Figure 6.13: (a) Locus of the critical values of a (= Ny∕Ng) at which the interaction
force between the grafted monolayers becomes attractive for fixed bulk free polymer density,
Pfv'f = 0.6. The chain lengths of the grafted polymers are Ng = 101 (■) and Ng = 151 (∙).
σg = σj = σ. (b) Locus of the critical value of a at which the interaction force between the
grafted monolayers becomes attractive for different bulk free polymer densities: pfσ'if = 0.6
(■), and Pfrf — 0.75 (∙). Ng = 101 and σg = σ∫ = σ.
value of a increases as the relative segment size of the grafted polymers increases.
This is due to the fact that the steric hindrance is higher for grafted monolayers
with bigger segments. Another interesting feature is that even for σg ≠ σy, the
repulsion∕attraction boundaries follows the same scaling relation, pgy∕~Ng oc cΓ2.
The steric hinderance between the two monolayers depends upon the volume of the
segments of grafted polymers, hence these different boundaries for different segment
sizes of the grafted polymer (relative to the size of free polymer segments) may scale
by <33. In fact, this is the case as shown in figure 6.14b. The figure shows that for
cases where the relative segment sizes of the grafted and free polymers are different,
172
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