New approach for SANS measurement of micelle chain mixing during size and morphology transitions

Chain exchange in amphiphilic block polymer micelles is measurable with time-resolved small-angle neutron scattering (TR-SANS) where contrast-matched conditions reveal chain mixing as reduced intensity. However, analyzing chain mixing on short time scales e.g. during micelle transformations remains challenging. SANS model fitting can quantify chain mixing during size and morphology changes, however short acquisition times lead to lower data statistics (higher error). Such data are unsuitable for form factor fitting, especially with polydisperse and/or multimodal scenarios. An integrated-reference approach, R(t), is compatible with such data by using fixed reference patterns for the unmixed and fully mixed states that are each integrated to improve data statistics (lower error). Although the R(t) approach is tolerant of low data statistics, it remains incompatible with size and morphology changes. A new shifting references relaxation approach, SRR(t), is proposed where reference patterns are acquired at each time point to enable mixed state calculations regardless of short acquisition times. The additional experimental measurements needed are described which provide these time-varying reference patterns. The use of reference patterns makes the SRR(t) approach size/morphology-agnostic, allowing for the extent of micelle mixing to be directly calculated without this knowledge. SRR(t) is thus compatible with arbitrary levels of complexity and can provide accurate assessment of the mixed state which could support future model analysis. Calculated scattering datasets were used to demonstrate the SRR(t) approach during multiple size, morphology, and solvent conditions (scenarios 1-3). The mixed state calculated from the SRR(t) approach is shown to be accurate for all three scenarios.