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Note that the concentration eventually decreases to the equilibrium bulk concentration. However, eq 3 predicts an infinite decay time when, in reality, the time is finite due to the finite dimensions of the liquid cell. That is, the assumed boundary conditions leading to eq 3 are no longer applicable once Dt is comparable to the AFM liquid cell dimensions.
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B is Boltzmann's constant. However, in small molecule systems, γ comes from the enthalpic term in the free energy associated with reduced coordination along the step edge relative to the interior of the island, which in turn comes from the strong intermolecular bonding in the condensed phase. Because colloidal condensation at a surface is driven by increasing the entropy of the solvent near the surface, this enthalpic effect is unimportant. Thus, once nucleated, clusters do not continue to grow into three dimensions and their growth rate does not increase with size as would be expected from the Gibbs-Thomson law.
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