Quasi-elastic scattering from droplets theory

2 Quasi-elastic scattering from droplets theory 

In this subsection, the theoretical background for SANS and neutron spin-echo measurements carried out with o/w- and w/o-droplet microemulsions will be presented. According to Milner, Safran and others, shape fluctuations in droplet microemulsions can be described in terms of spherical harmonics [42-44]. This offers the possibility to calculate a dynamic structure factor S(q,w) or its Fourier transform, i.e. the intermediate scattering function I(q,t) for the problem, which can be used to analyse dynamical measurements by neutron spin-echo spectroscopy [45]. For the scattering from thin shells I(q,t) was calculated [43] 

Unfortunately, in a typical NSE experiment the number of points obtained as a representation of this function is in most cases too small and the error of the individual points is too high to allow for a fit with more than two or three adjustable parameters or for an analysis using Laplace transformation - and maximum entropy methods [56]. Without information from additional experiments it is only possible to compute an effective diffusion coefficient from the data by using a first- or second-order cumulant analysis [57]. 

In the first studies of micro emulsions using NSE spectroscopy [18, 45], the q variations of the effective diffusion coefficients were afterwards fitted by expressions of the form given below 

---