potentiometric ion-selective...
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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.
πΈ = πΈπ + 2.3 π π
ππΉlog π (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 (25Β°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 electrodeβs 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
πΈ = πΈπ + 2.3 π π
ππΉlog(πππ + πππππ
π
π§ ) (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 βactiveβ 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 saltβsilver chloride (AgCl). The corresponding half-reactions inside electrode are as follows: -
Ag+ + e- β Ag (s) AgCl (s) + e- β 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 Β± 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:
πΆπ’ = πΆπ [ππ
ππ’ + ππ ] [10
βπΈπβ β
ππ’
ππ + ππ’]
β1
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: -
(ππ’ + ππ )10βπΈπ = ππ’ +
1
πΆπ’πΆπ ππ
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 β 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:
π¦ = π β π₯ + π
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:
π¦ = π β π₯
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:
π‘ =|π β π½|
π π=
|π β 0|
π π=
|π|
π π
Where sb is the standard deviation of the intercept defined as:
π π = π π β ββ π₯π
2ππ=1
π β β (π₯π β οΏ½Μ οΏ½)2ππ=1
Where se is a standard deviation of residues:
π π = ββ (π¦π β οΏ½ΜοΏ½)2π
π=1
π β 2
Where β (π¦π β οΏ½ΜοΏ½)2ππ=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:
π‘ππππ‘ = π‘1β
πΌ2
;πβπ
where Ο 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 π = π β π
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, β¦) 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:
π = β1
π β 1β β(π₯π β οΏ½Μ οΏ½)2
π
π=1
After, the confidence interval can be calculated:
πΏ1,2 = οΏ½Μ οΏ½ Β±π β π‘ππππ‘
βπ= οΏ½Μ οΏ½ Β± π οΏ½Μ οΏ½ β π‘ππππ‘
Wherein L1 and L2 represent the extreme limits of the confidence interval, tΞ± is the critical value
of the Student distribution for the chosen significance level Ξ±.
With a small number of parallel measurements (n << 10) the standard deviation can be
determined from the range (R):
π π = ππ β π
π = π₯πππ₯ β π₯πππ
Where kn is a coefficient of the Dean-Dixon test. Based on this test the extreme limits of the confidence
interval can be calculated:
πΏ1,2 = οΏ½Μ οΏ½ Β± πΎππππ‘ β π
Where KΞ± is the critical value of the Lordβs distribution for the chosen significance level Ξ±.
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 β Studentβs t-test:
t =|οΏ½Μ οΏ½ β π| β βπ
π =
|οΏ½Μ οΏ½ β π|
π π₯
Alternatively, using a range for a small set β Lord's correctness test:
π’0 =|οΏ½Μ οΏ½ β π|
π
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 Grubbβs test:
ππ =|οΏ½Μ οΏ½ β π₯π|
π π = β
1
πβ β(π₯π β οΏ½Μ οΏ½)2
π
π=1
Dean-Dixon test is used for the small set again:
ππ =π₯π β π₯πβ1
π
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, β¦)
2. Measurement uncertainty (standard deviation, β¦)
Based on this, the result is written as:
(value Β± uncertainty) unit
(y Β± 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 π¦ = π΄ + π΅ π’π = βπ’(π΄)2 + π’(π΅)2
2. Multiplication and Division π¦ = π΄ β π΅ π’π
π¦= β(
π’(π΄)
π΄)
2
+ (π’(π΅)
π΅)
2
3. Multiplication and Division π¦ = π΄ β π΅ π’π = βπ ππ·(π΄)2 + π ππ·(π΅)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.
π = π β π’π
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 Studentβs t-test used:
t =|οΏ½Μ οΏ½π΄ β οΏ½Μ οΏ½π΅| β βπ β 1
βπ π΄2 + π π΅
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 Lordβs test where is u compared to ucrit:
u =|οΏ½Μ οΏ½π΄ β οΏ½Μ οΏ½π΅|
π π΄ + π π΅
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 β 10-6 M
πΎπΆπ2+ ππ2+β = 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