Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chemical potential of a test hard sphere of variable size in hard-sphere
  fluid mixtures   A detailed comparison between the Boubl\'ik-Mansoori-Carnahan-Starling-Leland
(BMCSL)equation of state of hard-sphere mixtures is made with Molecular
Dynamics (MD) simulations of the same compositions. The Lab\'ik and Smith
simulation technique [S. Lab\'ik and W. R. Smith, Mol. Simul. \textbf{12},
23-31 (1994)] was used to implement the Widom particle insertion method to
calculate the excess chemical potential, $\beta \mu_0^\text{ex}$, of a test
particle of variable diameter, $\sigma_0$, immersed in a hard-sphere fluid
mixture with different compositions and values of the packing fraction, $\eta$.
Use is made of the fact that the only polynomial representation of $\beta
\mu_0^\text{ex}$ which is consistent with the limits $\sigma_0\to 0$ and
$\sigma_0\to\infty$ has to be of the cubic form, i.e.,
$c_0(\eta)+\overline{c}_1(\eta)\sigma_0/M_{1}+\overline{c}_2(\eta)(\sigma_0/M_{1})^2+\overline{c}_3(\eta)(\sigma_0/M_{1})^3$,
where $M_{1}$ is the first moment of the distribution. The first two
coefficients, $c_0(\eta)$ and $\overline{c}_1(\eta)$, are known analytically,
while $\overline{c}_2(\eta)$ and $\overline{c}_3(\eta)$ were obtained by
fitting the MD data to this expression. This in turn provides a method to
determine the excess free energy per particle, $\beta a^\text{ex}$, in terms of
$\overline{c}_2$, $\overline{c}_3$, and the compressibility factor, $Z$. Very
good agreement between the BMCSL formulas and the MD data is found for $\beta
\mu^\text{ex}_0$, $Z$, and $\beta a^\text{ex}$ for binary mixtures and
continuous particle size distributions with the top-hat analytic form. However,
the BMCSL theory typically slightly underestimates the simulation values,
especially for $Z$, differences which the Boubl\'ik-Carnahan-Starling-Kolafa
formulas and an interpolation between two Percus-Yevick routes capture well in
different ranges of the system parameter space.

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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
2
The categories of this paper are: math
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph