Dielectric Relaxation for Studying Molecular Dynamics of Pullulan in Water

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.

Physical Meanings of Fractal Behaviors of Water in Aqueous and Biological Systems with Open-Ended Coaxial Electrodes

The dynamics of a hydrogen bonding network (HBN) relating to macroscopic properties of hydrogen bonding liquids were observed as a significant relaxation process by dielectric spectroscopy measurements. In the cases of water and water rich mixtures including biological systems, a GHz frequency relaxation process appearing at around 20 GHz with the relaxation time of 8.2 ps is generally observed at 25 °C. The GHz frequency process can be explained as a rate process of exchanges in hydrogen bond (HB) and the rate becomes higher with increasing HB density. In the present work, this study analyzed the GHz frequency process observed by suitable open-ended coaxial electrodes, and physical meanings of the fractal nature of water structures were clarified in various aqueous systems. Dynamic behaviors of HBN were characterized by a combination of the average relaxation time and the distribution of the relaxation time. This fractal analysis offered an available approach to both solution and dispersion systems with characterization of the aggregation or dispersion state of water molecules. In the case of polymer-water mixtures, the HBN and polymer networks penetrate each other, however, the HBN were segmented and isolated more by dispersed and aggregated particles in the case of dispersion systems. These HBN fragments were characterized by smaller values of the fractal dimension obtained from the fractal analysis. Some examples of actual usages suggest that the fractal analysis is now one of the most effective tools to understand the molecular mechanism of HBN in aqueous complex materials including biological systems.