Pressure scanning volumetry

In the commonly used technique of scanning calorimetry, one measures the heat capacity, C-p, as a function of temperature T on heating or cooling a material at a fixed rate. In the study of liquid-glass-liquid transition, a calorimetry scan is modelled in terms of a non-exponential parameter, beta, and non-linearity parameter, x, which describe the shape of the C-p-scan as well as the time-and temperature-dependence of structural dynamics. A liquid also becomes glass on isothermal pressurizing and the glass is expected to become liquid on depressurizing. Here we describe the formalism of a technique in which the volume, V, may be measured as a liquid is isothermally pressurized at a fixed rate, r = (dp/dt)(T), to form glass, and also as the glass is isothermally depressurized at a fixed rate until it becomes liquid. We name it pressure scanning volumetry (PSV) and simulate the pressurizing and depressurizing scans of (dV/dp)(T) within the framework of non-exponential, non-linear structural relaxation. Hence we show how the features of simulated PSV scans change with change of, (i) the pressurizing and depressurizing rates, (ii) the parameters beta and x, and (iii) the volume of activation for characteristic relaxation time, delta V*. We also describe how the limiting fictive pressure, p'(f), can be determined from a PSV scan, and fit the PSV formalism to the available bulk modulus against p plot of atactic poly(propylene) at 297 K [S.P. Andersson, O. Andersson, Int. J. Thermophys. 18 (1997) 845-864] to obtain beta, x and delta V*. In addition to being of academic interest, the formalism would be useful for modelling polymer extrusion processes. The study may also stimulate commercial development of equipment with computer-controlled pressure-change for use in studies of academic and technological significance.