Exploring composition fluctuations and their dynamics in binary mixtures using coarse-grained molecular dynamics

Liquid-liquid extraction processes are central to the separation of rare earth elements and other strategic materials, yet their performance is often limited by third-phase formation and phase instabilities in the organic phase. Molecular simulation of these phase transitions is challenging due to the long-range structure that emerges in the organic phase near demixing. Here, we employ coarse-grained molecular dynamics simulations with the MARTINI 2.0 force field to investigate the structure, scattering behavior, and dynamics of a prototypical amide/diluent system: DMDBPMA in n-dodecane. Simulations spanning three extractant mole fractions (x = 0.226, 0.311, 0.404) and multiple temperatures (290-320 K) reveal equilibrium composition fluctuations whose scattering profiles in wavenumber q are well described by an Ornstein-Zernike form. Extracted correlation lengths and q = 0 intensities exhibit power-law growth consistent with 3D Ising critical exponents as the spinodal temperature is approached, with Tsp values ranging from ∼287 to 270 K and decreasing with increasing extractant fraction. Dynamical analysis of intensity autocorrelations identifies three processes: a slow diffusive mode with a strongly q-dependent relaxation time, a faster convective mode with a weakly q-dependent relaxation time, and a very fast vibrational mode. A parameter-free model for interdiffusion transport gives semi-quantitative agreement with the observed relaxation times at low q. We further quantify equilibration criteria, showing that simulation times of at least ∼100 slow-mode relaxation times are required to achieve converged statistics of critical fluctuations. Together, these results provide a predictive framework for connecting mesoscale structure and dynamics in extractant-diluent mixtures to q-dependent experimental measurements of liquid dynamics, including x-ray photon-correlation spectroscopy.