Viscous behaviour of supercooled liquids

The viscosities and densities of a number of aromatic hydrocarbons and esters have been measured from room temperature down to temperatures in the highly supercooled region. The densities of these liquids show a linear variation with temperature. The viscosities cannot be described by an Arrhenius-type equation but they can be represented precisely by a modified form of the Doolittle free volume equation. ln $$\eta = A'+B'/(T-T_0),$$ in which T$_0$ is the fundamental reference temperature for all molecular transport and relaxation processes. This temperature is below the normal glass-transition temperature, the latter being solely determined by kinetic effects. The constants $A'$, $B'$ and T$_0$ are determined for each liquid by a digital computer procedure, which minimizes the sum of the squares of the difference between the experimental and the predicted viscosity values. In di-n-butyl phthalate and di-(2-ethyl hexyl) phthalate, the molecules of which have relatively long side group attachments to the benzene ring, the above equation fits the observed viscosity values over the complete temperature range of measurement (approximately 210 to 370 $^\circ$K) with one set of values for $A'$, $B'$ and T$_0$. However, for some molecules with shorter side group attachments a discontinuity is found in the viscosity behaviour in the region of an 'intersection temperature', T$_K$. Below T$_K$ the above equation fits the observed viscosity values with one set of values for $A'$, $B'$ and T$_0$. A similar fit is found at temperatures above T$_K$ but with a different set of values for $A'$, $B'$ and T$_0$. This discontinuity in viscosity behaviour is attributed to the onset of aggregation of small numbers of molecules as the liquid is cooled through the temperature T$_K$, which is at or below the melting point. At temperatures below T$_K$ the molecular aggregate constitutes the unit of flow, while above T$_K$ the molecules flow as single units. This effect is strikingly apparent as the length of the side group attached to the benzene ring is reduced. Thus di-n-butyl phthalate exhibits no discontinuity whilst di-iso-butyl phthalate shows a marked discontinuity. Likewise a discontinuity is found in n-butyl benzene but not in n-hexyl benzene. At higher temperatures approaching the boiling point, the free volume description of viscous flow is superseded by an Arrhenius type of behaviour where the free volume is greater than 10 to 16% of the specific volume, depending on the liquid in question.