Stress-induced birefringence in the isotropic phases of lyotropic mixtures

In this work, the frequency dependence of the known mechano-optical effect which occurs in the micellar isotropic phases (I) of mixtures of potassium laurate (KL), decanol (DeOH), and water is investigated in the range from 200mHz to 200Hz. In order to fit the experimental data, a model of superimposed damped harmonic oscillators is proposed. In this phenomenological approach, the micelles (microscopic oscillators) interact very weakly with their neighbors. Due to shape anisotropy of the basic structures, each oscillator i (i=1,2,3,...,N) remains in its natural oscillatory rotational movement around its axes of symmetry with a frequency ω_{0i}. The system will be in the resonance state when the frequency of the driving force ω reaches a value near ω_{0i}. This phenomenological approach shows excellent agreement with the experimental data. One can find f∼2.5, 9.0, and 4.0Hz as fundamental frequencies of the micellar isotropic phases I, I_{1}, and I_{2}, respectively. The different micellar isotropic phases I, I_{1}, and I_{2} that we find in the phase diagram of the KL-DeOH-water mixture are a consequence of possible differences in the intermicellar correlation lengths. This work reinforces the possibilities of technological applications of these phases in devices such as mechanical vibration sensors.