Whitepaper How to Measure Conductivity over a Wide Range and at Ultra‐low Levels Ilium Technology’s Model 2100 conductivity meter and associated probes provide unprecedented range and sensitivity in conductivity measurements in liquid systems, from milli‐Siemens/cm down to as low as 1 femto‐Siemen/cm. To do so, they employ a number of proprietary and patent (pending) technologies. This paper will present some background on conductivity measurements and describe the technical approach used in order to provide a better understanding of the instrument’s capabilities. What is conductivity? Conductivity is a material property that quantifies the amount of current that will flow through a material in response to an applied electrical potential relative to the cross‐sectional area of the sample and the distance the current travels through the material. It is measured in Siemens/cm. One Siemen equals one amp of current per Volt of applied potential. Some older measurements may be seen in the literature using the unit Mhos/cm, a unit which is no longer used but which remains interesting because the name itself reflects the inverse relationship between resistance (R, measured in Ohms) and conductance (G, measured in Siemens formerly Mhos). Likewise, resistivity (ρ, measured in Ohm‐cm) is the inverse of conductivity (σ, measured in Siemens/cm) (equation 1). (1) G = 1/R and σ = 1/ρ It is important to distinguish between conductivity and conductance. The relationship is exactly analogous to the relationship between resistivity and resistance. Conductance and resistance are properties of specific circuit elements, while conductivity and resistivity are properties of materials. Both are governed by Ohm’s law (equations 2 and 3) relating current flow (I) to the applied potential (V). (2) R = V/I Substituting G = 1/R we get (3) G = I/V Conductivity can be a property of almost any material. The discussion that follows is limited to measurements of conductivity in liquid systems. Why measure conductivity? Conductivity measurements provide fast, continuous, inexpensive indications of changing electrical and material properties. This is useful in many research, development, analytical, quality control, and process control applications. Typical applications include: 
Solvent purity, additive concentration, additive titration, total dissolved solids. Ilium Technology Conductivity Whitepaper 
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DI water purity ‐ deionized (DI) pure water is a relatively poor electrical conductor compared to tap or salt water. At 25°C and pH 7, it has a resistivity of 18.2 million ohm‐cm (meg‐ohm‐
cm) or a conductivity of 55 nano‐Siemens/cm. It is the amount of ionized substances dissolved in the water which increases water's ability to conduct electricity above this value. Clean‐in‐place for solvents and water – the cleaning process is monitored by measuring the purity of the effluent solvent as indicated by its conductivity. Personal care and cosmetics – the purity, acidity, presence of additives, etc. of natural (e.g., vegetable) and synthetic (e.g., silicone) oils used in these products can be tracked by conductivity measurements. Jet fuels and other flammable, non‐polar solvents ‐ avoiding conditions leading to static discharge during pumping, transferring, filtering and mixing operations requires the conductivity of these materials to be kept above a minimum level of about 1 pico‐
Siemen/cm. Inks ‐ conductivity of ink dispersions is affected by both soluble components and charge on pigment particles. Conductivity measurements provide a means to track dispersant concentration and effectiveness. Paints and coatings ‐ conductivity of paint formulations is affected by both soluble components and charge on pigment particles. As with inks, conductivity measurement provides a means to track dispersant concentration and effectiveness. Why do I need a wide range of measurement? The range of conductivity measurements varies widely from application to application (figure 1), and may vary widely within a single process or experiment. A wide ranging measurement capability permits the user to: Follow a process ‐ In non‐aqueous systems, conductivities can easily swing over many decades with only relatively small changes in concentration of additives or impurities. The ability to follow that change with a single meter during a process can provide valuable, real‐time information. Replace multiple meters – Many commercial, industrial and academic laboratories must address a range of applications with a wide range of relevant conductivities. A single meter with a sufficiently wide range can eliminate the expense of multiple meters and the inconvenience and wasted time involved with switching meters for different applications. 2 Ilium Technology Conductivity Whitepaper Figure 1. Illustrating the conductivity measurement ranges associated with various applications. Measuring conductivity Conductivity of a liquid can be measured by immersing a pair of electrodes of known size, separated by a known distance and measuring the relationship between current flowing between the electrodes and the electrical potential applied to the electrodes (figure 2). Figure 2. Conductivity of a liquid is measured by determining the relationship between current and voltage between a pair of electrodes of known size and spacing immersed in the liquid. In this case the electrodes each have an area of 1 cm2 and are parallel and separated by a distance of 1 cm. If a current of 1 amp flows when a potential difference of 1 Volt is applied, the liquid has a conductivity of 1 Siemen/cm. 3 Ilium Technology Conductivity Whitepaper Problems with range The electrodes of a system designed to measure conductivity in aqueous samples are often configured as two rings separated by an insulator on a long thin cylindrical probe. The surface area of the electrodes and the distance between them are fixed. During measurement a potential difference is applied to the electrodes and the current emerges from one electrode and follows a curved path to return to the other electrode (figure 3). The length and shape of the current path are dependent, not only on the configuration of the probe, but also on the electrical characteristics of the liquid. Clearly, changes in path length will affect measured conductivity. For measurements over a limited range, the variation in path length can be accommodated by calibrating the probe with an appropriate standard of known conductivity. The calibration procedure determines the cell constant (the effective ratio of path length to electrode area) for a particular probe. The effects of changes in path length can be reduced by configuring the electrodes as concentric cylinders, however fringing at the edges of the electrodes can still introduce unacceptable variability over a wide measurement range. Figure 3. When electrodes are in‐line the current emerges from one electrode and follows a curved path to return to the other electrode. The length of the path varies with the conductivity and dielectric constant of the liquid, introducing errors into conductivity measurements that range widely. (Figure modified from Schwank and Green, Sensors 2007, 7, p553; available under public license, https://creativecommons.org/licenses/by/4.0/legalcode) Problems with sensitivity Early instruments designed for ultra‐low conductivities used DC measurements. While this technique can work in the low femto‐Siemen/cm range, it quickly runs into significant accuracy issues as conductivities approach and exceed 1 pico‐Siemen/cm. This is because as the conductivity increases, the rate of sample polarization becomes too fast for an accurate DC measurement to be made. AC measurements can eliminate this problem and work at both low and higher ranges. However, as the conductivity increases, the frequency required to stay ahead of the polarization effect also increases. As this occurs, additional AC signal components begin to overwhelm the sought after conductive component, once again leading to often unrecognized, but significant inaccuracies. At very low conductivities it becomes difficult to distinguish the conductivity signal from background noise. Although advanced signal processing techniques can extract accurate measurements from a noisy signal, it is important not to mistake an averaged noise signal for a valid conductivity measurement. 4 Ilium Technology Conductivity Whitepaper Ilium’s Model 2100 Conductivity Meter and Smart Probes Intelligent Signal Processing The Model 2100 Conductivity Meter and associated Smart Probes (figure 4) provide accurate measurements over a range of 12 decades from milli‐Siemens/cm down to 1 femto‐Siemens/cm. Traditional aqueous conductivity meters have difficulty measuring samples below about 1 micro‐
Siemen/cm, and none can measure below a few nano‐Siemens/cm. The Model 2100 uses adaptive wave forms, dynamic signal compensation, and adaptive noise suppression techniques to provide highly accurate measurements over an extraordinarily wide range of sample conductivities. Figure 4. Model 2100 Conductivity Meter and Smart Probe. Calibrated Smart Probes As we described in a previous section, conventional aqueous probes need calibration every decade. Moreover, calibration depends on the availability of accurate standards. Good conductivity standards below 10 micro‐Siemens/cm are notoriously difficult to obtain. At 10 micro‐Siemens/cm available standards have an accuracy of ± 2‐3%. At 1 micro‐Siemen/cm that accuracy degrades to ± 25%. For DI water in the nano‐Siemen range no standard is available. Ilium Smart Probes use concentric cylinder electrodes and incorporate guard electrodes to completely eliminate the effects of sample dependent variations in current path length on measurement accuracy (figure 5). The fully guarded probe design provides accurate measurements over the full design range of the probe without recalibration. Probes are calibrated using a NIST traceable procedure at the factory. All calibration data is stored in the probe from where it can be immediately retrieved by the model 2100 meter. Probes can be swapped as needed without recalibration. 5 Ilium Technology Conductivity Whitepaper All Smart Probes are also extremely easy to clean. They can be disassembled and reassembled in seconds with no change in the calibration or cell constant, providing complete reproducibility. This is an important advantage when measuring emulsions or particle dispersions such as paints and inks, which often leave particles or droplets deposited on the electrode surfaces. Figure 5. Ilium 1020 Smart Probe disassembled to show guard electrodes and signal electrode. The range of Smart Probes includes (figure 6): 
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1020 Smart Dip Probe, covering the range from 2.5 μS/cm down to 25 fS/cm, for general laboratory use. 1021 Smart Flow‐through Probe, covering the range from 2.5 μS/cm down to 25 fS/cm, for real‐
time, dynamic measurements in flowing liquids. 1010 Smart Dip Probe, covering the range from 1 mS/cm to 5 pS/cm, for higher conductivity applications. (Will be available soon). Low range Smart Dip Probe, covering the range from 0.5 µS/cm down to 1 fS/cm, for lowest conductivity applications. (Will be available soon). Figure 6. Showing the measurement ranges of various Ilium Smart Probes 6 Ilium Technology Conductivity Whitepaper Conclusions Ilium’s Model 2100 Conductivity Meter and associated Smart Probes provide accurate conductivity measurements over an extraordinarily wide range, from milli‐Siemens down to as low as 1 femto‐
Siemen. It is the only commercially available conductivity meter that can measure high, medium, low and ultra‐low conductivity with one conductivity meter. Its wide range allows users to follow wide ranging applications, such as clean‐in‐place processes, titrations, reactions and formulation processes, from start to finish. It can reduce capital expenditures by allowing one meter to replace as many as three conventional meters that would be required to cover the same measurement range. It can eliminate the wasted time and inconvenience otherwise required to change meters. Additional time savings accrue from the Smart Probes, which are factory calibrated and do not require recalibration during normal use. Calibration data is saved in the probe and automatically accessed by the meter, permitting instant probe exchange with no impact in reproducibility. Finally, the probes can be disassembled, cleaned and reassembled in minutes with no effect on calibration. The Model 2100 and Smart Probes are the only conductivity measurement system you will ever need. For more information, visit: www.iliumtechnology.com, email: info@iliumtechnology.com, or call us at: 781.333.4000. 7