Chapter 15
Adsorption from Supercritical Fluids 1
2
L. L. Lee and Henry D. Cochran 1
Department of Chemical Engineering and Materials Science, University of Oklahoma, 100 East Boyd Street, Norman, OK 73019 Chemical Technology Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831-6224
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2
Many important processes with supercritical (SC) fluids involve adsorption from SC fluids or desorption into SC fluids; examples include, regeneration of sorbents with SC fluids, S C fluid chromatography, and S C fluid extrac tion of hazardous chemicals from contaminated soils. In this work we ini tiate a fundamental, molecular-based study of adsorption from and desorp tion into SC fluids. Equilibrium properties and fluid structures in the vicin ity of the surface (W) are explored using integral equation theory. First, the equilibrium properties of a pure fluid A near W are studied as the fluid state approaches the critical point (CP); both attractive and repulsive A - W interactions are explored. Subsequently, the behavior of a dilute solute Β (i.e., system A+B+W) in the vicinity of W will be described under condi tions where the solvent A approaches its CP. We examine the degree of preferential adsorption of Β vis-a-vis attractive or repulsive interactions with A and W . The molecular mechanisms of SC adsorption are deter mined. The computational challenge of these calculations was considerable, and the necessarily limited range of the calculated correlation functions has resulted in useful qualitative, if not quantitative, information. Supercritical (SC) fluids are used as solvents in a number of processes in which equilibration is achieved between the SC solvent phase and a condensed phase. In some cases the condensed phase may be a solid surface upon which components may adsorb or from which components may desorb. Examples of such processes involving adsorption from a SC solution or desorption into a SC solution include regeneration of sorbents with SC fluids, SC fluid chromatography, and SC fluid extraction of hazar dous chemicals from contaminated soils. The present study was motivated by the importance of adsorption and desorption in these processes with SCfluids.The aim of this work was to improve the fundamental understanding of adsorption-desorption equilibrium between a solid surface and a SC fluid mixture. To our knowledge this problem has not been previously addressed from the perspective of molecular-based theory. Fundamental, theoretical study of adsorption has employed the techniques of density functional theory (e.g. 12), integral equation theory (e.g. 3-6), or molecular simulation (e.g. 7,8). In the present work, techniques based on integral equation
0097-6156/93/0514-0188$06.00/0 © 1993 American Chemical Society
In Supercritical Fluid Engineering Science; Kiran, E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992.
15.
LEE & COCHRAN
189
Adsorption from Supercritical Fluids
theory have been employed. In the simplest techniques for application of integral equation theory, due to Henderson, Abraham, and Barker (3), the wall(W)-particle(A) Ornstein-Zernike equation oo
oo
h w(z) = c w(z) + 2nÇ>A jdtc (t) J dssh^s) (1) — U-t\ is solved (with an appropriate closure approximation) under the approximation that hAAis) in equation 1 is taken as equal to the homogeneous total correlation function for the bulk fluid. In equation 1, h is the total pair correlation function, c is the direct correlation function, and p is the number density. The H A B integral equation approach is known (8) to produce results with important qualitative and quantitative failures. In contrast, the Henderson-Plischke-Sokolowski (HPS) approach (4,5) solves the inhomogeneous Ornstein-Zernike equation for the wall-particle system in Fourier space A
A
AW
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l}
i}
Λ(ζ ! ,z ,*) = £(z ι ,z ,*) + jdz'p(z')i(z ! ,z„k)h(z',z ,k) 2
2
(2)
2
where the Hankel transform is defined by 2
/(z ,z ,/:) = Jii r/(z ,Z2,r)exp[ikT] = 2^drr/(zi,Z2,r)/oar) 1
2
1
(3)
with an appropriate closure approximation plus one of several exact expressions for the inhomogeneous density in terms of the correlation functions. In equations 2 and 3, ζ ι is the distance from the wall of particle 1, z is the distance from the wall of parti cle 2, and r is the projection of the distance between particles 1 and 2 on a plane parallel to the wall. Compared with the H A B approach, solution of the inhomogene ous HPS equation is much more demanding computationally in terms of required memory and C P U cycles but is exact with an exact closure and is much more accurate with an approximate closure. 2
For an infinitely dilute solute Β dissolved in the solvent A , the HPS equation takes the form (A+B/W): h (2i,z ,k) AA
2
= c (z z ,k) AA
u
2
+ jdz'pAiz'WAAiz^ZtMcAAiz' ,ζ Λ) 2
(4)
and Λ^(ΖΙ,Ζ ,Λ) = 2 (Ζ ,Ζ ,Λ) + |^>Λ(Ζ )ΛΑ4(ΖΙ,Ζ/,Α:)^(Ζ ,Ζ2,/:) ,
2
λβ
1
/
2
(5)
In the present work we have applied the HPS approach to study adsorption equilibrium in systems where the fluid phase is either a pure SC fluid or a dilute solu tion of a solute in a fluid near the CP of the pure solvent. Previously this approach has not been applied to adsorption in fluid/wall systems with realistic (i.e., LennardJones) potentials when the fluid is a mixture or a near-critical S C fluid. So some development and testing of the calculational technique were prerequisite for this work. Calculation Method In numerical calculations it is often desirable to replace the function h by the continu ous indirect correlation function y=h-c; in this form equations 4 and 5 become JAA(ZUZ2^)
= \dz'p (z'yYAA(Z\*\k)C (z A
,Z ,K)
AA
2
,
^]dz p (zyc (z z\k)c (z\z ,k) A
AA
u
AA
(6)
2
and ΊΑΒ(Ζ\>Ζ2Λ) = )dz'p (z'yY (zi,z\k)c (z' ,z ,k) A
+
AA
AB
2
\dz'p (z')c (z ,z\k)c (z',Z ,k) A
AA
l
AB
2
In Supercritical Fluid Engineering Science; Kiran, E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992.
(7)
190
SUPERCRITICAL FLUID ENGINEERING SCIENCE
There are several possible choices for an exact relation between the inhomogeneous density p(z) and the correlation functions. We have chosen the one due to Wertheim (77) and to Lovett, Mou, and Buff (72). The W L M B relation is ainp(z!)
3βνν(ζ!)
dzi
dzi
+J^^-a(z ,z,,0) l"" dz'
(8)
1
For mixtures (A+B/W), W L M B assumes the form: 3lnMz.)
_
m
-
j g ^ z Q
dzi
JBglg
5
άζχ
^ , , , φ
(
9
)
1
0
)
dz
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and ^ ( z O
=
_ θ β ^ )
άζχ
~
ΘΜζΟ
5
dzi
y
(
dz
In our numerical calculations it has proven advantageous to rewrite the W L M B relation in terms of the cavity function y where g =h + 1 =ye and e = e x p H / / £ T ] so that equations 9 and 10 become —5 dzi
=y^(zi)J
