Ultrasonic study of fluctuations in polystyrene solutions

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Abstract
Measurements of the pulsed-ultrasound absorption spectra (1 to 91 MHz) and velocity (5 MHz) observed in monodisperse polystyrene (PS) solutions with toluene (Tol) and diethyl malonate (DEM) are reported and discussed extensively. The PS+Tol (good solvent) samples with a low concentration (φ≂0.05) and higher temperature (T≥0 °C) were weakly absorbing with nearly single-relaxation spectra. At high concentration (φ≂0.27) the PS+Tol spectra became the critical-fluctuation type. All PS+DEM (poor solvent) solutions had a large excess absorption αex with spectra well described by fitting the (binary-mixture) critical-fluctuation absorption calculations of Kroll and Ruhland (KR) and of Ferrell and Bhattacharjee (FB). The KR approach gave characteristic frequencies fc which obeyed an empirical (nonuniversal) scaling fc∼ΔT ρ, with ΔT the temperature interval above segregation on each isochore. Results indicate a slowing down (ρ>0) and strengthening of the fluctuations as ΔT→0. A crossover in ρ was observed with PS+DEM near but below the theta temperature (ρ smaller below). For critical-isochore samples ρ approached 1 as the PS molecular weight was increased toward 106. Near phase separations, spectra followed the approximate prediction of FB theory, αex∼f, f the sound frequency. The FB characteristic (half-attentuation) temperatures ΔT1/2 scaled with f, going from exponent 1/2 (for small molecules) to 1 as f was increased. Earlier data for PS in cyclohexane are reevaluated with the KR and FB methods with results similar to PS+DEM. These PS results are compared extensively with the work of Garland and Sanchez on a small-molecule binary-mixture critical point, where ρ was universal, fc two orders of magnitude higher at large ΔT, and ΔT1/2 tenfold smaller at low f. This study finds that fluctuation absorption occurs commonly in PS solutions and is due to energy fluctuations decoupled (nonuniversal exponents) from critical PS-composition fluctuations (known to be the binary-mixture type). Light scattering verified that the critical point was approached closely in PS+DEM. The sound velocity was independent of the PS molecular weight, but increased as a weak quadratic function of the concentration for all solvents. Mixture rules for the modulus predict this qualitative trend.