  In this paper we consider the Cahn-Hilliard equation endowed with Wentzell
boundary condition which is a model of phase separation in a binary mixture
contained in a bounded domain with permeable wall. Under the assumption that
the nonlinearity is analytic with respect to unknown dependent function, we
prove the convergence of a global solution to an equilibrium as time goes to
infinity by means of a suitable \L ojasiewicz-Simon type inequality with
boundary term. Estimates of convergence rate are also provided.
