Dynamics of a molecule’s growth: Ultrasonic relaxation studies

Abstract

Longitudinal velocity and attenuation of ultrasonic waves traveling through a liquid at different temperatures have been measured as its molecules combine irreversibly to form large entities and thereby decrease the diffusivity and increase the configurational restrictions to their dynamics. In addition, the number of covalent bonds formed are measured by calorimetry. From these data, the longitudinal modulus and compliance are calculated, and the molecular relaxation time and related properties are deduced and interpreted in terms of the number of covalent bonds formed, by a formalism that connects the size of the molecules in the liquid with its elastic behavior. This relaxation time increases monotonically with increase in the molecule’s size, tending to infinity as the number of covalent bonds formed approaches the Avogadro number. The complex plane plots of the modulus and compliance have a shape that is described by a skewed arc function, with a temperature dependent exponent γ, that ranges in values from 0.33–0.31 for modulus and 0.39–0.45 for compliance. Departure from this shape suggest significant contributions from nonzero shear viscosity for relatively small size of molecules, and contributions from a faster or β-relaxation process when the molecular size is large. The study reveals the behavior of a liquid as it is altered by a permanent change in the size of the diffusing entities.