We report the large-area assembly of anisotropic gold nanoparticles into lithographically defined templates with control over their angular position using a capillary force-based approach. We elucidate the role of the geometry of the templates in the assembly of anisotropic nanoparticles consisting of different shapes and sizes. These insights allow us to design templates that immobilize individual triangular nanoprisms and concave nanocubes in a shape-selective manner and filter undesired impurity particles from a mixture of triangular prisms and other polyhedra. Furthermore, by studying the assembly of two particles in the same template, we elucidate the importance of interparticle forces in this method. These advances allow for the construction of face-to-face and edge-to-edge nanocube dimers as well as triangular nanoprism bowtie antennas. As an example of the fundamental studies enabled by this assembly method, we investigate the surface-enhanced Raman scattering (SERS) of face-to-face concave cube dimers both experimentally and computationally and reveal a strong polarization dependence of the local field enhancement.
We propose an equilibrium embryo definition for homogeneous bubble nucleation within the pure component superheated Lennard-Jones liquid. The suggested embryo definition serves as an improvement to a previous (n,v) embryo model (Uline and Corti 2007). In that model, the constrained equilibrium between the bubble and the surrounding superheated liquid was maintained by placing n particles within a spherical volume v, without concern for the redundant counting of configurations and the relevance of the model to the dynamics of a nucleation process. To eliminate this redundancy, while only considering those embryos that should most likely appear at a transitional state, we now define the volume of the embryo via the use of a shell particle and only include n particles inside the volume that are deemed to be "vapor-like". The underlying free energy surface of formation of the new (n,v) embryo model is generated via Monte Carlo simulation and also approximately by a suggested density functional theory method. The resulting surface implies that small and locally confined regions of near-zero density serve as precursors initiating homogeneous bubble nucleation. Furthermore, the nonredundant counting of the embryo configurations yields a well-defined and sharp conduit in the free energy surface that directs the initially formed embryos toward the critical nucleus. We discuss how the suggested equilibrium embryo model aids in both the identification of the transitional configurations and calculation of the average number density of the critical nuclei within the superheated liquid phase, which is the focus of the companion paper (DOI 10.1021/jp404151h).
We present a new self-consistent thermodynamic formalism for the interfacial properties of nanoscale embryos whose interiors do not exhibit bulklike behavior and are in complete equilibrium with the surrounding mother phase. In contrast to the standard Gibbsian analysis, whereby a bulk reference pressure based on the same temperature and chemical potentials of the mother phase is introduced, our approach naturally incorporates the normal pressure at the center of the embryo as an appropriate reference pressure. While the interfacial properties of small embryos that follow from the use of these two reference pressures are different, both methods yield by construction the same reversible work of embryo formation as well as consistency between their respective thermodynamic and mechanical routes to the surface tension. Hence, there is no a priori reason to select one method over another. Nevertheless, we argue, and demonstrate via a density-functional theory (with the local density approximation) analysis of embryo formation in the pure component Lennard-Jones fluid, that our new method generates more physically appealing trends. For example, within the new approach the surface tension at all locations of the dividing surface vanishes at the spinodal where the density profile spanning the embryo and mother phase becomes completely uniform (only the surface tension at the Gibbs surface of tension vanishes in the Gibbsian method at this same limit). Also, for bubbles, the location of the surface of tension now diverges at the spinodal, similar to the divergent behavior exhibited by the equimolar dividing surface (in the Gibbsian method, the location of the surface of tension vanishes instead). For droplets, the new method allows for the appearance of negative surface tensions (the Gibbsian method always yields positive tensions) when the normal pressures within the interior of the embryo become less than the bulk pressure of the surrounding vapor phase. Such a prediction, which is allowed by thermodynamics, is consistent with the interpretation that the mother phase's attempted compression of the droplet is counterbalanced by the negative surface tension, or free energy cost to decrease the interfacial area. Furthermore, for these same droplets, the surface of tension can no longer be meaningfully defined (the surface of tension always remains well defined in the Gibbsian method). Within the new method, the dividing surface at which the surface tension equals zero emerges as a new lengthscale, which has various thermodynamic analogs to and similar behavior as the surface of tension.
The free energy of forming a droplet and a bubble with a given particle number n and volume v within the pure-component Lennard-Jones supercooled vapor and superheated liquid, respectively, are further explored using density-functional theory. Similar to what was found previously [M. J. Uline and D. S. Corti, Phys. Rev. Lett. 99, 076102 (2007); M. J. Uline and D. S. Corti, J. Chem. Phys. 129, 234507 (2008)], the limits of stability again appear within both free energy surfaces evaluated at two other metastability conditions, one closer to the binodal and one closer to the spinodal. Furthermore, an ad hoc bond connectivity criterion is also applied in an attempt, however approximately, to eliminate certain configurational redundancies that arise from the chosen droplet and bubble definitions. What results are free energy surfaces describing the formation of equilibrium embryos that should be an improved representation of the fluctuations that are relevant to those nonequilibrium embryos seen in an actual nucleation event. Finally, we discuss in some detail the use of the (n,v) reaction coordinate within the framework of an equilibrium-based theory and its relation to other descriptions of nucleation.
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