Significance: Nucleation is the process by which constituent building blocks first assemble to form a new substance. In the case of mineral formation from initially free ions in solution, the emergence of intermediary phases often determines the thermodynamics and kinetics of formation for the most stable phase. Our work on CaCO ₃ mineralization reevaluates a topic of intense discussion: Can nucleation be explained by theories established over a century ago, or should new physical concepts, as recently proposed, be adopted? Our data show that classical theories can indeed be used to describe complex mechanisms of crystallization. In addition, we provide information about the properties of intermediate phases, which will aid in the design of additives to control mineralization.

Graphite and related sp² carbons are ubiquitous electrode materials with particular promise for use in e.g., energy storage and desalination devices, but very little is known about the properties of the carbon–electrolyte double layer at technologically relevant concentrations. Here, the (electrified) graphite–NaCl(aq) interface was examined using constant chemical potential molecular dynamics (CμMD) simulations; this approach avoids ion depletion (due to surface adsorption) and maintains a constant concentration, electroneutral bulk solution beyond the surface. Specific Na⁺ adsorption at the graphite basal surface causes charging of the interface in the absence of an applied potential. At moderate bulk concentrations, this leads to accumulation of counter-ions in a diffuse layer to balance the effective surface charge, consistent with established models of the electrical double layer. Beyond ∼0.6 M, however, a combination of over-screening and ion crowding in the double layer results in alternating compact layers of charge density perpendicular to the interface. The transition to this regime is marked by an increasing double layer size and anomalous negative shifts to the potential of zero charge with incremental changes to the bulk concentration. Our observations are supported by changes to the position of the differential capacitance minimum measured by electrochemical impedance spectroscopy, and are explained in terms of the screening behaviour and asymmetric ion adsorption. Furthermore, a striking level of agreement between the differential capacitance from solution evaluated in simulations and measured in experiments allows us to critically assess electrochemical capacitance measurements which have previously been considered to report simply on the density of states of the graphite material at the potential of zero charge. Our work shows that the solution side of the double layer provides the more dominant contribution to the overall measured capacitance. Finally, ion crowding at the highest concentrations (beyond ∼5 M) leads to the formation of liquid-like NaCl clusters confined to highly non-ideal regions of the double layer, where ion diffusion is up to five times slower than in the bulk. The implications of changes to the speciation of ions on reactive events in the double layer are discussed.

The flux of trajectories in an extended reaction coordinate space characterising NaCl crystal nucleation pathways from biased and unbiased molecular dynamics simulations reveals multiple routes to phase separation far into the metastable zone.

The nucleation of protein condensates is a concentration-driven process of assembly. When modeled in the canonical ensemble, condensation is affected by finite-size effects. Here, we present a general and efficient route for obtaining ensemble properties of protein condensates in the macroscopic limit from finite-sized nucleation simulations. The approach is based on a theoretical description of droplet nucleation in the canonical ensemble and enables estimation of thermodynamic and kinetic parameters, such as the macroscopic equilibrium density of the dilute protein phase, the surface tension of the condensates, and nucleation free energy barriers. We apply the method to coarse-grained simulations of NDDX4 and FUS-LC, two phase-separating disordered proteins with different physicochemical characteristics. Our results show that NDDX4 condensate droplets, characterized by lower surface tension, higher solubility, and faster monomer exchange dynamics compared to those of FUS-LC, form with negligible nucleation barriers. In contrast, FUS-LC condensates form via an activated process over a wide range of concentrations.