Calculating the 'chain splay' of amphiphilic molecules: Towards quantifying the molecular shapes.

We report the first method to calculate a very important molecular level parameter of amphiphilic molecules- the 'chain splay'. The calculations employed a truncated cone geometry, as it is the most probable configuration adopted by various amphiphiles. This approach utilized known parameters including lipid length, cross-sectional area at the head group and molecular volume. This new parameter, i.e. the area at the chain end, perceived to be more sensitive than Israelachvili's famous shape factor or critical packing parameter (CPP). With relevant calculations, we demonstrate the fundamental roles of 'chain splay' to: a) reveal the critical contribution of molecular structure on average molecular shape and consequent self-assemblies, b) track the finest changes in molecular shapes within different bicontinuous cubic phases, c) obtain non-zero areas at the chain ends of amphiphiles that form normal (type 1) phases, d) back-calculate molecular volumes close to theoretical values, and e) find the link between molecular shapes and global curvatures of self-assemblies. This powerful feature advances our abilities towards quantitative estimation of spatial configurations adopted by amphiphilic molecules; moreover, it has a strong impact on predicting biomembrane structuring and nanoscale design of corresponding self-assemblies for a range of emerging applications.