Surface pressure isotherms at the air/water interface are reproduced for four different polymers, poly-L-lactic acid (PLLA), poly(dimethylsiloxane) (PDMS), poly(methyl methacrylate) (PMMA), and poly(isobutylene) (PiB). The polymers have the common property that they do not dissolve in water. The four isotherms differ strongly. To unravel the underlying details that are causing these differences, we have performed molecularly detailed self-consistent field (SCE) modeling. We describe the polymers on a united atom level, taking the side groups on the monomer level into account. In line with experiments, we find that PiB spreads in a monolayer which smoothly thickens already at a very low surface pressure. PM MA has an autophobic behavior: a PM MA liquid does not spread on top of the monolayer of PM MA at the air/water interface. A thicker PM MA layer only forms after the collapse of the film at a relatively high pressure. The isotherm of PDMS has regions with extreme compressibility which are linked to a layering transition. PLLA wets the water surface and spreads homogeneously at larger areas per monomer. The classical SCF approach features only short-range nearest-neighbor interactions. For the correct positioning of the layering and for the thickening of the polymer films, we account for a power-law van der Waals contribution in the model. Two-gradient SCE computations are performed to model the interface between two coexistent PDMS films at the layering transition, and an estimation of the length of their interfacial contact is obtained, together with the associated line tension value.