(671a) Corresponding States Theory for Adsorption on Energetically Rough Surfaces

CORRESPONDING STATES THEORY
FOR ADSORPTION ON ENERGETICALLY ROUGH SURFACES

Kaihang Shi, Erik Santiso and Keith E. Gubbins

 Department
of Chemical& Biomolecular Engineering, North Carolina State University,

Raleigh, NC 27695, U.S.A.

 

            The Principle of Corresponding States was
first proposed by van der Waals in 1881, based on his equation of state. The
Principle made it possible to predict the vapor pressure curve, including the
critical and normal boiling points, of liquids for which no measurements exist,
based on experimental data for other liquids. It quickly found use in this way
for predicting liquid properties for hydrogen and helium, neither of which had
been liquefied at the time.  When these light gases were later liquefied the predictions
were found to be accurate.  A more powerful derivation of the Principle is
based on statistical thermodynamics, which makes clear the assumptions involved
and provides a path to improve the theory so that it is more generally
applicable.  Subsequent generalizations of the theory of corresponding states,
in particular that due to Pitzer, provide the basis for the prediction of many
physical properties of homogeneous gases and liquids, and are widely used in
process simulation. However, these correlations are not applicable to highly
inhomogeneous or nanoscale systems, such as small drops, nanoparticles,
adsorbed thin films on solid substrates, polymer brushes, etc.

 

A statistical mechanical
analysis of the properties of a highly inhomogeneous nanoscale system shows
that the equilibrium properties (adsorption isotherms, isosteric heats, phase
change conditions, etc.) are determined by a small number of dimensionless
parameters, including the dimensionless width, H*, of the nanophase and
a microscopic wetting parameter, α_w, that is defined
in terms of intermolecular forces and solid structure; α_w
is a measure of wetting that applies at all scales and for any kind of adsorbed
film (gas, liquid or solid) [1,2].

We illustrate the usefulness of this approach using
examples drawn from both experimental and molecular simulation studies of
gas-liquid and liquid-solid phase separations [3,4], and pressure enhancement
in nanopores [5-7], with emphasis on simple pore geometries. These examples
illustrate the central role played by wetting, and also the breakdown of some concepts
and macroscopic laws, such as the equations of Kelvin, Laplace and
Gibbs-Thomson, for nano-phases confined within small pores. They also suggest
consistency tests for experimental data that should be applied in the event of
capillary condensation or other phase changes in mesoporous materials.

The approach can be extended to account for geometric
or energetic wall roughness [8], and to adsorbate molecules that interact with
site-site potentials having both Lennard-Jones and point charge sites.

Finally, we describe an application of corresponding
states theory (called conformal sites theory) to describe adsorption on
solid surfaces that are energetically heterogeneous, i.e. have a variety of
adsorption sites. The basic assumption in this theory is that all of the
intermolecular interactions between adsorption sites on the surface and molecules
in the adsorbed film conform to the same functional form, which includes
dispersion, overlap and Coulomb interactions.  The theory maps the
heterogeneous surface onto a homogeneous one, in which all adsorption sites
have the same energy. Through comparisons with molecular simulations for both
the heterogeneous surface and the homogeneous reference surface, we show that
the theory is accurate even when there is a large difference in energy between
the various surface sites.

 

 

 

Figure 1.  Experimental results
for the effect of confinement in cylindrical pores on the melting point of
various adsorbates.  Here CNT = carbon nanotube and α_w
is the microscopic wetting parameter; high values of α_w
indicate strong wetting.  For large pore widths the temperature shift is
approximately linear, as required by the Gibbs-Thomson equation, but departures
occur for smaller widths.

1.      
R
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Diagrams for Freezing in Porous Media”, Journal of Chemical Physics, 116,
1147-1155 (2002).

2.      
Keith E.
Gubbins, Yun Long and Malgorzata Sliwinska-Bartkowiak, “Thermodynamics of
Confined Nano-Phases”, Journal of Chemical Thermodynamics, 74,
169-183 (2014).

3.      
L.D. Gelb,
K.E. Gubbins, R. Radhakrishnan and M. Sliwinska-Bartkowiak, “Phase Separation
in Confined Systems”, Reports on Progress in Physics, 62,
1573-1659 (1999).

4.      
C.
Alba-Simionesco, B. Coasne, G. Dosseh, G. Dudziak, K.E. Gubbins, R.
Radhakrishnan and M. Śliwinska-Bartkowiak, “Effects of Confinement on
Freezing and Melting”, Journal of Physics: Condensed Matter, 18,
R15-R68 (2006).

5.      
Yun Long, Jeremy C. Palmer, Benoit
Coasne,  Małgorzata Śliwinska-Bartkowiak and Keith E. Gubbins,
“Pressure enhancement in carbon nanopores: A major confinement effect”, Physical
Chemistry Chemical Physics, 13, 17163-17170 (2011).

6.      
H. Drozdowski, M. Kempinski, M.
Śliwinska-Bartkowiak, M. Jazdzewska, Y. Long, J.C. Palmer and K.E.
Gubbins, „Structural Analysis of the Behavior of Water Adsorbed in Activated
Carbon Fibers”, Physical Chemistry Chemical Physics, 14,
7145-7153 (2012).

7.      
Yun Long,
Jeremy C. Palmer, Benoit Coasne, Małgorzata Śliwinska-Bartkowiak,
George Jackson, Erich A. Müller and Keith E. Gubbins, “On the Molecular Origin
of High Pressure Effects in Nanoconfinement: Effects of Surface Chemistry and
Roughness”, Journal of Chemical Physics, 139, 144701 (2013).

8.      
M.
Śliwinska-Bartkowiak, A. Sterczyńska, Y. Long and K.E. Gubbins,
“Influence of Microroughness on the Wetting Properties of Nano-Porous Silica
Matrices”, Molecular Physics, 112, 2365-2371 (2014).