The measurement of chain exchange kinetics for block polymer micelles has progressed with the use of time-resolved small-angle neutron scattering (TR-SANS). There, under contrast-matched conditions chain mixing can be deduced through intensity changes when mixing isotopically labeled polymer chains. However, the methods of calculating chain mixing has remained limited to cases with fixed size and morphology, or require extensive knowledge to model size/morphology changes. Thus, investigations of chain mixing during such changes have been historically hampered. Two popular methods are broadly used at present, comprehensive model fitting or a form-factor-agnostic approach to determine a relaxation function R(t). SANS model fitting in principle can identify mixing events during micelle transitions, however broad or multimodal distributions inhibit reliable fitting. In contrast, the R(t) approach avoids explicit models by using fixed reference patterns which prevents analysis of systems undergoing size/morphology changes. We introduce a new approach based on a shifting reference pattern termed SRR(t) that resolves the limitations of both of these prior approaches by using unmixable control samples. Here the unmixed scattering reference is derived from a unique combination of measurements to remain form-factor-agnostic while tolerating size/morphology changes during mixing. Several simulated data sets are used to demonstrate SRR(t) in different contexts where it accurately extracts the extent of chain mixing during size/morphology changes without any explicit knowledge of the form factor.

Form-factor-agnostic model to measure micelle chain exchange during morphological transitions

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