Abstract. We consider a model of hydrophobic homopolymer in interaction with an interface between oil and water. The configurations of the polymer are given by the trajectories of a simple symmetric random walk (Si)i≥0. On the one hand the hydropho-bicity of each monomer tends to delocalize the polymer in the upper half plane, that is why we define h, a non negative energetic factor that the chain gains for every monomer in the oil (above the origin). On the other hand the chain receives a random price (or penalty) on crossing the interface. At site i this price is given by β (1 + sζi), where (ζi)i≥1 is a sequence of i.i.d. centered random variables, and (s, β) are two non negative parameters. Since the price is positive on the average, the interface attracts the polymer and a localization effect may arise. We transform the measure of each trajectory with the hamiltonian β ∑N i=1 (1 + sζi)1{Si=0} + h ∑N i=1 sign(Si), and study the critical curve hsc (β) that divides the phase spaces in a localized and a delocalized area. It is not difficult to show that h0c(β) ≤ h s c (β) for every s ≥ 0, but in this article we give a method to improve in a quantitative way this lower bound. To that aim, we transform the strategy developed by Bolthausen and Den Hollander in [4] on taking into account the fact that the chain can target the sites where it comes back to the origin. Then we deduce from this last result a corollary in terms of pure pinning model, namely with the hamiltonian ∑N i=1(−u+ sζi)1{Si=0} we find a lower bound of the critical curve uc(s) for small s. In this situation, we improve the existing lower bound of Alexander and Sidoravicius [1]

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