Bridge function
The bridge functions are infinite series of irreducible diagrams Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle D_i} :
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B^{(2)}(r) = \rho^2 \frac{1}{2} D_1(r) + \rho^3 [D_2(r) + D_3(r)] + \rho^4[...]+...}
and
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B^{(1)}(r) = \frac{1}{3} B^{(2)}(r) + \rho^3 \left[\frac{1}{6}D_2(r) - \frac{1}{12}D_3(r)\right] + \rho^4[...]+...}
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho} is the density of the fluid.
Universality of the Bridge functional
For Rosenfeld's principle of the universality of the bridge functional see Ref. 2.
References
- Jean-Marc Bomont and Jean-Louis Bretonnet "Approximative “one particle” bridge function B(1)(r) for the theory of simple fluids", Journal of Chemical Physics 126 214504 (2007)
- Yaakov Rosenfeld "Free energy model for inhomogeneous fluid mixtures: Yukawa-charged hard spheres, general interactions, and plasmas", Journal of Chemical Physics 98 pp. 8126-8148 (1993)