Decay rate of critical concentration fluctuations in a binary liquid

Abstract

We report a detailed experimental study of the decay rate of the order-parameter fluctuations in the binary liquid 3-methylpentane and nitroethane near the critical mixing point. This system has the advantage that the decay rate can be measured close to the critical temperature without multiple-scattering corrections. The data cover a range $0.1<q\ensuremath{\xi}<27$, where $q$ is the wave number of the fluctuations and $\ensuremath{\xi}$ the correlation length. From the data we conclude that the decay rate $\ensuremath{\Gamma}$ varies at the critical temperature as $\ensuremath{\Gamma}\ensuremath{\propto}{q}^{z}$ with $z=3.06\ifmmode\pm\else\textpm\fi{}0.02$. The observed variation of the decay rate as a function of temperature and wave number is consistent with the behavior predicted by the mode-coupling theory of critical dynamics, but an accurate analysis of the data is limited by the lack of a systematic theoretical procedure for dealing with the short-wavelength contributions to the transport coefficients. The paper concludes with a discussion of the Stokes-Einstein relation between the diffusion coefficient and the viscosity coefficient near the critical point.