3. CHEM. SOC. FARADAY TRANS..1994. 90(1. 783-786 Water Adsorption in Active Carbons described by the Du binin-Astakhov Equation Fritz Stoeckli* and Timur Jakubovt Chemistry Department, University of Neuchatel, Av. de Bellevaux 51, CH-2000Neuchatel, Switzerland Andre Lavanchy GRD Laboratorium , CH-3700 Spiez,Switzerland It is shown that the adsorption of water by a variety clf active carbons can be described within the framework of Dubinin’s theory. Owing to the low values of the characteristic energy, E (0.8-2.5 kJ mol-’), the Dubinin- Astakhov equation becomes S-shaped in the range 0 3 < pipo < 0.7 and provides a good basis for the fit of the adsorption branch of type V isotherms near room temperature. The parameters of the equation are almost temperature invariant and consequently a good agreement IS also found in many cases for the enthalpies of immersion into water, as predicted by the extension of Dubinin’s theory.The adsorption of organic and simple inorganic molecules b?, active carbons corresponds to type I or type I1 isotherms and is well described by Dubinin’s theory.’ -3 In this approach. the micropore volume is gradually filled by the adsorbate. whose density varies with the strength of the adsorption potential. It is also assumed that at the end of the process. the average density is close to that of the free liquid. The adsorption of water, on the other hand. corresponds to a type V i~otherm,~owing to the low affinity of thic adsorptive for carbonaceous surfaces.A specific model has therefore been proposed by Dubinin and Serpinski‘ to describe the adsorption branch of the isotherm. (No quanti-tative description exists, so far, for the desorption branch.i It takes into account the fact that the adsorption of uater depends essentially on the presence of hydrophilic or so-called primary centres. where the formation of clusters begins. This type of adsorption and its thermodynamic consequence< have been investigated by different authors.6 lo In the present paper, we show that in the case of micro- porous carbons the adsorption branch of the water isotherm can also be described by the classical equation of Dubinin and Astakhov. .Vd = N,, exp[-(APE)”] In this expression. N, represents the amount adsorbed in mmol-at temperature T and relative pressure p/po ; .V.3c,is the limiting amount adsorbed in the micropores, A = RT In ( pojp); and n and E are temperature-invariant parameters.which depend on the system under investigation. Typicall), ti varies between 1.5 and 6--7. It is convenient to use the actual volume of the micropore system W, = Na, V,. where LA rep-resents the molar volume of the adsorbate. Since W, is an invariant. one often uses the volumes I+’ and W, and their ratio. instead of N, and N,, . It has been shown that the influence of the adsorbate could be expressed by a scaling factor p. called the affinity c(1effi- cient, such that E = PE,. By convention, the referznce vapour is benzene and /?(C,H,) = 1. For typical organic and inorganic vapours adsorbed by active carbons.E, varies from 15 to 30 kJ mol-I and. as shown recently,” it is an inierse function of the average micropore width L/nm = 10.8 (E, -1 1.4). t Permanent address Institute of Physical Chemistry, Ruman Academy of Sciences, Leninsktt Prospek t 3 1. 1 17915 mom)^. Russia 4 mathematical analysis shows that eqn. (1) has an inflex- .on point, but in the case of high values of E it is found at my low relative pressures. Consequently, the isotherm is -xactically of type I. On the other hand, for small values of E rt>pically E < 2-3 kJ mol-I near room temperature), the iso- *herm becomes markedly S-shaped and it can be used to tiescribe the adsorption branch of a type V isotherm.It .tppears that the water adsorption isotherm can be fitted to cqn. (1) practically over the entire range of relative pressures, .darting near or below p/po = 0.1. Moreover, it is also found $hat in the case of water, E and n do not vary appreciably xith temperature, which explains the satisfactory agreement Kith the known thermodynamic consequences of eqn. , 1 ),2,12.I3 such as the differential heat of adsorption and the >:nthalpy of immersion into water. These observations suggest that Dubinin’s theory provides ,i satisfactory background for the description of water idsorption by microporous carbons. In a later study, we shall <:ompare this approach with the generalized equation pro- 2osed by Sircar.I4 The latter also describes adsorption iso- ‘herms of types I.IV and V, but the underlying model is .Merent. Theoretical Following the model proposed by Dubinin and Serpinski, the idsorption of water occurs around primary centres, where ,:lusters are forrned.l5 In the region of 0.4 < pip, < 0.8, the sotherm is given by PIP, = u/[c(u, + U)(l -ka)] (2) In this equation, a represents the amount of water, usually n mmol g-adsorbed at p’p, ; a, is the number of primary :entres characterized by the number of molecules directly ittached to them, implicitly a 1 : 1 ratio; k is a constant related to the total amount of water, as,adsorbed at pip, = 1 ind c is the ratio between the rate constants of adsorption ind desorption. The relevance of c has been described else- lvhere and it appears that it is related to the molar enthalpy ,f immersion into water.The range of validity of eqn. (2) has recently been extended qy Barton er by adding a fourth parameter. It has also been shown that for typical active carbons -reated in uacuo at 400-5oO‘C and containing a uniform type .,f primary site (probably of the carbonyl type), the enthalpy Jf immersion into water is given by6.’ Ahi,J g--‘ = -25a, -0.6(a,-ao) (3) 784 For carbons with important external surface areas, S,, one should add the term -(0.035 J mV2)S,, but in most cases this is a relatively small correction. A mathematical analysis of eqn. (1) shows that the Dubinin-Astakhov isotherm is always S-shaped, but this feature becomes significant only for small values of E/RT.This is illustrated by the model isotherms of Fig. 1, where T= 293 K, n = 2 and E varies from 25 to 1. Under these conditions, E/RT decreases from 10.2 to 0.41 and the inflex- ion point is gradually shifted towards higher values of p/po. As a consequence, the isotherm changes from type I to type V. Fig. 2, on the other hand, shows the influence of n on the steepness of the isotherm for a typical case (E = 2 kJ mol-' 1.o $ 0.5 0.0 0.0 0.5 1.o PIP0 Fig. 1 Model isotherms corresponding to eqn. (1) with T = 293 K, n = 2 and E = 1 (a),2 (b), 4 (c), 9 (d) and 25 (e) 1.o $ 0.5 0.0 0.0 0.5 1.o PIP, Fig. 2 Model isotherms corresponding to eqn. (1) with T = 293 K, E = 2 and n = 1 (a),2 (b), 3 (c), 5 (d)and 9 (e) J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 and T = 293 K). It appears that for n = 1, the isotherm is almost linear. From a mathematical point of view, the features illustrated by Fig. 1 and 2 reveal the usefulness of eqn. (1) for the description of water adsorption by active carbons, as well as other systems, in general. Moreover, provided that E and n are temperature invariant, the thermodynamic consequences of eqn. (1) should also be valid. As shown elsewhere, the fol- lowing expression can be derived for the net differential heat of adsorption associated with the Dubinin-Astakhov eq~ation'*'~-~~ qnet= E[(ln i/e)lln + (aT/nXln 1/8)'/"-'] (4) where 8 = NJN,, and a is the thermal expansion coefficient of the pure adsorptive.(However, it may be slightly different in the adsorbed state.) Since qne' = qSt-AHvap,the integration of eqn. (4) from 8 = 0 to 1, leads to the molar enthalpy of immersion into the corresponding liquid. It is a negative quantity, given by AhJJ mol-I = -E(1 + df)T(l + l/n) (5) where r is the classical 'Gamma' function. If one introduces the micropore volume, W0/cm3 g-', and the molar volume of the adsorbate, VJcm3 mol-l, eqn. (5) becomes AhJJ g-' = -EWo(l + olT)r(l + l/n)/Vm (6) For the classical case of the Dubinin-Radushkevich equation, where n = 2, one obtains an expression which has been used extensively for the characterization of active carbon~~*~~' ',16 AhJJ g-' = -EW,(l + ~T)Z'/~/~V~(7) From the tabulated values of the 'Gamma' function," it appears that if n varies from 2 to 6, the numerical value of eqn.(6) increases by only 5%. This suggests that the enthalpy of immersion depends mainly on the parameters W,and E (or BE,) of the Dubinin-Astakhov equation. Experimental A number of well characterized active carbons were used and their main properties are given in Table 1. The techniques applied in the present study (water adsorption between 263 and 293 K and immersion calorimetry at 293 K) have been described in detail earlier.2-'6 The carbons present a wide range of structural properties, with average micropore widths between 0.7 and 2 nm. On the other hand, the number of hydrophilic centres, a,, varies between 1.3 and 8% of the total amount of water adsorbed by the different solids.This means that the inflexion point of Table 1 Main properties of the microporous carbons, derived from the adsorption of organic vapours and of water, by using eqn. (1) organic vapour water adsorption carbon E0BJ mol-' w0/cm3g -1 L/nm TJK EJkJ mol-' W0/cm3 g-' n 1 CMS 26.2 0.25 0.8 293 1.86 0.24 4.20 275 2.01 0.27 4.12 2 U-03B 21.1 0.43 1.1 293 1.37 0.43 4.68 3 U-03N 16.9 0.52 2.0 293 0.87 0.52 2.67 263 0.98 0.50 2.94 4 u-02 20.0 0.43 1.2 293 1.19 0.45 2.32 5 N-125 16.8 0.64 2.0 293 1.17 0.57 4.22 6 DCG-5 21.2 0.54 1.1 293 1.79 0.49 1.87 7 PLW 23.9 0.46 0.9 293 2.18 0.45 6.46 8 PLWK 22.9 0.41 0.9 293 2.27 0.45 7.55 9 ALCA 19.4 0.50 1.3 293 2.23 0.45 7.67 10 MSC-V 27.1 0.17 0.7 293 2.39 0.17 3.28 11 MSC-VR 27.1 0.19 0.7 293 1.89 0.17 4.61 J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 the water adsorption isotherm is shifted from p/po =0.7 to 0.3, as a,/a, increase^.^.^ Calculations were based on the thermal expansion coeffi- cient and the molar volume of the pure water, assuming that these properties were not too different in the adsorbed state. Results and Discussion The water adsorption isotherms were fitted to the Dubinin- Astakhov equation [eqn. (l)] and the corresponding results for n, E and W,(H,O) are given in Table 1. As illustrated by the typical examples shown in Fig. 3, eqn. (1) leads to a good fit for the various samples.In the case of samples CMS and U-03N the adsorption of water was investigated between 263 and 293 K. It appears that for both solids, the parameters n and E do not vary appreciably with temperature. Although the range of tem-perature is still limited to 30 K, this suggests that the require- ment for temperature invariance is fulfilled to a good approximation, at least near room temperature. As illustrated in Fig. 4,a plot of W/W, vs. RT In (po/p) leads to a unique characteristic curve1,* for each carbon, as found in the case of organic vapours. This also corresponds to an earlier observa- tion by Hassan et al.," for the adsorption of water by carbon BPL between 288 and 308 K. /* a 0 0.4 0.8 P/Po Fig.3 Fit of the water adsorption isotherms to eqn. (1) for carbons N-125 at 293 K (m), U-02 at 293 K (0)and CMS at 275 K (A).See also Table 1. 1 2 RT In(p,/p)/kJ mol-' Fig. 4 Characteristic curves for the adsorption of water by carbons CMS at 275 and 293 K (0,m) (a) and U-03N at 263 and 293 K (0,rn) (4 Table 2 Calculated and experimental enthalpies (in J g-') of immersion of the active carbons into water at 293 K Ahi 1 27 27 2 28 32 3 21 35 5 31 32 6 44 41 7 47 45 8 50 45 9 49 44 10 19 23 11 15 14 It is, therefore, not surprising to find a relatively good agreement between the enthalpies of immersion into water calculated by eqn. (6) and the corresponding experimental values obtained at T = 293 K (Table 2).In some cases, however, a poor agreement was observed. One reason may be the ageing of the material (some isotherms were determined several years ago), and/or the presence of water-soluble materials in the active carbon, two factors which affect Ahi. From a practical point of view, the description of water adsorption by means of the Dubinin-Astakhov equation [eqn. (l)] presents a number of advantages. First, it means that a relatively simple relation can be used to predict the adsorption isotherm at different temperatures and relative pressures, as in the case of organic vapours. In practice, only one isotherm is needed at a convenient temperature, for example 293 K, and the results can even be cross-checked with the corresponding enthalpy of immersion.However, the important property of temperature invariance must still be checked over a wider range of temperature and an important test will be provided by the comparison of Ah, measured at different temperatures (ca. 278 to 308 K) with the values pre- dicted by eqn. (6). Secondly, since n and E are almost temperature invariant, eqn. (4) can be used to calculate the corresponding heat transfer in the system. This possibility is of great importance in the case of dynamic adsorption of vapours by active carbons in the presence of water, and in the computer simula- tion of such proces~es.'~ From a theoretical point of view, on the other hand, the present study shows that nearly 50 years after its formulation, Dubinin's theory for the filling of micropores can be extended to the adsorption of water by active carbons.It is likely that this description also applies to other vapours with type I11 or V isotherms on carbons and possibly on other microporous solids. This aspect will be presented later. It is obvious that the present description can be transposed to the case where the water adsorption isotherm begins as type I at low pressures. The overall isotherm may simply be considered as a superposition of Langmuir and Dubinin- Astakhov contributions, including the thermodynamic conse- quences of the two models. At the present time, it is not possible to define exactly the meaning of parameters n and E in the case of water adsorp- tion.As shown above, mathematical modelling suggests that the 'steepness' of the isotherm depends on n,whereas E has a direct influence on the position of its inflexion point. As shown it depends on the state of oxidation of the surface. The data presented in Table 1 suggest that no direct corre- lation exists between E and the classical characteristic energy, E,, associated with type I or I1 isotherms. This is not too Table 3 Correlation between the characteristic energies, E/kJ mol-', obtained from eqn. (1) and (8),for T = 293 K E 1 5.6 1.86 2.04 2 2.5 1.37 1.25 3 2.1 0.87 1.18 4 1.3 1.19 0.98 5 1.6 1.17 1.03 6 3.6 1.79 1.57 10 7.9 2.39 2.65 11 3.8 1.89 1.58 surprising, since the adsorption of water depends essentially on specific sites, as opposed to the case of organic vapours where the adsorption potential within the micropores domi- nates the process of volume filling. One may therefore expect that E depends more on the hydrophilic/hydrophobic charac- ter of the solid expressed by a,/a,, than on the average micropore size.A possible correlation is suggested by comparison of eqn. (3) and (6) for the enthalpies of immersion into water, which are not mutually exclusive, and the following empirical rela- tion can be obtained, As shown in Table 3, for a number of systems the values of E obtained from eqn. (1) and (8), and T = 293 K, agree within 15-20%, which indicates some degree of self-consistency. Eqn.(8) also suggests that at room temperature E should be close to 0.6 kJ mol-l, when a, vanishes. The corresponding isotherm, with an average value of n near 3-4, should therefore describe the adsorption of water in the micropores of pure carbon. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 At the present time, further work is needed to explore the consequences of eqn. (1) and results will be presented in due course. References 1 M. M. Dubinin, Carbon, 1989,21,457; 1989,29,481. 2 D. C. Bansal, J. B. Donnet and H. F. Stoeckli, Active Carbon, Marcel Dekker, New York, 1988. 3 H. F. Stoeckli, Carbon, 1990,28, 1. 4 S. J. Gregg and K. S. W. Sing, in Adsorption, Surface Area and Porosity, Academic Press, London, 1982. 5 M. M. Dubinin and V.V. Serpinski, Carbon, 1981,19,402. 6 H. F. Stoeckli, K. Kraehenbuehl and D. Morel, Carbon, 1983, 21, 589. 7 F. Kraehenbuehl, C. Quellet, B. Schmitter and H. F. Stoeckli, J. Chem. SOC.,Faraday Trans. 1, 1986,82,3439. 8 M. J. B. Evans, Carbon, 1987,25,81. 9 S. S. Barton, M. J. B. Barton and J. MacDonald, Carbon, 1991, 29, 1105; 1992,31, 123. 10 H. F. Stoeckli and D. Huguenin, J. Chern. Soc., Faraday Trans., 1992,88,737. 11 H. F. Stoeckli, P. Rebstein and L. Ballerini, Carbon, 1990, 28, 907. 12 H. F. Stoeckli,Izv. Akad. Nauk SSSR (Ser. Khim.), 1981,63. 13 H. F. Stoeckli and F. Kraehenbuehl, Carbon, 1981,19,353. 14 S. Sircar, Carbon, 1987, 25, 39. 15 G. G. Malenkov and M. M. Dubinin, Izv. Akad. Nauk SSSR (Ser. Khim.), 1984, 1217. 16 H. F. Stoeckli, D. Huguenin and P. Rebstein, J. Chem. Soc., Faraday Trans., 1991,87, 1233. 17 W. H. Beyer, CRC Standard Mathematical Tables, CRC Press, Boca Raton, FL, 1981. 18 N. M. Hassan, T. K. Ghosh, A. L. Hines and S. K. Loyalka, Carbon, 199 1,29,68 1. 19 F. Meunier, F. M. Sun, F. Kraehenbuehl and F. Stoeckli, J. Chem. SOC.,Faraday Trans. 1,1988,84,1973. Paper 3/06455G;Received 28th October, 1993