Long Tails with Flower-like Conformations Undergo an Escape Transition in Homopolymer Adsorption Layers

De Gennes predicted that homopolymer adsorption on a solid-liquid interface results in an adsorption profile with a proximal, a central, and a distal region, wherein, for a good solvent, the central region has a self-similar structure with a density profile that decays as a power law with a coefficient of -4/3. Recent numerical self-consistent field (SCF) predictions for the long-chain length (N) limit revealed a more complex central region with an inner part, where the loops dominate the layer, with a (mean-field) power-law coefficient of -2 and an outer part, where tails dominate, with a "de Gennes" scaling of -4/3. The tails with length t < t* contribute to the inner part of the central region, and these have similar conformations as the loops. The outer part is populated by tails with a length t > t*, and these behave differently. With the increasing length of the tails, there exists a weak escape transition at t = t ^escape ≈ N/10. Long tails in the adsorption profile (t ≳ t* ∝ N ^0.733) show enhanced fluctuations due to this nearby escape transition, and this explains the excluded volume scaling for the outer part of the central region in SCF. With this interpretation, the -2 scaling found by SCF for the inner part should be classified as a mean-field result.