Effective Medium Model Applied to Biopolymer Solutions

Studying dielectric properties of heterogeneous systems is challenged by a problem of uncertainty of the ratio between dielectric permittivity of the system and dielectric permittivities of its components. Such ratios can be obtained in some cases using theoretical effective medium models. However, such models have not yet been developed for all the systems possible. Particularly, there is no effective medium model with filamentary inclusions. Such a theoretical model elaborated based on the fundamental principles of electrodynamics of continuous media is suggested in the present work. Any point of a filamentary inclusion with a length that is significantly greater than the thickness can be regarded as being located in a long cylinder-like fragment of the inclusion with stochastic direction of the cylinder axis relative to the external electric field. With this regard, electric field strength and electric induction values were averaged across the entire volume of a two-phase dielectric material. As a result, a model linking the dielectric permittivity of the two-phase system and the dielectric permittivities of both phases was elaborated. The model appears to be highly relevant for studying solutions of biopolymers, such as nucleic acids, fibrillar proteins and protein aggregates, polysaccharides, by means of electrical impedance spectroscopy, dielectric spectroscopy, and terahertz time-domain spectroscopy. The suggested theoretical model was successfully validated on a DNA solution within the terahertz region.