Conductivity (non-aqueous)

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Conductivity of toluene-methanol mixture within full composition range. Points – experiment. Line – results of calculation using model described in section Theory

There is large difference between conductivity of aqueous solutions and solutions based on non-polar liquids, like toluene, hexane etc. For instance, conductivity of aqueous standard is about 0.1413 S/m, whereas conductivity of non-polar toluene is around 10-10 S/m. Typical range of non-aqueous solutions conductivity is shown on the Figure on the right. This large difference is associated with qualitative differences in ionization of water and non-polar liquids, chemical nature of potential electrolytes that are very different, solvation of ions and ions interaction. Measurement methods are also very different due to very large differences in measured parameters.

History

It is known that liquids and liquids mixtures besides water conduct electric current since pioneering studies by Faraday in middle 19th century. Apparently the first dedicated experiments were initiated by Arrhenius and Ostwald according to the first publication on this subjected authored by Kablukoff in 1889 . He conducted his studies in Leipzig University and expressed acknowledgment to Ostwald and Arrhenius for their support. He studied conductivity of HCl in benzene, hexane, ether. He discovered that molar conductivity decays with dilution, which is opposite to the aqueous solutions. The second publication was made in 1906 by Plotnikow who worked in Kiev . He studied conductivities of methylbromide and ether. These liquids are practically non-conducting, whereas their mixture becomes conducting, at some concentrations as conducting as aqueous solutions. He pointed out that dielectric constant plays important role. This conclusion is widely accepted now after large number of studies overwide in the recent publication confirmed it during last century.

Classification of liquids according to dielectric constant

The observation by Plotnikov provides background for classification of liquids based on their dielectric constant ε introduced by Lyklema :

• non-polar if ε < 5
• low-polar 5 < ε < 12
• semi-polar ε >12
• polar ε >= 80

The polarity of a liquid declines with decreasing dielectric permittivity and this is reflected also in the liquid’s conductivity. Less polar liquids are usually less conductive. For instance, conductivity of semi-polar pure ethanol is above 10-4 S/m. In general, conductivity of polar and semi-polar liquids occurs for the same reasons as in aqueous solutions, nature of ions with their solvating layers is the same as in water. In contrast, conductivity of low- and non-polar liquids is orders of magnitude smaller than in aqueous solutions. For instance, conductivity of non-polar toluene is around 10-10 S/m. There are 3 factors that determine this difference.

Factor 1 – solubility. Simple electrolytes like inorganic salts that are used as electrolytes in aqueous solutions are not soluble in “low- and non-polar liquids”. The substance should possess hydrophobic tale for being soluble in such liquids, in addition to the polar head that ensures dissociation. Using of such “amphiphilic substances” for ionization of non-polar liquids was systematically introduced by Fuoss and Kraus in serial of papers in middle 20th century. .

Factor 2 – solvation. All ions is liquids are covered with “solvation layers” that statically stabilize cations and anions against re-aggregation into neutral entities. In aqueous solution the polar water molecules with large dipole moments build up these layers. The molecules of low- and non-polar liquids do not have large dipole moments which limit their interaction with the charge ion core. Instead, the neutral molecules of the added amphiphilic substance serve such solvating role building layers around the core charge. This was formulated by Morrison who stated that ions formed by amphiphilic substances in low- and non-polar liquids are “inverse micelles”.

Factor 3 – ion pairs. The low dielectric constant of non-polar liquids leads to much stronger attraction between cation and anion. Some of them come together and form neutral entity called “ion-pair”. This notion was introduced into electrochemistry in 1929 by Bjerrum . Ion-pair differs from the neutral molecule because solvating layers are incorporated into it. Ion-pairs restrict conductivity of non-polar liquids, similarly to ion-clouds of Peter Debye in aqueous solutions. Ion pair is stable if distance between ion cores is comparable to so-called Niels Bjerrum distance λ:

$$\lambda =\frac{e^2{z}^2}{4\epsilon {\epsilon }_{0}kT}$$

where e is elementary charge, k is the Boltzmann constant, T is temperature. In water the Bjerrum distance is only 0.71 nm, whereas in toluene with dielectric constant of 2.36 it is about 21 nm. This reflects much the stronger electrostatic attraction in non-polar liquids in the same distance between ions, which leads to a much higher probability of formation of ion pairs when compared to water.

Theory

Ions that are incorporated into ion pairs do not contribute to conductivity. This mechanism was considered in deriving theory of conductivity in low- and non-polar liquids by Onsager and Fuoss . Their theory was developed only for small concentrations of additives. It also contained un-essential terms of electrophoretic retardation, which made it quite convoluted. This term is negligible for low conducting liquids because Debye length is much longer than ion size. The new version of was suggested by Dukhin and Parlia . Here is their expression of conductivity K that takes ion-pairs into account:

$$K=\frac{eF}{4\pi \eta N_a{d}^4}EXP(-\frac{\lambda }{d})[\sqrt{1+(EXP\frac{\lambda }{d})*\frac{16}{3\pi N_a{d}^3\varphi C}}-1]$$

where d effective hydrodynamic ion size, Na is Avogardo number, C is molar concentration of ions in the pure solute liquid in mol/dm3, φ is volume fraction of solute.

This theory was verified with many different liquid mixtures with results published in several papers summarized in the paper . It was also verified and confirmed independently by the group from Carnegie-Mellon University

Here we reproduce results for mixture of toluene with methanol within full composition range on the Figure at the beginning of this article. It is seen that the theory fits experimental data within 7 orders of magnitude. The Dukhin-Parlia conductivity theory makes some important predictions.

Lines - conductivity multiplied by viscosity versus ion size calculated using theory described here for various values of the liquid dielectric constant. Histogram – is frequency of mentioning particular ion size from literature, 53 data points from 17 published papers.

The first one is the existence of "critical ion size". The figure on the right presents graphically dependence of conductivity on the ion size. It is seen that this dependence has maxima around 1 nm. This corresponds to a “critical ion size”. Ions with these sizes produce the highest conductivity of the solution, which is confirmed with data points from many studies that contain data on ion sizes.

Another theoretical prediction is regarding range of dielectric permittivity where ion pairs form. It turns out that this critical dielectric permittivity of solution is 10, ion pairs start forming when dielectric permittivity drops below 10. This prediction is valid if ionic strength of the liquids is low (<10-6 mol/l). This threshold shifts towards higher dielectric constants with increasing ionic strength.

Measurement

Photo of typical non-aqueous conductivity probe designed as concentric cylinders, used, for instance, in the paper

There are several peculiarities of measuring non-aqueous conductivity in low-and non-polar liquids. First of all, the current electric magnitude is much smaller by many orders of magnitude compared to aqueous solutions due to very low conductivity. Measurement of such low current requires probes with very high cell constants. It is achieved usually by employing design of concentric cylinders as shown on the Figure. Sample fills the gap between internal solid cylinder and external electrode which looks like a pipe. Secondly, there is no electrochemical reactions at electrodes, which eliminates potential electrodes polarization. Third, electric field must be applied in low frequency AC mode, usually a few tens of hertz. This prevents accumulation of ions at one of the electrodes, which would cause concentration polarization and measurement artifact.

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