The problem of (graphite) electrode polarisation*
* This can be largely overcome by using a low buffer concentration & matching the potentiometer value to the impedance of the cells i.e. for 5 mM buffer use a 10k pot; for a 1 mM buffer use a 47k pot.
I immediately encountered a phenomenon that I was aware of but had not realised would impact on this work; that is electrode polarisation.
When a voltage is applied to a pair of electrodes the current that flows between them causes a build-up of charges in the vicinity of the electrode surface. This charge accumulation is known as Helmholtz double layer formation (in it’s simplest form), is shown in a more generalised form in the diagram below & is the result of the charges in the solution migrating towards & accumulating at & near the electrode surfaces, as they carry current.
Initially, before the double-layer of charges form, the current that flows is unimpeded & defined by the ‘resistance’ of the solution, i.e. related to the concentration and form of the ions in the solution, the electrode surface area and the electrical circuit properties. However as the double-layer forms the ‘resistance’ to current flow into & out of the electrodes increases, and in some cases the current can be almost eliminated.
The overall polarisation is approximately exponential & occurs with a relaxation time of 10 milliseconds but for a 28kHz square wave at +/- 250 mV and with a half-cycle time of 18 microseconds, a significant proportion of the total possiblle polarisation builds up before the polarity switches. The polarisation is instantaneously eliminated but starts to accumulate in the reverse sense. Since both electrodes are carbon the effect is symmetrical.
An example of a pencil lead that polarises extensively is shown in the diagram below the polarisation scheme. Notably when I tested the RS commercial carbon electrodes for polarisation, I found that they showed little of this effect at 10 kHz. This is because the polarisation is much slower than pencil leads, however it does occur.
CONSTRUCTION OF VERY LOW COST
It is well-known that carbon can strongly absorb proteins. I have shown that the electrodes used here do NOT do so in a way that affects their performance, by incubating with 1.5% Bovine Serum Albumin for 2h. This had NO effect on the sensitivity of the cells.
The cell constants were measured as 1.27 & 1.34 & calculated as 1.2
The calculated value takes account of fringe fields
Note that the two cells are slightly different,which has consquences for the precision of the null point at balance owing to the slight difference in polarisation. I will try sometime to trim the one with the lower value to match the higher one.
The pencil leads required are: Club Excelsior HB. These are obtainable on the web but often only available in quite large numbers, however a pack of 6 is available from eBay. They are also available in many retailers and are often used as office/school pencils.
If you cannot locate this type you need to read the section below that describes the polarisation behaviour of (graphite) pencil leads & test and select an appropriate type that has low polarisation. This is very important.
The plastic base for the cells should be ca. 2 mm thick & bond well to Araldite, which is used for fixing the pencil leads and the surrounding section of plastic tube that will contain the liquid under study. The dimensions of the plastic lab tube need probably not be exactly as shown here, but should be similar.
To assemble the cell it is best to make a very simple jig. Simply drill two holes 8 mm apart in a piece of plastic or wood and 4 mm deep. Next drill two holes for the electrodes in a 2 cm x 2 cm square of the base plastic (ca. 2 mm thick). Place the base plastic over the jig, with the holes aligned, and insert the electrodes & push to the bottom of the holes in the wood/plastic. Now glue the electrodes to the base plastic as shown in the diagram above, allow to set (I use Rapid Araldite, i.e. ca. 5 min) & withdraw the assembly from the jig.
To complete the job glue the lab tube section to the base with Araldite, applying a thick layer around the outside of the join to give strength and attach the coax cable to the electrodes using the brass connectors from a 3 or 5 amp interconnector block. The inner brass sections are removed from the block by withdrawing the screws & then pulling out the brass inner part.
A completed cell before fixing into the box lid
The 3 amp connector whose inner (brass) part is used for the connection to the coax cable (remove the screws to retract the brass body from the plastic part)
I very quickly ran into a major problem! I dissected the leads from several pencils that I had lying around & set up a simple test rig [diagram below] to examine their properties.
One might think that this polarisation would not affect the outcome of experiments with this apparatus since the effect is symmetric as there are two cells. It should be eliminated by the differential amplifier i.e. the long tailed pair or op amp. However it turns out that there is, in practice, always some asymmetry which results from the slight inaccuracies in the construction of the electrode assemblies. For a non-professional constructor, without access to special equipment, precision jigs etc., it is not possible to make the TWO electrode assemblies accurately enough so that they match exactly to eliminate all asymmetry.
Any attempt to use a compensating resistor in place of one of the electrodes is doomed to failure as the polarisation (capacitance) aspect is not included.
Any asymmetry between the electrode pairs in terms of polarisation leads to an assymetrical waveform in the output from the bridge at balance. This is because the polarisation builds up rapidly at the early stages of the process, since it is exponential. This, in turn, leads to a ‘false’ output from the precision rectifier, that reflects the electrode asymmetry rather than the desired conductivity signal. The bridge thus cannot be properly balanced, even with identical samples in each cell.
Thus it is necessary to try to find pencil leads that show minimum polarisation. Since all but one of the pencil leads I examined polarised to a very significant extent, I selected the one with the best behaviour and made several forms of conductivity cells for use in tests. The diagram below shows the polarisation of the Club Excelsior HB pencil lead, used for the construction of the conductivity cells described above. Compare this with the diagram above where the polarisation is much greater.
The polarisation process reduces the current flowing in the cell
Potential Leakage problem with very low cost electrochemical cells
I made some cells using 3 ml spectrophotometer cuvettes, with the electrodes placed at the corners that worked very nicely for a while, but after a week or so the behaviour steadily deteriorated, with the resistance (more correctly reactance or impedance, since this is an ac phenomenon) of the cell increasing with use.
On close examination it appeared that the cells had leaked the electrolyte solution, through the Araldite seals & on to the electrical connections between the electrodes and the copper connecting wire. The connections to the wires were made using silver adhesive paint, which had plainly corroded under the influence of the electrolyte solutions used in calibrations & experiments. The Araladite did not bond well to the cuvette polystyrene.
To circumvent this problem it proved necessary to use a material for the base that bonded well to Araldite, to drill the 2 mm holes that hold the pencil leads in position much more carefully in a material that would give very clean edges and to seal the electrodes (from the underside) into the plastic of the cell base more carefully with Araldite.
Impedance of the electrode assemblies
For optimum sensitivity of a Wheatstone bridge the four resistances should be approximately the same at the start of an experiment. For an AC bridge the impedances should be similar.
The reactance of the buffer used in enzyme experiments is ca. 500 ohms for the 28 kHz square wave used in the bridge. [This increases during a 36 microsecond period of the half wave if polarisation occurs]. The reactance of the cells is close to 650 [633,670] ohms for a 0.1% NaCl solution that was used to calibrate & test the system.
This is the reason that a 1 k ohm potentiometer was chosen to balance the bridge, since each half gives a resistance of 500 ohms at balance before the start of an experiment & this leads to optimum sensitivity of the bridge. It is advisable to change the resistance of the potentiometer if a very different buffer is used to give as good a match as is practicable. However tests have shown that reasonable results can be obtained even if the buffer strength is reduced 10 – fold, while the potentiometer is unchanged (although clearly 10 k ohm pot would be better). For best results at lowest concentrations change the pot!
More generally a change of 1% in the overall ionic strength cane be measured when the pot is approximately (+/- 50%) matched to the impedance of the reaction solution. If the pot rsistance differs by more than 10-fold from the solution impedance the best that can be measured is a 10% change. This is a general rule that is valuable in planning experiments.
Performance of the very low cost electrodes assemblies
This design has proved very successful & resistant to electrolyte ingress after a long period of use. The electrical performance is very nearly as good as the RS commercial electrodes, there is some polarisation, but not enough to have a serious effect on performance in enzyme assays. Assays conducted as with the commercial electrodes gave very similar kinetic constants with perhaps slightly more noise.
Choosing a pencil to use for electrode construction
Unfortunately the pencil initially identified as containing a lead with low polarisation was not identifiable in terms of a manufacturer, so I had to start another search with a view to being able to recommend a specific brand of pencil, so that others will be able to repeat what I have done.
I purchased a wide range of pencils & supposed (without any good reason!) that the harder the lead, i.e. the higher the H number in the series from 3B (very soft) to 3H (very hard), the lower the polarisation would be. This turned out to be incorrect and the polarisation seems to depend upon the brand (make) of pencil rather than the hardness rating.
Eventually, after testing some 20 pencils, I found that one called Club Excelsior (HB grade) was much superior to any others, but not quite as good as the unidentified pencil used in the original tests described above! This pencil is available on the internet, but one has to purchase quite a large number (packs of 6 are available on eBay) – they are quite widely used as school pencils.
Cells constructed from the leads
used in Joiner’s/Carpenter’s pencils
The leads used in the above pencils are rectangular (usually 5 mm x 2.5 mm).
The construction method is very similar to that used for the cylindrical leads. It is necessary to make two rectangular holes for the electrodes as shown in the diagram. This was achieved by drilling two 2 mm holes (centres 2.25 mm apart) in each of the marked out rectangles that form the template for the assembly jig and then finishing the rectangular shapes with a miniature file.
To glue the electrodes in place I used a simple jig comprised of two pieces of plastic (total thickness 3mm) with the two rectangles to receive the leads cut in them at the correct distance. The plastic was placed below the base and the electrodes (12 mm long) inserted to give the correct depth (3 mm) of the electrodes above the base.
The electrical connections were made by using the tops (cut from the whole pin) of brass earth connector pins from (UK) 13 amp plugs. The existing holes were not big enough to take the leads but were enlarged using a small file to give the rectangular shape required. The electrical connections were soldered onto the brass parts. This arrangement worked well but was not a very elegant solution, since the filing of the brass was laborious!
The rectangular leads are much stronger than the cylindrical ones, so no reinforcement of the connections with Araldite was needed.
The first cells I made this way were the best I have made of any sort, being close in performance to the commercial RS cells. However the leads I used were from an unidentified joiner’s pencil (again!!) I had bought some years earlier. Hence the same problem that arose with the cylindrical leads arose again.
I purchased a number of joiner’s pencils from several sources and tested them for polarisation. Again there seemed no correlation between hardness and polarisation – the variation was between one manufacturer and another. Eventually I identified a pencil that had low polarisation, similar to but not quite as good as, the unidentified one I had used for the original cells. This was a Rexel BLACKEDGE HARD. This hard form must be used as the medium & soft forms are much more polarisable .
These pencils are widely available both in retailer’s outlets and on the net – they can also be bought in quite small numbers.
These cells have not been fully tested yet but do suffer one important disadvantage. The electrodes are mechanically rather fragile. It is important that stirring of the cells is done gently, otherwise some carbon is removed from the electrodes. This disadvantage means that the cells described earlier, made from cylindrical leads, are more suitable for general long term use. However the rectangular electrodes do have better electrical properties and come closest in performance to the commercial RS cells.
Components for the cell. Left to right. The earth pin from a 13 amp Uk electrical plug; top cut off & filed out to fit electrode rectangle; the base with the rectangles formed; the electrodes fixed in the base & below a section of the leads used
The assembled cells, with the lab tube section that holds the sample liquid seen upside down glued into the box lid
As mentioned elsewhere the polarisation is dependent on the current flow in the cell. Thus I have shown that the apparent time constant for the multiexponential polarisation increases from ca. 1 ms at 0.1% NaCl to ca. 10 ms at 0.01% NaCl. This increase is seen when the pot is changed from 1k to 10k to match the change in impedance of the solution in the cell and is less if the pot remains at 1 k, since the current flow is not reduced as much.
When the polarisation is lowered the assymetry seen at the balance position is decreased and so the 'zero' output of the bridge becomes much closer to true zero. This then allows lower concentrations of analyte to be measured; indeed down to low micromolar levels.
An increase of frequency to 28 kHz has significantly reduced the effect of polarisation.
A quantitative study of carbon electrode polarisation shows that the half time i.e. rate of polarisation is linearly dependent on the current flow in the circuit. This is exactly as would be the case with the charging/discharging of a condenser.
The completed cells are mounted into the lid of the sandwich box by cutting holes using a wood borer of the required size. Clamp the lid firmly while drilling the holes to avoid fraying round the edges. Finally glue in place using Araldite around the top rims of the cells, so that they project below the lid into the thermostatically controlled interior.
Cells with Metal walls - stainless steel
The cells described above with plastic walls take about 10 minutes to re-equilibrate if the temperature is disturbed from the equilibrium value (normally 25 deg) during an experiment. This can occasionally be a nuisance, so I made cells with stainless steel walls to see if they would equilibrate more rapidly. The cells are described at Temperature Equilibration. They are indeed better in this respect & for small temperature changes will re-equilibrate in about 30 seconds! A very large improvement. The cell should be briefly stirred with a pipette tip to achieve this. A surprise for me was the finding that the sensitivity (e.g. to the addition of NaCl) of the cells is virtually identical with that of the plastic-walled cells. I had thought that the conducting metal walls would 'short-out' some of the current between the electrodes, leading to a lower sensitivity.
Background to the design & construction of very low cost conductivity cells & other cost reductions
One of the main aims of the current project has been to devise & design a DIY apparatus that is as simple and low cost as possible, consistent with the demand for high sensitivity, accuracy & repeatability that the application requires.
Two items stand out as relatively expensive: the A/D converter as realised by a Pico Technology Dr DAQ board that costs ca. £90. This board is wonderfully versatile & has been invaluable during development of the apparatus. However to use the equipment in practice does not require such a versatile system. This aspect will be addressed in the future.
I initially used RS carbon electrodes at £32 each. These work well but were rather fiddly to adapt to the present purpose. Thus I set out to devise some very low cost simple electrodes. This has taken far longer than predicted but has now been achieved, as described above
The favoured material for the electrodes remains carbon for reasons of cost. Other materials I have tested, including gold & stainless steel, have not proved effective & platinum, which would be the ideal choice, since it does not polarise (see below) much, is much too expensive.
I had previously seen a number of websites that describe simple ‘kitchen’ type electrolysis experiments that have used pencil leads as electrodes & determined that I would take a similar approach as they are readily available.