Terahertz response of dipolar impurities in polar liquids: On anomalous dielectric absorption of protein solutions

A theory of radiation absorption by dielectric mixtures is presented. The coarse-grained formulation is based on the wave-vector-dependent correlation functions of molecular dipoles of the host polar liquid and a density structure factor of the solutes. A nonlinear dependence of the dielectric absorption coefficient on the solute concentration is predicted and originates from the mutual polarization of the liquid surrounding the solutes by the collective field of the solute dipoles aligned along the radiation field. The theory is applied to terahertz absorption of hydrated saccharides and proteins. While the theory gives an excellent account of the observations for saccharides, without additional assumptions and fitting parameters, experimental absorption coefficient of protein solutions significantly exceeds theoretical calculations with dipole moment of the bare protein assigned to the solute and shows a peak against the protein concentration. A substantial polarization of protein's hydration shell, resulting in a net dipole moment, is required to explain the disagreement between theory and experiment. When the correlation function of the total dipole moment of the protein with its hydration shell from numerical simulations is used in the analytical model, an absorption peak, qualitatively similar to that seen in experiment, is obtained. The existence and position of the peak are sensitive to the specifics of the protein-protein interactions. Numerical testing of the theory requires the combination of dielectric and small-angle scattering measurements. The calculations confirm that "elastic ferroelectric bag" of water shells observed in previous numerical simulations is required to explain terahertz dielectric measurements.