Dynamical fluctuation of the mesoscopic structure in ternary C12E5-water-n- octane amphiphilic system

Dynamical fluctuations of the bicontinuous microemulsion and lamellar structures in ternary C₁₂E₅-water-n-octane amphiphilic system are studied by means of neutron spin echo (NSE) spectrometry. The decay rates of the time correlation of the concentration were analyzed in terms of three theories: (1) A. G. Zilman and R. Granek, Phys. Rev. Lett. 77, 4788 (1996), (2) M. Nonomura and T. Ohta, J. Chem. Phys. 110, 7516 (1999), and (3) R. Granek and M. E. Cates, Phys. Rev. A 46, 3319 (1992), in the first of which a Langevin equation for membrane plaquettes and in the latter two of which time-dependent Ginzburg-Landau equations for the order parameters are considered. The result shows that the intermediate correlation functions I(q,t) for the ranges of 0<t<15 ns and 0<q<0.2 Å ^-1 are well fitted to a stretched exponential function in time, I(q,t)=exp[-(Γt)^2/3], for the bicontinuous microemulsion and the lamellar phases of the same systems with the relaxation rate Γ increasing as q³ in agreement with theory (1) from which the bending modulus of the membrane κ was estimated. For more restricted ranges of 0<t<5 ns and 0.05<q<0.15 Å ^-1 the NSE result can be expressed by an exponential function in time in agreement with theory (2) determined exclusively by hydrodynamic interactions and for extended range of 0<t<10 ns and 0.03<q<0.15 Å ^-1 by a nonexponential function in agreement with theory (3), from both of which the effective viscosities η₀ and η_eff of the system were estimated. The effective viscosity from the nonexponential η_eff is five times greater than that from the simple exponential η₀ that is almost the same as the literature value. The implication of this result is discussed in terms of the effective viscosity η_eff that takes into account the renormalization of the bending modulus of the membrane.