The dielectric properties of thin films can be modified relative to the bulk material because the interaction between film and substrate influences the mobility of the atoms or molecules in the first layers. Here we show that a strong scale effect occurs in nanometer size octadecylammine thin films. This effect is attributed to the different distribution of molecules depending on the size of the film. To accurately describe this effect, we have developed a model which is a reinterpretation of the linearized Thomas-Fermi approximation. Within this model, we have been able to characterize the polarizability of thin films independently of the thickness of the film.