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

approach each other, the ligand tails repel each other in a good solvent,allowing for nanocrystal dispersibility. According to a theory developed byVincent et al. [47], the total steric repulsive energy consists of osmotic A osmand elastic A elas contributions, and the total interaction energy A total is thesum of the forces:A total ¼ A vdW þ A osm þ A elasA total depends on nanocrystal size, ligand composition, length and graftdensity, and the solvent condition. The osmotic term A osm results from theenergetic balance between solvent–ligand tail and tail–tail interactions. Thesolvent conditions and ligand length l largely control A osm [47]:A osm ¼ 4pRk bT/ 2 1v solv 2A osm ¼ 4pRk bT/ 2 1v solv 2 d 2R 2v l2; l < d 2R < 2lv l 2 d 2R 1ln d 2R ; d 2R < l2l 4 lHere, v solv is the molecular volume of the solvent, / is the volume fractionprofile of the stabilizer extending from the particle surface, and v is the Flory–Huggins interaction parameter. In Flory–Huggins theory, v = 1 ⁄ 2 typicallyrepresents the boundary between a good solvent (v 1 ⁄ 2 ).The elastic repulsive energy A elas originates from the entropy loss thatoccurs upon compression of the stabilizing ligands, which is only important atinterparticle separations in the range d 2R< l [47]:A elas ¼ 2pRk bTl 2 /qx ln x 3 x 2MW 2 2x ¼ d2Rl( " # 6 ln 3 x )þ 3ð1 xÞ2Here, q and MW 2 represent the ligand density and molecular weight. Becausethe elastic term represents the physical compression of the stabilizer, this termis repulsive at all of the solvent conditions. The dispersion stability is essentiallycontrolled by the osmotic term because it becomes effective as soon asthe ligands start to overlap, l