Freezing in the density functional approach: Effect of third-order contributions
1988; American Institute of Physics; Volume: 88; Issue: 11 Linguagem: Inglês
10.1063/1.454354
ISSN1520-9032
Autores Tópico(s)nanoparticles nucleation surface interactions
ResumoThe widely used Ramakrishnan–Youssouff density functional theory of freezing (a functional expansion, usually truncated at second order, of the excess Helmholtz free energy Fex of the solid about Fex of the coexisting liquid) is extended in a straightforward manner to third order to study the convergence of the theory. The required three-particle direct correlation function of the liquid c(3) is obtained by using the weighted-density functional approximation to Fex as a generating functional. A freezing transition in the hard sphere system is obtained but the predicted coexistence conditions are much worse than those of the second-order theory and in poor agreement with simulations. The magnitude of the third-order contribution to the solid grand potential is typically about one-half of the second-order contribution. Expanding about the equal density liquid rather than the coexisting liquid includes a subset of terms exactly to all orders but fails to predict freezing at either second or third order. These results indicate that the convergence of the functional expansion is not sufficiently rapid to justify truncation at low orders. The generally good agreement predicted by the usual second-order theory is thus apparently fortuitous.
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