Ethane critical density

Fig. 7.17. Ortho-positronium annihilation rates at various values of ethane gas density D, at a temperature of 305.45 K. The solid line is a weighted average of the annihilation rates between 120 and 180 amagat. The broken line is the prediction for free ortho-positronium. The data are due to Sharma, Kafle and Hart (1984). Reprinted from Physical Review Letters 52, Sharma, Kafle and Hart, New features in the behaviour of ortho-positronium annihilation rates near the vapour-liquid critical point of ethane, 2233-2236, copyright 1984 by the American Physical Society.

In this chapter, we describe the density- and temperature-dependent behavior of the vibrational lifetime (TO of the asymmetric CO stretching mode of W(CO)6( 2000 cm-1) in supercritical ethane, fluoroform, and carbon dioxide (C02). The studies are performed from low density (well below the critical density) to high density (well above the critical density) at two temperatures one close to the critical temperature and one significantly above the critical temperature (68-70). In addition, experimental results on the temperature dependence of Ti at fixed density are presented. Ti is measured using infrared (IR) pump-probe experiments. The vibrational absorption line positions as a function of density are also reported in the three solvents (68,70) at the two temperatures. 

Figure 2 Pump-probe data for the asymmetric stretching CO mode of W(CO)6 ( 1990 cm-1) in supercritical ethane at the critical density (6.88 mol/L) and 343 K. The heavy line is a fit to a single exponential. The lifetime, Ti, equals 278 ps. Data scans in other solvents, temperatures, and densities were of similar quality.

C, for ethane, fluoroform, and C02, respectively. The near-critical isotherm temperatures for the three solvents were chosen so that the reduced temperatures (T/Tc) are essentially the same. For the near-critical isotherm, the lifetime decreases rapidly as the density is increased from low density. As the critical density, pc, is approached, the rate of change in the lifetime with density decreases (pc = 6.88, 7.56, and 10.6 mol/L, for ethane, fluoroform, and C02, respectively). The change in slope is more pronounced for C02. This is even more evident when the gas phase (zero density) contribution to the lifetime is removed from the data (see below). The difference between the C02 data and the other data will be discussed in Section V. The higher temperature isotherm data show a somewhat more uniform density dependence. Although the slope decreases with increasing density, there is a somewhat smaller change in slope than in the near-critical isotherm data. 

The force-force correlation function used here has a complicated form that can be determined by numerical evaluation. We examined the correlation function for ethane at 50° C as well as the critical density. With the Egelstaff quantum correction, the correlation function initially decays as 1-at2 for a very short time ( 15 fs). It then slows and becomes progressively slower at longer times. As mentioned above and as will be discussed in detail in connection with the experiments, the Fourier transform is taken at a relatively low frequency (150 cm-1), not the 2000 cm 1 oscillator frequency. For low frequencies, the very short time details of the correlation function are not of prime importance. Without the quantum correction, the strictly classical correlation function does not begin with zero slope at zero time, but, rather, it initially falls steeply. However, the quantum corrected function and the classical function have virtually identical shapes after 15 fs. As will be demonstrated below, the force-force correlation function contained in Equation (21) with Equations (22), (24), (25), (26), and (27) does a remarkable job of reproducing the density dependence observed experimentally. The treatment also works very well... 

Figure 10 (a) Ti (p, T) vs. density for the solvent ethane at 34°C and the best fit theoretically calculated curve. The theory was scaled to match the data at the critical density, 6.88 mol/L. The best agreement was found for u> = 150 cm-1, (b) Ti (p, T) vs. density for the solvent ethane at 50°C and the theoretically calculated curve. The scaling factor, frequency >, and the hard sphere diameters are the same as those used in the fit of the 34°C data. Given that there are no free parameters, the agreement is very good. 

Figure 15 shows the lifetime as a function of temperature at the critical density of carbon dioxide. With CO2 as the solvent there is no inverted region in which the lifetime becomes longer as the temperature is increased. Instead, the lifetime decreases approximately linearly. Thus the inverted behavior is not universal but is specific to the properties of the particular solvent. The fact that the nature of the temperature dependence changes fundamentally when the solvent is changed from ethane to C02 demonstrates the sensitivity of the vibrational relaxation to the details of the solvent properties. The solid line is the theoretically calculated curve. The calculation of the temperature dependence is done with no adjustable... 

Figure 4 Solvent-induced VER rate for the asymmetrical CO stretch mode of W(CO)6 in supercritical ethane at the critical density (6.87 mol/L) as a function of temperature. The solid diamonds are the experimental points, and the theory is given by the open circles.

Figure A2.5.31. Calculated TIT, 0 2 phase diagram in the vicmity of the tricritical point for binary mixtures of ethane n = 2) witii a higher hydrocarbon of contmuous n. The system is in a sealed tube at fixed tricritical density and composition. The tricritical point is at the confluence of the four lines. Because of the fixing of the density and the composition, the system does not pass tiirough critical end points if the critical end-point lines were shown, the three-phase region would be larger. An experiment increasing the temperature in a closed tube would be represented by a vertical line on this diagram. Reproduced from [40], figure 8, by pennission of the American Institute of Physics.

Figure 6-6 gives the viscosity of ethane.2 Note the similarity between this figure and the graph of the densities of pure hydrocarbons given in Chapter 2. The dotted line is the saturation line, and the point of maximum temperature on the dotted line indicates the critical point. 

Apart from polymerization processes with gaseous monomers above their critical points-for example, the synthesis of low-density poly(ethylene) - several SCFs have been tested as inert reaction media, such as ethane, propane, butane, and C02. Among these, scC02 is by far the most widely investigated, because it links positive fluid effects on the polymers with environmental advantages this makes scC02 the main candidate as an alternative to traditional solvents used in polymer syntheses. 

Figure 5. Vibrational frequency shifts as a function of density for two different vibrational modes in sub-critical ethane. The experimental and theoretical shifts are measured relative to their zero density vapor phase values (see table I).

Although the proposed mechanism is consistent for photolysis of iodine in helium, nitrogen and methane (24), substantive deviations were present at low densities and especially near the critical point of ethane. As Figure 3 shows, the quantum yields at these low densities are consistently below one, the value expected in this high diffusivity regime where kd k i. 

The magnitude and nature of the primary effect will be examined in terms of eq. (11) however, the present remarks are not limited to systems in which active rotations are absent. The discussion is based on calculations using the C2 model for the light molecule and the C2 model, modified to correspond to the measured frequencies for ethane- (Table VI) for the C2-di model. The complex for H rupture, is the semirigid complex 4, specified in II,B2 and Table I. The D-rupture complex (Table VI) was constructed in the same way and fits the Teller-Redlich product rule. The difference in critical energies for the two prototype reactions is Aeo = 1.38 keal. mole-1. The density of states for the molecules and the sum of states for the complexes are shown in Figures 3 and 4, respectively. 

Very few experiments have been performed on vibrational dynamics in supercritical fluids (47). A few spectral line experiments, both Raman and infrared, have been conducted (48-58). While some studies show nothing unique occurring near the critical point (48,51,53), other work finds anomalous behavior, such as significant line broadening in the vicinity of the critical point (52,54-60). Troe and coworkers examined the excited electronic state vibrational relaxation of azulene in supercritical ethane and propane (61-64). Relaxation rates of azulene in propane along a near-critical isotherm show the three-region dependence on density, as does the shift in the electronic absorption frequency. Their relaxation experiments in supercritical carbon dioxide, xenon, and ethane were done farther from the critical point, and the three-region behavior was not observed. The measured density dependence of vibrational relaxation in these fluids was... 

Figure 3 Vibrational lifetimes for the asymmetric CO stretching mode of W(CO)6 vs. density along two isotherms of three polyatomic supercritical fluids ethane (34°C panel a and 50°C panel b), fluoroform (28°C panel c and 44°C panel d), and carbon dioxide (33°C panel e and 50°C panel f). The upper panel for each solvent is an isotherm at 2°C above the critical temperature. In all six data sets, error bars (representing one standard deviation) are approximately the size of the points.

Before preceding, it is useful to consider the form of the force-force correlation function, which is given in Equation (21), with Equations (22), (24), (25), (26) and (27). The form of the force-force correlation function, derived using density functional formalism, is employed because it permits the use of very accurate equations of state for solvents like ethane and CO2 to describe the density dependence and temperature dependence of the solvent properties. These equations of state hold near the critical point as well as away from it. Using the formalism presented above, we are able to build the known density and temperature-dependent properties of the... 

Figure 10a shows the density dependence of the solvent-induced lifetime Ti(p, T) in ethane along an isotherm at 34° C, very close to the critical temperature (Tc). The values in the figure are obtained from the measured lifetimes and the intrinsic (zero density) lifetime using... 

Figure 14 shows the lifetime dependence on temperature in ethane at a constant density equal to pc. The data have a region, extending well above the critical temperature, in which the lifetime becomes longer as the temperature is increased. This behavior in ethane is unexpected and is in contrast to theoretically proposed trends of vibrational lifetimes with temperature at constant density (102,110). We will refer to this temperature range as inverted (16,111). 

One aspect of the last set of experiments on W(CO)6 in supercritical ethane that we have not yet discussed involves the possible role of local density enhancements in VER and other experimental observables for near-critical mixtures. The term local density enhancement refers to the anomalously high solvent coordination number around a solute in attractive (where the solute-solvent attraction is stronger than that for the solvent with itself) near-critical mixtures (24,25). Although Fayer and coworkers can fit their data with a theory that does not contain these local density enhancements (10,11) (since in their theory the solute-solvent interaction has no attraction), based on our theory, which is quite sensitive to short-range solute-solvent structure and which does properly include local density enhancements if present, we conclude that local density enhancements do play an important play in VER and other spectroscopic observables (26) in near-critical attractive mixtures. 

KrF excimer laser-induced reactions in the mixture of hydrocarbon/02/C02 under sub- and super-critical conditions were investigated. In the ethylene mixtures, the main products were ethylene oxide and acetaldehyde. The total quantum yield decreased with the increase of mixture density, but the branching ratio between the two products were almost independent on the density. The branching ratio was found to be what is expected if the reactive species is 0(3P). The reaction for other hydrocarbons including ethane and cyclohexane is also discussed. 

The density of the liquid phase of the system oleic acid/carbon dioxide increases with increasing pressure, whereas the density of the liquid phase of the system oleic acid/ethane decreases with increasing pressure. Therefore the hydrodynamics in a countercurrent column and mass transfer may dramatically depend on the activity of the near-critical fluid. 

---