We have constructed a model to predict the properties of non-ionic (alkyl-ethylene oxide) (CnEm) surfactants, both in aqueous solutions and near a silica surface, based upon the self-consistent field theory using the Scheutjens-Fleer discretisation scheme. The system has the pH and the ionic strength as additional control parameters. At high ionic strength. the solvent quality for the surfactant head groups is affected, which changes both the bulk and the adsorption behavior of the surfactant. For example, with increasing ionic strength, the CMC drops and the agregation increases. Surfactants adsorb above the critical surface association concentration (CSAC). The CSAC is a function of the surfactant and the surface properties. Therefore, the CSAC varies with both the ionic strength and the pH. We predict that with increasing ionic strength, the CSAC will first slightly increase but then drop substantially. The charge on the surface is pH dependent, and as the head groups bind through H-bonding to the silanol groups, the CSAC increases with increasing pH. We focus on adsorption/desorption transitions for the surfactants and compare these to the experimental data. Both the equilibrium predictions and the consequences for the kinetics of adsorption follow experimental findings. Our results show that molecularly realistic models can reveal a much richer interfacial behavior than anticipated from more generic models.