Recent Advances in the Field of Integral Equation Theories: Bridge Functions and Applications to Classical Fluids

Simple liquids’ quasiuniversality and the hard-sphere paradigm

“…The van der Waals picture has served liquid-state theory well for many years, in particular as the basis for highly successful perturbation theories [1,7,40], [62][63][64][65]. In regard to simple liquids' quasiuniversality there is also much to be learned from the van der Waals picture and the HS paradigm.…”

Thermodynamic Perturbation Theory of Simple Liquids

“…This was primarily due to the rapid increase in the power of computers. At the same time, the integral equation theory enjoyed renewed popularity with the extensively employed concept of thermodynamic consistency (25), but this aspect goes beyond the scope of this short review. Incidentally, we recall that the thermodynamic consistency consists to adjusting the isothermal compressibility obtained by two different routes.…”

“…24,25,26,27) and the structure factor S HS (q) can be calculated with great accuracy. That suggests replacing the repulsive part of potential in real systems by the hard-sphere potential that becomes the reference system, and precict the structural and thermodynamic properties of real systems with those of the hard-sphere fluid, after making the necessary adaptations.…”

Approximative “one particle” bridge function B(1)(r) for the theory of simple fluids

“…Contrary to B ͑1͒ ͑r͒, the study of B ͑2͒ ͑r͒ and the development of new and better closure relations for this function have been the subject of increasing interest. As attested in the literature, 5 over the past two decades several attempts have been made to improve upon these closure relations and to extend the range of validity of IE theory. Among these attempts, one finds closure relations whose improvement consists either ͑i͒ in providing accurate expressions 6-10 of B ͑2͒ ͑r͒ or ͑ii͒ in calculating it in a selfconsistent manner.…”