Theoretical Study of Adsorption on Activated Carbon

from Supercritical Fluid by SLD-ESD Approach

Xiaoning Yang, Carl T. Lira* Department of Chemical Engineering,

Michigan State University East Lansing, MI 48824

Tel: 517-355-9731 Fax: 517-432-1105

Email: Lira@egr.msu.edu

Abstract: In this paper, the simplified local density (SLD) theory is combined with the

ESD equation of state to study the adsorption of solutes from supercritical carbon dioxide

onto activated carbon. Firstly the model was applied to fit the adsorption of toluene+CO2

and benzene+CO2 by using only two temperature-independent parameters. It was shown

that this theoretical model is capable of describing the adsorption behavior for toluene

and benzene on activated carbon from supercritical carbon dioxide over wide temperature

and pressure ranges. Secondly we present a systematic theory analysis of adsorption

characteristics for finite and infinite dilution conditions in supercritical fluid by selecting

the toluene/CO2 as a model system. The characteristics of the competition adsorption on

adsorbent between solvent and solute were investigated. The effect of temperature,

pressure, bulk solute concentration, and the adsorbent structure size on the adsorption

behavior has been presented.

Key words: supercritical fluid, adsorption, SLD model, ESD equation of state

* To whom correspondence should be addressed.

2

Introduction:

The supercritical carbon dioxide processes in conjunction with solid media or

materials have increased attention in recent years due to the unique solvent characteristics

1. These processes involve solute extraction from solid matrices 2,3, solid adsorbent

regeneration and decontamination 4,5, and supercritical fluid chromatography 6,7, etc. To

develop and design these processes, it is very important to study and understand the

adsorption equilibrium between the solid and fluid phase. The adsorption isotherm for

solutes in the supercritical fluid determines the thermodynamic partitioning between

phases. Presently, although some experimental adsorption isotherm data can be found in

relevant supercritical literatures, the experimental data for solute adsorption equilibrium

from supercritical CO2 onto solid media is still very scarce. For adsorption in

supercritical fluids, not only the solute concentration, but also the system pressure and

temperature influence the adsorbent loading. The adsorbed phase often involves a non-

ideal fluid solution interacting with a highly complex solid surface 8,9. These phenomena

will increase the complexity in the study of supercritical fluid adsorption. Experimental

determination of adsorption isotherms for solutes in supercritical fluids is usually very

tedious, time consuming and challenging. So a thermodynamic model that has a

reasonable physical insight and theoretical basis and is capable of describing the

experimental data and explaining the adsorption mechanism, is highly attractive and

significant.

Usually the solute adsorption in supercritical fluids can be fitted by the common

empirical adsorption model, such as the Langmuir, the Freundlich and the Toth model

equations etc. In these models, the empirical parameters will vary as a function of

3

temperature. This shortcoming limits their wide applicability. Wu et al.10 present a

phenomenological thermodynamic model for the adsorption of toluene on activated

carbon form supercritical CO2. The P-R equation of state and the real adsorption solution

theory are applied to the bulk and adsorbed phase, respectively. However, in their model,

all parameters are temperature dependent and in each temperature dependence there are 8

parameters required in order to correlate the adsorption isotherm. Akman and Sunol 11

use the Toth isotherm and the P-R equation of state to model the phenol adsorption on

activated carbon. In their model they need the adsorption isotherm of phenol onto

activated carbon in aqueous solution as input data. Afrane and Chimowitz 12 develop a

statistical mechanical model that applies the lattice-solution model to represent the

adsorbed phase. With the additionally known information on heats of adsorption of

supercritical fluids on adsorbent, they use this model to correlate the solute distribution

coefficients in supercritical fluids between adsorbed and bulk phase at infinite dilution.

However, this model is incapable of representing the adsorption isotherm at finite dilute

conditions in supercritical fluids.

Most these models above, except the one by Wu et al.10, don't consider the solvent

competition effect on adsorption, which may play a very important role in adsorptive

processes 9. Also they don't reflect the effect of adsorbent structure on the adsorption

loading. Over the past decades, there has been rapid development in the application of

molecular simulation and density functional theory for the study of adsorption13. These

theoretical approaches consider the adsorbent structure, but are computationally intensive

for practical application in the present stage, especially for supercritical fluid adsorption.

Recently, a complete theoretical analysis has been conducted using Monte Carlo

4

simulation methods to study the adsorption characteristics of benzene onto activated

carbon in supercritical carbon dioxide 14. However, the molecular simulation results are

not compared with the experimental data.

Practical process design often require rapid methods for obtaining good

correlation and approximation of adsorption behavior over a wide range of pressures and

temperatures. Also the methods should have a clear physical insight for adsorption

phenomena with parameters as few as possible. The simplified local density (SLD)

approach 15,16 is a method that can be used with any equation of state and can offer some

predictive capability with only two temperature-independent adjustable parameters for

adsorption modeling of pure fluids in slit-shaped pores. Recently the SLD theoretical

approach was used to successfully model a variant of fluid adsorption17 by incorporating

with the Elliott, Suresh, Donohue (ESD) equation of state 18. This paper focuses on the

SLD approach with the ESD equation to study the adsorption of solutes onto activated

carbon from supercritical carbon dioxide. Toluene is selected as a model solute in this

study. The adsorption characteristics of toluene are investigated both at infinite dilution

and finite concentrations.

5

Theoretical Model:

The ESD equation of state proposed by Elliott et al. 18 is

4 9.51

1 1.9 1 1.7745c qYPV

RT Yη η

η η= + −

− + (1)

where V is the molar volume, T is temperature, and R is the ideal gas constant. η is the

reduced density (η=bρ). i ii

b x b= ∑ , xi is the fluid mole fraction and bi is the

component’s size parameter. c is a shape factor for the repulsive term ( i ii

c x c= ∑ ). q is a

shape factor for the attractive term ( 1 1.90467( 1) i ii

q c x q= + − = ∑ ). ρ is the molar

density, and

( )i i iji j

c x x cbη ρ= ∑ ∑ (2a)

( )i j ij iji j

qY qYb x x cq Yη ρ ρ= = ∑∑ (2b)

i ii

q YY Yb

x qη

η ρ= =∑

(2c)

1 1( ), ( )

2 2ijij i j j i i j j ibq b q b q cb c b c b= + = + (2d)

Yij is a temperature-dependent attractive energy parameter ( exp( / ) 1.0617ij ijY kTε= − ).

(1 ) ii jjij ijkε ε ε= − is the parameter for dispersion forces and kij is the binary

interaction coefficient. The equation can also be represented in terms of fugacity. Details

of the explanation for the equation and parameters are in the references 18,19 cited above.

Although the ESD equation also can represent associating fluids, none of the components

6

presented in this paper have associative characteristics, so the associating term is omitted

from this paper.

The SLD approach has been described in detail in the previous papers 15-17. Here we

just extend this theory to binary mixture. In the following section we use component A to

represent solute and component B for solvent. For the slit-shape pore system in the

modeling, the fluid-solid interaction potential with one wall for one component I (I=A,B)

is represented by 10-4 potential 20 :

( )410 42

1

4 4 4

0.2 0.5 0.5

( ) 4 0.5 0.5 0.5( 2 ) ( 3 ) ( 4 )

I atoms fsI fsI

EtaI EtaI EtaI Iz

EtaI I EtaI I EtaI I

απρ σ ε

α α α

− − +Ψ =

− − − + + +

(3)

where αI =3.35/σfsI (I=A, B). σfsI (Å) is the average value of the fluid molecule I and

solid molecular diameters [σfsI = ( σffI + σss) / 2]. EtaI=(z+0.5 σss)/ σfsI is the

dimensionless distance from the carbon centers in the first plane, and z is the particle

position in the slit relative to the carbon surface, as seen in the schematic diagram of the

pore model in Fig 1, where H is the slitwidth. ρatoms represents the number of carbon-

plane atoms per square Angstrom 20 (0.382 atoms/Å2). The fluid-solid potential in

relation to the second wall, Ψ2I(z) can be calculated by replacing EtaI in eq 3 with XiI,

which is the distance from the second wall divided by the fluid-solid diameter. The total

fluid-solid potential for component I is expressed as

1 2[ ] [ ] [ ]TI I Iz z zψ ψ ψ= + (4)

The chemical potential of fluid inside a porous medium can be described by two

contributions, that is, fluid-fluid contribution and fluid-solid contribution. At adsorption

7

equilibrium, the chemical potential in pore is equal to that in the bulk phase. For

component I in slit pore, we have,

, , ,[ , , ] [ , ( ), ( )] [ ]bulk I bulk I ff I I fs IT y T z x z zµ ρ µ ρ µ= + (5)

,0,

[ , ( ), ( )][ , ( ), ] [ ] ln

[ ]o ff I I

ff I I II

f T z x zT z x T RT

f Tρ

µ ρ µ = +

(6)

,0,

[ , , ( )][ , , ] [ ] ln

[ ]o bulk I bulk I

bulk I bulk I II

f T y zT y T RT

f Tρ

µ ρ µ = +

(7)

In these equations µbulk,I is the bulk chemical potential of component I at bulk

composition yI, µff,I is the fluid-fluid contribution to the chemical potential of component

I. 0

If and 0

Iµ are the standard state fugacity and chemical potential respectively, and µfs,I

is the fluid-solid contribution to the chemical potential ( , [ ]fs I A TIN zµ ψ= ), where NA is

Avogadro's number. The local chemical potential due to fluid-fluid interactions is

designated by µff,,I and dependent on T and local density ρ(z) and local composition xI(z).

Note that µff,I, µfs,I and fff,I are functions of z (position), but µbulk,I, 0

Iµ and 0

If are not.

Based on the above equations, an expression for fff,I can be derived,

, ,

( )[ , ( ), ( )] [ , , ] exp TIff I I bulk I bulk I

zf T z x z f T ykT

ρ ρ −Ψ = (8)

The fugacity of bulk fluid can be obtained through the ESD equation of state 18. Since

fbulk,I is independent of position in the pore and ψTI is dependent on position only, the

local fugacity fff,I can be calculated from eq (8). For a binary mixture, three equations will

be solved simultaneously for local composition (xA(z) and xB(z))and local density ρ(z).

8

, ,

( )[ , ( ), ( )] [ , , ] exp TAff A A bulk A bulk A

zf T z x z f T ykT

ρ ρ Ψ = − (9)

, ,

( )[ , ( ), ( )] [ , , ] exp TBff B B bulk B bulk A

zf T z x z f T ykT

ρ ρ −Ψ = (10)

( ) ( ) 1A Bx z x z+ = (11)

Within the slit pore, the local fugacity, ,ff If , can be calculated through the following

equation 17,18,

,

4 ( )4ln( ) ln[1 1.9 ( )]

1.9 1 1.9 ( )

ln(1 1.7745 ( ) ( ) ( )9.5 ( )

1.7745 ( ) ( )

9.5 ( ) ( ) ln[ ( ) ]

( ) 1 1.7745 ( ) ( )

Iff I I

j Ij I j j I II Ij

II II

cb zf c z

z

Y z z qY z bx Y b q b q Y b

Y z b Y z b

qY z b Y b zx z RT

Y z b Y z z

ρη

η

η

ρρ

η

= − − +−

+− + − ⋅

− ++

∑ (12)

where Y(z), ρ(z), and η(z)(=bρ(z)) are the local variables within the silt pore. The

position dependence of attractive energy parameter Yij has been given elsewhere 17. The

cross parameter εij used to calculate Yij uses the same Kij as the bulk phase.

The local density and local composition can be obtained by solving the above

equations. Thus, total adsorption per unit weight adsorbent is calculated by the following

expression.

0[ ( ) ( )]

2

z at far walltotal

AAz

Arean z x z dzρ

== ⋅∫ (13)

0[ ( ) ( )]

2

z at far walltotal

BBz

Arean z x z dzρ

== ⋅∫ (14)

9

where Area is the surface area per unit weight of the adsorbent. In the case of adsorption

in a slit with homogeneous parallel walls, the integration over the entire slit width is

divided by two since two walls contribute to the surface area of a slit.

In this study, the value of Area was taken as input data from the original publication

of the experimental data. Table 1 lists the pure component ESD parameters19 used in this

model, all of which are obtained from bulk fluid properties and were not adjusted

parameters in this study. The binary interaction coefficients for the mixtures were

obtained by fitting their VLE data 21,22 using the ESD equation of state, and they are also

given in Table 1. The values of σff for benzene and carbon dioxide are tabulated Lennard-

Jones diameters of each fluid,23 and σss = 3.4 Angstroms is the reported diameter of

carbon 20. For toluene the Lennard-Jones parameters are approximated by the critical

volume 23 1/ 3

22

( ) i i

CO CO

VcVc

σσ

= and crtical temperature 24 0.77 LJ

cTkε = .

In the calculation of adsorption loading for a binary mixture, usually three

adjustable temperature-independent parameters are needed, εfsI/k, the fluid-solid

interaction potential in Kelvin for each component I (I=A, B), and H (slit width in

angstroms). However, the fluid-solid interaction parameter for CO2 can be determined to

fit the adsorption of pure CO2 on activated carbon. In the previous work17, this parameter

is obtained from the CO2 adsorption data with εfs,CO2/k=105 K. So in this study, only two

temperature-independent parameters, the solute interaction parameter and slit-width, were

applied to represent the adsorption isotherms for binary systems. The parameter H

determines the upper limit of eqs (13) and (14).

10

Results and Discussions

Experimental data modeling

The model presented here was used to fit the adsorption data of toluene onto

activated carbon (Degussa, WSIV)25. Figure 2 shows the comparison of the

representation of model with the experimental results at three pressures in temperature

range 308 K-328 K. The model parameters were given in Table 2. As seen in Figure 2,

the model fitting is good with an average relatively deviation of 5.5%. The specific

surface area for this activated carbon is 1300m2/g as given in this reference 25. The model

does a good job of representing the temperature and pressure dependence of isotherms

with temperature-independent parameters. The temperature effect on the adsorption

isotherm is shown in Figure 3 at a fixed density. The temperature effect is small for such

temperature and density conditions, so the density is the main property influencing the

toluene adsorption loading from supercritical CO2. This phenomenon is widely known for

most solutes adsorbing from supercritical fluids 7,26.

The parameter values from the fitted results are reasonable. The interaction energy

parameter for toluene is larger than that for CO2. This is consistent with the fact that the

toluene is a more polarizable molecule and has more affinity for activated than carbon

dioxide. In previous work17, the SLD-ESD model was used to correlate the adsorption of

a series of pure components on activated carbon. That study17 showed that there is an

approximate correlation between the pure fluid Lennard-Jones parameters (εLJ/k) and the

fluid-solid interaction energy parameters (εfs/k). A rough linear relation exists as seen in

Figure 4. The interaction energy parameter for toluene in this study is reasonably located

in this line as seen in Figure 4. In Figure 4, the dashed line represents the result based on

11

the Lorentz-Berthelot (L-B) combination rule 20, which is usually lower than the fitted

values.

In order to further test this model, the adsorption of benzene27 on a different kind

activated carbon (Calgon BPL) from fluid carbon dioxide was also fitted using this model

proposed in this work. Figure 5 shows the comparison of experimental data and model

correlation at different conditions. Except under lower pressure, a good agreement is

obtained between experiment point and model value for adsorption isotherms. The

parameters for benzene/CO2 system are also given and shown in Table 2 and Figure 4,

respectively, which again confirms their reasonability and consistency. It should be

pointed out that while the ESD equation of state is developed to consider shape, the

current SLD approximation in this work uses the same shape factor in the adsorbed phase

as the bulk fluid phase. Also it assumes that the fluid-fluid interactions are spherically

symmetric in the derivation of the position dependence of the energy interaction

parameters17. This approximation may not be good near the surface of the wall for

complex molecules. An improved method to incorporate shape into the SLD near the wall

may further improve temperature dependence of adsorption modeling.

Competition adsorption characteristics

Previously it has been believed that the adsorption of carbon dioxide fluid could be

neglected and its function is mostly as continuum. Solute adsorption was thought as just

simply partitioning between solid surface and bulk fluid phases. Now it is now being

recognized that the adsorption of supercritical fluid, which plays an important role in the

solute adsorption separation processes9, might not be ignored. King (1987) 28

characterized the retention volumes of several solutes in chromatographic adsorption

12

column, alumina and resin, from supercritical fluid. According his qualitative analysis,

adsorption of supercritical fluid upon the adsorbent surface can affect the solute

adsorption/desorption through competitive adsorption. In order to understand the

adsorption mechanism of in a supercritical fluid mixture, it is very important to obtain the

information on solvent adsorption.

According to this proposed model here, the total adsorption loading of both solute

and solvent can be evaluated simultaneously. Thus, the competition adsorption can be

investigated thoroughly. Figure 6 shows the competition adsorption between toluene and

carbon dioxide against the pressure and density, and the results were calculated at 308 K

and 318 K from our SLD-ESD model when the mole fraction of toluene is 0.0002. Figure

7 gives the similar results only for toluene mole fraction equal to 0.005. As seen in Figure

6 and Figure 7, as pressure increases, the adsorption loading of toluene decreases while it

increases for carbon dioxide. This phenomenon is partly due to the fact that solvating

power of supercritical fluid is enhanced with increasing pressure. The solvating power of

supercritical fluid can be reflected by the variation of fugacity with pressure. The bulk

fugacity of toluene and CO2 were also given in Figure 6 (a) as a function of pressure. The

variation of the toluene fugacity with pressure shows a similar variation with the

corresponding adsorption loading. The fugacity behavior of CO2 determines its

adsorption increasing with pressure, which competes with toluene adsorption.

There are maxima in the solute adsorption loading far below the critical pressure

of carbon dioxide, which is consistent with the calculated result of molecular simulation

by Nitta and Shigeta 14. Also Shojibara et al 27 study the benzene adsorption upon

activated carbon from carbon dioxide, and show a maximum of adsorbed amount at a

13

pressure far below the critical pressure of carbon dioxide. It is also noted that the fugacity

of toluene shows a maximum value, which is similar with its adsorption behavior.

However, the pressure in maximum fugacity (around 3 MPa) is different from the

pressure in maximum toluene adsorption (below 1 MPa). According to the work of Nitta

and Shigeta14, the difference in pressures for maximum adsorption loading and maximum

fugacity is ascribed to the combination effects from the solvating power of supercritical

fluid and adsorption competition of solute and solvent 14. The theoretical computation

from the SLD model here confirms the important factors.

Comparing Figure 6 and Figure 7, it can be found that with an increase of toluene

mole faction the adsorption of toluene increases and the adsorption of carbon dioxide

decreases. This is reasonable since the adsorption is competitive and the adsorption

capacity of the adsorbent is limited. The influence that solvent competes in adsorption is

also experimentally confirmed by Subra et al. 29. In their work, the adsorption isotherms

of terpene mixtures on silica gel were measured in supercritical carbon dioxide. They also

measured the adsorption capacity of CO2 for several mixtures and showed that solvent

did indeed compete for adsorption. Further, if we assume that the solute adsorption might

be considered approximately as mono-layer coverage, the theoretical capacity can be

compared with the experimental work. For a toluene molecule, its adsorption area is

about 20 Å2 based on its diameter. With 1300m2/g in specific surface area for this

activated carbon, this yields a rough adsorption capacity of 10 mmol/g, which is far

above the measured equilibrium adsorption capacity for toluene (2~4 mmol/g). This

analysis, though very simple and approximate, indeed shows that there is a possibility for

solvent to be adsorbed.

14

A crossover phenomenon for total adsorption of toluene can be observed

around the pressure region around 6 MPa in Figures 6(a) and 7(a). The pressure in the

crossover region generally occurs at relatively higher pressure as bulk solute

concentration increases as shown in Figure 7(a). The crossover phenomenon is not new

and it can be explained by the combination effects of temperature and solvent density as

was observed for solute solubility in supercritical fluid 30. According to our calculation,

the CO2 total adsorption, however, does not show significant crossover behavior below

15 MPa, though the excess adsorption (not shown) for solvent does.

Figure 6(b) and Figure 7(b) give the adsorption amounts for the two substances

versus the fluid density. For our calculations where the solute mole fraction is 0.0002, the

two adsorption curves at the two temperatures did not cross each other in Figure 6 (b),

though they are almost undistinguishable at a fixed density (weak temperature

dependence). However at higher mole fraction, 0.005 in Figure 7 (b), the crossover

behavior is observed. For example, in the region around the critical density of CO2, the

higher the temperature, the larger the adsorption loading for toluene, while vice versa for

carbon dioxide. This phenomenon is hard to explain. It may also be explained as the local

density enhancement near critical point. Near critical point, usually there exists a local

density enhancement around the solute molecules, which has been thoroughly

investigated by different researchers 31,32. At higher solute concentration and 308 K, the

solvent density enhancement around the solute near critical point in the adsorbed phase

will lead to an increase in the solvent adsorption to a certain extent. This will cause that

the solvent adsorption at 308 K becomes relatively larger than that at 318 K. Conversely,

the strong adsorption competition will lead to a lower adsorption for toluene at 308 K.

15

However, this behavior is not obviously observed at lower solute concentration (0.0002)

as seen in Figure 6 (b). Further accurate experimental measurement and theoretical

analysis are necessary to explore this region.

The adsorption modeling may assist to define the optimal and efficient working

pressure in regeneration and decontamination of solid medium. From the above results

(Figure 6 and Figure 7), at very higher pressure, the adsorption amounts for toluene and

carbon dioxide are relatively pressure insensitive above 12 MPa. Although it has been

believed that increasing the fluid pressure will be benefit to desorption, it is not possible

to improve effectively the regeneration efficiency beyond certain value of pressure,

which has been pointed out by King 29. This theoretical calculation clearly confirms this

behavior. So for the toluene/CO2 system, the maximum pressure for the adsorbent

regeneration should be controlled around 10-12 MPa.

Effect of slit-width

In order to investigate the effect of slit-width on adsorption loading, the mean

density for component I (I=A, B) within slit-pore is given according to

,0

1[ ( ) ( )]

( )

z at far wall

II avezss

z x z dzH

ρ ρσ =

= ⋅− ∫ (14)

Figure 8 gives the mean density against the slit-width by this model. The calculated

conditions were carried out when toluene mole fraction is 0.001 for the pressure 7.7 MPa

and 15.0 MPa at 318 K. As seen in Figure 8, for slits above10Å the average density of

toluene decreases with the silt-width increasing while the average density for carbon

dioxide increases. The average density levels off as the slid-width reaches large values.

This is consistent with the weak interaction potential between the solid surface and

adsorbate molecules at large slit-width. In Figure 8, there is an oscillation of the toluene

16

adsorption density with the slit-pore width. This suggests that solute molecules may

adsorb with a highest density at a certain slit-width. This maximum solute density in our

study is similar with the work by Heuchel et al. (1999) 33, who use the molecular

simulation to study the gas adsorption in the slit-pore. So there must be an optimal pore

size associated with the maximum solute adsorption capacity. The optimal pore size in

our system is about 12-14 Å. According to the calculated results the effect of pressure on

the adsorption density for the solute and solvent shows a reasonable variation, that is, a

higher pressure causes lower solute adsorption and higher solvent adsorption.

Solute adsorption constant at infinite dilution

In supercritical fluid adsorption processes, for very dilute solutions the adsorption

isotherms show linearly. The adsorption loading of dilute solute is proportional to the

solute concentration in bulk phase. Usually the proportionality constant is defined as the

adsorption constant K as following

0limy

qK

C→= (15)

where q is the solute adsorption loading in mmol/g, and C is the solute concentration of

bulk phase in mmol/cm3, and y is the bulk solute mole fraction. The adsorption

equilibrium constant not only determines the separation extent, but also represents the

interaction between solute and the solid surface, so the knowledge of the adsorption

equilibrium constant is a key factor in designing the separation process. At present much

research work has focused on the determination of K by using the pulse chromatographic

technique, and the dependence of K on temperature and pressure has often been obtained

experimentally7,26. Also some interesting characteristics have been observed for

adsorption equilibrium constant. In this section, this proposed model was applied to

17

describe the adsorption equilibrium constant. We still used the toluene/ CO2 as the model

system with the same model fitted parameters as in the previous section. The effect of

temperature and pressure on the adsorption equilibrium constant was investigated.

For finite concentration, q/c varies with the solute concentration in bulk phase, so

it is essential to know how small the solute mole fraction (y) must be in order for q/c to

reach the limiting value. In adsorbed phase the solute mole fraction is usually much

higher in bulk phase. Figure 9 shows a typical result for the variation of q/c with the

solute mole fraction. The plotted values are determined by q/c at each bulk concentration.

As y approaches very small, the value of q/c becomes constant, which means that reaches

the infinite dilution limit. According our calculated results it is enough to reach infinite

dilution condition when the toluene mole fraction is 10-5. So in the next calculation, we

use 10-5 as the input solute mole fraction to calculate the adsorption equilibrium constant.

Density and pressure effect:

Figure 10(a) gives the variation of adsorption constant (ln(K)) with the pressure at

three difference temperatures. The adsorption constant increases with an increase in

temperature and a decrease in pressure. The density dependence of adsorption constant is

given in Figure 10(b). Increasing the fluid density will lead to a reduction of the

adsorption constant. At fixed density the effect of temperature on the adsorption

equilibrium constant is weak. The dependence of the adsorption constant on temperature

and pressure is consistent with the experimental results in literature 6,27.

Temperature effect:

Figure 11 shows the variation of the adsorption constant vs. temperature at two

pressures, 7.7 MPa and 15.0 MPa. The curves display pronounced maxima. At 7.7 MPa,

18

the adsorption constant has a maximum point at 353 K, while at 15.0 MPa., the

adsorption constant has a maximum point at 410 K. Beyond the maximum adsorption

point, the adsorption constant decreases with temperature increasing. This interesting

feature from our model reflects the effect of near-critical condition in supercritical fluid

and is identical to the experimental determination from literature. For example, Kelley

and Chimowitz 34 report the chromatographic capacity factor, which is related to the

adsorption equilibrium constant, for various solutes onto two different solid adsorbents,

octadecyl silica (ODS) and alumnia (Alox-T) from supercritical carbon dioxide.

According their results, at 9.1 MPa the capacity factor shows a maximum value at around

345-390 K and at 13.5 MPa the maximum point is at about 380 K. Similar results are

also reported by Shim and Johnston35 for the adsorption equilibrium constant of

naphthalene and phenanthrene between C18-bonded silica and supercritical carbon

dioxide. They obtained the maximum temperature of 350 K at 100 bar. This maximum

phenomenon of adsorption equilibrium constant with temperature at constant pressure has

been explained as the effect of the diverging nature of solute partial molar enthalpies in

this regime34,35. To clarify the mechanism of the maximum adsorption constant, the

variation of the absolute adsorption loading of toluene and carbon dioxide on activated

carbon with temperature were calculated at fixed pressures with the bulk toluene mole

fraction being 0.0002. The results and conditions are shown in Figure 12. The toluene

adsorption loading also displays a maximum point that is similar to the maximum

behavior of its adsorption constant at infinite dilution. On the other hand the

corresponding adsorption loading of carbon dioxide only shows a monotonic reduction

with temperature. It means that the carbon dioxide adsorption gives a weak competition

19

for adsorption at higher temperature. The density effect will become weak beyond the

temperature point corresponding to the maximum adsorption loading of solute.

The calculation for the adsorption constant at infinite dilution verifies again

that the theoretical model can describe the practical characteristics for adsorption in

supercritical fluids. Actually, the determination of adsorption equilibrium constant at

dilute condition is simple as compared with the adsorption equilibrium isotherms at finite

concentration. If this SLD-ESD model can be applied to the adsorption constant so that

its model parameters for the system studied can be obtained, then, the adsorption

isotherms for finite concentrations can be predicted. This will be very useful in

engineering applications. Additionally, this model doesn't require intensive computations

with usually CPU time of 200MHz PC being several seconds for a complete adsorption

isotherm.

Conclusions

In this study, we have extended the SLD approach by combining with the ESD

equation of state to represent the adsorption of solutes onto activated carbon from

supercritical carbon dioxide. This model used only two temperature-independent

parameters, the interaction parameter of solute with the adsorbent, and the slit-shaped

pore width, to describe isotherm behavior under different temperatures and pressures. By

testing the model with adsorption equilibrium data of toluene and benzene on activated

carbon from supercritical carbon dioxide, a good agreement between the model

representation and experimental data are obtained. It is shown that this model approach

with as few model parameters as possible can reasonably and correctly represent the

20

adsorption behavior of solutes in supercritical fluids. Future work is planned to test this

model for more experimental data.

We have also presented a theoretical analysis of solute adsorption at finite and

infinite dilution conditions in supercritical fluids. The characteristics of the competitive

adsorption between solute and solvent were investigated. The effect of temperature,

pressure, bulk solute concentration, and the adsorbent structure size on the adsorption

behavior has been clarified. According to this theoretical analysis, for fixed adsorbent

there are three important factors determining adsorption characteristics in supercritical

fluid: the interaction between solute and solid surface; the interaction between solvent

and solid surface; and solvating power of the supercritical fluid. The adsorption loading

in supercritical fluid is affected by the combination of the three factors.

Our results also show that for supercritical fluid adsorption there are optimum

temperature and pressure, and optimum adsorbent structure size, which may lead to an

optimum operation in adsorption and desorption processes. In summary, the SLD-ESD

model has proven to be a useful method both in practical application and theoretical

analysis.

21

Literature cited

1. McHugh, M. A. and Krukonis, V. J. Supercritical Fluid Extraction, Principles and Practices,

2nd. Butterworth-Heinemann, 1994.

2. Akgerman, A.; Erker, C.; and Ghoreishi, S. M. Supercritical Extraction of

Hexachlorobenzene from Soil. Ind. Eng. Chem. Res. 1992, 31, 333-339.

3. Park, S. and Yeo S. Separation Extraction of Phenols from Organically Modified Smectite.

Separation Science and Technology. 1999, 34(1), 101-113.

4. Recasens, F.; McCoy, B. J. and Smith, J. M. Desorption Processes: Supercritical Fluid

Regeneration of Activated Carbon. AIChE J. 1989, 35(6), 951-958.

5. Macnaughton, S. J. and Foster, N. R. Supercritical Adsorption and Desorption Behavior of

DDT on Activated Carbon Using Carbon Dioxide. Ind. Eng. Chem. Res. 1995, 34, 275-282.

6. Uchida, H.; Iwai, Y.; Nitta, M. and Arai, Y. Impulse Response Analysis for Adsorption of

2,6-and 2,7-Dimethylnaphthalenes in Supercritical Carbon Dioxide Using NaY-Type Zeolite.

Ind. Eng. Chem. Res. 1998, 37, 595-598.

7. Lee, C.; Byeon, S. H. Holder, G. D. Adsorption Characteristics of Toluene and Naphthalene

of Silica Gel Under Subcritical and Supercritical Conditions Using Chromatographic

Techniques. J. Chem. Eng. Japan. 1996, 29(4), 683-694.

8. Kikic, I.; Alessi, P.; Cortesi, A.; Macnaughton, S. J.; Foster, N. R. and Spicka, B. An

Experimental Study of Supercritical Adsorption Equilibria of Salicylic Acid on Activated

Carbon. Fluid Phase Equilibria, 1996, 117, 304-311.

9. Humayun R. and Tomasko, D. L. High-Resolution Adsorption Isotherms of Supercritical

Carbon Dioxide on Activated Carbon. AIChE J. 2000, 46(10), 2065-2075.

10. Wu, Y. Y.; Wong, D. S. H. and Tan. C. Thermodynamic Model for the Adsorption of

Toluene from Supercritical Carbon Dioxide on Activated Carbon. Ind. Eng. Chem. Res. 1991,

30, 2492-2496.

11. Akman, U. and Sunol, A. K. Modeling of Supercritical Desorber with an Equation-of State-

Based Isotherm. AIChE J. 1991, 37,(2), 215-224.

12. Afrane, C. and Chimowitz, E. H. A Molecular Thermodynamic Model for Adsorption

Equilibrium from Supercritical Fluids. J. Supercritical Fluids, 1993, 6(3),143-154.

13. Gubbina, K.E." Theory and Simulation of Adsorption in Micropores", Physical Adsorption:

Experiment, Theory and Applications, J. Fraissard and C. W. Conner, Eds., Kluwer,

Dordrecht, The Netherlands (1997).

22

14. Nitta, T. and Shigeta, T. Computer Simulation Studies of Adsorption Characteristics in

Supercritical Fluids. Fluid Phase Equilibria. 1998, 144, 245-256.

15. Rangarajan B.; Lira, C.T. and Subramanian, R. A Simplified Local Density Model for

Adsorption over Larger Pressure Ranges, AIChE J., 1995, 41, 838-845.

16. Subramanan, R.; Pyada, H.; Lira, C. T. An Engineering Model for Adsorption og Gases onto

Flat Surfaces and Clustering in Supercritical Fluids. Ind. Eng. Chem. Res., 1995, 34, 3830.

17. Soule, A. D.; Smith, C. A.; Yang, X.N. and Lira, C. T. Adsorption Modeling with the ESD

equation of State. Langmuir 2001 (In press).

18. Elliott, Jr. J. R.; Suresh, S. J. and Donohue, M. D. A Simple Equation of State for

Nonspherical and Associating Molecules. Ind. Eng. Chem. Res. 1990, 29, 1476-1485.

19. Elliott, J.R.; Lira, C.T. Introductory Chemical Engineering Thermodynamics, Prentice Hall,

Upper Saddle River, NJ, 1999.

20. Lee, L. L. Molecular Thermodynamics of Non-Ideal Fluids, Butterworths, 1988, 425.

21. Ng, H-J. and Robinson, D. B. Equilibrium Phase Properties of the Toluene-Carbon Dioxide

System. J. Chem and Engineering Data. 1978, 23(4), 325-327.

22. Puhala, A. S. and Elliott, Jr. J. R. Correlation and Prediction of Binary Vapor-Liquid

Equilibrium in Systems Containing Gases, Hydrocarbons, Alcohols, and Waters. Ind. Eng.

Chem. Res. 1993, 32, 3174-3179.

23. Reid, R.C.; Prausnitz, J.M.; Poling, B.E. The Properties of Gases and Liquids 4th, McGraw-

Hill: NY, 1987.

24. Purkait, A. R.; Mourier, P.; Caude, M. H. and Rosset, R. H. Evaluation of Effective Hard

Diameter from Properties of Liquids. Indian J. Pure Appl. Phys. 1981, 19, 973-978.

25. Lai, C-C. and Tan, C-S. Measurement of Effective Diffusivities of Toluene in Activated

carbon in the Presence of Supercritical Carbon Dioxide. Ind. Eng. Chem. Res. 1993, 32,

1717-1722.

26. Goto, M.; Sato, M. Satoshi, K. and Hirose, T. Impulse Response Analysis for Adsorption of

Ethyl Acetate on Activated Carbon in Supercritical Carbon Dioxide. Separation Science and

Technology. 1996, 31(12), 1649-1661.

27. Porto, J. S.; Sato, Y.; Takishima, S. and Masuoka, H. Adsorption Equilibria of Benzene on

Activated Carbon in Presence of Supercritical Carbon Dioxide. J. Chem. Eng. Japan. 1995,

28(3), 245-249.

28. King, J. W. "Supercritical Fluid Interaction at Gas-Solid Interfaces," ACS Symp. Ser.,

Washington, DC, 150 (1987).

23

29. Subra, P.; Vega-Bancel, A. and Reverchon, E. Breakthrough Curves and Adsorption

Isotherms of Terpene Mixtures in Supercritical Carbon Dioxide. J. Supercritical Fluids.

1998, 12, 43-57.

30. Gurdial, G. S. and Foster, N. R. Solubility of o-Hydroxtbenzoic Acid in Supercritical Carbon

Dioxide. Ind. Eng. Chem. Res. 1991, 30, 575.

31. Brennecke, J. F.; Tomasko, D. L.,; Peshkin, J. and Eckert, C. A. Fluorescence Spectroscopy

Studies in Dilute Supercritical Solutions. Ind. Eng. Chem. Res. 1990, 29, 1682.

32. Tucker, S. C., Solvent Density Inhomogeneities in Supercritical Fluids, Chem. Rev., 1999, 99,

391.

33. Heuchel, M.; Davies, G. M.; Buss, E. and Seaton, N. A. Adsorption of Carbon Dioxide and

Methane and Their Mixtures on an Activated Carbon: Simulation an Experiment. Langmuir.

1999, 15, 8695-8705.

34. Kelley, F. D. and Chimowitz, E. H. Near-Critical Phenomena and Resolution in Supercritical

Fluid Chromatography. AIChE J. 1990, 36(8), 1163-1175.

35. Shim, J-J. and Johnston, K. P. Phase Equilibria, Partial Molar Enthalpies, and Partial Molar

Volumes Determined by Supercritical Fluid Chromatography. J. Phys. Chem. 1991, 95, 353-

363.

24

Table 1. The Pure Component Parameters for the ESD equation of State

c q b(cm3/mol) εii/k (K)

CO2

Toluene

Benzene

1.832

1.971

1.769

2.585

2.849

2.465

10.534

36.227

29.544

178.269

332.752

336.454

ktouene-CO2=0.1058; kbenzene-CO2=0.0974

Table 2. The Fitted Parameters of the SLD-ESD Model

εfS,A/k (K) εfS,B/k (K) H (Å)

Toluene(A)-CO2(B)

Benzene(A)-CO2(B)

150

149

105

105

14.3

14.8

25

Figure captions: Figure 1. Schematic of a slit-shaped pore model showing the variables used to define distances in the SLD approach for a binary mixtture; EtaI = (z + 0.5σss)/σfsI, XiI = (H - EtaI*σfsI)/σfsI.

Figure 2. Adsorption of toluene (in CO2) on Degussa WSIV . Symbol: Exp. Data 25; Line: Model correlation. Figure 3. Effect of temperature on adsorption of toluene (in CO2) on Degussa WSIV at fixed densities. Symbol: Exp Data 25 ; Line: Model correlation.

Figure 4. Correlation of fluid-solid parameters and the Lennard-Jones parameter of the adsorbates 17. L-J parameters from Reid, et al.18 Dashed line: L-B rule. Solid points: fitted previously 17; Shaded points: this work. Figure 5. Adsorption of benzene(in CO2) on Calgon BPL. Symbol: exp data 27; Line: model correlation. Figure 6. Competitive adsorption of toluene/CO2 on activated carbon where the bulk mole fraction of toluene is 0.0002. Dashed line: 308 K; Solid line: 318 K. Figure 7. Competitive adsorption of toluene/CO2 on activated carbon where the bulk mole fraction of toluene is 0.005. Dashed line: 308 K; Solid line: 318 K. Figure 8. The effect of pore width on the mean adsorbed density of toluene and CO2 at 318 K. Dashed line: 7.7MPa ; Solid line: 15 MPa. Figure 9. Variation of q/c for toluene in CO2 as y approaches zero for different bulk conditions. Figure 10. The variation of adsorption constant with pressure and density. Figure 11. Variation of adsorption constant with temperature at fixed pressure. Figure 12. The total amount adsorbed against with the temperature at two pressures where the bulk mole fraction of toluene is 0.0002 Dashed line: 7.7 MPa; Solid line: 15 MPa.

H

z

EtaI*σfsI XiI*σfsI

Molecule I

Figure 1. Schematic of a slit-shaped pore model showing the variables used to definedistances in the SLD approach for a binary mixtture; EtaI = (z + 0.5σss)/σfsI, XiI = (H -EtaI*σfsI)/σfsI.

0

1

2

3

4

0 0.001 0.002 0.003 0.004 0.005 0.006

Mole fraction of toluene

Am

ou

nt

Ad

sorb

ed

(mm

ol/g

)

0.32 g/cm^3

0.45g/cm^3

0.69g/cm^3

95.0 bar

80.3 bar77.0 bar

308 K

0

1

2

3

4

0 0.002 0.004 0.006

Mole fraction of toluene

Am

ou

nt

Ad

sorb

ed

(mm

ol/g

)

0.32 g/cm^3

0.45 g/cm^3

0.69g/cm^3

89.0 bar

97.0 bar

128 bar

318 K

Figure 2. Adsorption of toluene (in CO2) on Degussa WSIV .

Symbol: Exp. Data 25; Line: Model correlation.

0

1

2

3

4

0 0.002 0.004 0.006

Mole fraction of toluene

Am

ou

nt

Ad

sorb

ed

(mm

ol/g

) 0.32 g/cm^3

0.45 g/cm^3

0.69 g/cm^3

99.0 b 114 bar

163 bar

328 K

Figure 3. Effect of temperature on adsorption of toluene (in CO2) on Degussa WSIV at fixed densities.

Symbol: Exp Data25 ; Line: Model correlation.

0

1

2

3

4

0 0.001 0.002 0.003 0.004

Mole fraction of toluene

Am

ou

nt

adso

rbed

(m

mo

l/g)

308 K

318 K

328 K

0.69 g/cm3

0

1

2

3

4

0 0.002 0.004 0.006

Mole fraction of toluene

Am

ou

nt

adso

rbed

(m

mo

l/g) 308 K

318 K

328 K

0.45 g/cm3

0

1

2

3

4

0 0.001 0.002 0.003 0.004

Mole fraction of toluene

Am

ou

nt

adso

rbed

(m

mo

l/g)

308 K

318 K

328 K

0.32 g/cm3

Figure 4. Correlation of fluid-solid parameters and the Lennard-

Jones parameter of the adsorbate 17. L-J parameters from Reid, et

al.18 Dashed line: L-B rule. Solid points: fitted previously 17; Shaded points: this work.

0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25

(εεεεff/k (K))1/2,,literature

ε εεε fs/

k (K

), f

itte

d

N2

CO

methane

CO2

ethaneethylene

acetylenepropane

propylene

butane

benzenetoluene

0.0

1.0

2.0

3.0

4.0

5.0

0 0.002 0.004 0.006

Mole fraction of benzene

Am

ou

nt

adso

rbed

(m

mo

l/g)

9.90 bar38.0 bar79.4 bar119 bar

313.2 K

0.0

1.0

2.0

3.0

4.0

0 0.002 0.004 0.006

Mole fraction of benzene

Am

ou

nt

adso

rbed

(m

mo

l/g)

38.0 bar79.4 bar119 bar

323.2 K

Figure 5. Adsorption of benzene(in CO2) on Calgon BPL.

Symbol: exp data 27; Line: model correaltion

0.0

2.0

4.0

6.0

8.0

10.0

0 5 10 15 20 25

Pressure (MPa)

Am

ou

nt

adso

rbed

(m

mo

l/g)

CO2

Toluene

(a)

0.0

2.0

4.0

6.0

8.0

10.0

0 0.2 0.4 0.6 0.8 1

Density(g/cm3)

Am

ou

nt

adso

rbed

(m

mo

l/g)

Figure 6. Competitive adsorption of toluene/CO2 on activated carbon where the bulk mole fraction of toluene is 0.0002. Dashed line: 308 K; Solid line: 318 K.

CO2

Toluene

(b)

Fugacity variation

0

2

4

6

8

10

0 5 10 15 20 25Pressure (MPa)

f CO

2(M

Pa)

0.00001

0.0001

0.001

0.01

0.1

1

f tolu

ene(

MP

a)

0.0

2.0

4.0

6.0

0 5 10 15 20 25

Pressure (MPa)

Am

ou

nt

adso

rbed

(m

mo

l/g) CO2

Toluene

(a)

0.0

2.0

4.0

6.0

0 0.2 0.4 0.6 0.8 1

Density(g/cm3)

Am

ou

nt

adso

rbed

(m

mo

l/g)

Figure 7. Competitive adsorption of toluene/CO2 on activated carbon where the bulk mole fraction of toluene is 0.005. Dashed line: 308 K; Solid line: 318 K.

CO2

Toluene

(b)

0

2

4

6

8

5 10 15 20 25 30 35 40

Pore width (A)

Mea

n d

ensi

ty

(mm

ol/c

m3 )

Figure 8. The effect of pore width on the mean adsorbed density of toluene and CO2 at 318 K. Dashed line: 7.7MPa ; Solid line: 15 MPa.

CO2

Toluene

4

6

8

10

0.0000010.000010.00010.001

Solute mole fraction y

ln(q

/c)

308 K, 7.7 MPa

318 K, 11MPa

328 K, 20 MPa.

Figure 9. Variation of q/c for toluene in CO2 as y

approaches zero for different bulk conditions.

2

4

6

8

10

5 10 15 20 25

Pressure (MPa)

ln(q

/c)

308 K

318 K

328 K

2

4

6

8

10

0 0.2 0.4 0.6 0.8 1

Density(g/cm3)

ln (

q/c

)

308 K

318 K

328 K

Figure 10. The variation of adsorption constant with pressure and density .

0

2000

4000

6000

8000

250 300 350 400 450 500 550 600

Temperature (K)

q/c

(cm

3 /g)

7.7 MPa

15 MPa

Figure 11. Variation of adsorption constant with temperature at fixed pressure.

0

2

4

6

8

10

250 300 350 400 450 500 550 600

Temperature (K)

Am

ou

nt

adso

rbed

(m

mo

l/g)

Figure 12. The total amount adsorbed against with the temperature at two pressures where the bulk mole fraction of toluene is 0.0002 Dashed line: 7.7 MPa; Solid line: 15 MPa.

CO2

Toluene