Thermodynamic properties, quantum fluids

Hie thermodynamic properties of fluids consisting of light molecules sometimes departs markedly from those of heavier molecules. These departures, the so-called quantum effects, result from two different phenomena, the exchange effect and the diffraction effect... 

Figure 7.4 illustrates the phase diagram of the 4He isotope in the low-temperature condensation region. The thermodynamic properties of 4He are fundamentally distinct from those of the trace isotope 3He, and the two isotopes spontaneously phase-separate near IK. Both isotopes exhibit the spectacular phenomenon of superfluidity, the near-vanishing of viscosity and frictional resistance to flow. The strong dependence on fermionic (3He) or bosonic (4He) character and bizarre hydrodynamic properties are manifestations of the quantum fluid nature of both species. 3He is not discussed further here. 

A new correction function for quantum effects in fluids is proposed, which can be coupled to any van der Waals type equation of state. With the new quantum correction, calculations of thermodynamic properties of hydrogen and hydrogen-containing mixtures are significantly improved. 

Note Liquid helium has unique thermodynamic properties too complex to be adequately described here. Liquid He I has refr index 1.026,dO.l 25, and is called a quantum fluid because it exhibits atomic properties on a macroscopic scale. Its bp is near absolute zero and viscosity is 25 micropoises (water = 10,000). He II, formed on cooling He I below its transition point, has the unusual property of superfluidity, extremely high thermal conductivity, and viscosity approaching zero. 

At the bases of the second basic assumption made, e.g., that the fluids behave classically, there is the knowledge that the quantum effects in the thermodynamic properties are usually small, and can be calculated readily to the first approximation. For the structural properties (e.g., pair correlation function, structure factors), no detailed estimates are available for molecular liquids, while for atomic liquids the relevant theoretical expressions for the quantum corrections are available in the literature. 

With the ongoing increase of computer performance, molecular modeling and simulation is gaining importance as a tool for predicting the thermodynamic properties for a wide variety of fluids in the chemical industry. One of the major issues of molecular simulation is the development of adequate force fields that are simple enough to be computationally efficient, but complex enough to consider the relevant inter- and intramolecular interactions. There are different approaches to force field development and parameterization. Parameters for molecular force fields can be determined both bottom-up from quantum chemistry and top-down from experimental data. 

The determination of dense fluid properties from ab initio quantum mechanical calculations still appears to be some time from practical completion. Molecular dynamics and Monte Carlo calculations on rigid body motions with simple interacting forces have qualitatively produced all of the essential features of fluid systems and quantitative agreement for the thermodynamic properties of simple pure fluids and their mixtures. These calculations form the basis upon which perturbation methods can be used to obtain properties for polyatomic and polar fluid systems. All this work has provided insight for the development of the principle of corresponding state methods that describe the properties of larger molecules. 

One additional important reason why nonbonded parameters from quantum chemistry cannot be used directly, even if they could be calculated accurately, is that they have to implicitly account for everything that has been neglected three-body terms, polarization, etc. (One should add that this applies to experimental parameters as well A set of parameters describing a water dimer in vacuum will, in general, not give the correct properties of bulk liquid water.) Hence, in practice, it is much more useful to tune these parameters to reproduce thermodynamic or dynamical properties of bulk systems (fluids, polymers, etc.) [51-53], Recently, it has been shown, how the cumbersome trial-and-error procedure can be automated [54-56A],... 

As stressed earlier, the actual pair interaction potential v(r) in a monatomic fluid depends on the quantum nature of the particles and is a function of their distance. No dependence on the temperature in these functions is included. As a matter of principle, such a thing cannot be. This absence is displayed clearly within the exact PI scheme when formulating the quantum statistical problem (e.g., Eqs. 25-27). However, in the semiclassical cases one finds potentials that are built by using the underlying v(r) as a reference, which is corrected so as to include quantum diffraction information (J, h,m) relevant to the system under study. This extra dependence can influence the calculation of semiclassical properties, as indicated by the thermodynamic derivative procedures [120]. 

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