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Multilayer Adsorption of Slightly Soluble Organic Compounds from Aqueous Solutions
JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO.
178, 764–769 (1996)
0175
Multilayer Adsorption of Slightly Soluble Organic Compounds from Aqueous Solutions 1 GRIGORIY L. ARANOVICH
AND
MARC D. DONOHUE 2
Department of Chemical Engineering, The Johns Hopkins University, Baltimore, Maryland 21218 Received June 18, 1995; accepted September 15, 1995
Adsorption isotherms are analyzed for slightly soluble organic components from water for a wide range of reduced concentrations. It is shown that the behavior of these systems can be modeled by an equation of the form a Å Ac/[(1 / Bc)(1 0 c/c0 ) d ] over the range of c/c0 from about 0.05 to 0.9. Here a is the adsorption amount, c is the concentration of organic compound in the water, c0 is a solubility limit for the organic compound, and A, B, and d are adjustable parameters. Comparison is made with experimental data for the adsorption of n-caproic acid, n-valeric acid, n-amyl alcohol, n-butyl alcohol, aniline, cyclohexanol, and phenol from aqueous solutions on carbon adsorbents. q 1996 Academic Press, Inc. Key Words: adsorption on carbon; slightly soluble organic components; adsorption from water; isotherm equation; multilayer adsorption from binary solutions.
INTRODUCTION
Adsorption of slightly soluble organic compounds from water is important in nature and in chemical processing (1). However, experimental data for such systems have been obtained over a wide range of reduced concentrations for only a few adsorbates. These data indicate multilayer adsorption as the concentration, c, of given compound approaches the solubility limit c0 . This behavior has been observed experimentally for adsorption of organic acids (n-caproic and n-valeric), alcohols (n-amyl and n-butyl), aniline, cyclohexanol, phenol, and others from aqueous solutions on carbon adsorbents (2). Adsorption isotherms for these binary liquid-phase systems have the same shape as for one-component vapors. This analogy suggests that lattice models for gas adsorption (3) might be used to describe binary solutions if the vacancies in the treatment of gases are replaced by solvent molecules. This leads to the same mathematical description for very different phenomena, adsorption of vapors and adsorption from liquid solutions. 1 This article is the result of work prepared under contract to the U.S. Government. By acceptance of this article, the publisher and/or recipient acknowledges the U.S. Government’s right to retain a nonexclusive, royaltyfree license in and to any copyright covering this paper. 2 To whom correspondence should be addressed.
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There has been much effort to describe adsorption isotherms of organic compounds from water using the BET equation (4). In the variables used to describe liquid systems, the BET equation may be written as a Å A * (c/c0 )/[(1 / B *c/c0 )(1 0 c/c0 )],
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[1]
where a is the value of the Gibbs adsorption (mmol/g), and A * and B * are constants. It has been shown by Hansen et al. (2) that the BET equation does not agree with experimental data if the range of reduced concentrations c/c0 is greater than about 0.5. Generally, it is found that the adsorption predicted by Eq. [1] is much larger than the experimental values when a wide range of concentrations are covered. To overcome this failure of BET isotherm, Gu (5) used Anderson’s modification of the BET equation (6, 7), a Å A * (c/c0 )/[(1 / B *c/c0 )(1 0 kc/c0 )],
[2]
where k is an additional adjustable parameter widening the applicable range of adsorption isotherm. Comparison of Eq. [2] with experimental data shows (5) that the values of k are 0.73 for n-caproic acid, 0.6 for amyl alcohol and phenol, and 0.4 for cyclohexanol. These results imply that the singularity in Eq. [2] is shifted from c0 to values in the range of 1.5 c0 to 2.5 c0 . Though this method seems to work well empirically, there does not seem to be any physical justification for this shift in the singularity. Here we show that the adsorption of slightly soluble organic compounds from aqueous solutions can be described without shifting the ‘‘natural’’ singularity at c Å c0 . To analyze multilayer adsorption we represent the singularity in adsorption with the equation a Å H(c)/(1 0 c/c0 ) d .
[3]
Here the singularity is modeled by the adjustable exponent d. The nondiverging part of the isotherm is represented by
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0021-9797/96 $18.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.
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APPLICATION OF MULTILAYER ADSORPTION ISOTHERMS TO AQUEOUS SYSTEMS
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MULTILAYER ADSORPTION
where
TABLE 1 Nature and Specific Surface Areas of Adsorbents Nature
Specific surface area (m2/g)
Artificial graphite Artificial graphite Artificial graphite Sugar charcoal Channel black
95.8 18.4 25.5 790 124
Adsorbent Carbon Carbon Carbon Carbon Carbon
A B E F H
the function, H(c), which is finite in the range 0 £ c £ c0 . In analysis of vapor adsorption data, H(c) is associated with the monolayer adsorption isotherm (8). An analogous interpretation seems reasonable for multilayer adsorption from binary solutions. The Langmuir isotherm (9) H(c) Å Ac/(1 / Bc)
[4]
is widely used as a suitable equation for analysis of monolayer adsorption of dilute solutes from aqueous solutions by carbon adsorbents [10]. Here A is Henry’s coefficient, and B is a coefficient related to monolayer capacity. Combining Eqs. [3] and [4] we have a Å Ac/[(1 / Bc)(1 0 c/c0 ) d ].
[5]
D Å (2eXY 0 eXX 0 eYY )/kT.
The Ono-Kondo equations relate the composition in each layer to the composition in the adjacent layers and the bulk. In these equations xY,i is the fraction of sites occupied by molecules of component Y in layer i, xb is the fraction of sites occupied with molecules of component Y in the bulk (in the solution), z0 is the bulk coordination number, z1 is the monolayer coordination number, z2 Å (z0 0 z1 )/2, k is Boltzmann’s constant, and T is the absolute temperature. The index i can take values from 2 to ` . For molecules which adsorb from the vapor phase, multilayer adsorption occurs when the partial pressure approaches the saturation vapor pressure. For conditions where the reduced pressure is less than about two-thirds, adsorption is in the first molecular layer only. A similar phenomena occurs with adsorption from the liquid phase. When the system is far from macroscopic phase separation, the adsorption is limited to the first molecular layer; however, multilayer adsorption occurs as the concentration approaches the saturation concentration. Equations [6] and [7] describe both adsorption of vapor and adsorption from binary liquid solution in the framework of lattice model. The only difference is that for vacancy solution (i.e., for vapor) we have
SIMILARITIES BETWEEN GAS ADSORPTION AND ADSORPTION FROM BINARY LIQUID SOLUTIONS
Here we consider lattice theory of adsorption for binary solutions. In this model the lattice contains two kinds of molecules, X and Y. There are interactions between the nearest neighbors, eXX , eXY , eYY for adsorbate–adsorbate interactions and e0X , e0Y for interactions of adsorbate molecules in the first monolayer with the adsorbent. In general, this model can be used to describe adsorption from binary liquid solutions (11). If one of the species has zero interaction energy, this result reduces to that for a one-component gas (12). The classical equations of thermodynamic equilibria for the lattice model with a boundary in the mean field approximation were derived by Ono and Kondo (3, 13). They are
eXX Å eXY Å 0.
/ [z1 (xY,1 0 xb ) / z2 (xY,2 0 xb ) 0 z2 xb ] D
[6]
and ln{xY,i (1 0 xb )/[xb (1 0 xY,i )]} Å [z0 (xY,i 0 xb ) / z2 (xY,i/1 0 2xY,i / xY,i01 )] D,
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[7]
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[9]
In this limit Eqs. [6] and [7] reduce to ln{xY,1 (1 0 xb )/[xb (1 0 xY,1 )]} Å { 0 e0Y 0 [z1 (xY,1 0 xb )e / z2 (xY,2 0 xb ) 0 z2 xb ] eYY }/kT
[10]
and TABLE 2 Solubilities of Organic Compounds in Water
ln{xY,1 (1 0 xb )/[xb (1 0 xY,1 )]} Å [ e0X 0 e0Y / z2 ( eXY 0 eX X )]/kT
[8]
Organic compound n-caproic acid n-Valeric acid n-Amyl alcohol n-Butyl alcohol Aniline Cyclohexanol Phenol
coida
IUPAC name
Boiling point (7C)
c0 (mol/liter)
Solubility (wt%)
Hexanoic acid Pentanoic acid 1-Pentanol 1-Butanol Aniline Cyclohexanol Phenol
200 186 136 117 183 158 180
0.0876 0.4857 0.2866 0.9850 0.3932 0.3906 0.8955
1.02 4.97 2.54 7.41 3.67 3.92 8.41
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ARANOVICH AND DONOHUE
FIG. 1. Adsorption isotherms for n-caproic acid from aqueous solutions on macroporous carbon adsorbents.
ln{xY,i (1 0 xb )/[xb (1 0 xY,i )]} Å 0 [z0 (xY,i 0 xb ) / z2 (xY,i/1 0 2xY,i / xY,i01 )] eYY /kT. [11]
Comparison of Eqs. [10] and [11] with Eqs. [6] and [7] shows that they are identical if (2eXY 0 eXX 0 eYY )liquid Å ( 0 eYY )gas
[12]
FIG. 3. Adsorption isotherms for n-amyl alcohol from aqueous solutions on macroporous carbon adsorbents.
This suggests that the mathematical form of the equations should be the same for these two different phenomena, i.e., the adsorption of a vapor and the adsorption of a solute from a binary liquid solution. COMPARISON WITH EXPERIMENTAL DATA FOR MACROPOROUS ADSORBENTS
[ e0X 0 e0Y / z2 ( eXY 0 eX X )]liquid Å ( 0 e0Y )gas . [13]
To compare Eq. [5] with experimental data, we have used the classical adsorption isotherms of Hansen et al. (2) for adsorption of n-caproic and n-valeric acids, n-amyl and nbutyl alcohols, aniline, cyclohexanol, and phenol on different
FIG. 2. Adsorption isotherms for n-valeric acid from aqueous solutions on macroporous carbon adsorbents.
FIG. 4. Adsorption isotherms for n-butyl alcohol from aqueous solutions on macroporous carbon adsorbents.
and
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TABLE 3 Parameters for Eq. [5] for Different Adsorbates on Macroporous Adsorbents Adsorbate
Parameter
Carbon A
Carbon B
Carbon E
Carbon H
n-Caproic acid n-caproic acid n-Caproic acid
A B d
5 12 0.37
0.9 9.4 0.34
1.03 7 0.34
5.1 10 0.42
n-Valeric acid n-Valeric acid n-Valeric acid
A B d
6.8 17 0.34
1.44 18 0.38
3.7 32 0.38
7.5 15 0.36
n-Amyl alcohol n-Amyl alcohol n-Amyl alcohol
A B d
7 17 0.32
2.2 25 0.38
3.9 32 0.38
7.5 15 0.31
n-Butyl alcohol n-Butyl alcohol n-Butyl alcohol
A B d
6 12.5 0.21
2.2 25 0.28
2.3 16 0.19
7.4 12 0.17
Aniline Aniline Aniline
A B d
28 43 0.26
6 54 0.34
5.8 25 0.24
19 32.5 0.32
Cyclohexanol Cyclohexanol Cyclohexanol
A B d
9 23 0.19
2.4 34 0.34
3 27 0.28
8.2 15 0.12
Phenol Phenol Phenol
A B d
21 38 0.27
4.3 34 0.2
4.6 23 0.2
15.5 25 0.31
carbon adsorbents A, B, E, F, H, with different specific surface areas, S (see Table 1). Adsorbents A, B, C, and H are macroporous with different S in the range from 18.4 to 124 m2 /g. Adsorbent F is microporous with S Å 790 m2 /g. Aqueous solubilities for the organic compounds studied are given in Table 2.
Figures 1–4 present adsorption isotherms for organic acids and alcohols from aqueous solutions on different macroporous carbon adsorbents at T Å 298 K (experimental and calculated from Eq. [5]). The parameters for Eq. [5] are given in Table 3. It can be seen from Figs. 1–4 that this three-parameter
FIG. 5. Adsorption isotherms for aniline from aqueous solutions on macroporous carbon adsorbents.
FIG. 6. Adsorption isotherms for cyclohexanol from aqueous solutions on macroporous carbon adsorbents.
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FIG. 7. Adsorption isotherms for phenol from aqueous solutions on macroporous carbon adsorbents.
model describes these data well over the whole range of c/c0 . Figures 5–7 show adsorption isotherms for aniline, cyclohexanol, and phenol from aqueous solutions on the same types of carbon adsorbents. As seen in Figs. 5–7, the experimental adsorption isotherms are described very well by Eq. [5], except for aniline on carbon A. For this case, there is only qualitative agreement between the model and the data. We believe that the errors in fitting the isotherm for aniline are due to an inadequacy of the Langmuir isotherm used for the function H(c) for this system. ADSORPTION ON MICROPOROUS ADSORBENTS
Equation [5] also can be used to fit experimental data for adsorption of slightly soluble organic compounds from aqueous solutions on microporous adsorbents. Figure 8 presents adsorption isotherms of n-caproic and n-valeric acids, n-amyl and n-butyl alcohols, aniline, cyclohexanol, and phenol from aqueous solutions on microporous carbon adsorbent F at T Å 298 K. Parameters of Eq. [5] for these data are given in Table 4.
FIG. 8. Adsorption isotherms for different compounds from aqueous solutions on microporous carbon adsorbent F.
A, B, E, and H. This reflects the difference in the isotherm shape between macroporous and microporous adsorbents. While isotherms for macroporous adsorbents have a strong singularity, this is not the case for microporous adsorbents. The small negative values of d (for aniline and phenol) imply that a goes down as c approaches c0 . This is possible because the Gibbs adsorption is the difference between the concentration in the adsorbed phase and that in the bulk. The Gibbs adsorption for microporous adsorbents can decrease if the pore space becomes filled with solute molecules at a concentration less than the solubility limit. The Gibbs adsorption in the limited adsorption space is n
a Å ∑ (xY,i 0 xb ),
where n is a number of monolayers. For the filled pores xY,i É 1 and from Eq. [14] we have that a É n(1 0 xb ).
ANALYSIS OF PARAMETERS
For adsorbent F, the values of d are very small and values of A and B are much larger than for macroporous adsorbents
[14]
iÅ1
[15]
As can be seen from Eq. [15], a goes down as xb (and therefore c) goes up.
TABLE 4 Parameters for Eq. [5] for Different Adsorbates on Microporous Adsorbent F (Fig. 8) Parameter
n-caproic acid
n-Valeric acid
n-Amyl alcohol
n-Butyl alcohol
Aniline
Cyclohexanol
Phenol
A B d
360 200 0.04
127 70 0.01
203 97 0.04
160 68 0.03
248 90 00.04
125 88 0.01
221 79 00.02
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MULTILAYER ADSORPTION
By analogy to multilayer adsorption of vapors, the ratio am Å A/B
[16]
can be interpreted as monolayer capacity of given compound. Table 5 presents values of am (in the units of mmole/ g) for the various organic compounds on the different carbon adsorbents. Table 6 presents ratios of am for adsorbents A, E, H, and F to the am for adsorbent B, r Å (am )/(am )B
[17]
TABLE 6 Values of r and m for Considered Systems Parameter
Carbon A
Carbon E
Carbon H
Carbon F
m rcaproic acid rvaleric acid ramyl alcohol rbutyl alcohol raniline rcyclohexanol rphenol
5.2 4.35 5 4.68 5.45 5.86 5.54 4.37
1.39 1.54 1.44 1.385 1.63 2.09 1.57 1.58
6.74 5.33 6.25 5.68 7 5.26 7.74 4.9
42.9 18.8 22.7 23.8 26.7 24.8 20.1 22.1
and ratios of their specific surface areas, m Å (S)/(S)B .
[18]
The ratios in Table 6 show that the values for r are very close to the values for m for macroporous adsorbents (for most values the deviations are not more than {20%). However, for the microporous adsorbent (carbon F) the values of r are about half those of m. Since using the BET surface area for microporous adsorbents is at least controversial, this discrepancy is not surprising.
Equation [5] can be used to fit experimental data for adsorption of slightly soluble organic compounds from aqueous solutions. In particular, this equation describes adsorption isotherms for n-caproic and n-valeric acids, n-amyl and n-butyl alcohols, aniline, cyclohexanol, and phenol from aqueous solutions on carbon adsorbents. Values of the exponent d depend on the type of adsorbent. For the macroporous samples studied, it is in the range of 0.12 to 0.42, with most values between 0.25 and 0.35. For microporous adsorbent F TABLE 5 Values of am for Different Systems
n-Caproic acid n-Valeric acid n-Amyl alcohol n-Butyl alcohol Aniline Cyclohexanol Phenol
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Carbon A
Carbon B
Carbon E
Carbon H
0.417
0.0957
0.147
0.51
1.8
0.4
0.08
0.116
0.5
1.81
0.412
0.088
0.122
0.5
2.09
0.48 0.651 0.391 0.553
0.088 0.111 0.0706 0.126
0.144 0.232 0.111 0.2
0.617 0.585 0.547 0.62
2.35 2.755 1.42 2.797
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ACKNOWLEDGMENT Support of this research by the Division of Chemical Sciences of the Office of Basic Energy Sciences, U.S. Department of Energy, under Contract Number DE-FG02-87ER13777, is gratefully acknowledged.
CONCLUSION
Adsorbate
the absolute value of this exponent not greater than 0.04. Further, values of the parameter A are 10–100 times larger and values of B are 5–10 times larger for microporous sample F than for macroporous ones. This can be related to the difference in specific surface area, Henry’s coefficients, and shapes of adsorption isotherms on macro- and microporous adsorbents.
Carbon F
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REFERENCES 1. Matsumoto, M. R., McGinley, P. M., Reed, B. E., and Jensen, J. N., Water Environ. Res. 64, 337 (1992); Zoungrana, T., Berrada, A., Douillard, J.-M., and Partyka, S., Langmuir 11, 1760 (1995). 2. Hansen, R. S., Fu, Y., and Bartell, F. E., J. Physical Colloid Chem. 53, 769 (1949). 3. Rowlinson, J. S., and Widom, B., ‘‘Molecular Theory of Capillarity.’’ Clarendon, Oxford, 1982. 4. Brunauer, S., Emmett, P. H., and Teller, E., J. Am. Chem. Soc. 60, 309 (1938). 5. Gu, T., J. Colloid Interface Sci. 85, 601 (1982). 6. Anderson, R. B., J. Am. Chem. Soc. 68, 686 (1946). 7. Brunauer, S., Skalny, J., and Boder, E. E., J. Colloid Interface Sci. 30, 546 (1969). 8. Aranovich, G. L., and Donohue, M. D., J. Colloid Interface Sci., accepted for publication. 9. Langmuir, J., J. Am. Chem. Soc. 38, 2221 (1916); J. Am. Chem. Soc. 40, 1361 (1918). 10. Jaroniec, M., and Madey, R., ‘‘Physical Adsorption on Heterogeneous Solids,’’ p. 302. Elsevier, Amsterdam, 1988. 11. Lane, J. E., ‘‘Adsorption from Solution at the Solid/Liquid Interface’’ (G. D. Parfitt and C. H. Rochester, Eds.), Chap. 2. Academic Press, London, 1983; Lane, J. E., Aust. J. Chem. 21, 827 (1968). 12. Rowlinson, J. S., and Swinton, F. L., ‘‘Liquids and Liquid Mixtures,’’ p. 70. Butterworth Scientific, London, 1982; Shulepov, Yu. V., and Aksenenko, Ye. V., ‘‘Lattice Gas.’’ Naukova Dumka, Kiev, 1981. 13. Ono, S., and Kondo, S., ‘‘Molecular Theory of Surface Tension.’’ Springer-Verlag, Berlin, 1960.
coida
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178, 764–769 (1996)
0175
Multilayer Adsorption of Slightly Soluble Organic Compounds from Aqueous Solutions 1 GRIGORIY L. ARANOVICH
AND
MARC D. DONOHUE 2
Department of Chemical Engineering, The Johns Hopkins University, Baltimore, Maryland 21218 Received June 18, 1995; accepted September 15, 1995
Adsorption isotherms are analyzed for slightly soluble organic components from water for a wide range of reduced concentrations. It is shown that the behavior of these systems can be modeled by an equation of the form a Å Ac/[(1 / Bc)(1 0 c/c0 ) d ] over the range of c/c0 from about 0.05 to 0.9. Here a is the adsorption amount, c is the concentration of organic compound in the water, c0 is a solubility limit for the organic compound, and A, B, and d are adjustable parameters. Comparison is made with experimental data for the adsorption of n-caproic acid, n-valeric acid, n-amyl alcohol, n-butyl alcohol, aniline, cyclohexanol, and phenol from aqueous solutions on carbon adsorbents. q 1996 Academic Press, Inc. Key Words: adsorption on carbon; slightly soluble organic components; adsorption from water; isotherm equation; multilayer adsorption from binary solutions.
INTRODUCTION
Adsorption of slightly soluble organic compounds from water is important in nature and in chemical processing (1). However, experimental data for such systems have been obtained over a wide range of reduced concentrations for only a few adsorbates. These data indicate multilayer adsorption as the concentration, c, of given compound approaches the solubility limit c0 . This behavior has been observed experimentally for adsorption of organic acids (n-caproic and n-valeric), alcohols (n-amyl and n-butyl), aniline, cyclohexanol, phenol, and others from aqueous solutions on carbon adsorbents (2). Adsorption isotherms for these binary liquid-phase systems have the same shape as for one-component vapors. This analogy suggests that lattice models for gas adsorption (3) might be used to describe binary solutions if the vacancies in the treatment of gases are replaced by solvent molecules. This leads to the same mathematical description for very different phenomena, adsorption of vapors and adsorption from liquid solutions. 1 This article is the result of work prepared under contract to the U.S. Government. By acceptance of this article, the publisher and/or recipient acknowledges the U.S. Government’s right to retain a nonexclusive, royaltyfree license in and to any copyright covering this paper. 2 To whom correspondence should be addressed.
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There has been much effort to describe adsorption isotherms of organic compounds from water using the BET equation (4). In the variables used to describe liquid systems, the BET equation may be written as a Å A * (c/c0 )/[(1 / B *c/c0 )(1 0 c/c0 )],
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[1]
where a is the value of the Gibbs adsorption (mmol/g), and A * and B * are constants. It has been shown by Hansen et al. (2) that the BET equation does not agree with experimental data if the range of reduced concentrations c/c0 is greater than about 0.5. Generally, it is found that the adsorption predicted by Eq. [1] is much larger than the experimental values when a wide range of concentrations are covered. To overcome this failure of BET isotherm, Gu (5) used Anderson’s modification of the BET equation (6, 7), a Å A * (c/c0 )/[(1 / B *c/c0 )(1 0 kc/c0 )],
[2]
where k is an additional adjustable parameter widening the applicable range of adsorption isotherm. Comparison of Eq. [2] with experimental data shows (5) that the values of k are 0.73 for n-caproic acid, 0.6 for amyl alcohol and phenol, and 0.4 for cyclohexanol. These results imply that the singularity in Eq. [2] is shifted from c0 to values in the range of 1.5 c0 to 2.5 c0 . Though this method seems to work well empirically, there does not seem to be any physical justification for this shift in the singularity. Here we show that the adsorption of slightly soluble organic compounds from aqueous solutions can be described without shifting the ‘‘natural’’ singularity at c Å c0 . To analyze multilayer adsorption we represent the singularity in adsorption with the equation a Å H(c)/(1 0 c/c0 ) d .
[3]
Here the singularity is modeled by the adjustable exponent d. The nondiverging part of the isotherm is represented by
764
0021-9797/96 $18.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.
AID
APPLICATION OF MULTILAYER ADSORPTION ISOTHERMS TO AQUEOUS SYSTEMS
coida
AP: Colloid
765
MULTILAYER ADSORPTION
where
TABLE 1 Nature and Specific Surface Areas of Adsorbents Nature
Specific surface area (m2/g)
Artificial graphite Artificial graphite Artificial graphite Sugar charcoal Channel black
95.8 18.4 25.5 790 124
Adsorbent Carbon Carbon Carbon Carbon Carbon
A B E F H
the function, H(c), which is finite in the range 0 £ c £ c0 . In analysis of vapor adsorption data, H(c) is associated with the monolayer adsorption isotherm (8). An analogous interpretation seems reasonable for multilayer adsorption from binary solutions. The Langmuir isotherm (9) H(c) Å Ac/(1 / Bc)
[4]
is widely used as a suitable equation for analysis of monolayer adsorption of dilute solutes from aqueous solutions by carbon adsorbents [10]. Here A is Henry’s coefficient, and B is a coefficient related to monolayer capacity. Combining Eqs. [3] and [4] we have a Å Ac/[(1 / Bc)(1 0 c/c0 ) d ].
[5]
D Å (2eXY 0 eXX 0 eYY )/kT.
The Ono-Kondo equations relate the composition in each layer to the composition in the adjacent layers and the bulk. In these equations xY,i is the fraction of sites occupied by molecules of component Y in layer i, xb is the fraction of sites occupied with molecules of component Y in the bulk (in the solution), z0 is the bulk coordination number, z1 is the monolayer coordination number, z2 Å (z0 0 z1 )/2, k is Boltzmann’s constant, and T is the absolute temperature. The index i can take values from 2 to ` . For molecules which adsorb from the vapor phase, multilayer adsorption occurs when the partial pressure approaches the saturation vapor pressure. For conditions where the reduced pressure is less than about two-thirds, adsorption is in the first molecular layer only. A similar phenomena occurs with adsorption from the liquid phase. When the system is far from macroscopic phase separation, the adsorption is limited to the first molecular layer; however, multilayer adsorption occurs as the concentration approaches the saturation concentration. Equations [6] and [7] describe both adsorption of vapor and adsorption from binary liquid solution in the framework of lattice model. The only difference is that for vacancy solution (i.e., for vapor) we have
SIMILARITIES BETWEEN GAS ADSORPTION AND ADSORPTION FROM BINARY LIQUID SOLUTIONS
Here we consider lattice theory of adsorption for binary solutions. In this model the lattice contains two kinds of molecules, X and Y. There are interactions between the nearest neighbors, eXX , eXY , eYY for adsorbate–adsorbate interactions and e0X , e0Y for interactions of adsorbate molecules in the first monolayer with the adsorbent. In general, this model can be used to describe adsorption from binary liquid solutions (11). If one of the species has zero interaction energy, this result reduces to that for a one-component gas (12). The classical equations of thermodynamic equilibria for the lattice model with a boundary in the mean field approximation were derived by Ono and Kondo (3, 13). They are
eXX Å eXY Å 0.
/ [z1 (xY,1 0 xb ) / z2 (xY,2 0 xb ) 0 z2 xb ] D
[6]
and ln{xY,i (1 0 xb )/[xb (1 0 xY,i )]} Å [z0 (xY,i 0 xb ) / z2 (xY,i/1 0 2xY,i / xY,i01 )] D,
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[7]
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[9]
In this limit Eqs. [6] and [7] reduce to ln{xY,1 (1 0 xb )/[xb (1 0 xY,1 )]} Å { 0 e0Y 0 [z1 (xY,1 0 xb )e / z2 (xY,2 0 xb ) 0 z2 xb ] eYY }/kT
[10]
and TABLE 2 Solubilities of Organic Compounds in Water
ln{xY,1 (1 0 xb )/[xb (1 0 xY,1 )]} Å [ e0X 0 e0Y / z2 ( eXY 0 eX X )]/kT
[8]
Organic compound n-caproic acid n-Valeric acid n-Amyl alcohol n-Butyl alcohol Aniline Cyclohexanol Phenol
coida
IUPAC name
Boiling point (7C)
c0 (mol/liter)
Solubility (wt%)
Hexanoic acid Pentanoic acid 1-Pentanol 1-Butanol Aniline Cyclohexanol Phenol
200 186 136 117 183 158 180
0.0876 0.4857 0.2866 0.9850 0.3932 0.3906 0.8955
1.02 4.97 2.54 7.41 3.67 3.92 8.41
AP: Colloid
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FIG. 1. Adsorption isotherms for n-caproic acid from aqueous solutions on macroporous carbon adsorbents.
ln{xY,i (1 0 xb )/[xb (1 0 xY,i )]} Å 0 [z0 (xY,i 0 xb ) / z2 (xY,i/1 0 2xY,i / xY,i01 )] eYY /kT. [11]
Comparison of Eqs. [10] and [11] with Eqs. [6] and [7] shows that they are identical if (2eXY 0 eXX 0 eYY )liquid Å ( 0 eYY )gas
[12]
FIG. 3. Adsorption isotherms for n-amyl alcohol from aqueous solutions on macroporous carbon adsorbents.
This suggests that the mathematical form of the equations should be the same for these two different phenomena, i.e., the adsorption of a vapor and the adsorption of a solute from a binary liquid solution. COMPARISON WITH EXPERIMENTAL DATA FOR MACROPOROUS ADSORBENTS
[ e0X 0 e0Y / z2 ( eXY 0 eX X )]liquid Å ( 0 e0Y )gas . [13]
To compare Eq. [5] with experimental data, we have used the classical adsorption isotherms of Hansen et al. (2) for adsorption of n-caproic and n-valeric acids, n-amyl and nbutyl alcohols, aniline, cyclohexanol, and phenol on different
FIG. 2. Adsorption isotherms for n-valeric acid from aqueous solutions on macroporous carbon adsorbents.
FIG. 4. Adsorption isotherms for n-butyl alcohol from aqueous solutions on macroporous carbon adsorbents.
and
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MULTILAYER ADSORPTION
TABLE 3 Parameters for Eq. [5] for Different Adsorbates on Macroporous Adsorbents Adsorbate
Parameter
Carbon A
Carbon B
Carbon E
Carbon H
n-Caproic acid n-caproic acid n-Caproic acid
A B d
5 12 0.37
0.9 9.4 0.34
1.03 7 0.34
5.1 10 0.42
n-Valeric acid n-Valeric acid n-Valeric acid
A B d
6.8 17 0.34
1.44 18 0.38
3.7 32 0.38
7.5 15 0.36
n-Amyl alcohol n-Amyl alcohol n-Amyl alcohol
A B d
7 17 0.32
2.2 25 0.38
3.9 32 0.38
7.5 15 0.31
n-Butyl alcohol n-Butyl alcohol n-Butyl alcohol
A B d
6 12.5 0.21
2.2 25 0.28
2.3 16 0.19
7.4 12 0.17
Aniline Aniline Aniline
A B d
28 43 0.26
6 54 0.34
5.8 25 0.24
19 32.5 0.32
Cyclohexanol Cyclohexanol Cyclohexanol
A B d
9 23 0.19
2.4 34 0.34
3 27 0.28
8.2 15 0.12
Phenol Phenol Phenol
A B d
21 38 0.27
4.3 34 0.2
4.6 23 0.2
15.5 25 0.31
carbon adsorbents A, B, E, F, H, with different specific surface areas, S (see Table 1). Adsorbents A, B, C, and H are macroporous with different S in the range from 18.4 to 124 m2 /g. Adsorbent F is microporous with S Å 790 m2 /g. Aqueous solubilities for the organic compounds studied are given in Table 2.
Figures 1–4 present adsorption isotherms for organic acids and alcohols from aqueous solutions on different macroporous carbon adsorbents at T Å 298 K (experimental and calculated from Eq. [5]). The parameters for Eq. [5] are given in Table 3. It can be seen from Figs. 1–4 that this three-parameter
FIG. 5. Adsorption isotherms for aniline from aqueous solutions on macroporous carbon adsorbents.
FIG. 6. Adsorption isotherms for cyclohexanol from aqueous solutions on macroporous carbon adsorbents.
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FIG. 7. Adsorption isotherms for phenol from aqueous solutions on macroporous carbon adsorbents.
model describes these data well over the whole range of c/c0 . Figures 5–7 show adsorption isotherms for aniline, cyclohexanol, and phenol from aqueous solutions on the same types of carbon adsorbents. As seen in Figs. 5–7, the experimental adsorption isotherms are described very well by Eq. [5], except for aniline on carbon A. For this case, there is only qualitative agreement between the model and the data. We believe that the errors in fitting the isotherm for aniline are due to an inadequacy of the Langmuir isotherm used for the function H(c) for this system. ADSORPTION ON MICROPOROUS ADSORBENTS
Equation [5] also can be used to fit experimental data for adsorption of slightly soluble organic compounds from aqueous solutions on microporous adsorbents. Figure 8 presents adsorption isotherms of n-caproic and n-valeric acids, n-amyl and n-butyl alcohols, aniline, cyclohexanol, and phenol from aqueous solutions on microporous carbon adsorbent F at T Å 298 K. Parameters of Eq. [5] for these data are given in Table 4.
FIG. 8. Adsorption isotherms for different compounds from aqueous solutions on microporous carbon adsorbent F.
A, B, E, and H. This reflects the difference in the isotherm shape between macroporous and microporous adsorbents. While isotherms for macroporous adsorbents have a strong singularity, this is not the case for microporous adsorbents. The small negative values of d (for aniline and phenol) imply that a goes down as c approaches c0 . This is possible because the Gibbs adsorption is the difference between the concentration in the adsorbed phase and that in the bulk. The Gibbs adsorption for microporous adsorbents can decrease if the pore space becomes filled with solute molecules at a concentration less than the solubility limit. The Gibbs adsorption in the limited adsorption space is n
a Å ∑ (xY,i 0 xb ),
where n is a number of monolayers. For the filled pores xY,i É 1 and from Eq. [14] we have that a É n(1 0 xb ).
ANALYSIS OF PARAMETERS
For adsorbent F, the values of d are very small and values of A and B are much larger than for macroporous adsorbents
[14]
iÅ1
[15]
As can be seen from Eq. [15], a goes down as xb (and therefore c) goes up.
TABLE 4 Parameters for Eq. [5] for Different Adsorbates on Microporous Adsorbent F (Fig. 8) Parameter
n-caproic acid
n-Valeric acid
n-Amyl alcohol
n-Butyl alcohol
Aniline
Cyclohexanol
Phenol
A B d
360 200 0.04
127 70 0.01
203 97 0.04
160 68 0.03
248 90 00.04
125 88 0.01
221 79 00.02
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MULTILAYER ADSORPTION
By analogy to multilayer adsorption of vapors, the ratio am Å A/B
[16]
can be interpreted as monolayer capacity of given compound. Table 5 presents values of am (in the units of mmole/ g) for the various organic compounds on the different carbon adsorbents. Table 6 presents ratios of am for adsorbents A, E, H, and F to the am for adsorbent B, r Å (am )/(am )B
[17]
TABLE 6 Values of r and m for Considered Systems Parameter
Carbon A
Carbon E
Carbon H
Carbon F
m rcaproic acid rvaleric acid ramyl alcohol rbutyl alcohol raniline rcyclohexanol rphenol
5.2 4.35 5 4.68 5.45 5.86 5.54 4.37
1.39 1.54 1.44 1.385 1.63 2.09 1.57 1.58
6.74 5.33 6.25 5.68 7 5.26 7.74 4.9
42.9 18.8 22.7 23.8 26.7 24.8 20.1 22.1
and ratios of their specific surface areas, m Å (S)/(S)B .
[18]
The ratios in Table 6 show that the values for r are very close to the values for m for macroporous adsorbents (for most values the deviations are not more than {20%). However, for the microporous adsorbent (carbon F) the values of r are about half those of m. Since using the BET surface area for microporous adsorbents is at least controversial, this discrepancy is not surprising.
Equation [5] can be used to fit experimental data for adsorption of slightly soluble organic compounds from aqueous solutions. In particular, this equation describes adsorption isotherms for n-caproic and n-valeric acids, n-amyl and n-butyl alcohols, aniline, cyclohexanol, and phenol from aqueous solutions on carbon adsorbents. Values of the exponent d depend on the type of adsorbent. For the macroporous samples studied, it is in the range of 0.12 to 0.42, with most values between 0.25 and 0.35. For microporous adsorbent F TABLE 5 Values of am for Different Systems
n-Caproic acid n-Valeric acid n-Amyl alcohol n-Butyl alcohol Aniline Cyclohexanol Phenol
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Carbon A
Carbon B
Carbon E
Carbon H
0.417
0.0957
0.147
0.51
1.8
0.4
0.08
0.116
0.5
1.81
0.412
0.088
0.122
0.5
2.09
0.48 0.651 0.391 0.553
0.088 0.111 0.0706 0.126
0.144 0.232 0.111 0.2
0.617 0.585 0.547 0.62
2.35 2.755 1.42 2.797
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ACKNOWLEDGMENT Support of this research by the Division of Chemical Sciences of the Office of Basic Energy Sciences, U.S. Department of Energy, under Contract Number DE-FG02-87ER13777, is gratefully acknowledged.
CONCLUSION
Adsorbate
the absolute value of this exponent not greater than 0.04. Further, values of the parameter A are 10–100 times larger and values of B are 5–10 times larger for microporous sample F than for macroporous ones. This can be related to the difference in specific surface area, Henry’s coefficients, and shapes of adsorption isotherms on macro- and microporous adsorbents.
Carbon F
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