Ion-selective Measurement (ISE)

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Ion-selective

Measurement

(ISE)

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Table of contents

1 Basic information

1.1 Introduction to ion-selective measurement1.2 Reference electrode design and principle of operation1.3 Concentration and activity1.4 Diffusion voltage, diffusion potential1.5 Stirrer1.6 Selectivity

2 Description of ion-selective electrodes

2.1 Solid-state electrodes2.2 PVC membrane electrodes2.3 Gas-sensitive electrodes

3 Calibration

3.1 One-point calibration3.2 Two-point calibration3.3 Multi-point calibration

4 Sample preparation

4.1 pH value4.2 Interfering ions4.2.1 Precipitation4.2.2 Complexing4.2.3 Cooking4.3 Trace analysis4.3.1 Shifting the nonlinear region of the characteristic curve4.3.2 Extraction4.3.3 Ion exchangers

5 Measurement methods

5.1 Direct potentiometry5.2 Incremental methods5.2.1 Standard addition5.2.2 Double standard addition5.2.3 Standard subtraction5.2.4 Sample addition5.2.5 Sample subtraction5.2.6 Standard addition with blank value correction5.3 Titration methods5.3.1 Direct titration5.3.2 Indirect titration5.3.3 Back titration5.3.4 End point indicator

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6 Maintenance and special information

6.1 Electrode contamination6.2 Cleaning the electrodes6.3 Storing the electrodes6.4 Faults during measurement and calibration6.5 Measuring ranges

7 Bibliography

8 Appendix: Interfering Ions

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1 Basic information

1.1 Introduction to ion-selective measurement

Ion-selective measurement is an analytical method that frequently offers advantages over othermethods. The most important advantages are:

1. Relatively low purchase costs2. Rapid arrival at measuring results3. Use in turbid and coloured solutions in which other methods such as photometry cannot

be applied.

This list of advantages could easily be extended.Of course, this method also has some disadvantages over other methods. At an error rate of 2-5%,the measuring accuracy is not particularly high. Nevertheless, it is perfectly adequate for manyapplications. Moreover, the method unfortunately cannot be used for every substance. It generallydoes not work for organic substances. However, it is particularly well suited for measuring ions, i.e.for the measurement of salts.

Ions, the components of salts, are electrically charged particles. When an electrode is introducedinto an ion solution, the ions interact with the electrode surface. Interaction means that ionsaccumulate on the electrode surface. This can be a two-part adsorption of the ions. Alternatively,ions may penetrate the electrode material. Finally, ions may become detached from the electrodeand enter into the solution. An electrode is an electrical conductor that is immersed in the solutionat one end and connected to a millivoltmeter at the other. In its simplest form, it is nothing morethan a simple metal wire. Incidentally, substances that form free mobile ions in aqueous solutionsare called electrolytes. Often this term is also used to refer to the ion solution itself.

What is the significance of the interaction of the ions with the electrode? Ions are electricallycharged particles. They carry an electrical charge onto the electrode, thereby generating a voltagebetween the electrode and the solution. In the ion-selective measuring technique, as shown below,the magnitude of this voltage is a function of the concentration of the ion to be measured.However, our measuring device in its present form is not yet capable of measuring a voltage at allsince the second input of the device has not yet been defined. It would be ideal if we could simplyconnect the second input directly to the solution. However, this cannot be accomplished withoutthe use of an electrical conductor. If we were to use such a conductor and immerse it in thesolution, the same processes that take place at the surface of the first electrode would also occurat this conductor. Experience in the field has provided us with a similar solution. The second inputis connected to a reference electrode. Essentially, this reference electrode operates in a mannersimilar to that already described above. However, it exhibits a constant voltage difference betweenthe electrolyte output, with which the reference electrode is immersed in the solution, and theconnection to the device. Thus, we have a fixed reference point with respect to which we canmeasure the voltage at the first electrode.

If the surface of the first electrode is now coated with an ion-selective substance, i.e. with asubstance that only interacts with a specific ion species, we then have the basic componentneeded for working with the ion-selective measuring technique. The ion-selective electrode and thereference electrode are collectively known as an electrode. If they are physically separated, theyare referred to as a two-probe electrode. If they are combined in a single probe, they are known asa combination electrode.

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As already indicated above, ion-selective measurement is about measuring voltage changes inorder to draw conclusions about ion concentrations. To do so, we need to establish a physical-mathematical relationship between these two parameters. This is provided by the Nernst equationas the expression:

clognFRT303,2EE 0 +=

E Measured voltage between the measuring and reference electrodes E0 Measured voltage between the measuring and reference electrodes at a concentration of c

= 1R Universal gas constant (R = 8.314 Joule mol-1 K-1)T Absolute temperature in Kelvin (the absolute temperature is defined as

T = 273.15 + t. The units are Kelvin K. t is the numerical value of the measuredtemperature in °C.

F Faraday constant (F = 96485 C mol-1)n Electrical ionic charge c Ion concentration

R and F are constants and therefore not of further concern. Since temperature appears in the Nernst equation, the measured voltage is a function of thetemperature.The ionic charge n influences a parameter we call the electrode slope.The Nernst slope is given by the expression:

nFRT303,2

Depending on the ionic charge, the slope has the following values in millivolt at 20°C and 25°C:

Ionic charge Slope 20°C Slope 25°C Examples+2 29.08 29.58 Copper (Cu2+), lead (Pb2+)+1 58.16 59.16 Sodium (Na+), potassium

(K+)-1 -58.16 -59.16 Fluoride (F-), chloride (Cl-)-2 -29.08 -29.58 Sulphide (S2-)

In practice, many electrode types actually achieve these slopes. Only a few do not. If the slopedecreases over time, this generally indicates ageing of the electrode. Finally, we should discussthe expression log c. While it may be difficult for some readers to understand this expression, thisshould not be grounds for rejecting the ion-selective measuring technique. After all, log c is usuallynot needed when performing standard measurements. Also, any good calculator today is capableof calculating the value.Example: Using a calculator that features the log function, enter the numerical value for concentration c andpress the log key. The number that appear on the display is the value of log c and can besubstituted in for log c in the Nernst equation.(A brief remark is in order regarding concentration c: For small and very small concentrations, theNernst equation applies without limitations. Deviations arise for larger concentrations. Later weshall see that this problem can be solved by introducing the activity parameter.)

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We will now try to plot the characteristic curve of an ion-selective electrode. This will make it easierto perform analyses later on. Also, this task is a good example that will help you understand thismeasurement technique.The characteristic curve of an ion-selective electrode represents the relationship between voltageE and concentration c. In other words, it is a graphic representation of the Nernst equation.Because of the log c expression, it is not practical to plot the concentration c itself on an axis. It ismuch more convenient to use the value of log c. The plot then takes on the form of a straight line.This procedure is easy to master. Using semi-logarithmic paper, we plot log c on the logarithmicaxis and voltage E on the other. An example illustrates how this is done. Now let us move on to the practical part. We will record the characteristic curve of a bromideelectrode. To do so, we require the following equipment and chemicals:

Instrumentation1 millivoltmeter (resolution of 0.1 mV, input impedance 1012 )1 bromide electrode (BR 500, Br 501)1 reference electrode (R 502)1 stirrer with stirrer bar1 electrode stand6 plastic beakers (150 ml volume)8 graduated flasks (100 ml volume)1 pipette (1 ml volume)1 pipette (10 ml volume)

Bromide standard with 10000 mg/l bromideConducting salt solution: solution of 5 mol/l or 425 g/l sodium nitrate(The reason for using conducting salt will be explained later on.)

We dilute the bromide standard to prepare two additional standard solutions, one of 100 mg/lbromide and the other of 1 mg/l bromide.

Preparation of the 100 mg/l bromide standard

Add 1 ml of 10000 mg/l bromide standard to a 100 ml graduated flask. The flask is filled to thecalibration mark with deionized water and mixed well.

Preparation of the 1 mg/l bromide standard

Add 1 ml of 100 mg/l bromide standard to a 100 ml graduated flask. The flask is filled to thecalibration mark with deionized water and mixed well.Measuring solutions are prepared in a similar manner according to the following table:

Concentration ofmeasuring solution

mg/l bromide

Volume ofstandard solution

ml

Standardsolution

mg/l bromide

Volume of conducting salt solution

ml

Measuredvalues

mV1000 10 10.000 2 -73.7

100 1 10.000 2 -15.810 10 100 2 43.3

1 1 100 2 101.90.1 10 1 2 152.8

0.01 1 1 2 170.3

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To prevent mistakes, the preparation of the 1000 mg/l bromide measuring solution is describedhere in detail.

Preparation of the 1000 mg/l bromide measuring solution

Add to a 100 ml graduated flask:10 ml 10000 mg/l bromide standard2 ml conducting salt solutionFill the flask to the calibration mark with deionized water and mix.

The other solutions are prepared in a similar manner according to the table. The measuringsolutions are now poured into plastic beakers and placed on the stirrer one after the other to bemeasured. The electrodes connected to the millivoltmeter are dipped into the solution with the aidof the electrode stand. The solution is stirred while readings are taken. The reason for stirring isdescribed later on.The measured value usually drifts at the beginning of a particular measurement. After some time,the readings stabilise and the final value can be read and recorded before the next solution ismeasured in a similar manner. To avoid transferring substances from one measurement solution tothe other, the electrodes are rinsed with deionized water after each measurement and the residualwater is blotted with a soft paper towel. Surely not every reader will be able to reproduce thesesteps immediately. Therefore, the table also contains the values we ourselves measured inmillivolts.

How can we graphically represent the characteristic curve of the bromide electrode?A look at the semi-logarithmic graph paper reveals that the lines have a 1-mm spacing in onedirection only. The voltage values are plotted in this direction, i.e. values of approx. –80 to approx.180 mV. We recommend that 1 mm be used to represent 1 mV. In the other direction the linespacing varies. This is the logarithmic scale. The lines are arranged in such a way that when theconcentration is plotted, the log c logarithm automatically generates a linear plot. This is preciselywhat we require and why the line spacing varies and repeats periodically. The same applies to the plotted numbers 2 to 10. For each number 10, we draw a short line andwrite below it the concentration of our measuring solutions, beginning from the right and movingalong in ascending order. We can now plot the measuring points as usual. Fig. 1 shows this graph.

Figure 1: Characteristic curve of a bromide electrode as a function of the decadic logarithm ofthe concentration

Characteristic curve of bromide electrode

170.3152.8

101.9

43.3

-15.8

-73.7-100

-50

0

50

100

150

200

0.01 0.1 1 10 100 1000

log c

Volta

ge m

V

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The following information can be gathered from this plot:

1. The plotted points for concentrations 1, 10, 100 and 1000 mg/l bromide lie in what is almost astraight line. This is the strictly linear part of the characteristic curve. The voltage differencebetween neighbouring points and, in general, between the concentrations, which have a ratioof 1 to 10, is 58.4 mV. We already encountered a value of this magnitude for the Nernst slope.In this case, however, it is referred to as the electrode slope. Mathematically, the value of thisslope is negative, i.e. S = -58.4 mV. This is easy to remember. All negatively charged ions, also known as anions, have negativeslopes. A positive slope can also occur. The characteristic curve is then rotated by approx. 90°.This is the case for all positively charged ions, which are also called cations.

2. The measuring points for concentrations 0.1 and 0.01 mg/l bromide no longer lie on the straightline. Thus, the characteristic curve has a nonlinear part. All ion-selective electrodes exhibit thisphenomenon. The reason for this behaviour is found in the electrode structure. The ion-selective membrane usually already contains the ion that is to be measured. Unfortunately,there are no perfectly insoluble substances in this field. Thus, a small quantity dissolves out ofthe membrane and introduces into the solution precisely that ion which is to be measured. Ifthe measured concentrations are low, the magnitude of the dissolved ion concentration issignificant. There is also another bothersome phenomenon found within this measuring range.The stabilisation period of the voltage can become extremely long. Frequently, one cannot besure at what point the final value has actually been reached.

3. The characteristic curve can be used to determine the concentration of an unknown sample.The sample is usually prepared in the same manner as the solution for recording thecharacteristic curve. In this particular case, 2 ml conducting salt solution are added to 100 mlsample. The voltage of the solution is determined during stirring. The voltage reading iscompared to the values in the plot of the characteristic curve and the correspondingconcentration is found. This is done by drawing a line parallel to the concentration axis from thevoltage value to the characteristic curve. At the point of intersection, a perpendicular is droppedto the concentration axis. The point of intersection with the concentration axis represents theconcentration value we are looking for.

To be precise, this value is actually the concentration of the measuring solution rather than of thesample itself. The sample was diluted. By performing a simple calculation, we can arrive at theconcentration of the sample. For example, let us assume we have a measured value of 25 mg/lbromide. Our measuring solution had 102 ml and the sample had 100 ml. Thus, the absolutebromide quantity in the plastic beaker is 25 mg/l * 0.102 l = 2.55 mg bromide. A 100 ml sampletherefore contains a concentration of 2.55 mg/0.1 l = 25.5 mg/l bromide.

Even if we haven’t yet done so practically, we have at least theoretically carried out the firstanalysis using the ion-selective measuring technique. Incidentally, when this measuring techniquewas first developed, it was used in just this way. Only later did some companies build the first ionmeters, which eliminated the need for recording measuring points. Today, modern ion meters arehighly advanced and simplify the task for the user by offering many additional functions. However,even these devices require that at least two points of the characteristic curve be recorded, i.e. twosolutions of know concentrations are needed. The user must enter these concentrations into thedevice. The device can then measure the corresponding voltages and determine the slope. Theslope is generally indicated on the display. This entire procedure is referred to as calibration. In thisparticular case, it is also known as a two-point calibration. Most users employ this method. Youshould proceed in such a way that the expected sample concentration lies between the twocalibration concentrations. This ensures that measurement imprecisions will have the lowestimpact on the results.

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When using new ion-selective electrodes for the first time, voltage stabilisation may be verysluggish at first. This does not necessarily mean that the electrode is defective. Rather, theelectrode first requires conditioning, meaning that it must be kept in a diluted standard solution forseveral hours. This builds a so-called solvent layer on the membrane surface that acceleratesvoltage stabilisation. Of course, there is a lot more to say on many of the topics discussed here.There is also much to add from the point of view of physics and chemistry. Up to now we have refrained from touching on these topics to give the reader a chance tounderstand the basics of ion-selective measurement without the distraction of extraneousinformation. On the following pages, we now make up for this lapse.

1.2 Reference electrode design and principle of operation

The most important property of a reference electrode has already been mentioned. At a fixedtemperature, it guarantees that the voltage between the measuring device connection and theelectrolyte outlet remains constant. The electrolyte will be referred to as the diaphragm from hereon in. A constant voltage is indispensable for being able to measure voltage changes at the ion-selective electrode. The function of the diaphragm is to provide the necessary electrical contactwith the measuring solution. This is established by an electrolyte passing through the diaphragm.There are several types of diaphragms, including the ground diaphragm, ceramic diaphragm,pinhole diaphragm and platinum wire diaphragm.

Ion-selective measurement usually employs the ground diaphragm. It has a relatively high flow rateand is easy to clean. It is also the diaphragm type that most reliably provides the defined electricalconditions with respect to the measuring solution. This issue is further discussed under DiffusionPotential or Diffusion Voltage. Since electrolyte continuously flows out of the reference electrode, itmust be ensured that there is always an adequate quantity of electrolyte inside the referenceelectrode. When performing measurements, the electrolyte level within the reference electrodeshould be about 1 cm higher than the level of the measuring solution.

How does the reference electrode generate a constant voltage? In the silver-silver chloridereference electrode, a silver wire coated with silver chloride plays a very important role. It is usuallyimmersed in a chloride solution. Depending on the chloride concentration, a constant silver ionconcentration is generated in the chloride solution (in a chemistry book, you will find this conceptunder solubility product). In accordance with the Nernst equation, the silver concentrationgenerates a constant voltage between the chloride solution and the silver wire. The processes thattake place at the silver wire have already been described in the introduction. This is the design of asimple reference electrode. For many applications, it does a good job of accomplishing therequired tasks.

However, what happens if we would like to measure small chloride ion concentrations? Then the ions that flow through the diaphragm into the solution are precisely those that we want tomeasure. Obviously, this does not allow for accurate measurement. In practice, therefore, thereference electrode consists of two parts. The actual reference electrode is contained in an internalchamber. Beyond it there is an additional diaphragm that leads to the outer chamber, which in turncomes into contact with the measuring solution through the ground diaphragm.The internal chamber has a chloride as an electrolyte (internal electrolyte, usually coloured), whilethe outer chamber contains an electrolyte of your choice (outer electrolyte). In this way we canselect the electrolyte that flows into the measuring solution to match the measuring task at hand.The outer chamber is also called the bridge or electrolyte bridge, and the electrolyte is alsoreferred to as the bridge electrolyte.

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As already indicated, the voltage between the device connection and the ground diaphragm is onlyconstant at a fixed temperature. A change in temperature brings with it a change in the voltage.This change is described by the Nernst equation and by the fact that the solubility of the silverchloride on the silver wire is temperature-dependent.

Discharge electrodeReference electrolyte solution

Internal bridge

Bridge electrolyte solution

Outer bridge

Figure 2: Reference electrode

Unfortunately, all voltages that contribute to the electrode voltage are temperature dependent. Wehave already noted the temperature-dependence of the electrode slope of the measuringelectrode. To keep measurement errors caused by temperature fluctuations to a minimum, there isa basic rule that says the calibration temperature and the measuring temperature may not differ bymore than 2°C. In modern WTW ion meters, the display blinks if this limit is exceeded. In additionto the silver-silver chloride electrode described here, which is the electrode type most commonlyused today, other types of reference electrodes are also available. They differ in the nature of theelectrochemical reactions on which they are based. The most familiar types are the calomelelectrode and the thalamide electrode.

The normal hydrogen electrode occupies a special position among electrodes. It is primarilyemployed in scientific research. It consists of a platinum plate that is coated with platinum blackand immersed in hydrochloric acid with a concentration of 1 mol/l. Pure hydrogen gas at apressure of p = 1 bar is bubbled over the electrode. By definition, this type of reference electrodehas a potential of 0 mV at all temperatures. Because it is difficult to handle, it is not used forstandard field work. Instead, either of the following electrodes are used: the silver-silver chlorideelectrode, which at 3 mol/l potassium chloride and a temperature of 25°C has a voltage of 208 mVwith respect to the normal hydrogen electrode; or the calomel electrode, which at a temperature of25° and a saturated potassium chloride solution exhibits a voltage of 244 mV with respect to thenormal hydrogen electrode.

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If a voltage measured against a particular reference electrode is to be converted to thecorresponding value for the normal hydrogen electrode, the following simple conversion equationis used:

fRegemH UUU +=

UH = Voltage that would be measured using the normal hydrogen electrodeUGem= Measured voltage with respect to the reference electrode actually in use URef = Voltage of the reference electrode actually in use with respect to the

normal hydrogen electrode

It is of no relevance which type of reference electrode is actually used for the ion-selectivemeasurement. It has no effect on the nature of the characteristic curve. The use of differentreference electrode merely causes the characteristic curve to shift to larger or smaller voltagevalues.

1.3 Concentration and activity

We have already established that for low ion concentrations, the Nernst equation yields the correctvoltage values. (This of course does not apply to concentrations in the nonlinear region of thecharacteristic curve). The calculated values closely coincide with the measured values. Whenmeasuring higher concentrations, however, deviations begin to appear. The ion solutions thenbehave as though a part of the ions were no longer present. There is an apparent loss in ions. Thisis a common phenomenon in chemistry. It is related to the fact that ions in high concentrationsimpede each other. To eliminate this source of error, a new entity, namely the activity, wasintroduced. The activity represents that portion of ions that are free to act. Mathematically, theactivity is defined by the following equation:

iii cfa ∗=

ai = Activity of ion ici = Concentration of ion ifi = Activity coefficient of ion i

The activity coefficient is a function of the concentration and approaches the value of fi = 1 as thesolution becomes more and more dilute. The activity then becomes equal to the concentration.With an increase in the concentration, the activity coefficient falls to values < 1 and the activitybecomes smaller than the concentration. It has been shown that the activity coefficient dependsnot only on the concentration, but also on the ionic charge. A parameter that takes this intoaccount is the ionic strength J. It is defined by the following equation:

∑= 2iizc5,0J

ci = Concentration of ion izi = Charge of ion i

A continuation of this line of thought produced a relationship between the activity coefficient fi andthe ionic strength J.

JAflog i −=

A = Constant

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This equation is a mathematical expression for what we already know, namely that the activitycoefficient depends on the ionic strength, which is a function of the concentration and charge of allions in a solution. The addition of a conducting salt to the calibration and measuring solutionsgenerates the same activity coefficient for all solutions. Under these conditions, the activity, whichcorrectly appears in the Nernst equation, is proportional to the concentration. Therefore, we canthen work with this entity as well. The difference between the activity and the concentration iscancelled out during calibration.

Concentration

Voltage

Concentration

Voltage

Figure 3: Relationship between the concentration and the measured signal without and with theaddition of a conducting salt

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1.4 Diffusion voltage, diffusion potential

Two different electrolyte solutions come into contact at the ground diaphragm of the referenceelectrode. They are the bridge solution and the measuring solution. Generally, they will differ intheir composition and concentration. A voltage will usually be generated at bridges of this type.The voltage is generated from the difference in the diffusion speeds of the different ion species.For example, if the cations of one solution diffuse more rapidly into the other solution than theanions, a positively charged liquid front will build up, which is followed by a negative front.Separated electrical charges always give rise to an electrical voltage. Unfortunately, this voltagelies within the measuring circuit and is included in the measurements. The diffusion voltage, or thediffusion potential as this voltage is also called, can rise to values of 30 mV under certainconditions. In particular, this may be assumed to be the case when solutions with very differentdiffusion properties, such as acids and neutral salt solutions, border on each other. Consideringthat a measurement error of 1 mV results in a 4% error in the measurement results for monovalentions and in an 8% error for divalent ions, it is clear that the diffusion voltage is the weakest link inthe measurement circuit. Luckily, errors such as these can be prevented. For example, the saltconcentration of the measuring solution can be raised. This is accomplished by adding salt to themeasuring solution as described in the previous section, which already counts as a samplepreparation. However, still more can be done. The generation of a diffusion voltage can be limitedby the selection of suitable salts. If the cations and anions wander at roughly the same speeds, theensuing diffusion voltage will only be small. This is the case for potassium chloride, potassium nitrate, ammonium chloride and, to a limiteddegree, for sodium nitrate and sodium chloride. The maintenance of identical calibration andmeasurement conditions is extremely important under this aspect. In technical jargon, the solutionsused to add salt to the calibration and measuring solutions are known as ISA solutions. Theabbreviation ISA stands for Ionic Strength Adjustor.

Figure 4: Balanced diffusion at the reference electrode diaphragm

Cl-

K+

K+

Referenceelectrode

Measuringmedium

Cl-K+

K+K+

K+

K+Cl-

Cl-

Cl-K+

K+

Cl-

Cl-

Cl-Cl-

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1.5 Stirrer

When working with ion-selective electrodes, we generally use a magnetic stirrer that allowsuniform and comparable stirring of all solutions. Stirring has a stabilising effect on the diffusionvoltage, that is, it brings about the constant values we require. Since this also accelerates thetransportation processes at the measuring electrode and at the diaphragm, the voltage stabilisationperiods are shortened as well. A disadvantage is that the stirrer can warm up the solution. Aninsulated plate between the stirrer and the vessel can effectively suppress this effect.

1.6 Selectivity

Up to now, we have assumed that every ion-selective electrode responds only to one type of ionand remains unaffected by all other species. Unfortunately, this is not the case. For almost allelectrodes, there are ions that we do not wish to measure, but that still affect the electrode signal.These ions are often called interfering ions and one speaks of interference error. Building on theNernst equation, Nikolsky developed an equation that carries his name and allows a mathematicaltreatment of the interference effect.

∑≠

∗++=ij

si

aa

n/njisi

i0 )aKa(log

FnRT303,2UU

ni Charge of ion to be measuredns Charge of interfering ion species ai Activity of the ion to be measured aj Activity of the interfering ion species Sum of all interfering ion species Kis Selectivity constant (measured ion – interfering ion)

Strictly speaking, the selectivity constant Kis is not really a constant since its value is a function ofthe ionic strength. Moreover, Kis is also dependent on the method of determination. This especiallyapplies to PVC membrane electrodes. In contrast, the selectivity constant of pure solid-statemembrane electrodes is clearly a function of the solubility products.The Nikolsky equation shows that the interference effect increases with a rise in the interfering ionconcentration and the selectivity constant. Therefore, it is advantageous to have a small selectivityconstant.

A small selectivity constant of 0.001 means that the interfering ion, if it has the same concentrationas the measured ion, causes only 1/1000 of the resulting voltage. However, it should be mentionedthat some manufacturers of ion-selective electrodes specify the selectivity constant as thereciprocal value. This is always the case when the formulation “more sensitive than” is used. Inpractice, selectivity constants > 1 may also be encountered. This means: The interfering ion playsa greater role in generating the voltage than the measured ion itself. This is often the case withcalcium electrodes, which are three times as sensitive to zinc ions than to calcium ions. As long asthe calcium ions are not measured in the presence of zinc ions, as is usually the case, this fact willbe of no importance.

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2 Description of ion-selective electrodes Ion-selective electrodes can be categorised into three groups according to their design:

1. Solid-state electrodes2. PVC membrane electrodes (matrix electrodes)3. Gas-sensing electrodes

2.1 Solid-state electrodes

The ion-selective membrane in these electrodes is a solid substance that is in direct contact withthe measuring solution. Substances suitable as membrane material possess a very small yetdetectable electrical conductivity, have ion-selective properties and are sparingly soluble in water,i.e. the solubility product is extremely small. Lanthanum fluoride is used for fluoride measurementsince it dissolves in water to only 19.5 g/l. This minute amount is dissociated, i.e. it is completelybroken down into ions.

−+ +↔ F3LaLaF 33

The ions are in equilibrium with the solid membrane and generate a voltage at the membrane thatis a function of the fluoride or lanthanum concentration. The membrane has a glassy appearanceand is very hard. The silver electrode is of similar design. A membrane of silver sulphide, Ag2S, isused. The solubility of this compound is almost a factor 10-10 smaller than the solubility of thelanthanum fluoride. The dissociation is described by the following reaction:

−+ +↔ 22 SAg2SAg

Just as the fluoride electrode responds to lanthanum and fluoride, the silver electrode responds tosilver and sulphide. Silver sulphide is very suitable for creating electrodes of the third type. Theseare electrodes whose membrane consists of a combination of silver sulphide, Ag2S, and either asulphide of a heavy metal, MeS, or a silver halide, AgX. Both types of compounds are sparinglysoluble in water. Electrodes with this membrane design respond to either the heavy metal or thehalite ion. The scope of identifiable ions is thus usefully extended. The method of operation ofthese electrodes can be explained by looking at the equilibrium equations. In the electrodes thatrespond to heavy metals, the components Ag2S and MeS are present in the membrane. Both existin the solution in a dissociated state:

−+ +↔ 22 SAg2SAg

−+ +↔ 22 SMeMeS

The second equilibrium is shifted to the left by the addition of the heavy metal ion, Me2+, i.e.insoluble heavy metal sulphide is formed and the concentration of the sulphide ions, S2-,decreases. This process affects the first equilibrium shown here. As the sulphide concentrationdecreases, the equilibrium is shifted to the right. This means: Silver sulphide, Ag2S, dissolves andthe concentration of the voltage-determining silver ions, Ag+, increases. The sensitivity of theAg2S/AgX mixtures to the halites has a similar explanation. Examples of electrodes with a heavymetal sulphide are the electrodes for lead, cadmium and copper; examples of electrodes with asilver halite are the electrodes for chloride, bromide, iodide and rhodanide.

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With regard to the copper electrode, it should be added that its ion-selective membrane isphotosensitive. The electrode voltage varies depending on the intensity of illumination in thelaboratory. This may no longer be tolerated by the acceptance criterion of modern ion meters. Also,the use of a copper chloride standard for the calibration should be avoided because it gives rise tothe following equilibrium:

CuSAgCl2Cl2CuSAg 22 +↔++ −+

The silver chloride on the membrane of the electrode is sparingly soluble and slowly converts thecopper electrode into a chloride electrode. It delivers an interference voltage that is a function ofthe chloride concentration. When measuring the sample, small chloride concentrations can betolerated to a certain degree. This depends on the concentration conditions. More information isprovided in the operating manuals of the copper electrode. The cyanide electrode represents aspecial case. It is actually a standard iodide electrode whose membrane consists of silver sulphide,Ag2S, and silver iodide, AgJ. The cyanide ion is a good complex builder for heavy metals andslowly dissolves the silver iodide of the electrode:

−− +↔+ JAgCNCNAgJ or

−−− +↔+ J)CN(AgCN2AgJ 2

The iodide electrode responds to the liberated iodide.Electrodes that slowly dissolve in the measured medium are also called corrosion electrodes. Careshould be taken not to leave them in the measuring solution for longer than necessary. The iodideelectrode, however, can do still more. The thiosulphate ion, like the cyanide ion, is capable offorming stable complexes with silver ions, which makes it possible to measure the thiosulphate.The iodide electrode can even be used to measure mercury silver ions within the concentrationrange of 10-4 to 10-8 mol/l. Mercury-II salts also dissolve the silver iodide.However, in this reaction it is the silver ion rather than the iodide ion that is liberated. This is ofsecondary importance for the measurement.

+++ +↔+ AgHgJHgAgJ 2

The last solid-state electrode to be discussed here is the sodium electrode. On the surface, it has adifferent design than the electrodes discussed up to now and is very similar to the pH electrodes.This is not a coincidence. After all, it was developed on the basis of the pH electrode. Theelectrode voltage of pH electrodes exhibits deviations from the linear characteristic that are calledalkaline error and acid error. The alkaline error can be increased by selecting a suitable glass type.If an electrode of this type is placed in a solution with a high constant pH value, it develops asensitivity for sodium ions. To establish and maintain the pH value, buffer solutions based onorganic amines are required. A sodium electrode can determine sodium concentrations as low as0.02 to 0.002 mg/l. However, preparation of the buffer requires very good water, i.e. water that islow in sodium, and very clean laboratory procedures since traces of sodium are widespread.

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2.2 PVC membrane electrodes (matrix electrodes)

There are many ions for which there are no known membrane substances that are sufficientlysparingly soluble to be able to use them in solid-state electrodes. However, there are substancesthat are in part organic which are able to form complexes with the ions to be measured or that haveion exchange properties. Substances such as these are dissolved in organic solvents. Thesubstance and solvent should be sparingly soluble in water. The ion to be measured is capable ofmigrating in both directions across the border area between the organic solvent and the water.This builds up a voltage jump. To create electrodes that are practical to use, the organic solvent ispolymerised into a PVC membrane together with the ion-selective organic substance. Manymanufacturers build PVC membrane electrodes that are similar in design to the solid-stateelectrodes, the only difference being that the PVC membrane is found at the end of the head whichis screwed onto the other part of the electrode. Because the PVC membrane is exhausted after ¼to 1 year at the latest, the availability of a separate, exchangeable measuring head lowers thecosts of measuring with these electrodes. The lifetime of the membrane largely depends on thefrequency of use.

2.3 Gas-sensing electrodes

These sensors are actually not counted among the ion-selective electrodes, since they aredesigned to respond to gasses. However, they can be used to determine ion concentrations aswell, and we will discuss them here briefly in this capacity. As an example, we will single out the ammonia electrode, which is used to determine ammoniumconcentrations. From a chemical point of view, the following equilibrium exists between theammonium ion, NH4

+, and ammonia, NH3:

−+ +↔+ OHNHOHNH 423

This equilibrium indicates that the ammonium ion dominates in a strongly acidic solution, whileammonia gas dominates in a strongly alkaline solution. Each form can be converted to the other byshifting the pH. There is an intermediate range in which the ammonium ion exists alongside theammonia in a particular ratio. At a pH of 9.25, the ratio is 1:1. At a pH of 12.25, only 1/1000 existsin the form of the ammonium ion, i.e. practically all ammonium ions will have been converted intoammonia.

How can the ammonia be measured in order to determine the concentration of ammonium ions? Inprinciple, the ammonia, which is dissolved in the alkaline solution, is allowed to diffuse through aTeflon membrane into a chamber that contains an ammonium chloride solution with a relativelyhigh concentration. The equilibrium shown above now takes effect, i.e. the ammonia reacts withwater and produces ammonium ions and OH- ions. The formulation of the equilibrium using themass action law yields the following expression:

+− ∗=

4

3

NH

NHOH a

aKa

aOH- Activity of the OH- ions

K Equilibrium constant aNH3 Activity of the ammoniaaNH4

+ Activity of the ammonium ion

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If we assume that the activity of the ammonium ion is constant, we have the following relationship:

3NHOH a´Ka ∗=−

This equation shows: When in equilibrium, the activity of the OH- ions is proportional to the activity of the ammonia. Dueto the diffusion equilibrium, this also applies to the activity of the ammonium ions in the originalsample. Thus, by measuring the voltage at a pH electrode, we can determine the ammoniumconcentration. The electrode design differs only marginally from the ion-selective measuringapparatus. We connect the ammonia electrode to our ion meter, calibrate the device with twoammonium standards that have been made alkaline and directly measure the ammoniumconcentration in the sample that has been made alkaline. To prevent ammonia from escaping fromthe solution, which would lead to a result that lies below the actual value, it is advisable to calibrateand measure in a closed vessel. If a closed vessel is used, the ammonia electrode does not evenhave to be dipped into the alkaline solution. Measurements can be made in the gaseous phasebecause it, too, builds up an equilibrium.

Electrodes that work on the same principle as the ammonia electrode described above have beenbuilt for other systems as well. The most important ones are:

Carbon dioxide/hydrogen carbonate Sulphur dioxide/hydrogen sulphiteHydrocyanic acid/cyanideHydrofluoric acid /fluorideHydrogen sulphide/Hydrogen sulphideNaturally, the sample preparation differs for each system and the solutions for establishing adefined pH value have different compositions.

3 CalibrationThe user can select from three different calibration procedures depending on the design andfeatures of the ion meter.

1. One-point calibration2. Two-point calibration3. Multi-point calibration

3.1 One-point calibration

A prerequisite to using this procedure is that you must have available to you an ion meter on whichthe slope of the characteristic curve can be adjusted and the characteristic curve itself can beshifted horizontally. The theoretical slope is usually used. The equipment is calibrated using asingle calibration standard. The electrode is dipped into the standard. The characteristic curve onthe ion meter is now shifted until the reference value of the calibration standard is reached. Thisprocedure is often the method of choice for production control purposes. The concentration of thecalibration standard should be very close to that of the product. Under these conditions, a slope that has not been precisely set to the actual value has littlebearing on the results. The advantage of this method is the speed with which both the procedureand a calibration check can be performed. Also, it avoids the expense of having to have a secondcalibration solution.

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3.2 Two-point calibration

The two-point calibration precisely defines the characteristic curve of the electrode by recordingtwo measuring points. At the same time it calculates the slope. Two calibration standards areneeded to record the two measuring points. Their concentration must be entered into the device. The standards are generally prepared by the user since solutions with a low concentration have alimited shelf life and also because the sample preparation must be taken into account whencalibrating. The concentrations of the calibration standard should differ by a factor of 10. A smallerdifference will have a negative effect the accuracy of the calibration. With a larger difference yourun the risk of going well into the nonlinear range of the characteristic curve. It is advisable todefine the calibration standards in such a way that the expected measured value lies between thetwo calibration points. Since the characteristic curve is a function of the temperature, the twocalibration standards must be at the same temperature. The temperature during measurementshould deviate as little as possible from this temperature. A deviation of 2°C is considered to bethe absolute limit.

Figure 5: Example of a two-point calibration

3.3 Multi-point calibration

The purpose of the multi-point calibration is to determine where the characteristic curve deviatesfrom a straight line during calibration in order to achieve a higher accuracy during measurement.This may not be of very great significance for a three-point calibration, since the user can selectthe required calibration points for the two-point calibration. However, if 5 or 6 calibration points areavailable, the nonlinear part of the characteristic curve can be reproduced, making this rangeavailable for measurement as well. The two-point calibration would fail in this region of the curve.In practice, the multi-point calibration reproduces the entire characteristic curve between thecalibration points. One method is to use the polygon procedure where the ion meter uses straightlines to connect the calibration points. However, a more accurate method is the polynomialprocedure. Here the device calculates the characteristic curve with a high degree of accuracyusing polynomials of the fourth order. Be aware that the polynomial is only defined between thefirst and last standard. Measuring samples outside of this range can lead to errors. This situationcan be avoided by selecting a more suitable calibration standard. Many ion meters output awarning when the measurement range limit is exceeded.When taking measurements, you should also know that the electrode voltages adjust very slowly inthe nonlinear range of the characteristic curve.

E2

E1

c1 c2

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Figure 6: Example of a 6-point calibration with a nonlinear region

4 Sample preparationSamples are prepared with the aim of ensuring that the conditions for measurement are optimal.After preparation, the sample to be measured should be in a condition where the ions are in a freestate. Any factors that arise from the measuring solution and can affect the electrode must beconstant at all times. This applies to both the calibration and the measuring solutions. Anyinterfering ions should be removed. The most important method of sample preparation has alreadybeen presented. It is the use of ISA solutions. In the calibration and measuring solutions, theconcentration of ISA solutions with a value of 1.1 should be 0.1 mol/l. The ISA solutions ensurethat the electrical conductivity of the solutions is adequate, the diffusion voltage remains constantand the activity coefficient of the measured ion also remains constant. If the sample already hasthis concentration of salts, then adding ISA solution would be superfluous. Solutions with a saltcontent greater than 1 mol/l are diluted as required. Other methods of sample preparation areavailable and are described here in detail:

4.1 pH value

It is necessary to establish specific pH ranges if the ion to be measured reacts with the H+ or OH-

ions at lower or higher pH values. The reaction products cannot be detected by the ion-selectiveelectrode. For example, if pH values are too high, the ions of the heavy metals silver, copper, leadand cadmium are precipitated as hydroxides. Likewise, the measurement of fluoride is disturbedbecause the OH- ions cause the lanthanum fluoride in the membrane to be converted intolanthanum hydroxide. Especially at low concentrations, the liberated fluoride ions simulate a higherfluoride concentration.On the other hand, incorrect measured values can also result from solutions that are too acidic.For example, this is the case for the fluoride, cyanide, sulphide and thiocyanate anions. Fromthese anions, H+ is taken up to form undissociated acids that cannot no longer be detected. As acorrective measure, it is advisable to substitute the ISA solution with a suitable buffer. Thespecifications in the application reports provided by the companies should be observed.

6-point calibration with a nonlinear region

170.3152.8

101.9

43.3

-15.8

-73.7-100

-50

0

50

100

150

200

0.01 0.1 1 10 100 1000

Concentration c

Volta

ge

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4.2 Interfering ions

As mentioned above, there is a very large number of different interfering ions, which is why onlythe most important examples will be discussed here. The procedures available for eliminatingthese interfering ions are precipitation, complexing and cooking.

4.2.1 Precipitation

High concentrations of lead interfere with cadmium measurement. Since lead sulphate is sparinglysoluble, an ISA solution of 5 mol/l sodium sulphate is used here. Iron-II ions interfere with themeasurement of lead, cadmium and copper. Several milliliters of hydrogen peroxide are added toraise the pH value to 5-6. By adding ammonia solution drop by drop, iron-III hydroxide precipitatesand can be filtered out. Calcium measurement is disturbed by the divalent ions of iron, copper,magnesium, nickel and zinc. These ions can be precipitated at a pH value of 8. The calcium can then be directly measured atthis pH value. Carbonates are destroyed prior to measurement (see below). Nitrate measurementis disturbed by iodide, cyanide, bromide, chloride, hydrogen sulphide and phosphate ions. Here, anISA solution containing silver sulphate is used. The interfering ions are precipitated. Specifically fornitrate measurement in the presence of chloride, WTW sells a nitrate TISAB solution that containssilver ions (TISAB: total ionic strength adjustment buffer). If carbon acids are also interfering withthe nitrate electrode, they can be precipitated by the addition of an ISA solution with 0.1 mol/laluminium sulphate.

4.2.2 Complexing

Often the ions to be determined are bound in complexes or are themselves complexing agents.Fluoride is an example for the latter case. Many metal ion species can form complexes withfluoride, which then can no longer be identified by an ion-selective electrode.Therefore, a TISAB solution is added to the sample solutions. The CDTA (Titriplex IV) contained inthe TISAB solutions enters into a more stable complex with the metal ion than with the fluoride.The fluoride is displaced from the original complex and can then be measured. A pH value of 5-6 isused. This procedure has proved effective in most cases. However, for aluminium and iron fluoridecomplexes, it is often more advantageous to use TIRON (disodium catechol disulphonate) at a pHvalue of 6-7.The other case also occurs, namely that the ion to be determined is made unavailable formeasurement by a complexing agent. To bring the ion into a form that is measurable, thecomplexing agent must be destroyed. For example, for the many different cyanide complexes, themetal ion can generally be liberated by treatment with acid. Dilute sulphuric acid will be sufficientfor complexes that are easily dissociated. Those that are more difficult to dissociate must betreated with concentrated sulphuric acid. Caution: extremely toxic hydrocyanic acid is producedwhen cyanide complexes are dissociated. The dissociation reaction must therefore be performedunder a good fume hood.

4.2.3 Cooking

Certain interfering ions can be removed by cooking. These include the cyanide ion. The sample ismade acidic and heated. Caution: In an acidic environment, the cyanide ions can form extremelytoxic hydrocyanic acid. Therefore, removal of the cyanide must take place under a fume hood.Carbonates can also be removed by this method. A different procedure is used if large quantitiesof ammonium ion are an interference factor. Here, the pH value is raised to approximately 13. Theheat causes the gaseous ammonia generated from the ammonium ion to escape. It has a bitingodour (fume hood).

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4.3 Trace analysis

Trace analysis requires the determination of concentrations that lie well within the nonlinear regionof the characteristic curve. The conventional measurement method cannot be applied in this case.There are, however, two other methods that will yield the required results. Firstly, an attempt canbe made to shift the nonlinear region of the characteristic curve toward smaller concentrations.Secondly, the ion to be determined can be enriched in order to achieve the required results.Extraction and ion exchangers are available to perform this procedure.

4.3.1 Shifting the nonlinear region of the characteristic curve

As already mentioned above, the nonlinear part of the characteristic curve is determined by themagnitude of the solubility product of the ion-selective membrane component. The smaller thesolubility product, the farther the linear part of the characteristic curve extends toward smallerconcentrations. Can the solubility product be reduced? This question must be answered affirmatively, since the solubility product is a function of thetemperature. Cooling the sample extends the linear part of the characteristic curve by 0.5-1decade. However, there is another method for lowering the solubility product. Ions are less soluble inorganic solvents, e.g. methanol, ethanol, propanol, dioxan and acetone, than in water. Thesolubility products fall accordingly.The addition of 50-60 % of an organic solvent can result in up to 3 decades. The application of thisprocedure presents no problems for solid-state electrodes. It should not, however, be used formatrix electrodes or gas-sensing electrodes. The electrodes may be permanently damaged.

4.3.2 Extraction

The measured ion is complexed and treated with an organic solvent that is immiscible with water.The formed complex must be more soluble in the organic phase than in the aqueous phase. Afterseparating the organic phase with a separating funnel, the complex must be destroyed. Now themeasured ion can be taken up with deionized water in a similar manner. The quantity of deionizedwater is substantially smaller than the original sample volume. This means that the concentrationincreases appreciably. A simple-to-use complexing agent for heavy metals is dithizone. Thecomplexes are called dithizonates. Formation and destruction of the complexes are achieved byshifting the pH value. Chloroform is a suitable organic solvent. As can be seen in the table, heavymetals can also be separated in some cases.

Extraction of heavy metals with dithizone

Substance Solubility ofcomplexes in chloroform

pH range for complexformation

pH range fordissociation

Lead 4 x 10-4 mol/l 8 to 10 < 6Cadmium 1 x 10-4 mol/l 7 to 13 < 5Cobalt 2 x 10-3 mol/l 7 to 9 < 5Copper 2 x 10-3 mol/l 0 to 5 > 9Nickel 2 x 10-3 mol/l 7 to 9 < 5Mercury 3 x 10-4 mol/l -1 to 4 > 9Silver 4 x 10-2 mol/l 0 to 6 > 9Zinc 3 x 10-2 mol/l 7 to 13 < 5

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4.3.3 Ion exchangers

The measured ions can also be enriched using ion exchangers. A large volume of sample passesthrough the exchanger column to bind the measured ions to the exchanger material. The boundions can then be extracted using a small quantity of acid, a base or a dissolved alkaline salt.Cellulose exchangers are suitable for the selective enrichment and separation of heavy metals.

5 Measurement methodsThere are many different applications of ion-selective measurement. Today, ion-selectiveelectrodes are encountered both in the laboratory and in industrial online applications. Of the manymeasuring procedures available, only the following will be discussed more closely here:

1. Direct potentiometry2. Incremental procedure 3. Titration procedure

5.1 Direct potentiometry

The basic principle behind the potentiometric procedure is the direct application of the Nernstequation. The concentration of a particular ion is to be measured. We require an electrode thatresponds to this ion. The ion meter has been prepared by means of the one-point, two-point ormulti-point calibration. Switching to the measuring mode allows the required ion to be determineddirectly. Direct potentiometry is the ion-selection measuring technique most frequently used.However, it is not ideally suited for every situation. This is due to the fact that if the samplepossesses a complex, unknown composition, the calibration solutions may differ markedly from themeasuring solution. This inevitably leads to measurement error. Other measurement methodshave been developed to work around this disadvantage.

5.2 Incremental methods

In incremental methods, a standard is added to the sample or a sample to the standard. Thevolumes of the sample and standard and of the standard concentration can be skilfully selected insuch a way that the actual measurement matrix barely changes. The sole purpose of thecalibration is to determine the slope. The following procedures are available:

1. Standard addition2. Double standard addition3. Standard subtraction4. Sample addition5. Sample subtraction6. Standard addition with blank value correction

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5.2.1 Standard addition

After calibration, the electrode is placed in the sample to determine its voltage. A standard isadded and the electrode voltage is remeasured. Sample volume, standard volume and standardconcentration must be entered into the ion meter. The device calculates the sample concentrationfrom these values. If the device is not equipped with the program for the standard addition, thesample concentration can be calculated with a pocket calculator. This also applies to theprocedures that follow below.

110)P1(CPC S/)UU(

STp )12 −+

= −

CP Sample concentrationCSt Standard concentrationU1 Electrode voltage of sample U2 Electrode voltage after standard addition P = VSt/VP = Addition ratio VSt Standard volumeVP Sample volume

The measuring range should lie within the linear region of the characteristic curve and encompassno more than one concentration decade. Addition of the standard should at least double the ionconcentration but increase it by no more than a factor of ten. The standard addition ratio should be1 %. Thus, the concentration of the added standard must be 100 – 1000 times that of the sample.

5.2.2 Double standard addition

Calibration is not required in this procedure. The electrode voltage of the sample is determined.Then standard is added to the sample in two separate steps and the electrode voltage isremeasured after each addition. The first addition must be 1 %, the second 2 % of the samplevolume. Again, the concentration of the standard is a factor of 100 - 1000 larger than theconcentration of the sample. The sample is calculated according to:

ST12

212

312

412

p C01,05741,1)U/U(3303,3

)U/U(7395,2)U/U(8490,0)U/U(0089,0C

−∆∆+∆∆−∆∆+∆∆

=

CP Sample concentration CSt Standard concentrationUP Electrode voltage of sample U1 Electrode voltage after first addition U2 Electrode voltage after second addition U1 = U1 UP

U2 = U2 UP

One advantage of this procedure is that it is independent of temperature. The procedure isparticularly well suited for general measurements and for taking measurements with a varying orvery extreme matrix (ionic strengths > 1 mol/l). Since three voltage measurements are required,the reproducibility lies at 6-12 % for a device error of 0.1 mV. Therefore, direct potentiometry orthe standard addition method is superior to the double standard addition method if more accuratemeasurements are required.

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5.2.3. Standard subtraction

In the standard subtraction method, a standard is added to the sample as well. In this case,however, rather than increasing the concentration of the measured ions, the standard decreases itbecause the standard combines with the measured ions to form either a sparingly solubleprecipitate or a very stable complex. This is equivalent to an incomplete titration. A prerequisite forthe application of this procedure is a small solubility product for the sparingly soluble substance ora large stability constant for the formed complex. Likewise, the addition of a standard should causeno more than a small change in the matrix composition. Therefore, an ISA solution is added toboth the sample and the standard. The volume of the addition may not exceed 10 % of the samplevolume. To achieve an adequate change in the electrode voltage, the sample concentration shouldbe reduced by at least half. Thus, the concentration of the standard must be a factor of 5-10 largerthan the concentration of the sample. In this procedure, the slope must be determined in aseparate step. The sample concentration is easiest to calculate if the standard concentration isprovided in units of mol/l. In this case, the result will also be in mol/l.

S/)UU(ST

p 1210)P1(1CPC −+−

=

CP Sample concentration (mol/l)CSt Standard concentration (mol/l)U1 Electrode voltage of sample U2 Electrode voltage after addition VP Sample volumeVSt Standard volumeS SlopeP = VSt/VP = Addition ratio

Generally, however, the concentration is required not in mol/l but in mg/l. Therefore, we have toconvert the concentration of the standards so that the measurement result, too, is given in mg/l.We have the following expression for converting the values when a precipitate is formed:

[ ]S/)UU(STp

STpSTp 1210)P1(1Az

PCAzC −+−

=

CP Concentration of sample (mg/l)CSt Concentration of standard (mg/l)zP Valency of sample ion zSt Valency of standard ion AP Atomic weight of sample ion ASt Atomic weight of standard ionU1 Electrode voltage of sample U2 Electrode voltage after addition S Electrode slopeVP Sample volumeVSt Standard volumeP VSt/VP = Addition ratio

This equation also applies when a complex is formed. In this case it should be noted, however,that the valences of the complex formation no longer necessarily coincide with the conventionalvalences.

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5.2.4 Sample addition

In the sample addition method, a sample is added to a standard that has been treated with ISAsolution. The electrode voltage is determined both before and after the sample addition. Theelectrode slope must be a known quantity. The sample should increase the standard concentrationby a factor of 2 to 10. The addition ratio of 1 % must not be exceeded if measurements are to beaccurate. Thus, the concentration of the standard must be 1/100 to 1/1000 of the concentration ofthe sample. The measurement is evaluated according to the following equation:

[ ]P

110)P1(CCS/)UU(

STp

12 −+=

−

CP Sample concentrationCSt Standard concentrationU1 Electrode voltage of the standard U2 Electrode voltage after sample addition S Electrode slope VP Sample volume VSt Standard volumeP = VP/VSt = Addition ratio

5.2.5 Sample subtraction

This procedure, too, is based on a standard that has been treated with ISA solution. The additionof the sample is performed as described in the last example. The same applies to thedetermination of the electrode voltages. However, the sample reduces rather than increases thestandard concentration. The standard ions are consumed by the formation of sparingly solublecompounds or very stable complexes. This procedure makes is possible to measure ions for whichthere is no specific electrode. Thus, a fluoride standard and a fluoride electrode can be used todetermine the aluminium concentration of a sample. There are two equations for calculating thesample concentration, depending on whether the concentration of the standard is given in mol/l orin mg/l. For units of mol/l:

P]10)1P(1[CC

S/)UU(ST

P

12 −+−=

CP Sample concentration (mol/l)CSt Standard concentration (mol/l)U1 Electrode voltage of standard U2 Electrode voltage after addition VP Sample volumeVSt Standard volumeS Electrode slopeP = VP/VSt = Addition ratio

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In contrast, if the standard concentration is given in mg/l, the following equation is used:

[ ]PAz

10)P1(1CAzC

STp

S/)UU(STpST

p

12 −+−=

CP Sample concentration (mg/l)CSt Standard concentration (mg/l)zP Valency of the sample ion zSt Valency of the standard ion AP Atomic weight of the sample ion ASt Atomic weight of the standard ion U1 Electrode voltage of standard U2 Electrode voltage after addition VP Sample volumeVSt Standard volumeS Electrode sampleP = VP/VSt = Addition ratio

Here, too, it should be noted that the valences of the complex formation do not necessarilycoincide with the conventional valences.

5.2.6 Standard addition with blank value correction

This procedure is suitable for determining concentrations that already lie within the nonlinearregion of the characteristic curve. The addition of a defined quantity of a standard solution (blankvalue) can be used to raise the concentration of the measured ions by approximately oneconcentration decade so that the overall concentration falls into the linear region of thecharacteristic curve. The overall concentration can be determined by means of the standardaddition. The blank value is subtracted from the overall concentration to find the sampleconcentration.Calibration takes place in the linear part of the characteristic curve. The standard quantity that isadded as a standard addition should at least double the overall concentration (sampleconcentration + blank value concentration). An addition ratio of 1 % requires a standard solutionwhose concentration is 100 times that of the overall concentration. The sample concentration iscalculated according to a modified equation for the standard addition:

)VCV()

VV1(

110)P1(PCC

P

BlBl

P

BlS/)UU(

STP 12

−+−+

= −

CP Sample concentration (mg/l)CSt Concentration of addition standard (mg/l)CBl Blank value concentration (mg/l)U2 Electrode voltage after additionU1 Electrode voltage before additionS Electrode slopeVP Sample volumeVBl Blank value volumeVSt Volume of addition standard P = VSt/(VP + VBl) = Addition ratio

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5.3 Titration methods

As mentioned in the introduction, the measuring results achieved on the basis of ion-selectiveelectrodes are often not as accurate as for other procedures. Titration procedures, for example,yield highly accurate results. Errors of only 0.1–0.5 % are not uncommon. The question is whetherthe advantages of both procedures could not be combined to achieve both accurate and rapidanalysis results. In titration procedures, the dissolved substance to be measured reacts withanother dissolved substance (volumetric solution or titrant) in a stoichiometrically precisely definedmanner. The concentration of the ion to be determined can be calculated from the required titrantvolume, the concentration of the titrant solution and the volume of the sample solution:

P

TTp V

CVC =

CP Concentration of sampleCT Concentration of titrant (volumetric solution)VP Sample volumeVT Volume of required titrant

The accuracy of the titration procedure depends strongly on how well the end point (equivalencepoint) of the chemical reaction can be determined. This task can be performed by an ion-selectiveelectrode. A calibration is not required since the only factor of interest here is the behaviour of thevoltage as a function of the added titrant volume. A pronounced voltage inflection point arises atthe titration end point. The volume of the required titrant can be precisely determined by means ofthis inflection point. Thus, the usual titration methods can be carried out in this manner.

5.3.1 Direct titration

The voltage of the electrode is directly determined via the ion concentration as it falls duringtitration.

5.3.2 Indirect titration

The voltage of the electrode responds to a titrant ion. This ion is continuously consumed until theequivalence point is reached. Only then does its concentration start to increase. A pronouncedvoltage inflection point results.

5.3.3 Back titration

If a distinct voltage inflection point does not arise at the equivalence point during direct or indirecttitration, an excess of titrant can be added. The excess titrant is now titrated with a second titrant,i.e. a back titration is performed. This operation must result in a voltage inflection that can beevaluated. The consumed quantity is subtracted from the first titrant volume to find the titrantvolume required for the equivalence point.

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5.3.4 End point indicator

This method can be used if ion-selective electrodes do not exist for the ion to be measured or thetitrant. An additional ion is added to the sample. An ion-selective electrode is available for this ion.The added ion must react considerably more strongly with the titrant than does the ion to bedetermined, i.e. in precipitation reactions, the precipitate has a distinctly smaller solubility productor, in complexing reactions, more stable complexes form than with the ion to be determined. Whentitrating, the added ion is first determined via an adequate voltage inflection point. After more titrantis consumed, a second voltage inflection point develops for the ion to be measured. The secondvoltage inflection point occurs because the added ion also is not fully consumed until the secondvoltage inflection point is reached. Karl Cammann provides a report on the titration of calcium withan EDTA titrant solution. The ion-selective electrode used is a copper electrode. The ions added are Cu2+ ions. It should benoted that, understandably, the first voltage inflection point does not develop if CuEDTA is usedinstead of Cu2+ ions from the start.

Finally, it should be mentioned that situations occasionally do arise in practice in which the titrationprocedures described here do not result in a titration curve that can be evaluated. This can beexplained by low ion concentrations immediately before or immediately after the equivalence point.Let us recall: when concentrations are very small, the electrode requires a relatively long time todisplay the actual voltage. Due to time constrictions, it can be very difficult to record a correcttitration curve. However, if the voltage inflection point develops too early or too late, thedetermination of the equivalence point becomes inexact. If a sluggish ion-selective electrode isbeing used, this effect is even more pronounced. There is yet another factor that has a similareffect. When concentrations are very low, we are no longer working in the linear region of thecharacteristic curve. The capacity to evaluate the titration curve suffers under this aspect as well.The inaccuracy thus arising in the determination of the equivalence point can be reduced or evenavoided by refraining from recording the entire titration curve and by titrating for the electrodevoltage at the equivalence point. This method is often used by automatic analysis equipment. Thelong waiting periods that usually occur when many measuring points are used are thus reduced toan acceptable level. Of course, the electrode voltage at the equivalence point must be known. Thisdoes not present a problem, however, because it can be determined using samples of knowncomposition.

6 Maintenance and special information

6.1 Electrode contamination

Solid-state electrodes always become contaminated when the sample contains an ion that entersinto a compound with a membrane component that has a lower solubility than a compound formedwith the measured ion. For example, iodide ions should not be present in a chloride solution sincethese would convert the silver chloride existing in the chloride electrode into silver iodide. Thesilver iodide is considerably less soluble than silver chloride. Mercury salts have a strongcontaminating effect on electrodes with a silver sulphide membrane. A silver electrode becomescontaminated at mercury-II concentrations of as little as 10-7 mol/l. This reason for this is theextremely low solubility of mercury silver sulphide. It is even less soluble than silver sulphide. Theabove-mentioned measurement of mercury salts with an iodide electrode is also affected by thistype of contamination. To avoid this effect, the inactive membrane surface must be polished with aspecial grinding foil prior to each measurement.

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Another ion that should be mentioned here that can lead to contamination of the electrode is thesulphide ion. It can displace the halide ion in the silver halide in halide electrodes, graduallyconverting the halide electrode into a silver sulphide electrode.

Halide electrodes can also become contaminated by substances with strong reducing properties.These substances reduce the silver ion of the halide to elementary silver. The silver coatingimpedes the required establishment of an equilibrium. The fluoride electrode, too, can becomecontaminated. As mentioned above, OH- ions convert the lanthanum fluoride into lanthanumhydroxide, which is also sparingly soluble. Therefore, fluoride electrodes should not be placed insolutions with a pH > 7. Moreover, the electrodes should not be cleaned with alkaline cleaningagents such as soap solutions. In this context, it should be pointed out that fluoride ions areextremely aggressive toward glass. Hydrogen fluoride dissolves HF glass, a process thatconsumes fluoride ions. Therefore, only plastic vessels should be used for measuring solutionsand standards containing fluoride. What can be done with a contaminated solid-state electrode? The only method of restoring the ion-selective activity is by removing the contaminated outercoating. Special grinding foils that employ an abrasive material of a very small grain sizes areavailable for this purpose. Together with water, these foils are suitable for producing a newmembrane surface. Nothing other than these foils should be used. Under no circumstances shouldfine-grain sandpaper be used. This would result in scratches that retard the stabilisation of theelectrode voltage.

After removal of the contaminated surface, the electrode must be kept in a standard solution toreturn the membrane to its final active state (conditioning). Contamination may also occur in thePVC membrane electrodes. A nitrate electrode would probably not survive extended exposure to achloride solution since the nitrate in the membrane would be substituted by the chloride. Anattempt may be made to remove the chloride by exposing the electrode to a nitrate solution, butthe success of such a measure would be highly uncertain.

6.2 Cleaning the electrodes

The easiest way to clean solid-state electrodes it by wiping off the electrode with a moist papertowel. The paper should be soft to avoid scratching the membrane. If this is ineffective, the papertowel can be moistened with spirit. Other organic solvents such as acetone should not beemployed because existing adhesive surfaces could become detached. In some cases, aneffective alternative is storing the electrode in dilute acids. Finally, the grinding foils andsubsequent conditioning already mentioned above are also suitable.Contamination of the sodium electrode (glass electrode) can be removed with simple householdcleansers and by gently wiping the electrode. Due to their special design, PVC membraneelectrodes can only be cleaned by rinsing them in deionized water.

6.3 Storing the electrodes

All electrode types can be stored for a limited time in the appropriate dilute standard solutions.Solid-state electrodes can be stored for longer periods in a dry state. The electrode is rinsed withdeionized water, carefully blotted dry with a soft paper towel and covered with a protective cap.The sodium electrode simply has to be rinsed with water. However, the protective cap contains a5.8 g/l sodium chloride solution to ensure that the membrane does not dry out.Similarly, the membrane of the pH electrode of the gas-sensing electrode also must not dry out.For the ammonia electrode, the protective cap is filled with 0.1 mol/l ammonium chloride solution.The PVC membrane electrode can also be stored in a dry state. The measuring heads arescrewed off of the shaft and the small glass bottles provided are used for storage.

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6.4 Faults during measurement and calibration

During measurement and calibration, faults with a variety of different causes can occur. Whilemodern measuring equipment can identify frequently occurring faults and warn the user with anerror message on the display, not all faults can be determined in this way. We attempt here topresent a list of some of the typical faults that every user will encounter at one time or another.The suggested corrective measures are intended to help eliminate the fault as quickly as possible.Some of the most common faults are as follows:

Fault Cause MeasuresThe display values jump backand forth erratically orOverflow appears in thedisplay.

It is likely that theelectric measuringcircuit is not closed.

Check whether: the measuring and reference

electrodes are properlyconnected.

there is a wire break. the protective caps have been

removed from the electrodes. the electrodes are immersed in

the measuring solution. the reference electrode is filled.

The displayed value isconstant and not affected bythe concentration of themeasuring solution

There is a short circuit Check whether: the measuring electrode

connector is clean and dry. there is a wire break. the ion-selective membrane is

leaky (fluoride electrode). the measuring head of a matrix

electrode is screwed onleaktight.

The display value oscillates The stirrer is disturbingthe measuring circuit

Switch off the stirrer. If the values now remain steady,replace the stirrer with a devicethat has a weaker magnetic field.

The display values either driftor they stabilise very slowly

The measuringelectrode iscontaminated and verysluggish

Clean the membrane and polish it ifnecessary. If this does noteliminate the problem, replace themeasuring electrode.

Measurement is takingplace at very lowconcentrations

Do not take any correctivemeasures. This behaviour isnormal at low concentrations.

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Fault Cause MeasuresThe stirrer is warmingup the measuringsolution.

Use a superior stirrer or aninsulating plate.

The laboratory air iswarming up themeasuring solution.

Do not use solutions out of therefrigerator. Bring measuringsolutions to room temperature first.

The characteristic curve hasa distinct horizontal shiftrelative to the curve shown inthe operating manual

The concentration of theinternal electrolyte ofthe discharge system ofone of the electrodeshas changed

Check the internal electrolyte of thereference electrode. If the interior electrolyte of themeasuring electrode has changed,replace the electrode.

The numerical value of theslope is below 54 mV or 25mV

Measurement in thenonlinear region of thecharacteristic curve

Corrective measures are notrequired. This behaviour is normal.

The calibration solutionhas been contaminatedwith the measured ion.The preparedconcentrations areincorrect.

Establish how the contaminationentered the calibration solution andtake the appropriate correctivemeasures.

The calibration solutionsdo not have the correctconcentration.

Find the error in calculation andavoid it in the future.

The electrode is old orcontaminated.

The electrode can still be cleanedor polished. If this does not help,replace the electrode.

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6.5 Measuring ranges

The following tables provide an overview of the measuring ranges of the ion-selectiveelectrodes offered by WTW. It should be noted that the lower limit of the measuring rangeis already located in the nonlinear region of the characteristic curve, where the ion-selective electrode no longer has the full electrode slope. This must be taken into accountwhen calibrating in order to keep the measurement error to a minimum. If the solution tobe measured exceeds the upper limit of the measuring range, this is not particularlyproblematic since a solution with a higher concentration can always be diluted to yield amore dilute solution that lies within the specified measuring range.

Solid-state electrodes

Species (ion) Model Measuring rangeLead (Pb2+) Pb 500 and Pb 501 10-6 ......10-1 mol/l,

0.2......20700 mg/l

Bromide (Br -) Br 500 and Br 501 5 x 10-6 .....1 mol/l0.4......79900 mg/l

Cadmium (Cd2+) Cd 500 and Cd 501 10-7.......10-1 mol/l0.01....11200 mg/l

Chloride (Cl-) Cl 500 and Cl 501 5 x 10 –5.....1 mol/l1.8...... 35500 mg/l

Cyanide (CN-) CN 500 and CN 501 8 x 10-6..10-2 mol/l0.2....... 260 mg/l

Fluoride (F-) F 500 and F 501 10-6 ...sat. mol/l0.02.... sat. mg/l

Iodide (J-) I 500 and I 501 5 x 10-8......1 mol/l0.006...127000 mg/l

Copper (Cu2+) Cu 500 and Cu 501 10-8........10-1 mol/l0.0006..6400 mg/l

Sodium (Na+) pNa 205a1000-S7 2 x 10-6......1 mol/l0.05.....23000mg/l

Silver (Ag+) Ag 500 and Ag 501 10-7............1 mol/l0.01..108000 mg/l

Sulphide (S2-) Ag 500 and Ag 501 10-7............1 mol/l0.003..32000 mg/l

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PVC membrane electrodes (matrix electrodes)

Species (ion) Model Measuring rangeCalcium (Ca2+) Ca 500 and Ca 501 5 x 10-7......1 mol/l

0.02....40000 mg/l

Fluoroborate (BF4-) BF 500 7 x 10-6......1 mol/l

0.6......86800 mg/l

Potassium (K+) K 500 and K 501 10-6............1 mol/l0.04....39000 mg/l

Nitrate (NO3-) NO 500 and NO 501 7 x 10-6......1 mol/l

0.4......62000 mg/l

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7 Bibliography

1. Cammann K.Das Arbeiten mit ionenselektiven ElektrodenSpringer Verlag, Berlin, Heidelberg, New York (1977)

2. Honold F., Honold B.Ionenselektive Elektroden Birkhäuser Verlag, Basel, Boston, Berlin (1991)

3. Degner R., Heilbock J.Fibel zur ionenselektiven MeßtechnikSelbstverlag, Wissenschaftlich-Technische Werkstätten GmbH & Co.KGD-82362 Weilheim i. OB (1986)

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8 Appendix: Interfering Ions

Lead electrode

Copper, mercury, and silver ions are poisoning the membrane and have to be absent.If the concentration of iron and cadmium ions exceeds those of lead the membrane will alsobe damaged.

Bromide electrode

Reduction agents will interfere.10 % systematic error will be observed by the following concentration ratio betweeninterfering and measured ion:

OH- Cl- NH3 S2O32- J- CN-

3 x 104 400 2 20 2 x 10-4 8 x 10-5

S2-

1 x 10-6

Cadmium electrode

Copper, mercury, and silver ions are poisoning the membrane and have to be absent.Lead- and iron ions only interfer, if the concentration is greater than those of cadmium

Chloride electrode

10 % systematic error will be observed by the following concentration ratio betweeninterfering and measured ion:

OH- NH3 S2O32- Br- S2- J-

80 1,2 x 10-1 1 x10-2 3 x 10-3 1 x 10-6 5 x 10-7

CN-

2 x 10-7

Cyanide electrode

Interfering complexes with Ni2+, Cd2+ , and Cu2+, strong reduction agents.10 % systematic error will be observed by the following concentration ratio betweeninterfering and measured ion:

Cl- Br- J- S2-

1 x 106 5 x 103 0,1 must not be present.

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Fluoride electrode

pH < 4: development of hydrofluoric acid, pH > 8: Development of lanthanuim hydroxide onthe membrane. Ions that form complexes: Fe3+ , Al3+, Si4+ and other. All these interferencescan be avoided by using TISAB. TISAB adjustes an optimum pH-range and forms withcations described above complexes stronger than fluroride. Fluoride complexes will bedisintegrated.

Iodide electrode

Interfering ions: bismuth Bi3+, cadmium Cd2+ , and lead Pb2+ (forming complexes), strongreduction agents.10 % systematic error will be observed by the following concentration ratio betweeninterfering and measured ion:

Cl- S2O32- Br- CN- S2-

1 x 106 1 x 105 5 x 103 0,4 <10-6

Mercury must not be present.

Copper electrode

Complexes with acetate, citrate, ammonium, proteinic acids, EDTA interfer the copper determination.Mercury and silver ions poison the membrane.No interferences under following conditions:

Cu2+ x Cl- 2 < 1,6 x 10-6

Cu2+ x Br- 2 < 1,3 x 10-12

Fe3+ < 0,1 Cu2+

The the potential drift of the copper sulfide/silver sulfide-membrane is light-sensitive.

Silver-Sulfide electrode

Interfering agents: mercury ions, proteins. The interfering proteins can be disintegrated byHNO3In presence of hydrogen peroxide the membrane will be oxidated.Measuring of sulfides is only in basic solutions possible, otherwise sulfide is only as HS-

and H2S available. The oxidation of sulfide by oxygen in a basic solution has to beprevented by adding 50% SAOB II-solution to the sample.Preparation of SAOB II-solution:Fill 600 ml de-salinitated water, 200 ml 10 mol/l sodium hydroxide, 35 g ascorbinic acid, and67 g EDTA in a 1 l graduated flask. If every component has dissolved add de-salinatedwater up to the 1 l graduation.

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Calcium electrode

10 % systematic error will be observed by the following concentration ratio betweeninterfering and measured ion:

Pb2+ Hg2+ H+ Sr2+ Fe2+ Cu2+

0,01 4 4 6 20 40

Ni2+ NH4+ Na+ Tris+ Li+ K+

50 200 200 300 300 400

Ba2+ Zn2+ Mg2+

700 1000 1000

Fluoroborate electrode

10 % systematic error will be observed by the following concentration ratio betweeninterfering and measured ion:

ClO4- (d) J- (b) ClO3

- (d) CN- (b) Br- (b) NO2- (c)

5 x 10-4 5 x 10-3 5 x 10-2 5 x 10-1 1 1

NO3- (d) HCO3

- (a) CO32- (a) Cl- (b) H2PO4

- (b) HPO42- (b)

5 30 30 50 80 80

PO43- (b) OAC- (e) F- (d) SO4

2- (b)80 200 600 1000

Measures from a) to e) can be used to reduce the influence of interfering ions:

a) Carbonates and hydrogencarbonates can be removed by adding acid to the sample.b) Addition of 0.5 g of silver sulfate per 100 ml of the sample leads to precipitation of

the interfering ion.c) Nitrites will be removed by adding 0.3 g amodisulfonic acid per 100 ml of the

sample.d) These ions can not be removed by simple measures.e) Carbonic acids can be removed by using of a 1-molar alumina-ISA-solution instead

of a ammonium sulfate-ISA-solution

Standard solution have to be prepared the same way as samples.

Potassium electrode

10 % systematic error will be observed by the following concentration ratio betweeninterfering and measured ion:

Cs+ NH4+ Tl+ H+ Ag+ Tris+

0,3 6 6 10 1000 1000

Li+ Na+

2000 2000

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Nitrate electrode

10 % systematic error will be observed by the following concentration ratio betweeninterfering and measured ion:

ClO4+ J- ClO3

- CN- Br- NO2-

0,0001 0,005 0,05 0,1 0,7 0,7

HS- HCO3- CO3

- Cl- H2PO4- HPO4

2-

1 10 20 30 50 50

PO43- OAC- F- SO4

2-

50 200 600 1000

Sodium electrode

1 % systematic error will be observed by the following concentration ratio betweeninterfering and measured ion:

H+ Li+ K+ NH4+

1 x 10-3 1 5 20

Silver ions must not be present.

Ammonia electrode

Interfering agents: volatile amines.