Figure 6.2: (a) Segment density profiles vs z∣Ng of hard chains tethered to a hard wall
for Ng = 50 (solid curve), 100 (dot dashed curve), 150 (dashed curve) and pgσ2 = 0.1. The
predictions are from modified iSAFT. (b) Brush height h (■) and average brush height
< z > (∙) vs Ngplgi for hard chains tethered to a hard wall for Ng = 50, 100 and 150 at
different grafting densities. The dashed curves are linear fits to the data.
chain length (z∕Ng) at a fixed pg, where pg is the grafting density and Ng is the
number of segments in the chain. The profiles overlap each other except near the
end of the brush where the profiles show a gradual exponential decay (instead of a
parabolic decay). The shape of the density profiles in figures 6.la, 6.lb, and 6.2a are
similar to the SCFT prediction [227] for the density profile at good solvent condition
as p(z) = C∖pg^ — C2{z∕Ng')21 where C1 and C2 are constants independent of pg and
Ng. Furthermore, this density profile predict a scaling relationship for the average
brush height (< z >) as < z >~ Ngplg3 in accordance with the scaling theories of
158
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