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Electrical Conductivity

Electrical conductivity is the ability of a material to carry electrical current. In water, it is generally used as a measure of the mineral or other ionic concentration. Conductivity is a measure of the purity of water or the concentration of ionized chemicals in water. However, conductivity is only a quantitative measurement: it responds to all ionic content and cannot distinguish particular conductive materials in the presence of others. Only ionizable materials will contribute to conductivity; materials such as sugars or oils are not conductive.

In a metal conductor, electrical current is the flow of electrons and is called electronic conductance. In water, electrical current is carried by ions since electrons do not pass through water by themselves. This is electrolytic conductance.

When a voltage is applied between two inert electrodes immersed in a solution, any ions between them will be attracted by the electrode with the opposite charge. Ions will move between electrodes and produce a current depending on the electrical resistance of the solution. This is the basis of conductivity measurement—an application of Ohm’s law. For high purity waters, it is common to express conductivity as its reciprocal, resistivity.

To prevent altering the sample by major ionic movement and electrochemical reaction at the electrodes, alternating current is always used for measurement. With AC the polarity changes frequently enough that ions do not move or react significantly. Measuring systems must control the voltage, frequency and current density to minimize errors due to electrode polarization and capacitance. Modern instrumentation may change one or more of these variables automatically, depending on the conductivity range being measured.

Units of Measure

Conductivity is the conductance of a standardized volume of water with 1 cm² cross-sectional area and electrodes spaced 1 cm apart as shown in Figure 1. The same results will be obtained with various geometries as long as the ratio of length / area is equal to 1 cm^-1, the cell constant. Units of measure are related as listed in the table below. Since most conductivity values are quite small, unit multiplier prefixes of milli (m, 10^-3) and micro (m, 10^-6) are commonly used.

Units Related to Conductivity Measurement

* Most users employ units of S/cm. However, SI conductivity units used in some parts of the world are S/m which can easily be confused. 1 S/cm = 100 S/m.

The standardized geometry of the cell constant assures that conductivity measurement is a property of the sample and not of the sensor. The cell constant is determined with precision by calibration in known conductivity standard solutions. Accepted standard potassium chloride solutions are established in an ASTM standard method. Standard reference materials are also available from NIST.

Cell constants other than 1 cm^-1 may be used as long as the measuring instrument readout is normalized accordingly. A lower cell constant sensor is needed to enable the measuring instrument to make accurate measurements in low conductivity (high resistivity) samples. Higher cell constants are needed to measure in high conductivity samples. The exact requirements depend on the measuring instrument.

Most practical cells do not use the parallel plate electrode arrangement of Figure 1. They have greater durability and allow more convenient installation with other arrangements. For example, typical pure water sensors for on-line measurement use concentric electrodes that maintain the spacing and geometry for 0.01 to 0.1/cm constant. A variety of two-electrode process conductivity sensors is illustrated in Figure 2.

Conductivity of very dilute solutions can be calculated from physical chemistry data based on Equation 1 which sums the conductivity contribution of all ions in the solution.

L  =  r  *  S (l_i * c_i)                                                                                                    (1)

L  =  conductivity

r  =  density of water

l_i   =  equivalent ionic conductance of ion ‘i’

c_i   =  concentration of ion ‘i’

Temperature Effects

Conductivity is affected by temperature since water becomes less viscous and ions can move more easily at higher temperatures. Conventionally, conductivity measurements are referenced to 25 °C though occasionally a 20 °C

 reference is used. The variation with temperature is apparent in Equation 1 since l_i, and to a lesser degree, r are temperature dependent. The conductivity of most ions increase in conductivity by about 2.2% of their value per °C which allows for simple temperature compensation. This is suitable for most mid-range conductivity measurements. Very low and very high conductivity samples require special handling of temperature effects.

As water is purified below 5 µS/cm (>0.5 MW×cm), the small amount of hydrogen (H+) and hydroxide (OH-) ions from water itself become a significant part in the total conductivity. That is, the concentrations, c_i. in Equation 1, of H⁺ and OH^- must be included. Water self-ionizes to a much greater degree at higher temperatures, producing a higher concentration of ions. Those ions are also more conductive. The temperature coefficient increases to 4 – 7 %/°C, depending both on purity level and temperature, with both effects being non-linear. These effects are evident in Figure 3. Specialized high purity temperature compensation must be employed to achieve accurate measurements in this low conductivity range. 

Highly concentrated solutions also exhibit deviant behavior. In modest concentration ranges, conductivity is roughly proportional to concentration. At higher concentrations, Equation 1 does not apply and ionic interference restricts the mobility of the ions. Conductivity levels off and in many cases decreases with increased concentration as shown in Figure 4. Measurement near the peaks of these curves is ambiguous and cannot be relied on for inference of concentration since there are two possible values. Highly conductive solutions also have lower temperature influence, typically less than 2 % / °C.

Alternative Measurement Technologies

Figure 1 and its description above refer to the conventional two-electrode sensor and measurement technique. Four-electrode conductivity measurement uses a sensor incorporating four electrodes. It is useful for highly conductive and/or dirty water samples which would foul the surfaces or plug the narrow passages of conventional high constant two-electrode sensors.

Four-electrode measurement applies AC through the sample via two outer drive electrodes as shown in Figure 5. These electrodes may become fouled and the circuit will compensate to maintain the AC current level constant. Two inner measuring electrodes are used to sense the voltage drop through the portion of solution between them. The circuit makes a high impedance AC voltage measurement, drawing negligible current and making it much less affected by additional resistance due to fouling of the measuring electrode surfaces. Sensors for four electrode conductivity measurement are shown in Figure 6.

Inductive (also known as non-contact, electrodeless or toroidal) conductivity measurement is made without any direct electrical contact with the sample. The sensor consists of two parallel coils sealed within a doughnut-shaped insulated probe as shown in Figures 7 and 8. The instrument energizes one coil with AC. A weak AC current is induced into the surrounding sample, depending on its conductivity. That current, in turn, induces a signal into   the measured coil which provides the measurement signal. The sample acts like the core of a transformer.  A temperature sensor is incorporated into the probe body to enable compensation in the instrument.

Because there are no electrodes in contact with the sample, extreme fouling conditions can be tolerated. Coatings can cause errors only if there is so much accumulation that it reduces the diameter of the hole. Care is needed in installation of inductive sensors to allow for the specified spacing around it. Otherwise the cross-section of sample immediately around the probe (cell constant) will be affected and recalibration may be required.

Total Dissolved Solids (TDS)

TDS is sometimes inferred from conductivity and is reported in units of parts per million. However, the relationship of conductivity and concentration is not standardized and to be meaningful, should be specified whenever TDS units are used. Typical conversions are based on sodium chloride (which may also be called salinity) at approximately 0.5 ppm TDS per mS/cm. Alternatively, a “natural water” mineral composition including bicarbonates would have a conversion of 0.6 – 0.7 ppm TDS per mS/cm. Conversions may also be slightly non-linear with concentration.

Figures

Figure 1 – cell constant = 1 cm electrode spacing divided by 1 cm² cross-sectional area of sample

Figure 2 – Conventional two-electrode conductivity sensors: 0.1 cm^-1 in retractable housing, 0.1 cm^-1 in flow chamber, sanitary 0.1 cm^-1, 10 cm^-1 insertion, 50^-1 cm insertion, long 0.1 cm^-1 insertion, short 0.1 cm^-1 insertion.   

Figure 3 – High Purity Water Conductivity vs. Temperature

Figure 4 – Conductivity vs. Concentration at 25°C

Figure 5 – Four-electrode Conductivity Measurement

Figure 6 – Four-electrode Conductivity Sensors

Figure 7 – Inductive Conductivity Measurement

Figure 8 – Inductive Conductivity Measurement Equipment

Bibliography

1.       Standard Test Methods for Electrical Conductivity and Resistivity of Water, D1125, American Society for Testing and Materials, Conshohocken, PA.

2.       Certificate of Analysis, Aqueous Electrolytic Conductance Standard Reference Materials 3190-3193, 3198-3199, National Institute of Standards and Technology, U. S. Department of Commerce, Gaithersburg, MD.

3.       Standard Test Method for Electrical Conductivity and Resistivity of a Flowing High Purity Water Sample, D5391, American Society for Testing and Materials, W. Conshohocken, PA.

4.       Weast, R. C. ed., CRC Handbook of Chemistry and Physics, 59^th ed, CRC Press, West Palm Beach, FL, 1978, pp. D265–D314.