Collapse of grafted chains in poor solvents

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Abstract
A mean field theory of the collapse of grafted chains (consisting of N monomers) in a poor solvent is presented. The collapse behaviour of nonoverlapping grafted chains is identical to that of free coils but with no phase separation. This « strong » collapse, in which the coil radius R decreases continuously from R ∼ N3/5 in a good solvent to R ∼ N1/3 in a poor solvent, is replaced by « weak » collapse for densely grafted layers. Such a layer when undergoing « weak » collapse becomes thinner, yet the chains remain stretched even in poor solvents, and the layer thickness is linear in N past the collapse. For low densities the « weak » collapse is associated with a first order phase transition. An increase in grafting density takes the system through a critical point into a gradual collapse regime