The name is absent

grafting densities, and bulk free polymer concentrations. More detailed study on this
issue was done by Ferreira et. al. [206]. Using continuous SCFT, they found that the
boundary between the repulsive and attractive domains follows the scaling relation,
P₉VN_g oc a ² for both densely and sparsely grafted monolayers. It has to be noted
that in all these theoretical studies, the grafted polymers are chemically identical to
the surrounding free polymers, except for their degree of polymerization. Hence, this
problem of entropie interactions between two grafted monolayers in a matrix of parent
homopolymer is theoretically and numerically equivalent to the case for the wetting
behavior of homopolymer on a chemically identical grafted monolayer [207, 206, 208].
When a homopolymer comes in contact with a chemical identical grafted monolayer at
high grafting densities, a positive surface tension arises due to the entropie constraints
and the homopolymer dewets the brush. The phenomena is known as autophobic-
ity [209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224].
Autophobicity indirectly spurs the effective attraction between two grafted monolay-
ers in the homopolymer matrix as the system would rather prefer to replace the two
brush-homopolymer interfaces by a single brush-homopolymer interface [206]. Matsen
and Gardiner [208] used this analogy to show that the repulsion∕attraction bound-
ary satisfies the scaling relation, p_gV~N _g oc α^-0∙⁷, using a numerically more accurate
Fourier-Space algorithm for SCFT than the real-space algorithm used by Ferreira et.
al.

Another statistical mechanics based approach that has been applied to polymer

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