The Dielectric Properties of β-Lactoglobulin in Aqueous Glycine Solutions and in the Liquid Crystalline State

The dielectric constant ε′ and loss factor ε″ of solutions of β‐lactoglobulin dissolved in aqueous 0.48, 1.5, and 2.5 molar glycine, and the dielectric constant of β‐lactoglobulin liquid crystals have been measured for frequencies between 0.01 and 5.0 megacycles. The data show a broader frequency range of dispersion and absorption and a smaller value of ε″_max than is predicted by the Debye theory for a system characterized by a single relaxation time. The disparity between the experimental data and the Debye theory increased with the concentration of lactoglobulin and was greater than expected on the basis of the small effects of protein concentration on other physical properties of β‐lactoglobulin, e.g., sedimentation constant. Dielectric constants for ``zero'' and ``infinite'' frequencies have been obtained by the Cole circular‐arc method of extrapolation. The frequency dependence of ε′ and ε″ was found to be well represented by the empirical equation of Cole and Cole, ${\epsilon }^{\prime }{\mathrm{-i\epsilon }}^{\mathrm{\prime \prime }}{\mathrm{=\epsilon }}_{\infty }{\mathrm{+(\epsilon }}_0{\mathrm{-\epsilon }}_{\infty }{\text{)/[1+(iωτ}}_0{)}^{\text{1−α}}]$ . In this equation ε₀ and ε_∞ are, respectively, the dielectric constants for zero and infinite frequencies, ω = 2π times the frequency, τ₀ is a generalized relaxation time, and α is a constant, 0<α<1. For α = 0, the equation reduces to that of Debye for a system characterized by a single relaxation time. For the solutions of β‐lactoglobulin α was found to range from 0.08 to 0.4, depending upon the lactoglobulin and glycine concentrations. The relaxation time varied from 7.5 to 25 × 10⁻⁸ sec. for a change in lactoglobulin concentration of 3.5 to 94.0 grams per liter. The dipole moment is estimated to be 790±26 × 10⁻¹⁸ e.s.u.