The theory of dielectric relaxation in a model polar liquid is developed and applied to experimental data. The model is a spherical Onsager cavity, with a uniform dielectric background described by the high frequency limit ε∞ and containing a permanent point dipole. The dipole moment undergoes rotational Brownian motion in the cavity. Dielectric friction on the rotating dipole is taken into account and leads to a frequency-dependent relaxation time. Earlier theoretical results, obtained first by Klug, Kranbuehl, and Vaughn and by Fatuzzo and Mason, are rederived. When the rotational Brownian motion is spherically isotropic, approximate Debye relaxation is found. When the rotational Brownian motion of the dipole is restricted to a constant angle with respect to some fixed axis, approximate Davidson–Cole relaxation is found. Experimental data on glycerol and i-amylbromide are analyzed this way.
We present here a detailed theory of electronic surface quantum states in a low magnetic field, as well as of their effects on the microwave surface impedance. A marked oscillatory structure in the microwave absorption as a function of magnetic field has been carefully observed by Khaikin and by Koch et al. The quantized magnetic surface levels are bound states of electrons trapped against the surface by the magnetic field. Even though these levels are somewhat analogous to Landau levels, they have considerably different properties. Resonant transitions between these levels give rise to a series of spectral lines in the surface impedance, just as cyclotron resonance is a result of transitions between Landau levels. The present effect is essentially quantum in nature, however. A considerable amount of quantitative information can be extracted from the experimental data. The Fermi velocity, radius of curvature of the Fermi surface, and mean free time at certain points on the Fermi surface can be obtained. Most novel, however, is the fact that one can extract information on the scattering of electrons by the surface, as a function of impact angle.
The full polarization properties of anisotropic biomolecule optical scattering are investigated theoretically. By using a simple ellipsoid model of a single biomolecule, the scattering fields and Mueller matrices are derived from fundamental electromagnetism theory. The energy of scattered photons is not necessarily equal to that of the incident laser beam. This theory can be generally applied to the experiments of fluorescence, Raman scattering, and second-harmonic generation. Fitting of a single tetramethylrhodamine-labeled lipid molecule's anisotropic imaging experiment is demonstrated. This theory has provided a fundamental simulation analysis tool of understanding and developing the optical polarimetric sensing science and technology of the anisotropic biomolecules and biomedium. The medium dielectric constant of the model ellipsoid provides a theoretic background for correlating the optical polarization properties of a biomolecule to its microscopic electronic structure.
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