Nonexponential relaxations in dense microemulsion near the glasslike transition

Extensive quasielastic-light-scattering, small-angle neutron scattering, and neutron-spin-echo (NSE) spectroscopic measurements have been performed on a three-component microemulsion system containing bis(2-ethylhexylsulfosuccinate) (AOT) (surfactant), D₂O, and decane (oil) at two temperatures in the one-phase region. By fixing the molar ratio of water to AOT at w=40.61, the average radius of spherical surfactant coated water droplets can be maintained at 58 A{} with a polydispersity index of 22%. The volume fraction {φ} of the droplets can be continuously varied from 0.1 to 0.75, spanning the entire range from the dilute gas all the way to the close-packed glass by adjusting the oil content of the microemulsion. The static structure factors and the time-dependent density correlation functions of these densely packed spherical droplets were systematically measured as a function of the volume fraction.As {φ} increases from 0.1 to 0.75, the structure factor gradually evolves from a smooth function of the order unity into a highly oscillatory function, with the height of the first diffraction peak around 2 and higher, similar to that of a dense liquid. At the same time the time-dependent density correlation function exhibits pronounced nonexponential relaxation. The Kohlrausch-Williams-Watts (KWW) stretched exponential function, exp[-(t/T)^β], has been shown to fit the density correlation function over most of the time range of the measurements, which covers nearly three decades, at Q values of about 10^-3 A^-1, typical in a light scattering experiment. The exponent {β}, starting from an initial value of unity at {φ}=0.1, gradually decreases to about 0.6 at φc{~}0.65 and increases thereafter. The relaxation time T shows a trend to diverge at {φ}{~}φc, approximately following the Vogel-Fulcher law. These features bear striking similarity to a glasslike transition predicted by recent mode-mode coupling theories of dense liquids. The KWW function also fits very well the time-dependent density correlation function at {φ}=0.6, measured by NSE (Q{~}0.2 A^-1). Thus, the KWW function is shown to be valid for the Q range spanning from 0.001 to 0.2 A^-1. The relaxation time, to a good approximation, scales like Q^-2/β.