Potentiometric Ion-Selective Electrodes

An ion-selective electrode (ISE), is a type of electrochemical sensor that converts the activity of a

specific ion dissolved in a solution into an electrical potential. The voltage of such electrode is

dependent on the logarithm of the ionic activity, according to the Nernst equation.

𝐸 = 𝐸𝑜 + 2.3 𝑅𝑇

𝑛𝐹log 𝑎 (1)

Where Eo = a constant for a given cell (It is unique for the analyte, and also includes the sum of the potential differences at all the interfaces other than the membrane/sample solution interface.) R = the gas constant T = the Temperature in Kelvin n = the ionic charge F = the Faraday constant a = the activity of the ion in the sample solution and the expression 2.3RT/nF is termed the Slope Factor

For example, the slope at 298K (25°C) has a value of 59.16 mV, when measuring Potassium ions, (i.e. n = +1). This is termed as the Ideal Slope Factor, and means that for each tenfold change in potassium concentration, an ideal measuring system will sense a change of 59.16 mV. The measurement of slope factor gives an indication of the performance of the electrode system. If the slope value is lower than the ideal slope factor, it signifies a loss in electrode’s performance. A number of factors such as interference from other ions, use of incorrect calibration, loss of electrolyte in the electrode or blockage of the reference junction, can be responsible for it and should be checked in such a case. The ion-selective membrane situated between the two aqueous phases, i.e., between the sample and inner solution that contain an analyte ion forms an essential part of the ISEs. It can be made of glass, a crystalline solid, or a liquid. The potential difference across the membrane is measured between the two reference electrodes positioned in the respective aqueous phases.

reference electrode 2 || sample solution | membrane | inner solution || reference electrode 1

Figure 1: Schematic of a measurement setup using an Ion-Selective Electrode

1. Selectivity and interferences

Ion-selective electrodes are selective but not specific. They can respond to other ions in solution

although it is not designed to do so. The ion to be determined is referred as the primary ion

(determinant) and other ions to which the electrode responds are known as interfering ions

(interferent). The preference of an electrode for the determinant over the interferent is called

the selectivity of the electrode. This preference, is expressed as a ratio called the selectivity

coefficient, or ratio. Each electrode has its own set of selectivity coefficients. For example:

KK+/Na+ = 2.6 x 10-3

primary ion interfering ion

Meaning that the preference for K+ (potassium) over Na+ (Sodium) for this electrode is 1 to 2.6 x 10-3 or 385:1. This means that the electrode is 385 times more selective to K+ than Na+. To take into account, the response of the electrode to an interfering ion an additional term is added to equation 1

𝐸 = 𝐸𝑜 + 2.3 𝑅𝑇

𝑛𝐹log(𝑎𝑖𝑗 + 𝑘𝑖𝑗𝑎𝑗

𝑛

𝑧 ) (2)

Where aj is the activity of the interfering ion with charge z and kij is the selectivity coefficient,

which is the response of the electrode to the interfering ion relative to its response to the primary ion.

2. Activity vs Concentration Ion-selective electrodes respond directly to the activity of an ion, rather than to its concentration. The concentration is the number of ions in a specific volume, this definition assumes that all of those ions have a similar behavior. However, ions do not always behave similar to one another: some are active i.e. exhibit properties associated with that ion, and some are not active. The number of active ions is called the activity of the solution. This means it is a relative term describing how “active” an ion is compared to when it is under standard state conditions. This characteristic is often a decided advantage, since the metabolic behavior of an ion is often more directly related to its activity. For example, the physiological effects of calcium in serum are related to the ionized Ca2+ activity rather than the total calcium concentration, which also includes protein-bound and complexed calcium species. In dilute solutions though, the ionic activity and the concentration are practically identical but in solutions containing many ions, activity and concentration may differ. This is why dilute samples are preferred for measurement with ISE's. However, it is possible to 'fix' the solution so that activity and concentration are equal. This can be done by adding a constant concentration of an inert electrolyte to the analyte solution. This is called an Ionic Strength Adjustment Buffer (I.S.A.B.). Thus in dilute solutions, the ion selective electrode will measure concentration directly.

3. Types of electrode There are four types of ion selective electrode whose construction and mode of operation differ considerably. These are: 1. Glass body electrode 2. Solid state (crystalline membrane) 3. Liquid ion exchange (polymer membrane) 4. Gas sensing type 1. Glass body electrodes The most common ISE is the glass-bodied pH electrode. Glass membranes are made from an ion-exchange type of glass (silicate or chalcogenide). This type of ISE has good selectivity, but only for several single-charged cations; mainly H+, Na+, and Ag+. 2. Solid state ion selective electrode In these type of electrode, the electrode potential of the standard and the sample solutions is measured across a solid, polished crystalline membrane. The crystalline material is prepared from a single compound or a homogeneous mixture of compounds (for example, the fluoride ISE has a Lanthanum Fluoride crystal)

3. Polymer membrane ion selective electrode These electrodes contain a polymeric membrane containing a selective ion exchanger, the liquid membranes are hydrophobic and immiscible with water. They are most commonly made of plasticized poly (vinyl chloride). By doping the membranes with a hydrophobic ion (ionic site) and a hydrophobic ligand (ionophore or carrier) that selectively and reversibly forms complexes with the analyte, these membranes are made selective. The electrode potential of solutions is measured by their effect on the ion exchange material. This type of ion-selective electrode is subject to more interferences than other ISEs due to complex properties of ion exchangers.

Figure 2: Schematic view of the equilibrium between sample, ion-selective membrane, and inner filling solution (cell 1). The cation-selective membranes are based on (A) cation exchanger (R-), (B) electrically neutral ionophore (L) and anionic sites (R-), and (C) charged ionophore (L-) and cationic sites (R+). The aqueous solutions contain an analyte cation (I+) and its counter anion (X-). 4. Gas sensing type The gas sensing type of ISE use a membrane separating a sample and a filling solution. The gas from the sample solution (for e.g., liberation of ammonia by adding a caustic solution to it) permeates through the membrane and changes the pH of the filling solution. The change in pH is proportional to the concentration. This gives a quantitative measurement of the analyte gas in the sample solution.

Figure 3: Schematic of the sensing portion on the 4 main types of Ion-selective/gas sensing electrodes

4. Reference Electrodes The potential of an Ion Selective Electrode can only be measured against an appropriate reference electrode in contact with the same test solution. Reference electrodes are electrodes with a stable and well-known electrode potential. By employing a redox system with constant (buffered or saturated) concentrations of each participant, a chemical equilibrium can be maintained inside them which is responsible for a constant value of the electrode potential. A silver chloride electrode is among the most commonly used reference electrodes, it is usually the internal reference electrode in pH meters. The electrode functions as a redox electrode by maintaining the equilibrium between the silver metal (Ag) and its salt—silver chloride (AgCl). The corresponding half-reactions inside electrode are as follows: -

Ag+ + e- ⇋ Ag (s) AgCl (s) + e- ⇋ Ag (s) + Cl-

This reaction is characterized by fast electrode kinetics, meaning that a sufficiently high current can be passed through the electrode with the 100% efficiency of the redox reaction (i.e., dissolution of the metal or cathodic deposition of the silver-ions). The reaction obeys these equations in solutions ranging from pH 0 to 13.5. The standard electrode potential E0 against standard hydrogen electrode (SHE) is 0.230 V ± 10 mV.

5. Methods of analysis 5.1 Potentiometry In potentiometry, the potential of a solution between two electrodes is passively measured,

affecting the solution very little in the process. One of the electrode which has constant potential

is called the reference electrode, while the other electrode whose potential changes with the

composition of the sample is called indicator electrode. Therefore, the potential difference

between the two electrodes is indicative of the composition of the sample. Potentiometry is a

non-destructive technique, assuming that the electrode is in equilibrium with the solution we are

measuring the potential of the solution. Potentiometry usually uses an ion-selective electrode,

so that the potential solely depends on the activity of this ion of interest. The time taken by the

electrode to establish equilibrium with the solution will affect the sensitivity or accuracy of the

measurement.

5.2 Calibration Curve Method

This is the simplest and most widely used method of obtaining quantitative results using Ion

Selective Electrodes. Standard solutions are prepared by serial dilution of a concentrated

standard. The recommended Ionic Strength Adjustment Buffer (ISAB), is added to each standard

as well as to the unknown samples. The measurement of the potential difference between the

ISE and the reference electrode for standard solution yields the calibration curve. The electrode

potential of each of the unknown solutions is then measured and the concentration of the ion is

read directly from the calibration curve.

Since the response of the ISE is linear to the logarithm of the activity (or concentration in case of

dilute samples) of the analyte ion of interest, the calibration curve is plotted between the

measured potential difference vs the logarithm of the concentration of the standard solution.

Figure 6: Ca2+ ion-selective electrode (ISE) calibration curve

Unknown sample

5.3 Standard Addition Method

The method of standard addition is a type of quantitative analysis approach often used in

analytical chemistry whereby the standard is added directly to the aliquots of analyzed sample.

This method is used in situations where sample matrix also contributes to the analytical signal, a

situation known as the matrix effect, thus making it impossible to compare the analytical signal

between sample and standard using the traditional calibration curve approach. The electrode

potential of a known volume of unknown solution is measured. A small volume of a known

solution is added to the first volume and the electrode potential re-measured, from which the

potential difference (E) is found. By solving the following equation, the unknown concentration

can be found:

𝐶𝑢 = 𝐶𝑠 [𝑉𝑠

𝑉𝑢 + 𝑉𝑠] [10

∆𝐸𝑆⁄ −

𝑉𝑢

𝑉𝑠 + 𝑉𝑢]

−1

where: Cu = concentration of the unknown; Cs = concentration of the standard; Vs = volume of

the standard; Vu = volume of the unknown; E = change in electrode potential in mV; S = slope

of the electrode in mV. It is calculated by plotting E vs log[C] curve and, it is the slope factor of

the electrode, giving information about its performance.

Rearranging the formula, we get: -

(𝑉𝑢 + 𝑉𝑠)10∆𝐸𝑆 = 𝑉𝑢 +

1

𝐶𝑢𝐶𝑠𝑉𝑠

Figure 7: A standard addition curve

x-intercept = N moles; This implies that there are N moles of analyte in Vs volume of sample,

Hence, the concentration of analyte in sample solution = N/Vs moles/L

Therefore, the concentration of analyte in original solution can be calculate by C1V1 = C2V2

6. Basic Statistics

6.1 Calibration Curve

Generally, the main aim of analytical chemistry is to detect the presence of the analyte and to

determine its amount (if possible). Apart from the absolute methods such as volumetric or

gravimetric analysis all analytical methods require some sort of calibration. Calibration means

the assignment of the dependent variable values (signal value – current, potential, absorbance,

conductivity, etc.) to the independent variable values (concentration, volume, weight, etc.). The

calibration includes two necessary steps. First is the construction of the regression model from

the results of calibration standard analyses. The second step is the usage of the calibration model

for the determination of x value.

Figure 8: Example of a calibration curve

The most common and simplest calibration model is a linear regression model. Mathematically

expressed as:

𝑦 = 𝑎 ∙ 𝑥 + 𝑏

Where a is the slope and b is the intercept. Both of the parameters are loaded with errors. The

error value depends on the number of calibration points and the repetition variance. In the case,

where the intercept is statistically non-significant is the equation reduced to:

𝑦 = 𝑎 ∙ 𝑥

6.1.1 Intercept Significance T-test

The t-test determines whether the coefficient b deviate significantly from the predicted value .

Commonly, it is tested whether parameter b differs significantly from the origin:

𝑡 =|𝑏 − 𝛽|

𝑠𝑏=

|𝑏 − 0|

𝑠𝑏=

|𝑏|

𝑠𝑏

Where sb is the standard deviation of the intercept defined as:

𝑠𝑏 = 𝑠𝑒 ∙ √∑ 𝑥𝑖

2𝑛𝑖=1

𝑛 ∙ ∑ (𝑥𝑖 − �̅�)2𝑛𝑖=1

Where se is a standard deviation of residues:

𝑠𝑒 = √∑ (𝑦𝑖 − �̂�)2𝑛

𝑖=1

𝑛 − 2

Where ∑ (𝑦𝑖 − �̂�)2𝑛𝑖=1 is the regression sum of squares.

The result value is compared with value tcrit (you can obtain it using T.INV excel function) and:

If t < tcrit then the hypothesis holds. Which means that the intercept is not statistically significant

and the straight line goes through the origin.

If t > tcrit then the hypothesis is denied that means the intercept is significant, and the straight

line does not go through the origin.

The critical value of the T-test is defined as:

𝑡𝑐𝑟𝑖𝑡 = 𝑡1−

𝛼2

;𝑛−𝜐

where υ represents degrees of freedom and n is a number of points in the calibration curve. The

degrees of freedom depend on the type of model equation. Generally, the equation 𝜐 = 𝑛 − 𝑘

holds true. The k is a number of constants in the regression equation.

6.2 Result Errors

The purpose of the measurement is to determine the value of the measured quantity that

characterizes the given property. By repeating the measurement, we come to a conclusion that,

despite considerable precision, we do not always get the same value, but the values differ from

each other. This is due to the fact that individual measurements are loaded with various effects

of noise, which are generally referred to as errors. The result of such a repeated measurement

can then be expressed by an appropriate estimate of the mean (mean, median, …) and the

degree of variance of this value (dispersion, standard deviation, expanded uncertainty,

confidence interval).

Figure 9. Graphic illustration of accurate and precise measurements

Depending on the cause, we can divide the errors into three basic groups:

6.2.1 Random Errors

If the measurement is repeated several times, the random errors are shown with the same

probability for both positive and negative values. Their size is given by the statistical distribution

width of the measurement. They are caused by a variety of causes and cannot be removed.

However, they can be statistically evaluated, and we can estimate the size of their contribution.

Moreover, their influence on the measurement can be reduced by increasing the number of

repetitions.

These errors affect the precision of the measurement; in other words the tightness of the match

between repeated measurements under the same conditions. This phenomenon is generally

called uncertainty (uc). The uncertainty can be express in many ways; e.g., a standard deviation,

an expanded uncertainty, or a confidence interval. Basic estimation of uc is the standard

deviation s which is defined as:

𝑠 = √1

𝑛 − 1∙ ∑(𝑥𝑖 − �̅�)2

𝑛

𝑖=1

After, the confidence interval can be calculated:

𝐿1,2 = �̅� ±𝑠 ∙ 𝑡𝑐𝑟𝑖𝑡

√𝑛= �̅� ± 𝑠�̅� ∙ 𝑡𝑐𝑟𝑖𝑡

Wherein L1 and L2 represent the extreme limits of the confidence interval, tα is the critical value

of the Student distribution for the chosen significance level α.

With a small number of parallel measurements (n << 10) the standard deviation can be

determined from the range (R):

𝑠𝑅 = 𝑘𝑛 ∙ 𝑅

𝑅 = 𝑥𝑚𝑎𝑥 − 𝑥𝑚𝑖𝑛

Where kn is a coefficient of the Dean-Dixon test. Based on this test the extreme limits of the confidence

interval can be calculated:

𝐿1,2 = �̅� ± 𝐾𝑐𝑟𝑖𝑡 ∙ 𝑅

Where Kα is the critical value of the Lord’s distribution for the chosen significance level α.

6.2.2 Systematic Errors

In the overall result, systematic errors are displayed by shifting the measured value in a

comparison to the correct value. In the case of one value, we are talking about the accuracy of

the measurement - the consistency of the measured value with the reference value (different

technique, SRM, etc.). In the case of an average value obtained from repeated measurements,

we are talking about the truthfulness of the measurement - the consistency between the average

value of the infinite number of repeated measurements and the reference value. They are caused

by the use of inappropriate methodology, poor calibration or interferences. They can be detected

by comparing with another device or by comparing it with a reference material value. The cause

can be found, and this type of error can be removed. Systematic errors can be quantified using

so-called bias - the difference between the mean value of the measurement result and the

reference value. Accuracy test can be done either with SD – Student’s t-test:

t =|�̅� − 𝜇| ∙ √𝑛

𝑠=

|�̅� − 𝜇|

𝑠𝑥

Alternatively, using a range for a small set – Lord's correctness test:

𝑢0 =|�̅� − 𝜇|

𝑅

6.2.3 Gross Errors

This type of error is caused, by the improper recording of the measured quantity, the sudden

failure of the instrument or failures in the procedure. Gross errors cause the measurement to be

significantly different from the other repetitions. Gross errors thus affect both the precision and

the accuracy of the measurement. A residual test can reveal these gross errors. These errors can

and should be avoided with personal thoroughness during measurement and appropriate

instrument maintenance.

Gross errors can be revealed with Grubb’s test:

𝑇𝑛 =|�̅� − 𝑥𝑛|

𝑆 𝑆 = √

1

𝑛∙ ∑(𝑥𝑖 − �̅�)2

𝑛

𝑖=1

Dean-Dixon test is used for the small set again:

𝑄𝑛 =𝑥𝑛 − 𝑥𝑛−1

𝑅

Usually only the lowest and highest values are tested. If they are loaded with gross errors, the

test has to be done for second lowest/highest value too.

6.3 Measurement uncertainty

Measurement uncertainty yields quantitative information about the quality of the analysis results.

According to the exact definition, measurement uncertainty is the expression of the statistical dispersion

of the values attributed to a measured quantity. So, the result combines two parts:

1. Measured value (mean, median, …)

2. Measurement uncertainty (standard deviation, …)

Based on this, the result is written as:

(value ± uncertainty) unit

(y ± U) unit

6.3.1 Propagation of Uncertainty

In many cases, the result of the analysis is affected by more quantities (with their own

uncertainties). Due to that fact, the combined uncertainty has to be calculated.

Mathematical Operation Example Formula

1. Addition and Subtraction 𝑦 = 𝐴 + 𝐵 𝑢𝑐 = √𝑢(𝐴)2 + 𝑢(𝐵)2

2. Multiplication and Division 𝑦 = 𝐴 ∙ 𝐵 𝑢𝑐

𝑦= √(

𝑢(𝐴)

𝐴)

2

+ (𝑢(𝐵)

𝐵)

2

3. Multiplication and Division 𝑦 = 𝐴 ∙ 𝐵 𝑢𝑐 = √𝑅𝑆𝐷(𝐴)2 + 𝑅𝑆𝐷(𝐵)2

The last step in the evaluation is the calculation of so-called expanded uncertainty U which is a

part of the final report. Expanded uncertainty is an interval in which the real value of the

measured quantity lies with high reliability.

𝑈 = 𝑘 ∙ 𝑢𝑐

Where k is the coefficient of expansion, which is equal to two (for a 95 % level of reliability).

6.4 Equivalency of obtained results

Usually, the equivalency is considered when the comparison of the results is needed. Results

might be provided by a different method, person, laboratory, etc.

For the equal number of repetitions in all tested sets of values is the Student’s t-test used:

t =|�̅�𝐴 − �̅�𝐵| ∙ √𝑛 − 1

√𝑠𝐴2 + 𝑠𝐵

2

The t value is compared to tcrit and if t tcrit for the total number of repetitions 2n-1 and the

chosen level of significance, the difference of the arithmetic means is statistically significant. The

same rule holds for the Lord’s test where is u compared to ucrit:

u =|�̅�𝐴 − �̅�𝐵|

𝑅𝐴 + 𝑅𝐵

7. Experimental Part

7.1 Measuring the concentration of Ca2+ ion in the unknown sample using bulk ISE

1. Prepare 100ml of 0.1 M of calcium chloride (CaCl2) solution by weighing appropriate

quantity of CaCl2

2. Dilute the aforementioned solution to make 100ml each of calibration solution of 10-2,10-

3, 10-4,10-5,10-6 M concentration of CaCl2

3. Measure the potential of the ISE with respect to Ag/AgCl using direct potentiometry in

the electrochemical cell

4. Plot the calibration curve of potential difference ( E) vs log [concentration]. Check the

deviation of the slope from Ideal Slope Factor (+29.58 mV in case of divalent Ca2+ ion) to

check the performance of the system.

5. Measure the potential of the unknown sample and calculate the concentration using the

calibration curve

7.2 Optimization of chip electrode system for measurement of Ca2+ ion

For this electrode the Ca2+ ion-selective membrane needs to be deposited directly on the gold

microelectrode and equilibrated for 30 mins in 10-3 M CaCl2 solution before analysis.

1. Dissolve the given Ca2+ ion-selective membrane in a small amount of Tetrahydrofuran

(THF) (~ 50-100 ml of THF). Adjust its viscosity with additional amount of THF so that it

is sufficiently viscous to form a thin layer on the electrode upon evaporation of THF

2. Put a drop of the aforementioned solution on the gold contact of the chip electrode and

gently evaporate the solvent using nitrogen (case should be taken not the fully dry the

membrane)

3. Equilibrate the electrode by immersing the ion-selective membrane in 10-3 M CaCl2

solution for 30 mins

4. Check the on chip electrode by performing calibration curve method described above and

compare your results with the bulk ISEs.

5. After optimization of membrane casting process, other analyte solutions such as tap

water, calcium tablets, milk, etc., can be monitored. Provided they are diluted

appropriately with Ionic Strength Adjustment Buffer (I.S.A.B)

6. For complex matrices (such as milk), Standard Addition Method can be employed. This

will reduce the matrix interference effect and will improve the accuracy of the

measurement in these samples.

7.3 Important information for Ca2+ ion-selective electrode

Type of membrane: Liquid ion exchange membrane

Concentration range: 100 – 10-6 M

𝐾𝐶𝑎2+ 𝑀𝑔2+⁄ = 2.5 x 10-4 (Depends on the electrode, membrane)

Ion Matrix/Sample Electrode Method Sample Preperation

Ca2+ Water Calcium ISE Calibration Curve

Use KNO3 as ionic strength

adjuster

Ca2+ Milk Calcium ISE Standard Addition

Dissolve in 0.1 M sodium

nitrate

Ca2+ Sugar Solutions Calcium ISE Both Standard and spiking solution

should be made in sucrose solution

Ca2+ Wines Calcium ISE Standard Addition

Dry ash the sample and dissolve the

residue in HCL. Adjust pH to

6.5-7.0

Ca2+ Beer Calcium ISE Standard Addition

Adjust the pH of the beer to

5.5-6.0

8. References:

1. Lamb, R. E., Natusch, D. F., O'Reilly, J. E., & Watkins, N. (1973). Laboratory experiments with

ion selective electrodes. Journal of Chemical Education, 50(6), 432.

2. Zoski, C. G. (Ed.). (2006). Handbook of electrochemistry. Elsevier.

3. Faulker, A. B. L. (2001). Electrochemical Methods, Fundamentals and Application.

4. Mt.com. (2020). [online] Available at: https://www.mt.com/dam/MT-

NA/pHCareCenter/Ion_Selective_Measurement_APN.pdf