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Configurational probabilities for symmetric dimers on a lattice: An analytical approximation with exact limits at low and high densities
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10.1063/1.2780159
/content/aip/journal/jcp/127/13/10.1063/1.2780159
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/13/10.1063/1.2780159

Figures

Image of FIG. 1.
FIG. 1.

(a) A central dimer with eight sides and two ends. (b) The end view and the side view of the site positions around a central dimer for 3D lattice. Sites labeled B are assumed to have bulk properties. (c) Positions of the neighboring dimer adjacent to the central dimer. (Note that the figure shows configurations of dimers on 3D lattice; for 2D lattice, the only change is the exclusion of configuration .)

Image of FIG. 2.
FIG. 2.

(Color online) Dependence of internal energy on at .

Image of FIG. 3.
FIG. 3.

(Color online) Dependence of on at different temperatures (from bottom to top , , , ). The solid curves represent calculated using the proposed theory, and the open circles represent calculated using Eq. (20).

Image of FIG. 4.
FIG. 4.

(Color online) Dependence of configurational probabilities on at for 3D lattice. The curves represent predictions based on the proposed theory (when and ), and the symbols represent Monte Carlo (MC) simulation results.

Image of FIG. 5.
FIG. 5.

(Color online) Dependence of configurational probabilities on at for 2D lattice. The curves represent predictions based on the proposed theory (when , , and ), the filled symbols represent MC simulation results, and the open symbols represent pocket MC simulation results.

Image of FIG. 6.
FIG. 6.

(Color online) Dependence of configurational probabilities on at for 2D lattice. The curves represent predictions based on the proposed theory (when , , and ), the filled symbols represent MC simulation results, and the open symbols represent pocket MC simulation results.

Image of FIG. 7.
FIG. 7.

(Color online) Dependence of configurational probabilities on at for the 3D case. The curves represent predictions based on the proposed theory (when , , and ), the filled symbols represent MC simulation results, and the open symbols represent pocket MC simulation results.

Image of FIG. 8.
FIG. 8.

(Color online) Dependence of configurational probabilities on at for the 3D case. The curves represent predictions based on the proposed theory (when , , and ), the filled symbols represent MC simulation results, and the open symbols represent pocket MC simulation results.

Tables

Generic image for table
Table I.

Mass balance equations for 2D square lattice.

Generic image for table
Table II.

Chemical potential balance equations for 3D cubic lattice.

Generic image for table
Table III.

Chemical potential balance equations for 2D square lattice.

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/content/aip/journal/jcp/127/13/10.1063/1.2780159
2007-10-05
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Configurational probabilities for symmetric dimers on a lattice: An analytical approximation with exact limits at low and high densities
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/13/10.1063/1.2780159
10.1063/1.2780159
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