Abstract
This joint work between a philosopher and two chemists illustrates the practical scientific need for improved approaches to multiscale modeling. Nucleation models are essential to predicting the composition, structure, and growth rate, of nanoscale materials synthesis, and many models of nucleation exist. Classical nucleation models, for example, aim to predict the rate of nucleation based on the relationship between the thermodynamic properties of surface free energy and volume free energy. This model employs concepts that describe system-wide phenomena (e.g., surface area and volume) which treats nucleation as a bulk, continuous, and system-wide process. Other models of nucleation aim to describe the patterns of formation of the seeds or “nuclei” in the newly formed phase, predicting and explaining how a particular nucleus will grow and when it is more likely for a new nucleus to form vs. an existing nucleus to continue to grow. One example is the LaMer model, which predicts the homogeneous nucleation of a colloid based on the concentration of precursor over time. At low precursor concentrations, formation of nuclei is unfavorable and does not occur until the precursor reaches a critical concentration, at which point a burst nucleation event occurs. After this event monomer concentration is too low to continue nucleation and the nuclei enter the growth phase. These models employ concepts that describe the individual nuclei as individual solids, occasionally with internal structure of their own. Such models treat nucleation as an aggregate of individual microscale nucleation events. We argue that in bulk chemistry, physics, and materials science, the success of employing these different types of models jointly is due in part to the high degree of scale separation between the dynamics of the macroscale model and the dynamics of the microscale model. We contrast this rationale for the success of a modeling strategy with rationales that appeal to one or the other model being the more “fundamental” model of the system and with rationales that aim to draw a relationship of emergence between the two types of models. Then, we use Simon and Millstone’s research program in the thermodynamics and chemical kinetics of nanoparticle formation to raise a modeling challenge: how should nanochemists adapt nucleation models to the nanoscale? Nucleation plays a central role in the formation of a class of nanomaterial known as colloidal metal nanoparticles (CMNPs). Synthesizing CMNPs faces a variety of practical challenges related to the need to keep the particles from growing above the nanoscale, as well as the need to create a group of particles that are all of the same size, shape, and crystal structure. Solving these problems requires the use of nucleation models, but at the nanoscale, there is no longer the same degree of scale separation between macroscale and microscale nucleation models. We conclude by discussing what strategies are available to nanochemists for rationalizing the use of both types of nucleation models.
