Global analysis of correlation functions: Dynamic light scattering from polymers and block copolymers

Dynamic light scattering has become a standard technique for investigating colloidal suspensions, polymer solutions, melts, blends, gels and other more complex systems. The experimental field autocorrelation function 1(t) can often be well modeled by a Laplace transform relating 1(t) to a distribution of decay times A(). In simple systems, A() can usually be directly related to a distribution of molecular weights, particle sizes, diffusion coefficients, relaxation times or other physically relevant quantities. With constrained regularization methods, the parameter-free estimation of A() has become straightforward. In complex systems, the resulting A() may contain several components the identification of which is not always obvious. The problem often originates in a superposition of components that have different variations of the decay time with the scattering vector. We present a method based on a simultaneous fit of several autocorrelation functions (ACF) measured at several different scattering angles, which, using simple and reasonable assumptions, yields a robust analysis of the spectra of decay times. The application of the method is illustrated on simulated autocorrelation functions as well as on real experimental data obtained on a variety of polymer systems.