This paper presents a systematic classification of multilayer-adsorption phenomena on attractive substrates, with emphasis on the buildup of thick films. The approach is based on statistical mechanics and includes adsorption-desorption effects and the interrelation of bulk and surface behavior. The surface phase diagram depends qualitatively on the relative strengths and ranges of adatom-adatom and adatom-substrate attractions. When the adatom-substrate attraction dominates (strong substrate), the film builds up uniformly, as the bulk adatom density increases, and the excess surface density diverges at coexistence (complete wetting). The buildup proceeds via an infinite sequence of discrete layer transitions (layering) at low temperatures (below the roughening temperature $T_R$ and smoothly at higher temperatures, as originally noted by de Oliveira and Griffiths. Substrates of intermediate strength are characterized by a wetting temperature $T_W$ above which wetting at coexistence is approached. The relative values of $T_W$ and $T_R$ define three subregions: When $T_W<T_R$ layering occurs, with an infinite sequence of transitions between $T_W$ and $T_R$ when $T_R\lesssim T_W$, layer transitions have coalesced into a single thick-film—thin-film transition (prewetting); when $T_R\ll T_W$, prewetting may disappear, leaving only a critical-wetting transition on the coexistence axis. For still weaker substrates, wetting is incomplete at all temperatures; however, a variety of drying phenomena may occur on the high-density side of bulk coexistence. Specific calculations are given for a lattice-gas model at $T=0\mathrm{}$ and in the mean-field approximation. Conclusions are informed, in addition, by certain exact results and symmetries. The last section includes a critical discussion of the relation of the lattice-gas model to the real world and a brief review of relevant experimental data.

• Received 25 May 1982

DOI:https://doi.org/10.1103/PhysRevB.26.5112