Density profiles of a LJ vapor near a weakly attractive surface with long-range fluid wall potential was studied along the pore coexistence curve. There are two localized density maxima near the pore wall: the first one is caused by localization of the molecules in the minimum of the fluid-wall potential, and the second one reflects adsorption of molecules at the first layer at higher densities. In addition, a third, weak density maximum is observed close to the critical temperature due to the competition between the long-range attractive tail of the fluid-wall potential and the effect of missing neighbors. This maximum separates the region of a gradual density depletion toward the surface due to the missing neighbor effect and the adsorption region further from the surface, where the density gradually increases toward the surface due to the attractive fluid-wall potential. When approaching the bulk critical temperature, this maximum moves away from the surface due to the divergence of the bulk correlation length. Applicability of various equations to describe the vapor density profiles is examined. Excess adsorption of vapor at low temperatures turns into excess depletion at higher temperatures. The crossover temperature increases with increasing pore size and strengthening fluid-wall interaction. The problems of the theory of the surface critical behavior of Ising models in a case of a non vanishing surface field and its mapping on a fluid is discussed. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 200605.70.Jk Critical point phenomena, 05.70.Np Interface and surface thermodynamics, 64.70.Fx Liquid-vapor transitions, 68.43.-h Chemisorption/physisorption: adsorbates on surfaces,
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