The effect of the ion exchanger site-counterion complex formation on the selectivities of ISEs

Talanta 44 (1997) 1735 – 1747

The effect of the ion exchanger site-counterion complex formation on the selectivities of ISEs V.V. Egorov *, N.D. Borisenko, E.M. Rakhman’ko, Ya.F. Lushchik, S.S. Kacharsky Institute of Physico-Chemical Problems, Belarusian State Uni6ersity, Leningradskaya Str. 14, 220080 Minsk, Belarus Received 18 June 1996; received in revised form 7 January 1997; accepted 3 February 1997

Abstract Using the model of ideally associated solution, the effect of ion association of the ion exchanger sites with main and foreign counterions on the selectivity of ISEs based on liquid ion exchangers has been considered. Equations which describe the potentiometric selectivity coefficient as a function of ion association constants in the membrane phase and of standard free energies of transfer of the determined and foreign ions from water to the membrane are obtained for the following main cases: (a) the determined and foreign ions are single-charged; (b) the determined ion is double-charged and the foreign ion is single-charged. It is shown that in the case of single-charged main and foreign ions, the ratio of the ion association constants has a great effect on the potentiometric selectivity of membranes, only if the ion exchanger sites produce less strong associates with the determined counterion as compared with the foreign one. Otherwise, this effect is insignificant. The selectivity for double-charged ions should increase, other things being equal, as the first constant of association of these ions with the ion exchanger sites increases. The effect of producing ion triplets of the type I2R ( 9 ) on the selectivity of ISEs is also considered. Experimental data are presented which illustrate the effect of the nature of the ion exchanger on the potentiometric selectivity. Some procedures employing the factor of ion association for increasing the potentiometric selectivity of liquid ion exchange membranes are considered. © 1997 Elsevier Science B.V. Keywords: Electrodes; Ion association; Potentiometric selectivity

1. Introduction The presence of relationship between the potentiometric selectivity of ISEs and the relative strength of binding main and foreign ions with the ion exchanger site follows directly from Sandblom, Eisenman and Walker’s theory [1] and is one of the most important conclusions of Nikol* Corresponding author.

sky-Schultz’s general theory of glass electrodes [2], whose main statements are applicable to some extent to membanes based on liquid ion exchangers. Stover and Buck [3,4] have shown that apart from forming ion pairs, the ratio of mobilities of ion exchanger sites and counterions in the membrane phase can also have an important effect on the selectivity coefficient. It should be noted that this effect increases with ion association. Armstrong and co-workers [5–7] have shown that

0039-9140/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S 0 0 9 - 9 1 4 0 ( 9 7 ) 0 0 0 4 2 - 8

1736

V.V. Egoro6 et al. / Talanta 44 (1997) 1735–1747

mobilities of ion exchanger sites and counterions in plasticized polyvinylchloride membranes can differ by more than an order of magnitude. Thus, the possibility of exhibition of the mentioned effect seems quite realistic. On the other hand, experiments have shown that the nature of the ion exchanger usually does not have an important effect on ISE selectivity [8 – 11]. It is interesting to note that similar data were obtained both for fully dissociated nitrobenzene-containing membranes and for membranes with a relatively low dielectric constant. In general, this situation is consistent with results of the works on ion association [12,13], from which it follows that ion exchanger site-counterion association constants are almost independent of the ion nature. Moreover, Morf has shown [14] that even in those cases when charged ionophore tends to selective interaction with one of the ions, this property of the charged ionophore cannot be transformed completely into potentiometric selectivity. Therefore, for some time the concept prevailed that use of charged ionophores was not so promising as compared with neutral carriers as concerns achievement of high potentiometric selectivity. However, for the recent 10 – 15 years the various anion-selective electrodes based on charged ionophores (derivatives of vitamin B12 [15–18], porphyrins [19 – 28], phthalocyanins [29], tin-organic, palladium-organic compounds [30 –34] etc.) were described which were able to form sufficiently strong complexes with the determined ion. Selectivity of such electrodes differed substantially from selectivity of the Hofmeister series, which could not be explained reasonably within the formalism developed in [14]. Egorov and co-workers [35,36] have shown that the theoretical prohibition of the transformation of the selective ion exchanger affinity to the determined ion into potentiometric selectivity could be overcome, if the concentration of free ions of selective ion exchanger is stabilized in the membrane so that it could not change greatly in the course of the ion exchange reaction with the interfering ion. To do this, it was suggested to introduce into the membrane a lipophilic ionic additive having charge opposite to that of the ion exchanger sites and forming a rather well dissociating salt with the

latter. It was shown experimentally that this procedure could, for example, increase substantially the selectivity to the cations of primary-tertiary amines as compared with quaternary ammonium cations which, according to [37], form less strong ion associates. The mechanism of functioning of the membranes based on highly selective ion exchangers (or charged carriers, according to the classification [38]) was thoroughly considered by Schaller and co-workers [39–41]. In particular, they showed that introduction of a lipophilic ion additive into the membrane was very important in the case of cation-selective electrodes but not so important in the case of anion-selective electrodes, since PVC membranes always contain anion admixtures that actually function as a lipophilic additive and provide selectivity close to optimal. Those authors obtained quantitative expressions for the electrode response and selectivity coefficients as a function of the membrane composition, solvation and complex formation parameters, which is important both for understanding of the functioning mechanism of such ISEs and for optimization of membrane compositions and measurements conditions. In the present contribution the influence of the features of ion exchanger site-counterion interaction on the potentiometric selectivity of the membranes being in contact with sample solution containing both primary and interfering ions is discussed. New experimental data are presented which illustrate the effect of the ion exchanger nature on ISE selectivity.

2. Experimental

2.1. Reagents 2.1.1. Ion exchangers Quaternary ammonium salts, namely, trinonyloctadecyl-ammonium (TNODA), dimethyldioctadecylammonium (DMDODA) and N,N,N-tridecyl-2-hydroxyethylammonium (TDHEA) were synthesized by stepwise alkylation of octadecylamine (the first two salts) and monoethanolamine, respectively, by halogen alkyls following the method of Veigand-Hilgetag [42].

V.V. Egoro6 et al. / Talanta 44 (1997) 1735–1747

The produced compounds were isolated and purified by extraction in the octane – dimethylformamide system [43]. For all compounds produced the contents of the main substance determined by nonaqueous potentiometric titration with respect to halogen ion was at least 99%. The contents of amine impurities in these compounds determined spectrophotometrically in the form of ion associates with picric acid following Lestchev et al. [44] did not exceed 0.01%. Trinonyloxybenzenesulphonic acid (TNBS) was produced by alkylation of pyrogallol by nonyl bromide followed by sulphonation [45]. The product was isolated and purified by extraction in the hexane – dimethylsulphoxide system. Di(2-decyloxyphenyl)phosphate (D(2DP)P) and di(3-nonyloxyphenyl)phosphate (D(3NP)P) were produced in the reaction of phosphorus chloroxide with the appropriate alkoxyphenol. These compounds were synthesized and purified following the procedure used for these kind of compounds [46]. For the last three compounds, the contents of the main substance determined by nonaqueous potentiometric titration amounted to at least 97%.

2.1.2. Plasticizers and sol6ents Dibuthylphthalate (DBP), 1-bromnaphthalene (BN), o-nitrophenyloctyl ester (NPOE) and organic solvents toluene, nitrobenzene and cyclohexanone of reagent grade were purified by distillation. Dioctylphenylphosphonate (DOPP) was synthesized in the reaction of phenylphosphonedichloride with octanol following Cosolapoff [47]. Then, the product was isolated from the reaction mixture by extraction in the hexane and water/dimethylsulphoxide mixture (1:4). The isolated plasticizer was purified in the chromatographic column filled with S40/100 silicagel; the mobile phase was a chloroform/methanol mixture (9:1) [48]. Trihexylphosphate (THP) was purified from acid admixtures by treatment of hexane solution of the reagent with sodium hydroxide solution in the water/dimethylformamide mixture following [49]. 3-Nonyloxyphenol (NOP) was produced by alkylation of resorcinol by nonyl bromide. The product was distilled after extraction from the reaction mixture.

1737

2.1.3. Polymer matrices and aqueous electrolytic solutions Polyvinylchloride PZh-S70 was used as a polymer matrix of ISE membranes. Aqueous electrolytic solutions were prepared using distilled water. Dry salts used for these purposes were of at least analytical reagent grade. 2.2. Preparation of samples Membranes of ISEs were prepared following the standard method [50]. The membrane compositions are presented in Table 1. Various interesting series of compounds of quaternary ammonium were obtained by ion exchange.

2.3. Measurements of ion exchange constants Exchange of chloride for sulphate was studied at the constant temperature T=2939 1 K in the toluene-water system at an ion exchanger concentration of 1.7 · 10 − 2 M. The contents of sulphate ions in the water phase varied in the range 0.005– 1 M. After the system attained equilibrium the chloride ion concentration in the aqueous and organic phases was found by potentiometric titration by silver nitrate solution, and the sulphate ion concentration was found from the difference using the material balance equation. It was observed that the anion exchange constant depended substantially on the sulphate ion concentration, which is consistent with the available literature information [51] and can be ascribed to formation of the complex anion NaSO4− . Estimated concentration constants of anion exchange are given in Table 2.

2.4. Measurements of ion association constants Ion association was studied at T=2939 1 K in the toluene–nitrobenzene system containing 10% v/v of nitrobenzene at constant current. Electric conductivities of a series solutions of quaternary amonium salts (QAS) were determined at concentrations of 10 − 2 –10 − 7 M. Then, the constants of ion association were calculated from the formula: kass = (1− a)/(a 2 · C)

V.V. Egoro6 et al. / Talanta 44 (1997) 1735–1747

1738

2.5. Potentiometric measurements

1.2 · 10−1

1.2 · 10−1 1.2 · 10−1 1.2 · 10−1 1.2 · 10−1 1.2 · 10−1 1.2 · 10−1 1.2 · 10−1 1.2 · 10−1

TDHEA TNODA

66.6 66.6

57 57

66.6

66.6 66.6 66.6

K pot ij =

ai (10(E2 − E1)/u − 1) (aj)zi/zj

where ai and aj are the activities of the main and foreign ions; zi and zj are the charges of the main and foreign ions; E1 and E2 are the potentials of ISE in the background and mixed solutions; u is the slope of the electrode function.

3.1. The model of ideally associated solution. Single-charged ions In media with low and moderate dielectric constants such as ISEs membranes (except those based on nitrobenzene or nitrogroup-containing plasticizers), liquid ion exchangers are present mainly in the form of ion associates with appropriate counterions, when the relative amount of free ions in the membrane is negligible. In these systems, the ion exchange constant determined experimentally is described by the equation:

66.6

66.6

NPOE 1-BN THP

(1) K (2) ij = K ij · KjR/KiR

(1)

where K (2) ij is the equilibrium constant of the ion exchange process, e.g., for cation-exchanger: 33.3 33.3 33.3 33.3 33.3 33.3 33.3 33.3 28.5 28.5 33.3 33.3 33.3

K(2) ij

I II III IV V VI VII VIII IX X XI XII XIII

DBP

Plasticizer (%, w/w) PVC (%, w/w) Membrane

Table 1 The composition of produced ISE membranes

Potentiometric measurements were taken at T= 2939 1 K with an I-130 digital ionometer with an EVL-1M.3 silver–silver chloride reference electrode. Selectivity coefficients were determined with the method of mixed solutions for SO24 − ion selective electrode with a constant sulphate-ion background of 10 − 3 M and against the background of main ion of 0.1 M for the other ISEs. K pot was calculated from the equation: ij

3. Results and discussion

66.6 66.6 66.6

DOPP

Ion exchanger (M)

TNBS

2.5 · 10−2

2.5 · 10−2

D(3NP)P

2.5 · 10−2

D(2DP)P

DMDODA

1.2 · 10−1

14 14

NOP (w/w, %)

where a is the dissociation degree of QAS found with Stokes’ method [52], C is the concentration of QAS in the solution.

+ J+ aq + RI “ I aq + RJ (1) ij

(2)

K is the ion exchange constant only determined by standard free energies of transfer of ions I and J and is independent of the nature of the ion exchanger:

V.V. Egoro6 et al. / Talanta 44 (1997) 1735–1747

1739

Table 2 The effect of the ion exchanger nature on the ion association, ion exchange and potentiometric parameters Ion exchanger

Ion

Ion association constant

KSO2−, Cl−* for CSO2− 4

−2

5 · 10 TNODA

DMDODA

SO2− 4 Cl− Pic− TPhB− SO2− 4 Cl− Pic− TPhB−

4.6 · 108 4.9 · 109 3.1 · 108 4.1 · 107 4.8 · 108 8.0 · 109 5.9 · 108 2.7 · 107

4

M

K pot SO2−, Cl 4

1.0 M

4.8 · 101

5.0 · 102

1.5 · 103 (IX)

7.2 · 10−1

5.0

6.5 · 101 (X)

+ − + 2− * KSO2−, Cl− is the equilibrium constant of the process: .2 Cl−+SO2− 4 ···(R )2 “2 Cl ···R +SO4 4

0 0 K (1) ij =exp[(DG i −DG j )/RT],

(3)

KiR and KjR are the constants of ion association of I + and J + counterions with the ion exchanger sites R − . Thus, as it was shown by Eisenman [1], in highly associated systems, the ion exchange selectivity depends directly on the ratio of the constants of association of the ion exchanger sites with the corresponding counterions. While considering the potentiometric selectivity, we restrict ourselves to the model including only the effect of the foreign ion J + on the interphase potential at the membrane – solution interface, assuming that for membranes based on liquid ion exchangers, the diffusion potential inside the membrane is unimportant. If the differences of the activities of ions I + and J + in the nearboundary layer and in the bulk of the sample solution are neglected, the effect of the foreign ion J + consists in changing the activity of the main ion I + in the membrane phase. In the first approximation this change may be described in terms of the concentration constants of ion exchange and of ion association. In the case of associated systems, concentrations of free (solvated by the solvent but not bound to the associates) ions is described by the equation: C( i =

C( iR KiR · C( R

(4)

where C( R is the concentration of the free ion exchanger site R − . In the approximation of the model of ideally associated solution, this concentration is described by the equation

C( R =

'

C( iR C( jR + KiR KjR

(5)

where C( iR and C( jR are the equilibrium concentrations of the corresponding ion associates described by the equations C( iR =

C( tot R · Ci Ci + K (2) ij · Cj

(6)

C( jR =

(2) C( tot R · K ij · Cj Ci + K (2) ij Cj

(7)

where C( tot R is the total concentration of the ion exchanger in the membrane. It follows from Eqs. (4) and (5) that the change in the concentration of free counterions I + in the membrane that characterizes the interfering effect of the foreign ion J + is determined not only by completeness of the ion exchange process but also by the ratio of the ion association constants. Let the condition KiR \ KjR be satisfied. According to Eqs. (1) and (2) this should lead to a decrease in the concentration of the associate JR in the membrane. However, decrease in the portion of the less strong ion associate JR is compensated for, to a great extent, by its greater ability to generate free site R − , which, according to Eq. (4), is accompanied by decrease in the concentration of the free counterion I + in the membrane. As a result, use of a selective ion exchanger producing stronger associates with the ion I +should not lead to appropriate increase in the potentiometric selectivity.

V.V. Egoro6 et al. / Talanta 44 (1997) 1735–1747

1740

In this case the equation that expresses explicitly the experimentally determined potentiometric selectivity coefficient in terms of exchange parameters of the system can be easily obtained from the theory of ISEs based on liquid ion exchangers developed by Morf. According to [14], for an electrode immersed into the solution studied that contains simultaneously the determined and interfering ions the membrane potential is described by the equation: E = E 0i +(1−t) · RT/F ln(ai +K (1) ij aj) +t · RT/F ln(ai +K (2) ij )

(8)

where t is the electric transport number of the ion (2) exchanger site R − , and K (1) ij and K ij are physically the same as was defined above. Assuming the diffusion potential to be zero, which is valid at t= 0.5 and combining Eq. (8) with Nikolsky’s equation: · aj) E=E 0i +RT/F ln(ai +K pot ij

(9)

we obtain (1) 1/2 1/2 K pot · (ai +K (1) ij = [(ai +K ij aj) ij · KjR/KiR)

−ai]/aj

(10)

As follows from [3 – 7], neglect of the diffusion potential could hardly be considered quite reasonable. Nevertheless, to simplify the formalism, the assumption is ordinarily used in consideration of the effect of ion association on the potentiometric selectivity of the membrane [39 – 41,53]. If only foreign ions J + are presented in the solution analysed, Eq. (10) is reduced to the equation obtained in [39] for the separate solution method: (1) 1/2 K pot ij = K ij (KjR/KiR)

be seen that K pot ij  1 is the necessary condition for attainment of high selectivity for the ion I + . In this case the ratio of ion association constants KiR/KjR is important only at KiR B KjR. On the contrary, at KiR ] 10KjR further increase in the constant of association of the ion exchanger site R − with the main ion I + has actually no effect on K pot which tends to (1/2)K 1ij. In the case when ij 1 K ij  1, changes in the ratio KiR/KjR has some effect on K pot at KiR \ KjR as well. However, this ij case has no practical interest, since K pot is always ij 1/2 larger than 1, tending to (K (1) . ij ) Of course, by virtue of the assumptions made, the above scheme does not reflect the real situation quite rigorously. Nevertheless, it seems useful since it allows us to follow, at least qualitatively, the effect of ion association on K pot ij . The present conclusions agree well with experimental data on the effect of the nature of the quaternary ammonium cation on K pot ij . The data are summarized in Table 3. It can be seen that an ISE based on salts of TDHEA containing a solvation-active OH group in the direct vicinity to the ion exchange centre, exhibit higher selectivity to sulphonate- and carboxylate-containing anions in the presence of perchlorate and picrate ions as compared with ISEs based on salts of TNODA. The observed effect can reasonably be explained

(11)

When the association constants are equal (KjR = KiR), Eq. (10) is reduced to Nikolsky’s ordinary equation. In the general form analysis of Eq. (10) is rather difficult. Meanwhile, since this equation express explicitly the dependence of K pot on the ij constants of ion exchange and ion association, the effect of these parameters on K pot can be investiij gated in a simple way by mathematical modelling. The obtained results are presented in Fig. 1. It can

Fig. 1. Calculated selectivity coefficients for I ( 9 ) over J ( 9 ) for ion exchanger based membranes. To calculate the selectivity coefficients according to Eq. (10), the following assumptions were made: ai =aj =1 · 10 − 2 M; K (1) equals 1 · 103 (hollow ij circle); (filled circle); 1 · 10 − 3 (hollow triangle).

V.V. Egoro6 et al. / Talanta 44 (1997) 1735–1747

1741

Table 3 The effect of membrane components on the values of ISE selectivity coefficients in the presence of foreign ions Determined ion

Trichloroacetate

Plasticizer

Dibuthylphthalate

1-Naphthalenesulphonate Dibuthylphthalate 2,4-Dinitrobenzoate

Dibuthylphthalate

Toluenesulphonate Toluenesulphonate Toluenesulphonate Toluenesulphonate

Dibuthylphthalate Trihexylphosphate 1-Bromnaphthalene o-Nitrophenyloctyl ester

Kpot ij (TNODA) K pot ij (TDHEA)

Selectivity coefficients Ion exchanger TNODA

Ion exchanger TDHEA

1 −1 ClO− )* 4 : 4.5 · 10 (8 · 10 Pic−: 2 · 104 (4 · 102)* −1 ClO− )* 4 : 10 (1.7 · 10 Pic−: 6 · 103 (1 · 102)* 2 −1 ClO− )* 4 : 1 · 10 (9 · 10 Pic−: 5 · 104 (5 · 102)* 2 ClO− 4 : 8 · 10 2 ClO− : 3 · 10 4 2 ClO− 4 : 5.5 · 10 3 ClO− : 1 · 10 4

1 −1 ClO− )* 4 : 2 · 10 (4 · 10 Pic−: 1.5 · 104 (2 · 102)* −1 ClO− )* 4 : 4 (1 · 10 Pic−: 4 · 10 (6 · 101)* 1 −1 ClO− )* 4 : 4 · 10 (5 · 10 Pic−: 3 · 104 (3 · 102)* 2 ClO− 4 2.5 · 10 2 ClO− : 1.4 · 10 4 2 ClO− 4 : 2.5 · 10 2 ClO− : 3 · 10 4

2.25 (2.0)* 1.3 (2.0)* 2.5 (1.7)* 1.5 (1.7)* 2.5 (1.8)* 1.7 (1.7)* 3.2 2.1 2.2 3.3

* The membranes contain 14% w/w 3-nonyloxyphenol.

by increase in the strength of ion associates produced by anions with TDHEA cations as a result of formation of a hydrogen bond additional to electrostatic interaction. It is natural that the strength of this bond should depend on polarity of the anion, increasing from picrate and perchlorate to sulphonate- and carboxylate-containing anions. This effect results in a 10 – 20-fold increase in the ion exchange constants for exchange of benzoic acid derivatives for perchlorate and 2,4dinitrophenolate ions [54]. However, K pot values ij change only by a factor of 1.5 to 3. It is noteworis almost thy that the observed change in K pot ij independent of the nature of the plasticizer and persists in the presence of the specific solvating additive resorcinol monononyl ester. Selectivity of such ISEs can be increased somewhat, if the membrane is manufactured so that it functions as an indirect electrode, when only a small part of the selective ion exchanger (5–10%) is in the form of the determined ion I and the other part is in the form of more lipophilic ion A which is slightly capable of being displaced by the main ion to the near-electrode layer of the sample 4 solution (K (2) iA ]10 ). If this electrode is immersed in solution of the determined ion I, the concentrations of the ion associates IR and AR in the membrane remain almost invariant. Thus, the concentration of the lipophilic ion A, that appears in the near-electrode layer as a result of ion

exchange, is proportional to the concentration of the main ion I in the sample solution and the potential is a linear function of Ci. In this case the effect of the foreign ion J should be exhibited to the extent at which it leads to changes in the concentration of the ion associate IR in the boundary layer of the membrane, i.e. in accordance with the experimental ion exchange constant K (2) We tested this method for a ij . toluenesulphonate selective electrode based on TDHEA (picrate was used as a lipophilic anion) and found that in the presence of perchlorate as a foreign ion the electrode selectivity was two times higher as compared to ISE based on individual salt form of this ion exchanger. The electrode works effectively at least 6 month and its main analytical characteristics (the detection limit, the slope of the emf response, stability of the potential) are not inferior to ISEs based on individual salt form, because of which the suggested method can be recommended for practice. If the ion to be determined produces less strong associates with the ion exchanger site as compared with the interfering one, as it follows from the results discussed, the potentiometric selectivity always can be improved by decreasing the ratio of ion association constants KjR/KiR. In the case of quaternary ammonium cations ions) and primary–tertiary ammonium cations or alkaline metal cations (foreign ions) the required effect can

 '

V.V. Egoro6 et al. / Talanta 44 (1997) 1735–1747

1742

be easily achieved by using plasticizers with high dielectric constant, that according to [55], results in leveling of ion association constants. The efficiency of this procedure is confirmed experimentally as when o-nitrophenyloctyl ester or nonyl ester of o-nitrobenzoic acid is substituted for dibutylphthalate or dioctylphthalate, selectivity to quaternary ammonium cations becomes 3–10 times higher [35].

E= E 0i + RT/2F ln ai 2 + K (1) ij a j

0 i

' n

E =E +(1−t) · RT/F ln

1 2 ai + K (2) ij a j − 4

2 + K (1) ij a j

+t · RT/F ln

'

'

· a 2j) Ei = E 0i + RT/2F ln(ai + K pot ij

'

1 2 ai + K (2) ij a j + 4

'

n

(2) K (1) ij K ij + 4

'

(2) K (1) K (1) ij K ij ij ai + 2 4 aj

(16)

(17)

With account of Eqs. (13) and (14), Eq. (17) can be transformed to the following form convenient for analysis: 1 K (3) ij K K pot · tot jR ij = 2 C( R KiR +

1 (2) 2 K ij a j 4

1 (2) 2 K ij a j 4

Combining Eq. (15) with Nikolsky’s expanded equation for single- and double-charged ions:

K pot ij =

If the membrane contains liquid ion exchanger, which is the salt of single-charged site R − with double-charged counterion I 2 + , according to [14], the membrane potential in the solution containing both the main ion I 2 + , and the foreign singlecharged ion J + is described by the equation:

'

(15)

we find:

3.2. The model of ideally associated solution. Double-charged ions

1 2 ai + K (2) ij a j + 4

'

1 K (3) ij KjR · 2 C( tot R KiR



2

+2

aiK (3) ij KiRR a 2jC( tot R KiR

(18)

where K (3) ij , a hypothetic ion exchange constant in a fully dissociated system, is described by the equation:

n

1 (2) 2 K ij a j 4 (12)

where 2 (2) K (1) ij =(2KiRR/KjR) · K ij

(13)

2 ( tot K (2) ij =(KjR · kj) /(2C R · KiR · KiRR · ki)

(14)

KiR and KjR are the ion association constants characterizing the ion pairing of ion exchanger site R − with counterions I 2 + and J + respectively, KiRR is the ion association constant characterizing the ion pairing of ion exchanger site R − with single-charged complex IR + , ki and kj are so-called individual distribution coefficients proposed by Eisenman [1], C( tot R is the total concentration of ion exchanger sites in the membrane. Neglecting the diffusion potential and assuming t =0.5, we obtain

2 0 0 K (3) ij = k j /ki exp[(DG i − 2 DG j )/RT]

(19)

DG and DG are standard free energies of transfer of ions I and J + from aqueous phase into membrane. Eq. (18) is equally valid for anion exchange membranes too. It follows from Eq. (18) that increase in KiR as well as increase in C( tot R should always be accompanied by increase in the potentiometric selectivity for double-charged ions in the presence of singlecharged ones. On the contrary, increase in K (3) ij and increase in KjR should always lead to increase in the interfering effect of single-charged ions. This situation seems quite reasonable. At first glance, it is surprising that increase in the second constant of ion association of the primary ion with the ion exchanger site (KiRR) is accompanied by deterioration of the selectivity. Two oppositely directed factors act in this situation. On the one hand, in accordance with ion exchange equilibrium, increase in KiRR should lead to decrease in the concentration of ion associate JR in the membrane. On the other hand, as KiRR increases 0 i

0 j 2+

V.V. Egoro6 et al. / Talanta 44 (1997) 1735–1747

the role of the ion associate JR in the production of free ion exchanger sites R − becomes more important, so that even small concentration of ion associate JR is able to lead to an essential change in the concentration of free sites R − , and, as a result, of free ions I 2 + in the membrane. Eventually, the net action of these factors leads to a weak dependence of K pot on KiRR. ij If in the analysed solution foreign ions J + are only present, Eq. (18) is simplified to: (3) ( tot K pot ij = (K ij · KjR)/(C R · KiR)

(20)

It can be easily shown that Eq. (20) fully agrees with the expression of K pot obtained in [39] for ij ions of different charges when it is determined by the separate solution method: K pot ij =



C( i kj ki C( j

zi/zj

(21)

where C( i and C( j are the concentrations of free ions I zi and J zj in the boundary layer of the membrane, which is in contact with the sample solution containing the only ions I zi or J zj, respectively. Since, as follows from the Eigen-DenisonRamsey-Fuoss’ theory [56], KiR KiRR, the dissociation of single-charged associate IR + makes a negligible contribution to the concentration of free sites R − . Therefore, according to the equation of electroneutrality, in the absence of ion J + C( R $ C( Ri. As a result, the concentration of free ions I 2 + in the membrane is described by the equation C( i =

C( iR 1 $ KiR · C( R KiR

C( j = C( R =

C( tot R KjR

exchange affinity to sulphate-ion depends substantially on the nature of the ion exchanger: the sulphate–chloride exchange constant becomes 70–100 times lower in the case of substitution of DMDODA for TNODA. Meanwhile, the ratio of the second constants of association of sulphateion and of single-charged ions with cations of these ion exchangers changes slightly. It suggests a strong dependence of the first constant of association of sulphate-ion on the nature of the ion exchanger. This suggestion seems quite reasonable in view of the fact that the sulphate-ion whose charge is distributed uniformly among four oxygen atoms is able to interact specifically with positively charged hydrogen atoms nearest to the cation centre provided their steric accessibility. It is evident that the interaction in the case of atoms carrying negative and positive charges, oriented in an optimal way and located at the closest distance from one another, should be more effective in comparison with ‘indifferent’ electrostatic attraction of ions when this interaction is impossible because of steric hindrances. This should lead to increase in the sulphate-ion association constant and manifest itself in potentiometric selectivity, which agrees qualitatively with experimental results (see Table 2). It is interesting that in the case of indirect electrode, when 10% of DMDODA is in the sulphate form, and 90% is in the form of lypophilic borohydride B10H210− , the value K pot SO24 − , Cl − is 3.5 times lower as compared with ISE based on (DMDODA + )2SO24 − [57].

(22)

If the membrane is in contact with solution containing only the foreign ion J + , the concentration of free ions J + in the membrane phase is described by the equation:

'

1743

(23)

Bearing in mind that k 2j /ki =K (3) ij and substituting Eqs. (22) and (23) into Eq. (21), we obtain Eq. (20). The present theoretical conclusions agree qualitatively with experimental data. It can be seen from the data summarised in Table 2 that ion

3.3. Violation of the model of ideally associated solution. The effect of forming ion triplets on ISE selecti6ity If the ion exchanger interacts with the determined ion not only following the electrostatic interaction mechanism, but is also able to form coordination bonds with them and this ability is partly preserved after forming an ion-pair, favourable conditions are provided for formation of ion triplets of the type I2R ( 9 ): Ks

IR+ I ( 9 ) “ I2R ( 9 )

(24)

V.V. Egoro6 et al. / Talanta 44 (1997) 1735–1747

1744

In this case the ion associate IR is a kind of neutral carrier for I ( 9 ) and the equilibrium constant of this process is formally similar to the complex formation constant. The equation which expresses the experimentally determined potentiometric selectivity coefficient in terms of ion exchange, ion association and complex formation constants can be obtained as follows. In the solution of determined ion the membrane potential is described by the equation: E1 =E 0i 9 u lg[(ai)1/C( 0i]= E 0% i 9u lg(ai)1

(25)

where C( 0i is the initial concentration of the ion I ( 9 ) in the membrane. In the presence of the foreign ion J ( 9 ) in the solution studied, the equation is valid: E2 =E 9 u lg[(ai)/C( i]= E 9u lg(ai +K 0 i

0%

pot ij

· aj) (26)

where C( i is the concentration of the free ion I ( 9 ) in the membrane being in contact with the mixed solution. Subtracting Eq. (25) from Eq. (26) and performing simple manipulations, we obtained: ( 0i/C( i −1) K pot ij = ai/aj · (C

(27)

If the total portion of ions in membrane is relatively small, i.e. the ion exchanger primarily occurs in the form of ion-pairs, without foreign ions the concentration of ion triplets is described by the equation C(

0 i 2R

= C( · C 0 i

tot R

· KS

(28)

With account of the equation of electroneutrality we obtain C( 0R =C( 0i +C( 0i2R) = C( 0i · (1 +C( tot R · KS)

(29)

Finally, expressing the value of C( in terms of the constant of ion association and substituting C( 0R from Eq. (29), we have 0 i

C( 0i =

C( tot R = KiR · C( 0R

'

KiR

C( tot R · (1 +C( tot R · KS)

(30)

In the presence of the foreign ion J not tending to formation of ion triplets, the condition of electroneutrality becomes (j C( R =C( i(1+ C( tot R · KS) +C

(31)

In this case it is assumed that the addition of I to the ion associate RJ is characterized by the same equilibrium constant KS. Otherwise, more bulky expressions are obtained but the essence of the conclusions remains basically the same. Expressing the free ion concentrations C( i and C( j in terms of ion association constants, we obtain C( R = (1+ C( tot R · KS) ·

C( iR C( jR + KiR · C( R KjR · C( R

(32)

Solving the above equation for C( R and substituting the obtained value in Eq. (4), we obtain: C( i =

C( iR

KiR

·

'

1 ( iR + (1+C( tot R · KS) · C

KiR · C( Rj KjR

(33)

Substituting Eqs. (30) and (33) into Eq. (27) and expressing equilibrium concentrations C( iR and C( jR by Eqs. (6) and (7), one can evaluate K pot ij . The qualitative effect of forming ion triplets on K pot can be traced by comparison of the ratios ij C( 0i /C( i for the case considered and for ideally associated solution, when there are no ion triplets. It follows from Eqs. (30) and (33) that C( 0i C( tot R = · C( i C( Ri

'

C( Ri + C( Rj ·

ki 1 · kj 1+ C( tot R · KS (34)

'

If ion triplets are absent, then C( 0i =

C( tot R KiR

(35)

'

And according to Eqs. (4) and (5) we obtain: C( 0i C( tot R = · C( i C( Ri

C( Ri + C( Rj ·

ki kj

(36)

Comparison of Eqs. (34) and (36) shows that in the case of forming ion triplets the contribution of the second term in the expression under the radical sign decreases proportionally to the factor (1+C( tot R ~ · ~KS), which should be exhibited in the appropriate increase in the potentiometric selectivity for I. To summarize, it can be stated that forming ion triplets leads to increase in the concentration of free ion exchanger sites in the membrane. As a result, the concentration of the free

V.V. Egoro6 et al. / Talanta 44 (1997) 1735–1747

1745

Table 4 The effect of the nature of the ion exchanger on cation exchange membrane selectivity reversible to calcium cation Membrane

XI XII XIII

Selectivity coefficients relative to cations Li+

Na+

NH+ 4

K+

Mg2+

Fe2+

Cu2+

Zn2+

10−2 2 · 10−1 5 · 104

2 · 10−2 1.6 · 10−2 1.6 · 102

10−1 6 · 10−2 8 · 102

7 · 10−3 4 · 10−3 6

2.5 · 10−2 5 · 10−3 10−1

2 · 10−2 10−2 4 · 10−1

1.6 · 10−2 1.3 · 10−2 1.6 · 10−1

1.3 · 10−2 1.3 · 10−2 2.5 · 10−1

ions I is also stabilized and not subjected to strong changes when rather small numbers of low-strength associates RJ penetrate into the membrane. This mechanism is likely to be realized in some anion-selective electrodes based on charged carriers capable of forming coordination bonds with appropriate anions. We have found a very strong effect of the nature of the ion exchanger on the ISE selectivity in the study of Ca2 + – ISEs based on derivatives or orthophosphoric acid (see Table 4). For membranes based on TNBS and D(3NP)P the selectivity series typical of membranes based on dialkyl(aryl) phosphoric acids is observed. On the contrary, for membranes based on D(2DP)P the selectivity for single-charged ions, especially, for Li + , increases substantially (by 4 and more orders of magnitude). At present, we have no experimental data that could give inequivocal and complete explanation of the mechanism of the observed phenomenon. However, a most probable reason seems to be exhibition of a kind of the crown effect by D(2DP)P molecules containing alkoxysubstitutents in the ortho-position, which provide favourable conditions for coordination of single-charged ions that results in forming ion triplets:

For double-charged cations solvated effectively by strong base dioctyl-phenylphosphonate, formation of such complexes should be less beneficial.

4. Conclusion The present experimental and theoretical results indicate that feasibilities of transforming ion exchange selectivity into potentiometric one are substantially different for single- and double-charged ions. In ideally associated ion exchange membranes, that do not contain ionic admixtures, increase in the efficiency of interaction of the ion exchanger with determined single-charged ions has an important effect on the value of K pot only ij when KiR B KjR, which agrees with theoretical results [14]. However, if KiR \ KjR, then without special procedures intended to stabilize the ion exchanger sites R ( 9 ) concentration in the membrane phase, which are described in [35,39–41], the gain in K pot is not high, as a rule. The case, ij when the ion exchanger sites form ion triplets of type I2R ( 9 ) with the determined ion can be exception. In this case ion associate IR functions as a kind of a neutral carrier for determined ion I ( 9 ). In the case of double-charged ions, increase in the first constant of ion association of the main ion with the ion exchanger sites (KiR), all other things being equal, should always lead to benefit in potentiometric selectivity.

Acknowledgements The has been carried out under financial support of the International Science Soros Foundation, Project MW 6000.

1746

V.V. Egoro6 et al. / Talanta 44 (1997) 1735–1747

References [1] J. Sandblom, G. Eisenman, J.L. Walker, J. Phys. Chem. 71 (1967) 3862. [2] B.P. Nikolsky, M.M. Shultz, Vestnik LGU 4 (1963) 73. [3] F.S. Stover, R.P. Buck, Biophys. J. 16 (1976) 753. [4] F.S. Stover, R.P. Buck, J. Phys. Chem. 81 (1977) 2105. [5] R.D. Armstrong, M. Todd, Electrochim. Acta 32 (1987) 155. [6] R.D. Armstrong, Electrochim. Acta 32 (1987) 1549. [7] R.D. Armstrong, G. Horvai, Electrochim. Acta 35 (1990) 1. [8] A. Jyo, M. Torikai, N. Ishibashi, Bull. Chem. Soc. Jpn. 47 (1974) 2862. [9] K. Kina, N. Maekawa, N. Ishibashi, Bull. Chem. Soc. Jpn. 46 (1973) 2772. [10] A. Jyo, H. Mihara, N. Ishibashi, Denki Kagaku 44 (1976) 268. [11] E.A. Materova, T. Ya. Bart, in: Ion Exchange and Ionometry, Vol. 4, Leningrad University Publishing House, Leningrad, 1984, p. 92. [12] R.D. Armstrong, P. Nikitas, Electrochim. Acta 30 (1985) 1627. [13] E.M.J. Verpoorte, A.D.C. Chan, D.J. Harrison, Electroanalysis 5 (1993) 845. [14] W.E. Morf, The Principles of ISEs and of Membrane Transport, Mir, Moscow, 1985. [15] P. Schulthess, D. Ammann, W. Simon, C. Caderas, R. Stepanek, B. Kra¨utler, Helv. Chim. Acta 67 (1984) 1026. [16] P. Schulthess, D. Ammann, B. Kra¨utler, C. Caderas, R. Stepanek, W. Simon, Anal. Chem. 57 (1985) 1397. [17] R. Stepanek, B. Kra¨utler, P. Schulthess, B. Lindemann, D. Ammann, W. Simon, Anal. Chim. Acta 182 (1986) 83. [18] S. Daunert, L.G. Bachas, Anal. Chem. 61 (1989) 499. [19] D. Ammann, M. Huser, B. Kra¨utler, B. Rusterholz, P. Schulthess, B. Lindemann, E. Halder, W. Simon, Helv. Chim. Acta 69 (1986) 849. [20] S.C. Ma, N.A. Chaniotakis, M.E. Meyerhoff, Anal. Chem. 60 (1988) 2293. [21] N.A. Chaniotakis, S.B. Park, M.E. Meyerhoff, Anal. Chem. 61 (1989) 566. [22] X. Li, D.J. Harrison, Anal. Chem. 63 (1991) 2168. [23] S.B. Park, W. Matuszewski, M.E. Meyerhoff, Y.H. Liu, K.M. Kadish, Electroanalysis 3 (1991) 909. [24] E. Bakker, E. Malinowska, R.D. Schiller, M.E. Meyerhoff, Talanta 41 (1994) 881. [25] E. Malinowska, M.E. Meyerhoff, Anal. Chim. Acta 300 (1995) 33. [26] D. Gao, J.-Z. Li, R.-Q. Yu, G.-D. Zheng, Anal. Chem. 66 (1994) 2245. [27] D. Gao, J. Gu, R.-Q. Yu, G.-D. Zheng, Analyst 120 (1995) 499. [28] D. Gao, J. Gu, R.-Q. Yu, G.-D. Zheng, Anal. Chim. Acta 302 (1995) 263. [29] J. Li, X. Wu, R. Yuan, G. Lin, R. Yu, Analyst 119

(1994) 1363. [30] V.A. Zarinskij, L.K. Shpigun, V.M. Shkinjov, B.Ya. Spivakov, V.M. Trepalina, Yu.A. Zolotov, Zh. Anal. Khim. 35 (1980) 2137. [31] S.A. Glasier, M.A. Arnold, Anal. Chem. 60 (1988) 2540. [32] S.A. Glasier, M.A. Arnold, Anal. Lett. 22 (1989) 1075. [33] N.A. Chaniotakis, K. Jurkschat, A. Ru¨chlemann, Anal. Chim. Acta 282 (1993) 345. [34] I.H.A. Badr, M.E. Meyerhoff, S.S.M. Hassan, Anal. Chem.. 67 (1995) 2613. [35] V.V. Egorov, V.A. Repin, T.A. Ovsyannikova, Zh. Anal. Khim. 47 (1992) 1685. [36] V.V. Egorov, in: Conf. Chemical Sensors Proceedings Abstracts, St. Petersburg, 1993, p. 123. [37] C.R. Witschonke, C.A. Krauss, J. Am. Chem. Soc. 69 (1947) 2472. [38] Y. Umezawa, Handbook of Ion-Selective Electrodes: Selectivity Coefficients, CRC Press, Boca Raton, FL, 1990. [39] U. Schaller, E. Bakker, U.E. Spichiger, E. Pretsch, Anal. Chem. 66 (1994) 391. [40] U. Schaller, E. Bakker, E. Pretsch, Anal. Chem. 67 (1995) 3123. [41] U. Schaller, E. Bakker, E. Pretsch, A.C.M. Models in Chemistry 131 (1994) 739. [42] Veigand-Hilgetag, The Methods of the Experiment in Organic Chemistry, Khimia, Moscow, 1968. [43] E.M. Rakhman’ko, G.L. Starobinets, V.V. Egorov, A.L. Gulevich, S.M. Lestchev, E.S. Borovski, Fresenius Z. Anal. Chem. 335 (1989) 104. [44] S.M. Lestchev, E.M. Rakhman’ko, G.L. Starobinets, Zh. Anal. Khim. 34 (1979) 2244. [45] Ya. F. Lushchik, Some Regularities of the Functioning and Analytical Application of Cation-Selective Electrodes based on Lipophilic Sulphonic Acids and their Compositions with Neutral Carriers, Dissertation Abstracts, Minsk, 1988. [46] G.H. Griffiths, G.J. Moody, J.D.R. Thomas, J. Inorg. Nucl. Chem. 34 (1972) 3043. [47] G.M. Cosolapoff, J. Am. Chem. Soc. 69 (1947) 2020. [48] V.V. Egorov, E.A. Pavlovskaya, Ya.F. Lushchik, Zh. Anal. Khim. 47 (1992) 2011. [49] T.M. Alkhazishvili, N.V. Astakhova, V.V. Egorov, Z.F. Kirpichnikova, L.V. Koleshko, E.M. Rakhman’ko, G.L. Starobinets, Yu. M. Tarasova, A.N. Khutsishvili, USSR Author Cert. N 1310401, IB, 1987, N 18. [50] K. Cammann, Das Arbeiten mit ionselektiven Elektroden, Springer, Berlin, 1979. [51] E.M. Rakhman’ko, N.A. Sloboda, S.A. Lagunovich, Zh. Neorg. Khim. 35 (1990) 2409. [52] R.A. Robinson, R.H. Stokes, Electrolyte Solutions, Moscow, 1968. [53] E. Bakker, M. Na¨gele, U. Schaller, E. Pretsch, Electroanalysis 7 (1995) [54] A.L. Gulevich, V.V. Egorov, E.M. Rakhman’ko, A.P. Podterob, V.A. Repin, Vestsi Akad. Navuk RB, in press.

V.V. Egoro6 et al. / Talanta 44 (1997) 1735–1747 [55] A.L. Gulevich, Extraction of Alkylsulphates and Lypophilic Carbon Acids by Quaternary Ammonium Salts and its Analytical Application, Dissertation Abstracts, Minsk, 1982.

.

1747

[56] E.G. Gordon, The Organic Chemistry of Electrolyte Solutions, Mir, Moscow, 1979. [57] V.V. Egorov, N.D. E.M. Rakhman’ko, N.A. Sloboda, S.S. Kacharsky, Zh. Anal. Khim. in press.