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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
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Affiliations:
1 Department of Chemical and Biomolecular Engineering, The Johns Hopkins University, Baltimore, Maryland 21218, USA
a) Electronic mail: yimingchen@jhu.edu
b) Author to whom correspondence should be addressed.
J. Chem. Phys. 127, 134903 (2007)
/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

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 .)

FIG. 2.

(Color online) Dependence of internal energy on at .

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).

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.

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.

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.

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.

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

Table I.

Mass balance equations for 2D square lattice.

Table II.

Chemical potential balance equations for 3D cubic lattice.

Table III.

Chemical potential balance equations for 2D square lattice.

/content/aip/journal/jcp/127/13/10.1063/1.2780159
2007-10-05
2014-04-18

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