A new adsorption–desorption model for water adsorption in activated carbon

CARBON

4 7 ( 2 0 0 9 ) 1 4 6 6 –1 4 7 3

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A new adsorption–desorption model for water adsorption in activated carbon D.D. Do*, S. Junpirom, H.D. Do Department of Chemical Engineering, University of Queensland, St. Lucia, Qld 4072, Australia

A R T I C L E I N F O

A B S T R A C T

Article history:

A new model is developed to describe the adsorption and desorption branches of water

Received 5 November 2008

adsorption in activated carbon. This model is an extension of a previous adsorption model

Accepted 23 January 2009

proposed by Do and Do [Do DD, Do HD. A new model for water adsorption in activated car-

Available online 3 February 2009

bon. Carbon 2000;38:767–73] to account for desorption. The desorption branch is resulted from the relaxation of water clusters inside the micropore to form superclusters because of the presence of neighbouring clusters. The rates of formation and decomposition of these superclusters are low enough to reflect the relaxation process, and the large hysteresis observed experimentally is resulted from the decomposition of the superclusters to smaller clusters before they are desorbed from the micropores. We test this model against a number of experimental data, and the description is reasonable and the dependence of the model parameters on treatment (oxidation or reduction) is discussed. Ó 2009 Elsevier Ltd. All rights reserved.

1.

Introduction

Water adsorption in activated carbon has been one of the important problems in purification, with examples such as volatile organic compounds (VOCs) removal from air where adsorption of VOCs is affected by the presence of water despite the hydrophobicity of carbon [1–4]. This is because of the presence of the functional groups on the surface, mostly at the edges. They act as the nucleating sites for water to attach to and grow into clusters. Depending on the concentration of the functional groups the initial adsorption of water at low concentration can be noticeable, and when the humidity is reasonably high the water adsorption capacity is very high and competes well with VOCs adsorption. Due to the importance of this problem, many works has been devoted to study water adsorption, both from theoretical and experimental points of view. Molecular simulation has also been used to further elucidate the mechanism of water adsorption, and much work is needed to progress further in this area.

The early attempt to analyse the water adsorption data is the work by Dubinin and Serpinsky (DS) [5,6], which was based on a kinetic theory of water sorption onto sorption sites at which the water concentration increase linearly with loading. An allowance for the finite capacity was also taken into account. This equation has some success in describing some experimental data, but it can not describe adsorption in activated carbon with high concentration of functional group. Modifications of the DS equation have limited success. Another limitation of the DS equation is that the maximum amount that water can be adsorbed in activated carbon is not clearly manifested in the model. The maximum capacity as described by the DS equation is a function of all parameters, especially the kinetic parameter. The dependence of the maximum capacity on kinetic parameters is debatable but one would expect that the pore volume should play a key part on the maximum capacity. The DA equation was also applied by Stoeckli et al. [7] because of the S-shape nature of this equation, which is distinctly observable when the characteristic energy is

* Corresponding author: Fax: +61 7 3365 2789. E-mail address: [email protected] (D.D. Do). 0008-6223/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2009.01.039

CARBON

4 7 ( 20 0 9 ) 1 4 6 6–14 7 3

sufficiently low. Although it describes some data, it does not point to the specific mechanism of water adsorption. As a result the application of the DA equation is very limited. Another equation is that proposed by Talu and Meunier [8], and it is basically involved the clustering of water molecules around chemisorption sites. However, it does not explain the role of the microscopic structure of activated carbon in the adsorption of water. Recently, a model based on cluster formation and penetration of clusters into the micropore was developed by Do and Do [9]. This model can describe different shapes of water adsorption isotherm for carbonaceous materials, and most importantly it accounts for the microstructure of activated carbon, with functional groups present at the edges of the basal planes of the graphitic units. Water molecules adsorb around the functional groups in the form of cluster and when this water cluster is large enough they will enter the micropores. Since the introduction of the Do and Do (DD) model, various modifications have been proposed by various authors. Neitsch et al. [10] proposed a modification to the DD model, namely cluster formation induced micropore filling (CIMF), which assumes the cluster size is variable. Cossarutto et al. [11] modified the DD model by using a Langmuir equation to describe adsorption on functional groups. Lagorsse et al. [12] applied the DD model and used the water cluster size of 7 molecules (heptamer). They also proposed an equation to describe desorption which involves two consecutive mechanisms of detaching the clusters in micropores and surface functional groups based on the cluster dissociation into smaller clusters. Furmaniak et al. [13] developed an equation which is termed heterogeneous Do–Do model (HDDM). This model accounts for the distribution of adsorption energy of the functional group. In addition, molecular simulation using grand canonical Monte Carlo has been applied to study the mechanism of water adsorption in porous solid [14–20]. These porous solids were carbon slit pores and single-walled carbon nanotubes which were incorporated with surface heterogeneity such as surface functional groups and defective surface. These works gave a better insight of molecular mechanism of water adsorption. However, the complexity of the real solids including a distribution of pore sizes and shape, distribution of types and locations of surface functional groups, are a challenging issue in this area. In this paper, we propose a new model for adsorption and desorption of water in activated carbon. Our premise for the hysteresis in the adsorption–desorption isotherm lies on the relaxation of water clusters inside the micropore. We will develop this theory in Section 2 and discuss the effects of model parameters in Section 3. Finally, we test the new theory with experimental data to show the potential of the new equation.

2.

Theory

We assume that carbon materials are composed of graphitic carbon and amorphous carbon. The volume space between the graphitic units composing of a few graphite layers constitutes micropores, and the functional groups are located at the edges of the basal planes of the graphite units. Due to the

1467

strong hydrogen bonding of water molecule with the functional group, the initial adsorption occurs at the functional groups, and further water adsorption will occur on top of the chemisorbed water molecules via the hydrogen bonding between water molecules. This process results in the growth of the water cluster as the pressure is increased. When this cluster has reached a critical size, it will attain a sufficient dispersive energy with the micropore to enter it [21,22]. This micropore adsorption will proceed with the progress of adsorption until the micropore volume is filled with water. Depending on the pore shape and size, the packing of water is not as effective as that of simpler molecules because of the requirements of correct orientation for hydrogen bonding. As a result, the volume occupied by water is usually smaller than that occupied by simple molecules, such as argon. What we have described is the mechanism for adsorption. For desorption, another process is involved. Once the water clusters have entered the pore, these clusters are then combined to form superclusters, resulted from the hydrogen bonding among water clusters to further reduce the free energy. This process is slow and is not detectable during the time frame of adsorption. Having described a mechanism for water adsorption and desorption, a mathematical model for adsorption and desorption can be developed. The following assumptions are made in our theoretical development: 1. The functional groups and the micropore units are randomly distributed. Each functional group interacts with one water molecule. 2. The rate constants for all processes are constant. 3. The water cluster consists of a finite number of water molecules.

2.1.

Adsorption theory

For the sake of completeness, the adsorption theory of Do and Do is summarized here as some of the equations will be used in the development of the new desorption theory. The hydrogen bonding of water (denoted as A) with a functional group S follows the typical mass action law (Assumption 1). A þ S $ AS

ð1Þ

The rates of adsorption and desorption per unit functional group are: ra ¼ ka ½A½S rd ¼ kd ½AS

ð2aÞ ð2bÞ

with the rate constants ka and kd being concentration-invariant (Assumption 2). We use the square bracket to represent the concentration. We will relate the water concentration in the gas phase [A] to pressure later. At equilibrium these two rates are equal, i.e. ½AS ¼K ½A½S

ð3Þ

The water complex AS will then form a site for further water adsorption by hydrogen bonding to form a complex A2S, which is in turn form a site for the formation of a complex A3S and so on. We have in general for the complexation of AnS

1468

CARBON

A þ An S $ Anþ1 S

4 7 ( 2 0 0 9 ) 1 4 6 6 –1 4 7 3

ð4Þ

X

ra ¼ kl;a ðVl  Vl ½Aa l Þ X

½An S

ð10aÞ

n¼aþ1

whose equilibrium requires the concentrations of relevant species to satisfy the following equation

rd ¼ kl;d ðVl ½Aa l Þ

½Anþ1 S ¼ Kp ½A½An S

where the rate of entry into the micropore is the product of the empty volume that is available for adsorption and the concentrations of the complexes that have enough water molecules to release clusters of size a. At equilibrium, we equate the rates of adsorption and desorption to get (with Kl being the equilibrium constant for micropore adsorption)

ð5Þ

for n = 1, 2, . . .. Here we assume that the equilibrium constant Kp is the same, irrespective of the cluster size, and this equilibrium constant is different from the constant K in Eq. (1). Our next task is to relate the concentrations of the free functional group [S] and the complex [AnS] in terms of the water concentration in the gas phase [A]. The conservation of the functional group sites requires: S0 ¼ ½S þ ½AS þ ½A2 S þ   

ð6Þ

Combining Eqs. (3), (5), and (6) leads to expressions for the free site concentration and water complexes written in terms of the water concentration in the gas phase: X S0 n ¼1þ KKn1 p ½A ; ½S n

½AS ¼ K½A;

n ½An S ¼ KKn1 p ½A

ð7Þ

for n = 2, 3,. . .. Having the concentrations of the free sites and all complexes {AnS}, the concentration of water clustering around the functional groups can be obtained by summing concentrations of all complexes ½An S, C m ¼ ½AS þ 2½A2 Sþ 3½A3 S þ    þ n½An S þ   . Combining this with Eq. (7), we obtain the desired expression for the water concentration around the functional groups, written in terms of water concentration in the gas phase. P n n1 n nKKp ½A ð8Þ Cm ¼ S0 P n1 1 þ n KKp ½An That is about adsorption in the neighbourhood of the functional groups at the edges of the micropores. The amount of water around the functional groups can not account for what is observed experimentally, but it is critical in the adsorption into the micropores as it is required for that to happen. Now we will consider the adsorption of water into the micropores. For this to happen, water molecules must enter the micropores in the form of a cluster because a single water molecule does not have sufficient potential energy to adsorb inside the micropore. This cluster is produced from the clusters of water around the functional group. We write the following equation to account of this detachment of water clusters from the water molecules around the functional group (Assumption 3) An S $ ½Aa l þ Ana S

ð9Þ

for n = a + 1, a + 2,. . .. Here ½Aa l represents the cluster residing inside the micropore. The parameter a represents the water cluster size inside the micropore (from the data of Kaneko group, this parameter is either 5 or 6, but we leave it as a parameter). The concentration in the micropore is defined in terms of volumes i.e. [Aa]l is the volume of water cluster per unit volume of the micropore. Let Vl be the volume of the micropore, then Vl[Aa]l is the volume occupied by water clusters. By assuming the mass action law for the processes of entry and departure from the micropore, we write the rates of these processes as follows:

½Ana S

ð10bÞ

n¼aþ1

½Aa l ¼

Kl

P

P Kl n¼aþ1 ½An S P n¼aþ1 ½An S þ n¼aþ1 ½Ana S

ð11Þ

Let VM be the molar volume of water, the number of moles of water adsorbed inside the micropore per unit micropore volume is: P ½Aa l Kl n¼aþ1 ½An S 1 P P ð12Þ ¼ VM VM Kl n¼aþ1 ½An S þ n¼aþ1 ½Ana S Substituting Eq. (7) into the above equation yields the following equation for the adsorbed concentration in the micropore written in terms of the gas phase water concentration. P n Kl n¼aþ1 Kn1 ½Aa l 1 p ½A ¼ ð13Þ P P n na1 VM VM Kl n¼aþ1 Kn1 ½Ana p ½A þ n¼aþ1 Kp Thus the total water adsorbed concentration is the sum of that for the functional group and that for the micropore, that is: P Kl n¼aþ1 fKp ½Agn P Cl ¼ Cls P Kl n¼aþ1 fKp ½Agn þ n¼aþ1 fKp ½Agna P ðK=Kp Þ n¼1 nfKp ½Agn P þ S0 ð14Þ 1 þ ðK=Kp Þ n¼1 fKp ½Agn where Cls is the saturation concentration of water in the micropore. The second term on the RHS of the above equation will reduce to the following form when the size of the cluster is allowed to increase indefinitely P Kl n¼aþ1 xn ðKf Þx P ð15Þ þ S0 Cl ¼ Cls P ð1  xÞ½1 þ ðKf  1Þx Kl n¼aþ1 xn þ n¼aþ1 xna where x ¼ K p ½A and Kf = K/Kp. The resulting second term in the RHS of Eq. (15) is simply the BET type equation. It represents a multi-clustering of each functional group with many water molecules. This term becomes infinite when x = 1, suggesting that x is the reduced pressure of water, and therefore the general adsorption isotherm equation is: P P Kl n¼aþ1 xn Kf n¼1 nxn P P þ S ð16Þ Cl ¼ Cls P 0 Kl n¼aþ1 xn þ n¼aþ1 xna 1 þ Kf n¼1 xn

2.2.

Desorption theory

The isotherm that we just described above is for adsorption. Here we postulate that once the water clusters have entered the pore they will rearrange themselves to attain lower free energy by forming hydrogen bonding with each other. This is a slow process and is not observable during the time frame of adsorption. Once adsorption has been achieved and sufficient time is allowed for the relaxation to complete,

desorption will occur as a result of the decomposition of superclusters to smaller clusters which are then desorbed from the micropore. It is this series of events that makes desorption of water to occur at a lower pressure, resulting in a hysteresis. Additional, the similar picture of relaxation process was seen in the simulation works for a system of fluid adsorption in mesoporous solid [23,24]. They described the hysteresis region as a result of a local minimum free energy, arisen from the co-processes between the very slow dynamics and equilibration of density states. Because of this slow dynamics the equilibration time plays a role in governing the hysteresis [19]. Let us now develop this desorption isotherm. The processes of forming clusters around the functional groups and entering the micropores are the same as before. The difference is the relaxation process. Here we assume that b water clusters inside micropore are going through the polymerization reaction to form a supercluster as follows: bAa () Aab

ð17Þ

This relaxation, per se, does not change the number of water molecules inside the micropore, but it does affect the equilibrium between the gas phase and the adsorbed phase. The rate constants for forward and reverse reactions are kR,f and kR,r, and they are lower than other rate constants that we have considered in the adsorption scheme above such that this relaxation process is not seen in the adsorption cycle. Equilibrium equation of Eq. (17) is: KR ¼

½Aab 

ð18Þ

½Aa b

where [Aab] is the concentration of the superclusters. The KR is the relaxation equilibrium constant, it implicitly accounts for a role of equilibration time, the larger KR the shorter equilibration time. Therefore the volumes of supercluster and regular cluster are Vl[Aab] and Vl[Aa], and the empty volume in the micropore is: Vl  Vl ½Aab   Vl ½Aa 

ð19Þ

which is the volume that is available in the desorption phase. The water concentration as number of moles per unit micropore volume is: q ¼ ð½Aab  þ ½Aa Þ=VM

ð20aÞ

b

q ¼ ðKR ½Aa  þ ½Aa Þ=VM

X

n¼aþ1

½Ana S

where x is the reduced partial pressure. For a given pressure x, the above equation can be solved for [Aa], and then the water adsorbed density is calculated in Eq. (20b). This set of equation is general and is applicable for adsorption branch in which we simply set KR to zero. As a special case of the relaxation where the parameter b = 1 (in which water cluster relaxes in orientation to gain lower free energy), we can solve Eq. (22) for the concentration of the regular cluster inside the micropore and finally the concentration of water in both micropores and the neighbourhood of functional groups P Kl ð1 þ KR Þ n¼aþ1 xn P P Cl ¼ Cls Kl ð1 þ KR Þ n¼aþ1 xn þ n¼aþ1 xna P Kf n¼1 nxn P þ S0 ð23Þ 1 þ Kf n¼1 xn

3.

ð21bÞ

n¼aþ1

Equating these two rates and following the same procedure as we did earlier for adsorption, we obtain: P ½Aa  n¼aþ1 xna Kl ¼ ð22Þ P ð1  ½Aa   KR ½Aa b Þ n¼aþ1 xn

Results and discussion

First we study the effects of model parameters on the behaviour of adsorption and desorption isotherms. Fig. 1 shows a typical water adsorption and desorption isotherm. The values for the parameters of the isotherm equation are shown in Table 1. All parameters are fixed except the parameter representing the adsorption into the micropore, Kl. We see that an increase in the partition coefficient into the micropore (Kl) results in a faster onset of adsorption. The isotherm curve basically can be divided into two distinct regions. The first region where the reduced pressure is about less than 0.2 represents the adsorption around the

ð20bÞ

The desorption isotherm is simply the relationship between this and the partial pressure of water in the gas phase, and therefore the remaining task is to relate [Aa] to the water partial pressure in the gas phase. This is done as follows. The rates of adsorption and desorption in micropore when the micropore is composed of both regular and superclusters: X ½An S ð21aÞ ra ¼ kl;a ðVl  Vl ½Aa   Vl ½Aab Þ rd ¼ kl;d ðVl ½Aa Þ

1469

4 7 ( 20 0 9 ) 1 4 6 6–14 7 3

Water adsorbed amount (mmol/g)

CARBON

20 Kμ = 200

15 Kμ = 100

10

5

0 0.0

0.2

0.4

0.6

0.8

1.0

Reduced pressure Fig. 1 – Plot of the water adsorption–desorption isotherm versus the reduced pressure. Effects of the partition coefficient into the micropore (Kl).

Table 1 – Parameters used in the computation of Fig. 1. Cls S0 Kf a Kl KR

20 mmol/g 0.2 mmol/g 100 6 100, 200 10

1470

CARBON

4 7 ( 2 0 0 9 ) 1 4 6 6 –1 4 7 3

functional group, where the mechanism is by hydrogen bonding with the functional group. The second region is greater than 0.2, where the water concentration around the

20

15

1.0 α = 20

10

0.8

5

0.6

[Aαβ ]

Water adsorbed amount (mmol/g)

25

α= 5

β= 1

0.4

0 0.0

0.2

0.4

0.6

0.8

β= 3

1.0

Reduced pressure

0.2

Fig. 2 – Effects of the cluster size on the adsorption– desorption isotherm.

0.0 0.0

0.1

0.2

0.3

0.4

Fig. 5 – Effects of the relaxation process on the desorption isotherm when considering the relationship between [Aab] and [Aa] at KR = 10 with different b.

20 KR = 30

15

a

KR = 10

25 Exp-adsorption Exp-desorption Model-adsorption Model-desorption

10

Water adsorbed amount (mmol/g)

Water adsorbed amount (mmol/g)

[Aα ]

5

0 0.0

0.2

0.4

0.6

0.8

1.0

Reduced pressure Fig. 3 – Effects of the equilibrium constant of the relaxation on the desorption isotherm.

20

BPL activated carbon 15

10

5

0 0.0

0.2

0.4

0.6

0.8

1.0

0.8

1.0

b

20

β=3

15

β=1

10

5

0 0.0

0.2

0.4

0.6

0.8

Reduced pressure Fig. 4 – Effects of the polymerization of the relaxation process on the desorption (KR = 10).

1.0

Water adsorbed amount (mmol/g)

Water adsorbed amount (mmol/g)

Reduced pressure

25

BPL-HNO3 activated carbon 20

15

10

5

0 0.0

0.2

0.4

0.6

Reduced pressure Fig. 6 – Fitting of the model equation to the series of BPLactivated carbon experimental data; original carbon (a) and acid treated carbon (b).

CARBON

1471

4 7 ( 20 0 9 ) 1 4 6 6–14 7 3

Table 2 – The values of the optimized parameters obtained from the fitting of model to the experimental data of BPLactivated carbon series. Sample: BPL

Adsorption

0.84 1.55

a

Kf

Kl

b

KR

17.1 15.6

11 6

13.9 3.7

234.5 99.7

1 1

7.6 1.1

functional group is high enough to induce the adsorption into the micropore. Fig. 2 shows the effect of the critical size of water cluster, a. The greater in this parameter, the slower is the onset of water adsorption into the micropore. This is simply because larger pressure is required for the formation of water clusters around the functional group to reach that critical size. Once these large clusters enter the pore they contribute rapidly to increase in the amount adsorbed. This is simply due to the large number of water molecules for each cluster. Thus an increasing in the critical size a, will result in a slower onset of adsorption and sharper rise in the isotherm once the onset has occurred. Similar behaviour is observed for desorption, i.e. we see the sharper decrease in the desorption branch. Next we show the effect of the relaxation in the micropore on the adsorption–desorption isotherms. Fig. 3 shows these isotherms for KR = 10 and 30. As expected, an increase in the relaxation equilibrium constant delays the desorption and hence the hysteresis is larger. Finally, we illustrate the effect of polymerization in the relaxation process in Fig. 4. It is seen that the width of the hysteresis loop decreases with increasing in b. This decrease is resulted from the ‘‘smaller’’ supercluster concentration, [Aa], and therefore the desorption is easier because of the lower number of superclusters that need to be desorbed. Fig. 5 shows how the supercluster concentration changes with b.

4.1.

BPL carbon

Experimental data of water adsorption on BPL-activated carbon samples [25] were used to test the theory. These samples are different in concentration of functional group. It is seen that the model describes well the adsorption isotherm (Fig. 6). In the case of desorption branch, the model captures the trend of the data. The values of parameters obtained from the fitting are tabulated in Table 2. It is shown that the acid oxidation increases the surface functional group as expected, as is revealed by the higher value of S0. The micropore capacity (Cls) decreases slightly after acid oxidation, and this is probably due to blocking of some micropores by the added functional groups. The critical size of water cluster (a) is seen

Exp-adsorption Exp-desorption Model-adsorption Model-desorption

25 20

Original-ACC-5092-15

15 10 5 0 0.0

0.2

0.4

0.6

0.8

Reduced pressure

b

Comparison with experimental data

Data of water adsorption on activated carbon are abundantly available in the literature. Comparing their data with those for hydrocarbons, the water equilibrium data seem to scatter a lot more and this is usually attributed to the difficulties in the measurement of water adsorption isotherm as well as the slow relaxation of water clusters, a phenomenon of which that we postulate in this paper.

30

25

Acid treated-ACC-5092-15 20

15

10

5

0 0.0

0.2

0.4

0.6

0.8

Reduced pressure

c

25

Water adsorbed amount (mmol/g)

4.

a Water adsorbed amount (mmol/g)

Original Acid treated

Cls (mmol/g)

Water adsorbed amount (mmol/g)

S0 (mmol/g)

Desorption

Hydrogen treated-ACC-5092-15

20

15

10

5

0 0.0

0.2

0.4

0.6

0.8

Reduced pressure Fig. 7 – Fitting of the model equation to the series of ACC5092-15 experimental data; original carbon (a), acid treated carbon (b), and hydrogen treated carbon (c).

1472

CARBON

4 7 ( 2 0 0 9 ) 1 4 6 6 –1 4 7 3

Table 3 – The values of the optimized parameters obtained from the fitting of model to the experimental data of ACC-509215 series. Sample: ACC-5092-15

Adsorption S0 (mmol/g)

Original Acid treated Hydrogen treated

0.17 3.89 0.12

Cls (mmol/g)

a

Kf

25.7 11.7 23.8

17 4 30

995.2 6.1 595.4

to be a function of surface functional group concentration, the higher concentration the smaller of cluster size. For pores with low or no functional group the cluster size has to be large to acquire sufficient potential to reside inside the pores. On the other hand, for pores with high concentration of functional groups, their presence can stabilize smaller clusters, allowing them to be confined within the pore. In fitting the desorption branch, we find that the optimized value for b is one. This means that the relaxation in the micropore is due to the re-orientation of water clusters. Another observation of the desorption parameters is that the relaxation equilibrium constant is greater with larger cluster size, suggesting that it is easier to form supercluster from large clusters.

4.2.

Activated carbon fiber cloth

Next, we test the model Eq. (23) with adsorption data of water on activated carbon fiber cloth, which are reported by Sullivan et al. [26]. The parent sample was treated with nitric acid to increase the concentration of functional group, and treated with hydrogen to reduce it. The data of these samples are used to test the model proposed here. We see that the model describes very well the data in adsorption branch, as shown in Fig. 7. The desorption model also describes reasonably well the data. The optimized parameters are summarized in Table 3. It is seen that the concentration of surface functional groups (S0) has a correct trend as expected as acid oxidation gave the highest concentration of surface functional group and hydrogen treating gave the lowest. Comparing the results of micropore capacity parameter, the acid oxidation shows the strong effect in decreasing from the original value of 25.7–11.7 mmol/g. This is similar to what we have observed earlier with BPL samples, which is argued to be the blocking effect of additional functional group. The cluster size is variable with a smallest size of 4 molecules for the acid treated sample, and the largest of 30 molecules for hydrogen treated carbon, supporting our argument earlier for BPL that the functional groups can stabilize the cluster, i.e. they can make the critical size of cluster smaller.

5.

Desorption

Conclusion

We have presented a new isotherm model to describe adsorption and desorption of water onto activated carbon. The hysteresis commonly observed experimentally is attributed to the slow relaxation of water clusters inside the micropore. We test the new equation with a number of experimental data of activated carbon with acid treatment and hydrogen treatment, and the description of the isotherms is found to

Kl 4321.1 68.8 37682.1

b

KR

1 1 1

20.0 4.4 764.6

be satisfactory. Inspection of the optimized values of the model parameters reveals a number of interesting points: (i) acid treatment increases the concentration of the functional group while hydrogen treatment reduces it, (ii) water capacity in the micropore is decreased with acid treatment and this could be due to the pore blockage by the functional group, and (iii) the water cluster size is smaller with acid treatment and this is argued to be due to the stabilization of small clusters by the functional group. This theoretical model remains to be justified with the molecular simulation, and it is the subject of our future investigation.

Acknowledgment This project is supported by the Australian Research Council.

R E F E R E N C E S

[1] Bagreev A, Bashkova S, Bandosz T. Dual role of water in the process of methyl mercaptan adsorption on activated carbon. Langmuir 2002;18:8553–9. [2] Salame II, Bandosz T. Adsorption of water and methanol on micro- and mesoporous wood-based activated carbons. Langmuir 2000;16:5435–40. [3] Salame II, Bagreev A, Bandosz T. Revisiting the effect of surface chemistry on adsorption of water on activated carbons. J Phys Chem B 1999;103:3877–84. [4] Salame II, Bandosz T. Interactions of water, methanol and diethyl ether molecules with the surface of oxidized activated carbon. Mol Phys 2002;100:2041–8. [5] Dubinin MM, Serpinsky VV. Isotherm equation for water adsorption by microporous carbonaceous adsorbents. Carbon 1981;19:402–3. [6] Dubinin MM, Zaverina ED, Serpinsky VV. The sorption of water vapour by active carbon. J Chem Soc 1955:1760–6. [7] Stoeckli F, Jakubov T, Lavanchy A. Water adsorption in active carbons described by the Dubinin–Astakhov equation. J Chem Soc Faraday Trans 1994;90:783–6. [8] Talu O, Meunier F. Adsorption of associating molecules in micropores and application to water on carbon. AIChE J 1996;42:809–19. [9] Do DD, Do HD. A new model for water adsorption in activated carbon. Carbon 2000;38:767–73. [10] Neitsch M, Heschel W, Suckow M. Water vapor adsorption by activated carbon: a modification to the isotherm model of Do and Do. Carbon 2001;39:1437–8. [11] Cossarutto L, Zimny T, Kaczmarczyk J, Siemieniewska T, Bimer J, Weber JV. Transport and sorption of water vapour in activated carbons. Carbon 2001;39:2339–46. [12] Lagorsse S, Campo MC, Magalhaes FD, Mendes A. Water adsorpiton on carbon molecular sieve membranes:

CARBON

[13]

[14]

[15]

[16]

[17]

[18]

[19]

4 7 ( 20 0 9 ) 1 4 6 6–14 7 3

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