Langmuir 1995,11, 1297-1303
1297
Comparison of Energy Distributions Calculated for Active Carbons from Benzene GadSolid and LiquidSolid Adsorption Data M. Heuchelt and M. Jaroniec" Department of Chemistry, Kent State University, Kent, Ohio 44242 Received September 15, 1994. In Final Form: January 19, 1995@ Adsorption isotherms of benzene from both gas phase and dilute aqueous solutions have been used to calculate the energy distribution functions for six commercial active carbons. The energeticheterogeneity of these microporous carbons was discussed in relation to their pore-size distributions evaluated from nitrogen adsorption isotherms.
Introduction Up to now the gas-phase and liquid-phase adsorptions seem to be more or less separated areas. While the gas adsorption data have been often used to characterize the microporosity of carbonaceous the liquidsolid adsorption measurements (especially those involving dilute aqueous solutions, which are of great practical seldom employed to study these i m p ~ r t a n c e 1, ~ ,were ~ There are only several works which addressed heterogeneity effects in physical adsorption at both gadsolid and liquidsolid interfaces and provide a quantitative comparison of these phenomena (see monog r a p h ~and ~ , ~references therein). However, there is a great practical interest in studying these effects for heterogeneous solids. The global heterogeneity of an active carbon consists of both chemical and geometrical heterogeneities. The former case refers to various surface impurities as well as different functional groups, mostly oxygen groups present on the surface. Geometrical heterogeneity is due to cracks, pits, and steps as well as to pores of different sizes and shapes. Both chemical and geometrical heterogeneities, especially those associated with existence of fine pores, contribute to unique sorption properties of active carbons. Due to a complex heterogeneity of active carbons the overall adsorption isotherm of a single component is expressed by the followingintegral equation: 2,3
In other words, the experimental adsorption isotherm Z(y)is expressed by a n integral over a n integration range t Permanent address: Institute of Physical and Theoretical Chemistry, University of Leipzig, D-04103 Leipzig, Germany. Abstract published in Advance ACS Abstracts, April 1, 1995. (1) Dubinin, M. M. Progr. Membr. S u q . Sci. 1976, 9, 1. (2) Rudzinski W.;Everett D. H.Adsorption of Gases on Heterogeneous Surfaces; Academic Press: New York, 1991. (3) Jaroniec, M.; Madey, R. Physical Adsorption on Heterogeneous Solids; Elsevier: Amsterdam, 1988. (4) Suffet, I. H.; McGuire, M. J. (Eds.)Actiuated Carbon Adsorption of Organics from Aqueous Phase; Ann Arbor Sci. Publ.: Ann Arbor, 1980. (5) McGuire,M. J.;S f l e t , I. H. (Eds.)Treatment of Water by Granular Activated Carbon;American Chemical Society: Washington DC, 1983. (6) Sircar, S.AIChE Symp. Ser. 1986, 81, 58. (7) Jaroniec, M.; Choma, J.;Burakiewicz-Mortka,W. Carbon, 1991, 29 1294. -_ --- -. (8) Choma, J.; Burakiewicz-Mortka,W., Jaroniec, M.; Gilpin, R. K. Langmuir 1993, 9, 2555. (9) Chmutov, K. V.; Larionov, 0. G. Prog. Su$. Membr. Sci. 1981, 14, 237.
*
I
A where y denotes the equilibrium pressure or concentration. The subintegral function in eq 1 is the product of a local adsorption isotherm z ( x y ) and a distribution function F(x). The explicit form of the integral kernel, i.e., the local adsorption isotherm z(xy),will be discussed later. In the current paper four different distribution functions F(x) were discussed: (i)F(H), the pore-size distribution calculated from nitrogen adsorption data at 78 K; (ii)F(v), the adsorption energy distribution evaluated from adsorption data of benzene vapor; (iii) F(U21), the energy distribution obtained from adsorption data of benzene from dilute aqueous solutions; and (iv) the F(0)-distribution of the difference in the Gibbs free energies of benzene and water. The above mentioned distributions were evaluated by inverting the integral eq 1. At present, there are advanced numerical methods, e.g., INTEG'O and CAEDMON," which can be employed to solve eq 1. Three types of distributions were calculated by using the same numerical program (INTEG), which employs a regularization method.1° A special emphasis was given on interpretation of the energy distribution functions for active carbons. Both microporosity and surface heterogeneity may contribute to the global energetic heterogeneity of active carbons, and some information about their contributions can be obtained on the basis of experimental adsorption data. As can be seen from eq 1,to obtain the required information about adsorbent heterogeneity one needs to assume the local adsorption isothermz(xy), e.g., a model for adsorption in uniform pores of the size H or the model for adsorption on an energetically homogeneous surface with the adsorption energy U. The validity of these physicochemicalmodels can be proved by adsorption experiments and computer simulations. Recent achievements in computer simulations of gas adsorption in micropores12-14and on heterogeneous surfaces (see ref 15 and references therein) showed that simulation techniques can be used successfully to generate the well-defined adsorption data. Especially, the simulated adsorption data for carbon-like pores are needed to study the relationship between microporosity,surface heterogeneity, and global energetic heterogeneity of active carbons. Unfortunately, to our knowledge there is no extensive simulation data for benzene adsorption on active carbons. (10) v. Szombathely, M.; Brauer, P.; Jaroniec, M. J.Comput. Chem. 1992, 13, 17. (11) Koopal, L. K; Vos, C. H. W. Langmuir l993,9, 2593. (12) Peterson, B. IC;Heffelfinger, G. S.; Gubbins, K. E.; van Swol, F.J. Chem. Phys. 1990,93, 1. (13) Sokolowski, S.;Fischer, J. J. Chem. Phys. 1990,93,6787;Mol. Phys. 1990, 71,393. (14)van Megen, M.; Snook, I. J. Chem. Phys. 1980, 72, 2907. (15) Bojan, M. J.; Steele, W. A. Langmuir 1993, 9, 2596.
0743-7463/95/2411-1297$09.00/00 1995 American Chemical Society
1298 Langmuir, Vol. 11, No. 4, 1995
Heuchel and Jaroniec
Table 1. Information about the Commercial Active Carbons Studied ~~
active carbon code CAL F200
GW RIAA RIB RIC a
BET surface areaa (m2/e;) 950 f 15 (1100) 830 f 15 (900)
source of carbon Calgon Calgon
810 f 15 (900) 1500 f 20 (1500) 1100 f 20 (1150) 990 f 20 (980)
Calgon Norit Norit Norit
~
short description and application from bituminous coals; used for decolorizingliquid mixtures from bituminous coals; used for purifying drinking water and adsorption of phenols, detergents, and pesticides from bituminous coals; used for purifying drinking water particle size 0.5 mm; liquid phase applications particle size 0.5 mm; liquid phase applications particle size 0.5 mm; liquid phase applications
Manufacture values are given in the brackets.
Vernov and Steele16-19carried out detailed simulations of benzene adsorption on graphite. Because graphitic microcrystals are the main structural units in active carbons, the results ofthese studies were very helpful to determine the interaction parameters for the local adsorption model and compare the resulting adsorption energies with those characteristic for the benzene-graphite system. This paper is organized as follows: First, adsorption experiments are described briefly. Next, the methods of calculation of the pore-size distribution [F(H)Iand adsorption energy distributions obtained from the gaslsolid [F(U)I and liquidlsolid [F(Uzl)l adsorption data are reported. Finally, the resulting distributions for six active carbons are compared and interpreted in order to get some information about the microporosity and surface heterogeneity of these active carbons.
Experimental Section Experimental adsorption isotherms of benzene on active carbons used in the current work were published previously.8 Both types ofequilibrium benzene isotherms, Le., those from the vapor phase and those from dilute aqueous solutions, were measured a t 293 K on six active carbons obtained from Calgon Carbon (Pittsburgh, PA)and Norit Co. (Amersfort, The Netherlands). Information about these carbons is summarized in Table 1. Other details are given in ref 8. Nitrogen adsorption isotherms were measured a t 77.2 K by using a volumetric apparatus ASAP-2000from Micromeritics. These isotherms were used to calculate the pore-sizedistributions for the carbons studied. Methods. Calculation of the Pore-Size Distribution. The nitrogen adsorption data a t 77.2 K were used to obtain information about the "geometrical" heterogeneity of active carbons studied. In this case the local isotherm that represents adsorption in uniform pores was calculated via the density functional theory.20-22This theory allows calculation of the density profile of nitrogen in a pore represented by two parallel walls separated by a distance, H.23It was assumed that the gas present in a slitlike open pore was in the equilibrium with the gas phase a t fixed temperature and pressure. The amount adsorbed at a given pressure can be easily calculated from the density profile. Repeating these calculations over a range of pressures gave the local adsorption isotherm z(H,p)for a defined pore size, H. By varyingH a set of local isotherms was determined numerically. These isotherms were used to determine the pore size distribution from experimental adsorption data according the following (16)Vernov, A.; Steele, W. A. Langmuir 1991,7,3110. (17)Vernov, A.; Steele, W. A. Langmuir 1991,7,2817. (18)Vernov, A.; Steele, W. A. Langmuir 1992,8,155. (19)Vernov, A.; Steele, W. A. Proceeding of Fourth International Conference on the Fundamentals of Adsorption, Kyoto, Japan, 1992,p 695. (20)Evans, R.Adu. Phys. 1979,28,143. (21)Tarazona, P.Mol. Phys. 1984,52, 81;Phys. Rev. A 1986,31, 2672. (22)Lastoskie, C.; Gubbins, K. E.; Quirke, N. Langmuir 1993,9, 2693. (23)Balbuena, P.B.;Gubbins, K. E. Fluid Phase Equilibria 1992, 76,21.
integral, which is a special form of eq 1:
203)= j-z03Jn F(H)dH
(2)
where Z(p) is the experimental adsorption of nitrogen a t the equilibrium pressure (p), z(p,H) is the quantity adsorbed at the same pressure (p) in the pore of size H,and F(H)is the pore-size distribution. The function F(H)describes the distribution ofthe pore volumes with respect to the pore size. The DFT software, basing on the density functional theory and a regularization method, was obtained from Micromeritics (Norcross, GAY4and used to invert eq 2 numerically with respect to F(H). Calculation of the F(U)-Distributionsfrom the Vapor Adsorption Data. The energy distribution F(U)was calculated from the adsorption data of benzene vapor by assuming that the adsorbent surface has a continuous distribution of adsorption sites with respect to the adsorption energy U. In this case, the surface coverage e(p) was represented by the integral equation that describes gas adsorption on an energetically heterogeneous solid: 2,3
(3) where Ol(p,V, is the energy-dependent local adsorption isotherm. The distribution function F(U),which quantitatively characterizes the adsorbent heterogeneity, after multiplication by dU denotes the fraction of the surface with adsorption energies between U and U -k dU. All advanced methods proposed t o calculate the adsorption energy distribution function from gas adsorption data by means of eq 3 require assumption of the local isotherm. Without additional information about the system one is forced to use a simple model for the local adsorption. In the current work the well-known Fowler-Guggenheim (FG) equation was applied:
with
where KL is the Langmuir constant for adsorption on monoenergetic sites and the preexponential factor K",(T) is expressed in terms of the partition functions for an isolated molecule in the gas and surface phases. "he above factor was estimated according to Adamson method.25~26In the FGmodel the lateral interactions are described by the interaction energy parameter, ut. An application of the FG local isotherm (eq 4) requires the knowledge of the surface phase capacity [Z,(p)l for adsorption in the micropores and the interaction parameter (w).To find the w-value that describes interactions between nearest neighbors, we used the simulation results for benzene on graphite." At T =298K,the average benzene-benzene lateral interaction energy increased linearly with the surface coverage up to two monolayers. (24) DFT-program,Micromeritics Instrument Corp., Norcross, GA, 1993. (25)Adamson, W. A.; Ling, I. Adu. Chem. Ser. 1961,33,51. (26)Adamson, W.A. Physical Chemistry of Surfaces; Wiley: New York, 1990.
Energy Distributions for Active Carbons Table 2. Sorption Parameters Obtained from Nitrogen Adsorption Isotherms by Using the DFT Software volume of the active total area total volume pores with carbon code in pores (m2/g) in pores (mug) H 50.75 nm in % CAL 770 0.37 30 F200 310 0.19 9 GW 300 0.18 6 RIAA 1150 0.63 19 RIB 990 0.42 45 RIC 1090 0.40 55 At the monolayer coverage the w-value was 1.25 kJ/mol. Although our experiments were done at a slightly different temperature (T= 293 K),the corresponding value kg = 150 K was assumed in all calculations. Assumption of the monolayercapacity, which allows conversion of the experimental quantity 203)to the surface coverage 0(p) = Z(p)/Z,, is very important for interpretation ofthe F(U)-function. If the value of the saturation capacity is used for Z,, as a quasi“monolayer”capacity, than peaks appearing on the distribution F(U)can represent either interactions ofbenzene molecules with surface sites or condensation ofbenzene molecules. In that case, the interpretation of F(U)only in terms of the “surface heterogeneity” is diffi~ult.~’An estimation of the total number of molecules adsorbed on the surface would be possible only if the true pore structure and the total surface of pores are known. The extraction ofthe monolayer capacity from the micropore capacity is difficult for microporous carbon^.^ Therefore, we used the micropore capacity obtained by using the &-methods instead of the monolayer capacity. We tried to convert the total specific surface areas calculated by the DFT software (see Table 2) to the monolayer capacity by using the value 0.35 nmVmolecule as the cross-sectional area of benzene, which resulted from the simulations of benzene adsorption on graphite a t T = 298 K.17 For some carbons the DFT specific surface areas were smaller than the BET ones and the resulting capacities were underestimated in comparison to those obtained by the standard BET method. Evaluation of F(U23 from Adsorption Data of Benzene from Dilute Solutions. Although in many papers devotedto adsorption from dilute solutions the gas-solid isotherm equations were used by replacing in them the adsorbate pressure (p) with the solute concentration (c), a rigorous treatment of adsorption from dilute solutions on a heterogeneous solid should be obtained on the basis of the theory of adsorption from liquid mixtures over the whole concentration region. For adsorption of a binary liquid mixture “1+2”ona heterogeneous solid surface, each adsorption site is characterized by the adsorption energies of both components, i.e., energies U1 and UZ.Because of the competitive adsorption of the components 1and 2, each adsorption site can be characterized by the energy difference Uzl= UZ- Ul,3 and then the local mole fraction x2s = xzS(xz,UZIj is a function of this difference. The total mole fraction of component 2 in the surface and may be expressed as follows: phase s is qts
where the normalized distribution function F(U21)characterizes the adsorbent heterogeneity in terms of Uzl. I t is worth keeping in mind the peculiarity of the distribution function defined in terms of the difference in the adsorption energies of both components. So, an energetically homogeneous surface in terms of the distribution F(U21) does not require the constancy of U1and UZto be maintained over the whole adsorbent surface. IfF(U1) and F(U2)have identical shapes and are shifted on the energy axis, then the difference UZI= UZ- UIis also constant for all adsorption sites. On the other hand, if, e.g., UI = const for all sites, than F(U21) should have a shape similar t o F(U2) but shifted on the energy axis. An approach based on the competitive character of adsorption for dilute solutions was proposed by Sircar,2swho started it with the definition of the excess adsorption. When the solute’s (27) Heuchel, M.; Jaroniec, M. Manuscript in preparation. (28) Sircar, S.; Myers, A. L.; Molstad, M. C. Trans. Faraday SOC. 1970,66,2354.
Langmuir, Vol. 11, No. 4, 1995 1299 (component 2) concentration is very small,the excess adsorption of the solute could be identified with the absolute adsorbed amount, i.e., nZe = n2 a t x2 x 0. For dilute solutions, one may further assume
a2 = xzyzm= ~4x290~
a, = x l = 1
(7)
where ai is the activity of the component i in the bulk phase and yz” is the activity coefficient of the solute a t its infinite dilution. yz” = l/x2s01is large for weakly soluble solutes. The ratio between the mole fraction of the solute and its limiting solubility is usually expressed by the ratio of the corresponding concentrations, c2/ c ~ With ~ these ~ ~ specifications . the well-known Everett isotherm for adsorption from binary liquid mixtures reduces to the following expression:
where noz is the saturation or monolayer adsorption capacity of the solute. The equilibrium constant Kzl is defined as follows:
(9) where KO,,(T) is the temperature-dependent factor. This factor is defined as the ratio of the molecular partition functions for the internal degrees of freedom of isolated molecules of the solute and solvent in the surface and bulk phases. ,K&(T) is usually assumed to be independent of Uzl (in the current calculations this factor was assumed t o be 1). In the case of competitive adsorption, the local isotherm eq 8 assumes that the saturation or monolayer capacities of the solute and solvent are equal. For the later discussion it is important to mention that eq 8 is also valid, if solute molecules are adsorbed preferentially. An extension of this framework to describe competitive adsorption from dilute solutions on heterogeneous surfaces, when solute and solvent have different sizes, is straightforward. Except for the adsorption energy distribution there are other distribution functions used in the literature to describe the adsorbent heterogeneity on the basis of adsorption data from dilute solutions. Choma et al.8 used a semiempirical DubininAstakhovZ9equation for the local isotherm and described the adsorbent heterogeneity attributed to the microporosity of active carbons. To get information about solid heterogeneity, Sircar6 calculated the function F(0) with 0 = A(azo- ap)/(RT),which in fact represents the distribution of the difference between the Gibbs free energies of the pure solute (2) and solvent (1)on a given type of adsorption site. The local isotherm is valid for very dilute solutions on sites characterized by a limiting selectivity parameter (So) and included the effects of the bulk-phase nonideality, unequal adsorbate sizes, and competitive adsorption. The integral equation for this adsorption model has the following form:
where r (=nol/noz) is the ratio of the saturation capacities of the solvent and solute. The limiting selectivity (So)is given by
(11) If entropic effects play a minor role in the adsorption process, than it would be possible to relate Gibbs free energy to the adsorption energy via the Gibbs-Helmholtz relationship.
Results and Discussion Pore-Size Distribution. The normalized pore-size distributions F ( H )for all six active carbons are shown in (29) Dubinin, M. M.; Astakhov, V. A. I2u. M a d . Nauk SSSR, Ser. Khim. 1971,71, 5.
1300 Langmuir, Vol. 11, No. 4, 1995
Hewhel and Jaroniec
1 o,lou 0
.
5
0
1
1
0 45
!!ilk, 0 40L 0 351
1I
CAL
io20
,
0 10
0
e0.30-
2030-
U
Y
c 0 25-
0.25-
1 0 20-
e 0 20-
0 15-
0 15-
:I:(~4,+ 1
0.00 0.05
0 05 0.00
F200
0 35 401
,
0
10 20 30 40 50 60
10 20 30 40 50 60
0 00 0
Pore Width [Angilrom]
0 40L
RIM
0.35-
0
.
0.451
,
0 435 0;
g0.30IL
E 0 251020
1020.
q a, ,
n ".""nn 0
10 20
,
30 40 50 60
Pore Wldlh [Anprlrom]
5
0
10 20 30 40 50 60 Pore Wldth [Angrtrom]
7
.-1 0 5.0 0.45. 0.40-
RIB
0.35-
RIC
20.30. U
E 0.25-
z= 0.200.15-
lil!!L-
0.00 0.05
0
10 20 30 40 50 60 Pore Width [Angrtrom]
0.100.050.ooL 0
10 20 30 40 50 60 Pore Width (Angrtrom]
Figure 1. Pore-size distributions [F(H)Iobtained from the experimental nitrogen adsorption isotherms for active carbons: CAL, F200,and GW (panel a) and RIAA,RIB, and RIC (panel b). Figure la,b. The corresponding pore volumes are summarized in Table 2. Analyzing the minimum of the benzene-graphite potential, Vernov and Steele17found that the most probable molecule-solid distance is 0.357 nm for horizontally adsorbed molecules and 0.475nm for those oriented perpendicularly to the surface. These data suggest that benzene molecules adsorb very strongly in the slit pores with widths of about 0.7 nm. The fraction of these small micropores was evaluated from the poresize distribution (cf. Table 2). The active carbons studied showed various properties. The F200 and GW carbons were quite similar and their total pore volumes were 0.19 and 0.18 m u g , respectively. For both carbons the fraction of micropores below 0.75 nm did not exceed 10%. In contrast, the total pore volume of CAL was nearly doubled (about 0.37 m u g ) and the fraction of small micropores was much higher. The RIAA active carbon had the highest total pore volume (0.63mL1 g), but only about 20% ofthe total pore volume is occupied by small micropores. The RIB and RIC carbons possessed similar pore volumes, i.e., 0.42 and 0.40 m u g , but the smallest micropores occupied about half of this volume. For RIC carbon the distribution of the smallest pores seemed to be more homogeneous (see sharp peak a t 0.7 nm in Figure lb) than that for RIB. Concluding, the RIB and RIC carbons possessed the highest microporosity, RIAA had the highest total pore volume, and F200 and GW contained the smallest fractions of the micropores below 0.75 nm. Energy Distributions from the GadSolid Adsorption Data. In adsorption from the gas phase the space adjacent to the pore walls (in which the adsorption field induced by the solid surface is significant) is filled a t low pressures. The adsorption energy distributions evaluated from the benzene vapor adsorption data for six carbons are shown in the upper rows of Figures 2 and 3. These distributions were calculated from the data points below the monolayer coverage of the total surface. The regu-
larization parameter was y = 0.1.lo The energy oflateral interactions was assumed to be w/kB = 150 K. For all six carbons the normalized distribution functions look similar. The main features of the distributions are a distinct peak located between 30 and 60 kJ/mol and a smaller peak or shoulder at the higher energy range (60-64 kJ/mol). The peak maxima of the gadsolid distributions are given in Table 3. They lie in a range from 41 to 47 kJ/mol and are in good agreement with other adsorption measurem e n t ~ ,which ~ ~ , provided ~~ the adsorption energy values between 38 and 42 kJ/mol. The small peakhhoulder found in the distributions is located between 60 and 64 kJ/mol. If the main peak represents the adsorption of benzene on the graphitic walls, then the small shoulder a t higher energies could represent the adsorption energy of benzene in very small pores. In the slitlike pore model this is the case when benzene molecules interact with both walls of the slit, e.g., if benzene is adsorbed in the pores of widths about 0.75 nm. We tried to relate the volume of these pores with the peak area representing the number of adsorption sites with energies greater 58 kJ/mol. For the Norit carbons there is a proportionality between these quantities, but not for Calgon carbons. The partially negative result can be explained by the fact that the main peak on the distribution cannot be attributed to benzene adsorption on the micropore walls only, but could be partly due to the benzene condensation in the small pores. The FG-model assumed to represent the local adsorption is not capable of distinguishing between these kinds of interactions. Energy Distributions from LiquidISolid Adsorption Data. Before discussing heterogeneity effects in adsorption from dilute aqueous solutions, the vapor adsorption of the pure solvent should be considered. It is known from experimental studies that interactions of (30)Isirikyan, A. A.; Kiselev, A. V. J . Phys. Chem. 1961,65, 601. (31)Pierotti, R.A.; Smallwood, R.E.J.Colloid Interface Sci. 1966, 22, 469.
fi!-jq
Energy Distributions for Active Carbons gasisolld
Langmuir, Vol. 11,No.4,1995 1301
1 !omLL nnl
-
""I
F200
006
-
5 0 02
1
0 02
0.00 20
20
60
40
80
100
U [kJ/mI]
.
1
6
40
bo
80
100
0 00
40
llquld/solid 1
1
80
60
100
U [kJimoll
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0 0
.
1
8
7
I
1 0
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I
20
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!oo\//
0 02
0 00
gas/solld
10
20
30
40
0
10
U,, [kJimoll
20
30
40
U,, LkJimoll
Figure 2. Energy distribution functions for benzene on active carbons CAL,F200, and GW. The curves (top row) represent the F(U)-distributionscalculated from the vapor-phase adsorptiondata for thep/pO-valuesbelow 0.05 using INTEG with the FG-model for the local adsorption. The curves (bottom row) represent F(U21) for benzene adsorption from aqueous dilute solutions for the same carbons using INTEG with Langmuir-type local isotherm. gaolsolid
gas/solid
gasisolld O0
8
;ooj
1
0 06
,
0 02
0 02
1
0 00
OM)
20
40
U IkJImoll
60
80
100
20
liquid/solld
80
40
80
q300
U IIcJimoll
u [kJlmolJ
Ilquld/solld
liquld/aolid
0 38
%k
008
004
004
0 00
000
0
10
20
30
40
ow
0
10
[kJlmoll
20
30
40
0
20
10
30
40
Ua3[kJlmoll
U,, [kJ/moll
Figure 3. Energy distributions as in Figure 2 for the RIAA,RIB, and RIC active carbons. Table 3. Peak Maxima of the Energy Distributions for Benzene on the Active Carbons Studied"
active carbon code CAL F200 GW
RIAA RIB RIC
U (kJ/mol)[peak height (mol/kJ)] main peak small peakb 44 (0.071) 47 (0.052) 44 (0.051) 41 (0.065) 44 (0.062) 46 (0.049)
64 (0.011) 64 (0.016) 60 (-) 62 (-1 60 (-) 63 (0.014)
% of sites with
U > 58 kJ/mol 17 23 23 12 19 23
(U) 5 75 (kJ/mol)
47.8 49.8 49.1 48.8 46.0 46.7
a Energy distributions were calculated by using the option of the INTEG program for the FG local adsorption model and patchwise surfaces. The F(U-distributionsfor the GW, RIAA, and RIB carbons do not have a small peak but only a shoulder.
water molecules with the pore walls are weak and the pore space is filled in a manner analogous to the mesopore filling, i.e., weak adsorption before a critical pressure and complete pore filling afterward. During the initial stage of the adsorption process, water molecules are anchored to the surface polar groups present on the pore walls. Next, the primary adsorbed water molecules attract via
hydrogen bonding other water molecules and form clusterlike structures. For a carbon immersed in water more or less the whole pore volume is filled with water. If a small amount of benzene is added to the waterlcarbon system, benzene displaces water molecules and fills the total volume of the carbonaceous pores. In a simplified picture, the situation in the pores is as follows: the pore
1302 Langmuir, Vol. 11, No. 4, 1995
Heuchel and Jaroniec
Table 4. Peak Maxima of the F(Uai)-Distributionsfor Benzene Adsomtion from Dilute Aaueous Solutions' ~~
CAL F200
GW RIAA RIB RIC a
% of sites with
Uzl (kJ/mol) [peak height (moVkJ)]
active carbon code
main peak
small peak
7.5(0.127) 7.0(0.141) 7.5(0.130) 7.5(0.142) 7.0(0.139) 7.0(0.108)
16.5(0.031) 18.0(0.021) 18.0(0.023) 18.0(0.014) 16.0 (0.034) 16.0 (0.061)
UZI> 13.5kJ/mol
(Uzd (kJ/mol)
15 14 18 9 18 30
7.8 8.5 9.3 8.5 9.2 10.3
Energy distributions calculated by using the option of the INTEG program for the local adsorption isotherm given by eq 8. 0 04 0
0
3
~
~
5
2 002
2
~
~
002
2
002
4. 0 0 1
4 001
b
001
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000
-
I
-50 -25
0
25
50
75 100
.,
0 04
-
1
0 0 3 a
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:
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B[J/gl
2
0
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50
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7 5 1w
-50 -25
BlJ/gl
0
25
50
7 5 100
B[J/gl
~
--I&0 0 1
001~
ow
0 00
-50 -25
002
0
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50
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100
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'i
001
0 00
0
25
BIJlgl
ewgi
?
50
75
100
-50 -25
0
25
50
75
100
B[J/gl
Figure 4. Distributions of the difference in the Gibbs free energy of benzene and water calculated from the liquidkolid adsorption isotherms of benzene on the active carbons studied by inverting eq 10.
volume is filled with a n aqueous solution except a small volume adjacent the graphitic pore walls, which is occupied by adsorbed benzene molecules. The equilibrium concentration of benzene near the pore walls is influenced by two opposite effects: (i)interaction with the wall and (ii) solvation phenomena in aqueous solution. Thus, the adsorption process can be modeled by two steps: (i) dissolvation of benzene out of the aqueous solution and (ii) its adsorption on the carbon surface. The heat of adsorption for benzene vapor on graphite (A,,& was estimated about 38 kJ/m0117and the solvation energy for transferring benzene from the gas phase to water at 298 K was reported as As0lvU= 30-32 kJ/m01.~~ The adsorption energy of benzene from a dilute aqueous solution estimated on the basis of AadsUand AsodJshould be about 6-8 kJ/mol. This value explains nicely the maxima on the distribution functions F(U21)at U21-values about 7-8 kJ/mol. Since U21 represents the difference in the adsorption energies of benzene and water, the adsorption energy for water on the carbon surface should be very small.
All energy distributions showed a second smaller peak (see Table 21, which could be related (similarly as in the case of the F(U-distributions obtained from vapor adsorption data) to enhanced interactions of benzene molecules with the walls of very small pores. The correlation of the heights of these small peaks with the volume fractions of fine pores, Le., pores with widths below 0.7 nm, was nice for the Norit carbons. In the case of the Calgon carbons this correlation was not visible, which was consistent with the results obtained on the basis of ~
~
~
~
~~~~~~
(32)Ben-Naim, A.Solvation Thermodynamics;Plenum Press: New York, 1987.
the gaslsolid adsorption data. This could be due to differences in the surface properties ofboth types of active carbons. A comparison of the distribution functions obtained from the gas-phase and liquid-phase benzene adsorption data showed a slightly higher resolution of the energy distribution from the liquid-phase adsorption. So, the small high-energy peaklshoulder on the energy distributions appeared to have better resolution in the case of energy distributions obtained from the liquid-phase adsorption data (see lower panels in Figures 2 and 3). This could be due to the special behavior of water in carbonaceous pores. In contrast to the common situation for adsorption from liquid mixtures, where the competitive adsorption of both components 1and 2 occur on the same sites, in the case of benzene/water systems only one component interacts mainly with the surface. Molecular interactions between benzene and neighboring water molecules reduce slightly its interaction with the carbon surface. Note that the distributions shown in Figures 2 and 3 and the distribution functions reported previouslf for the same gaslsolid and liquidholid systems are not identical: the distributions discussed in ref 8 were defined in terms of the adsorption potential (which is the negative change in the Gibbs free energy) whereas the current distributions are defined in terms of the adsorption energy (which is related to the enthalpy). The main reason that the adsorption potential distributions reported previously8coincided quite well and did not show the above mentioned small peakhhoulder was a n a priori assumption of the y-type distribution (which has the form of a single asymmetrical peak) for describing the experimental data. In the current work, the adsorption energy distributions were calculated by
Energy Distributions for Active Carbons applying a regularization method, which does not require an additional assumption about the shape of the distribution curve. F(@-DistributionFunctions. As was mentioned in the introduction, Sircar6 used the F(@-distribution to characterize the heterogeneity effects in adsorption from dilute solutions on porous solids. The F(8)-function provides information about the changes in the Gibbs free energies of benzene and water on a heterogeneous solid. Shown in Figure 4 are the F(B)-distributions for all six carbons. The differential F(@-distributionswere calculated from the liquidsolid adsorption isotherms of benzene by inverting the integral eq 10 with respect t o F(8). Equation 10containsthe local isotherm, which was derived for a competitive adsorption model by assuming different sizes of benzene and water molecules. In contrast to the energy distributions shown in Figures 2 and 3, the F(8)distribution functions (cf., Figure 4) possess one peak, which starts a t negative values of F(B). This part of the F(0)-distribution is related to the preferential adsorption of water molecules on oxygen functional groups present on the carbon surface and seems to be overestimated. Thus, the local adsorption model assumed in the integral eq 10 for adsorption of benzene from dilute aqueous solutions on microporous carbons seems to be less realistic than that discussed above. Note that acomparison oftheF(U21) andF(0)-distributions is not straightforward. Only if the entropic effects are constant over the micropore range should the F(8)-distribution be similar to the energy d i ~ t r i b u t i o n .Another ~~ possible source of disagreement of these distributions is the difference in the assumed models for the local adsorption. (33) Everett, D.H.Langmuir 1993,9 , 2586.
Langmuir, Vol. 11, No. 4, 1995 1303
Conclusions Comparative studies of the pore-size and energy distributions showed that the knowledge of the pore-size distribution is helpful in interpretation of the energy distribution b d i o n s . The resulting energy distributions for benzene adsorption on active carbons gave some evidence for interactions of benzene molecules with graphitic planes and very small micropores. It was shown that the energy distributions obtained from the adsorption data of benzene from dilute aqueous solutions can be interpreted by assuming a strong adsorption of benzene inside small pores and on the carbon surface (Langmuirtype adsorption)and extremelyweak interactions of water molecules with the carbon substrate. Due to this special behavior of benzenelwater solutions on the carbon surface the liquidsolid adsorption data gave the energy distributions that showed slightly higher resolution than those obtained from the gas-phase adsorption data. This result is unusual and its further study would be desirable. In addition, the current work demonstrated that simulations performed for the micropores of different properties were very helpful to interpret the adsorption isotherms on strongly heterogeneous solids like active carbons and to understand better the relation between microporosity and surface heterogeneity of these materials.
Acknowledgment. The authors wish to thank Professor J. Choma from the Military Academy (Warsaw, Poland) for sending the tabulated data for benzene adsorption and fruitful discussions, Dr. J. Olivier from Micromeritics, Inc. (Norcorss,GA), for providing the DFT software, and Mr. K. Koch from Leipzig University (Leipzig,Germany) for providing the nitrogen adsorption data. This work was supported partially by Corning, Inc. LA940739K
