A holistic view of nucleation and self-assembly
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Classical nucleation theory
Crystallization is a pervasive phenomenon in synthetic, environmental, and biological systems. The majority of important technological materials, from semiconductors to pharmaceuticals, are crystalline. Ice crystals forming in the atmosphere influence the balance of solar energy reaching the Earth, while minerals impact soil fertility and carbon retention, and represent dynamic reservoirs of crystal formation and transformation. In living systems, crystallization is exploited to produce functional tissues both through the assembly of ordered protein matrices and through the formation of biominerals such as bones and teeth. The interplay between living systems and the environment often takes place through crystal formation and dissolution. We owe our oxygen atmosphere to iron reduction and oxidation reactions by microbes at this interface, and the vast volume of carbonates in the geological record and modern-day oceans are a product of the intimate relationship between biota and minerals going back one billion years. These phenomena impact global seawater chemistry and the flux of CO2 into and out of the atmosphere.
Crystallization starts with nucleation, a phenomenon that was first explained in terms of thermodynamic principles by J.W. Gibbs in the 1870s.1 Although Gibbs was considering the formation of raindrops—condensation of water into droplets from humid air—the principles of what has come to be known as “classical nucleation theory” (CNT) were later applied to crystal formation.2 The key insight that Gibbs provided was that, unlike a simple chemical reaction, nucleation is not a spontaneous process, even when the chemical potential change in producing the new phase is negative (i.e., the system is supersaturated). Rather, a free-energy barrier, ∆Gc, must be overcome before a nascent crystal nucleus can grow to macroscopic size (Figure 1a[i]).3 This article will address nucleation from solutions, however, the concepts apply equally to vapor and melt crystallization. According to CNT,4 the barrier ∆Gc exists because the appearance of the solid phase also creates a phase boundary with a surface tension. While the chemical potential drop ∆μ associated with transfer of ions, atoms, or molecules from the solution to the solid nucleus (Figure 1b) contributes to
James J. De Yoreo, Physical Sciences Division, Pacific Northwest National Laboratory; Department of Materials Science and Engineering, University of Washington, USA; [email protected] doi:10.1557/mrs.2017.143
• VOLUME • www.mrs.org/bulletin 2017 Materials Research Society MRS 42 • ofJULY 2017 Downloaded© from https:/www.cambridge.org/core. Columbia University Libraries, on 11 Jul 2017 at 06:06:43, subject to theBULLETIN Cambridge Core terms use, available at https:/www.cambridge.org/core/terms. https://doi.org/10.1557/mrs.2017.143
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A HOLISTIC VIEW OF NUCLEATION AND SELF-ASSEMBLY
As Equation 1 shows, the barrier itself contains two important parameters. One is σ, which can be controlled in the laboratory, and t
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