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Adsorption of phenols from aqueous solutions equilibriacalorimetry and ki


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Adsorption of phenols from aqueous solutions: equilibria, calorimetry and ki‐ netics of adsorption Przemys?aw Podko?cielny, Krzysztof Nieszporek PII: DOI: Reference: To appear in: Received Date: Accepted Date: S0021-9797(10)01220-8 10.1016/j.jcis.2010.10.034 YJCIS 16298 Journal of Colloid and Interface Science 3 July 2010 15 October 2010

Please cite this article as: P. Podko?cielny, K. Nieszporek, Adsorption of phenols from aqueous solutions: equilibria, calorimetry and kinetics of adsorption, Journal of Colloid and Interface Science (2010), doi: 10.1016/j.jcis. 2010.10.034

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Adsorption of phenols from aqueous solutions: equilibria, calorimetry and kinetics of adsorption
Przemys?aw Podko cielny*, Krzysztof Nieszporek Faculty of Chemistry, Department of Theoretical Chemistry, Maria Curie-Sk?odowska University, pl. M. Curie-Sk?odowskiej 3, 20-031 Lublin, Poland

Abstract The brief theoretical description of the phenols adsorption from aqueous solutions on carbonaceous adsorbents i.e. activated carbons (ACs) and activated carbon fibers (ACFs) has been presented. The description includes adsorption equilibria, calorimetry as well as kinetics of adsorption. The generalized Langmuir-Freundlich (GLF) isotherm equation has been used to study of the cooperative effect of the surface heterogeneity and the lateral interactions between the admolecules. Theoretical isosteric heats of adsorption connected with the GLF model have been estimated too. Knowledge of both adsorption equilibria and heats of adsorption is fundamental for adequate description of any adsorption process. To correlate the kinetic data of the studied systems, the theoretical equations developed from Statistical Rate Theory (SRT) of Interfacial Transport were applied. The most advantageous of the proposed model of calculations is the set of common parameters appearing in each type of expressions, which significantly extends the possibility of their interpretation. Theoretical studies were fully reviewed using the literature experimental adsorption data. They included the data of phenols adsorption both on ACs and ACFs surfaces.

Keywords: Phenols; Activated carbons; Activated carbon fibers; Heat of adsorption; Kinetics
*

Corresponding author

E-mail address: przemyslaw.podkoscielny@poczta.umcs.lublin.pl Tel: + 48 81 5375518; Fax: + 48 81 5375685

1. Introduction Phenolic compounds are probably the most widely studied compounds in the field of wastewater treatment, as they are permanent pollutants released into the water by a large number of industries. Considering that adsorption of phenols on activated carbons (ACs) is one of the most important applications of ACs, a large number of studies have been carried out to examine this issue [1-20]. There are two most common physical forms, in which AC is used, i.e., powder-like AC and granular one. The activated carbon fiber (ACF) is a new form of activated carbon which has been extensively developed during the last twenty years. It is known that both ACs and ACFs have strongly heterogeneous surfaces [2,5-8,21-23]. The heterogeneity of surface stems from two sources known as geometrical and chemical. Geometrical heterogeneity is the result of differences in shapes and sizes of pores, but chemical heterogeneity is associated with different surface functional groups. Both chemical and geometrical heterogeneities contribute to the unique sorption properties of ACs and ACFs. ACFs have drawn increasing attention in recent years as novel adsorbents for purifying wastewaters from phenols [24-30]. The raw materials of ACFs are polyacrylonitrile fibers, cellulose fibers, phenol-formaldehyde resin fibers, pitch fibers etc. They are first pyrolysed and subsequently activated with the aid of carbon dioxide or steam (temp. 700-1000 oC) [25]. Consequently, there are as many different types of ACFs as there are kinds of precursors. ACFs are extremely microporous materials with high surface areas from 1000 m2/g to over 2000 m2/g [31,32]. Adsorption rates of ACFs are several dozen times higher than those obtained on the granulated AC due to the large external surface area of the fibers and to the direct connection of micropores to this area, which involves a decrease in mass-transfer resistance [27,31]. The small and uniform fiber diameter compared with that of granules of ACs allows for faster adsorption (and desorption) for the same AC weight [31,32]. Additionally, ACFs are characterized by narrow and uniform pore size distribution, so stronger interactions of ACF/adsorbate are possible. It is known that some ACFs perform normal adsorption even when the concentration of phenol in wastewater is in the few ppm range, which is not achievable by other adsorbents. The main objective of the present paper is proposal of the comprehensive theoretical description of the phenols adsorption from aqueous solutions on carbonaceous adsorbents i.e. ACs and ACFs. Such comprehensive description includes both adsorption equilibria and calorimetry as well as kinetics of adsorption. The generalized Langmuir-Freundlich (GLF) 2

isotherm equation has been applied to study of the cooperative effect of the surface heterogeneity and the lateral interactions between the adjacent molecules. Additionally, theoretical isosteric heats of adsorption connected with the GLF model have been estimated too. It is assumed that the heat of adsorption profile exhibits both the degree of energetic heterogeneity of liquid-solid system and the strength of the interactions between the neighboring admolecules [33,34]. So, the knowledge of both adsorption equilibria and heats of adsorption is fundamental for adequate description of any adsorption process. On the other hand, the adsorbent and the solution are brought into contact for a limited period of time in the industrial process of wastewaters purification [35,36]. Thus, knowledge of kinetic features is indispensible to provide the principal information required for the design and operation of adsorption equipment used for wastewater treatment. To correlate the kinetic data of the studied systems, the theoretical expressions developed from Statistical Rate Theory (SRT) of Interfacial Transport [37-45] have been applied. Our theoretical studies were fully examined based on the literature experimental adsorption data [46-49]. They included the data of phenols adsorption both on ACs and ACFs surfaces. We used the data of p-nitrophenol adsorption from aqueous solution on viscosebased ACF [46], the data of phenol adsorption from aqueous solution on oil-palm-shell AC [47], 2,4-dichlorophenol adsorption from aqueous solution on polyvinyl alcohol-based ACF [48] and lastly, the data of 2-bromophenol adsorption from aqueous solution on low cost slurry waste-based AC [49].

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2. Theory 2.1. Equilibrium adsorption In the scientific literature on the equilibrium adsorption phenomena, many isotherm equations can be found. Some of them are strictly empirical and others are obtained by using some theoretical assumptions. One of the most important theories describing adsorption equilibrium is the Integral Equation (IE) approach. IE can be used not only to obtain the new isotherm equations but also to make theoretical backgrounds for empirical isotherms. The fundamental expression of IE approach describing single-solute adsorption from dilute solutions on the energetically heterogeneous surface has the form [50-52]:

θ t ( c, T ) =

Nt = θ (ε , c, T ) χ (ε ) d ε M ?

(1)

where θ t (c, T ) is the average fraction of surface coverage by the molecules at an adsorbate concentration c , θ (ε , c, T ) is the fractional coverage of a certain class of adsorption sites, characterized by the adsorption energy ε (local isotherm), N t is the adsorbed amount, M is the adsorption maximum capacity, χ (ε ) is a differential distribution of the number of adsorption sites among various adsorption energies and ? is a range of possible energy values. For the mathematical convenience ? is often assumed to be the interval (?∞, + ∞). Most of the applications of IE approach relates to the Langmuir model of localized adsorption (as a local isotherm) and its extensions taking into account the interactions between adsorbed molecules. The really existing adsorption energy distribution functions are expected to have a complicated form. However, they can be approximated by some “smoothed” functions, the shape of which is described by a relatively small number of parameters. To calculate integral (1) many types of adsorption energy distribution functions χ (ε ) can be used. The Gaussianlike function, the so-called non-symmetrical function and the rectangular function have often been used to represent the real adsorption energy distributions. Use of Gaussian-like function in the Condensation Approximation (CA) and suitable local isotherm results in an isotherm equations which very well describe phenols adsorption. Such isotherm is LangmuirFreundlich (Sips) [5,6,8,16,22,23,51] assuming lack of lateral interactions between molecules. The isotherm which takes into account lateral interactions is e.g. generalized Langmuir-

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Freundlich (GLF) isotherm [23,42] as well as isotherms derived in terms of Flory-Huggins and Wilson vacancy solution models [23]. On the other hand, reliability of quasi-Gaussian distribution functions obtained by regularization method was independently confirmed by GCMC simulation method [22]. The Gaussian-like function has the following form [22,23]:
1

χ (ε ) =

η

exp

ε ? ε0 η
2

ε ? ε0 1 + exp η

(2)

where ε 0 is the most probable value of the adsorption energy and η ∈ (0,1) is the heterogeneity parameter which is proportional to the distribution width. Equation (2) is a normalized symmetrical distribution which is defined for ε ∈ (? ∞ ,+∞ ) . The simple way to take into account the interaction effects between the adsorbed molecules is to use the Mean Filed Approximation (MFA). When the surface is energetically homogeneous the MFA leads to the relation:
? s = ? s , 0 + ωθ

(3)

where ? s ,0 is the chemical potential of the reference system of non-interacting molecules and
ω is the parameter characterizing the interaction energy of a given molecule with those

adsorbed on the nearest-neighbour occupied adsorption sites. The isotherm which takes into account interactions between molecules is e.g. the FowlerGuggenheim (FG) isotherm [53-55]. It has the following form:
Kc exp

ε + ωθ ε + ωθ
kT kT

θ (ε , c, T ) =
1 + Kc exp

(4)

where K is the equilibrium constant, k- the Boltzmann constant, T- the temperature. When the surface is energetically heterogeneous Eq. (4) describes the fractional coverage of the homogeneous patch characterized by the adsorption energy ε . In the case of the energetically heterogeneous surface and when the adsorption energies are distributed between adsorption sites in the random order the FG equation takes the form:
θ (ε , c, T ) =
kT ε + ωθ t 1 + Kc exp kT Kc exp

ε + ωθ t

(5)

5

In this case, the potential of the average force field acting on adsorbed molecules (created by the presence of other molecules) is the function of the average surface coverage θ t . Unfortunately Integral (1) cannot be strictly solved with the energy distribution function (2) and with one of the local isotherms (4) or (5). The Condensation Approximation (CA) in such a common case is the most frequently used method to calculate this integral [50,55-59]. CA is based on the assumption that adsorption proceeds in an ideally “stepwise” fashion in the sequence toward increasing adsorption energies. It means that the local isotherm θ in Eq. (1) is replaced by the following step function:
θ (ε , c, T ) → θ c (ε , c, T ) =
0 for ε < ε c 1 for ε ≥ ε c

(6)

Then,

θ t (c, T ) = χ (ε ) d ε = ??(ε c )
εc



(7)

where ε c can be found from the relation:
? 2θ ?ε 2 =0
ε =ε c

(8)

For both isotherms defined by Eqs. (4) and (5), condition (8) is fulfilled when θ (ε = ε c ) = 1 / 2 . For random topography [60], ε c is defined as follows:

ε c = ?kT ln Kc ? ωθ t
Eqs. (7) and (9) [23]:
Kc exp

(9)

The equilibrium isotherm for the case of random topography can be obtained by combining
kT / η

ε0
kT

exp
kT / η

θt =

ωθ t η

1 + Kc exp

ε0
kT

ωθ t exp η

(10)

where η is the heterogeneity parameter which is proportional to the distribution width and

η ∈ (0,1) .
The above expression is known as the generalized Langmuir-Freundlich (GLF) equation for the case of lateral interactions between adsorbed molecules [42]. Isotherm (10) is useful to analyze the experimental adsorption isotherms in the function c vs.
N t . Although, in the literature the use of isotherm (10) in the linear form is frequently

6

suggested, the adjustment of the experimental isotherms by linear form of Eq. (10) can lead to overestimated values of the maximum capacity M . Practically, the correct choice of the model of the energetic topography in the case of real adsorption systems is difficult. Some reasons which can lead to proper use of the surface energetic topography model can be drawn from the analysis of the experimental procedure of the adsorbent preparation. 2.2. Calorimetry The correct analysis of the enthalpic effects accompanying the adsorption phenomena can lead to more valuable information about an adsorption system than adsorption isotherms [33,34]. The decrease of the isosteric heat of adsorption with adsorbate loading is characteristic for the energetically heterogeneous surfaces, but the increase of the heat curves is characteristic of homogeneous adsorbents and the cooperative interactions between the adsorbed molecules. Independence of the heat of adsorption of the adsorbed amount indicates the balance between the strength of the cooperative adsorbate - adsorbate interactions and the degree of heterogeneity of the adsorbent - adsorbate interactions. The basic equation which makes it possible to obtain expressions for isosteric heats of adsorption qst has the following form:
q st = ? k

? ln c ? (1 / T )

(11)
Nt

The simplest method to obtain the theoretical expressions for qst is the transformation of the adequate isotherm equation for ln c and its differentiation over (1 / T ) . For that reason we rewrite isotherm (10) as follows:
η / kT

θt cK exp = kT 1 ? θt

ε0

exp ?

ωθ t
kT

(12)

Combination of Eq. (11) and isotherm (12) leads to the expression for isosteric heat of adsorption qst for the surface characterized by random topography: q st = q st ,0 ? η ln where
q st , 0 = k ? ln K ' ? (1 / T )

θt + ωθ t 1 ? θt

(13)

(14)
Nt

7

and K ' = K exp{ε 0 / kT }. It can be seen that in the expression (13), the common parameters occur with those corresponding to the adsorption isotherm equation (10). So, only single quantity qst , 0 should be adjusted by using the experimental heat curves. The parameter qst , 0 frequently called as “non-configurational” isosteric heat only shifts the heat curves on the ordinate axis. 2.3. Kinetics As we mentioned in Introduction, the main goal of the present paper is the complete theoretical description of the adsorption experiment. Accordingly, now we focus our attention on the rate of adsorption. There are many papers dealing with the theoretical description of the experimental kinetic isotherms in the literature. In most cases authors use old, well known expressions, for example Lagergren [61], pseudo-second order equation [62,63] etc. In the adsorption systems, in which the rate of adsorption is not mainly controlled by diffusion effects, the speed of surface reaction depends on the interaction energy of the adsorbed molecules with surface and with neighbouring particles. The first, still commonly used equation of adsorption kinetics was developed by Lagergren [61]. It is the first order with respect to adsorption – the pseudofirst order (PFO) equation. It has the following form:
d N (t ) = k1 ( N ( e ) ? N (t )) dt

(15)

where N(t) is the amount adsorbed at time t, N(e) is the amount adsorbed at equilibrium and k1 is the pseudo-first-order rate constant for the adsorption process. After integration and applying boundary conditions, t = 0 to t and N(t = 0) = 0 to N(t) , the integrated form of equation (15) is obtained, ln( N ( e ) ? N (t )) = ln N ( e ) ? k1t The above linear form of PFO equation is known just as the Lagergren equation. Another simple and probably the most widely used expression is the adsorption dependent pseudo-second order (PSO) equation [62,63],
d N (t ) = k 2 ( N (e ) ? N (t )) 2 dt The linear dependence is the mostly used form of this equation, i.e. t/N(t) vs. t, (17)

(16)

8

t 1 1 = t+ N (t ) N ( e ) k2 ( N (e) ) 2

(18)

where k2 is the rate constant of pseudo-second-order adsorption. It is known that the transport of substance from the solution to the surface of the adsorbent occurs in several steps. However, the overall process of adsorption may be controlled by one or more steps, such as film (or external) diffusion, pore diffusion and adsorption on the pore surface, or combination of more than one step [64]. The intra-particle diffusion model [65,66] enables investigation of the possibility of intra-particle diffusion by using the following equation: N(t)=kid t2 + C thickness of the boundary layer [67]. If using equation (19) gives a straight line, then the adsorption process is controlled by intraparticle diffusion only. However, if the data display multi-linear plots, then more steps influence the adsorption process. The Bangham’s equation [68] can be used to check if porediffusion is the only rate-controlling step or not in the adsorption process, log log c0 kb m = log + α log t c 0 ? N (t )m 2.303V are the constants, ( < 1) and V is the volume of solution. (20) (19) where, kid is the intra-particle diffusion rate constant and C is a constant connected with the

where c0 is the initial concentration of the adsorbate in solution, m – the adsorbent mass per liter of solution, kb and diffusion. 2.3.1. Statistical Rate Theory (SRT) of Interfacial Transport At the beginning of 80’s a relatively new approach was proposed by Ward, Findlay and Rizk [37] which can be used to describe kinetics of many different experimental adsorption systems. Statistical Rate Theory (SRT) of Interfacial Transport is based on the simple assumption that the chemical potentials of the adsorbed molecules ? s and the bulk molecules
?b are the most fundamental quantities determining the features of adsorption kinetics. On the

If equation (20) represents well the data, then the adsorption kinetics is limited by the pore

basis of quantum mechanics and thermodynamics, Ward et al. have developed the following rate expression [37]:

9

? ? ?s ? ? ?b dθ = K ls exp b ? exp s dt kT kT

(21)

where K ls describes the exchange rate between the liquid and adsorbed state at equilibrium [42]. SRT was extensively used to study the adsorption/desorption phenomena both in the gassolid and liquid-solid phases [38-45]. The amount of adsorbate in the bulk phase strongly prevails over the adsorbed portion, so after the system is isolated and equilibrated, the adsorbate concentration in the solution, c, does not change much, c( e ) = c . Then, the chemical potential of the adsorbed phase ? s can be calculated by using isotherm (12). In the case of random topography, ? s /kT can be written as follows:

?s
kT

= ? ln K '+

η
kT

ln

θt ωθ t ? (1 ? θ t ) kT

(22)

The chemical potential of bulk phase ? b has the well-known form:

?b
kT

=

? b,0
kT

+ ln c

(23)

The rate of adsorption onto the surface with random topography can be obtained by using Eqs. (21), (22) and (23):
dθ t ωθ t = K ls K 0 c exp dt kT 1 ? θt
η / kT η / kT

θt

ωθ t 1 ? 0 exp ? kT K c

θt 1 ? θt

(24)

where K 0 = K ' exp{? b, 0 / kT } .

There is no doubt that the initial adsorbate concentration in the bulk phase c0 has significant influence on the rate of adsorption. The actual adsorbate concentration can be calculated from the following relation [39,42]:
c = c0 ? Mθ t V

(25)

where V is the volume of solution. While looking into Eq. (24), a problem in its practical application can be found. Namely, SRT expression includes the elements:

((1 ? θ t ) / θ t )η / kT

and ( θ t /(1 ? θ t ))η / kT . Considering

the case when the adsorption system is strongly energetically nonideal, these elements can lead to non-physical behaviour of Eq. (24) in the low or high surface coverage region:

10

θ t →0

lim

1 ? θt

θt

=∞

and

θ t →1

lim

1 ? θt

θt

=0

The high value of the heterogeneity parameter η / kT enhances such effects. It seems that this failure can be the result of Condensation Approximation application during the theoretical derivation of the GLF equation (10). Rudzi ski and P?azi ski [42] considered the SRT approach for strong surface heterogeneity and when the pure equilibrium isotherms are described by GLF equation (10), the appropriate approximation can be used. Namely, as both the heterogeneity of adsorbent – adsorbate interactions and the lateral interactions between the adsorbed molecules increase the adsorption potential (heterogeneity and the interaction effects become practically indistinguishable) - they can be represented by the so-called “effective heterogeneity” [42]. Then, the GLF equation (10) can be easily approximated by the simpler Langmuir-Freundlich equation [42]:

θt

(K c ) = 1 + (K c )
' kT

η

'

kT

(26)

η

Further, we can state that the same experimental data can be satisfactorily approximated by FG equation (5), too. So, while calculating the rate of adsorption by using SRT Eq. (24), we can assume η / kT = 1 (Eq. (5)). Now, the SRT expression can be used in nearly whole region of surface coverages. The negligence of the energetic heterogeneity of adsorbate- adsorbent interactions is correct especially in the low region of surface coverage because in this case adsorption occurs in a similar way to that on the energetically homogeneous surface. Summing up, we obtained SRT kinetic equation (24) by using equilibrium isotherm (12) which ensures the consistency of our complex theoretical studies.

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3. Results and discussion

In the theoretical section we showed theoretical expressions for isotherm, heat effects and rate of adsorption for the random topography of adsorption sites. Taking into account that ACs and ACFs have geometrically disordered surfaces, such sorbents are well represented by this type of surface topography. The most advantageous of the proposed model of our calculations is the set of common parameters appearing in each type of expressions. Such a model of calculations significantly extends the possibility of interpretation of the best-fit parameter values too. In many cases, the use of only one type of the experimental data can lead to erroneous conclusions. Looking for convincing verification of the developed theoretical equations we applied the following requirements: a) the experiment for a given adsorption system should involve equilibrium, kinetic and calorimetric data measured at the same or comparable temperatures as well as it should include the set of experimental data for a few temperatures; b) the experimental kinetic isotherms should be measured from very low adsorption times (surface coverages) up to the coverages close to that corresponding to equilibrium; c) the reported data should contain a possibly large number of experimental points. Our theoretical studies were extensively tested using experimental adsorption data taken from literature [46-49]. They included the data of p-nitrophenol adsorption from aqueous solution on viscose-based ACF [46], data of phenol adsorption from aqueous solution on oilpalm-shell AC [47], 2,4-dichlorophenol adsorption from aqueous solution on polyvinyl alcohol-based ACF [48], and finally the data of 2-bromophenol adsorption from aqueous solution using low cost slurry waste-based AC [49]. The concise porosity characteristics of adsorbents used as well as codes for them are included in Table 1. 3.1. Equilibrium adsorption The adsorption isotherms of p-nitrophenol from aqueous solutions on viscose-based ACF at 293 K, 308 K and 323 K are presented in Fig. 1. The symbols denote the experimental data [46], whereas the lines are theoretical isotherms estimated from generalized LangmuirFreundlich (GLF) equation (10) for the surface characterized by random topography. It can be seen that the adjustments of GLF to the experimental isotherms are very good. The results of calculations for equation (10) are summarized in Table 2. The table includes the values of monolayer capacity M, heterogeneity parameter k/ , the mean equilibrium constants 12

K ' = K exp(ε 0 / kT ) and the product of the interaction energy between two molecules adsorbed on two nearest – neighbour adsorption sites ω /k. The obtained parameters of energetic heterogeneity are dependent on the entire adsorption system: “adsorbent/phenolic compound”, but they are not property of adsorbent or adsorbate solely.
500

450 400 350 300 250 200 150

ACF1 / p-nitrophenol

Nt [mg/g]

293 K 308 K 323 K

100 -100

100

300

500

700

900

c [mg/dm3]

Fig. 1. Adsorption isotherms of p-nitrophenol from aqueous solutions on viscose-based ACF at various temperatures. The symbols are the measured values of isotherms [46] and the lines are the theoretical isotherms calculated from GLF equation (10). Generally, increasing solution temperature decreases the adsorption capacity M, indicating that the adsorption process is apparently exothermic. The best uptake of p-nitrophenol was observed at 293 K. The parameters k/ and /k are temperature-independent and should be common for all isotherms measured at different temperatures. The adsorption isotherms of phenol from aqueous solutions on oil-palm-shell AC [47] at five different temperatures are presented in Fig. 2. As previously, the perfect adjustment of GLF Eq. (10) to the experimental data is obtained.

13

350
AC1 / phenol

300 250

Nt [mg/g]

200 150 100 50 0
298 K 303 K 313 K 318 K 323 K

0

50

100

150

200

250

300

350

400

c [mg/dm3]

Fig. 2. Adsorption isotherms of phenol from aqueous solutions on oil-palm-shell AC at various temperatures. The symbols are the measured values of isotherms [47] and the lines are the theoretical isotherms calculated from GLF equation (10). Table 3 includes the results of calculations for the GLF equation. Parameter M values were found to decrease with the increasing temperature, which indicates that the adsorption process of phenol is favoured at lower temperatures. The adsorption isotherms of 2,4-dichlorophenol from aqueous solutions on polyvinyl alcohol-based ACF [48] at four different temperatures are presented in Fig. 3. The agreement between the theoretical and experimental isotherms is good as in the case of other adsorption systems studied. A comparison of adsorption isotherms at various temperatures shows that adsorption decreases with the increasing temperature. The results of calculations for GLF equation (10) are summarized in Table 4. The analogical observations relating to parameter changes can be seen as for other earlier analyzed adsorption systems.

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400 350 300

ACF2 / 2,4-dichlorophenol

Nt [mg/g]

250 200 150 100 50 0 -10 10 30 50 70 90 110
293 K 303 K 313 K 323 K

130

150

c [mg/dm3]

Fig. 3. Adsorption isotherms of 2,4-dichlorophenol from aqueous solutions on polyvinyl alcohol-based ACF at various temperatures. The symbols are the measured values of isotherms [48] and the lines are the theoretical isotherms calculated from GLF equation (10). It is believed that the isotherm shape can provide quasi-qualitative information on the nature of the solute-surface interaction. The adsorption isotherms in Figs. 1-4 belong to type L in Giles’s classification [69], except for the 2,4-dichlorophenol curve (Figure 3) which is similar to type H isotherm. Type L means that the aromatic ring adsorbs parallel to the surface and that no strong competition exists between the adsorbate and the solvent to occupy the adsorption sites. However, the H class (high affinity) results from strong adsorption at very low concentrations giving rise to an apparent intercept on the ordinate. The enhanced attraction with the surface in the case of 2,4-dichlorophenol is due to the electron-withdrawal phenomenon of the two chlorine substituents, as they reduce the overall electron density of the aromatic ring [2,6,18,70,71]. On the other hand, polyvinyl alcohol-based ACF [48] possesses very narrow micropores (- high adsorption potential), thus it can also be reason for the strong interactions of concentrations. The last analyzed system was the adsorption of 2-bromophenol from aqueous solutions on slurry waste-based AC [49] at 298 K and 318 K. The adsorption isotherms are shown in Fig. 4. Table 5 includes the results of calculations. It should be noticed that in the analyzed 2,4-dichlorophenol with the ACF surface at very low solute

15

system values of K ' = K exp(ε 0 / kT ) are expressed in dm3/mol (unit for concentration is mol/dm3). Contrary to the previously analyzed systems, the parameter M values were found to increase with the increasing temperature, indicating that the adsorption process is apparently endothermic.
240
AC2 / 2-bromophenol

200 160

Nt [mg/g]

120 80 40 0
298 K 318 K

0

0.0003

0.0006

0.0009

0.001

c [mol/dm3]

Fig. 4. Adsorption isotherms of 2-bromophenol from aqueous solutions on slurry waste-based AC at various temperatures. The symbols are the measured values of isotherms [49] and the lines are the theoretical isotherms calculated from GLF equation (10). 3.2. Heat effects of adsorption The next stage of our studies is analyzing heat effects accompanying adsorption of phenolic compounds on carbonaceous adsorbents studied [46-49]. Unfortunately, the experimental heats of adsorption were inaccessible for the analyzed adsorption systems, so we could calculate the theoretical ones only. From the theoretical analysis of the experimental equilibrium adsorption isotherms by GLF equation (10) we obtained the quantities: M, K ' ,
k / η and ω / k . These parameters can just be used to calculate the theoretical isosteric heats

of adsorption qst in terms of Eq. (13) - connected with the GLF model of adsorption for the case of random topography. Thus the occurrence of common parameters is the significant advantage of both equations. 16

Figures 5-8 present the theoretical isosteric heats of

adsorption of different phenolic

adsorbates from aqueous solutions estimated based on aforementioned Eq. (13). The calculations were carried out by using the parameters included in Tables 2-5, respectively.

Fig. 5. Theoretical isosteric heats of p-nitrophenol adsorption from aqueous solutions on viscose-based ACF, calculated based on Eq. (13). The calculations were performed by using the parameters included in Table 2. In Figures 6 and 7 only three theoretical heats are presented (for three different temperatures) because some curves approximately overlap each other and they are poorly visible. In all analyzed systems (Figs. 5-8), the isosteric heats of adsorption decrease with the increasing surface coverage which means that energetic heterogeneity plays a more substantial role than lateral interaction effects. It should be noted that the correctness of adjustment of Eq. (10) to the experimental adsorption isotherms (Figs. 1-4) is confirmed by the regular temperature dependence of the theoretical isosteric heats of adsorption for a given adsorption system (Figs. 5-8).

17

Fig. 6. Theoretical isosteric heats of phenol adsorption from aqueous solutions on oil-palmshell AC, calculated based on Eq. (13). The calculations were performed by using the parameters included in Table 3.

Fig. 7. Theoretical isosteric heats of 2,4-dichlorophenol from aqueous solutions on polyvinyl alcohol-based ACF, calculated based on Eq. (13). The calculations were performed by using the parameters included in Table 4. 18

All calculated heats of adsorption decrease from positive to negative values. It is not surprising because we presented the results of our calculations not in the form of relationship qst vs.
t

but by (qst – qst,0 ) vs.

t

. This was dictated by the fact that we did not have the

values of the parameter qst,0 which could only be calculated from fitting theoretical heats to experimental ones. However, as already mentioned earlier, experimental heats of adsorption were inaccessible for the analyzed adsorption systems. The parameter qst,0 i.e. nonconfigurational isosteric heat only shifts the heat curve on the ordinate axis. So, knowing the qst,0 parameter values we would obtain positive values of isosteric heats qst and use the coordinates qst vs. activated carbons. The sharp decrease of the isosteric heat at low surface coverage followed by a slower drop at higher coverage is observed for all analyzed systems with the exception of pnitrophenol /viscose based ACF system (Figure 5). For this system, the isosteric heat of adsorption has big values in the wide range of initial surface coverages. It is known that molecules are located first on the high energy sites. Big values of isosteric heat of adsorption are connected with adsorption of p-nitrophenol on the high energy sites located in micropores. Viscose-based ACF [46] is highly microporous material wherein the micropore volume represents ca. 74% of the total volume. Surface area (BET) of the fiber is large – 1413 m2/g. Other analyzed carbonaceous adsorbents have lower microporosity. On the other hand, although the SEM photograph of viscose-based ACF [46] allows to explore the surface on the mesopores level only, but it initially indicates the some surface not-uniformity after pnitrophenol adsorption. It is interesting, Dery?o-Marczewska and Marczewski [16] observed distinctly higher heterogeneity effects in the case of para-derivatives than ortho-derivatives (closeness of functional groups of ortho-derivatives may be "sensed" by the surface as a single, functional group). Besides they concluded that bigger size and/or larger number of groups of an phenolic adsorbate lead to a higher heterogeneity for the same surface. Generally, the adsorption mechanism of phenols is complex. It is often assumed that competition exists between solute adsorption in the smallest micropores and on active sites located in larger micropores. In the smallest micropores the “ - ” dispersion interactions are the strongest. However, it can be supposed that carbonyl and basic groups on the surface that take part in donor - acceptor complex formation with phenols are located mainly in larger micropores (and the increase in their concentration can favor adsorption in those pores) [14,70,72].
t

. The qst,0 parameter values are usually the order of twenty kJ/mol for

19

Fig. 8. Theoretical isosteric heats of 2-bromophenol from aqueous solutions on slurry wastebased AC, calculated based on Eq. (13). The calculations were performed by using the parameters included in Table 5. 3.3 Kinetics of adsorption The last stage of our investigations is theoretical description of adsorption kinetics. For this purpose the Statistical Rate Theory of Interfacial Transport was used [38-45]. Figures 912 present the comparisons of the experimental kinetic isotherms for the systems studied [4649] with the theoretical isotherms (lines) calculated from the SRT equation (24) for the surface characterized by random topography. The values of the obtained best-fit parameters are included in Table 6. The table presents the values of monolayer capacity M, the product of the interaction energy between two molecules adsorbed on the two nearest – neighbour adsorption sites ω /kT, the rate constants Kls as well as values of K 0 = K ' exp{? b, 0 / kT } . Besides, the technical parameters of the investigated adsorption systems [46-49] such as mass of adsorbent mads, initial sorbate concentration c0, volume of solution V are presented in Table 6, too. The agreement between the theoretical kinetic isotherms and the experimental ones is good for all analyzed systems which emphasizes the utility of the SRT model for the description of kinetics of phenols adsorption both on ACs and ACFs surfaces.

20

400

300

ACF1 / p-nitrophenol

N(t) [mg/g]

200

100 4 g ACF1/dm3 0

0

20

40

60

80

100

120

140

time [min]

Fig.9. Comparison of the experimental kinetic isotherms for p-nitrophenol / ACF1 [46] with the theoretical isotherms (lines) calculated from the SRT equation (24). The values of the obtained best-fit parameters are included in Table 6.
1.2

Aqueous phase concentration [mg/dm3]

120 100 80 60 40 20 0

AC1 / phenol

1.1 1 0.9 0.8

AC1 / phenol

N(t) [mg/g]

0.7 0.6 0.5 0.4 0.3 0.2 0.1

c0 = 38 mg/dm3 c0=117 mg/dm3

c0 = 38 mg/dm3 c0=117 mg/dm3
0 20 40 60 80

0

20

40

60

80

0

time [h]

time [h]

Fig.10. Comparison of the experimental kinetic isotherms for phenol / AC1 [47] with the theoretical isotherms (lines) calculated from the SRT equation (24). The values of the obtained best-fit parameters are included in Table 6.

21

240 ACF2 / 2,4-dichlorophenol 200

160

N(t) [mg/g]

120

80 T = 303 K T = 323 K

40

0

0

10

20

30

40

time [h]

Fig.11. Comparison of the experimental kinetic isotherms for 2,4-dichlorophenol / ACF2 [48] with the theoretical isotherms (lines) calculated from the SRT equation (24). The values of the obtained best-fit parameters are included in Table 6.
100 90 80 70 AC2 / 2-bromophenol

N(t) [mg/g]

60 50 40 30 20 10 0 0 2 4 6 c0= 69.2 mg/dm3 c0=103.8 mg/dm3

8

10

12

time [h]

Fig.12. Comparison of the experimental kinetic isotherms for 2-bromophenol / AC2 [49] with the theoretical isotherms (lines) calculated from the SRT equation (24). The values of the obtained best-fit parameters are included in Table 6.

22

Originally, except for phenol/AC1 system [47], the kinetics for other systems was described in terms of pseudo-second-order (PSO) model (systems: p-nitrophenol/ACF1 [46] and 2,4dichlorophenol/ACF2 [48]) or pseudo-first-order (PFO) model - 2-bromophenol/AC2 system [49]. It should be noted that recently a theoretical interpretation for (PFO) and (PSO) models based on SRT has been derived [35,38,39] which additionally indicates the universal character of this theory.
4. Conclusions

The comprehensive theoretical description of the phenolic compounds adsorption from aqueous solutions on activated carbons and activated carbon fibers has been proposed. Such full description includes adsorption equilibria, calorimetry and kinetics of adsorption. The most advantageous of the proposed model of our calculations is the set of common parameters appearing in each type of expressions. Such a consistent model of calculations extends the possibility of the interpretation of the obtained values of the best-fit parameters. The generalized Langmuir-Freundlich (GLF) isotherm equation connected with the quasiGaussian distribution of adsorption energies has been applied to investigate the cooperative effect of the surface heterogeneity and the lateral interactions between the admolecules. The perfect adjustments of GLF isotherm to the experimental data have been obtained. Then theoretical isosteric heats of adsorption connected with the GLF model have been estimated. For the all analyzed systems, the isosteric heats decrease with the increasing surface coverage which indicates that energetic heterogeneity plays a more essential role than lateral interaction effects. Additionally, correctness of adjustment of GLF isotherm to the experimental equilibrium adsorption data (Figs. 1-4) is confirmed by the regular temperature dependence of the theoretical isosteric heats of adsorption for a given adsorption system (Figs. 5-8). The last stage of our investigations was theoretical description of adsorption kinetics based on the Statistical Rate Theory (SRT) of Interfacial Transport. The chemical potential of the adsorbed phase
s

was determined in terms of the GLF isotherm. The agreement between the

theoretical kinetic isotherms and experimental ones was good for all analyzed systems. Therefore, the utility of the SRT model for the description of kinetics of phenols adsorption on the ACs and ACFs surfaces has been confirmed. Currently the SRT model is still extensively developed with success by distinguished research groups.

23

References

[1] [2] [3] [4] [5] [6] [7] [8] [9]

L.R. Radovic, C. Moreno-Castilla, J. Rivera-Utrilla, in: L.R. Radovic, (Ed.), Chemistry and Physics of Carbon, A Series of Advances, vol. 27, 2001, p. 227. A. D browski, P. Podko cielny, Z. Hubicki, M. Barczak, Chemosphere 58 (2005) 1049. A.P. Terzyk, J. Colloid Interf. Sci. 275 (2004) 9. C. Moreno-Castilla, Carbon 42 (2004) 83. P. Podko cielny, A. D browski, O.V. Marijuk, Appl. Surf. Sci. 205 (2003) 297. K. László, P. Podko cielny, A. D browski, Langmuir 19 (2003) 5287. K. László, P. Podko cielny, A. D browski, Appl. Surf. Sci. 252 (2006) 5752. P. Podko cielny, K. László, Appl. Surf. Sci. 253 (2007) 8762. F.C. Wu, R.L. Tseng, J. Colloid Interf. Sci. 294 (2006) 21. (2005) 11863.

[10] P.J.M. Carrott, P.A.M. Mourao, M.M.L.R. Carrott, E.M. Gonvalves, Langmuir 21 [11] A.R. Khan, R. Ataullah, A. Al-Haddad, J. Colloid Interf. Sci. 194 (1997) 154. [12] S. Haydar, M.A. Ferro-Garcia, J. Rivera-Utrilla, J.P. Joly, Carbon 41 (2003) 387. [13] J.M. Chern, Y.W. Chien, Water Res. 36 (2002) 647. [14] S. Nouri, F. Haghseresht, Adsorption 10 (2004) 79. [15] X.H. Deng, Y.H. Yue, Z. Gao, J. Colloid Interf. Sci. 192 (1997) 475. [16] A. Dery?o-Marczewska, A.W. Marczewski, Appl. Surf. Sci. 196 (2002) 264. [17] K. László, A. Sz cs, Carbon 39 (2001) 1945. [18] C. Moreno-Castilla, J. Rivera-Utrilla, M.V. Lopez-Ramon, F. Carrasco-Marin, Carbon 33 (1995) 845. [19] F. Stoeckli, M.V. López-Ramón, C. Moreno-Castilla, Langmuir 17 (2001) 3301. [20] M.L.Zhou, G. Martin, S. Taha, F. Sant'Anna, Water Res. 32 (1998) 1109. [21] P. Podko cielny, K. Nieszporek, Appl. Surf. Sci. 253 (2007) 3563. [22] P. Podko cielny, K. Nieszporek, P. Szabelski, Colloids Surf. A 277 (2006) 52. [23] P. Podko cielny, Colloids Surf. A 318 (2008) 227. [24] R.-S. Juang, R.-L. Tseng, F.-C. Wu, S.-H. Lee, Separ. Sci. Technol. 31 (1996) 1915. [25] C. Brasquet, P. Le Cloirec, Carbon 35 (1997) 1307. [26] R.-S. Juang, F.-C. Wu, R.-L. Tseng, J. Chem. Eng. Data, 41 (1996) 487. [27] C. Brasquet, P. Le Cloirec, Langmuir 15 (1999) 5906. [28] P.A. Quinlivan, L. Li, D.R.U. Knappe, Water Res. 39 (2005) 1663. [29] C. Brasquet, E. Subrenat, P. Le Cloirec, Water Sci. Technol. 39 (1999) 201. 24

[30] E.Ayranci, O. Duman, J. Hazard. Mater. B 124 (2005) 125. [31] R. T. Yang, Adsorbents: Fundamentals and Applications, John Wiley & Sons, Inc., Hoboken, New Jersey USA, 2003. [32] A. Sakoda, K. Kawazoe, M. Suzuki, Wat. Res. 21 (1987) 712. [33] W. Rudzi ski, K. Nieszporek, J.M. Cases, L.I. Michot, F. Villieras, Langmuir 12 (1996) 170. [34] K. Nieszporek, M. Drach, P. Podko cielny, Sep. Purif. Technol. 69 (2009) 174. [35] W. Rudzi ski, W. P?azi ski, J. Phys. Chem. C 111 (2007) 15100. [36] W. Rudzi ski, W. P?azi ski, Adsorption 15 (2009) 181. [37] C.A. Ward, R.D. Findlay, M. Rizk, J. Chem. Phys. 76 (1982) 5599. [38] W. Rudzi ski, W. Plazi ski, J. Phys. Chem. B 110 (2006) 16514. [39] W. Rudzi ski, W. Plazi ski, Appl. Surf. Sci. 253 (2007) 5827. [40] W. Rudzi ski, W. Plazi ski, Environ. Sci. Technol. 42 (2008) 2470. [41] W. Rudzi ski, W. Plazi ski, Langmuir 24 (2008) 5393. [42] W. Rudzi ski, W. Plazi ski, J. Colloid Interf. Sci. 327 (2008) 36. [43] S. Azizian, H. Bashiri, H. Iloukhani, J. Phys. Chem C 112 (2008) 10251. [44] S. Azizian, H. Bashiri, Langmuir 24 (2008) 11669. [45] K. Nieszporek, Appl. Surf. Sci. 255 (2009) 4627. [46] D. Tang, Z. Zheng, K. Lin, J. Luan, J. Zhang, J. Hazard. Mat. 143 (2007) 49. [47] A. C. Lua, Q. Jia, Adsorption 13 (2007) 129. [48] J.-P. Wang, H.-M. Feng, H.-Q. Yu, J. Hazard. Mat. 144 (2007) 200. [49] A. Bhatnagar, J. Hazard. Mat. B 139 (2007) 93. [50] M. Jaroniec, E. Madey, Physical Adsorption on Heterogeneous Solids, Elsevier, Amsterdam, 1988. [51] A. Dery?o-Marczewska, M. Jaroniec, in: E. Matijevi (Ed.), Surf. Colloid Sci., Plenum Press, New York, vol. 14, 1987, p. 301. [52] M. Heuchel, M. Jaroniec, Langmuir 11 (1995) 1297. [53] R.H. Fowler, Proc. Camb. Phil. Soc. 32 (1936) 144. [54] R.H. Fowler, E.A. Guggenheim, Statistical Thermodynamics, Cambridge, University Press, London, 1949. [55] W. Rudzi ski, K. Nieszporek, H. Moon, H.-K. Rhee, Heterogeneous Chem. Rev. 1 (1994) 275. [56] L.B. Harris, Surface Sci. 15 (1969) 182. [57] G.F. Cerofolini, J. Low Temp. Phys. 6 (1972) 473. 25

[58] G.F. Cerofolini, Thin Solid Films 23 (1974) 129. [59] S. Ross, J.P. Olivier, On Physical Adsorption, Interscience Publishers, Inc., New York, 1964. [60] T.L. Hill, J. Chem. Phys. 17 (1949) 762. [61] S. Lagergren, Handlingar 24 (1898) 1. [62] Y.S. Ho, G. McKay, D.A.J. Wase, C.F. Foster, Adsorp. Sci. Technol. 18 (2000) 639. [63] G. Blanchard, M. Maunaye, G. Martin, Wat. Res. 18 (1984) 1501. [64] M.S. Bilgili, J. Hazard. Mat. 137 (2006) 157. [65] W.J. Weber, J.C. Morris, J. Sanit. Eng. Div. ASCE 89 (1963) 31. [66] V.C. Srivastava, M.M. Swamy, I.D. Mall, B. Prasad, I.M. Mishra, Colloids Surf. A 272 (2006) 89. [67] K. Kannan, M.M. Sundaram, Dyes Pig. 51 (2001) 25. [68] C. Aharoni, S. Sideman, E. Hoffer, J. Chem. Technol. Biotechnol. 29 (1979) 404. [69] C.H. Giles, D. Smith, A. Huitson, J. Colloid Interf. Sci. 47 (1974) 755. [70] J.S. Mattson, H.B. Mark, Jr., M.D. Malbin, W.J. Weber, Jr., J.C. Critenden, J. Colloid Interf. Sci. 31 (1969) 116. [71] M. Streat, J.W. Patrick, M.J. Camporro Perez, Wat. Res. 29 (1995) 467. [72] A.P. Terzyk, J. Colloid Interf. Sci. 268 (2003) 301.

26

Table1 Main textural characteristics of adsorbents used [46-49]

BET Adsorbent Code surface area (m /g) ACF1 AC1 ACF2 viscose-based ACF [46] oil-palm shell AC [47] polyvinyl alcohol-based ACF [48] AC2 slurry waste-based AC [49] 380 1413 1183 702
2

Total pore volume (cm3/g) 0.69 0.69 0.28

Micropore volume (cm3/g) 0.51 0.38 -

Average pore diameter (nm) 1.95 2.33 0.7 (micropores) 3.9 (mesopores)

-

-

-

Table 2 Parameters characterizing adsorption of p-nitrophenol from aqueous solutions on viscosebased ACF [46] in terms of generalized Langmuir-Freundlich (GLF) (Eq. (10)) Adsorption System (K) p-nitrophenol / ACF1 293 308 323 (mg/g) 845.54 808.67 758.94 9.07*10
-4

Temperature

M

k

η
(1/K)

K exp

ε0
kT

ω
k

(dm3/mg) 0.00122 0.00133 0.00111

(K) 18.411

27

Table 3 Parameters characterizing adsorption of phenol from aqueous solutions on oil-palm-shell AC [47] in terms of generalized Langmuir-Freundlich (GLF) (Eq. (10)) Adsorption System (K) 298 phenol/ AC1 303 313 318 323 (mg/g) 389.62 377.11 277.54 232.41 201.20 0.0028 Temperature
M k

η
(1/K)

K exp

ε0
kT

ω
k

(dm3/mg) 0.00972 0.00819 0.00740 0.00889 0.00905

(K)

313.23

Table 4 Parameters characterizing adsorption of 2,4-dichlorophenol from aqueous solutions on polyvinyl alcohol-based ACF [48] in terms of generalized Langmuir-Freundlich (GLF) (Eq. (10)) Adsorption System (K) 2,4dichlorophenol/ ACF2 293 303 313 323 (mg/g) 384.43 369.14 364.03 348.70 0.00194 Temperature
M k

η
(1/K)

K exp

ε0
kT

ω
k

(dm3/mg) 0.10800 0.11367 0.08849 0.10754

(K) 603.576

28

Table 5 Parameters characterizing adsorption of 2-bromophenol from aqueous solutions on slurry waste-based AC [49] in terms of generalized Langmuir-Freundlich (GLF) (Eq. (10))

Adsorption System

Temperature

M

k

η
(K) (mg/g) 217.91 222.75 (1/K) 0.003

K exp

ε0
kT

ω
k

(dm3/mol) 1843.27 2304.79

(K) 374.359

2-bromophenol/ AC2

298 318

Table 6 Values of parameters used while fitting kinetic experimental data [46-49] presented in Figs. 912 by SRT equation 24

Adsorption System (code) ACF1 AC1

T

M

ω
kT

V

c0

m ads

K ls

K0

(K) 293 323

(mg/g) 409.4 167.9

(dm3) 0.5 0.05

(mg/dm3) 1000 117 38

(g) 4 1 1.00?10-2 1.29?10-3 3.54?10-4 2.39?10-5 1.09?10-3 5.24?10-7 6.75?10
-6

(dm3/mg) 1.99?10-2 5.54?10-5 9.45?10-5 4.55?10-1 1.36?10-2 204.8 20.8

0.0351 2.0249

ACF2

303 323

347.7 337.9 218.3

1.9137 1.7952 0.7619

lack of information 69.2 103.8

AC2

298

0.01

0.01

29

Caption to figures

Fig. 1. Adsorption isotherms of p-nitrophenol from aqueous solutions on viscose-based ACF at various temperatures. The symbols are the measured values of isotherms [46] and the lines are the theoretical isotherms calculated from GLF equation (10). Fig. 2. Adsorption isotherms of phenol from aqueous solutions on oil-palm-shell AC at various temperatures. The symbols are the measured values of isotherms [47] and the lines are the theoretical isotherms calculated from GLF equation (10). Fig. 3. Adsorption isotherms of 2,4-dichlorophenol from aqueous solutions on polyvinyl alcohol-based ACF at various temperatures. The symbols are the measured values of isotherms [48] and the lines are the theoretical isotherms calculated from GLF equation (10). Fig. 4. Adsorption isotherms of 2-bromophenol from aqueous solutions on slurry waste-based AC at various temperatures. The symbols are the measured values of isotherms [49] and the lines are the theoretical isotherms calculated from GLF equation (10). Fig. 5. Theoretical isosteric heats of p-nitrophenol adsorption from aqueous solutions on viscose-based ACF, calculated based on Eq. (13). The calculations were performed by using the parameters included in Table 2. Fig. 6. Theoretical isosteric heats of phenol adsorption from aqueous solutions on oil-palmshell AC, calculated based on Eq. (13). The calculations were performed by using the parameters included in Table 3. Fig. 7. Theoretical isosteric heats of 2,4-dichlorophenol from aqueous solutions on polyvinyl alcohol-based ACF, calculated based on Eq. (13). The calculations were performed by using the parameters included in Table 4. Fig. 8. Theoretical isosteric heats of 2-bromophenol from aqueous solutions on slurry wastebased AC, calculated based on Eq. (13). The calculations were performed by using the parameters included in Table 5. Fig.9. Comparison of the experimental kinetic isotherms for p-nitrophenol / ACF1 [46] with the theoretical isotherms (lines) calculated from the SRT equation (24). The values of the obtained best-fit parameters are included in Table 6. Fig.10. Comparison of the experimental kinetic isotherms for phenol / AC1 [47] with the theoretical isotherms (lines) calculated from the SRT equation (24). The values of the obtained best-fit parameters are included in Table 6.

30

Fig.11. Comparison of the experimental kinetic isotherms for of the obtained best-fit parameters are included in Table 6. Fig.12. Comparison of the experimental kinetic isotherms for obtained best-fit parameters are included in Table 6.

2,4-dichlorophenol / ACF2

[48] with the theoretical isotherms (lines) calculated from the SRT equation (24). The values 2-bromophenol / AC2 [49]

with the theoretical isotherms (lines) calculated from the SRT equation (24). The values of the

31

350
AC1 / phenol

300 250

Nt [mg/g]

200 150 100 50 0
298 K 303 K 313 K 318 K 323 K

0

50

100

150

200

250

300

350

400

c [mg/dm3]

The generalized Langmuir-Freundlich (GLF) isotherm equation has been applied to study the cooperative effect of the surface heterogeneity and the lateral interactions between the adjacent molecules.

32

Research highlights

? Energetic heterogeneity plays a more essential role than lateral interaction effects ? Utility of the SRT model for the description of adsorp. kinetics has been confirmed ? Set of common parameters in each type of theoret. eqs (consistency of approach)

33


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