Improved Separate Solution Method for Determination of Low

Mar 13, 2014 - ... equally charged primary and foreign ions by SSM linearly depend on time to ... Comparison of theory with experiment and critical ev...
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Improved Separate Solution Method for Determination of Low Selectivity Coefficients Vladimir V. Egorov,*,† Elena A. Zdrachek,‡ and Valentine A. Nazarov‡ †

Department of Analytical Chemistry, Belarusian State University, Leningradskaya str., 14, 220030 Minsk, Belarus Research Institute for Physical Chemical Problems of the Belarusian State University, Leningradskaya str., 14, 220030 Minsk, Belarus

‡

S Supporting Information *

ABSTRACT: Simple, fast, and theoretically substantiated experimental method for determination of improved selectivity coefficients is proposed. The method is based on the well-known fact that low selectivity coefficients determined by the separate solution method (SSM) are time-dependent and, upon our finding, this dependence is a well-defined linear function of time raised to the certain negative power. In particular, the selectivity coefficients obtained for equally charged primary and foreign ions by SSM linearly depend on time to the minus one-fourth. It was found that extrapolation of experimental data using this function to the intersection with Y axes gives reliable values of rather low selectivity coefficients (down to n × 10−7), which strongly differ from those measured using SSM and correspond well with the values obtained using the modified separate solution method (MSSM) proposed by Bakker. At the same time, the new method is free of one very essential limitation inherent to MSSM, namely, it is applicable after the conditioning of electrodes in the primary ion solution and can be repeated many times.

S

decades, 7−22 and IUPAC recommendations underwent grounded criticism.11−17 It was established that the main reason for KPot A,B bias is the increase of the primary ion concentration in the near-boundary layer of the sample solution due to its leaching from the membrane according to the ion exchange at the membrane/ solution interface3,9,10,23 and/or transmembrane transport from the inner solution.24,25 So about a dozen approaches to eliminate the leaching of the primary ion into the sample solution or to reduce it based on the optimization of the electrode design and/or the membrane composition was proposed; the main findings have been summarized by E. Bakker et al.26,27 Some of them allow for the elimination of the transmembrane transport of the primary ion completely; however, only one very specific and not always feasible method (preparation of the sample solutions using a background of a selective ligand which binds the primary ion into a hydrophilic complex, while the activity of the foreign ion is not changed)28,29 allows for the elimination of the effect caused by the ion-exchange process on the electrode potential. So all the above-mentioned approaches allow for the diminishment of the fluxes of the primary ion in the direction to the sample solution, thus reducing the KPot A,B bias, however, as a rule, they can not eliminate them completely.

electivity is evidently the most important characteristic of the ion-selective electrodes (ISEs), so correct determiPot ) is of great nation of the selectivity coefficients (KA,B importance both for chemist analysts and (perhaps to an even greater extent) for the developers of new selective ionophores. It is well-known, however, that the selectivity coefficients obtained for highly discriminating electrodes according to IUPAC methods based on Nikolsky−Eisenman equation1,2 are usually overestimated, leveled, and depend both on the method employed and specific measuring conditions.3−5 As a result, selectivity coefficients determined for very similar membrane compositions by different authors often poorly agree with each other, so the analysis of published data often does not allow for the revelation of any correlations between the selectivity parameters, on the one hand, and the peculiarities of the nature of primary and foreign ions and the membrane composition, on the other hand, thus impeding the progress in potentiometry. The matter is the main prerequisite for correct determination of the selectivity coefficients, near-Nernstian response slope in the foreign ion solution (which is directly emphasized in IUPAC recommendations) often cannot be fulfilled for highly discriminating electrodes. As an alternative, the so-called matched potential method (MPM) not based on the Nikolsky−Eisenman equation and not requiring the Nernstian response slope was proposed.6 However, the selectivity coefficients obtained by MPM often strongly depend on the measuring conditions and are also biased. So the problem of correct determination of the selectivity coefficients is actually very topical; it was widely discussed for several © 2014 American Chemical Society

Received: January 31, 2014 Accepted: March 13, 2014 Published: March 13, 2014 3693

dx.doi.org/10.1021/ac500439m | Anal. Chem. 2014, 86, 3693−3696

Analytical Chemistry

Letter

The most effective and substantiated approach for obtaining unbiased selectivity coefficients, the so-called modified separate solution method was proposed by Bakker5,17 who introduced an experimental protocol significantly different from that recommended by IUPAC. The essence of the method is that the membrane should be initially prepared in the form of the foreign ion and should have no contact with the primary ion before the potential in the foreign ion solution is measured. Under such conditions, Nernstian response slopes are attained in the solutions of the foreign ions and unbiased selectivity coefficients, which can differ from those measured according to IUPAC methods, where up to 10(!) orders of magnitude27 can be obtained. This finding was of revolutionary significance for the field of potentiometry, thus substantiating the feasibility for dramatic improvement of many electrodes and reevaluating the limits of the potentiometric method of analysis. However the Bakker’s procedure can be performed only once, so it cannot be applied to the electrodes which had already been used for real sample analysis and is inapplicable of monitoring the selectivity alterations of the electrode during its practical application. A very similar approach based on the voltage span measurements has lately been described by E. Lindner et al.30 It should be stated here that the main idea of the approaches listed above was to create some specific conditions which could provide the Nernstian response in the foreign ion solutions. All these methods utilize substantially different measuring protocols from those recommended by IUPAC and are somewhat cumbersome and inconvenient for routine practice. In contrast, the method we proposed does not require creation of any specific conditions and it can be used if the response slope in the foreign ion solutions is close to a half-Nernstian one (this situation is often observed in practice). The method is based on the well-known fact that the KPot A,B bias caused by the primary ion flux into the sample solution is time-dependent,31−33 and it decreases regularly with the increase of time. So it is possible to obtain KPot A,B values close to unbiased ones by extrapolating the KPot A,B − t dependence to t → ∞. The method can be performed similarly to the SSM technique (the most popular one due to its simplicity14) with the exception that the potential recording in the stirring solution of the foreign ion should be carried out twice at strictly fixed time instants. After that, the improved selectivity coefficient can be estimated from the pair of experimentally obtained KPot A,B values. Two ion exchanger-based electrodes, namely the tetrabuthylammonium-selective electrode (Bu4N+-SE) based on tetrakis(4-chlorophenyl) borate and the picrate-selective electrode (Pic−-SE) based on tridodecylmethylammonium were chosen for the investigation. The choice was made for the reason that high lipophilicity of Bu4N+ and Pic− ions assures rather high selectivity of the corresponding electrodes against different foreign ions, on the one hand, while the specific nature of Bu4N+ and Pic− should guarantee the absence of the impurities of these ions in salts of foreign ions, on the other hand. The last problem is often the critical one, which impedes correct selectivity determination for inorganic ions.26 Typical dependencies of the selectivity coefficients on time determined according to the separate solution method [we will SSM ] are presented in Figure 1. As to be designate them as (KPot A,B) Pot SSM values regularly decrease with the time assumed, (KA,B) increase; however, even after 30 min when the potential drift is SSM less than 0.1 mV/min, the measured (KPot values are still A,B) much higher in comparison with unbiased ones designated as

Figure 1. Selectivity coefficient−time dependencies for Pic−−SE in 1.0 × 10−2 M and 1.0 × 10−1 M NO3− solutions.

Pot SSM (KPot values A,B)Bak ker. So the procedure for extrapolating (KA,B) to infinite time had to be elaborated. All the theoretical considerations given below are based on the phase-boundary potential model.34 For equally charged primary (A) and foreign (B) ions, the potential of the electrode in the foreign ion solution (EB) can be described by the eqs 1 or 2:35

EB = EA0 +

θ log[(KAPot, B)SSM ·aB] z

(1)

EB = EA0 +

θ log[a′A + (KAPot , B)Bakker · a′B ] z

(2)

E0A

where is the electrode potential in the primary ion solution with 1 M activity, θ is defined as RT/F, where R is the universal gas constant, T is the absolute temperature, F is the Faraday constant, z is the charge number of the ions to be studied, aB is the foreign ion activity in the bulk of the sample solution, strokes at the aA, aB symbols denote the corresponding ions activities in the surface layer of the sample solution near the membrane/solution interface. If the decrease of the foreign ion activity in the boundary layer caused by the ion-exchange process can be neglected (aB′ ≈ aB), it follows from eqs 1 and 2: Pot SSM (KAPot − , B)Bakker = (KA , B)

a′ A aB

(3)

The term (aA′ /aB) is known as the selectivity coefficient bias. It can be shown that under the condition when the transmembrane flux of the ion A can be neglected and the main reason for the ion A appearance in the sample solution is the ion exchange at the membrane/solution interface the following equation is valid: a′A = (KAB· c′A ·aB·q)1/2

KBA

where process:

KAB =

(4)

is the equilibrium constant of the ion-exchange

a′ A · c ′ B a′ B · c ′ A

Symbols without horizontal bars here further denote the sample solution phase, while those with horizontal bars denote the membrane phase. q is the generalized diffusion parameter defined by the equation: 3694

dx.doi.org/10.1021/ac500439m | Anal. Chem. 2014, 86, 3693−3696

Analytical Chemistry

q=

Letter

and the obtainment of the utmost values of the selectivity coefficients (KPot A,B)lim. Pot One can see that (KA,B )lim values are in rather good accordance with the corresponding (KPot A,B)Bak ker values. MoreSSM over, as far as the linearity of the functions, (KPot − t−1/4 is A,B) SSM very good; it is not necessary to obtain a large set of (KPot A,B) values for fixed instants of time. It is sufficient to carry out only two measurements for the time instants t1 and t2, and the (KPot A,B)lim value can be calculated according to the simple formula:

DB δA · DA δB

where D A , DB are the diffusion coefficients of the corresponding ions, δA, δB − the thicknesses of the corresponding diffusion layers. With the assumption that the ion-exchange equilibrium is strongly shifted to the left, for the membrane sufficiently selective to the primary ion A, the ion A concentration in the boundary layer of membrane is very close to that in the bulk of the membrane, so the eq 4 can be rewritten as follows: a′A = (KAB· cRtot·aB·q)1/2

(KAPot , B)lim =

(5)

where cRtot is the total ion-exchanger concentration in the membrane phase. Under fixed stirring conditions, the thickness of the diffusion layer in the water phase (δA) is constant, while the thickness of the diffusion layer in the membrane phase ( δB) is the function of time3 and can be described by the equation: δB ≈ (π · DB ·t )1/2

(6)

(7)

where ⎛ K B· c tot ·δ · D 1/2 ⎞1/2 const = ⎜⎜ A R A 1/2B ⎟⎟ ⎝ DA ·aB·π ⎠

t1−1/4 − t 2−1/4

(9)

One can see from Table 1 that (KPot A,B)lim values calculated according to eq 9 for different t1 and t2 pairs are in a good agreement with each other and with the values obtained as the linear regression intercept. The method is not time-consuming, actually it is even faster in comparison with SSM, taking into account that the time required to achieve the acceptable potential drift in the foreign ion solution can be rather long. The main practice criterion of the method applicability is the slope of the electrode response in the foreign ion solution. In particular, for equally charged primary and foreign ions, the slope close to half-Nernstian means the predominant contribution of the primary ion activity (aA′ ) into the potential value (see eqs 2 and 5). If the slope of the electrode response is significantly lower than half-Nernstian, the method can not be applied. A proper choice of the time instant at which the potential should be recorded is of crucial importance for the precision of the method. It was found that the instant of the first measuring should not be too short to minimize the inaccuracy caused by nonmomentary response of the electrode. On the other hand, the instant of the second measurement should not be too long. Otherwise inaccuracy due to the potential drift caused by some other reasons besides the alteration of aA′ in the near-electrode layer can arise (see the Supporting Information). Potential readings within 2−10 min intervals from the immersion of the electrode into the sample solution were found to give the best results. To minimize the influence of contaminations originated from the membrane, the electrode should be thoroughly washed with water of the highest purity up to the steady-state potential, and measures should be undertaken to prevent transmembrane ion fluxes from the inner solution. Thus, an experimentally simple and theoretically substantiated method for determination of improved selectivity coefficients is proposed. The method was proven to be applicable for reliable determination of the selectivity coefficients in the region from 1 × 10−3 to n × 10−7. The method possesses rather good reproducibility; standard deviation as a rule does not exceed 30% in (KPot A,B)lim values or 0.1 logarithmic units. Obtained (KPot A,B)lim values, in contrast with SSM (KPot values, are much less dependent on the foreign ion A,B) concentration (see Figure 2 and the Supporting Information). As far as the response slope close to the half-Nernstian one can usually be achieved for the vast majority of practically relevant electrodes except for the most discriminating ones, we believe the proposed method will be rather useful for correct estimation of the selectivity coefficients. It can be shown theoretically that for the primary and foreign ions with different charge values (zA ≠ zB), the utmost selectivity coefficients can

where t is the time since the instant when the electrode was immersed into the stirred solution of the foreign ion. So one should expect that the selectivity coefficient bias is to be a linear function of t−1/4: a′ A = const ·t −1/4 aB

SSM −1/4 SSM −1/4 (KAPot − (KAPot ·t2 , B)2 · t1 , B)1

(8)

SSM Consequently (KPot − t dependencies shown in Figure 1 A,B) can be linearized too. It turned out that all experimentally SSM obtained (KPot values actually give extremely good linear A,B) function versus t−1/4 with correlation coefficients of 0.997− 0.999 (see Figure 2 and the Supporting Information). So extrapolation of these functions to intersect with the ordinate axis allows for the elimination of the selectivity coefficient bias

SSM Figure 2. Dependencies (KPot − t−1/4 for Pic−-SE in 1.0 × 10−2 M A,B) − −1 and 1.0 × 10 M NO3 solutions.

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Letter

Pot Table 1. Comparison of (KPot A,B)Bak ker Values with the Intercepts of the Linear Regressions and (KA,B)lim Values Calculated for Different Pairs, t1 and t2

log(KPot A,B)lim log ions A and B

cB (M)

Pic−, Br−a Pic−, NO3−

1.0 1.0 × 10−2 1.0 × 10−1 1.0 × 10−2

Pic−, C6H5SO3− +

Bu4N , Na Bu4N+, Et4N+ +

Bu4N , Et3NH+

+

1.0 1.0 1.0 1.0

× × × ×

10−1 10−2 10−1 10−2

1.0 × 10−1 1.0 × 10−3

(KPot A,B)Bak ker

n = 3,

intercept of the linear regression (2.30 − 10.19 min)

t1 = 2.30 min, t2 = 5.26 min

t1 = 5.26 min, t2 = 8.22 min

t1 = 2.30 min, t2 = 8.22 min

−6.53 −5.24 −5.33 −5.50

−6.48 −5.12 −5.34 −5.61

−6.48 −5.34 −5.33 −5.16

−6.48 −5.20 −5.34 −5.38

−4.12 ± 0.06

−5.16 −4.39 −4.51 −3.84

−5.15 −4.34 −4.47 −3.77

−5.16 −4.34 −4.51 −3.87

−5.15 −4.34 −4.49 −3.81

−3.33 ± 0.03

−4.08 −3.18

−4.07 −3.15

−4.07 −3.20

−4.07 −3.17

−3.29

−3.30

−3.29

−3.29

P = 0.95

−6.47 ± 0.02 −5.49 ± 0.03 −5.46 ± 0.03 −4.52 ± 0.10

1.0 × 10−2

Since it was found that the response slope of Pic−−SE in bromide solutions with a concentration of 0.1 M and lower was much less than half− Nernstian (KPot A,B)lim values were calculated only for the 1.0 M Br solution. a

Pot SSM be obtained from the linear dependence (KA,B ) − t−{zA/[2(zA + zB)]}. In this case, the appropriate response slope is expected to be close to [θ/(zA + zB)]; however, experimental verification for widening of the developed method to nonequally charged ions is required.

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(12) Zhang, W.; Falker, A.; Demuth, C.; Spichiger, U. E. Anal. Chim. Acta 1998, 375, 211. (13) Ren, K. Fresenius J. Anal. Chem. 1999, 365, 389. (14) Macca, C. Electroanalysis 2003, 15, 997. (15) Lewenstam, A.; Hulanicki, A. Selective Electrodes Rev. 1990, 12, 161. (16) Horvai, G. Sens. Actuators, B 1997, 43, 94. (17) Bakker, E. Anal. Chem. 1997, 69, 1061. (18) Kane, P.; Diamond, D. Talanta 1997, 44, 1847. (19) Deyhimi, F. Talanta 1999, 50, 1129. (20) Tohda, K.; Dragoe, D.; Shibata, M.; Umesawa, Y. Anal. Sci. 2001, 17, 733. (21) Egorov, V. V. Russ. J. Gen. Chem. 2008, 78, 2455. (22) Bakker, E. J. Electroanal. Chem. 2010, 639, 1. (23) Maj-Zurawska, M.; Sokalski, T.; Hulanicki, A. Talanta 1988, 35, 281. (24) Mathison, S.; Bakker, E. Anal. Chem. 1998, 70, 303. (25) Gyurcsányi, R. E.; Pergel, E.; Nagy, R.; Kapui, J.; Lan, B. T. T.; Toth, K.; Bitter, J.; Lindner, E. Anal. Chem. 2001, 73, 2104. (26) Szigeti, Z.; Vigassy, T.; Bakker, E.; Pretsch, E. Electroanalysis 2006, 18, 1254. (27) Radu, A.; Peper, S.; Bakker, E.; Diamond, D. Electroanalysis 2007, 19, 144. (28) Sokalski, T.; Maj-Zurawska, M.; Hulanicki, A. Mikrochim. Acta 1991, 103, 285. (29) Bakker, E. Sens. Actuators, B 1996, 35, 20. (30) Bereczki, R.; Takacs, B.; Gyurcsanyi, R. E.; Toth, K.; Nagy, G.; Langmaier, J.; Lindner, E. Electroanalysis 2006, 18, 1245. (31) Lingenfelter, P.; Bedlechowicz-Sliwakowska, I.; Sokalski, T.; Maj-Zurawska, M.; Lewenstam, A. Anal. Chem. 2006, 78, 6783. (32) Morf, W. E.; Pretsch, E.; de Rooij, N. F. J. Electroanal. Chem. 2008, 614, 15. (33) Morf, W. E.; Pretsch, E.; de Rooij, N. F. J. Electroanal. Chem. 2009, 633, 137. (34) Bakker, E.; Bühlmann, P.; Pretsch, E. Talanta 2004, 63, 3. (35) Egorov, V. V.; Zdrachek, E. A.; Nazarov, V. A. Electroanalysis 2012, 24, 76.

ASSOCIATED CONTENT

S Supporting Information *

SSM Experimental details, more (KPot − t−1/4 dependencies, and A,B) some practical recommendations for applying the proposed method are included in the Supporting Information. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +375-17-209-53-00. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the Belarusian Republican Foundation for Fundamental Research (“Youth science −2013” Project C13Y016) for financial support of this research.

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REFERENCES

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dx.doi.org/10.1021/ac500439m | Anal. Chem. 2014, 86, 3693−3696