The density of liquid sulfur near the polymerization temperature

Abstract

We have measured the density of liquid sulfur as a function of temperature near the polymerization temperature. We measure between 424 and 445 K, with a precision in density of 2×10−5 and an accuracy of 5×10−4. We see upward shifts of the density within 3 K of the polymerization temperature of about 8×10−4 with each cycle in temperature; these shifts could be due to the reaction of the sulfur with the quartz cell, or to the persistence of metastable polymeric forms of sulfur. Thus we consider the data from the first heating run to be the best, since the sample was then the purest. Our results differ from those in the literature in that, while we see a change in slope at the transition, we do not see a sharp minimum or a singularity. We compare our data to two models of the sulfur polymerization as a second order phase transition: the mean field model [A. V. Tobolsky and A. Eisenberg, J. Am. Chem. Soc. 81, 780 (1959)] and the n→0 magnet model [S. J. Kennedy and J. C. Wheeler, J. Chem. Phys. 78, 1523 (1983)]. Both models assume that the sulfur forms linear polymers which are in an ideal solution in monomeric sulfur, and that the thermal expansions of monomeric and polymeric sulfur are linear within the temperature range under consideration. For the most physically reasonable choice of thermodynamic parameters for the models, the mean field model describes the data better than does the n→0 model. The n→0 model is superior if the change of specific volume on polymerization is adjusted. One possible explanation is that sulfur belongs in the n=1 universality class, not in the n→0 class.

The low-pressure phase diagram of sulfur

“…Zheng and Greer [26] also measured the density of saturated liquid sulfur at much lower temperatures, around that of the lambda transition. Although these measurements were taken with great care showing the detailed variation of q l in that temperature range they have not been useful to the present section since the equation we are aiming at to obtain the vaporization curve is not valid for temperatures below T % 0.5 Á T c [1].…”

“…The standard deviation of this fitting is r(q g ) = 0.009 kg Á m À3 and r = 1.000. The density of the saturated liquid has been measured by Zheng and Greer [26] and by Rau et al [13] covering the temperatures from T = (424.75 to 444.54) K and T = (623 to 1193) K, respectively. These values are described by the equation [37] q ' =ðkg Á m À3 Þ ¼ q c…”

High-resolution inelastic x-ray scattering to study the high-frequency atomic dynamics of disordered systems

“…The full line is the zero-frequency, simple hydrodynamics prediction for Γ /q 2 , from Refs. [56][57][58]. The dotted vertical line marks the λ-transition temperature at 432 K. The difference between the ultrasound data and the zero-frequency ones corresponds to the liquid to rubber transition that takes place at frequencies lower than 6 MHz and only in the high-temperature polymeric phase.…”

Density functional and Monte Carlo studies of sulfur. II. Equilibrium polymerization of the liquid phase

“…Polymerization reduces the thermal expansion coefficient, 11 and this is illustrated in Fig. 13, where we show the T dependence of the densities (T) of polymerized samples and a liquid comprising S 8 rings.…”

“…6,7 At T ϭ432 K, sulfur undergoes a liquid-liquid transition ͑ transition͒ usually interpreted as the ring opening polymerization ͑ROP͒ of S 8 . This transformation, a simple example of entropy driven polymerization, is revealed by a change of color, 8 anomalies in the specific heat, 9,10 and volume expansion coefficient 11 and a dramatic increase of viscosity. 12,13 Other properties of the system ͑such as the structure factor͒ are less affected.…”