- Email: [email protected]

Heterogeneity of active carbons in adsorption of phenol aqueous solutions P. PodkosÂcielny, A. DaÎbrowski*, O.V. Marijuk Faculty of Chemistry, Department of Theoretical Chemistry, Maria Curie-Skøodowska University, pl. Mariji Curie-Skøodowskiej 3, 20-031 Lublin, Poland Received 26 June 2002; accepted 30 September 2002

Abstract Energetic heterogeneity of activated carbons prepared from bituminous coals is investigated on the basis of adsorption isotherms of phenol from the dilute aqueous solutions. The Langmuir±Freundlich (L±F) equation has been used to estimate the monolayer capacity values of carbons studied. Adsorption energy distribution functions have been calculated by using algorithm INTEG based on a regularization method. Analysis of these functions for carbons provided signi®cant comparative information about their heterogeneity. # 2002 Elsevier Science B.V. All rights reserved. PACS: 68.45.D (solid±¯uid interfaces); 68.45.-v (solid±¯uid interfaces) Keywords: Adsorption from solutions; Heterogeneity; Activated carbons; Surface phase capacity; Statistical analysis

1. Introduction Phenolic compounds exist widely in the industrial ef¯uents such as those from oil re®neries and the coal tar, plastics, leather, paint, pharmaceutical, and steel industries. Since they are highly toxic and, in general, not amenable to biological degradation, methods of treatment are continuously being modi®ed and developed. Of all the methods, adsorption appears to offer the best prospects for overall treatment, especially for the ef¯uents with moderate and low concentrations. Because granular or powder activated carbon (AC) has a good capacity for adsorption of organic *

Corresponding author. Tel.: 48-81-537-5605; fax: 48-81-537-5685. E-mail address: [email protected] (A. DaÎbrowski).

matter, it is the most widely used adsorbent for this process [1±3]. ACs can be prepared from a variety of raw materials. The most frequently used precursors are hard coal, brown coal, wood, coconut shells and some polymers [4,5]. However, their application is usually limited due to its high cost. On the other hand, many agricultural and wood wastes such as cane pith, sawdust, maize cob, fruit kernels and straw can be the starting materials for the production of ACs [1,6±8]. Our main objective in this paper was investigation of the heterogeneity effects in phenol adsorption from water on the selected active carbons. We utilized the literature experimental data [9] concerning phenol adsorption from the aqueous solutions on the ACs prepared from bituminous coals. These carbons are widely used in removing organic compounds from

0169-4332/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 ( 0 2 ) 0 1 1 5 4 - 6

P. PodkosÂcielny et al. / Applied Surface Science 205 (2003) 297±303

298

industrial wastewater [10,11]. Generally, there are few papers devoted to the studies of heterogeneity in adsorption of aromatic compounds from water [3,12±16]. The Langmuir±Freundlich (L±F) equation was chosen as appropriate to estimate the value of the monolayer capacity. It is justi®ed by the fact, that shapes of the experimental adsorption isotherms re¯ect monolayer adsorption of phenol on the carbons studied. The ordinary Langmuir equation is very often used to estimate the monolayer capacity in phenolic aqueous solution adsorption [5±9], but we think that it is abused, taking into account that this equation can be properly used for the description of localized monolayer adsorption on the homogeneous surfaces. The energy distribution function is the fundamental value that describes heterogeneous properties of solid adsorbents. The Fredholm integral equation of the ®rst kind must be solved in order to ®nd this function. This integral equation is of numerically ill-posed nature. It means, that the small changes in the overall adsorption isotherm caused by experimental errors can in¯uence the distribution function signi®cantly [17,18]. The exclusive use of the least squares method for solving ill-posed problems can lead to distorted results. A regularization method [17±20] has been employed, which takes into account the ill-posed character of the integral equation. 2. Theoretical The L±F equation was used with success for estimation of the monolayer capacity value in the case of binary non-electrolytic liquid mixtures adsorption on the solid surfaces [21,22]. This equation was chosen as appropriate to estimate the value of the monolayer capacity in the case of dilute solutions too. It has the following form [14]: yt c

L F cl n K L F cl n0 1 K

(1)

where yt c is the fractional coverage of the adsorbent L F the equilibrium constant for a heterosurface, K geneous solid, c the solute equilibrium concentration, l the heterogeneity parameter 0 < l < 1, n the absolute adsorbed amount of the solute, and n0 the monolayer adsorption capacity of the solute.

The linear form of the L±F equation is given by ln

yt 1

yt

L l ln c l ln K

F

(2)

L F are made Calculations of parameters l and K assuming the linear regression model, Y AL F x BL F . Value of the monolayer adsorption capacity n0 is calculated by means of the Minuit procedure [23]. The error function has the following form: ^ Q

k X

nexp

ntheor 2

(3)

i1

where nexp denotes the experimental values of adsorbed amount of solute, i.e. phenol, but ntheor are the theoretical ones. As it was mentioned earlier [21,22], that it is easier ^ min vs. n0, changing value of to look for minimum: Q the parameter n0 with a de®nite ``step'' in the linear equation. However, this procedure does not always ensure ®nding a distinct minimum, and parameters of the monolayer capacity do not always have physical meaning. It has been shown that reliability of the parameters obtained in terms of linear equations depends on the results of statistical analyses [21,22,24]. In this work, such an analysis comprises the following steps: (1) determination of the sum of the squares of the remainders, (2) determination of the correlation coef®cient and realization of the signi®cance test for this coef®cient, (3) determination of the signi®cance test for the coef®cients AL F and BL F of the regression straight line, (4) calculation of the mean standard deviations L F , (5) determination of for the parameters l and K the con®dence interval for the heterogeneity parameter l, and (6) determination of the con®dence interval for the regression straight line, and of the tolerance interval for those experimental values that depart from the regression line. As particular stages of the statistical analysis have already been described [21,24], attention should be paid to those quantities that are characteristic of the L±F equation. The mean L F, standard deviations of the parameters, l and K have the corresponding forms: @l 2 2 2 sl saL F s2aL F (4) @aL F

P. PodkosÂcielny et al. / Applied Surface Science 205 (2003) 297±303

and s2K L

F

bL F bL F 2 2 exp sa L F aL F a2L F 1 bL F 2 2 exp sbL F aL F aL F 2bL F 2bL F 2 exp s aL F abL a3L F

(5)

F

The variances s2a ; s2b ; and s2ab can be calculated from the known relations [24]. The con®dence interval for the heterogeneity parameter, l, is as follows: aL

F

s L a

F

ta;n < l < aL

F

s L a

F

ta;n

(6)

where ta,n are the random variables tabulated of Student's t-test for a given signi®cance level of the test a and n k 2 [25]. All the points, (xi, yi) i 1; . . . ; k, beyond the tolerance limits may be neglected in the calculations [21,22,24]. The proper tolerance area can be written as L F

^yi

L F

s Di

L F

ta;n < E Di < ^yi

L F

s Di

ta;n

(7)

L F ^yi

axi b i 1; . . . ; k, where the function, represents a measure for the estimation of the expected L F value, Ei Y; sDi the root of the variance of the difference, Di yi Ei Y. Determination of the tolerance interval enables elimination of the data with a large experimental error, which allows to correct values of the monolayer adsorption of solute. 2.1. Calculation of the adsorption energy distribution function Generally, for the dilute solutions, the total fractional coverage of solute, yt c, in the surface phase may be expressed as follows [18,20]: Z E12 max Fx exp E12 =RT F E12 dE12 yt c E12 min 1 Fx exp E12 =RT (8) where F F c; yt is a model-dependent function [18], F E12 the normalized distribution function, E12 E1 E2 the energy difference of both components (i.e. phenol and water), x c=csol , where csol is

299

the solubility of the solute, R the universal gas constant, and T the absolute temperature. The function, F, accounts for all molecular interactions in the bulk and surface phases. It depends on the model assumed for those phases and on the topography of adsorption sites on the solid surface. If a lattice model is used to describe molecular interactions in both phases, F can be represented by the ratio of the molecular partition functions for the surface and bulk solutions [18]. In our calculations this function was assumed to be equal 1 [20]. The program INTEG [17] based on the regularization method was used for inverting Eq. (8) with respect to the energy distribution function, F E12 . A regularization method does not require any additional assumption about the shape of the energy distribution curve. Eq. (8) is the linear Fredholm integral equation of the ®rst kind, which can be written in a more general form as follows: Z b g y K z; yf z dz (9) a

where g y is a known function, which can be calculated from the experimental adsorption isotherm; the integral kernel, K z; y, represents the local isotherm of Eq. (8); and f z F E12 denotes the energy distribution function. The regularization method requires discretisation of the integral equation by a quadrature method. So, Eq. (9) needs to be transformed into a system of the linear equations, g Af. One-dimensional matrices g and f represent the functions g and f, respectively, and A is a two-dimensional matrix that represents the kernel, K z; y. Regularization consists in replacing the ill-posed problem of minimizing the functional, jjAf gjj2 , by a well-posed one, which smoothes the distribution function and distorts it only insigni®cantly. This can be made by adding the term, gjjCfjj2 , to the minimization functional [17]: S f jjAf

gjj2 gjjCfjj2

(10)

The regularization parameter g is a measure for weighing both terms in Eq. (10) and ||Cf||2 is de®ned in the following form [17±19]: Z b jjCfjj2 f 2 z dz (11) a

P. PodkosÂcielny et al. / Applied Surface Science 205 (2003) 297±303

300

By introducing integral (11) into Eq. (10), possible oscillations of the adsorption distribution function may be suppressed. 3. Experimental 3.1. Preparation and characterization of carbon samples The experimental adsorption data have been taken from literature [9]. Two Australian bituminous coals, Black Water (BW) and Mt Thorley (MT) were used as precursors of ACs. The major difference in the ultimate analysis of both carbons was the oxygen content 7.4 wt.% for BW carbon and 11.8 wt.% for the MT one. The O/C atomic ratio was 0.067 for BW carbon and 0.11 for MT one. Carbonization of the carbon samples was carried out in a vertical cylindrical furnace with nitrogen ¯ow at 100 cm3/min [9]. The samples were heated from room temperature to a maximum temperature of 1173 K. Following the carbonization process, the resulting chars were gasi®ed in the stream of CO2 at the maximum temperature for heat treatment. ACs with various extents of burn-off (%) were prepared. The low-temperature (77 K), nitrogen adsorption/ desorption isotherms were measured using the apparatus Micromeritics, ASAP 2000 [9]. Surface areas and micropore volumes of the samples were determined from the BET and Dubinin±Radushkevich (D± R) equation, respectively. Subtraction of the micropore volumes (from D±R equation) from the total amounts (determined at p=p0 0:98) provided the volumes of mesopores [26]. The average pore diameters were calculated assuming their cylindrical shape by means of the equation: d 4Vp =SBET , where Vp is the sorption capacity of pores.

Table 1 includes characteristics of ACs studied [9]. Each active carbon has been designated by using the nomenclature of its coal precursor followed by the burn-off level reached in CO2 gasi®cation. This table includes the speci®c surface area SBET, volume of the pores Vp, volume of micropores Vmicro, and external pore volume Vext, respectively. The last column The active includes the average pore diameter d. carbons studied are mainly microporous, as indicated by the results in the table. Table 1 shows that the surface area and the pore volume increase upon the activation process. The proportion of mesopore volume and the average pore diameter show increase with the burn-off level for the BW carbons, but this in¯uence is less signi®cant for MT carbons [9]. 3.2. Sorption from the dilute aqueous solutions of phenols The adsorption isotherms were determined by the static method for BW and MT active carbons for the phenol aqueous solution at 303 K. An aqueous solution (500 mg/dm3) was prepared by mixing an appropriate amount of phenol with distilled water. The measurement of isotherms consisted in placing a ®xed amount of the carbon sample (0.2±1.2 g) and 100 cm3 of the aqueous solution in a ¯ask. The ¯ask was then put in a constant-temperature bath for 24 h, with a shaker speed 100 rpm. Upon equilibration, all samples were ®ltered. The concentration of phenol over the sample was determined using the UV-Vis spectrophotometer (Shimazu, UV-1201) [9]. 4. Results and discussion The experimental adsorption isotherms of phenol from aqueous solutions on active carbons studied at

Table 1 Textural characteristics of the ACs studied [9] Active carbon

SBET (m2/g)

Vp (cm3/g)

Vmicro (m3/g)

Vext (cm3/g)

d (nm)

BW17 BW51

204 300

0.10 0.22

0.094 0.1452

0.006 0.0748

2.0 2.9

MT21 MT40

321 528

0.17 0.29

0.1513 0.2465

0.0187 0.0435

2.1 2.2

P. PodkosÂcielny et al. / Applied Surface Science 205 (2003) 297±303

Fig. 1. Adsorption isotherms from the aqueous phenol solutions on active carbons BW17, BW51, MT21 and MT40. Symbols are the measured values, but solid lines present the theoretical curves calculated by usage of the L±F equation.

303 K are presented in Fig. 1. The symbols denote the experimental points, but the solid lines present the theoretical isotherms calculated by usage of the L±F equation (1). The shape of the experimental isotherms re¯ects that the phenol uptake on the carbon surface is monolayer [27]. The results of calculations for L±F equation are summarized in Table 2. The table includes the value of monolayer capacity n0, the value of the mean equili L F , the heterogeneity parameter l, brium constant K ^ L F and the value of the the sum of deviation squares Q correlation coef®cient rL F , respectively. Column 7 presents the results of the signi®cance test referring to the correlation coef®cient rL F . Existence of the correlation between the variables XL F and YL F is

301

denoted by the symbol ``'' (`` '' denotes non-existence of correlation). The last two columns present the results of the signi®cance test of the coef®cients AL F and BL F . The parameters AL F and BL F are signi®cant (AL F 6 0 or BL F 6 0), so this fact is denoted by ``''. Otherwise there should be used the symbol `` ''. As all the results of the signi®cance tests are denoted by the symbols ``'', this indicates reliability of all the parameters obtained. Table 2 shows that the monolayer capacity values increase with the extent of carbon burn-off for BW and MT carbons. Besides, MT carbons have higher adsorption capacities than the BW ones. As can be seen, within the column 3, values of the heterogeneity parameters, l, decrease, which indicates increase of the energetic heterogeneity of adsorbents studied. However, Table 2 does not include all the results of statistical analyses performed with regard to the linear form of the L±F equation. For illustrative purposes, only the results for the active carbons, BW17 and MT21, will be discussed in detail. For the former carbon, the mean standard deviations are as follows: sl 0:0369 and sK L F 0:0615. The con®dence interval for the heterogeneity parameter, l, values can be determined from the inequality, 0:788 < l < 0:931. For the carbon, MT21, it holds sl 0:0253, sK L F 0:0769; the con®dence interval for l is 0:697 < l < 0:796. In Fig. 2, the illustrative results corresponding to the linear form of the L±F equation for adsorption of phenol on BW17 active carbon at 303 K, are shown. This ®gure presents the best-®t straight solid line, 90% con®dence interval placed between the dotted lines and 90% tolerance interval placed between the dashed lines. The symbols denote the values: ln c vs. ln yt = 1 yt . Fig. 3 shows the corresponding results for the active carbon, MT21.

Table 2 Parameters for the linear form of L±F equation (2) ^ Q

rL

Correlation

AL

1.553 3.381

0.041974 0.051640

0.994 0.996

2.075 7.489

0.032976 0.011475

0.997 0.997

Active carbon

n0 (mmol/g)

l

L K

BW17 BW51

0.803 0.862

0.860 0.780

MT21 MT40

1.239 1.683

0.747 0.522

F

F

Significance test for F

BL

F

302

P. PodkosÂcielny et al. / Applied Surface Science 205 (2003) 297±303

Fig. 2. Linear form of the L±F equation for adsorption of phenol on BW17 active carbon at 303 K. The best-®t straight solid line is denoted by the solid line, 90% con®dence interval is placed between the dotted lines and 90% tolerance interval is placed between the dashed lines.

Fig. 3. Linear form of the L±F equation for adsorption of phenol on MT21 active carbon at 303 K. The best-®t straight solid line is denoted by the solid line, 90% con®dence interval is placed between the dotted lines and 90% tolerance interval is placed between the dashed lines.

Fig. 4. Adsorption energy distribution function for the BW17 active carbon denoted by the solid line, compared to the distribution function for the BW51 active carbon (dashed line).

The results of calculations of the adsorption energy distributions are shown in Figs. 4 and 5. As can be seen, studied carbons exhibit broad adsorption energy distributions. The numerically stable functions were obtained with the regularization parameter, g 0:1. Fig. 4 presents the adsorption energy distribution function for the BW17 active carbon denoted by the solid line, compared to the distribution function for the BW51 active carbon (dashed line). The single peak of the energy distribution function for BW17 shows a maximum at about E12 E1 E2 18 kJ=mol. The peak for the BW51 active carbon with the maximum about 20.5 kJ/mol is lower, broader and ``shifted'' towards higher energy in comparison to the peak for BW17. Generally, direction of these changes is well correlated with the global microporosity increase of carbons studied, expressed by, Vmicro (see Table 1), regardless of the fact, that percent share of micropores diminishes during activation. Besides, the value of the heterogeneity parameter l (L±F equation) for BW51 is smaller than for BW17 (see Table 2). Otherwise, we know that the smaller the value of the heterogeneity parameter l the broader the adsorption distribution function; i.e. it covers a larger area of possible adsorption energies E12.

P. PodkosÂcielny et al. / Applied Surface Science 205 (2003) 297±303

303

with the carbon surface. As it has been expected, the energy distribution peaks proceeded to higher energy with the increase of micropore volumes. Besides, they became lower and more broadened. It coincides well with the changes of the heterogeneity parameter, l, values (i.e. l becomes smaller) in L±F equation. References

Fig. 5. Adsorption energy distribution function for the MT21 active carbon denoted by the solid line, compared to that for the MT40 active carbon (dashed line).

Fig. 5 presents the adsorption energy distribution function for the MT21 active carbon denoted by the solid line, compared to that for MT40 active carbon (dashed line). The peak of the energy distribution function for MT40 shows a maximum at about E12 21:2 kJ/mol, and it is lower, more broadened and ``shifted'' towards higher energy in comparison to the MT21 peak (maximum at about 19.5 kJ/mol). Remarks and conclusions are similar to the BW series of active carbons. 5. Conclusions The L±F equation is suitable for calculation of the values of the monolayer capacities in the case of dilute solutions and should be more frequently applied instead of the ordinary Langmuir equation, originally formulated for adsorption on homogeneous surfaces. The energy distribution functions are useful for comparing heterogeneities of different solids with respect to one selected liquid mixture, because uncertainties in evaluating F E12 are analogous for all systems studied. One should stress, that the function F E12 for dilute aqueous solutions should be interpreted by assuming strong interaction of phenol and very weak one of water

[1] M. Streat, J.W. Patrick, M.J. Camporro Perez, Water Res. 29 (1995) 467±472. [2] B.I. Dvorak, D.F. Lawler, G.E. Speitel, D.L. Jones, D. Badway, Water Environ. Res. 65 (1993) 827±839. [3] A. Deryøo-Marczewska, A.W. Marczewski, Langmuir 13 (1997) 1245±1250. [4] K. Laszlo, A. Bota, L.G. Nagy, Carbon 38 (2000) 1965±1976. [5] K. Laszlo, A. Szucs, Carbon 39 (2001) 1945±1953. [6] R.-S. Juang, R.-L. Tseng, F.-C. Wu, Adsorption 7 (2001) 65±72. [7] F.-C. Wu, R.-L. Tseng, R.-S. Juang, J. Environ. Sci. Health A 34 (9) (1999) 1753±1775. [8] M.N. Alaya, M.A. Hourieh, A.M. Youssef, F. El-Sejariah, Adsorpt. Sci. Technol. 18 (1) (2000) 27±42. [9] H. Teng, C.-T. Hsieh, J. Chem. Technol. Biotechnol. 74 (1999) 123±130. [10] M. Greenbank, S. Spotts, Water Technol. 16 (1993) 56±59. [11] W.-C. Ying, E.A. Dietz, G.C. Woehr, Environ. Progr. 9 (1990) 1±9. [12] M. Jaroniec, A. Deryøo, J. Colloid Interf. Sci. 84 (1981) 191. [13] G. MuÈller, C.J. Radke, J.M. Prausnitz, J. Colloid Interf. Sci. 103 (1985) 466 and 484. [14] M. Jaroniec, R. Madey, Physical Adsorption on Heterogeneous Solids, Elsevier, Amsterdam, 1988. [15] A.W. Marczewski, A. Deryøo-Marczewska, M. Jaroniec, J. Chem. Soc., Faraday Trans. 1 84 (1988) 2951. [16] W. RudzinÂski, R. Charmas, S. Partyka, J.Y. Bottero, Langmuir 9 (1993) 2641. [17] M.v. Szombathely, P. BraÈuer, M. Jaroniec, J. Comput. Chem. 13 (1992) 17. [18] M. Heuchel, P. BraÈuer, M.v. Szombathely, U. Messow, W.D. Einicke, M. Jaroniec, Langmuir 9 (1993) 2547. [19] M. Heuchel, M. Jaroniec, R.K. Gilpin, P. BraÈuer, M.v. Szombathely, Langmuir 9 (1993) 2537. [20] M. Heuchel, M. Jaroniec, Langmuir 11 (1995) 1297. [21] P. PodkosÂcielny, A. DaÎbrowski, Colloids Surf. A 162 (2000) 215. [22] P. PodkosÂcielny, A. DaÎbrowski, R. Leboda, Colloids Surf. A 182 (2001) 219. [23] F. James, M. Roos, Comput. Phys. Commun. 10 (1975) 343. [24] A. DaÎbrowski, P. PodkosÂcielny, Langmuir 13 (1997) 3464. [25] W. Oktaba, E. Niedokos, Mathematics and Basis of Statistical Mathematics, PWN, Warsaw, 1980. [26] F. Rodriguez-Reinoso, M. Molina-Sabio, M.T. Gonzalez, Carbon 33 (1995) 15±23. [27] M.J. Munoz-Guillena, M.J. Illan-Gomez, J.M. Martin-Martinez, A. Linares-Solano, C. Solinas-Martinez deLecea, Energy Fuel 6 (1992) 9±15.