The thermodynamics of aggregate development, structure, and size

Soil's aggregated structure is fundamental for the functioning of soil, and aggregation is a crucial process within pedogenesis. While aggregates are often considered stable entities, bonds between aggregate forming materials can form, consolidate, and break over time. Consequently, individual aggregates are subject to permanent restructuring and do not show a final spatial configuration that remains stable. Instead, only the temporal average of aggregate features converges to a constant value and –in case the system comprises a large ensemble of aggregates– a situation of thermodynamic equilibrium will establish over time. The dynamics of disaggregation and restructuring might be equally important for the establishment of aggregate structure as the aggregation mechanisms themselves and should therefore be considered when modeling structure formation. We conducted a comprehensive numerical analysis to reveal the interplay of aggregation mechanisms and the breaking of aggregate bonds in a physicochemical framework that combines three-dimensional transport with DLVO-type surface interactions. The attractive and repulsive energies between aggregate forming materials were used to model the temporal dynamics and stability of bonds in a heuristic manner. Despite the ongoing formation and breaking of bonds, we show that aggregation approaches a thermodynamic equilibrium depending on the physicochemical environment. Specifically, an ensemble of aggregates of sufficient size to provide robust statistical averages converges to a state of constant mean properties, e.g., aggregate size and aggregate morphology. Aggregates and their structure should therefore be considered dynamic entities, where an ensemble might reach a steady-state equilibrium, but each individual aggregate does not.