PEM theoretical studies
There have been very few attempts to describe theoretically the electrostatic self-assembly, and all of them are build-up on severe assumptions hard to test experimentally; specifically they assume that PEM are equilibrium structures. Netz and Joanny  considered the formation of multilayers in a system of semiflexible polyelectrolytes (PE), assuming that the deposited layer structure was fixed, providing a solid charged substrate for the next layer. Mayes et al  applied a similar idea to flexible PE. Both these models neglect interpenetration (interdigitation) and chain complexation between the layers, which are usual features found in experimental works about PEMs. The oppositely limit of strong intermixing of PE between neighbouring layers was considered by Castlenovo and Joanny  by incorporating the complex formation between oppositely PEs into self-consistent field equations. Unfortunately this equations are limited to solutions of high ionic strength, were electrostatic interactions can effectively be treated as short-range interactions. Despite these huge efforts, the strong correlations existing between oppositely charged polyions, provides a formidable challenge for their theoretical description. In this respect, numerical simulations could be of great help.