The behavior of a polymer near a repulsive surface may be modified if the entire surface or its edges or corners are covered by an attractive layer. If the attraction is strong enough, the polymer will undergo an adsorption transition [1]. When several elements of the object, such as edges and surfaces, attract, we may have competing adsorption transitions. We used analytical and numerical methods to study this process.

In the case of adsorption of a two-dimensional ideal polymer to an attractive corner of a repulsive wedge, we analyzed the unbinding transition of the polymer [2]. The divergence of the localization length is governed by an exponent that varies continuously with the angle of the wedge (when reflex). Close to the transition point the probability density of end-to-end distance has a power law distribution. If both the corner of a wedge and its surface are attractive, then the attraction to the corner may differ from that to the remaining of the surface, either because of the different surroundings of the corner, or due to the fabrication process. The adsorption to the corner may coexist with adsorption to the surface, and the polymer may be in four different states depending on the strength of each attraction. We mapped out the phase diagram [3].

Our two-dimensional results also apply to adsorption of an ideal polymer to a wedge in three dimensions, and can be viewed as a special case of competing and coexisting transitions between objects of different dimensionalities.

[1] K. Binder, in Phase Transitions and Critical Phenomena, Vol. 8,edited by C. Domb and J. L. Lebowitz (Academic Press, London, 1983), pp. 1-144.

[2] R. Halifa Levi, Y. Kantor and M. Kardar, preprint arXiv:1710.08797 (2017).

[3] R. Halifa Levi, Y. Kantor and M. Kardar, to be published.