Mixing Rules

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Mixing rules determine how dielectric constant varies with concentration. For many materials the permittivity e of a mixture containing volume fraction f_a of non-polar polymer A with relative permittivity e_a and volume fraction f_b of additive material with relative permittivity e_b is given by

e^1/3 = f_ae_a^1/3 + f_be_b^1/3

In two component mixtures, the volume fraction concentrations add to one and the additive concentration is proportional to the cube root of the permittivity.

The Proceptor analyzer determines concentrations of ingredients in mixtures based on differences in the electrical properties of the ingredients. Most polymers are relatively non-polar and they therefore have low permittivities, between 2 and 4. Fillers and additives are more polar and have higher permittivities. The higher the concentration of additive, the greater the permittivity of the mixture.

Mixing rules facilitate the quantitative determination of chemical concentrations and the estimation of resolution in prospective applications.

Examples: materials quantitatively measured with Proceptor in-line dielectric analyzers:

additives

fillers

comonomer ratios

solvents

chlorination

air