Impedimetric and Potentiometric Investigation of a Sulfate Anion

Article pubs.acs.org/ac

Impedimetric and Potentiometric Investigation of a Sulfate AnionSelective Electrode: Experiment and Simulation Mohammad Mazloum-Ardakani,*,† Abdolhosein Dehghan Manshadi,‡ Mojtaba Bagherzadeh,§ and Hadi Kargar‡ †

Department of Chemistry, Faculty of Science, Yazd University, Yazd, I. R. Iran Departmentof Chemistry, Payame Noor University, P.O. Box 19395-4697 Tehran, I. R. Iran § Waste Management Department, NFCRS, Nuclear Science and Technology Research Institute, Isfahan, 81465-1589, I. R. Iran ‡

S Supporting Information *

ABSTRACT: A new anion-selective polyvinyl chloride (PVC) membrane electrode based on {6,6′-diethoxy-2,2′-[2,2-dimethylpropane-1,3-diylbis(nitrilomethylidyne)]diphenolato}nickel(II)monohydrate as a carrier for the sulfate anion is reported. In this work, a new strategy for optimizing membrane components by electrochemical impedance spectroscopy (EIS) is presented. The performance of this electrode was investigated using potentiometric and EIS techniques. The potentiometric results indicated that the prepared electrode had a Nernstian slope of −28.9 ± 0.1 mV in a linear concentrations range of 1.0 × 10−6 to 3.0 × 10−1 M, a detection limit of 6.3 × 10−7 M, an applied pH range of 4.0−9.0, and a response time of less than 15 s; while using the EIS technique, the linear concentrations range was 1.0 × 10−9 to 1.0 × 10−1 M and the pH range increased to 4.0−10.0. Finally, the impedance spectra were simulated using the Maple 13 software. A comparison of the experimental data and information obtained from the simulation confirmed the accuracy of the impedance measurement of this electrode.

I

impedance.12 Then, a zwitterionic bis(guanidium) by Fibbioli et al.,13 a Schiff base complex of Zn(II) by Shamsipur et al.,14 and pyrilium perchlorate derivatives by Ganjali et al.15 were used as ionophores for the preparation of a sulfate anionselective electrode. Recently, Sathyapalan et al. predicted the optimal recognition site by a density functional theory simulation for the design of a sulfate-selective electrode.16 Considering the limitation of laboratory facilities, required materials, and equipment, complications from use of the chemicals and most importantly, the time needed for testing and calculations, there is a need to research the simulation of electrochemical processes. Often, these processes are governed by rates of mass transfer and homogeneous chemical reactions, so a series of differential equations can be written to describe them that are difficult or impossible to solve. Therefore, a numerical model of electrochemical systems is installed on a computer and allowed to evolve by a set of algebraic laws derived from the differential equations and a simulation of experiment is performed.4 In this paper, the simulation of impedance spectra of sulfateselective electrode was performed. The theory of EIS is based on the Nernst−Planck equation coupled to the Poisson equation (NPP), which can only be solved analytically under idealized conditions.17 The first numerical solution of the NPP

on-selective electrodes, as an important class of chemical sensors with properties such as simplicity, fast response, wide linearity range, and low cost are able to detect a particular species of cationic or anionic components in samples.1,2 The potentiometric method is often used for measuring cations and anions by the ion-selective electrode, where the potential is measured under the conditions of zero-current.3 Electrochemical impedance spectroscopy (EIS) is another technique used for evaluating interactions within the membrane.3 In this technique, using an alternating small magnitude signal creates a perturbation at a steady state in the system.4 Currently, EIS is a powerful tool for studying the mechanisms of electrochemical reactions, measuring the dielectric and transport properties of materials, and investigating passive surfaces.5 Despite the performance of the EIS technique, little research has been conducted about the application of this technique on ion-selective PVC membranes. In this paper, the EIS technique is used as an impedimetric detection method, which is a nondestructive transduction technique to detect different species.6 The first ion-selective electrode for the sulfate anion was made by Hirsch-Ayalon in 1965.7 Pungor and Havas in 1966 and Rechnitz et al. in 1967 prepared sulfate-selective membranes using a precipitate-impregnated silicone rubber.8,9 Although these electrodes exhibited a relatively good potentiometric response, their selectivity toward the sulfate ion was not sufficient.10 In 1998, Nishizawa et al. prepared the first sulfate-selective electrode based on PVC.11 In 1999, Li et al. investigated the response mechanism of the electrode by ac © 2012 American Chemical Society

Received: August 12, 2011 Accepted: January 30, 2012 Published: January 30, 2012 2614

dx.doi.org/10.1021/ac203260e | Anal. Chem. 2012, 84, 2614−2621

Analytical Chemistry

Article

equations was presented by Cohen and Cooley in 1965.18 Then, in 1978, Brumleve and Buck related the impedance spectra to physical parameters.19 Other studies were performed by Gabrielly et al. in 2004, which simulated the impedance spectra of an ion-selective electrode in the steady state and at an electroneutral condition.20,21 Kucza et al. in 200617 and Grysakowski et al. in 200822 presented similar research to solve the NPP equations. Studies performed in this area have only been theoretical, and there is no research that compares the experimental and theoretical data. The purpose of this study was fabrication of a new sulfate anion-selective electrode and examination of its behavior using potentiometry and EIS techniques. Additionally, the impedance spectra of this electrode were simulated using the Maple 13 software.

(FRA) software and an electrochemical cell consisting of three electrodes: a SCE as reference electrode, a Ag/AgCl electrode embedded in the sulfate-selective membrane as the working electrode, and a platinum electrode as the counter electrode. During this analysis, which was performed at an amplitude of 5 mV and a frequency range of 10 000−0.1 Hz with 50 frequency points, the sample solution was fully static and the system was held at the open circuit potential (OCP). In order to interpret the EIS data obtained in the whole frequency range, an equivalent circuit including a solution resistance (Rs), a double layer capacitance (Cdl), and a charge transfer resistance (Rct) was used.

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RESULTS AND DISCUSSION Evaluation of the Ionophore and Sulfate Anion Interaction. To study the interaction of the ionophore and the sulfate anion, three methods, including UV−vis, potentiometry, and impedance, were used. Evaluation of UV−Visible Spectra. The UV−vis spectra of the ionophore and the mixed sulfate-ionophore are illustrated in Figure 1A. A comparison of these two spectra indicates that a relatively good interaction is made between the ionophore and sulfate ion. A peak appearing at a wavelength of 415 nm in the ionophore spectrum and decreasing in height in the mixed ionophore and sulfate anion spectrum confirms the interaction of this ion with the desired complex. Evaluation of Potentiometric Studies of Different Anions. To evaluate the selectivity of the ionophore toward the sulfate ion, potentiometric experiments were performed on different anions with a concentration range from 1.0 × 10−9 to 1.0 × 10−1 M. These studies were carried out under the same experimental conditions using a 1.0 × 10−2 M solution of the corresponding anions as the internal solution of the electrode. Considering the influence of ionic additives on the selectivity of the electrode, this stage was performed without the presence of these additives. The results of this study are presented in Figure 1B. As can be observed, the slope of the potentiometry responses obtained for the other anions are much lower than that predicted by the Nernst equation, and the electrode does not show a Nernstian behavior for salicylate, chlorate, perchlorate, nitrate, thiocyanate, and phosphate. However, the potentiometric curve of the sulfate anion indicates a relatively good selectivity of the ionophore for this anion. Moreover, it should be noted that the curve slope of phosphate ions is low, but with having three negative charges, this low slope can be interference. Evaluation of EIS Studies of the Membrane with and without Ionophore. In this study, impedance measurements were carried out on the membrane with and without ionophore, and 1.0 × 10−2 and 1.0 × 10−3 M solutions of sodium sulfate as the internal and external solutions of the electrode were used, respectively. Finally, their complex plan plots were generated and compared. As shown in Figure 1C, the charge transfer resistance of the membrane without ionophore (41.252 Mohm) is more than that of the membrane with ionophore (12.739 Mohm). These results can be attributed to increasing the electrical conductivity with the available ionophore that can reduce Rct. This explanation confirms the results obtained from the UV−vis and potentiometry studies. Optimization of Membrane Composition. In this section, two methods, potentiometry and impedance, were used for optimizing the membrane components.

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EXPERIMENTAL SECTION Materials and Reagents. Methyl trioctyl ammonium chloride (MTOAC) was purchased from Sigma. High relative molecular weight PVC, dioctyl phthalate (DOP), tetrahydrofuran (THF), potassium or sodium salts of all the anions, and all other chemicals were purchased from Merck, except potassium thiocyanate, which was purchased from Fluka. The Schiff base complex of {6,6′-diethoxy-2,2′-[2,2-dimethylpropane-1,3-diylbis(nitrilomethylidyne)]-diphenolato}nickel(II) monohydrate was used as the ionophore which was synthesized in our laboratory.23 All the solutions were prepared using double distilled water. The pH adjustments were made with dilute nitric acid and sodium hydroxide solutions as required. UV−Visible Spectroscopy. The ultraviolet−visible (UV− vis) spectrum of the solutions was measured using a UV−vis spectrophotometer (GBC Scientific Equipment Ltd., Australia, model Cintra 6) equipped with UV-Lite software. This study was performed on the ionophore and mixture of the ionophore and sulfate ion (1.0 × 10−4 M). Ethanol was used as the solvent to prepare the ionophore solution. Electrode Preparation. A mixture of DOP, MTOAC, and the ionophore was dissolved in fresh THF. PVC was dissolved in THF separately and was added to the mixture. The total mass of these compounds should be 0.1 g. An opening PVC tube with 3 mm in diameter and 2 cm in length was dipped into the mixture for about 10 s to form a 0.3 mm thick transparent membrane and was kept at room temperature for about 12 h. Then, the tube was filled with the sulfate ion solution and conditioned by submersion in a 1.0 × 10−2 M SO42− solution for 4 h. Finally, the sulfate-selective electrode was prepared by incorporating the tube to a saturated calomel electrode (SCE). Potentiometric Measurements. Potentials were measured with a digital pH-ion meter (Zag Chimi, Iran, model 162) and an electrochemical cell consisting of two electrodes; a SCE as the reference electrode and a Ag/AgCl electrode embedded in a sulfate anion-selective membrane as the working electrode. The performance of the electrode was investigated by measuring its potential in prepared solutions in a concentration range from 1.0 × 10−9 to 1.0 M. During these measurements, the sample solution was stirred using a magnetic stirrer. Additionally, the pH changes were measured using a pH meter (Metrohm, Switzerland, model 480) and a pH electrode (Metrohm, Switzerland, model 6.0232.100). Electrochemical Impedance Measurements. EIS measurements were carried out using a potentiostat/galvanostat instrument (Autolab PGSTAT 302, Eco Chemie B.V., Utrecht, Netherlands) controlled by Frequency Response Analyser 2615



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Figure 2. (A) The potentiometric response of different electrodes made with different percentages of the membrane components. (B) Complex plan plots of different electrodes made with different percentages of membrane components. (Points and lines indicate the experimental and fitting data, respectively.) Numbers show the different electrodes made with different percentages of the membrane components. A table of the percentage of the membrane component is in the Supporting Information.

addition of 1% MTOAC increased the slope of the potentiometry response from 7.0 ± 0.2 mV decade−1 (electrode no. 1, Figure 2A) to 19.7 ± 0.3 mV decade−1 (electrode no. 2, Figure 2A). In fact, the lipophilic salts not only reduce the membrane resistance but also enhance the response behavior and selectivity and reduce interferences in the sample anions.24,25 However, the ionophore used here is a neutral complex and formed a negative complex with sulfate in the membrane. The addition of MTOAC neutralizes the negative charges in the inner membrane, so no significant amount of counter ions can be co-extracted into the membrane with the primary ion. Therefore, the membrane is permeable only to ions of the same charge signed as the primary ion.26 Finally, the best response was observed with a membrane composed of 30% PVC, 60.5% DOP, 6% ionophore, and 4% MTOAC (electrode no. 11). This electrode exhibited a good Nernstian slope of −28.9 mV decade−1. In addition, in changing the concentration of the internal electrode solution, the linear range extended to 1.0 × 10−6 to 3.0 × 10−1 M. Optimization by Impedance. In this section, a new approach for optimizing the membrane composition of the ionselective electrodes was proposed. For this purpose, the membranes made with different component percentages were studied using the EIS technique. In these evaluations, the internal and external solutions of the electrode were 1.0 × 10−2 M and 1.0 × 10−3 M sodium sulfate, respectively.

Figure 1. (A) The UV−vis absorption spectra of the ethanol solution of ionophore 1.0 × 10−4 M and ionophore 1.0 × 10−4 M treated with 1.0 × 10−4 M Na2SO4 solution. (B) Comparison of the potentiometric response of different anions with an internal solution 1.0 × 10−2 M. (C) Complex plan plots of the membrane with and without ionophore. (Points and lines indicate the experimental and fitting data, respectively.)

Optimization by Potentiometry. Several membrane compositions were investigated by varying the ratio of PVC, plasticizer, ionophore, and ionic additive. Potentiometric results of the electrodes made with different percentages of membrane components are presented in Figure 2A. A comparison of the first (without MTOAC, electrode no. 1, Figure 2A) and second electrodes (1% MTOAC, electrode no. 2, Figure 2A) indicated that the potentiometric response of the membrane greatly improved with the addition of the lipophilic cationic additive (MTOAC) to the membrane, and it has a useful influence on the performance of the membrane electrode. However, the 2616



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Figure 3. (A) The influence of the internal solution concentration of the sulfate anion-selective electrode on the potential response of the electrode. (B) Complex plan plots of the sulfate anion-selective electrode with an internal solution of 1.0 × 10−7 M sulfate ion. (Points and lines indicate the experimental and fitting data, respectively.) (C) The influence of the internal solution concentration on the Rct. (D) The influence of the internal solution concentration on the Cdl.

Table 1. Comparison of the Different Techniques Used to Measure the Sulfate Anion by Sulfate Anion-Selective Electrode technique potentiometry electrochemical impedance spectroscopy one-impedance for one-concentration

slope by Rct by Cdl freq.: 520 Hz freq.: 120 Hz

−28.9 mV 0.9876 Mohm 0.0575 0.7574 Mohm 0.9703 Mohm

linear range/M 3.0 1.0 1.0 1.0 1.0

× × × × ×

10−1 10−1 10−1 10−1 10−1

to to to to to

1.0 1.0 1.0 1.0 1.0

× × × × ×

10−6 10−9 10−9 10−9 10−9

pH range

comments

4.0−9.0 4.0−10.0 4.0−10.0

simple, fast response, low-cost possible of calculated Rct, Cdl, and kapp increasing the rate

Figure 4. (A) The influence of the pH changes on the potential response of the sulfate-selective electrode. (B) Complex plan plots of the sulfateselective electrode at different pH values with an external solution concentration of 1.0 × 10−2 M sulfate ion. (Points and lines indicate the experimental and fitting data, respectively.) (C) The influence of the pH changes on the Rct. (D) The influence of the pH changes on the Cdl.

According to the impedance spectra and Rct values of the different electrodes (Figure 2B), we observed that when the slope of the potentiometric curve is nearer to the Nernstian slope, the Rct value is reduced so that its value for electrode 11 reaches to 12.7 Mohm. This decrease may be due to increasing the electrical conductivity on the membrane surface. Influence of the Internal Solution Concentration on Characteristics of the Electrode. The concentration of the internal solution is effective in the range of the linear concentration and the Nernstian slope of the potentiometric curve of ion-selective electrodes. Therefore, these measurements were carried out with internal solutions of 1.0 × 10−2, 1.0 × 10−3, 1.0 × 10−4, 1.0 × 10−6, and 1.0 × 10−7 M sodium sulfate. As observed in Figure 3A, diluting the internal solution to 1.0 × 10−7 M sodium sulfate in the presence of the nitrate

interference ion increased the linear concentration range to 1.0 × 10−6 to 1.0 × 10−1 M. The presence of the interference ion in the internal solution extended the linear Nernstian response range and lowered the detection limit.27 In order to draw the electrode response curve, after placing the membrane in 1.0 × 10−2 M sodium sulfate solution for 4 hours with the internal solution concentration of 1.0 × 10−7 M sodium sulfate in the presence of nitrate ion, potentiometric measurements were performed in concentration range from 1.0 × 10−8 to 1.0 M. This electrode had a good response to the sulfate ion and exhibited a good Nernstian slope of −28.9 ± 0.1 mV in the linear concentration range of 1.0 × 10−6 to 3.0 × 10−1 M and a detection limit of 6.3 × 10−7 M. The effect of the internal solution concentration on the impedance spectra of this sensor was performed similar to the 2617



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of 1.0 × 10−7 M sodium sulfate are depicted in Figure 3B, that its points and lines indicate the experimental and fitting data, respectively. Comparing the complex plan plots of different internal solution concentrations reveals that when the concentration is decreased, the impedance spectrum exhibits more regular behavior. This process is consistent with the performance of the electrode during the potentiometric measurements, except that the concentration range of measurements in the impedance technique are much wider. For further evaluation, the diagrams of the Rct and −log Cdl versus the −logarithm of the sodium sulfate concentration for different concentrations of the internal solution are presented in parts C and D of Figure 3, respectively. As can be seen using the impedance method, the linear range of sulfate ion concentration with this electrode increases, so the linear concentration range is reached at 1.0 × 10−9 to 1.0 × 10−1 M when an internal solution of 1.0 × 10−7 M sodium sulfate was used. Moreover, reducing the internal concentration decreased the overall Rct value. Two calibration curves were constructed using the Rct and Cdl values obtained from the internal solution of 1.0 × 10−7 M sodium sulfate, which are summarized in Table 1. Influence of pH Changes on the Electrode Characteristics. According to study of pH adjustments influence on the potentiometric response of the sulfate anion-selective electrode, the electrode was examined using two different concentrations 1.0 × 10−2 and 1.0 × 10−3 M sodium sulfate, while the concentration of internal solution was 1.0 × 10−7 M. To avoid changing the concentration due to changes in volume, nitric acid or sodium hydroxide solutions were added to new sodium sulfate solutions in each stage of the pH adjustment. Finally, after the pH measurement, the relevant potential was read. As shown in Figure 4A, in the pH range of 4.0 to 9.0, no change was observed in the Nernstian response of the electrode. At higher pH values, the potential decreases because the membrane responds to both sulfate and hydroxide ions. At lower pH values, the potential increases due to the protonation of sulfate ions and the quantitative formation of hydrogen sulfate. Additionally, the potential changes at low pH can be attributed to the interference of the hydronium ion in the ionophore complex.15,28 To evaluate the effect of the pH changes on the impedance measurements, the experiments were performed using two external solution concentrations of 1.0 × 10−2 and 1.0 × 10−3 M sodium sulfate. In this study, the internal solution of the electrode was 1.0 × 10−7 M sodium sulfate. For example, the complex plan plots of the 1.0 × 10−2 M are presented in Figure 4B. The results indicate that little change occurs in the impedance spectra at a wide range of pH values. However, because of overlapping spectra, these changes are not so obvious, and for further evaluation, diagrams of Rct and −log Cdl versus the pH changes of the solution were plotted in parts C and D of Figure 4, respectively. Figure 4C indicates that measuring sulfate ions in the pH range of 4.0−10.0 is possible and that the Rct is increased at pH values greater than 10.0 and less than 4.0. Additionally, according to Figure 4D, the effect of the pH changes on the double layer capacitance in the pH range of 4.0−10.0 is not great. Impedance Measurement by the One-Impedance for One-Concentration Method. Impedance measurements in a wide range of frequency for several samples, fitting the data and its calculations, take a long time. To resolve these problems, the “one-impedance for one-concentration” approach presented by Karimi et al.6 was used. For this purpose, the measurements

Figure 5. (A) Complex plan plots of the sulfate-selective electrode with internal solution concentration of 1.0 × 10−7 M sulfate ion by using the “one-impedance for one-concentration” method at two frequencies of 520 and 120 Hz. (B) The calibration curve obtained from this method in these frequencies.

Table 2. Potentiometric Selectivity Coefficients for the Sulfate Anion-Selective Electrode Determined Using the FIM and FPM interference ion ClO4− IO4− IO3− Sal− SCN− ClO3− PO43− HPO42− CrO42− CO32− NO2− NO3− Cl− BrO3− citrate SO32−

Kpot (FIM) 7.90 5.60 2.50 6.28 3.95 4.98 6.79 2.50 4.46 8.89 3.53 1.99 2.80 1.40 3.15 1.58

× × × × × × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−2 10−2 10−3 10−4 10−3 10−3 10−3 10−2 10−3 10−3

Kpot (FPM) 1.26 7.94 1.58 1.00 1.19 1.48 9.26 5.00 7.08 8.91 9.12 1.10 1.99 1.58 1.00 4.79

× × × × × × × × × × × × × × × ×

10−3 10−4 10−3 10−3 10−3 10−3 10−3 10−3 10−4 10−4 10−4 10−3 10−3 10−2 10−3 10−3

potentiometric method for concentrations of 1.0 × 10−2, 1.0 × 10−3, 1.0 × 10−4, 1.0 × 10−6, and 1.0 × 10−7 M sodium sulfate. This study was performed with concentrations of sodium sulfate ranging from 1.0 × 10−1 to 1.0 × 10−12 M. The complex plan plots of the different internal solution concentrations were obtained, and the values of the interfacial parameters (Rs, Rct, and Cdl) were calculated. For example, the complex plan plots 2618



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Table 3. Comparison of the Proposed Electrode Properties with the Other Sulfate-Selective Electrodes ref

methods

12 14 15 30 31 32 present work

Nerstian slope (mV/decade)

potentiometry ac impedancea potentiometryb potentiometryc potentiometry potentiometry potentiometry potentiometry potentiometry EIS

−28.5 −29.7 −29.3 −29.7 −29.6 −28.9 −28.9 −28.9

± ± ± ± ± ± ±

0.9 0.7 0.5 0.8 0.5 0.4 0.1

linear range (M)

detection limit (M)

3.16 × 10−5 to 5.0 × 10−1

3.16 × 10−5

5.0 1.0 8.0 4.0 1.0 1.5 1.0 1.0

× × × × × × × ×

10−5 10−7 10−7 10−5 10−6 10−6 10−6 10−9

to to to to to to to to

1.0 1.0 1.0 4.0 1.0 4.8 3.0 1.0

× × × × × × × ×

10−1 10−1 10−1 10−2 10−2 10−2 10−1 10−1

2.8 8.5 4.0 4.0 8.0 9.0 6.3 1.0

× × × × × × × ×

10−5 10−8 10−7 10−5 10−7 10−7 10−7 10−9

a

The ac impedance was used only for study of the response mechanism of the electrode. bPotentiometric measurements were carried out by a polymeric membrane electrode (PME). cPotentiometric measurements were carried out by a coated graphite electrode (CGE).

M sodium sulfate. Figure 5A depicts the complex plan plots of these measurements. In addition, the value of total impedance (|Z|) was calculated and plotted versus the −log C (Figure 5B). Therefore, two calibration curves were obtained with a slope of 0.9703 Mohm and r2= 0.9982 at the 120 Hz frequency and a slope of 0.7574 Mohm and r2 = 0.9976 at the 520 Hz frequency. Comparison of the Applied Methods. Characteristics of the different techniques used to measure the sulfate ion using the sulfate anion-selective electrode are summarized in Table 1. Although the impedance technique does not have the positive features of the potentiometric method, such as fast response, low cost, and simplicity, increasing the linear range to 1.0 × 10−9 to 1.0 × 10−1 M, high precision, a wider range of pH, and the possibility of calculating parameters such as charge transfer resistance, double layer capacitance, and the apparent rate constant, demonstrate the high ability of this technique. It is noticeable that the difference in the potentiometric and impedance methods for the measurement of the sulfate anion is the large amount of charge transfer resistance. The results of the potentiometric measurements indicate that the used parameter is potential that its value is in limit of “mV”. Therefore, the possibility of environmental noise is high. However, in impedance studies, the parameter obtained in measurements is charge transfer resistance so that its values are in limit of “Mohm” that its magnitude reduces the effect of environmental factors on the results. On the other hand, to reduce the time required for testing and the data fitting calculations, the “one-impedance for oneconcentration” method was used. Although with this method,

Figure 6. (A) Simulated complex plan plots of the sulfate anionselective electrode with an internal solution of 1.0 × 10−7 M sulfate ion. (B) Simulated and experimental values of Rct. (C) Simulated and experimental values of Cdl. Points and lines indicate the experimental and simulated data, respectively.

were performed in a range of frequencies (10 000−0.1 Hz) for two concentrations of 1.0 × 10−1 and 1.0 × 10−9 M sodium sulfate. For concentrations of 1.0 × 10−2 to 1.0 × 10−8 M sodium sulfate, two frequencies of 520 and 120 Hz were selected as the start and end points of the measurement, and experiments were performed only at these two frequencies. In this study, the concentration of internal solution was 1.0 × 10−7

Table 4. Values of the Interfacial Parameters Estimated by Approximation of the EIS Simulated and Experimental Data Obtained on Sulfate Anion-Selective Electrode with Concentration of Internal Solution 1.0 × 10−7 M and Different Concentrations of External Solution experimental data concentration (M) 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

× × × × × × × × ×

−1

10 10−2 10−3 10−4 10−5 10−6 10−7 10−8 10−9

−2

Cdl (F cm ) 8.87 6.98 5.79 5.01 4.45 3.96 3.54 3.23 2.94

± ± ± ± ± ± ± ± ±

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

× × × × × × × × ×

10 10 10 10 10 10 10 10 10

simulated data −1

−2

Rct (Mohm)

kapp (cm s )

Cdl (F cm )

3.97 ± 0.1 5.04 ± 0.1 6.09 ± 0.1 7.04 ± 0.1 7.91 ± 0.1 8.88 ± 0.1 9.94 ± 0.1 10.92 ± 0.1 11.99 ± 0.1

−10

−11

1.68 1.32 1.09 9.46 8.41 7.50 6.67 6.10 5.55

× × × × × × × × ×

2619

10 10−9 10−8 10−8 10−7 10−6 10−5 10−4 10−4

8.626 6.902 5.753 4.929 4.313 3.851 3.450 3.137 2.874

× × × × × × × × ×

10 10−11 10−11 10−11 10−11 10−11 10−11 10−11 10−11

Rct (Mohm) 3.968 4.959 5.949 6.944 7.936 8.888 9.920 10.912 11.910

kapp (cm s−1) 1.678 1.342 1.119 9.586 8.388 7.489 6.710 6.100 5.589

× × × × × × × × ×

10−10 10−9 10−8 10−8 10−7 10−6 10−5 10−4 10−4



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the calculation of parameters including Rct, Cdl, and the apparent rate constant (kapp) is impossible, but its fast response and high accuracy for measuring the sulfate ion in a linear concentration range of 1.0 × 10−9 to 1.0 × 10−1 M are considered the benefits of this method. Therefore, this method is very helpful in quantitative measurements because the measurement speed is increased by reducing the calculations and test time. Potentiometric Selectivity Coefficients. The most important property of any ion-selective electrode is its response to the primary ion in the presence of other ions in solution, which is expressed in terms of the potentiometric selectivity pot coefficient.29 Selectivity coefficients for the sulfate ion (Ksulfate,j ) were determined by the mixed solution methods (MSM), including the fixed interference method (FIM) and the fixed primary method (FPM). Selectivity coefficients of the different anions are summarized in Table 2 and clearly indicate that the designed anion-selective electrode has good selectivity toward the sulfate anion, and only bromate, phosphate, and hydrogen phosphate anions are interferences in the potentiometric measurements of the sulfate ion. Comparison with Other Sulfate-Selective Electrodes. Properties of our electrode regarding other sulfate-selective electrodes are shown in Table 3. As can be seen, the potentiometric linear range and detection limit of our electrode are improved compared to other electrodes except one of them, Ganjali et al. presented a sulfate polymeric membrane sensor with detection limit 4.0 × 10−7 M and a concentration range 8.0 × 10−7 to 1.0 × 10−1 M.15 However, in our work the linear range reached to 1.0 × 10−9 to 1.0 × 10−1 M and the detection limit decreased to 1.0 × 10−9 M using the EIS technique, which was much better than other electrodes.12,14,15,30−32 Analytical Application of the Electrode. To evaluate the analytical application of the anion-selective electrode prepared for the sulfate ion, two drug samples containing iron sulfate and zinc sulfate were measured using different methods. The obtained results were measured of the amount of sulfate with three times irritation. Concentration of sulfate ion in iron sulfate drug using potentiometry, EIS and one-impedance for one-concentration methods was obtained (4.23 ± 0.20) × 10−1, (4.31 ± 0.20) × 10−1 and (4.29 ± 0.20) × 10−1 M, respectively in which their comparison with real value ((4.50 ± 0.20) × 10−1 M) by statistical methods, the accuracy of results of all three methods was confirmed. Also, Potentiometric, EIS and one-impedance for one-concentration results of zinc sulfate drug were (1.36 ± 0.02) × 10−2, (1.25 ± 0.02) × 10−2, and (1.33 ± 0.02) × 10−2 M, respectively. So because of its real value ((1.53 ± 0.02) × 10−2 M) and statistical studies, the results of all three methods are acceptable. Simulation. Simulation is a numerical approach to solve some differential equations, but it is conceptually simpler than other numerical techniques.1 In this paper, the impedance spectra of the sulfate-selective electrodes were simulated by the finite difference method. Additionally, the approach of Brumleve and Buck19 was used in the simulation. Model Design. The first step in the simulation is the selection of a model whose type and complexity depends on the type of system and its conditions. In this model, the electric fields (E) are placed at the boundaries of each element, while the concentrations (C) are defined in the middle of the elements, except at the interfaces, where there is effectively a half of a volume element. Also, the membrane thickness was divided into 71 parts in which its two halves are mirror images

of each other. A total of 20 points near each interface have equal distances, and the other 31 points were expanded with an exponential function to the middle of the membrane. Definition of Describing Equations of the System. Describing the equations of the system should be defined according to the type of system and its reactions and written as codes in the software. These equations should be coded in a way that can be calculated at various places and times, in other words are matched with the model. For our system, these equations included the Nernst−Planck, Poisson, continuity, and total membrane potential equations that were completely described by Brumleve and Buck.19 Before putting the describing equations of the system in the designed model, the parameters should be dimensionless.4 Finally, the equations are converted to the finite difference form that is compatible with the designed model. Simulation of the Impedance Spectra. For this simulation, a computer system with a CPU Core i7 920 and 4 GB RAM was used. The designed model, input parameters, and obtained equations were written as codes in the Maple 13 software. Then, the equations substituted in the model were solved by the Newton algorithm (also known as the Newton− Raphson), which includes the solution of Jacobian matrix.33 In this method, 100 iterations were used to obtain convergent results, and the concentrations and potential were calculated at different times. The impedance of the system can be determined using the Fourier transformation of the potential−time response to a small current perturbation. The impedance spectra of the sulfate-selective electrode were obtained by inputting these relations in the software as codes. To compare the optimized experimental results and simulated data in this simulation, the internal solution concentration of the electrode was set at 1.0 × 10−7 M sodium sulfate, and the simulation was performed in the concentration range of 1.0 × 10−9 to 1.0 × 10−1 M, which had a linear response. Simulated complex plan plots of this electrode are shown in Figure 6A. In this figure, points and lines indicate the experimental and simulated data, respectively. There are only slight differences in the impedance spectra at lower concentrations of the sulfate ion, and at other concentrations, the simulated and experimental data fit well. Adaptation of points and lines confirms the performance of the impedance technique and the simulation of its spectra. In addition, the simulated and experimental data presented in Table 4 show that these data are similar. The simulated and experimental values of kapp were calculated and are presented in Table 4. To validate these results, diagrams of the simulated and experimental Rct and −log Cdl values were plotted versus the −log Csulfate and are presented in parts B and C of Figure 6, respectively. By comparing these diagrams, the similarity of the experimental and simulated Rct and Cdl data is clear.

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CONCLUSIONS In this work, a new sulfate anion-selective electrode was prepared, and a new strategy for optimizing membrane components by the EIS method was presented. Additionally, the performance of this electrode was investigated using potentiometric and EIS techniques. Potentiometric results indicate that this electrode has a good Nernstian slope of −28.9 ± 0.1 mV in the linear concentration range of 1.0 × 10−6 to 3.0 × 10−1 M and a detection limit of 6.31 × 10−7; but by using the impedimetric method, the linear concentration range increased to 1.0 × 10−9 to 1.0 × 10−1 M and the applied pH 2620



Article

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range improved to 4.0−10.0. Another benefit of the EIS technique is the possibility of calculating the values of parameters such as Rct, Cdl, and kapp. On the other hand, to reduce the time required for testing and the data processing calculations, the “one-impedance for one-concentration” method was used, which has a linear concentration range of 1.0 × 10−9 to 1.0 × 10−1 M. Finally, the impedance spectra were simulated using the Maple 13 software. The comparison of the experimental data and the information obtained from the simulation demonstrated the accuracy of the impedance measurement of the anion-selective electrode.

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ASSOCIATED CONTENT

S Supporting Information *

Additional information as noted in text. 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]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the Payame Noor University Research Council (center of Ardakan), the Yazd University Research Council, the IUT Research Council and the Excellence in Sensors for financial support of this research.

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REFERENCES

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Impedimetric and Potentiometric Investigation of a Sulfate Anion

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