Davidson-cole analysis of complex dynamic light scattering spectroscopy for nonionic surfactant systems

In conventional dynamic light scattering (DLS) experiment we detect the scattered light from randomly induced fluctuations of particle concentrations, so that the phases of the scattered lights are completely incoherent. We have developed a new DLS method before, based on the optical excitation of a coherent mode and the phase-sensitive detection of the scattered light. In our method, like the dielectric relaxation spectroscopy, we measure the response function towards an external optical field and obtain complex light scattering spectra. Therefore, there should be an analogy between conventional dielectric spectroscopy and our method. To verify the applicability of our method for multi-component system, we performed complex dynamic light scattering to the non-ionic surfactant systems and successfully measured complex DLS spectra of both binary solutions of ionic surfactants pentaethylene glycol dodecyl ether (C₁₂E₅) and water, and ternary mixtures composed of C₁₂E₅, hexanol, and water. Cole-Cole diagram of these spectra showed real-axis symmetry with distorted like lemniscate. We found that these complex data fitted better with Davidson-Cole type complex functions in view of analogy between complex DLS and complex dielectric spectroscopy. We think this is the first example of the complex fitting application of Davidson-Cole function for DLS spectra, which implies the possibility of wave number dependence of the characteristic time in Davidson-Cole function.