Figure 6.7: (a) Comparison of the total segment density profiles of the two grafted mono-
layers (Nfl = 101, pgσ2 = 0.03) at different separations from modified iSAFT with the
simulation results from Murat and Grest [247]. The symbols denote the simulations results
for H — 50 σ (à) and H = 30 σ (■). The curves are the theoretical results, (b) Interaction
force between the two grafted monolayers as a function of the separation between them.
ers as a function of the compression ratio for different grafting densities and chain
lengths. At fixed ps, the force curves for different chain lengths almost overlap each
other. This suggests that the interaction force scales with pg. The scaling theory
of Alexander [51] states that for the good solvent conditions, the interaction force
should scale as / ~ pig2F{H∕2Ho). Figure 6.9 plots the interaction force scaled by
p3g2 as a function of the compression ratio for different interacting monolayers with
different polymer chain lengths and grafting densities. As can be seen from the figure,
modified iSAFT is in agreement with the scaling relation.
165
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