DIY Conductometry

In this post, I will cover how to build a relatively simple circuit that will allow you to monitor the conductivity of electrolytic (saline) solutions. Conductometry is widely used in chemistry for on-field water analysis, titration or to study chemical reactions kinetics. The circuit proposed here consists of a two-electrodes probe inserted in the liquid to be analysed and will output an analog voltage that is proportional to the conductivity of the liquid. It covers a large range of concentration, from medium concentration (typically on the order of 1N) down to very dilute solutions, such as demineralized water. The actual dynamic range of the circuit was tested to be at least 1:100 and is fixed by a resistor that you can change to adapt to the concentration ranges that you are working with. Only the highly concentrated solution (more than about 1N) cannot be reached by the circuit presented here.

A picture of the circuit is given on Figure 1. You can download the Gerber files at the end of the post to print the PCB yourself.

But let us first start with the basics: what is (electrical) conductivity?

The best answer I can give is that conductivity is the ability of a medium to transfer charges. In metals, such as a copper wire, this is achieved by the atoms outer layer electrons shells which share a sea of electrons. When electrons are inserted in the wire by the mean of a potential, it makes the electron sea flows down through the wire up to the other end.

In an ideal world, electrons will then just flow through the wire. However, we do not live in an ideal world and the copper wire medium is actually pretty chaotic. Because of the heat, even at ambient temperature, there is a lot of small random motion of the atoms which then collide with the electrons. These collisions create an energy loss which is linearly proportional to the amount of electron flowing down through the wire. This translates mathematically to the most basic empirical formula used by electricians: the Ohm law, V = I*R. In this equation, V is the potential (energy) lost in the metal wire, I is the amount of electrons flowing per second and R is the proportionality factor that will depend on both the chemical nature of the metal and the geometry of the conductor. The bigger the factor R, the larger the energy loss for the same amount of electrons flowing in the wire. Hence we say that R is the resistance of the wire because it opposes charges transfer. Measuring this proportionality factor is then relatively easy because we can use the Ohm law. All we have to do is to apply a potential difference between the two ends of the wire and measure the current flowing in the system. This is basically what you do when you connect a resistor to an ohm-meter as the internal battery of the ohm-meter will send a small voltage (mine is 100 mV) to the resistor and will measure the current flowing.

In chemistry, things work about the same except that we do not have a sea of electrons to transfer charges and that people prefer talking of conductance instead of resistance. Conductance being the exact opposite as the resistance and so we can say G = 1/R and reformulate the Ohm law as V = I/G.

Usually, the first attempt that almost any curious student do to measure conductivity of a chemical solution is to plug two electrodes to his ohm-meter and dip these electrodes in the liquid to be analysed. However, this does not work and if you try the experiment, you will read a constantly changing value on your ohm-meter that will never settle. To understand what is happening at the electrode when it is immersed in the saline solution we will have to go a bit deeper into the science that study the interactions of chemistry and electricity: electrochemistry.

First of all, let us have a look at what are saline solutions. In fact, and to be more general, we will talk about electrolytic solutions. When some chemicals, being liquids, solid or gases, are dissolved in a solvent like water, they will be torn apart by the molecules of the solvent into two or more charged species. Why some chemicals are split apart and other not is the mystery of quantum mechanics, let us say at the moment that the whole system is more stable like that (it minimizes the free energy of the system). We will call these smaller charged entities ions and we will have positive and negative ions. Because of the electro-neutrality principle, when a neutral electrolyte is dissolved, it splits into exactly the same amount of positive and negative charges. For instance, kitchen salt sodium chloride, NaCl, will be split into positively charged sodium ions, Na⁺, and negatively charged chloride ions, Cl^-. Sulfuric acid, H₂SO₄, on its side will separate into two protons, H⁺, and one sulphate ion SO₄^2-. Note that the sulphate ion brings two negative charges such that it compensates the two positive charges of the released protons.

Also, and because things are never black and white, electrolytes will never completely dissolve into the solvent. You will often here of strong and weak electrolytes but the fact is that there is always a limit to how much a component can dissolve. Mathematically, this is expressed as the product of the activities (which are linked to concentrations) of the ions being less or equal to a tabulated constant. Strong electrolytes will have very large constants and weak electrolytes will have low ones. Trickier cases are the ones with several dissociations like sulfuric acid because the two protons are not released simultaneously and the first reaction has a much larger constant than the second reaction. Dissolution reactions of strong electrolytes are often represented by a normal arrow and dissolution reactions of weak electrolyte are represented by a double arrow, meaning that there is still some of the reactant present too:

This means that, except at very high concentrations, when you dissolve sulfuric acid in water you will have no H₂SO₄ remaining but a lot of H⁺, HSO₄^- and some SO₄^2-. Note that if you remove protons by, say, neutralizing them with a base, you will increase the amount of SO₄^2- and decrease the amount of HSO₄^- until there is no more protons to be offered to the base.

The notions of strong and weak electrolytes are important to keep in mind when studying conductometry because the conductivity of the solution will depend on the actual charged species available and only applies then to the dissociated compounds.

So an electrolytic solution is a big soup of charged species. Why can’t it conduct current like metals?

To understand this, remember that the way the electrons move into the copper wire. When we insert an electron from the battery, it takes the place of an electron from the sea of electrons and allows then one to leave the copper wire to enter the rest of the electrical circuit. In our electrolytic solution, there is no sea of electrons but only a bunch of charged molecules or atoms that holds their electrons too well to allow for a transfer mechanism like in the metal conductor.

When a small potential is applied to an electrode, the electrons do not flow into the system. Instead, a small amount of electrons (or positive holes) accumulates in the electrode by the action of the potential difference but no charge transfer occurs between the electrode and the solution. The best the solution can do is to “stick” its oppositely charged ions on the wall of the electrodes from electrostatic attraction. So on one electrode you will have a layer a positive ions and on the other one a layer of negative ions. This layer is actually very thin because it repels further positive (or negative) ions from approaching the electrodes. It is called the electrolytic double layer and is about 0.1 nm thick.

The process occurring in a solution of NaCl is represented in Figure 2.

Now, if you remember well your lessons, you know that when a bunch of negative charges face positive charges and that no transfer can occur between the two layers, you get a capacitor which is like a reservoir of electrons. When you plug in a capacitor to a battery, it will start accumulating positive charges on one side and negative charges on the other, creating a current flow in the system. As the reservoir fills up, the potential increases between the two sides of the capacitor until the potential of the battery is not powerful enough to compensate this repulsion of adding more charges to the capacitor. And this is exactly what happens when you put the two electrodes of your ohm-meter into the solution because, at first, there will be a small current flowing into the system because the electrodes reservoirs are empty which will fool the ohm-meter into thinking that the current is actually flowing through a resistor while it is not. This will last only the time to completely fill up the reservoirs when no current will further flow leading the ohm-meter to display very high resistance. If by any chance you already tried using a larger potential (> 1 Volt) on an electrolytic solution, then you may have experienced a very different phenomenon taking place: bubbles start forming on the electrodes or the electrodes itself seems to dissolve into the solution. This is an electrolysis reaction and we want to avoid it at any cost.

We have seen that at small potentials the electrons cannot be transferred from/to the solution. But as the potential is increased the electrons becomes more “energetic” and, at some point, they will jump right into a positively charged ion. The opposite reaction occurs at the positive electrons where it becomes sufficiently energetic to allow an electron to be taken from the negatively charged ions. When this happens, a current indeed flows through the system but we also change the nature of the chemicals inside the solution. For instance, a solution of sodium chloride will be converted into hydrogen and highly toxic chlorine gaz. These reactions are well beyond the scope of this post but the important thing to remember is that the relation between current and voltage in such reactions do not follow the Ohm law and the resistance of the solution cannot be inferred from these two values. In fact, in building our conductometer, we will have to be very careful and use a low-enough potentials such that no reaction occurs between the electrodes and the electroactive species.

Let us now put these reactions apart and go back to our capacitor filling up. If we repeat the experiment with different salt concentrations, we will notice that the two electrodes system capacitance fills up faster with more concentrated solutions. This is because more dilute solutions have less ions travelling and it therefore takes more time for the electrode to reach its complete capacity. Hence the name “resistance” (and conductance) of the solution because it will take more or less time to fill up the capacitance of the electrode.

To understand how the conductometric probe will respond to an input signal, we have to study its impedance first. A good equivalent circuit is given in Figure 3. It includes the two electrodes double layer capacitance, C_e, the solution resistance, R, and the parasitic capacitance, C_p, which results from the capacitor formed by the two electrodes as the gap between them closes up.

The impedance of the system is then:

As an order of magnitude, C_e will be on the order of 10 to 100 µF and C_p will be on the order of 10 pF or more. Actual values will depend on the geometry of the electrodes and their processing. For instance, platinized “black” platinum electrodes have much larger capacitance because they offer a very large surface of contact when compared to a simple square copper surface. This is due to the extremely rough surface of the platinum when looked at the nanometer scale.

Also, and as the frequency increases, we may identify three regimes:

- At low frequencies the term 1/ωC_e becomes important when compared to R and ωC_p is still low so the overall impedance will be fixed by the electrolytic double layer capacitance. In Figure 3, this corresponds to the current being blocked by the two series capacitances of the electrode.

- At high frequencies the term ωC_p becomes much larger than 1/R and all the current will leak through the parasitic capacitance.

- At medium frequencies there will be a plateau where the impedance is proportional to the solution resistance over a range of frequencies with little impact of the capacitances elements. This is the operational range that we would like to use.

The optimal frequency will depend on the probe geometry and processing and it is dangerous to try to transfer the results obtained with one type of probe to another one. For instance, commercial conductometer uses platinized platinum electrodes and operates at 750 Hz typically while our circuit here will operate at around 13 kHz with its custom probe. The probe used here consists of two thick 2.0 mm copper wires of about 15 mm long and separated by 5 mm. A picture of the probe is shown in Figure 4. I used a POM plastic piece with precise drilling to hold the wires in place and get more consistent results.

If you would like to experiment with a new type of probe, the best thing to do is to record its actual response over a large range of frequencies. This can be done with a frequency generator such as the Protek 9205 that I am using, a current to voltage converter such as the one of Figure 7 and an oscilloscope to monitor the output. You can also use the full circuit of Figure 7 provided you use a stronger low-pass filter so as to cut even the very low frequencies that you will be analysing.

I made the experiment with the copper wire probe and plotted the results on Figure 5. The first and third regimes can be seen as the (almost) straight lines at the beginning and at the end of the plot. The plateau regime is not obvious but occurs at about 8-40 kHz for the most diluted solution. The size of the plateau however decreases as the concentration increases. This is particularly obvious with the more concentrated solution where the signal drop very fast as the frequency increases. In fact, for frequencies above 20 kHz, concentrated solutions cannot be distinguished anymore from more dilute ones anymore as the green curve drops below the orange one.

For the circuit presented here, I have chosen a frequency of 13 kHz because it is the one that maximize the sensitivity in the solutions of medium to low concentrations (<20 g/l NaCl). If you would like to study concentrated solutions as well, then operating around 4 kHz is probably a better idea.

Let us now analyse our conductometer circuit. It is composed of three main parts:

- Generating the input sine wave with a fixed amplitude that is low enough to prevent reactions at the electrodes

- Collecting and converting the alternating current to a proportional voltage

- Convert this alternate voltage to a dc voltage proportional to the amplitude of the alternating sine wave.

The first part was built using a four stage RC filter with a feedback gain of 12.5. Theoretically, a gain of 11.7 would already be enough but because of components tolerances, a slightly higher gain is generally required. If you cannot get the circuit to oscillate, try replacing R6 by a 18k resistor to bring the gain to 15. It is however not a good idea to directly try with a higher gain because it will produce more distortions in the signal. The circuit should now oscillate around 13 kHz. If you would like more information on how to get different oscillation frequencies, please read my [»] previous article to get more information on this.

The amplitude of the sine wave is then reduced by the trimmer RV1 to about 40 mVrms. You can tune the amplitude using an oscilloscope with its input probe connected to the “probe+” pin. I would not recommend using an AC voltmeter for that because they are not designed to operate at frequencies different than 50 Hz, except if you have a professional true RMS voltmeter. If you don’t have an oscilloscope, connect a 1.8k resistor matched to R7 to the probe pins and tune the output to about 36 mV dc. There is a small difference between the two because 40 mVrms corresponds to a peak amplitude of 56.6 mV and the alternative to dc converter that is used in this circuit has a gain of 0.637 (2/pi).

I found the 40 mVrms amplitude to be working nice but you can use a different value if you prefer. Just a few rules of thumb:

- Higher amplitude will reduce the effect of noise on the measurement and increase the SNR. Just try to avoid potentials above 0.1 Volts dc to prevent reaction at electrodes from happening.

- Lower amplitude will result in higher achievable conductance measurement. This is because the maximum current that can be delivered by the TL074 op-amp is about 5 mAmp and because G = I/U, the lower U, the higher the maximum conductance can be for a given maximum current.

The second and third parts of the circuit comprise a current-to-voltage converter and a rms output stage. The resistor R7 will fix the conductance range accepted by the circuit. You can use a fixed resistor or a selector with different resistor values. I got good results for medium concentration (from 25 g/l to 0.25 g/l of NaCl) with a 1.8k resistor. If you would like to analyse more dilute solutions such as tap water or demineralized water, you will have to use a higher resistor value, probably up to 180k.

The output of this current-to-voltage converter then enter a full-wave rectifier which has already been discussed in [»] this previous article. The rectified output then enters a second order Butterworth low-pass filter which will remove the carrier frequency (13 kHz). It has a -3 dB cut-off frequency of 20 Hz so you can keep track of dynamic phenomenon with this circuit.

Finally, a TC962 is used to power-up the op-amp from a 9-12 Vdc source.

The circuit was then tested with a 25 g/l NaCl solution, successively diluted to 0.25 g/l using a 50 ml graduated flask. 10 ml samples were taken every time to get a conductivity reading and the resulting values are plotted on Figure 9.

Please note that the data of Figure 9 are presented on a logarithmic scale and so the trend shown as linear is actually a power law. Some fluctuations can be observed but they are probably due to the accuracy of the successive dilutions procedure used. The trend is however shown to be reproducible for a 1:100 concentration range with only one resistor. Larger range can certainly be obtained by using a selector with different resistor values. Still, a 1:100 dynamic range is already enough to analyse reaction kinetics, follow titrations and monitor drinking water conductivity.

Analysing the results of Figure 9 is not an easy task because the increase of conductance of a solution with concentration does not follow a linear law. I would then recommend calibrating the circuit with successively diluted solutions before inferring any absolute value from its output. Also, and as of now, the circuit outputs a conductance value which depend on the geometry of the probe. Most scientific texts will discuss in terms of conductance per length unit (typically, µSimens/cm or mSiemens/cm). The more accurate way of getting the cell constant of the probe that you are using is to order a calibration solution of known conductivity or to get a recipe of such a solution (even tough that will be less accurate).