Numerical simulations about PEM´s
There exist few computational studies about electrostatic self-assembly of PEM. In a seminal paper on layer formation on a spherical substrate  it has been demonsrtated that additional non-electrostatic forces are needed to produce nice PEMs. This suggests that multilayering is possibly not an equilibrium phenomenon evidence of which has been also observed experimentally . Similar conclusions have been drawn for other geometries using either Molecular Dynamics (MD) or Monte Carlo (MC) techniques [24, 25]. Another outcome is, that these studies have confirmed the fuzzy nature of PEMs (molecules in one layer interpenetrate other layers) , although almost perfect periodic oscillations of the density differences between monomers belonging to positively and negatively charged PE have been found. MC studies (see refs. in ) have reported stability as well as the microstructure of the PE layers to be especially sensitive to the strength of the non-electrostatic short range attraction between the PE and the charged substrate. In addition, the thickness of the adsorbed layer is observed to decrease when increasing PE concentration or surface charge density, although the total adsorbed amount displays a non-monotonic dependence on polymer concentration. It was also demonstrated that the formation of multilayers as well as the extent of layer intermixing depends on the molecular weight of the PE chains and the fraction of charge on its backbone. The presence of ionic pairs between oppositely charged PE that form the layers have been claimed as a possible important factor in stabilizing the multilayer films. In the last years, MD studies for the assembly of flexible PE onto flat charged surfaces  have suggested the formation of thermodynamically stable structures from bulk mixture solutions. This is a controversial, very basic issue that opposes to some experimental reports, and certainly needs to be clarified.