Mesoscopic Correlations in Aqueous Alkylamine Mixtures Between Molecular and Micro Emulsions

TL;DR

The paper develops a mesoscopic bridge formalism that links site-site Ornstein-Zernike theory to Teubner-Strey field-theory descriptions, proposing that mesoscopic correlations arise from a long-range mesoscopic component of the bridge function. Using aqueous alkylamine mixtures as a testbed, it shows that TS-like kernels capture domain-scale oscillations and pre-peaks in X-ray spectra, while a microscopic decomposition of the direct correlation function reveals how mesoscopic information can be encoded in b^{(MR)}. The work provides a microscopic basis for the TS kernel, enabling a unified treatment of molecular-scale fluctuations and mesoscale organization, and argues for integrating mesoscopic bridge terms into conventional closures to describe soft-matter self-assembly. Overall, it offers a framework to connect microscopic interactions with emergent mesoscale structures in complex fluids, with implications for interpreting structure in aqueous and amphiphilic systems.

Abstract

Understanding how molecular correlations give rise to mesoscale organization is central to the physics of complex fluids such as hydrogen-bonded mixtures. In this work, we develop a mesoscale bridge formalism that connects the site-site Ornstein-Zernike (SSOZ) framework to the field theoretical Teubner-Strey (TS) approach. This bridge highlights how local orientational correlations, typically lost in the SSOZ closure, reemerge as effective long-range components at the mesoscale. The resulting theory provides a unified description of density fluctuations spanning molecular to mesoscopic length scales. The approach is illustrated using X-ray scattering spectra from simulated and experimental hydrogen-bonded fluids, showing that the TS representation captures the essential features of the mesoscale structure. Beyond this specific application, the proposed formalism offers a general route to interpret the structural crossover between microscopic interactions and collective mesoscale organization in complex fluids, including aqueous and amphiphilic systems.

Figures (8)

• Figure 1: Snapshot of the 30% aqueous-hexylamine mixture illustrating the water domains surrounded by nitrogen atoms which delimitate them from the alkyl "bath".
• Figure 2: Illustration of the TS fitting of the scattering pre-peaks for aqueous-hexylamine, for various hexylamine mole fractions x shown in each panels. The x-ray spectra are shown in blue lines, and the TS fitting curves in red lines. The lower panels are for the experimental dataour_expt_amin and the upper panels for the simulation data our_simu_amin. The domain sizes $d$ and OZ correlation lengths $\xi$ are given in each panel.
• Figure 3: Illustration of the TS fitting of the scattering pre-peaks for aqueous-octylamine, for various hexylamine mole fractions x shown in each panels. The line and other details are as in Fig.\ref{['Fig.TS-HEX']}
• Figure 4: Typical atom-atom correlation functions for the 20% aqueous-hexylamine mixture, illustrating the short (main panel), medium (lower inset) and long/meso (upper inset) range behaviour. The neat liquid correlation functions are shown in dashed lines in the main panel (black for water and green for hexylamine). The thin lines in the upper inset are the TS fitting extension of Eq.(\ref{['gr-TS']}).
• Figure 5: Typical atom-atom correlation functions for the 30% aqueous-octylamine mixture. The plot details are as in Fig.\ref{['Fig-grTS-hex']}