Integral equation theory for the four bonding sites model of I. Structure factor and compressibility associating fluids

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Abstract
The Wertheim integral equation theory for associating fluids is reformulated for the study of associating hard spheres with four bonding sites. The association interaction is described as a square well saturable attraction between these sites. The associative version of the OrnsteinZernike integral equation is supplemented by the Percus-Yevick-like closure relation and solved analytically within an ideal network approximation, in which the network is the result of the crossing of ideal polymer chains. The structure factor S(k) is obtained for both symmetrical network and polymer chain cases. It is shown that S(k) exhibits a peculiarity (a socalled pre-peak) at small wavenumbers, connected with the formation of relatively large molecular aggregates due to highly directional saturable bonds. The magnitude and location of the pre-peak as functions of density theta and association Ks are analysed. Based on the analysis of the S(k = 0) limit, the behaviour of the isothermal compressibility χ T is studied and the gas–liquid critical point is predicted to exist. The result for the spinodal curve is also reported.