all of the segments to satisfy stoichiometry. That is, although the average segment
density profiles agree well with the simulation results, the density of the individual
segments in a chain averaged over the system are not equal. As an example, consider
the case of a single chain tethered to a hard surface, the segment tethered at the
surface fixes the position of the second segment within the bonding length (without
overlapping the surface or other segments), the second segment fixes the third and
so on. With no solvent present, the chain tries to reduce its configurational entropy
by coiling around. This limits the chain to within a few molecular diameters from
the surface as seen in the simulation results shown in the figures 3.3a for a hard
chain and 3.3b for an ideal chain. An ideal chain is more collapsed onto the surface
than a hard chain due to absence of volume exclusion. iSAFT was tested for hard
chain tethered at a hard surface. Comparisons with simulation results (figure 3.3a)
show that the theory predicts that the chains are too extended. The reason for the
stoichiometry problem and the issue with the tethered chains appears to be related
to the fact that in the present theory each segment only has information about the
segments it is bonded to. Ideally, each segment on the chain should have information
about the chemical potential of every other segment on the chain. In iSAFT, although
the bond connectivity has been accounted for while defining the association Mayer-/
function, the later segments somehow do not know that the first segment is tethered
to the surface, and hence they try to reach out further away from the wall. However,
this information can be propagated along the chain by having the theory enforce
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