This workshop is the fourth to be held under the EC program NETIAM (New and Emerging Themes in Industrial and Applied Mathematics), which emphasises new and emerging applications of mathematics in the real world.

The aim of the workshop is to identify new and emerging areas in which mathematics can provide understanding of the behaviour of materials based on modelling at a molecular scale. Crystalline solids are quite well understood at the atomistic level and there is much well-developed molecular modelling of polymers, but the complexity of proteins, and of interfaces, at the molecular level both present current challenges.

1. Proteins. For large molecules like proteins, with an atomic weight of say 100,000 or more, even going from the nano-scale (nm) to the micro-scale (mm) is still a relatively uncharted area. Questions arise how one can scale properties of relatively small clusters of atoms in a molecule, for which one can understand and calculate suitable properties based on quantum mechanics, to a larger entity. To this end, one needs to combine these atoms into appropriate larger clusters, which in turn constitute a larger molecule and the question is whether it is possible to obtain a `Russian doll-like' hierarchy of models encompassing each other. A more classical approach like homogenisation may fail if one wants to keep the function of proteins intact. This function is, to a large extent, dependent on the occurrence of the right functional groups at the right position on the complex entangled and folded protein. An added complexity here is that the shape and degree of entanglement of the protein, and therefore its function, may change because of changes in the environment (for example, changes in pH value). A further complexity is that the structure of proteins involves four levels, each one carrying its own length scale. Mathematical techniques currently used include molecular dynamics simulations, more empirical mechanical models of the molecules, and density functional theory.
2. Interfaces. Other complexity problems arise at solid-solid interfaces, with different relevant length scales. Roughly speaking one has to deal with the bulk behaviour of the two constituting phases and the behaviour of the two regions in each phase near the interface. For both inorganic and polymeric materials depletion of certain components will take place causing a different microstructure or morphology in the interfacial regions. Moreover, for mesoscopic properties controlled by the interface, like adherence, again one has not only to consider the ideal interface but also interfaces having defects. This area is relevant to problems involving coatings (particularly for thin coatings), and electrical contacts in microelectronics, interfaces in environmental, biochemical or biomedical sensors and nanotechnological devices including, of course, quantum computers. For other surface-controlled processes, notably catalysis, the proper representation of surfaces and their dynamic behaviour poses comparable problems.

The above-mentioned research areas call for a systematic approach in which both computational and materials input are required.