Research Article
The Intramolecular Pressure and the Extension of the Critical
Point’s Influence Zone on the Order Parameter
Jose Luis Rivera, Homero Nicanor-Guzman, and Roberto Guerra-Gonzalez
Facultad de Ingenier´ ıa Qu´ ımica, Universidad Michoacana de San Nicol´ as de Hidalgo, 58000 Morelia, MICH, Mexico
Correspondence should be addressed to Jose Luis Rivera; rivera jose l@yahoo.com
Received 20 April 2015; Revised 23 July 2015; Accepted 26 July 2015
Academic Editor: Sergei Sergeenkov
Copyright © 2015 Jose Luis Rivera et al. his is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
he critical point afects the coexistence behavior of the vapor-liquid equilibrium densities. he length of the critical inluence zone
is under debate because for some properties, like shear viscosity, the extension is only a few degrees, while for others, such as the
density order parameter, the critical inluence zone covers up to hundreds of degrees below the critical temperature. Here we show
that, for ethane, the experimental critical inluence zone covers a wide zone of tens of degrees (below the critical temperature)
down to a transition temperature, at which the apparent critical inluence zone vanishes, and the transition temperature can be
predicted through a pressure analysis of the coexisting bulk liquid phase, using a simple molecular potential. he liquid phases
within the apparent critical inluence zone show low densities, making them behave internally like their corresponding vapor
phases. herefore, Molecular Dynamics simulations reveal that the experimentally observed wide extension of the critical inluence
zone is the result of a vapor-like efect due to low bulk liquid phase densities.
1. Introduction
Vapor-liquid equilibrium (VLE) for pure components is
present between the triple and critical points; from a tran-
sition temperature between these two points (closer to the
critical point) up to the critical point (critical inluence
zone), equilibrium liquid phases start to behave more like
their corresponding vapor phases [1], characterized by larger
density changes than those close to the triple point for the
same temperature changes. In the critical inluence zone
(CIZ), the coexisting vapor and liquid densities approach
asymptotically, indicating a strong inluence of the critical
behavior on the coexisting densities, and the universal power
law describes their diference:
Δ =
0
, (1)
where Δ =
−
V
is the order parameter of phase transition,
and
V
represent the liquid and vapor coexisting densities,
respectively, = (
− )/
,
is the critical temperature,
is a universal critical exponent, and
0
is a constant
dependent on the luid. Below the transition temperature
(down to the triple point), Δ deviates from the universal
power law, and the correct value of Δ can be calculated by
the introduction of nonasymptotic corrections [2, 3]. Water
order parameters (experimental) in the CIZ show a linear
behavior and follow (1) down to ∼130
∘
below
(transition
temperature). In comparison, a pure Lennard-Jones luid in
the CIZ follows the universal power law for almost all its
coexistence region [4]. he wide inluence zone in the order
parameter is unexpected, since the critical inluence on other
properties (shear viscosity) only covers a few degrees below
[4, 5], and a diferent phenomenon (other than the critical
point inluence) is afecting the length of the apparent CIZ.
Clearly, the main diference between the Lennard-Jones luid
and water is the nature and length of the intermolecular
interactions present in the water molecule, but, in this study,
we study a second diference between these two systems,
which is the presence of intramolecular interactions in the
water molecule, not present in the Lennard-Jones luid, but
the study based on intramolecular forces is not completely
independent of a study based on intermolecular forces.
Intra- and intermolecular (pair efective) forces are not
completely independent in equilibrium liquid phases; for
a speciic luid, its liquid phases in equilibrium close to
the triple point will have in average more compressed
molecules (higher compressive intramolecular forces) than
Hindawi Publishing Corporation
Advances in Condensed Matter Physics
Volume 2015, Article ID 258601, 8 pages
http://dx.doi.org/10.1155/2015/258601