The role of the critical compressibility factor in the equation of state for the critical fluid

Based on the literature data of PVT measurements, the amplitudes of the equations of the critical isotherm D0(Zk), the critical isochore Г0(Zk), the phase boundaries В0(Zk) are expressed in terms of the critical factor of compressibility of the substance Zk=PkVk/RTk in the entire fluctuation region near the critical point. By doing so, a phenomenological method has been used for calculating the values of the critical exponents of the fluctuation theory of phase transitions based on the introduction of small parameters into the equations of the fluctuation theory. It has been shown that, within the limits of the PVT measurement errors, these dependences D0(Zk) and В0(Zk) on the compressibility factor are linear, and Г0 practically does not depend on the compressibility factor Zk. The relationship of these amplitudes with the amplitudes a and k of the linear model of the system of parametric scale equations of state of substance near the critical point has been established. It has been shown that the dependences k(Zk) and а(Zk) are also linear in the entire fluctuation region near the critical point. The obtained dependences k(Zk) and а(Zk) agree with the known relationship between the amplitudes of the critical isotherm D0(Zk), critical isochore Г0(Zk), phase boundaries В0(Zk) Aerospace Institute of the National Academy of Sciences of Ukrainewithin the framework of the system of parametric scaling equations. The relations а(Zk), k(Zk) make it possible, on the basis of a linear model of the system of parametric scale equations of state of substance, to determine such important characteristics of the critical fluid as the temperature and field dependences of the correlation length Rc(T,m) and the fluctuation part of the thermodynamic potential Ф(T,m) in the entire fluctuation region near the critical point. Then, based on the form of the fluctuation part of the thermodynamic potential Ф(T,m)~Rc(T,m)-3, the results obtained allow one to calculate the field and temperature dependences of the thermodynamic quantities for a wide class of molecular liquids in the close vicinity of the critical point (DP<10-3, Dr<10-2, t<10-4), where precision experiments are significantly complicated, and its can also be used when choosing the conditions for the most effective practical application of the unique properties of the critical fluid in the newest technologies.

INTEGRAL EQUATION STUDY OF THE CORRELATION LENGTHS IN IONIC FLUIDS

The restrict primitive model of ionic systems is investigated with the integral equation theory. Using the correlation functions calculated in the reference hypernetted chain approximation, we get (i) the Lebowitz lengths at different densities and temperatures, (ii) the density–density correlation lengths along different isochores approaching the spinodal curve from above. The Lebowitz length obtained by us has better agreement with the Monte Carlo simulation results than the generalized Debye–Hückel theory. Along the critical isochore, the Lebowitz length remains finite when approaching the critical temperature from above, while the density–density correlation lengths diverge as t-1/2 with t = (T - Ts)/Ts, where Ts is the temperature on the spinodal line.

Critical Raman line shape behavior of fluid nitrogen

Isotropic Raman line shapes of simple molecular fluids exhibit critical line broadening near their respective liquid-gas critical points. In order to observe this phenomenon, it is essential that the band position of a given vibrational mode is density-dependent, and that vibrational depopulation processes negligibly contribute to line broadening. Special attention was given to the fact that the isotropic (i.e., nonrotationally broadened) line shape of liquid N2 is affected by resonant intermolecular vibrational interactions between identical oscillators. By means of the well-chosen isotopic mixture (14N2).975 - (14N15N).025, the temperature and density dependences of shift, width, and asymmetry of the resonantly coupled 14N2 and, depending on the S/N ratio available, of the resonantly uncoupled 14N15N were determined, with up to milli-Kelvin resolution, in the coexisting liquid and gas phases and along the critical isochore, using a highest-resolution double monochromator and modern charge-coupled device detection techniques. Clear evidence was found that vibrational resonance couplings are present in all dense phases studied.

Two-Loop RG Calculation of Sound Attenuation and Dispersion Near the Liquid-Gas Critical Point

We calculate the singular part of the sound attenuation and dispersion near the liquid-gas critical point on the critical isochore above T c . It is shown that the corresponding scaling function is related to the correlation function <ψ2ψ2> of two composite operators of the Halperin-Hohenberg–Siggia model H.1 Using the renormalization group (RG) and ∊-expansion we obtain this scaling function in second order in ∊.