and
1u⅛(rmin} - ulal(rc) if σaβ<r < rmin
°t, “ . (4.43)
ua0(-r) - uaβ(rc) if rmin <Г <Γc
rmin = ⅛1^σa0 is the position of potential minima. It is to be noted that in modified
iSAFT the pure repulsion is treated as hard repulsion (with temperature and density
independent hard sphere diameter).
As a rigorous test of modified iSAFT to predict the fluid structure of such a
heteronuclear chain, the density profiles of lipid molecules adsorbed at a surface are
calculated first. The surface is a flat wall and the surface-segment interaction as a
function of the distance from the surface is given by the integrated LJ potential.
Va(z) =
2τΓ 6wq
3
(4.44)
where ewa = 1 and σwa = 1.44. For C = O1 the surface-segment interaction is purely
repulsive.
Two kinds of Surface-Iipid systems are studied. In the first case all the segments
of the lipid molecule have purely repulsive interactions among themselves and with
the surface (case RR). The density profiles of both the head and the tail segments
of the lipid for this case are shown in figure 4.За. The results from modified iSAFT
are compared with results from molecular dynamics simulation by Frischknecht and
Frink [118]. The figure shows excellent agreement between the theoretical predictions
and simulation results.
100