Guide to ISE Measurements, Chap. 6) LIMITATIONS and CONSTRAINTS on the application of ISE measurements

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Beginners Guide to ISE Measurement. Chapter 6.

LIMITATIONS and CONSTRAINTS
on the application of ISE measurements.
Last update 21 Oct 2016

The three main limitations on Ion Selective Electrode measurements are the effect of interference from other ions in solution, the effect of the ionic strength of the solution reducing the measured activity relative to the true concentration at high concentrations, and potential drift during a sequence of measurements.

a) Ionic Interference and Selectivity Coefficients.

ISEs are not ion-specific. All are sensitive to some other ions to some extent. For many applications these interferences are insignificant (unless there is a high ratio of interfering ion to primary ion) and can often be ignored. In some extreme cases, however, the electrode is far more sensitive to the interfering ion than to the primary ion and can only be used if the interfering ion is only present in trace quantities or even completely absent. In some systems the interfering ion can be removed by chemical means (chiefly precipitation or complexing) and many manufacturers can supply detailed instructions and special reagents to accomplish this, but this can be a laborious and time-consuming process and most analysts prefer to avoid this if possible.

The ability of an ion-selective electrode to distinguish between different ions in the same solution is expressed as the Selectivity Coefficient. If the primary ion for which the electrode is sensitive is A and the interfering ion is B then a selectivity coefficient of 0.1 would mean that the electrode is ten times more sensitive to A than to B. If the coefficient is 1 then the electrode is equally sensitive to both. Unfortunately the selectivity coefficient is not constant and depends on several factors including the concentration of both elements, the total ionic strength of the solution, and the temperature. According to the British Standards Specification for Ion-Selective Electrodes, all manufacturers should provide details of the conditions under which the SC was measured, including concentrations of both ions, for all ISEs which they supply. This should assist potential users in properly evaluating the significance of this limitation for their own particular application - but all this information is not always available. Thus the value quoted in the electrode specifications is necessarily only a general guide and cannot be used to make accurate corrections for the interfering ion in any simple manner.

Method for Correcting for Interfering Ions.
If the analyst is unsure if an interfering ion will be a problem, or if he wishes to make a correction for its presence, then it is possible to measure the SC directly in a typical sample and obtain a more accurate assessment of the interference than provided by the manufacturer.
First measure the concentration of the interferent and the apparent concentration of the primary ion in the sample, using the appropriate ISE for each ion. Then add more interferent - sufficient to ensure a significant (say 10%) increase in the signal for the primary ion. The amount to add can be roughly calculated from the initial concentration measurements and the indicative SC quoted in the electrode specifications.
Then measure the apparent concentration of the primary ion again and calculate the SC for the interferent from the increase caused by the known amount added. e.g. if the added interferent increased it's concentration by 10ppm and this produced a 1 ppm increase in the measured value of the primary ion then the SC would be 0.1. Subsequent sample measurements can then be made by measuring both the primary ion and interferent and using the measured SC to make a more accurate correction for the interference.
See: Practical example and details of the method.
However, it must be noted that the accuracy and precision of this correction may be quite variable and will need to be tested for validity and reliability for each particular application before being used on a routine basis. Furthermore it will probably only be effective for ions with selectivity coefficients less than 1 and require a fairly uniform amount of interferent in the samples.

Possible Alternative to using Selectivity Coefficient If the interfering ion is fairly constant in the samples and is not too concentrated (ie will not cause too much of an error in the measured ion concentration - say not more than 100%) Then it may help to minimize this error by spiking the standards with the same concentration of interfering ion as in the samples. But this will inevitably lead to a raising of the lower limit of concentration for reasonable routine measurements.

Probably the most common example of interference is that of potassium on ammonium and vice-versa. Potassium is a very common element and is present in most natural substances. The selectivity coefficient for K of the NH4 electrode is approximately 0.1. This means that if there are equal concentrations of NH4 and K in a solution, then the K will contribute about 10% to the NH4 signal. To put it another way, if a sample contains ten times more K than NH4 then the ISE analysis will give an apparent concentration for NH4 of approximately twice as much as is actually present. A further complication is that NH4 also has a slight effect on the K electrode which may become significant at high NH4 to K ratios. Until recently, these interferences have limited the use of the ammonium ISE to only those applications where a high NH4 to K ratio can be guaranteed. See Chapter 14 for information on recent research.

Another typical example of interference is that of the chloride ion on the nitrate electrode. In this case the selectivity coefficient is only about 0.003. This means that an equal concentration of chloride would only add about 0.3 % to the nitrate signal. Nevertheless, in many natural waters the Cl/NO₃ ratio can be as high as 50:1 or even more, thus causing a possible 15 or 20% increase in the apparent NO₃ signal. In this case however, the chloride ion can be removed from solution by precipitating as the sparingly soluble silver chloride. So, by adding measured quantities of the appropriate reagents to samples and standards, the analyst can overcome this problem in the laboratory. Nevertheless, it must be noted that silver salts are relatively expensive and so adopting this procedure can add significantly to the cost of analysis.

b) Ionic Strength and Activity Coefficients: Activity versus Concentration.

Ion selective electrodes measure the concentration of ions in equilibrium at the membrane surface. In dilute solutions this is directly related to the total number of ions in the solution but at higher concentrations, inter-ionic interactions between all ions in the solution (both positive and negative) tend to reduce the mobility and thus there are relatively fewer of the measured ions in the vicinity of the membrane than in the bulk solution. Thus the measured voltage is less than it would be if it reflected the total number in the solution and this causes an erroneously low estimate of the concentration in samples with a high concentration and/or a complex matrix.

Ionic Strength is a measure of the total effect of all the ions in a solution. It is the sum of the molar concentration multiplied by the square of the valency of all the ions. The effective concentration measured at the electrode head is known as the activity of the ion. In general chemical terms it is the number of ions taking place in any chemical reaction – measured in concentration units. The activity coefficient is the ratio of the activity divided by the concentration. This is a variable factor and depends on the valency and ionic radius of the measured ion and the total ionic strength of the solution.

The activity coefficient is always less than one and becomes smaller as the ionic strength increases; thus the difference between the measured activity and the actual concentration becomes higher at higher concentrations. This effect causes two main problems in ISE measurement. Firstly, when constructing a calibration graph using concentration units, the line is seen to curve away from linearity as the concentration increases (it remains straight, up to the highest concentrations if activity units are used). Thus, if concentration units are used, it is necessary to measure many more calibration points in order to define the curve more precisely and permit accurate interpolation of sample results. Secondly, it is most likely that the sample solutions will contain other ions in addition to the ion being measured and the ionic strength of the samples may be significantly higher than that of the standards. Thus there will be an incompatibility between the calibration line and the measured samples leading to errors in the interpolated results.

It is possible to calculate the activity coefficient for the primary ion in a simple pure solution where the composition and relative concentration of all the ions is known. Thus the measured activity can be converted into concentration results for simple solutions - but in most practical applications this is not possible, or very difficult and time-consuming.

The Ionic Strength (I) can be calculated from I = 0.5 x Sum (ci x Zi²)
Where c is the concentration in Moles and Z is the valency.

The Activity Coefficient (f) can then be found from:
-Log(f) = [(0.51 x Z² x SQR(I)) / (1 + (3.29 x d x SQR(I))] - (0.1 x Z² x I)
Where: Z = the ionic charge, I = the ionic strength of the solution, d = the ionic radius in nanometres.

Note that it is generally accepted that this formula is only accurate up to about I = 0.1 Molar. At higher ionic strength other factors come into play which make the calculation of activity coefficients virtually impossible and thus most ISEs cannot be used reliably above this concentration.

The table below can be used as a guide in deciding whether or not the samples to be measured have sufficiently low Ionic Strength that the activity effect can be ignored.

Also see: Ionic Strength and activity calculator (MS Excel file)

Activity Coefficients and likely error (i.e. under-estimate) in concentration measurement for different Ionic Strength Solutions.

Ion	Valency	Ionic	Ionic Strength	Activity	% error in
	(Z)	Radius(nm)	(mol/L)	Coefficient	Concentration
NH4, Ag	1	0.25	0.5	0.664	34%
			0.1	0.762	24%
			0.01	0.899	10%
			0.001	0.965	4%
			0.0001	0.988	1%
K, Cl, Br, I, CN, NO2, NO3	1	0.3	0.5	0.688	31%
			0.1	0.771	23%
			0.01	0.901	10%
			0.001	0.965	4%
			0.0001	0.988	1%
F, ClO4, SCN	1	0.35	0.5	0.710	29%
			0.1	0.779	22%
			0.01	0.902	10%
			0.001	0.965	3%
			0.0001	0.988	1%
Na	1	0.45	0.5	0.748	25%
			0.1	0.795	21%
			0.01	0.905	10%
			0.001	0.965	3%
			0.0001	0.989	1%
Pb, CO3	2	0.45	0.5	0.313	69%
			0.1	0.399	60%
			0.01	0.670	33%
			0.001	0.869	13%
			0.0001	0.955	5%
Ba, Cd, Hg, S	2	0.5	0.5	0.341	66%
			0.1	0.413	59%
			0.01	0.674	33%
			0.001	0.869	13%
			0.0001	0.955	5%
Ca, Cu	2	0.6	0.5	0.396	60%
			0.1	0.439	56%
			0.01	0.682	32%
			0.001	0.870	13%
			0.0001	0.955	4%

For samples with high ionic strength, there are five possible methods which can be used to avoid the error introduced by the difference between activity and concentration.

1) Bring the ionic strength to the same level in both the calibrating standard solutions and the samples by adding a suitable Ionic Strength Adjustment Buffer (ISAB) to both - see below, section c).

2) Dilute the samples to a level where the ionic strength effect is insignificant – but make sure that the detected ion is still within the linear range of the electrode.

3) For samples with complex but known matrix, make up the standards in a similar solution which does not contain the detected ion, or any which would interfere with the measurement.

4) Use the Activity Coefficient to calculate the concentration from the activity. As noted above, the activity coefficient can be calculated for simple solutions with known concentrations of all the ions, but this is not possible in many practical applications, where the samples may have a complex or unknown matrix.

5) Use the Standard Addition (or Sample Addition) Method where the voltage is measured before and after a measured small volume of standard (or sample) is added to a larger measured volume of sample (or standard) and the ionic strength is not altered significantly.
See later, Chapter 10, and www.nico2000.net/datasheets/staddl.html.

c) Ionic Strength Adjustment Buffers.

The most common way of overcoming the effect of the variable ionic strength of the solutions is to attempt to make them all the same. Theoretically, this can be done by adding, equally to all standards and samples, another solution of high ionic strength which does not contain the ion to be measured, or any likely interferent. These solutions are known as Ionic Strength Adjustment Buffers (ISAB). The idea is that they are added in sufficient quantity to completely swamp the ionic effects of the host solutions and hence give a uniform ionic strength in all samples and standards. In this case the straight-line calibration curve can be constructed using concentration units and the unknown concentrations can be read directly from the calibration graph. Note that there is no need to recalculate the standard concentrations after adding ISAB as long as all standards and samples are treated in the same way.

It must be noted, however, that most recipes for the addition of ISAB only produce an increase in ionic strength of 0.1M and thus will only be effective if the IS of the original sample is much lower than 0.1M. Furthermore, the difference between activity and concentration is relatively small at low Ionic strengths and can often be ignored in many practical applications – see table above.

Most ISE suppliers also supply ISABs. These vary in composition depending on the detected ion and occasionally contain other components which actively suppress interfering ions and/or control the pH value. In many cases the composition of these solutions are carefully guarded ‘trade secrets’ and the reagents are simply labelled as e.g. "ISAB for nitrate electrode".

d) Potential Drift.

The effect of potential drift can easily be seen if a series of standard solutions are repeatedly measured over a period of time. The results show that the difference between the voltages measured in the different solutions (i.e. the electrode slope) remains essentially the same but the actual value generally drifts in the same direction by several millivolts (ie, not random variation or instability). This is somewhat surprising in view of the fact that many ISE specifications quote a potential drift of less than 1 mV per day. However, it must be noted that this figure is an attempt to define the drift which is attributable to the ISE alone - but this is impossible to measure directly due to variations in other potential differences in other parts of the measuring system. The most significant of these is the liquid junction potential of the reference electrode.

Although the LJP does not drift significantly once stabilised in a solution at constant temperature, it can change by several millivolts every time a reference electrode is immersed in a new solution, or even re-immersed in the same one. Thus the quoted ISE drift factor only applies when the ISE and reference are constantly immersed in a 1000 ppm solution at constant temperature. Furthermore, constantly removing and replacing an ISE in different solutions will produce hysteresis (or memory) effects, the extent of which depends on the relative concentrations of the new and old solutions. Thus if the same solution is re-measured after measuring a different one it cannot be expected to give exactly the same millivolt reading the second time.

In view of these various sources of potential drift, some manufacturers include a more realistic figure of 3 mV per 8 hour working day in the electrode specifications.

For most ISE applications these effects are insignificant when compared to the overall reproducibility and accuracy requirements, but, for the most precise work, steps must be taken to try to minimise these effects - see Chapter 8.

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