selective electrodes and analytical problems. Kalman Nagy is Research Manager at SINTEF Applied Chemistry. He obtained his M.Sc. in Chemistry (1962) at the Norwegian Institute of Technology. From 1965 to today he has been at SINTEF. He has written about 50 original articles and patents, mostly on electrochemical sensors and analytical chemistry. He is a member of the Norwegian Chemical Society. Kristin Sy6erud otained her Ph.D. degree in 1992 on developing a new method for selectivity determination of ion selective electrodes. She has been a research scientist at SINTEF since 1988 working mostly with tasks related to analytical chemistry: e.g. development of solid state sensors, application of ion selective electrodes and with spectroscopy (FTIR).