The set of equations represented by eq. 3.9 can be solved for Хд(г) using Picard’s
fixed point iteration.
The second method evaluates the free energy functional due to association based
on the (bulk) homogeneous association free energy using a weighted density approx-
imation. Since the hard sphere and association interactions are of similar range, the
same weighted density is used for both the terms. Hence,
AEX,assOC[p(r)] = f drp(r)ʃ-[p(r)]j (3.11)
where ∕αssoc[p(r)] is the homogeneous association free energy per unit volume evalu-
ated at the weighted density, p(r).
⅜) lʌ
2 2/ ’
(3.12)
βfassoc[p^] = £ (ln⅛4(r) -
A∈Γ ×
and
X,l(ri) = 1 + ∑B,r ⅛,(σ; ta)⅛⅛)⅛) ' (3'13)
Both the methods were successfully applied to associating hard spheres confined
between two hard walls. However, the first method requires the solution of two
integral equations and is computationally expensive. Hence, method 2 was used by
Segura, Chapman and co-workers in all their later works with associating fluids [108,
109]. This approach has been widely applied to investigate the effect of association on
the phase behavior and structure of associating fluids confined between hydrophobic
70
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