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Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

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Nanocrystal growth can occur <strong>by</strong> two different general mechanisms.The first involves the diffusion-limited growth of the particles <strong>by</strong> monomeraddition to the particles. The second is growth <strong>by</strong> aggregation of nanocrystals.Aggregative growth leads to broad log-normal size distributions,whereas diffusion-limited growth leads to a narrowing of the size distribution.The moments of the size distribution, l 1 = r 3 /r h and l 3 = r 1 /r 3 provide aquantitative determination of the growth p mechanism, where r 1 ¼ Rr 1 =N l isthe arithmetic mean radius, r 3 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3Rr1 3=N l is the cube mean radius, andr h ¼ N l = Rð1=r 1 Þ is the harmonic mean radius, where N l is the total numberof particles. Nanocrystals formed through condensation of free atoms orsmall oligomers onto growing metal cores are relatively monodisperse withl 1 = l 3 = 1, whereas coagulative growth results in broad size distributionswith l 1 > 1.25 and l 3 < 0.905 [25,26]. Figure 5 shows representative examplesof size distributions for silver nanocrystals that formed primarily <strong>by</strong>diffusion-limited growth and aggregative growth. Note the broad size distributionthat results from aggregative growth compared to diffusion-limitedgrowth [26].Figure 5 Histograms of perfluorodecanethiol-capped silver nanocrystals synthesizedin supercritical carbon dioxide under good (80jC and 345 bar, dotted line) andpoor (80jC and 207 bar, solid line) solvent conditions. Under good solvent conditions,the particle size is smaller and the size distribution moments (A 1 and A 3 ) are closer tounity.<strong>Copyright</strong> <strong>2004</strong> <strong>by</strong> <strong>Marcel</strong> <strong>Dekker</strong>, <strong>Inc</strong>. <strong>All</strong> <strong>Rights</strong> <strong>Reserved</strong>.

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