Beginners Guide to ISE Measurement. Chapter 3.

BASIC THEORY OF ISE MEASUREMENTS.

Also see: Introduction to Ion Analysis

Ion-Selective Electrodes are part of a group of relatively simple and inexpensive analytical tools which are commonly referred to as Sensors. The pH electrode is the most well known and simplest member of this group and can be used to illustrate the basic principles of ISEs.

This is a device for measuring the concentration of hydrogen ions and hence the degree of acidity of a solution - since pH is defined as the negative logarithm of the hydrogen ion concentration;

i.e. pH=7 means a concentration of 1x10^-7 moles per litre. (To be more precise, the term ‘concentration’ should really be replaced by ‘activity’ or ‘effective concentration’. This is an important factor in ISE measurements. The difference between activity and concentration is explained in more detail later (Chapter 6), but it may be noted here that in dilute solutions they are essentially the same. Nevertheless, in order to avoid confusion, the more familiar term (concentration) will be used in this section.)

The most essential component of a pH electrode is a special, sensitive glass membrane which permits the passage of hydrogen ions, but no other ionic species. When the electrode is immersed in a test solution containing hydrogen ions the external ions diffuse through the membrane until an equilibrium is reached between the external and internal concentrations. Thus there is a build up of charge on the inside of the membrane which is proportional to the number of hydrogen ions in the external solution.

Because of the need for equilibrium conditions there is very little current flow and so this potential difference can only be measured relative to a separate and stable reference system which is also in contact with the test solution, but is unaffected by it (see later for a discussion of reference electrodes). A sensitive, high impedance millivolt meter or digital measuring system must be used to measure this potential difference accurately.

The potential difference developed across the membrane is in fact directly proportional to the Logarithm of the ionic concentration in the external solution. Thus, in order to determine the pH of an unknown solution, it is only necessary to measure the potential difference in two standard solutions of known pH, construct a straight line calibration graph by plotting millivolts versus pH (= - Log [H⁺]) then read off the unknown pH from the measured voltage.

In order to measure the electrode potential developed at the ion-selective membrane the ISE/pH electrode must be immersed in the test solution together with a separate reference system and the two must be connected via a millivolt measuring system. At equilibrium, the electrons added or removed from the solution by the ISE membrane (depending on whether it is cation or anion sensitive) are balanced by an equal and opposite charge at the reference interface. This causes a positive or negative deviation from the original stable reference voltage which is registered on the external measuring system.

The relationship between the ionic concentration (activity) and the electrode potential is given by the Nernst equation:

E = E⁰ + (2.303RT/ nF) x Log(A)

Where E = the total potential (in mV) developed between the sensing and reference electrodes.

E⁰ = is a constant which is characteristic of the particular ISE/reference pair.

(It is the sum of all the liquid junction potentials in the electrochemical cell, see later)

2.303 = the conversion factor from natural to base10 logarithm.

R = the Gas Constant (8.314 joules/degree/mole).

T = the Absolute Temperature.

n = the charge on the ion (with sign).

F = the Faraday Constant (96,500 coulombs).

Log(A) = the logarithm of the activity of the measured ion.

Note that 2.303RT/nF is the Slope of the line (from the straight line plot of E versus log(A) which is the basis of ISE calibration graphs) and this is an important diagnostic characteristic of the electrode - generally the slope gets lower as the electrode gets old or contaminated, and the lower the slope the higher the errors on the sample measurements.

For practical use in measuring pH, it is not normally necessary for the operator to construct a calibration graph and interpolate the results for unknown samples. Most pH electrodes are connected directly to a special pH meter which performs the calibration automatically. This determines the slope mathematically and calculates the unknown pH value for immediate display on the meter.

These basic principles are exactly the same for all ISEs. Thus it would appear that all can be used as easily and rapidly as the pH electrode: i.e. simply by calibrating the equipment by measuring two known solutions, then immersing the electrodes in any test solution and reading the answer directly from a meter. Whilst it is certainly true that some other ions can be measured in this simple fashion, it is not the case for most. Unfortunately, some ISE advertising material tends to gloss over this fact and gives the reader a rather rosy view of the capabilities of this technique. There are several factors which can cause difficulties when ISE technology is applied to the measurement of other ions. These are listed below and discussed in more detail in later sections. Nevertheless, it must be stressed here that as long as these difficulties are recognised and steps are taken to overcome them, then ISEs can still be a very useful and cost-effective analytical tool.

i) In contrast to the pH membrane, other ion-selective membranes are not entirely ion-specific and can permit the passage of some of the other ions which may be present in the test solution, thus causing the problem of ionic interference.

ii) Most ISEs have a much lower linear range and higher detection limit than the pH electrode. Many show a curved calibration line in the region 10^-5 to 10^-7 moles/l and very few can be used to determine concentrations below 1x10^-7 moles/l. Thus, for low concentration samples, it may be necessary to construct a calibration graph with several points in order to define the slope more precisely in the non-linear range.

iii) The calculation of ionic concentration is far more dependent on a precise measurement of the potential difference than is the pH, because the pH depends on the order of magnitude of the concentration rather than the precise value. For example it would take an error of more than 5 millivolts to cause a change of 0.1 pH units, but only a 1 millivolt error will cause at least a 4% error in the calculated concentration of a mono-valent ion and more than 8% for a di-valent ion. This is because the theoretical value for the slope at 25°C is 59.2 for mono-valent ions and 29.6 for di-valent ions. In practical application, however these slopes can vary considerably because of variations in temperature, deviations from "ideal" behaviour, and minor impurities or contamination of the ion-selective membrane, or if samples are measured near the detection limit of the electrode, in the non-linear range. The critical factor is not so much the actual value of the slope but that this should be as high as possible and remain constant over the range of concentrations and the time period required for the analyses. Thus, when measuring other ion concentrations, it is essential to take extra precautions to minimise any errors in the measurement of the electrode potential.

iv) For ion concentration measurements, steps must be taken to minimise the effect of the Ionic Strength of the sample. This is because pH is defined as the log of the Activity of the ion (which is measured directly by any ISE) but most measurements of other ions require the actual concentration, which can differ significantly from activity in samples with complex matrices and high Ionic Strength.

v) It is more usual to plot a calibration graph using the ionic concentration with a logarithmic scale on the X-axis rather than the pX factor (analogous to pH) on a linear axis.

vi) Some ISEs will only work effectively over a narrow pH range.