Critical fluctuations in a binary mixture of polyethylene glycol and polypropylene glycol studied by ultrasonic and light scattering experiments

The critical mixture of polypropylene glycol (M=1000 g/mol) and polyethylene glycol (M=400 g/mol) is investigated by light scattering and ultrasonic experiments in the homogeneous one-phase region (explored temperature and frequency range of the ultrasonic experiment are 0.1 K\ensuremath{\leqslant}T-${\mathrm{T}}_{\mathrm{C}}$ \ensuremath{\leqslant}21.3 K and 0.4 MHz\ensuremath{\leqslant}f\ensuremath{\leqslant}30 MHz; ${\mathrm{T}}_{\mathrm{C}}$ is the critical temperature). The composition of the critical mixture was determined by measuring the volume ratios of the separated phases in the inhomogeneous two-phase region (criterion of equal volumes). The ultrasonic measurements are interpreted by a dynamic scaling theory for low molecular weight binary critical mixtures of Bhattacharjee and Ferrell. The characteristic time scale of the dynamics of the critical concentration fluctuations is described by the frequency ${\mathrm{\ensuremath{\omega}}}_{\mathrm{C}}$ =2D/${\ensuremath{\xi}}^{2}$ (D is the mutual diffusion coefficient and \ensuremath{\xi} the correlation length), which can also be expressed by ${\mathrm{\ensuremath{\omega}}}_{\mathrm{C}}$ =${\mathrm{\ensuremath{\omega}}}_{0}$ ${\mathrm{\ensuremath{\varepsilon}}}^{\mathrm{z}\ensuremath{\nu}}$ [\ensuremath{\varepsilon}=(T-${\mathrm{T}}_{\mathrm{C}}$ )/${\mathrm{T}}_{\mathrm{C}}$ is the reduced temperature; ${\mathrm{\ensuremath{\omega}}}_{0}$ is the critical amplitude and z\ensuremath{\nu} is the critical exponent]. The experimental values are ${\mathrm{\ensuremath{\omega}}}_{0}$ =22.2 MHz from light scattering experiments and ${\mathrm{\ensuremath{\omega}}}_{0}$ =30 MHz from ultrasonic data (within the frame of the Bhattacharjee-Ferrell theory). The low mutual diffusion coefficient of the mixture (D=${\mathrm{D}}_{0}$ ${\mathrm{\ensuremath{\varepsilon}}}^{\mathrm{\ensuremath{-}}\ensuremath{\nu}}$ , \ensuremath{\nu} is the critical exponent; ${\mathrm{D}}_{0}$ is the critical amplitude, with the experimental value from dynamic light scattering ${\mathrm{D}}_{0}$ =4.0\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ ${\mathrm{cm}}^{2}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ ) allows us to study the high frequency behavior of critical ultrasound attenuation in the range 10${10}^{6}$ (\ensuremath{\Omega}=\ensuremath{\omega}/${\mathrm{\ensuremath{\omega}}}_{\mathrm{C}}$ is the reduced frequency; \ensuremath{\omega} is the angular frequency of the measurement). The data follow the dynamical scaling theory well.

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