Inverse transformation: unleashing spatially heterogeneous dynamics with an alternative approach to XPCS data analysis

Abstract

X-ray photon correlation spectroscopy (XPCS), an extension of dynamic light scattering (DLS) in the X-ray regime, detects temporal intensity fluctuations of coherent speckles and provides scattering-vector-dependent sample dynamics at length scales smaller than DLS. The penetrating power of X-rays enables XPCS to probe the dynamics in a broad array of materials, including polymers, glasses and metal alloys, where attempts to describe the dynamics with a simple exponential fit usually fail. In these cases, the prevailing XPCS data analysis approach employs stretched or compressed exponential decay functions (Kohlrausch functions), which implicitly assume homogeneous dynamics. This paper proposes an alternative analysis scheme based upon inverse Laplace or Gaussian transformation for elucidating heterogeneous distributions of dynamic time scales in XPCS, an approach analogous to theCONTINalgorithm widely accepted in the analysis of DLS from polydisperse and multimodal systems. Using XPCS data measured from colloidal gels, it is demonstrated that the inverse transform approach reveals hidden multimodal dynamics in materials, unleashing the full potential of XPCS.