Beginners Guide to ISE measurement. Chapter 11.
a) General Discussion
The accuracy (how close the result is to the true value) and precision (= reproducibility; i.e. how close are a series of measurements on the same sample to each other) of ISE measurements can be highly variable and are dependent on several factors. The concentration is proportional to the measured voltage and so any error in measurement will cause an error in the concentration, but this is not directly proportional. It depends on the slope of the calibration line. For mono-valent ions with a slope of around 55 millivolts per decade of concentration, an error of 1 mV in measuring the electrode potential will cause a 4% error in the concentration, whereas for di-valent ions, with a slope of around 26, the error will be more like 8% per mV. It must also be noted that the slope becomes less at the lower end of the concentration range, in the non-linear area, and hence the error per mV can be even greater at low concentrations. Thus it is important to use a meter which is capable of measuring the millivolts accurately and precisely. With modern meter technology this is not normally the limiting factor, although for the most precise work it can be beneficial to adopt multiple-sampling techniques (i.e. by using an integrating voltmeter or computer interface) in order to ensure the most reliable voltage measurements.
Apart from the accuracy and precision of the measuring device (meter or computer interface), the most important factors in achieving the most precise
results is controlling the electrode drift and hysteresis (or memory), and limiting the variability in the Liquid Junction Potential of the reference electrode, so that
the measured voltage is reproducible. The amount of the drift and
hysteresis effects can vary significantly between different ions and different
electrode types, with crystal membranes being generally more
stable than PVC - techniqes for controlling or minimising drift
and hysteresis are described elsewhere in this work (Chapter 9).
The accuracy of the results is affected by several other factors:
By taking special precautions to overcome drift problems (such as frequent recalibration and ensuring that you wait for stable readings, or read after a regular time interval), and by adding special ISABs to equalise activity effects and remove interfering ions, direct potentiometry can give very reasonable results (reproducibility of ± 2 or 3%, one standard deviation, and accurate within these precision limits). Even without taking these precautions, it is possible to achieve satisfactory reproducibility and accuracy (± 10 to 15%) for many applications where the highest accuracy is not necessary and ionic strength and interfering ions are not a problem.
b) Reproducibility Experiments using an Ammonium Electrode.
Some of the suggestions in the foregoing discussion, and the levels of accuracy and precision achievable with careful work, can be illustrated with the results of some experiments conducted by the author. Reproducibility tests were carried out using an ELIT 8 mm diameter, solid-state ammonium electrode (PVC membrane) with a lithium acetate double junction reference electrode and pure ammonium solutions (no ISAB). Standard solutions containing 1 ppm and 10 ppm NH4+ were used for calibration and a 5 ppm solution was used as the test sample. Measurements were made after immersing the electrodes in approximately 50 mls of solution in a 100 ml beaker, swirling the solution for 5 secs. then leaving to stand for 20 secs. Each millivolt measurement was the average of ten readings taken at one second intervals. The electrodes were rinsed with a jet of de-ionised water, then soaked in a beaker of water for twenty seconds, then dabbed dry with a low-lint tissue between each measurement. The solutions were measured in the sequence 1 ppm, 5 ppm, 10 ppm, and this pattern was repeated six times. The data were obtained using a meterless PC interface and specially written software.
For this experiment, the concentration results were calculated with an EXCEL spreadsheet using the Nernst equation in the standard form for a straight line: y = mx + c.
y is the measured voltage,
m is the electrode slope
(calculated from the two-point calibration data: (V1-V2)/ ((Log ppm1) - (Log ppm2))),
x is the logarithm of the concentration in the sample,
c, the intercept on the y axis, is Eo.
The experimental data were processed in several different ways:
1) Using only the first measurement of the two standards to define the slope and intercept, six measurements of the 5 ppm sample, taken over approximately half an hour, gave an average of 4.71 ± 0.14 ppm (±2.96% one standard deviation). However it was noticeable that successive measurements gave progessively lower values due to electrode drift after calibration (causing a difference of nearly 8% between the highest and lowest results).
2) The drift effect was compensated for by recalculating each result using different values for the slope and intercept as defined by the standards measured immediately adjacent to each sample measurement. This produced a significant improvement in the reproducibility and only a random variation in the results rather than a progressive drift downwards. This clearly demonstrates the importance of measuring samples soon after calibration. The average concentration this time was 4.90 ± 0.06 ppm (±1.20%, 1 S.D.) Although remarkably precise and very close to the true value, the accuracy of this average is not quite within the precision limits. As noted above, this can probably be explained by variation in the electrode slope and this suggestion is supported by examining the individual slope values which can be calculated from the various measurements. The average value for six determinations of the slope between 1 and 5 ppm was 55.92 ± 0.92 whereas that between 5 and 10 ppm was 58.21 ± 0.78; i.e. there is a significant difference in slope between the two adjacent ranges.
3) A third method of calculating these results, using the slope defined by the first calibration for all samples but a different intercept value as given by each successive two-point calibration, was less satisfactory and gave 4.87 ± 0.12 ppm (± 2.35%) which is only slightly better than the results using only a single calibration at the beginning. Thus these data would appear to suggest that the effect of electrode drift is more significant in producing changes in the measured slope between different sample measurements rather than producing a change in the calculated value for the intercept. This conclusion is also borne out by examining the individual calibration data. Whereas the average slope between 1 and 10 ppm was 56.74 ± 0.51 (± 0.90%) for six successive measurements and these showed a gradual drift downwards (57.49, 57.04, 56.84, 56.64, 56.49, 55.98) the associated intercept calculations showed a more random distribution and gave a much more precise average value of 346.18 ± 0.26 mV (± 0.07%).
c) Reproducibility of Chloride Measurements.
A second experiment using the same techniques as above, but with a chloride (crystal membrane) electrode and calibration standards of 25 and 250 ppm also yielded very impressive results. Eight measurements of a 100 ppm test solution gave an average of 95.4 ± 0.6 ppm (± 0.63%) when two-point calibrations were made immediately prior to each sample measurement. Again the relatively poor accuracy is probably due to the calibration standards being relatively far from the measured sample and thus the calculated slope was probably not exactly correct for the 100 ppm range.
d) Standard Addition and Sample Addition Methods
These methods can potentially yield even more accurate and precise results than direct potentiometry because the calibration and sample measurement stages are made essentially at the same time and in the same solution (so that Ionic Strength and temperature differences are not significant) - and the electrodes remain immersed throughout the measurements so that hysteresis, memory, and variations in the reference electrode liquid junction potential are eliminated. They are paticularly useful for samples with high ionic strength or a complex matrix. See Standard & Sample Addition Methods for a full description and experimental results for precision and accuracy.
e) Conclusions from the Experimental Data.
These experimental results demonstrate that in order to obtain the best possible accuracy and precision, it is important to measure samples soon after calibration and to use standard solutions that closely bracket the expected range of sample concentrations. Furthermore, for direct potentiometry measurements, it is best to make a full two-point recalibration every time, in order to obtain the most precise value for the slope, rather than just making a single point recalibration and assuming that the slope is constant. This is not necessary for Standard and Sample Addition techniques because of the possibility of recalculating the results for a known standard to "fine tune" the slope measurement in the middle of the concentration range expected for the samples.
These results show that it
is possible to obtain accuracy and precision levels of better
than ± 3% fairly easily, and better than ± 2% by making more
frequent calibrations or by using Standard or Sample Addition techniques (better than ± 1% for some crystal
membrane electrodes). Thus it has been shown
that, with careful use and a full consideration of all the
limiting factors, ISE technology can be compared favorably with
other analytical techniques which require far more sophisticated
and costly equipment.