ANALYST. JUNE 1991, VOL. 116 589 Mechanistic Study of Fluoride Ion Sensors Werner Moritz and Lothar Muller Department of Chemistry, Humboldt Universitat Berlin, Bunsenstrasse I , 0- 1080 Berlin, Germany Fluoride ion sensitive semiconductor sensors were investigated with regard t o the influence of pH, the limit of detection obtained and the response time. The results are the same as those obtained for a well-known single crystal electrode. The dissolution rate of LaF3 was determined using the isotope 140La. The OH-IF- exchange reaction and the isotope exchange kinetics of fluoride ions between the solution and the sensor layer were investigated. In the pH range from 4 t o 8 it could be concluded that both the limit of detection and the response time are determined by the ion-exchange rate.Keywords: Sensor; fluoride ion; lanthanum(///) fluoride; ion exchange; influence of pH Starting with the results of Frant and Ross,l LaF3 single- crystal electrodes have found wide application. The possibility of using thin polycrystalline layers of LaF3 for ion-selective field effect transistors (ISFETs) was shown previously .2 Sensor properties such as the sensitivity, the selectivity, the influence of pH and the limit of detection are identical with those for a single crystal and a polycrystalline layer. There- fore, the results concerning the sensor mechanism should be valid for both. The lower limit of detection with fluoride ion selective electrodes was shown to be about 1 x 10-6 rnol dm-3.1.34 The reason for this limit is still under discussion. Often it has been assumed that the limit of detection of fluoride is affected by the dissolution of LaF3.7 The solubility product of the single crystal should then be 1 x 10-29 or 1 x 10-30 (mol dm-3)4.1,3 However, Baumann4 found that the dissolution of LaF3 is a very slow process.Equilibrium was not established even after 20 d, hence, it was concluded that the solubility product must be greater than 1 x 10-24 (mol dm-3)4. Buffle et aZ.3 explained the limit by desorption of F- from the electrode and cell surfaces. In this instance, rinsing the electrode for a long period of time should give an improved limit. The influence of different buffer systems was shown by Kauranen,s who provided an explana- tion by assuming different complexes of La3+. The response of fluoride single-crystal electrodes after a change in F- concentration has previously been investi- gated*--'O and showed that the response time depends on the concentration. The best fit of the change of potential with time was attained using an empirical equation as proposed by Muller11 : where E, = the potential at time t , El = the equilibrium potential in the first solution and a and b = empirical values.For long periods of time in eqn. (l), eqn. (2) follows On the basis of eqns. (1) and (2) we obtain aib = t50 (3 1 where Eeq = the equilibrium potential in the second solution and tsO = the time for half of the potential change. The influence of pH on the electrode potential is well known for the fluoride ion sensor. An exchange of OH- in the solution for F- in the surface of the LaF3 was supposed, but no experimental evidence was presented.In the present work sensor properties for thin LaF3 layers on semiconductor structures are related to exchange experiments with OH- and dissolution kinetics of the layer and ion-exchange experiments using the isotope 18F. Experimental Lanthanum(m) fluoride layers (250 nm thick) were produced by vapour deposition on the semiconductor/isolator substrates ( Si02/Si3N4) and with subsequent characterization by capaci- tance voltage (C-V) measurements as described previously.2 The shift of the C-V curves on the voltage axis can be expressed as the change in gate voltage (U,) or electrode potential ( E ) which are identical in this study. The dissolution of the LaF3 layers was investigated by using the isotope "La, produced by neutron activation of the complete structure (semiconductor, isolator and LaF3 layer).The rotating disc principle was used to prevent diffusion problems. The dissolution rate was calculated from the increase in activity of the solution (20 ml). For the step-wise change in concentration, the wall-jet principle was used for the semiconductor sensors. The injection principle was used for measurements with the single-crystal electrode. The exchange of OH- ions between the solution and the LaF3 layer was investigated using a thin-layer method. The sandwich structure used is shown in Fig. 1. An area of 2 cmz of the LaF3 layer was in contact with 0.1 ml of an alkaline solution. After establishing the exchange equilibrium, a portion of 0.02 ml was removed and mixed with the same volume of total ionic strength adjustment buffer (TISAB). In this solution the F- concentration was measured using a F- ISFET.Before the experiments the layers were stored in 0.1 rnol dm-3 NaF, pH 5.5 for more than 2 h and then rinsed for 2 h with de-ionized water. The ion-exchange kinetics of fluoride ions were investigated using the isotope 18F in solution. The rate of exchange was calculated from the activity of the LaF3 layer after exposure to the solution for different times. (For further details see reference 12.) Results and Discussion Influence of pH The influence of pH on the potential of the F- sensor, using a thin LaF3 layer on a semiconductor substrate, is shown in Fig. 2 for different concentrations of F- ion.There is a well- established correlation with the results for the single-crystal electrode.13 No significant influence of pH was found in the range 4-9 in a 1 X 10-4 mol dm-3 NaF solution. The pH-independent range is a function of the F- concentration; it becomes smaller for lower F- concentrations. There is some hysteresis depending on the direction of the pH change, as shown for 1 x 10-4 mol dm-3 NaF (Fig. 2). At a pH of less than 4 the concentration of free F- is diminished by the reaction [shown in eqn. (4)] in the solution. H+ + 3F- HF + 2F- HF2- + F- F HF32- (4)590 0 - $400 -. 3 d -200 ANALYST, JUNE 1991, VOL. 116 - - I 1 Silicon La F3 I i I Silicon I Fig. 1 Schematic diagram of the cross-section of the sandwich structure used for the investigation of the exchange of OH- and F- 0 2 4 6 8 10 PH Fig.2 Effect of pH on the potential (hence UG) for different fluoride concentrations: 1 and 2, 1 X 3, 1 X lo+; and 4, 1 x 10-6 mol dm-3 NaF. The arrows show the direction of the pH change Hence, the fluoride sensor works correctly by detecting the activity of the free ions. It is generally assumed that the performance of the fluoride electrode does not depend on pH in the range 4-9. Experi- ments in this pH range (Fig. 3) showed that this is not true for the limit of detection. It is markedly influenced by a change in the pH from 4 to 8. Ferry et aZ.14 published a dependence of the limit of detection on pH in the range 11-13. In order to give a general view, their results are given in the same figure (Fig.3). The influence of fluoride concentration and pH on the potential of the electrode (or difference in gate voltage, Uc) can be expressed by eqn. (5) E = EO + RT/zFln(aF + A x aoHBj (5) where Eo = standard potential, R = gas constant, 7' = absolute temperature, z = charge number, F = Faraday constant A = constant giving the influence of pH, and a activity of the ion. By using a plot of the logarithm of the apparent concentra- tion at the limit of detection against pH, the exponent B , characterizing the effect of pH, was found to be 0.21 in the pH range 4-8 [correlation coefficient (Y) = 0.9974 and A = 5.6 X 10-81. At pH 11-13 the influence of pH is more pronounced15 and B is equal to 0.5. The influence of pH on the limit of detection was shown to be the same for the single-crystal electrode as for the polycrystalline layer.Note that eqn. (1) is not the Nikolsky-Eisenmann equation which would necessi- tate that B = 1. Dynamic Response The dynamic response of the semiconductor structure with a thin polycrystalline LaF3 layer is shown in Fig. 4. Attempts to obtain a linear relation on graphs for log Elt or E l P were not successful. Only by using eqn. (1) transformed into eqn. (6) was a linear relation (I- >0.9999) obtained for the poly- crystalline layer and for the single-crystal electrode. t/(E, - El) = bt + u ( 6 ) -300 1 \ E D C B A k 2 -Log (cF-/rnol 4 dm-3) 6 8 Fig. 3 Influence of pH on F- sensitivity and lower limit of detection. pH: A, 4; B, 5; C, 6; D, 7; E , 8; F, 11; G, 12; and H, 13 (curves F-H were obtained using values given in reference 14) As shown in Fig.4 the response time of the fluoride sensor depends on the concentration of the ion to be analysed. In this respect it differs from many other ion-selective electrodes. Furthermore, it can be concluded that the F- diffusion in the solution is not the process determining the dynamic response of the electrode. As the time taken for half of the potential change, t50, is directly related to the parameters a and b of eqns. (1)-(3j, tso can be used as a characteristic value for the response. The dependence of 150 on the F- concentration can be approxi- mated by eqn. (7), with a value of the exponent rn = -0.55 k 0.17. (7) For F- concentrations >1 X 10-5 rnol dm-3 and pH <8, the equilibrium potential is not influenced by the pH.Therefore, it was surprising that a dependence of t50 on pH was obtained. The influence of the pH of the solution on the logarithm of the response time is shown in Fig. 5. A quantitative relation is given in eqn. (8) with n = 0.20 t 0.05. The effect of pH on the response time was also shown to be true for single-crystal electrodes. The comparison of the response time of several single-crystal electrodes yields significant differences between individual electrodes. The same was reported by Mertens et a1.9 The response time for the thin LaF3 layers was between 0.25 and 1.6 s for a change in concentration from 1 X 10-5 to 1 X 10-4 mol dm-3 NaF (pH = 5.5). These values either agree with the results for the single-crystal or are slightly better. Dissolution of LaF3 The rate of dissolution of polycrystalline LaF3 layers in H 2 0 was investigated in order to check whether it bears any relationship to the limit of detection.Long-term experiments were restricted by the decay time of 140La (half-life, 40.6 h). Results for the first 100 min of the dissolution are given in Fig. 6. The linear dependence of the dissolved LaF3 on time is a result of a reaction order equal to 0. Dissolution rates were found to be in the range from 1.2 x 10-13 to 3.6 x 10-12 mol cm-2 min-1. This slow process means that during the first few hours only one atomic layer is dissolved. Considering this and the inhomogeneity of the polycrystalline layer it can be deduced that the dissolution rate decreases with time. Therefore, after 4 days of rinsing, the dissolution rate is 4 x 10-14 rnol cm-2 min-1.There is a reaction order equal to 0 for 80 h as shown in Fig. 7. It was not possible to determine the solubility product because it was impossible to obtain a solution of constant concentration within the decay time of 140La. The slowANALYST, JUNE 1991, VOL. 116 591 0 1 I I I 0 5 10 15 t/S Fig. 4 mol dm-3 NaF Response of LaFi layers on semiconductor substrates: 1. 1 x and 3 , l x 10-4 + 1 x 10-3 + 1 x 10- 5 ; 2 , l x 10-5 + 1 x 1.5 I I -0-5 2 6 8 PH Fig. 5 solution: 1 , 1 X 10-6 -+ 1 X 10-5: and 2. 1 x 10-5 + 1 X mol dm-3 NaF Dependence on the response time (fs0) on the pH of the dissolution process observed makes the values given in the literature for the solubility product of the single crystal appear doubtful.4 N I $ 3 E - z 2 0 F . Q 1 I I 0 10 50 100 tlmin Fig. 6 Dissolution of LaF3 in water; short time range I 0 10 50 80 Fig. 7 Dissolution of LaF3 in water; long time rangc tlh ~- ~ Table 1 Concentration of F- released from a 250 nm LAF3 layer in 10 min coH-lmol dm-' cp-lmol dm-' 1 x 10-3 1 x 10-2 3 x lo-' 4.5 x 10-5 9.0 x 10-5 3.2 x lo-* 1 8.7 x 10-4 Exchange of Fluoride Ions for Hydroxide Ions In order to determine the reason for the interference by OH- the exchange reaction between OH- in solution and F- in the LaF3 layer was investigated by using the sandwich structure mentioned above (Fig. 1). Various concentrations of KOH solution of from 1 x 10-3 to 1 rnol dm-3 KOH were used. The F- concentrations measured in the solutions after 10 min are given in Table 1.During this time the exchange equilibrium was established. It can be seen that the F- concentration released increases with increasing OH- ion concentration. The results given in Table 1 might possibly be explained in one of two ways, firstly by an OH- for F- exchange or, secondly, by a dissolution of the layer. In 1 mol dm-3 KOH the amount of F- released corresponds to a 19 nm layer of LaF3. In experiments using the isotope 14oLa, the dissolution rate of LaF3 in 1 rnol dm-3 KOH was found to be <0.05 nm min- 1.6 Therefore, dissolution of the layer cannot explain the F- concentrations given in Table 1. If the F- concentration is caused b y an exchange of OH- for F-. the reaction i11 the revrese direction should be equally possible.In order to examine this the sandwich structure was filled with a buffered (TISAB, pH 5.5) 3.3 X mol dm-3 NaF solution following the experiment with 0.1 rnol dm-3 KOH. The reduction of F- concentration in the solution should be an indication of the reverse exchange reaction. The results show that 65% of the F- released in the first experiment re-entered the layer. (The difference between this and 100% being attributed to the new equilibrium established and experimental errors.) The ion-exchange experiments were repeated more than 20 times with the same layer without any changes in the results. It can therefore be concluded that there is a reversible exchange of OH- from the solution with F-- in the LaF3 layer. This provided another problem, the distribution of OH- in the layer.Two possibilities exist: (i) enrichment of OH- in the surface; or (ii) homogeneous distribution of OH- through the whole layer (250 nm). When using LaF3 layers of different thickness (18 and 250 nm) the release of F- was proportional to the thickness used (within an experimental error of 10%). Therefore, it could be concluded that there is a nearly constant concentration of OH- throughout the layer, from the surface to a depth of at least 250 nm. No experiments with layers of greater thickness were carried out. The exchange equilibrium OH-(s) + F-(1) T-, OH-(1) + F-(s) (9) between the ions in the lattice (1) and in the solution (s) can be writ ten : DOH = K(COH/CF)/[l -k K(COH/CF)] ( 10) where DF and DOH = site filling factors for F- and OH-, respectively, and DF + DOH = 1.For small values of D O H in eqn. (lo), eqn. (11) is obtained. DO€[ = KcOH/cF (11) Experiments starting with Dorr = 0 (with a layer condi- tioned in 0.1 rnol dm-3 NaF of pH 5.5 before the experiment)592 ANALYST, JUNE 1992. VOL. 116 lead to a definite relation between the concentration of F- released and DoEr: DOH = s x CF The value of S, the constant for the geometry of the sandwich structure, can be calculated from the density and thickness of the layer and the volume of the solution. From eqns. (11) and (12) we can obtain eqn. (13) as follows: (12) CF = (KcoH/S)’ (13) According to eqn. (13) there should be a square-root relationship between the concentrations of F- released and OH- in the solution. The dependence of the logarithm of the concentrations cF and cOH, obtained in the exchange experi- ments, is shown in Fig.8. For concentrations of greater than 1 x 10-2 mol dm-3 KOH the slope is 0.49, which agrees with eqn. (13). For lower concentrations a smaller value for the slope was found, indicating that K is not constant if the concentration changes by many orders of magnitude. This corresponds to the concentration dependence of the free enthalpy of ions in a mixed crystal not being ideal. An equilibrium constant of K = 9 x 10-5 was calculated using the results shown in Fig. 8. For the site filling factor DOH a value of 0.037 was obtained at pH 13 in 1 x 10-4 mol dm-3 NaF solution. This means that there is an unexpectedly high level of OH- ions in the F- ion sites in the LaF3. Note that the combination of the solubility products of LaF3 and La( OH), yield eqn.(14), which does not coincide with the experimental results. cF = cOHIKF(L)/KOH(L)]’ (14) Fluoride Ion Exchange Rate In order to improve the knowledge about the processes that determine the potential, the exchange of F- between the solution and LaF3 was investigated using the isotope 1SF. These results are given elsewhere in more detail.12 It was shown that neither the diffusion of F- in the solution nor in the LaF3 is the rate determining step for ion exchange; it was found to be the transfer rate of the F- through the phase boundary. From the experiments follows the important fact that the exchange rate is not only a function of fluoride concentration but also of pH. The influence of pH on the exchange rate ( v ) is shown in Fig.9 for different F- concentrations. Equation (15) represents the effect of the composition of the solution on the rate of isotope exchange v = k C F p ( C O H ) 4 (15) with p = 0.69 and q = -0.22. In 1 rnol dm-3 NaFsolutions at a pH of 5.5, v has a value of 5.25 x 10-8 rnol cm-2 min-’. Conclusions The limit of detection cannot be explained by dissolution of LaF3, because from the dissolution rate it follows that it would take hours in order to obtain a concentration of only about 1 x mol dm-3 in solution. This is still below the limit of detection. A calculation of the stationary surface concentration of F- during the dissolution was accomplished by assuming that the rates of dissolution and diffusion in the solution were equal.By using the 1. Fick’s law with a diffusion layer thickness of 1 X cm and a dissolution rate of 4 x 10-14 the surface concentration of F- was found to be 2 x 10-10 rnol dm-3. Therefore, it can be concluded that dissolution cannot be the reason for the limit of detection of polycrystalline LaF3 layers. As the dissolution rate of single-crystalline material is smaller than that for polycrystalline materials the same is true for a single-crystal electrode. As a result of our experiments it is obvious that the influence of pH is more pronounced than previously thought. The limit of detection, the response time and the exchange rate of fluoride ions all depend on the pH. For the limit of detection two different mechanisms should be discussed. At high pH values, an exchange reaction between OH- in the solution and F- in the LaF3 layer was proven to occur.The concentration of F- released corre- sponds to the limits of detection obtained by Ferry et a1.14 The dependence of the F- concentration on pH according to eqn. (13) leads to the same exponent (0.5) as for the limit of detection and the apparent OH- sensitivity. Therefore, for a high pH, it is concluded that the limit of detection and the apparent OH- sensitivity are the result of the F- ions released by the exchange reaction. An attempt to use the results of the exchange of OH- for F- in the interpretation of the limit of detection over pH 4-9 gives a discrepancy between B = 0.21, for the limit of detection, and the exponent (0.5) obtained from the exchange experiments. Furthermore, a calculation of the F- concentration released at pH 5 , using eqn.(13), gives 3 x 10-8 mol dm-3. This concentration is considerably lower than the detection limit. Hence, the limit of detection appears to be inexplicable by consideration of the equilibrium conditions. It is evident that in the pH range 4-9 the limit of detection, response time and the fluoride ion exchange rate depend on the pH with a value of the exponent close to 0.2. Therefore, kinetic reasons have been proposed in order to explain the OH- dependencies.6 Cammannls used the concept of mixed potentials, derived from electrode kinetics, for ion-selective electrodes. For the fluoride electrode, the equality of the currents for F- and OH- exchange would lead to a mixed potential and finally, to the limit of detection.With increasing I 1 ‘ I 5 s 3 2 1 0 -Log (coH/mol d ~ n - ~ ) Fig. 8 concentration of OH- Variation in the F- concentration released as a function of the 0” 11.5 d 12.0 1 5 6 7 8 PH Fig. 9 1 x 10-4; B, 2 x 10-6; and C. 5 x 10-7 mol dm-3 NaF Dependence of the rate of fluoride ion exchange on pH: A,ANALYST, JUNE 1991. VOL. 116 593 concentration of one of the ions the current increases and it is only this ion that determines the potential. The fluoride ion exchange rates are available from the 18F experiments. An attempt was made previously to try to determine the OH- exchange rate, but it was noted that it was the same as for the fluoride ion in a solution of the same potential.16 This can now be explained because of the release of fluoride ions at high pH.Therefore, it seems to be impossible to measure the exchange rate of OH- at the interface of the LaF3 layer and the solution. Hence, it is not possible to calculate the mixed potential or to construct an Evans’ diagram. The dependence of the fluoride ion exchange rate on the pH is consequently only an indication, for kinetic reasons, of the limit of detection. Comparing the response time experiments and the 18F exchange rates it is evident that the influence of the F- concentration and pH is the same. The exponents m and n of eqns. (7) and (8) are in concordance (but opposite in sign) with p and q of eqn. (15). The difference between the exponents obtained, might be explained by experimental error. This leads to the conclusion that the rate determining step of the potential change by concentration increase is the F- transfer between the solution and the LaF3 layer.Johansson and Norberg17 derived an equation that de- scribes the response of an ion-selective electrode, by using the Butler-Volmer relation that has ion transfer as the rate determining step. They obtained an exponential relation, but as stated above such a relation cannot be used to describe the response of the fluoride ion sensor. The reverse of the exchange rate is correlated to the exchange resistance, R , : R1 = RT/z’Fv (16) By using the exchange resistance and a double-layer capaci- tance C1, at the phase boundary, between the LaF3 layer and the electrolyte, in parallel, it is possible to calculate the response time.t = ClRl (17) But the response is, again, exponential. It has previously been shown that it is possible to get an approximation of the hyperbolic response according to eqn. (1) by a combination of two resistors and two capacitors, thus, leading to a sum of the exponential terms.6 However, two problems were not solved: (i) the physical sense of the second resistor and the capaci- tance are not sufficiently explainable; and (ii) in eqn. (1) only one kinetic parameter is required in order to describe the entire response curve. The use of four variables is not acceptable,6 however, a better model for describing the whole response curve of the fluoride sensor was not found. On the other hand, the experimentally obtained response time could be calculated by using eqns.(16) and (17) at different values of F- concentration and pH of the solution and using a constant capacity, typical for the double layer (1 x 10-5 cm-2 of F-), and the F- ion exchange rate determined for that condition. Consequently, this proved that the F- ion exchange is the rate determining step for the response of the F- ion sensor, but there is still an absence of an adequate physical model for the mathematical description of the response curve. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 References Frant, M. S., and Ross, J . W., Science, 1966, 154, 1553. Moritz, W., Meierhofer, I . , and Miiller, L., Sensors and Actuators, 1988, 15, 211. Buffle. J . , Parthasarathy, N., and Haerdi. W., Anal. Chim. Acta, 1974, 68, 253. Baumann, E. W., Anal. Chim. Acta, 1971, 54, 189. Kauranen. P., Anal. Letters, 1977, 10, 451. Moritz, W., Dissertation B, Humboldt-Universitat Berlin, Germany, 1988. Evans, P. A., Moody, G. J., andThomas, J . D. R., Lab. Pract., 1971, 20, 644. Hawkings, R. C., Corriveau, L. P. V., Kutshneriuk. S. A., and Wong, P. Y., Anal. Chim. Acta, 1978, 102, 61. Mertens. J . , van den Winkel, P., and Massart. D. L., Anal. Chem., 1976,48, 272. Nagy, K., and Fjeldly, T. A., Proceedings of the Third Symposium on lon-Selective Electrodes. Matrafiired. Germany, 1980, p. 287. Miiller, R. H.. Anal. Chem., 1969,41, 113A. Moritz, W.. Herbst. A.. and Heckner. K.-H.. 2. Phys. Chem., in the press. Vesely, J . , and Stulik, K . , Anal. Chim. Acta, 1974, 73, 157. Ferry, D., Machtinger, M., and Bauer, D., Analusis, 1984, 12. 90. Cammann, K . , Das Arbeiten Mit Ionenselektiven Elektroden, Springer-Verlag, Berlin, 1973. Cammann, K.. and Rechnitz, G. A., Anal. Chem.. 1976, 48, 856. Johansson, G., and Norberg, K., J. Electroanal. Chem., 1968, 18, 239. Paper 0/05565 D Received December 11 th, 1990 Accepted February 19th, 1991