Composition Dependence of Relative Permittivities of Binary Solvent Mixtures
Authors: Ogasawara Masaru , Suzuki Shohei , Nambu Noritoshi 
Published: February 2020

Binary solvent mixtures exist as liquids over a wide range of temperatures and pressures. For the rational use of the solvent mixtures it is essential to know their physical and chemical properties as functions of their composition and the ambience. The excess functions of physical constants (∆X
sln
E) can be represented in the polynomial form of the molar fraction (x
2) of the cosolvent by the empirical Redlich-Kister equation.
The equation clearly satisfies the condition that ∆X
sln
E is zero at x
2 = 0 and at x
2= 1. The physical constants of solutions include relative static permittivity, refractive index, viscosity, vaper pressure, etc. The relative permittivity reflects the ease with which dielectric polarization proceeds. The relative permittivity is a measure of the solvent’s ability to insulate opposite charges from each other and has a very significant effect on the strength of the interactions between ions especially in dilute solutions. Electrostatic attractions and repulsions between ions are smaller in solvents with higher relative permittivities.
We consider a binary solvent mixture containing molecules “1” and “2”. The numbers of the molecules “1” and “2” are N
1 and N
2, respectively. Assuming the tetrahedral quadruplets (ijkl) in a liquid state and the random distribution of the solvent molecules, we have derived the equation of the dependence of relative permittivity (ε
r sln) on the composition of a binary solvent mixture. We obtained the coefficients (ai
) of the relative permittivities in the Redlich-Kister equation.

a
0 is a dominant factor governing ∆X
sln
E. a
0 may reflect the difference in the cooperative orientation polarization between the same and different types of dipoles. a
1 and a
2 may represent the difference in the contribution of the two components to the cooperative orientation polarization.
We investigated the relative permittivities (ε
r sln) and excess relative permittivities (∆ε
r sln
E) of binary mixtures of ethylene carbonate (EC) and linear carbonate as a function of the composition at 25 ºC. The symbol x
2 denotes the molar fraction of a low-viscosity solvent: 2-fluoroethyl methyl carbonate (2FEMC) or ethyl methyl carbonate (EMC). EC is a cyclic carbonate, whereas 2FEMC and EMC are linear carbonates. EC and EMC are commonly used as high-polarity and low-viscosity solvents, respectively, for lithium-ion batteries.
The equations of the composition dependence of ε
r sln and ∆ε
r sln
E fitted experimental data. The ε
r sln of the EC−2FEMC binary mixture was higher than that of the EC−EMC counterpart. The value of a
0 found in the EC−2FEMC binary solvent system (−49) was less negative than that in the EC−EMC binary solvent system (−51). These findings suggest that the amount of the cooperative orientation polarization of the EC−2FEMC binary mixture is larger than that found for the EC−EMC counterpart. The attraction between EC and 2FEMC molecules can be based on nonconventional weak intermolecular hydrogen bonding (CF−H···O or C−H···F−C). The weak hydrogen-bonding system does not exchange its proton and therefore it is no more a genuine hydrogen bond; it is an electrostatic attraction between positive charge on the hydrogen and negative charge on the organic fluorine or the organic oxygen.