Small-angle scattering measurements of complex macromolecules in solution are used to establish relationships between chemical structure and conformational properties. Interpretation of the scattering data requires an inverse approach where a model is chosen and the simulated scattering intensity from that model is iterated to match the experimental scattering intensity. This raises challenges in the case where the model is an imperfect approximation of the underlying structure, or where there are significant correlations between model parameters. We examine three bottlebrush polymers (consisting of polynorbornene backbone and polystyrene side chains) in a good solvent using a model commonly applied to this class of polymers: the flexible cylinder model. Applying a series of constrained Monte-Carlo Markov Chain analyses demonstrates the severity of the correlations between key parameters and the presence of multiple close minima in the goodness of fit space. We demonstrate that a shape-agnostic model can fit the scattering with significantly reduced parameter correlations and less potential for complex, multimodal parameter spaces. We provide recommendations to improve the analysis of complex macromolecules in solution, highlighting the value of Bayesian methods. This approach provides richer information for understanding parameter sensitivity compared to methods which produce a single, best fit.
K E Y W O R D SBayesian analysis, bottlebrush, neutron scattering, small-angle scattering
| INTRODUCTIONCharacterization of the solution-state properties of macromolecules is one of the fundamental means of evaluating the relationship between structural parameters and conformation, which in turn controls properties ranging from self-assembly to rheology. Small-angle X-ray scattering and neutron (small-angle neutron scattering [SANS]) scattering are the workhorse methods for performing this characterization. Modern instrumentation allows rapid, routine collection of data from solution samples and, as a result, much of the challenge in utilizing these techniques resides with the proper interpretation and modeling. Small-angle scattering data are typically modeled with an inverse-iterative approach, where simulated data from a real-or Fourier-space model is iteratively fit to a set of experimental data. The parameters of the model are then interpreted to describe the structure and