Beyond the Average: Revealing Hidden Heterogeneity with X-ray Scattering

Many systems in chemistry, physics, and biology cannot be described by a single structure. Proteins fluctuate among conformations, polymers adopt a range of dimensions, and nanoparticle samples contain distributions of sizes. This heterogeneity can influence function and material properties, yet many experiments report only an ensemble average. Moreover, the average size obtained from an experiment may not be the ordinary mean we would most naturally like to know. Measuring the spread of the ensemble can therefore improve our understanding of both its heterogeneity and its average.

Small-angle X-ray scattering, or SAXS, provides structural information about nanoscale systems in solution, but instrumental blurring can obscure the distinction between particle size and size variation. I will introduce TENOR-SAXS, an approach that turns this limitation into a measurement tool. By deliberately varying the effective resolution of a two-dimensional scattering pattern, we can separate instrumental and sample contributions and estimate the variance of the underlying ensemble. I will explain the physical idea behind this counterintuitive use of blur, present tests on simulated compact particles and flexible chains, and discuss its potential for extracting more complete structural information from existing SAXS measurements.