Estimating the Selectivity Coefficient of Cl-ISE using Polynomial Regression

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1 Estimating the Selectivity Coefficient of Cl-ISE using Polynomial Regression OTILIA CANGEA 1, CATALINA CALIN 1 *, CRISTINA POPA 1, OCTAV PANTEA 1, ELENA RADU 2 1 Petroleum-Gas University of Ploiesti, 39 Bucuresti Blvd.,100680, Ploiesti, Romania 2 National Research & Development Institute for Chemistry and Petrochemistry ICECHIM, 202 Splaiul Independentei Str., , Bucharest, Romania The paper describes a study concerning the estimation of the selectivity coefficient of Cl - ISE, an important analysis in the context of optimizing the specific performance characteristics. The authors have studied the interference of mol/lconcentrations Br - -, I - and F - ions upon Cl-ISE, by computing the selectivity coefficients for a set of 6 experimental data. Subsequently, the research was extended on a 100 data set using MATLAB polynomial regression and thus generating the estimated values of the corresponding selectivity coefficients, the smallest correlation error being obtained for Br - interference. Keywords: selectivity coefficient, interference ions, Cl-ISE, polynomial regression Studying electrode selectivity is a very important aspect considering the optimization of the performance characteristics of the chloride-ion selective electrode (Cl- ISE). Selectivity may be defined as the ability of the analytical or bioanalytical employed method to measure and discriminate the analytes in a test section where specific interferences were of set purpose inserted. Depending on the manner in which the analyte identity is established, the interferences can inhibit the confirmation by glitching the signal derived from the analyte, by increasing or decreasing the analyte concentration, or by modifying the gradient of the sampling curve. The development of ion selective electrodes is well established in important researches performed in the fields of environmental, agricultural, industrial, and clinical analysis [1-6]. ISE electrodes are used to measure ion concentration in water, food, and pharmaceuticals [7]. Actually, a close inspection of the influence of interference ions upon the measurement performed with a potentiometric sensor has given proof of the disturbances thus produced, that occur because the membranes are not perfectly selective, allowing the passage of the interference ions [8]. M. Mascini and A. Liberti have studied ion selective electrodes used for measurement in fresh waters and have determined the corresponding selectivity [9] Ṫhe selectivity coefficient is given by the ratio defined by the electrode response to the X species versus the electrode response to the Y interfering species. If those species have the same ion charge, then the selectivity coefficient is defined as: Considering this, one may conclude that the lower the value of the selectivity coefficient for one ion, the less the interference of the respective ion. As a general rule, the behavior of the ion-selective electrodes can be described by the equation: (1) where a x is the activity of the X analyzed ion and a y the activity of the Y interfering ion. The charge of the ion is n x, the charge of the interference ion is n y, and k xy is the selectivity coefficient as defined above, considering the sign in front of the term ln as plus if X is a cation, and as minus if X is an anion [10]. G. de Vera et.al. determined the selectivity coefficient of a chloride ion selective electrode [11] and F. Deyhimi presented a new method for the determination of the potentiometric selectivity coefficients of ion-selective electrode [12]. The aim of this research is to evaluate the selectivity coefficients for Cl-ISE in solutions that have Br -, I -, and F - as interference ions, using for analysis the technique of direct potentiometry at zero current and a multiple regression method for estimating the values of the selectivity coefficients, being a well known fact that the statistical methods that process the experimental data are being often used in the related scientific literature [13, 14]. The potentiometric method is based upon measurements of the potential of the electromotive force of a galvanic element. Direct potentiometric determinations are almost always performed using ion selective electrodes, which are capable of rapid and selective measurements of the analyte concentration. ISE is an electrochemical sensor based on a thin selective membrane that acts as a recognition element and must be used together with a reference electrode in order to form a complete electrochemical cell. The values of the potential are linear, depending on the logarithm of the ions activity in solution. This relationship is described by the Nernst equation [10]. In order to estimate the values of the selectivity coefficients, polynomial regression was used. This method, frequently encountered in the research related publishing [15], allows the prediction of a Z variable using a polynomial function that describes the relationship between the variable Z and a set of two independent variables (X, Y). The method involves two aspects: generating the structure of the regression equations and determining the (2) * catalina.calin20@yahoo.com; Tel: (+40) REV.CHIM.(Bucharest) 67 No

2 coefficients a i associated to the function minimization, known as the least squares method, considering the formula: where z exp,i are the real data, n is the number of data points, and z c,i are the estimated data. The estimated data are determined using the formula: where f j (x,y) is the nonlinear function that depends on the input data. Experimental part The laboratory devices used for the experimental part are (fig. 1): graduated flasks (1 L, 500 ml 250 ml, 50 ml); graduated pippetes; burette; analytic balance; chlorideion selective electrode; Berzelius glasses; graduated cylinder; ph-meter; calomel electrode; KNO 3 bridge; steamer. Using bidistilled water, solutions of Cl - from NaCl, of F - from NaF, of Br - from NaBr and of I - from NaI were prepared, previously dried at C. There were prepared a stock solution of 1 M Cl - at 1 L graduated flask and an intermediate stock solution of 2x10-1 M of Cl - at 500 ml graduated flask. Standard solutions in the range 10-1 M to 10-6 M of fluoride, (3) (4) bromide and iodide were made by successive dilution from the 1 M stock solution. The solutions that were measured have known ion concentration values, namely 10-1 M of Cl - and the range 10-1 M to 10-6 M of fluoride, bromide and iodide, as shown in table 1. Potential measurements were obtained using a RADELKIS chloride-ion selective electrode. All the used reactives are of analytic purity. The research experimental part was carried out at a laboratory located at Petroleum-Gas University of Ploiesti In order to determine the concentration of a ion (cation or anion), direct potentiometry at zero current is a wellknown technique that performs the measurement of the electromotive voltage of a potentiometric cell, composed of an indicator electrode (ion-selective electrode for the Cl - anion) and a reference electrode of calomel, and represented as follows: Hg,Hg 2 Cl 2 / KCl 0.1 M // measuring solution// Cl -ISE The values of the cell electromotive voltage obtained for known increasing concentration solutions of Cl - ions are used in order to draw the graphical representation of the calibration line. Results and discussions The paper presents the results of three studies of interferences upon Cl-ISE, namely the interference of the Br - ion, of the F - ion and of the I - ion. Considering the Nernst equation, one can determine the formula that computes the selectivity coefficient corresponding to Br - interference: (5) Fig.1. Laboratory apparatus where [Cl - ] = 10-1 mol/l. Similar formula are required for F - and I - interferences. Considering this, the K 1 values (table 1), K 2 values (table 2) and K 3 values (table 3) of the selectivity coefficients obtained considering the Br -, F - and, respectively, the I - interferences are presented, also allowing a comparison Table 1 CONSIDERING Br - INTERFERENCE Table 2 CONSIDERING F - INTERFERENCE Table 3 CONSIDERING I - INTERFERENCE REV.CHIM.(Bucharest) 67 No

3 Fig. 2. Polynomial curve interactive graph for Br - interference Fig. 3. Polynomial curve interactive graph for F - interference of these values with those resulted from a regression evaluation, with the conclusion that the regression evaluated selectivity coefficients have estimated values that very well approximate the computed values. Considering the fact that the numerical computing environment MATLAB is strongly recommended for applications specific to experimental data processing by its graphical properties and resources, as well as for the facilities of its dedicated toolboxes [16], using a polytool Statistics Toolbox function that fits a polynomial curve to (x,y) data and displays an interactive graph, there were obtained the graphical representations corresponding to Br -, F - and, respectively, I - interferences, displayed in figure 2, figure 3 and figure 4, and the respective linear Poly12 model and Poly22 model that define the dependency between the Br -, F - and, respectively, I - interferences upon Cl-ISE (x values) and the E n cell electromotive voltage (y values). For any x value, the default curves define a 95% Fig. 4. Polynomial curve interactive graph for I - interference confidence interval for a new observation of y taken at the respective x value. The linear model Poly22 for the Br - interference corresponding polynomial curve is: +p20*x^2 + p11*x*y + p02*y^2, (6) bounds): p00 = ; p10= ; p01= ; p20= ; p11= ; p02= 4.313e- 06. Linear model Poly12 for the F - interference corresponding polynomial curve is: +p11*x*y + p02*y^2, (7) bounds): p00= ; p10 =0.1656; p01= ; p11 = ; p02 =1.499e-05. Linear model Poly12 for the I - interference corresponding polynomial curve is: +p11*x*y + p02*y^2, (8) bounds): p00 = ; p10 = ; p01 = ; p11 = e-05; p02 = e-06. Hereinafter, considering a wider range for the x values, X=0:0.001:0.1 (values from 0 to 0.1 mol/l, with mol/ l sample) and for the y values, Y=0:1:100 (values from 0 to 100 mv, with 1 mv sample), MATLAB Statistics Toolbox has generated a 100 data set of K estimated selectivity coefficients values, as presented in table 4. Table 4 ESTIMATED SELECTIVITY COEFFICIENTS USING POLYNOMIAL REGRESSION REV.CHIM.(Bucharest) 67 No

4 Conclusions The results of the research carried out at the laboratory located at Petroleum-Gas University of Ploiesti, with the aim to evaluate the selectivity coefficients for Cl-ISE in solutions with Br -, I -, F -, lead to emphasizing the following specific findings: - a comparison between the computed values of the selectivity coefficients and those resulted from a regression evaluation leads to the conclusion that the estimated REV.CHIM.(Bucharest) 67 No

5 obtained values are well correlated to the computed ones, with a particular mention to the fact that the smallest correlation error is obtained for Br - interference, so that multiple regression estimation proves to be a good method for aproximating the selectivity coefficients; - extending the 6 experimental data set to a 100 data set and generating the respective selectivity coefficients allow originating a database that can be used in related researches concerning analysis and interpretation of other various experiments carried out using Cl-ISE, such as in environment samples of fresh or industrial waters, or in soil samples; - the knowledge of selectivity coefficient values for the studied concentrations of interference ions enables computing Cl - in the analyzed samples and, thus, carrying out corrections and increasing the accuracy of data processing. References 1.RUMENJAK, V., MILARDOVIC, S., KRUHAK, I., GRABARIC, B. S., Clinica Chimica Acta, 335, (1 2), 2003, p GANDIA-ROMERO, J.M, BATALLER, R., MONZON, P., CAMPOS, I., GARCIA-BREIJO E., VALCUENDE, M., SOTO J., Sensors and Actuators B:Chemica, 222, 2016, p PERDIKAKI, K., TSAGATAKIS, J. K., CHANIOTAKIS, N. A., Mikrochim. Acta, 136, 2001, p GAO, X., ZHANG, J., YANG, Y., LU S., Materials Science Forum, , 2011, p RIEGER, M., LITVIN, P., Journal of Plant Nutrition, 21(2), 1998, p CALUGAREANU, M., NAGY, G., JOSCEANU, A. M., NAGY, L., Rev. Chim. (Bucharest), 64, no.2, 2013, p APOSTU, M., BIBIRE, N., TANTARU, G., VIERIU, M., PANAITE, A. D., AGOROAEI, L., Rev. Chim. (Bucharest), 66, no.5, 2015, p DIMESKI, G., BADRICK, T., ANDREW, ST. J., Clinica Chimica Acta, 411(5 6), 2010, p MASCINI, M., LIBERTI A., The Science of the Total Environment, 37, 1984, p DANET, A.F., Metode Electrochimice de Analiza, Editura Stiinifica, Bucuresti, DE VERA, G., CLIMENT, M.A., ANTON, C., HIDALGO, A., ANDRADE, C., Journal of Electroanalytical Chemistry, 639, 2010, p FARZAD, D., Talanta, 50(5), 1999, p STANCU, A., CALIN, C., PANTEA, O., ENE, C., Rev. Chim. (Bucharest), 66, no.6, 2015, p CANGEA, O., Identificarea Sistemelor, Editura MatrixRom, Bucuresti, OPRESCU, E., STEFAN, E., POPA, C., BOLOCAN, I., 15 th SGEM Multidisciplinary Scientific GeoConference, Section Renewable Energy Sources and Clean Technologies, 4, 2015, p CANGEA, O., POPOVICI, D., PANTEA, O., Rev. Chim. (Bucharest), 59, no.7, 2008, p.802. Manuscript received: REV.CHIM.(Bucharest) 67 No