Hard-sphere mixture excess free energy at infinite size ratio

This article presents the exact limiting value of the derivative of the exc ess Helmholtz energy, A(E), with respect to molecular size at constant temp erature, density and composition for a binary mixture of hard spheres with an infinite size ratio (sigma(11)/sigma(22)-->infinity); i.e., lim(sigma 22 -->0)[(partial derivative A(hs)(E)/RT)/partial derivative sigma(22)](T),(rh o,x,sigma 11) = (pi/W)rho x(1)x(2)sigma(11)(2)/(1-(pi/6)rho x(1)sigma(11)(3 )). This limiting value is compared with the Mansoori-Carnahan-Starling-Lel and (MCSL) and also used to test the limits of some commonly used models in estimating the excess free energy of solvents in mixtures or polymer solut ions. The models evaluated include the van Laar, Wilson, Edmond-Ogston, Flo ry-Huggins, Lacome-Sanchez, Scott-Magat, and Chen et al. It is shown that w hile the MCSL equation of state produces the same limiting value as the exa ct value reported here the other mixture models deviate from the exact valu e. This expression may be utilized to correct the mixture theories at their infinite size ratio limits. (C) 1999 American Institute of Physics. @S0021 -9606(99)50807-6].