- Email: [email protected]
Time lag of ion exchange in the gel layer of hydrogen-ion-selective glass electrodes
Electroanalytical Chemistry and lnterfacial Electrochemistry, 49 (1974) 1-5
l
© Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
TIME LAG OF ION EXCHANGE IN THE GEL LAYER OF HYDROGENION-SELECTIVE GLASS ELECTRODES
BO KARLBERG
Department of Analytical Chemistry, University of Ume~, S-901 87 Ume~ (Sweden) (Received 16th February 1973; in revised form 21st August 1973)
It has earlier been shown 1 that the gel layer of hydrogen-ion-selective glass electrodes has a small ion-exchange capacity, about 10 -s tool cm -2 bulb area. When a glass electrode is transferred between acidic and basic solutions more than 90~ of the total e.m.f, change occurs within a few minutes while the time period required to obtain the steady e.m.f, value may amount to several tens of minutes. By measuring the ion-exchange extent at different times it was concluded that the ion-exchange process and the later e.m.f, changes are correlated. It has been possible to make predictions about the ion-exchange kinetics of glass electrodes 2'3 based on the theory of Helfferich 4'5. When initially the faster of the two ions is present in the exchanger, i.e., the gel layer, the exchange 15rocess is faster than if the slower ion is present there. The gel-layer thickness can be reduced through etching and as a consequence the time required for the interdiffusion to reach completion is reduced. Drying treatments of the electrode have been shown to reduce the interdiffusion rate. This was attributed to lowered mobilities of the ions in the gel layer in the absence of water for the same driving forces. The present work deals with the time lag for the ion-exchange process in the gel layer of hydrogen-ion-selective glass electrodes. The lag can be used for qualitative arguments on the response-time-properties. In addition, it should be possible to interrelate parameters such as the gel-layer thickness, the interdiffusion coefficients and the diffusion coefficients of individual ions. EXPERIMENTAL
Electrodes The glass electrodes were stored in dilute aqueous HC1 for several weeks. After this time they were considered to be fully hydrated which means that the thickness of the total gel layer should not change upon further storage in the same solution. The etched condition of an electrode was achieved through immersion in.a 2~o aqueous HF solution for 2 min. Partially hydrated electrodes were produced by storing etched electrodes in the above-mentioned HCI solution. To inhibit this hydration process, the glass electrodes were rinsed with pure isopropanol and wiped carefully with a tissue paper and then tested without delay. If repeated measurements were performed with a partially hydrated electrode, soaking in water between the tests was avoided since the response time properties were found not
2
B. KARLBERG
to change during test periods of the order of several hours. The drying procedure consisted of placing the bulb of the glass electrode for 1 to 2 h in a warm airstream (60-70°C) obtained from a hair drier. The electrode rods were turned in such a way that the glass surfaces were as uniformly exposed as possible. Only glass electrodes with fully developed gel layers were dried in this way and they are termed "dried" electrodes in the following. E.m.f. measurements
The glass electrode was removed from the aqueous storing solution (or from the etching solution), and rinsed with pure isopropanol and wiped. It was preequilibrated in a 0.01 M HC104 isopropanol solution containing 0.01 M sodium or lithium perchlorate. The electrode was then removed from this solution, wiped, and transferred to a 0.01 M di-isopropylamine isopropanol solution. This basic solution was also 0.01 M with respect to the sodium or lithium perchlorate salt. The e.m.f, was recorded on a Mosley 680 recorder by using an operational amplifier as follower (Analog Devices Model 301) until it had attained a steady value. The time periods required to obtain this steady value within 20 and 10 mV, respectively, were evaluated and the difference, At10.20, was calculated (see Fig. 1). The reference electrode was always allowed to equilibrate in the test solution in question for at least 15 min. The glass electrode was then removed from the basic solution and re-immersed in the acidic solution. The e.m.f, recording and the evaluation of At10.20 for this process were performed similarly.
2O
"t o
10
Total em.f, change-
20
~ 600 mV
t~
H° exchanged for Na°
o
10
20
30
40
50
60
time elapsed from the electrode transfer/minutes__
Fig. 1. Typical e.m.f, changes obtained after transfers of a glass electrode (Beckman E-2) from an acidic to a basic isopropanol solution and vice versa. Ion-exchange capacity measurements
The method adopted for ion-exchange capacity measurements has been described in detail earlier 1. The basic immersion' solution comprised a 0.01 M diisopropylamine isopropanol solution containing sodium or lithium perchlorate (0.01 M). An immersion time of 60 min was chosen. The electrode was then removed, rinsed and wiped, and transferred to a 0.01 M HC104 isopr0panol solution (4 ml). The alkali metal ion content in this "leakage solution" was determined by flame emission spectroscopy. The value of the lithium ion-exchange capacity thus obtained
TIME LAG OF ION EXCHANGE IN GLASS ELECTRODES
3
m a y be too high since the c o n t i n u o u s leakage of l i t h i u m ions from the b u l k glass will c o n t r i b u t e to the total a m o u n t analysed. RESULTS AND DISCUSSION Typical e.m.f, changes o b t a i n e d after transferring a glass electrode ( B e c k m a n E-2) from the acidic to the basic i s o p r o p a n o l s o l u t i o n a n d v i c e v e r s a are shown in Fig. 1. T h e p o i n t s o n the e.m.f, change curves where a t t a i n m e n t s of the steady value w i t h i n 20 a n d 10 m V have j u s t occurred, have been e v a l u a t e d ; the corres p o n d i n g time periods are d e n o t e d by t2o a n d tlo. Differences t l o - t 2 o will be referred to as Atlo.2o. I n the basic s o l u t i o n a certain fraction of the sites in the external, loose p a r t of the gel layer will be occupied by alkali metal ions. The extent of this process depends o n the basicity a n d the alkali metal c o n t e n t of the solution. F o r the c o m p o s i t i o n of the basic s o l u t i o n used in all the experiments reported here some of the electrodes will n o t be completely saturated by alkali metal ions in the gel layers. The a m o u n t s of the exchanged ions are therefore referred to as a p p a r e n t ion-exchange capacities. I n T a b l e I values of the differences Atlo.2 o a n d the a p p a r e n t i o n - e x c h a n g e capacity are t a b u l a t e d for a n u m b e r of c o m m e r c i a l glass electrodes in different states. T h e significance of the q u a n t i t y At~o,2 o is s h o w n in Fig. 1. By using the exoression for the time lag 6 TABLE1 Atlo.2o-VALUES (cf. Fig. 1) AND APPARENT ION-EXCHANGE CAPACITY FOR GLASS ELECTRODES OF DIFFERENT STATES Electrode
Electrode state
A t 1o,20/s From acid to base
Beckman E-2 Ingold 201
Ingold LoT
Ingold HA Metrohm UX
hydrated hydrated etched dried hydrated etched etched and then hydrated 1 h dried hydrated etched dried hydrated hydrated hydrated etched etched and then hydrated 1 h dried
Alkali metal ion
DH/Dio~ calculated
From base to acid
Apparent ionexchange capacity/ nmol cm-2
120 25 15 190 35 ~,4 ~4
765 240 105 550 220 ~8 ~7
Na ÷ Li ÷ Li ÷ Lit Na ÷ Na + Na +
6.4 9.6 7.0 2.9 6.3 ,~ 2 ~,2
-
120 55 35 310 240 60 190 ~8 ~7
405 555 430 860 1930 110 720 20 15
Na + Li t Lit Lit Nat Na + Na t Na ÷ Na t
3.4 10.2 12.3 2.8 8.0 1.8 3.8 ~ 2.5 ~2
-
325
1040
Na ÷
3.2
-
1.5 0.8 8.0 2.4 1.8 5.4 4.5 19.6 2.1 19.0 3.5 2.5
4
B. KARLBERG Atlo.z o = K 12/Dion
(1)
where K is a constant dependent upon the choice of the mV-values the ratio DIj/Dion has been calculated for each pair of At 10, 20-values as the ratio between these values, l is assumed not to change during the time required to measure a Atl0.z0-value pair for each electrode and electrode state. The choice of 20 and 10 mV is arbitrarily made. The calculated Dn/Dio n ratios are independent of this choice with some restrictions. If too high mV-values are taken this will lead to small values of t, for which the interdiffusion coefficient varies significantly and is not equal to the individual diffusion coefficient of the ion present in deficit within the exchanger. Too small mV-values, on the other hand, give an uncertainty in the evaluation of the t-values due to the small slope of the response curve in the vicinity of the steady-state value. We examine the results obtained for the fully hydrated states of the electrodes in Table I. For the electrodes Beckman E-2, Ingold 201 and Ingold LoT, the calculated ratios DH/D~o,, valid within the loose gel layer, are of the same order of magnitude as the corresponding ratios for the ions in an aqueous solution if these are calculated from equivalent ionic conductivity data. The ratios DH/DNa and DH/DL~ in water are about 7.0 and 9.0, respectively, at infinite dilution. For the Ingold HA and the Metrohm UX electrodes significantly lower values of the Dn/DNa ratio have been obtained. This may be due to a more rigid structure in the gel layers of these two electrodes leading to a lower water content in comparison with the other electrodes. It has been established that the self-diffusion coefficient for both hydrogen ions and alkali metal ions decreases when the concentration of supporting electrolyte in a solution increases up to several M (ref. 7). The decrease for hydrogen ions is percentally larger than the decrease for sodium or lithium ions. If the site molarity is high in the loose part of the gel layer, a low value of the ratio DH/DNa is to be expected in comparison with the value of 7.0, calculated from an aqueous solution at infinite dilution. A rough estimation of the molarity of sites can be made. Suppose that the loose gel layer thickness is 200 A, and the ionexchange capacity 2 × 10 -8 mol cm -2. The molarity of sites will then be 10. This is undoubtedly a high value though very uncertain. However, the estimation reflects that the site molarity might influence the DH/Dion-ratio. All the fully hydrated glass electrodes, which were dried in a warm air stream, showed a retarded response. Large At~ 0. z0-values were obtained throughout. The calculated Dn/Dion~-ratios are lower compared with the normal "wet" state which should mean that the values of the individual ion mobilities in the gel layer become approximately equal. The drying treatment may lead to a shrinking of the gel layer due to the removal of water molecules. If this possible shrinking is neglected, i.e., l is constant, lower diffusion coefficients appear for the individual ions within the dried exchanger. For the hydrogen ions the decrease is largest. This is reasonable since the proton transfer via water molecules is made more difficult when water is removed. An eight-fold decrease of DH may be estimated for the Ingold 201 electrode. The mobilities of the alkali metal ions in the gel layer are also lowered by the drying treatment but not to a similar extent. The apparent ion-exchange capacity may be taken as a direct measure of the
TIME LAG OF ION EXCHANGE IN GLASS ELECTRODES
5
thickness of the exchanger, 1. Assuming that the diffusion coefficients for sodium and lithium ions in the exchanger phase do not change when an electrode is etched, it should be possible to interrelate the apparent ion-exchange capacity of the electrode in different states by using eqn. (1). Values of 3.2 and 2.7 nmol cm -2 are estimated for the Metrohm UX electrode in the etched state and in the state "etched and then hydrated 1 h', respectively, when the value of 19.0 nmol cm-2 is taken as a reference value for the fully hydrated electrode state. Corresponding values measured are 3.5 and 2.5 nmol cm -2 (see Table I). If the same.estimations are made for the Ingold 201 electrode, values of 1.5 and 1.4 nmol cm -2 are obtained using 8.0 nmol cm-2 as a reference value. These values deviate somewhat from the measured quantities, 2.4 and 1.8 nmol cm-2, probably due to the small and uncertain At-values. For the lithium ion exchange, interrelations of the capacity values have been performed for Ingold 201 and Ingold LoT electrodes. The values (nmol cm -2) for the electrodes in mentioned order are estimated 1.0 and 4.8, measured 0.8 and 4.5, reference 1.5 and 5.4. The agreement between the estimated and measured values is good. Diffusion coefficient ratio (or mobility ratio) data in the literature are scanty for hydrated glass s. The reason for this must be the poor knowledge of the structure and properties of hydrated glass. In any event the gel layer of hydrogenion-selective glass electrodes must be regarded as a phase with finite extension. ACKNOWLEDGE MENTS
The author wishes to thank Prof. G. Johansson and Dr. J. Lindberg for valuable discussions, and Dr. M. Sharp for improving the English of the manuscript. This work was supported by grants from the Swedish Natural Science Research Council. SUMMARY
The loose external part of the gel layer of a hydrogen-ion-selective glass electrode acts as a cation exchanger with fixed anion sites. In the last period of a complete ion exchange the rate of the process is governed by the ion present in deficit in the exchanger. Estimates of self-diffusion coefficient ratios for interdiffusing ions have been made by using the result obtained from e.m.f, measurements and by applying the time lag function. The e.m.f, measurements were performed during the apparently complete ion-exchange process in the gel layer of the glass electrode. REFERENCES 1 2 3 4 5 6 7 8
B. Karlberg, J. Electroanal. Chem., 45 (1973) 127. B. Karlberg, J. Electroanal. Chem., 42 (1973) 115. B. Karlberg, Anal. Chim. Acta, 66 (1973) 93. F. Helfferich, 1on Exchange, McGraw-Hill, New York, 1962, Ch. 6. F. Helfferich in J. A. Marinsky (Ed.), 1on Exchange, Vol. 1, Marcel Dekker, New York, 1966, Ch. 2. F. Helfferich, 1on Exchange, McGraw-Hill, New York, 1962, Ch. 8. L. A. Woolf, J, Phys. Chem., 64 (1960) 481. R. H. Doremus in G. Eisenman (Ed.), Glass Electrodes for Hydrogen and Other Cations, Marcel Dekker, New York, 1967, Ch. 4.
l
© Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
TIME LAG OF ION EXCHANGE IN THE GEL LAYER OF HYDROGENION-SELECTIVE GLASS ELECTRODES
BO KARLBERG
Department of Analytical Chemistry, University of Ume~, S-901 87 Ume~ (Sweden) (Received 16th February 1973; in revised form 21st August 1973)
It has earlier been shown 1 that the gel layer of hydrogen-ion-selective glass electrodes has a small ion-exchange capacity, about 10 -s tool cm -2 bulb area. When a glass electrode is transferred between acidic and basic solutions more than 90~ of the total e.m.f, change occurs within a few minutes while the time period required to obtain the steady e.m.f, value may amount to several tens of minutes. By measuring the ion-exchange extent at different times it was concluded that the ion-exchange process and the later e.m.f, changes are correlated. It has been possible to make predictions about the ion-exchange kinetics of glass electrodes 2'3 based on the theory of Helfferich 4'5. When initially the faster of the two ions is present in the exchanger, i.e., the gel layer, the exchange 15rocess is faster than if the slower ion is present there. The gel-layer thickness can be reduced through etching and as a consequence the time required for the interdiffusion to reach completion is reduced. Drying treatments of the electrode have been shown to reduce the interdiffusion rate. This was attributed to lowered mobilities of the ions in the gel layer in the absence of water for the same driving forces. The present work deals with the time lag for the ion-exchange process in the gel layer of hydrogen-ion-selective glass electrodes. The lag can be used for qualitative arguments on the response-time-properties. In addition, it should be possible to interrelate parameters such as the gel-layer thickness, the interdiffusion coefficients and the diffusion coefficients of individual ions. EXPERIMENTAL
Electrodes The glass electrodes were stored in dilute aqueous HC1 for several weeks. After this time they were considered to be fully hydrated which means that the thickness of the total gel layer should not change upon further storage in the same solution. The etched condition of an electrode was achieved through immersion in.a 2~o aqueous HF solution for 2 min. Partially hydrated electrodes were produced by storing etched electrodes in the above-mentioned HCI solution. To inhibit this hydration process, the glass electrodes were rinsed with pure isopropanol and wiped carefully with a tissue paper and then tested without delay. If repeated measurements were performed with a partially hydrated electrode, soaking in water between the tests was avoided since the response time properties were found not
2
B. KARLBERG
to change during test periods of the order of several hours. The drying procedure consisted of placing the bulb of the glass electrode for 1 to 2 h in a warm airstream (60-70°C) obtained from a hair drier. The electrode rods were turned in such a way that the glass surfaces were as uniformly exposed as possible. Only glass electrodes with fully developed gel layers were dried in this way and they are termed "dried" electrodes in the following. E.m.f. measurements
The glass electrode was removed from the aqueous storing solution (or from the etching solution), and rinsed with pure isopropanol and wiped. It was preequilibrated in a 0.01 M HC104 isopropanol solution containing 0.01 M sodium or lithium perchlorate. The electrode was then removed from this solution, wiped, and transferred to a 0.01 M di-isopropylamine isopropanol solution. This basic solution was also 0.01 M with respect to the sodium or lithium perchlorate salt. The e.m.f, was recorded on a Mosley 680 recorder by using an operational amplifier as follower (Analog Devices Model 301) until it had attained a steady value. The time periods required to obtain this steady value within 20 and 10 mV, respectively, were evaluated and the difference, At10.20, was calculated (see Fig. 1). The reference electrode was always allowed to equilibrate in the test solution in question for at least 15 min. The glass electrode was then removed from the basic solution and re-immersed in the acidic solution. The e.m.f, recording and the evaluation of At10.20 for this process were performed similarly.
2O
"t o
10
Total em.f, change-
20
~ 600 mV
t~
H° exchanged for Na°
o
10
20
30
40
50
60
time elapsed from the electrode transfer/minutes__
Fig. 1. Typical e.m.f, changes obtained after transfers of a glass electrode (Beckman E-2) from an acidic to a basic isopropanol solution and vice versa. Ion-exchange capacity measurements
The method adopted for ion-exchange capacity measurements has been described in detail earlier 1. The basic immersion' solution comprised a 0.01 M diisopropylamine isopropanol solution containing sodium or lithium perchlorate (0.01 M). An immersion time of 60 min was chosen. The electrode was then removed, rinsed and wiped, and transferred to a 0.01 M HC104 isopr0panol solution (4 ml). The alkali metal ion content in this "leakage solution" was determined by flame emission spectroscopy. The value of the lithium ion-exchange capacity thus obtained
TIME LAG OF ION EXCHANGE IN GLASS ELECTRODES
3
m a y be too high since the c o n t i n u o u s leakage of l i t h i u m ions from the b u l k glass will c o n t r i b u t e to the total a m o u n t analysed. RESULTS AND DISCUSSION Typical e.m.f, changes o b t a i n e d after transferring a glass electrode ( B e c k m a n E-2) from the acidic to the basic i s o p r o p a n o l s o l u t i o n a n d v i c e v e r s a are shown in Fig. 1. T h e p o i n t s o n the e.m.f, change curves where a t t a i n m e n t s of the steady value w i t h i n 20 a n d 10 m V have j u s t occurred, have been e v a l u a t e d ; the corres p o n d i n g time periods are d e n o t e d by t2o a n d tlo. Differences t l o - t 2 o will be referred to as Atlo.2o. I n the basic s o l u t i o n a certain fraction of the sites in the external, loose p a r t of the gel layer will be occupied by alkali metal ions. The extent of this process depends o n the basicity a n d the alkali metal c o n t e n t of the solution. F o r the c o m p o s i t i o n of the basic s o l u t i o n used in all the experiments reported here some of the electrodes will n o t be completely saturated by alkali metal ions in the gel layers. The a m o u n t s of the exchanged ions are therefore referred to as a p p a r e n t ion-exchange capacities. I n T a b l e I values of the differences Atlo.2 o a n d the a p p a r e n t i o n - e x c h a n g e capacity are t a b u l a t e d for a n u m b e r of c o m m e r c i a l glass electrodes in different states. T h e significance of the q u a n t i t y At~o,2 o is s h o w n in Fig. 1. By using the exoression for the time lag 6 TABLE1 Atlo.2o-VALUES (cf. Fig. 1) AND APPARENT ION-EXCHANGE CAPACITY FOR GLASS ELECTRODES OF DIFFERENT STATES Electrode
Electrode state
A t 1o,20/s From acid to base
Beckman E-2 Ingold 201
Ingold LoT
Ingold HA Metrohm UX
hydrated hydrated etched dried hydrated etched etched and then hydrated 1 h dried hydrated etched dried hydrated hydrated hydrated etched etched and then hydrated 1 h dried
Alkali metal ion
DH/Dio~ calculated
From base to acid
Apparent ionexchange capacity/ nmol cm-2
120 25 15 190 35 ~,4 ~4
765 240 105 550 220 ~8 ~7
Na ÷ Li ÷ Li ÷ Lit Na ÷ Na + Na +
6.4 9.6 7.0 2.9 6.3 ,~ 2 ~,2
-
120 55 35 310 240 60 190 ~8 ~7
405 555 430 860 1930 110 720 20 15
Na + Li t Lit Lit Nat Na + Na t Na ÷ Na t
3.4 10.2 12.3 2.8 8.0 1.8 3.8 ~ 2.5 ~2
-
325
1040
Na ÷
3.2
-
1.5 0.8 8.0 2.4 1.8 5.4 4.5 19.6 2.1 19.0 3.5 2.5
4
B. KARLBERG Atlo.z o = K 12/Dion
(1)
where K is a constant dependent upon the choice of the mV-values the ratio DIj/Dion has been calculated for each pair of At 10, 20-values as the ratio between these values, l is assumed not to change during the time required to measure a Atl0.z0-value pair for each electrode and electrode state. The choice of 20 and 10 mV is arbitrarily made. The calculated Dn/Dio n ratios are independent of this choice with some restrictions. If too high mV-values are taken this will lead to small values of t, for which the interdiffusion coefficient varies significantly and is not equal to the individual diffusion coefficient of the ion present in deficit within the exchanger. Too small mV-values, on the other hand, give an uncertainty in the evaluation of the t-values due to the small slope of the response curve in the vicinity of the steady-state value. We examine the results obtained for the fully hydrated states of the electrodes in Table I. For the electrodes Beckman E-2, Ingold 201 and Ingold LoT, the calculated ratios DH/D~o,, valid within the loose gel layer, are of the same order of magnitude as the corresponding ratios for the ions in an aqueous solution if these are calculated from equivalent ionic conductivity data. The ratios DH/DNa and DH/DL~ in water are about 7.0 and 9.0, respectively, at infinite dilution. For the Ingold HA and the Metrohm UX electrodes significantly lower values of the Dn/DNa ratio have been obtained. This may be due to a more rigid structure in the gel layers of these two electrodes leading to a lower water content in comparison with the other electrodes. It has been established that the self-diffusion coefficient for both hydrogen ions and alkali metal ions decreases when the concentration of supporting electrolyte in a solution increases up to several M (ref. 7). The decrease for hydrogen ions is percentally larger than the decrease for sodium or lithium ions. If the site molarity is high in the loose part of the gel layer, a low value of the ratio DH/DNa is to be expected in comparison with the value of 7.0, calculated from an aqueous solution at infinite dilution. A rough estimation of the molarity of sites can be made. Suppose that the loose gel layer thickness is 200 A, and the ionexchange capacity 2 × 10 -8 mol cm -2. The molarity of sites will then be 10. This is undoubtedly a high value though very uncertain. However, the estimation reflects that the site molarity might influence the DH/Dion-ratio. All the fully hydrated glass electrodes, which were dried in a warm air stream, showed a retarded response. Large At~ 0. z0-values were obtained throughout. The calculated Dn/Dion~-ratios are lower compared with the normal "wet" state which should mean that the values of the individual ion mobilities in the gel layer become approximately equal. The drying treatment may lead to a shrinking of the gel layer due to the removal of water molecules. If this possible shrinking is neglected, i.e., l is constant, lower diffusion coefficients appear for the individual ions within the dried exchanger. For the hydrogen ions the decrease is largest. This is reasonable since the proton transfer via water molecules is made more difficult when water is removed. An eight-fold decrease of DH may be estimated for the Ingold 201 electrode. The mobilities of the alkali metal ions in the gel layer are also lowered by the drying treatment but not to a similar extent. The apparent ion-exchange capacity may be taken as a direct measure of the
TIME LAG OF ION EXCHANGE IN GLASS ELECTRODES
5
thickness of the exchanger, 1. Assuming that the diffusion coefficients for sodium and lithium ions in the exchanger phase do not change when an electrode is etched, it should be possible to interrelate the apparent ion-exchange capacity of the electrode in different states by using eqn. (1). Values of 3.2 and 2.7 nmol cm -2 are estimated for the Metrohm UX electrode in the etched state and in the state "etched and then hydrated 1 h', respectively, when the value of 19.0 nmol cm-2 is taken as a reference value for the fully hydrated electrode state. Corresponding values measured are 3.5 and 2.5 nmol cm -2 (see Table I). If the same.estimations are made for the Ingold 201 electrode, values of 1.5 and 1.4 nmol cm -2 are obtained using 8.0 nmol cm-2 as a reference value. These values deviate somewhat from the measured quantities, 2.4 and 1.8 nmol cm-2, probably due to the small and uncertain At-values. For the lithium ion exchange, interrelations of the capacity values have been performed for Ingold 201 and Ingold LoT electrodes. The values (nmol cm -2) for the electrodes in mentioned order are estimated 1.0 and 4.8, measured 0.8 and 4.5, reference 1.5 and 5.4. The agreement between the estimated and measured values is good. Diffusion coefficient ratio (or mobility ratio) data in the literature are scanty for hydrated glass s. The reason for this must be the poor knowledge of the structure and properties of hydrated glass. In any event the gel layer of hydrogenion-selective glass electrodes must be regarded as a phase with finite extension. ACKNOWLEDGE MENTS
The author wishes to thank Prof. G. Johansson and Dr. J. Lindberg for valuable discussions, and Dr. M. Sharp for improving the English of the manuscript. This work was supported by grants from the Swedish Natural Science Research Council. SUMMARY
The loose external part of the gel layer of a hydrogen-ion-selective glass electrode acts as a cation exchanger with fixed anion sites. In the last period of a complete ion exchange the rate of the process is governed by the ion present in deficit in the exchanger. Estimates of self-diffusion coefficient ratios for interdiffusing ions have been made by using the result obtained from e.m.f, measurements and by applying the time lag function. The e.m.f, measurements were performed during the apparently complete ion-exchange process in the gel layer of the glass electrode. REFERENCES 1 2 3 4 5 6 7 8
B. Karlberg, J. Electroanal. Chem., 45 (1973) 127. B. Karlberg, J. Electroanal. Chem., 42 (1973) 115. B. Karlberg, Anal. Chim. Acta, 66 (1973) 93. F. Helfferich, 1on Exchange, McGraw-Hill, New York, 1962, Ch. 6. F. Helfferich in J. A. Marinsky (Ed.), 1on Exchange, Vol. 1, Marcel Dekker, New York, 1966, Ch. 2. F. Helfferich, 1on Exchange, McGraw-Hill, New York, 1962, Ch. 8. L. A. Woolf, J, Phys. Chem., 64 (1960) 481. R. H. Doremus in G. Eisenman (Ed.), Glass Electrodes for Hydrogen and Other Cations, Marcel Dekker, New York, 1967, Ch. 4.