Modified Meister-Kroll theory

The theory presented above has been based on the Evans-Tarazona density funetional approaeh. Therefore its generalization to multieomponent systems is not instantaneous. However, a modified Meister-Kroll theory, introdueed by Riekayzen et al. [143,144], does not suffer from the above-mentioned drawbaek and provides an aeeurate deseription of nonuniform simple (nonassoeiating) fluids. 

FiG. 10 Normalized density profiles p z)/for the associating fluid at a hard wall. The association energy is jk T — 7 and the bulk density is p = 0.2098 (a), e ykgT = 5 and the bulk density equals 0.9038 (b). The solid and dashed lines denote the results of the modified Meister-Kroll theory and the theory of Segura et al., respectively. The Monte Carlo data in (a) are marked as points. (From Ref. 145.)... 

The latter relation is the final equation for the density profile, resulting from the modified Meister-Kroll-Groot theory if applied to associating fluids [145]. 

Fig. 10(a) presents a comparison of computer simulation data with the predictions of both density functional theories presented above [144]. The computations have been carried out for e /k T = 7 and for a bulk fluid density equal to pi, = 0.2098. One can see that the contact profiles, p(z = 0), obtained by different methods are quite similar and approximately equal to 0.5. We realize that the surface effects extend over a wide region, despite the very simple and purely repulsive character of the particle-wall potential. However, the theory of Segura et al. [38,39] underestimates slightly the range of the surface zone. On the other hand, the modified Meister-Kroll-Groot theory [145] leads to a more correct picture. 

In Fig. 10(b) one can see the density profiles calculated for the system with /kgT = 5 and at a high bulk density, p = 0.9038. The relevant computer simulation data can be found in Fig. 5(c) of Ref. 38. It is evident that the theory of Segura et al, shghtly underestimates the multilayer structure of the film. The results of the modified Meister-Kroll-Groot theory [145] are more consistent with the Monte Carlo data (not shown in our... 

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