Direct Comparison of Kinetic and Thermodynamic Influences on Gold Nanomorphology

Under a given set of conditions, nanomaterials can crystallize into structures that are entirely inconsistent with the bulk material and may adopt a range of faceted morphologies that depend on the particle size. A size-dependent phase diagram, a graphical representation of the chemical equilibrium, offers a convenient way to describe this relationship among the size, morphology, and thermodynamic environment. Although creating such a diagram from conventional experiments is extremely challenging (and costly), theory and simulation allow us to use virtual experiments to control the temperature, pressure, size, structure and composition independently. Although the stability and morphology of gold nanoparticles has been addressed numerous times in recent years, a critical examination of the literature reveals a number of glaring contradictions. Typically gold nanoparticles present as multiply-twinned structures, such as icosahedra and decahedra, or faceted monocrystalline (fcc) shapes, such as truncated octahedra and cuboctahedra. All of these shapes are dominated by various fractions of {111} and {100} facets, which have different surface atom densities, electronic structure, bonding, chemical reactivities, and thermodynamic properties. Although many of the computational (and theoretical) studies agree on the energetic order of the different motifs and shapes, they do not necessarily agree with experimental observations. When discrepancies arise between experimental observations and thermodynamic modeling, they are often attributed to kinetics. But only recently could researchers analytically compare the kinetics and thermodynamics of faceted nanoparticles. In this Account, we follow a theoretical study of the size, shape, and structure of nanogold. We systematically explore why certain shapes are expected at different sizes and (more importantly) why others are actually observed. Icosahedra are only thermodynamically preferred at small sizes, but we find that they are the most frequently observed structures at larger sizes because they are kinetically stable (and coarsen more rapidly). In contrast, although the phase diagram correctly predicts that other motifs will emerge at larger sizes, it overestimates the frequency of those observations. These results suggest either a competition or collaboration between the kinetic and thermodynamic influences. We can understand this interaction between influences if we consider the change in shape and the change in size over time. We then use the outputs of the kinetic model as inputs for the thermodynamic model to plot the thermodynamic stability as a function of time. This comparison confirms that decahedra emerge through a combination of kinetics and thermodynamics, and that the fcc shapes are repressed due to an energetic penalty associated with the significant departure from the thermodynamically preferred shape. The infrequent observation of the fcc structures is governed by thermodynamics alone.