Alexander [51] and de Gennes [52], where < z > can be defined as
z >=
ʃ zp{z)dz
fρ(z)dz ’
(6.29)
< z > is calculated for a number of polymer brushes at various Ng and pg. Figure 6.2b
shows that modified iSAFT follows the scaling relation for < z >. The maximum
distance to which the brushes extend away from the wall is defined as the brush height
h. Figure 6.2b also shows that h follows the same scaling relation. Numerically, h is
calculated as the normal distance from the wall after which the total segment density
of the tethered chains, pσ3 < 10~6.
Figure 6.3: (a) Segment density profiles of attractive chains tethered to a hard wall for
Ng = 200 and pgσ2 = 0.1 at e∕kT = 0 (∙), T* = 4 (à), T* = 3 (■) and T* = 2 (▼). Symbols
are the simulation results from Grest and Murat [230] and curves are the predictions from
modified iSAFT. (b) Average brush height, < z > vs Ngρ1f∕3 for attractive chains tethered
to a hard wall at T* = 4 (good solvent), for Ng = 50, 100 and 200 at different grafting
densities. Symbols are the prediction from modified iSAFT and the dashed curve is linear
fit to this data.
159
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