Reading Motion in Polarized Polymer Electrolytes: Heterodyne XPCS with Explicit Acquisition-Time Alignment

Abstract

Spatially resolved operando measurements combine information about material motion with the acquisition schedule used to observe it. This study examines that coupling in heterodyne X-ray photon correlation spectroscopy of polarized polystyrene-block-poly(ethylene oxide)/LiTFSI electrolytes. The analysis concerns fitted speed magnitudes at five nominal positions in three cells, with electrochemical records defining the electrical transitions. A coherent-field derivation establishes why an intensity correlation cannot distinguish opposite directions of translation. A time-alignment calculation then separates a connected sequence of observations from an estimated simultaneous profile. Of 426 measurement rows, 400 contain finite fitted records; 48 complete profiles satisfy phase-preserving interpolation rules. The five-position timestamp span is approximately 25 minutes. Median root-mean-square alignment adjustments are 0.0139, 0.0251 and 0.0464 nm s⁻¹ for cells N, O and P. The largest individual adjustment is 0.320 nm s⁻¹. Spatial slope signs change in four retained profiles from P, without implying reversal of the polymer velocity. Comparisons with monotone cubic interpolation, stricter temporal bracketing and exclusion near electrical transitions delimit these observations. The study connects interference physics, electrical timing, spatial registration and the interpretation of fitted quantities through numerical examples and measurement-based figures. Its central educational task is to identify which physical conclusions the recorded observable can support.