Viscoelastic relaxation in liquid mixtures

The authors have previously described a model from which the viscoelastic relaxation of supercooled liquids in alternating shear can be predicted. According to this model, the complex compliance of the liquid is represented by the equation $J^\ast = 1/G_\infty[1 + 1/j\omega\tau + 2/(j\omega\tau)^\frac{1}{2}],$ where G$_\infty$ is the limiting high frequency shear modulus and $\tau$ is the Maxwell relaxation time (= $\eta$/G$_\infty$). Measurements have now been made of the viscoelastic properties of binary mixtures of pure liquids which separately conform to the description of the above model and results obtained on seven such mixtures are reported in this paper. In all cases, it is found that viscoelastic relaxation in these systems can be accounted for by the introduction of a single additional constant, K, into the equation for the complex compliance such that $J^\ast = 1/G_\infty[1 + 1/j\omega\tau + 2K/(j\omega\tau)^\frac{1}{2}].$ The value of the constant K is found by comparing experimental results over the region of viscoelastic relaxation with a family of curves computed for different values of K. For binary mixtures in which the two components have either closely similar molecular weights or are isomers, the original model (K = 1) applies for all concentrations investigated. However, if the components of the mixture differ appreciably in molecular weight, a systematic variation of K with mole fraction is found. A single curve of K against mole fraction of the lower molecular weight components represents the results obtained on four such mixtures of liquids which differ significantly in molecular composition. The maximum value of K is 1$\cdot$8 at 0$\cdot$8 mole fraction and the minimum value is 0$\cdot$25 at 0$\cdot$2 mole fraction. For all mixtures K is equal to unity at 0$\cdot$5 mole fraction. Results are given for a number of other liquidsincluding white oil (K = 1) and castor oil, for which K is equal to 2$\cdot$90. Without exception, all non-polymeric liquids on which measurements have been made show a viscoelastic behaviour in cyclic shear which can be fitted by the present model with an appropriate choice for the value of the constant K. Agreement between the calculated curves and experimental results is within experimental error over the ranges of frequency and temperature employed in this work. In accordance with previous work, K is equal to unity for pure supercooled liquids.