Ballone-Pastore-Galli-Gazzillo

The Ballone-Pastore-Galli-Gazillo (BPGG) (1986) (Eq. 3.8 Ref. 1) closure relation, developed for hard sphere mixtures, is given by

$B(r)=\left[1+s\gamma \left(r\right)\right]^{1/s}-1-\gamma \left(r\right)$

where $s=15/8$. It has its origins in the Martynov-Sarkisov closure (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 s=2} ). The value of 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 s} can be determined by a self-consistency condition. Notice that for 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 s=1} the BPGG approximation reduces to the hyper-netted chain closure.

References

1. P. Ballone; G. Pastore; G. Galli; D. Gazzillo "Additive and non-additive hard sphere mixtures" Molecular Physics, 59 pp. 275-290 (1986)