Theoretical approaches to charged surfaces

We summarize some of our recent theoretical and numerical work on the behaviour and structure of charged surfaces. Due to the coupling of effects on vastly different length scales, a complete treatment of charged surfaces is out of reach with present computer power. On the other hand, some progress can and has been made by concentrating on one specific aspect at a time with a suitably chosen numerical method. We discuss four such calculations, each using a different computational scheme, that yield various levels of description of charged surfaces. (i) Coarse grained Monte Carlo simulations of idealized surfaces incorporate large-length-scale fluctuation and correlation effects in the counterion cloud at a charged surface. (ii) Brownian dynamics simulations of more realistic, structured surfaces give modified counterion distributions and also allow one to estimate dynamic and non-equilibrium quantities such as the mobility of counterions at charged surfaces. (iii) All-atomistic molecular dynamics simulations of water at surfaces correctly reproduce water structuring effects at surfaces such as hydration and hydrophobic dewetting. (iv) On the nanoscopic level, quantum mechanical ab initio calculations give the effective interactions between oppositely charged groups in vacuum and in solution. The real theoretical challenge is to correctly piece together results obtained on all these different length scales.