Scattering from laterally heterogeneous vesicles. I. Model-independent analysis

This is the first of a series of papers considering the scattering from laterally heterogeneous vesicles. Here, it is shown that contrast variation studies on unilamellar vesicles can be analyzed in a model-independent manner to detect lateral segregation in model membranes. In particular, it is demonstrated that the Porod invariant, Q = \textstyle\int q^{2}I (q )\,{\rm d}q, is related to the scattering length density contrast between compositionally distinct regions in a heterogeneous membrane. The formation of domains and the concomitant identification of phase boundaries as a function of either membrane composition or temperature can therefore be detected in the changes taking place in Q.