High-Frequency Shear Viscosity of Low-Viscosity Liquids

Abstract

A thickness shear quartz resonator technique is described to measure the shear viscosity of low-viscosity liquids in the frequency range from 6 MHz to 130 MHz. Examples of shear-viscosity spectra in that frequency range are presented to show that various molecular processes are accompanied by shear-viscosity relaxation. Among these processes are conformational variations of alkyl chains, with relaxation times $\tau _{\eta }$ of about 0.3 ns for $n$-pentadecane and $n$-hexadecane at 25 $^{\circ }$C. These variations can be well represented in terms of a torsional oscillator model. Also featured briefly are shear-viscosity relaxations associated with fluctuations of hydrogen-bonded clusters in alcohols, for which $\tau _{\eta }$ values between 0.3 ns ($n$-hexanol) and 1.5 ns ($n$-dodecanol) have been found at 25 $^{\circ }$C. In addition, the special suitability of high-frequency shear-viscosity spectroscopy to the study of critically demixing mixtures is demonstrated by some illustrative examples. Due to slowing, critical fluctuations do not contribute to the shear viscosity at sufficiently high frequencies of measurements so that the non-critical background viscosity $\eta _\mathrm{bg}$ of critical systems can be directly determined from high-frequency shear-viscosity spectroscopy. Relaxations in $\eta _\mathrm{bg}$ appear also in the shear-viscosity spectra with, for example, $\tau _{\eta }\,\approx$ 2 ns for the critical triethylamine–water binary mixture at temperatures between 10 $^{\circ }$C and 18 $^{\circ }$C. Such relaxations noticeably influence the relaxation rate of order parameter fluctuations. They may be also the reason for the need of a special mesoscopic viscosity when mutual diffusion coefficients of critical polymer solutions are discussed in terms of mode-coupling theory.