The self-assembly of molecules on surfaces into 2D structures is important for the bottom-up fabrication of functional nanomaterials, and the self-assembled structure depends on the interplay between molecule-molecule interactions and molecule-surface interactions. Halogenated benzene derivatives on platinum have been shown to have two distinct adsorption states: a physisorbed state and a chemisorbed state, and the interplay between the two can be expected to have a profound effect on the self-assembly and phase behaviour of these systems. We developed a lattice model that explicitly includes both adsorption states, with representative interactions parameterised using density functional theory calculations. This model was used in Monte Carlo simulations to investigate pattern formation of hexahalogenated benzene molecules on the platinum surface. Molecules that prefer the physisorbed state were found to self-assemble with ease, depending on the interactions between physisorbed molecules. In contrast, molecules that preferentially chemisorb tend to get arrested in disordered phases. However, changing the interactions between chemisorbed and physisorbed molecules affects the phase behaviour. We propose functionalising molecules in order to tune their adsorption states, as an innovative way to control monolayer structure, leading to a promising avenue for directed assembly of novel 2D structures. (C) 2016 AIP Publishing LLC.