Dependence of the permittivity on solvent mixing ratio

I am doing DFT calculations on an organometalloid compound to assess whether it dissociates into an ion pair in different solvents. I suppose that the more polar the solvent is the more stable this compound should be in its dissociated form. To achieve this I want to successively increase the permittivity of the solvent mixture using PCM. It was stated that this compound is well soluble in a 1:1 mixture of water and acetonitrile and now I am wondering if I can just calculate the mean permittivity value of both solvents and imply it in my PCM calculation to simulate this solvent environment. So my question is if the permittivity is directly proportional to the mixing ratio of two solvents.




You can consult reference (1) and others cited therein. [Nikitin and Lyubartsev](http://archive.ambermd.org/201704/att-0061/20721_ftp.pdf) explain:



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> Experimental data 26 [[Venables and Schmuttenmaer](https://doi.org/10.1063/1.475902)] show that the dielectric permittivity of water–acetonitrile mixture is about linear in terms of the volume ratio.
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[![enter image description here](https://i.stack.imgur.com/DcChx.png)](https://i.stack.imgur.com/DcChx.png)


*My interpretation* of volume ratio (or more accurately, volume fraction, which is used in Fig. 5) is that it is computed from the equivalent volumes of pure components that would be combined, so it can be translated linearly into a molar fraction. The alternative is that it implies application of a way of computing the partial molar volume of the components, since the density of the mixtures is *not* linear in the mole fraction (see Fig. 4).


*References*


(1) Nikitin, A. M.; Lyubartsev, A. P. New Six-Site Acetonitrile Model for Simulations of Liquid Acetonitrile and Its Aqueous Mixtures. *J. Comput. Chem.* 2007, **28** (12), 2020–2026. <https://doi.org/10.1002/jcc.20721>.


(2) Venables, D. S.; Schmuttenmaer, C. A. Far-Infrared Spectra and Associated Dynamics in Acetonitrile–Water Mixtures Measured with Femtosecond THz Pulse Spectroscopy. *The Journal of Chemical Physics* 1998, **108** (12), 4935–4944. <https://doi.org/10.1063/1.475902>.


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