Electrical Conductivity and Ionic Radii

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A user commented on how and why are ionic radii used in OLI's electrical conductivity model?

Are the hydrated radii for complex ions such as CaHCO3+, CaPO4-, etc. calculated in OLI software? If so, where can user find the output and how are they calculated?

The radius values that may appear in the OLI databanks are not used anymore. These are crystallographic radii used in Helgeson EOS estimations. They were used for aqueous and ion species even though they came from crystallographic data. Peiming Wang (OLI) says the ionic radii are used in the calculation of electrical conductivity. These values are stored in the file LIMCON.DAT (another text file). If no data exists then a mean-spherical approximation (hard shell) is used to estimate the radius and then the distance between the ions are calculated. The parameters are not exposed to the output stream directly only via the electrical conductivity values calculated.

In the OLI paper on Electrical conductivity that Peiming Wang wrote 2 radii are used, crystallographic radii and effective ionic radii. How are these related to hydrated radii?

In the OLI electrical conductivity model, OLI did use the “crystallographic” radii and “effective” radii. The crystallographic radii are the default values of the effective radii when the ionic interactions are all set zero, as the effective radii have been defined (empirically) as a function of the ionic concentrations and dependent also on the ion-interactions. The function is empirical as there is no a priori knowledge to relate these two. The effective radii was introduced specifically for concentrated ionic solutions to reflect the effects of concentrations and interactions between ions and other solute and solvent components. The crystallographic ones can generally be used only at low concentrations (up to ~1 molal) based on the underlying model (with Mean Spherical Approximation approach); more concentrated solutions depend on the effective radii for the corrections.

There are published papers and books by Yizhak Marcus and other that have more information on the subject. The book by Marcus “Ion Properties” (Marcel Dekker, Inc. New York, 1997) has a chapter called “ionic radii” that discuss this. There are a number of references included in that chapter.

I understand that crystallographic radii and effective ionic radii are used in electrical conductivity model. However what the user is asking is hydrated radii. Do you mean hydrated radii = effective ionic radii? I though these were different.

A simple answer is no. The effective ionic radii consider not only the hydration (by solvent water) but also effects of other species (ions, molecules) in solutions. We do not use hydrated radii in our models (both thermos and transport properties). To my knowledge, the hydrated ionic radii is in general inversely related to the non-hydrated radii (e.g. crystallographic), as the attraction of water molecules around an ion depends on that ion's density of charge, smaller ions (and thus ions of greater ionic potential) attract more water molecules. There are lots of discussions on the subject including the references I provided in the previous email that they can research on.

Editor: James W Berthold Author: Peiming Wang