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ʃ *2exp(-∕¾'d(rι, r2))j⅛?7(r2)) .                (3.29)

The long range attraction is included using the mean field approximation.

1 m m p

Λεx^‰} = 5∑∑∕    *1⅛r,→,∣K∙(r<W  (3.30)

Z α=l /3=1 ∙'lr2-ril>σα∕3

These functionals are based on segment densities, hence only first order decoupled
differential (Euler-Lagrange) equations have to be solved in order to obtain the density
profiles of the segments.

The theory performs very well in comparison with the DFTs developed by Kierlik
and Rosinberg [102] and Yu and Wu [61]. The density profiles of the individual
segments are in better agreement with simulation results. The theory was successfully
applied to model polymer solutions and blends, even blends of branched and linear
chains. Dominik et. al. [114] extended the theory to real systems and calculated the
surface tension of n-alkanes and polymer melts.

3.7 Conclusions

As discussed in the previous section, iSAFT offers a distinct advantage over the
other DFTs based on TPTl. Comparisons for model polymer systems show that
iSAFT provides a computationally efficient segment-density based approach with an
accuracy equivalent to other molecular density or simulation based approaches. Do-
minik et. al. [114] even calculated the surface tension of n-alkanes, PS and LLDPE

77



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