Inverse micelle size calculated from the dielectric property

6A Inverse micelle size calculated from the dielectric property 

The size of the inverse micelle can be roughly estimated with the conductivity equation shown in Eq.(94). However, as mentioned earlier, this equation is only valid for solid particle and may give a wrong estimation for the size of inverse micelles. Since the dielectric spectroscopy can provide the information on the relaxation time of the micelle moving under an electric field, the size of micelle is thus able to be determined via the dielectric measurement. 

Einstein [65] derived that the average of the square of the displacement from the initial position of a particle can be expressed as  

Since the root mean square (rms) displacement = (3jc ), Eq. (80) can be rewritten as  

The relaxation time i can be correlated with the dielectric dispersion peak frequency, fmax, at which the dielectric loss tangent shows a maximum value, 

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