Alcohol Clustering Mechanisms in Supercritical Carbon Dioxide Using Pulsed-Field Gradient, Diffusion NMR and Network Analysis: Feedback on Stepwise Self-Association Models

27 Al NMR diffusometry of Al13 Keggin nanoclusters

Although nanometer-sized aluminum hydroxide clusters (i.e., ϵ-Al₁₃ , [Al₁₃ O₄ (OH)₂₄ (H₂ O)₁₂ ]⁷⁺ ) command a central role in aluminum ion speciation and transformations between minerals, measurement of their translational diffusion is often limited to indirect methods. Here, ²⁷ Al pulsed field gradient stimulated echo nuclear magnetic resonance (PFGSTE NMR) spectroscopy has been applied to the AlO₄ core of the ϵ-Al₁₃ cluster with complementary theoretical simulations of the diffusion coefficient and corresponding hydrodynamic radii from a boundary element-based calculation. The tetrahedral AlO₄ center of the ϵ-Al₁₃ cluster is symmetric and exhibits only weak quadrupolar coupling, which results in favorable T₁ and T₂ ²⁷ Al NMR relaxation coefficients for ²⁷ Al PFGSTE NMR studies. Stokes-Einstein relationship was used to relate the ²⁷ Al diffusion coefficient of the ϵ-Al₁₃ cluster to the hydrodynamic radius for comparison with theoretical simulations, dynamic light scattering from literature, and previously published ¹ H PFGSTE NMR studies of chelated Keggin clusters. This first-of-its-kind observation proves that ²⁷ Al PFGSTE NMR diffusometry can probe symmetric Al environments in polynuclear clusters of greater molecular weight than previously considered.

Cluster Identification Using Modularity Optimization to Uncover Chemical Heterogeneity in Complex Solutions

Structural heterogeneity is commonly manifested in solutions and liquids that feature competition of different interparticle forces. Identifying and characterizing heterogeneity across different length scales requires multimodal experimental measurement and/or the application of new techniques for the interrogation of atomistic simulation data. Within the latter, the parsing of networks of interparticle interactions (chemical networks) has been demonstrated to be a valuable tool for identifying subensembles of chemical environments. However, chemical networks can adopt a wide variety of topologies that challenge generalizable methods for identifying heterogeneous behavior, and few network analysis algorithms have been proposed for multiscale resolution. In this study, we apply a method of partitioning using the graph theoretic concept of clusters and communities. Using a modularity optimization algorithm, the cluster partition creates subgraphs based on their relative internal and external connectivities. The methodology is tested on two soft matter systems that have significantly different network topologies so as to probe its ability to identify multiple scale features and its generalizability. A binary Lennard-Jones fluid is first examined, where one component causes subgraphs that have high internal network connectivity yet are still connected to the rest of the interparticle network of interactions. The impact of connectivity and edge weighting on the cluster partition is investigated. In the second system, hierarchically organized molecular structures comprised of hydrogen bonded water molecules are identified at a liquid/liquid interface. These structures have a much more sparse network with significantly varied internal connectivity that is a challenge to differentiate from the background hydrogen bonding network of water molecules at the instantaneous interface. The organized macrostructures are effectively isolated from the background network using the cluster partition, and a time-dependent implementation allows us to reveal their reactivity. These studies indicate that cluster partitioning based upon intermolecular network connectivity patterns is broadly generalizable, depending only on user-defined intermolecular connectivity, is operable across different length scales, and is extensible to the study of dynamic phenomena.