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Microscopic dynamics of complex fluids in the early stage of spinodaldecomposition (SD) is strongly intertwined with the kinetics of structuralevolution, which makes a quantitative characterization challenging. In thiswork, we use x-ray photon correlation spectroscopy to study the dynamics andkinetics of a protein solution undergoing liquid-liquid phase separation(LLPS). We demonstrate that in the early stage of SD, the structural relaxationkinetics is up to 40 times slower than the dynamics and thus can be decoupled.The kinetic decay rate is inversely proportional to time in the early stage,followed by a nearly constant behavior during the coarsening stage. Themicroscopic dynamics can be well described by hyper-diffusive ballistic motionswith a relaxation time exponentially growing with time in the early stagefollowed by a power-law increase with fluctuations. These experimental resultsare further supported by simulations based on the Cahn-Hilliard equation. Theestablished framework is applicable to other condensed matter and biologicalsystems undergoing phase transitions and may also inspire further theoreticalwork.

Interplay between Kinetics and Dynamics of Liquid-Liquid Phase Separation in a Protein Solution Revealed by Coherent X-ray Spectroscopy