I would like to compute dielectric constants of organic:aqueous mixtures. Would linear addition of the dielectric constants of the pure solvents give reliable results? For example, for a volume fraction of 0.3 THF (dielectric = 7.5) in water (dielectric = 79), one may compute 0.3*7.5 + 0.7*79 = approximately 57.6 ?
Yes, maybe quasi-realistic for some simple (model) cases.
Such a linear model for Dielectric constants, κ, scales (quasi-)linearly (C ~ κ)[1], mainly, as their virtual (micro or nano) Capacitors; so, your linear model can be an initially good approximation, alike in a quasi-parallel connection[2] (d/A -> 0[1]) of (micro or nano) Capacitors' morphology[3], e.g. in accordance with their (micro or nano) phases' morphology.
1. In the parallel plate capacitor, the capacitance is given by: C = κ ε0 A / d , where,
C is the capacitance of the parallel plate capacitor.
κ is the dielectric constant.
𝜺0 is the permittivity of the free space.
A is the area of parallel conducting plates plates
d is the separation between parallel conducting plates plates
2. In a parallel connection of Capacitors, the total capacitance is given by: C = C1 + C2 + ...
3. Investigation of water electrical parameters as a function of measurement frequency using cylindrical capacitive sensors https://www.sciencedirect.com/science/article/pii/S0263224112002710
iin my opinin, instead of direct volume fraction, mole fraction on weigth basis may give better approximation.
The linear addition of dielectric constant (as you mentioned in the question) is not used as I know. In order to predict or calculate the dielectric constant of a mixture, you can use an equation called Kraszewski equation.
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