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

provides a conceptual framework for understanding the disorder–order phasetransition observed for sterically stabilized metal nanocrystals. One couldhypothetically calculate the free energy of the solid and fluid phases,0011XX U i;jF ¼ kT ln@exp@AAkTconfigurationði;j;bondsÞwhere k is Boltzmann’s constant. Because A(r) is either 0 or l,01XU i;jexp@A0 if r V 2R¼kT 1 if r > 2Rði;j;bondsÞand therefore, the free energy depends only on the possible configurations orpacking geometries in the fluid; it depends only on the entropy of the system.At low nanocrystal densities, the disordered fluid can achieve many moreconfigurations than the ordered phase and it is thermodynamically favored.However, at relatively high densities, the solid phase allows the particlesgreater free volume relative to the dense fluid. For example, the fcc latticeexhibits a maximum packing density of 0.74, whereas the disordered phasefreezes into a closest packed glass at a volume fraction of 0.68. The disorder–order phase transition for hard spheres has therefore been termed a disorderavoidingphase transition where the entropic driving force results from anincrease in microscopic disorder that exceeds the macroscopic configurationalentropy loss due to crystallization [40,41]. These considerations alsohold true in two dimensions, even though true long-range order cannot exist.In fact, Gray and co-workers [34,42] found that nanocrystal monolayers canproceed through a fluid–hexatic–hexagonal close-packed (hcp) phase transitionunder the appropriate conditions.Conceptually, an understanding of hard-sphere crystallization is importantfor understanding nanocrystal superlattice formation. However, thenanocrystals are not truly hard spheres and the interparticle interactionenergies can exceed 1/2 kT for particles less than 10 nm in diameter, despitetheir small size [10,33]. In 1995, Ohara et al. revealed that size-dependent vander Waals attractions between particles resulted in the formation of polydisperseaggregates of Au nanocrystals, with the largest particles located on theinterior of the aggregate and progressively smaller particles located on theexterior [43]. The aggregation was reversible and the particles were readilyredispersed with the addition of organic solvent. Molecular dynamics simulationsalso confirmed the importance of the van der Waals attraction on theformation of the aggregates. The interparticle attraction has been found to bevery important to superlattice formation [36,44].Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.