Precursor nanoparticles that form spontaneously on hydrolysis of tetraethylorthosilicate in aqueous solutions of tetrapropylammonium (TPA) hydroxide evolve to TPA-silicalite-1, a molecular-sieve crystal that serves as a model for the self-assembly of porous inorganic materials in the presence of organic structure-directing agents. The structure and role of these nanoparticles are of practical significance for the fabrication of hierarchically ordered porous materials and molecular-sieve films, but still remain elusive. Here we show experimental findings of nanoparticle and crystal evolution during room-temperature ageing of the aqueous suspensions that suggest growth by aggregation of nanoparticles. A kinetic mechanism suggests that the precursor nanoparticle population is distributed, and that the 5-nm building units contributing most to aggregation only exist as an intermediate small fraction. The proposed oriented-aggregation mechanism should lead to strategies for isolating or enhancing the concentration of crystal-like nanoparticles.

A mathematical model is developed to describe aggregative crystal growth, including oriented aggregation, from evolving pre-existing primary nanoparticles with composition and structure that are different from that of the final crystalline aggregate. The basic assumptions of the model are based on the ideas introduced in an earlier published report [Buyanov and Krivoruchko, Kinet. Katal. 1976, 17, 666-675] to describe the growth of low-solubility metal hydroxides (e.g., iron oxides) by oriented aggregation. It is assumed that primary particles can be described as pseudo-species A, B, and C, which have the following properties: (1) fresh primary particles (colloidally stable inert nanoparticles, denoted as A), (2) mature primary particles (partially transformed nanoparticles at an optimum stage of development for attachment to a growing crystal, denoted as B), and (3) nucleated primary particles (denoted as C1). The evolution of primary particles, A --> B --> C1, is treated as two first-order consecutive reactions. Crystal growth via crystal-crystal aggregation (Ci +) is described using the Smoluchowski equation. The new element of this model is the inclusion of an additional crystal growth mechanism via the addition of primary particles (B) to crystals (Ci): (B + ). Two distinct, but constant, kernels (K not equal K') are used. It is shown that, when K' = 0, a steplike crystal size distribution (CSD) is obtained. Within a range of K'/K values (e.g., K'/K = 10(3)), CSD with multiple peaks are obtained. Comparison with predictions of models that do not include the intermediate stage of primary particles (B) indicates pronounced differences. Despite its simplicity, the model is able to capture the qualitative features of CSD evolution that have been obtained from crystal growth experiments in hematite, which is a system that is believed to undergo oriented aggregation.

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A multiscale simulation model was developed to simulate shape evolution during copper electrodeposition in the presence of additives. The model dynamically coupled a kinetic Monte Carlo ͑KMC͒ model ͑for surface chemistry and roughness evolution͒ with a finite volume ͑FV͒ model ͑for transport and chemical reactions in the electrolyte͒ and a level-set code ͑for tracking macroscopic movement of the metal/electrolyte interface͒. The KMC code was coarse-grained and used a multisite mesoparticle approach to account for the adsorption of large molecules. A multilevel grid approach was used to achieve numerical efficiency and accurate interface tracking. The model was demonstrated for an application involving in-fill of two-dimensional trenches by copper electrodeposition with additives ͓bis͑3-sulfopropyl͒disulfide͔, polyethylene glycol, chloride, and l-͑2-hydroxyethyl͒-2imidazolidinethione. Demonstration calculations were carried out with use of initial estimates for the physicochemical parameters associated with a proposed reaction mechanism. The approach was found to be feasible for computing stable, dynamic behavior during macroscopic shape evolution over extended periods of time while simultaneously tracking microscopic roughness evolution associated with nearly molecular scale events at the surface. Numerical results include predictions of the surface concentration distributions as a function of time and distance for each reactant, product, and intermediate species associated with the proposed reaction mechanism.

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Copper electrodeposition in submicron trenches

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