Insights into surface structures and thermodynamics are provided for nitrogen adsorption on two nonporous alumina adsorbents and two macroporous silica adsorbents by modelling high-resolution data using the simple Langmuir isotherm equation combined with pressure-varying flexible least squares. The fitted parameters, maximum adsorption capacity and standard Gibbs energy change for each adsorbent show multiple steps that are assumed to be indicative of transitions to different complete monolayer and multilayer structures. Pressure-varying N2 cross-sectional areas for three of the adsorbents are calculated by assuming that one of the steps is the Brunauer-Emmett-Teller monolayer with molecular area 16.2 Å2. The silica with added octyldimethylsilyl groups has pressure-varying parameter profiles that differ from the other adsorbents and here the N2 cross-sectional area is assumed to be 21.3 Å2 to ensure consistency with the literature surface area. Seven monolayers and multilayers are identified across the four adsorbents, and corresponding molecular areas compare favourably with reported values. At low pressures, adsorption occurs at the strongest sites, and is localised and dependent on surface heterogeneity and topography. Up to five complete, two-dimensional lattice structures are apparent in the mid-pressure ranges. At high pressures, multilayers and liquefaction points are observed and are independent of surface composition and heterogeneity.