Critical dielectric constant measurements and high pressure phase diagram studies in binary liquid sytem

Abstract

The main conclusions of the present study have been summarised below. The data have been fitted to the extended scaling equation: C = C? (A t + B t? + …) The present study shows that the exponent (?) characterising the capacitance behaviour over the entire reduced?temperature range 5 × 10?? < t < 8 × 10?³ is ? = 0.65. This is similar to the resistivity behaviour observed on the same system and similar systems. However, very close to Tc (t < 5 × 10??) the exponent ? = 0.89 is obtained. Using the best?fit parameters A and B obtained in the region t > 5 × 10??, ?(t) has been determined as a function of temperature over the range 5 × 10?? < t < 8 × 10?³. We, however, find that ? does not change much over the entire range (0.89–0.82). These parameters are, however, not the best?fit parameters over the entire temperature range. A similar behaviour has been observed at all frequencies. As mentioned in Chapter I (Sec. 1.9.1.2), the various theories predict either a (1 – ?) singularity or a –(2? – 1) singularity for d?/dt. Our experiment agrees better with the latter theory when data over the entire range are included and analysed. However, very close to Tc (t < 10??) a (1 – ?) exponent seems to fit the data. Thus, it indicates that a crossover from a (1 – ?) exponent to a (2? – 1) exponent is possible. However, experimental studies on a few other systems only can confirm this result. (i) In all the three systems studied, dTc/dP has been found to be positive. dTc/dP is of the order of 15–25 mK/bar in all cases. These are an order of magnitude smaller than that given by the Pippard relation or the two?scale?factor universality relation. (ii) There is good agreement between the present value of ? and Tc at atmospheric pressure with those of earlier workers. This rules out the possibility of the shift in Tc being due to impurities. It has been found that ? does not change appreciably with pressure for all these three systems. (iii) The coexistence curves at elevated pressures have been determined. The order?parameter exponent ? has been found to be independent of pressure in all cases, thus justifying the smoothness postulate. There are several unanswered questions regarding the coexistence curve of binary liquids, namely: (a) proper choice of order parameter, (b) asymptotic region in these systems, (c) asymptotic value of ?, (d) whether the simple power?law expression is sufficient to describe the data - if not, are the current correction?to?scaling expressions consistent with the data, (e) whether there is a diameter singularity. In order to answer these questions, a resolution of two to three orders of magnitude better than that of the present study is required. This is, however, very difficult to achieve in high?pressure studies. Precise measurement of the quantity (dTc/dP) is of considerable interest. The order of magnitude of the diverging part of the weakly diverging quantities such as thermal expansion and specific heat can be estimated using the Pippard relation or the two?scale?factor relation. A system with a large dTc/dP value can be chosen for these studies.