Isochore measurements

Historically, the first experimental determinations of the vapor densities and pressures approaching the critical region of a metal were made for mercury. Bender (1915, 1918) carried out pioneering measurements of vapor densities up to about 1400 °C. The samples in these studies were enclosed in strong fused quartz capillaries. In 1932, Birch made the first measurements of the vapor pressure of mercury and obtained realistic values for the critical temperature and pressure. Birch found values = 1460 °C and = 1610 bar, results that are remarkably close to the most accurate values available today (Table 1.1). A number of groups in various countries have contributed subsequently to the pool of pVT data currently available (Hensel and Franck, 1966, 1968 Kikoin and Senchenkov, 1967 Postill et al., 1968 Schonherr et al., 1979 Yao and Endo, 1982 Hubbard and Ross, 1983 Gotzlaff, 1988). The result is that the density data for mercury are now the most extensive and detailed available for any liquid metal. Data have been obtained by means of isothermal, isobaric, or isochoric measurements, but as we have noted in Sec. 3.5, those obtained under constant volume (isochoric conditions) tend to be preferable. In Fig. 4.10 we present a selection of equation-of-state data that we believe to be the most reliable now available for fluid... 

The phase boundaries of the Pd-X (X = H,D,T) system were determined from pressure concentration temperature data because of the high risk of handling PdT samples outside our tritium loading equipment. Pd forms no stable oxide layers as is the case for or Nb that prevent the tritium to leave the sample. The boundaries between the miscibility gap and the 3-phase were obtained from the shape of the desorption isotherms. The values of concentration and temperature of the solvus line between the a- and the two phase regions a+3 were obtained by quasi isochoric measurements. A PdX sample with the concentration x slightly in the miscibility gap was heated in small temperature steps so that the concentration of the sample decreased and finally belonged to the pure a-phase. The change of slope in the equilibrium pressure as a function of the inverse temperature is interpreted as the intersection with the solvus line. 

Besides shear-induced phase transitions, Uquid-gas equilibria in confined phases have been extensively studied in recent years, both experimentally [149-155] and theoretically [156-163]. For example, using a volumetric technique, Thommes et al. [149,150] have measured the excess coverage T of SF in controlled pore glasses (CPG) as a function of T along subcritical isochoric paths in bulk SF. The experimental apparatus, fully described in Ref. 149, consists of a reference cell filled with pure SF and a sorption cell containing the adsorbent in thermodynamic equilibrium with bulk SF gas at a given initial temperature T,- of the fluid in both cells. The pressure P in the reference cell and the pressure difference AP between sorption and reference cell are measured. The density of (pure) SF at T, is calculated from P via an equation of state. 

Several techniques are available for measuring values of interaction second virial coefficients. The primary methods are reduction of mixture virial coefficients determined from PpT data reduction of vapor-liquid equilibrium data the differential pressure technique of Knobler et al.(1959) the Bumett-isochoric method of Hall and Eubank (1973) and reduction of gas chromatography data as originally proposed by Desty et al.(1962). The latter procedure is by far the most rapid, although it is probably the least accurate. 

A first study refers to liquid water [77]. The signals AS q,x) and A5[r,r] were measured using time-resolved X-ray diffraction techniques with 100 ps resolution. Laser pulses at 266 and 400 nm were employed. Only short times x were considered, where thermal expansion was assumed to be negligible and the density p to be independent of x. To prove this assumption, the authors compared their values of AS q, x) to the values of AS q) obtained from isochoric (i.e., p = const) temperature differential data [78-80]. Their argument is based on the fact that liquid H2O shows a density maximum at 4 °C. Pairs of temperatures Ti, T2 thus exist for which the density p is the same constant density conditions can thus be created in this unusual way. The experiment confirmed the existence of the acoustic horizon (Fig. 8). 

The swelling behavior of poly(N-isopropylacrylamide) has been studied extensively [18,19]. It has been shown that this gel has a lower critical point due to the hydrophobic interaction. Such a swelling curve is schematically illustrated in Fig. 9. The gel is swollen at a lower temperature and collapses at a higher temperature if the sample gel is allowed to swell freely in water. The volume of the gel changes discontinuously at 33.6°C. The swelling curves obtained in this way correspond to the isobar at zero osmotic pressure. On the other hand, the friction coefficient is measured along the isochore, which is given in Fig. 9,... 

During the friction measurement, a test tube containing a small piece of gel is placed in the same water bath and the appearance of the gel is continuously monitored. The decrease of the diameter of the free gel from the isochore diameter is less than 10% at the highest temperature of the present friction experiment. This observation confirms that the gel swelling or shrinking as a whole should not have a significant effect on the friction measurement. A slight opacity of the gel develops in the gel in the vicinity of the temperature at which the friction of the gel diminishes and is presumably due to the dynamic density fluctuations. 

Correlation function measurements were made along four critical isochores for each of the three systems CO -n-heptane,... 

Plot of the measured decay rates and the calculated critical and background contributions along a critical isochore of the.benzene-CO system at 97.9 mol % CO and Pc = 0.546 g/cm. ... 

Systematic investigations of the laser-cluster interaction were carried out by simultaneously measuring high-resolution X-ray emission spectra and ion energy spectra produced by the laser irradiation of micron-sized Ar clusters at laser intensities of 1018 to 1019 W/cm2. To suppress the creation of preplasma, we designed a special conical nozzle and eliminated the laser prepulse. The results indicate that the explosion time scale for micron-sized clusters is much longer than that for nanometer-sized clusters. It is found that hot electrons produced by a higher contrast pulse (a smaller prepulse) allow the isochoric... 

We now turn to measurements of the constant-volume heat capacity, Cy, along the critical isochore. In Fig. 5 we show Cy as measured in NVT and pVT simulations of a system with a = 6 and L = lOer. The bulk critical... 

Abstract A synthetic pure water fluid inclusion showing a wide temperature range of metastability (Th - Tn 50°C temperature of homogenization Th = 144°C and nucleation temperature of Tn = 89°C) was selected to make a kinetic study of the lifetime of an isolated microvolume of superheated water. The occluded liquid was placed in the metastable field by isochoric cooling and the duration of the metastable state was measured repetitively for 7 fixed temperatures above Tn. Statistically, metastability lifetimes for the 7 data sets follow the exponential reliability distribution, i.e., the probability of non nucleation within time t equals. This enabled us to calculate the half-life periods of metastability r for each of the selected temperature, and then to predict i at any temperature T > Tn for the considered inclusion, according to the equation i(s) = 22.1x j Hence we conclude that... 

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