Langmuir 1989,5,839-844
839
Extension of the Langmuir Equation for Describing Gas Adsorption on Heterogeneous Microporous Solids M. Jaroniec,f X. Lu, and R. Madey* Department of Physics, Kent State University, Kent, Ohio 44242
J. Choma Institute of Chemistry WAT, 00908 Warsaw, Poland Received October 13,1988. In Final Form: February 3, 1989 A general integral equation for gas adsorption on heterogeneous microporous solids is proposed. This equation and the Langmuir adsorption model are used to formulate an alternative description of adsorption in nonuniform micropores to that based on the Dubinin-Radushkevich equation. Model studies and experimental examples are provided to confirm the utility of the above description for representing gas adsorption on heterogeneous microporous solids.
presence of various functional groups, atoms, and impurities on the mesopore surface, and various imperfections Significant progress in the theory of gas adsorption on of this surface.15 The adsorbent heterogeneity, which heterogeneous microporous solids was made during the consists of structural and surface heterogeneities of a popast decade.'+ An important step in this theory was the rous solid, may be described by the global distribution generalization of the Dubinin-Radushkevich (DR) equafunction of adsorption energy. By separating the amounts tion for describing gas adsorption on solids with a Gaussian adsorbed in the micropores and on the mesopore surfaces, micropore-size di~tribution.~J Jaroniec and c o - ~ o r k e r s ~ - ~ ~we can estimate the respective contributions to the global showed that the y-type micropore-size distribution leads energy distribution function from structural and surface to simple expressions for the overall adsorption isotherm heterogeneities of a porous s01id.I~ and for other thermodynamic functions that characterize Further considerations in this paper will deal with adadsorption equilibrium on heterogeneous microporous sorption in the micropores; thus, the derived equations solids. may be used to describe gas adsorption on completely In spite of these achievements, the presest theoretical microporous solids or to analyze the extracted adsorption description of adsorption on heterogeneous microporous isotherm ami@)from the total adsorption isotherm at@). solids is still far from complete; moreover, it suffers from Let us consider a microporous solid that possesses many a disadvantage that is connected with the semiempirical classes of micropores, with each class containing uniform character of the DR equation.12 In this paper, we propose micropores of identical sizes. It was shown previously' that a general integral equation for gas adsorption on heteroeven uniform micropores are sources of the energetic geneous microporous solids. Starting with this general heterogeneity in the sense that molecules adsorb in these equation and assuming the Langmuir model for the local micropores with different adsorption energies 6. Let adsorption, we will formulate an alternative description X0(x,t)denote the differential distribution function of the of gas adsorption on heterogeneous microporous solids to adsorption energy e in uniform micropores characterized that based on the DR equation. Model studies are perby the linear dimension x (e.g., in the case of slitlike miformed for the micropore-size distribution represented by cropores x is their half-width). The distribution function a set of the constant distribution functions. Benzene adX o(x,e) satisfies the normalization condition sorption isotherms measured on two commercial samples S,Xo(x,t) dt = 1 of activated carbons are used to verify the above theoretical description. where A is the energy integration region. The structural heterogeneity of micropores may be described by the General Relationships micropore-size distribution J ( x ) , which also satisfies the For porous solids (e.g., activated carbons), the total normalization condition adsorbed amount a, is the sum of the amounts adsorbed L J ( x ) dx = 1 in the micropores (ad) and on the mesopore surface Comparison of an adsorption isotherm a,@), where p is where S2 is the integration region for x . The energy disthe equilibrium pressure of the adsorbate, with the tribution function that characterizes the energetic hetestandard adsorption isotherm measured on a reference nonporous solid permits the extraction of the adsorbed (1) Jaroniec, M.; Madey, R. Physical Adsorption on Heterogeneous amount amifrom the total adsorbed amount at. This exSolids; Elsevier: Amsterdam, 1989 and references in Chapter 8. (2) Stoeckli, H. F. J. Colloid Interface Sci. 1977, 59, 184. traction may be performed according to the a, method.13 (3) Dubinin, M. M. Carbon 1985,23, 373. The extracted values of amiand ameare sources of in(4) McEnaney, B.; Mays, T. J.; Causton, P. D. Langmuir 1987,3,695. formation about the structural and surface heterogeneities (5) McEnaney, B. Carbon 1988,26,267. (6) Rozwadowski, M.; Wojsz, R. Carbon 1984,22, 363. of a porous s01id.l~ The source of the structural hete(7) Jaroniec, M.; Piotrowaka, J. Monatsh. Chem. 1986, 117, 7. rogeneity of a porous solid is the presence of micropores (8) Jaroniec, M.; Choma, J. Mater. Chem. Phys. 1986, 15, 521. of different sizes and shapes; this heterogeneity may be (9) Jaroniec, M. Langmuir 1987, 3, 795. (10) Jaroniec, M.; Madey, R; Lu, X.;Choma, J. Langmuir 1988,4,911. characterized by the micropore-size distribution func(11) Jaroniec, M.; Madey, R. J. Phys. Chem. 1988,92, 3986. ti~n.~JO The surface heterogeneity is generated by the Introduction
Permanent address: Institute of Chemistry, M. Curie-Sklodowska University, 20031 Lublin, Poland.
(12) Jaroniec, M.; Marczewski, A. W. Monatsh. Chem. 1984,115,997. (13) Jaroniec, M.; Madey, R.; Choma, J.; McEnaney, B.; Mays, T. Carbon 1989,27, 77. (14) Jaroniec, M.; Madey, R. Carbon 1987,25, 579. (15) Jaroniec, M.; Brauer, P. Surf.Sci. Rep. 1986,6, 65.
Qi43-7463/89/2405-Q839$01.5Q~Q 0 1989 American Chemical Society
840 Langmuir, Vol. 5, No. 3, 1989
Jaroniec et al.
rogeneity of a heterogeneous microporous solid is X,i"(t) = JXo(x,e) J(x) dx
A=€-% (3)
Here X"(x,c) is the energy distribution function for uniform micropores of the linear dimension x , and J(x) describes the distribution of the micropores with respect to their size x . Let Bo(p,e) denote the degree of filling of the micropore space at a constant temperature T,an equilibrium pressure p , and an adsorption energy e; then, the degree of filling of all micropores in a heterogeneous microporous solid as a function of p is given by the following integral equation: (4) where A is the energy integration region. The integral eq 4 is identical with that used to describe adsorption on energetically heterogeneous solid surfaces.16 Replacement in eq 4 of the energy distribution function X,io(e) by the integral eq 3 gives
(9)
Thus, the adsorption potential A may be used to characterize the energetic heterogeneity of micropores. By expressing the pressure p in terms of the adsorption potential A (cf. eq 8), we can rewrite eq 6
&,(A) = lB(x,A) n J ( x ) dx
(10)
B,(A)
Bmi*[Poexp(-A/RT)] =
(11)
B(x,A)
B*[x,poexp(-A/RT)]
where
= B*(x,p)
(12)
Note that the function Bd*(p) is the adsorption isotherm, whereas BJA) is the characteristic adsorption curve.18 For strongly heterogeneous microporous solids,the integral eq 10 may be defined in the region (0,-)399 i.e. emi(A) = lmB(x,A) 0 J(x) dx
(13)
(5) The adsorption potential distribution Xd(A) associated with the characteristic adsorption curve BJA) is given by
The integral eq 5 may be transformed to &,i*(P) = l Bn* ( x , p ) J ( x ) dx
(6)
e*(x,p) = L e o ( p , c ) X O ( ~ , €dc)
(7)
where
The above theoretical considerations show that there are two possibilities for describing gas adsorption on heterogeneous microporous solids: the first possibility is based on the well-known integral eq 4 and the second on the integral eq 6. The solution of the well-known integral eq 4 requires the assumption of an isotherm equation BO(p,e) that describes adsorption on energetically homogeneous adsorption sites (e.g., the Langmuir isotherm equation). A disadvantage of this approach is that the energy distribution function Xdo characterizes a global energetic heterogeneity of the micropores and provides no information about the distribution of these micropores with respect to their sizes. The solution of the integral eq 6 requires the assumption of an isotherm equation B*(x,p) that describes adsorption in uniform micropores. An equation for B*(x,p) is obtained from the integral eq 7 if B o ( p , e ) and X0(x,e)are known. The isotherm Bo(p,e) describes adsorption on energetically homageneous adsorption sites and may be represented by the Langmuir equation; however, the energy distribution X0(x,4) describes the energetic heterogeneity of uniform micropores with a linear dimension x . Usually, the integral eq 6 is presented in terms of the adsorption potential A, which is defined as3 A = -AG = R T In ( p o / p ) (8) Here the adsorption potential A is equal to the change in the Gibbs free energy taken with a minus sign, p is the equilibrium pressure of the adsorbate, p o is the saturation vapor pressure, Tis the absolute temperature, and R is the universal gas constant. The normal liquid in equilibrium with its saturated vapor at pressure p o and temperature T is assumed the standard state. In terms of the condensation approximation, the adsorption potential A is equal to the adsorption energy c expressed with respect to the energy eo that characterizes the standard ~tate,'~i.e. (16) Jaroniec, M. Adu. Colloid Interface Sci. 1983, 18, 149.
where B'jx,A) = dB(x,A)/dA. The average adsorption potential A may be expressed as follows:
Note that the final result in eq 15 contains the function B(x,A), which describes adsorption in uniform micropores.
Assumption of the Langmuir Model for Representing Local Adsorption Usually, the local adsorption isotherm B*(x,p) that appears in the integral eq 6 is represented by the DR equat i ~ n . ~ *As~ mentioned **~ earlier, B*(x,p)may be obtained by means of the integral eq 7. In this paper, we propose to represent the local isotherm B*(x,p)by the LangmuirFreundlich (LF) equation?
e*
= b/Pm)'/El
+ 03/~m)"I
(16)
where v and p mare parameters. Equation 16 was proposed initially by Chakravarti and Dhar.19 Sipszoshowed that this equation may be obtained by means of the integral eq 7 with the Langmuir local isotherm BO(p,e) and a symmetrical quasi-Gaussian energy distribution. DubininZ1n and Jaroniec and Marczewskiz3showed that the LF and (17) Jaroniec, M. in Churacerization ojPorouu Solids;Unger, K . K., Rouquerol, J., Sing, K. S. W., Karl,H., Eds.;Elaevier: Amsterdam,1988;
p 213. (18) Dubinin, M.
M.Prog. Surf. Membr. Sci. 1976, 9, 1. (19) Chakravarti, D. N.; Dhar, N. R. Kolloid 2. 1927,43, 377. (20) Sipe, J. R. J. Chem. Phye. 1949, 16, 420. (21) Dubinin, M. M. Izv. Akad. Nauk SSR, Ser. Khim. 1978, 78,17. (22) Dubinin, M. M.Izu. Akad. Nauk SSR,Ser. Khim. 1978,78,529. (23) Jaroniec, M.; Marczewski, A. W. J. Colloid Interface Sci. 1984, 101,280.
Langmuir, Vol. 5, No. 3, 1989 841
Langmuir Equation f o r Gas Adsorption DR equations have similar behaviors over a wide pressure region; this comparison permitted a derivation of the relationships between the parameters of these equations?233 Note that for Y = 1 eq 16 reduces to the Langmuir isotherm. In this paper, we use the Langmuir model to represent adsorption in uniform micropores only on the subset of sites with the same adsorption energy. Because uniform micropores possess sites with a distribution of adsorption energies,' the volume filling of uniform micropores is represented by the LF eq 16, which takes into account this energy distribution. Let us present the LF eq 16 in terms of the adsorption potential A 6 = (1 + exp[y(A - Am)])-' (17) where
n
E
e
$ 1
3k
4
z
v)
P)
6,JA)
= Jm[l+ K exp(axA)]-'J(x) dx 0
(24)
The adsorption potential distribution Xmi(A)associated with eq 24 is
X,i(A) = --
CYKX
-
exp(axA)
J ( x ) dx [l + K exp(axA)I2 (25) The average adsorption potential A associated with the adsorption potential distribution Xd(A) may be calculated according to eq 15:
A
=
dA
JJS,-r
1
+
K
exp(cuxA)]-' dA]J(x) dx
In
'1
dl L1 I n
k
0
a 0 k
(18) A m = RT In (Po/Pm) y = v/RT (19) On the basis of our previous s t ~ d i e sdealing ~ ~ * ~with ~ the comparison of the LF and DR equations, we obtain y = ax (20) A, = a , / x (21) For slitlike micropores, the constants a and a, may be approximated as a = 2.83c'I2/8 and a, = 0.89Ofl/~'/~, where 8 is the similarity coefficient that characterizes the adsorbate only and c is the proportionality constant between the structural parameter of the DR equation and the squared value of the half-width x.3,8 The constant c, estimated on the basis of the benzene adsorption measurements on different microporous activated carbons,318 is equal to 0.00694 [mol/(kJ.nm)12; thus, a = 0.2358 mol/(kJ.nm) and a, = 10.68 kJ.nm/mol. The value 0.89 in the constant a, was chosen to give identical values for the average adsorption potential associated with the DR and LF equations. Substitution of eq 20 and 21 into eq 17 gives 6(x,A) = [ l + K exp(axA)]-' (22) where K = exp(-aa,) = const = 0.0806 (23) The assumption of eq 22 for representing the function B(x,A) in the integral eq 13 gives:
r
d
W
0.5
1.0
0.5 1.0
U
2
Micropore Dimension, x(nm) Figure 1. Micropore-size distributionsfor four representative sets of constant distribution functions. on a microporous solid may be expressed by means of Bd(A) given by eq 24 and Xd(A) given by eq 25;9however, the immersion enthalpy for a microporous solid and the geometric surface area of the micropores may be expressed by means of the average adsorption potential A given by eq 26."
Representation of the Micropore-Size Distribution A simple analytical solution of the integral eq 24 may be obtained for a constant microporesize distribution that is defined as
,
The solution of eq 24 for the constant micropore-size distribution J ( x ) is
+
6,i(A) = ( x , - x J ' ~ ~ [ l K exp(axA)]-' dx
Application of eq 28 is limited to microporous solids characterized by the constant distribution function (viz., eq 27). A more complex micropore-size distribution may be represented by a set of the constant distribution functions. According to the IUPAC classification of the pore sizes,25the widths of micropores are below 2 nm. Because x is the half-width of the slitlike micropores, the values of x < 1 nm for this class of pores and the maximum value of x may be assumed to be x , = 1 nm. On the basis of the molecular sizes of adsorbates, we can estimate the minimum value of x (i.e., xl) that characterizesthe smallest micropores of a solid accessible to the adsorbate molecules. The interval (xl,x,J is usually between 0.1 and 1.0 nm and may be divided into n - 1 equal subintervals: (x1,x2), (x2,x3), ..., (xi,xi+J, ..., (x,.+x,). Usually, the assumption that n = 4 or 5 is sufficient to represent the real micropore-size distribution.26 Figure 1 illustrates a micropore size distribution J(x)represented by a set of the constant distribution functions. Generally, such a composition of the constant distribution functions may be expressed as
The differential molar enthalpy and entropy of adsorption (24) Jaroniec, M.; Madey, R.; Rothatein, D. Pol. J. Chem. 1989,63, in
press.
(25) Sing, K. S. W., et al. Pure Appl. Chem. 1985,57,603. (26) Sing, K. S. W. In Characterization of Porous Solids; Unger, K. K., Rouquerol, J., Sing, K. S. W., Karl, H., Eds.; Elsevier: Amsterdam, 1988; p 89.
842 Langmuir, Vol. 5, No. 3, 1989
J(x) =
fi for x i < x
Xi+l
- Xi
Jaroniec et al. n
5 xi+l
(i = 1, 2, ..., n - 1) (29)
where
4
W
'i
m
d0
Here f j denotes the volume fraction of the micropores of sizes between xi+l and xi. The characteristic adsorption curve emi(A) associated with the micropore-size distribution function J ( x ) (viz., eq 29) is given by 0.0
0
1 -aAAx In
z[
1 + KeaA(xl+ihr)
1 + KeaA[xl+(i-l)Ax]
10
20
30
40
Adsorption P o t e n t i a l , A (kJ/mole)
I
fi
(31)
Figure 2. Characteristic adsorption curves @,(A) calculated according to eq 28 for the constant micropore-size distributions defied in the regions 0.1,l.O (dashed curve) and 0.3,0.8(dotted curve). The solid curve was calculated according to eq 22 for x = 0.55 nm.
Equation 31 was derived by assuming that Ax = - xi = const for i = 1, 2, ..., n - 1. For n = 4, eq 31 contains only three unknown parameters: f l , f i , and the micropore capacity am? that is used to define emi
emi = ad/am?
(32)
where ad is the amount adsorbed in the micropores. The parameters a and K are defined by eq 20 and 23, respectively; x1 may be determined on the basis of the molecular sizes of adsorbates. Because the maximum half-width of the slitlike micropores ( x , = 1 nm) is known,and because n is assumed to be equal to 4, the value of Ax = (x, - xl)/(n - 1). The adsorption potential distribution X,,JA) associated with eq 31 is fiK
x r.+ l euxi+lA- xieax,A + KheaA(Xi+*i+l)
(1
+ Kea@)(1 + Keaxi+lA)
-
.'........_. .._.
3 (d
4
a,
p:
0.0
0
10
20
30
40
Adsorption P o t e n t i a l , A (kJ/mole) Figure 3. Characteristicadsorption curves Bd(A) associated with the three simplest types of micropore-sizedistributions, b, c, and d in Figure 1. These curves were calculated according to eq 31 for n = 4, x1 = 0.1 nm, x4 = 1.0 nm, and Az = 0.3 nm.
+
where xi = x1 (i - 1)Ax for i = 1,2, ...,n. The expressions for Bd(A) (viz., eq 31) and Xd(A) (viz.,eq 33) are sufficient to calculate the differential molar enthalpy and entropy of adsorption according to the general expressions derived previou~ly.~
Results and Discussion To illustrate the properties of the isotherm eq 28 and 31, we performed suitable model studies. Figure 2 presents the characteristic adsorption curves emi(A)calculated according to eq 28. The dashed curve in this figure was calculated for the constant distribution J(x) defined in the region of x from 0.1 to 1.0 nm, whereas the dotted curve is associated with the constant distribution J ( x ) defined in the region of x from 0.3 to 0.8 nm. In both cases, the average value 2 is equal to 0.55 nm. These curves are compared with the solid curve, which corresponds to the Dirac 6-function J(x) for uniform micropores with x = 0.55 nm. This solid curve was calculated according to eq 22. The curves in Figure 2 reveal nearly identical behavior at low values of the adsorption potential A and approach unity when A tends to zero. These curves are similar also in the region of moderate values of A up to about 20 kJ/mol; for larger values of A, they differ significantly in
that adsorption on strongly heterogeneous microporous solids is larger than that on uniform microporous solids. This result can be seen by comparing the dashed curve for the constant distribution defined in the region (0.1, 1.0) with the solid curve calculated for uniform micropores. Figure 3 presents model calculations performed according to eq 31 in order to show the influence of the type of micropore-size distribution on the behavior of &,(A). This figure shows the characteristic adsorption curves Bd(A) calculated for the micropore-size distributions presented in panels b, c, and d of Figure 1. In this case, the curves B,(A) coincide only in the region of very low values of A. the curve Bd(A) associated with the micropore distribution b lies above the other curves, which are associated with distributions c and d, because the fraction of small micropores is largest for curve b. To verify eq 31, we used a gravimetric method to measure the benzene adsorption isotherms on BPL and PA activated carbons at 293 K. The BPL carbon was obtained from the Calgon Carbon Corp. in Pittsburgh, PA, the PA activated carbon from the Barnebey-Cheney Co. in Columbus, OH. Both activated carbons were designed for use in vapor-phase applications. The experimental benzene adsorption isotherms were analyzed by the a,-
Langmuir, Vol. 5, No. 3, 1989 843
Langmuir Equation for Gas Adsorption Table I. Parameters Obtained from the a, Analysis of Benzene Adsorption Isotherms on BPL and PA Activated Carbons at 293 K maximum amount adsorbed in mesopore surface area micropores ado, activated carbon mmolla Sm., m2/a BPL 4.31 80 PA 3.19 20 ~~
Table 11. Adsorption Parameters for BPL and PA Activated Carbons Evaluated by Means of Eq 31 for n = 4 carbon parameter symbol BPL PA adsorption capacity ado, mmol/g 5.3 3.5 min micropore size q,nm 0.5 0.4 1.0 1.0 max micropore size x4, nm micropore fraction fl 0.04 0.40 0.80 0.60 f2 fs 0.16 0.00 mean micropore size ft, nm 0.17 0.62 ratio a,t(eq 31)/ad0(a,method) 1.23 1.13 n
4
3
--
I
'
I
I I
r'
2 --
- 1
1 --
I
t
[
I
f
r-7
4 ; ;
r-
ot
I
0.0 0.2 0.4 0.6 0.8 1.0
Micropore Dimension, x(nm) Figure 5. Microporeaize distribution function for BPL activated carbon with micropore fractionsfi = 0.04nm, f i = 0.80 nm, and j3 = 0.16 nm and for PA activated carbon with micropore fractions f i = 0.40 nm, f2 = 0.60 nm, and fa = 0.00 nm.
1.2-l
W
-
-2
1.01.01
f
0.8-
0 a
0 BPL O
0.04.-
3
2 a
e
-
0.6-
0
, f
6
r
--- BPL
/ \ \
\
0.4.0.4
: 0.2-
3 td
4
2
0.0 0
5
10
15
20
25
30
Adsorption Potential, A (kJ/mole) Figure 4. Characteristic curves Od(A) for the adsorption of benzene on BPL and PA activated carbons at 293 K. The solid lines represent theoretical isotherms calculated according to eq 31, whereas the dashed lines denote the LF isotherms.
method; this analyais was carried out by using the standard benzene adsorption isotherm measured by Isirikyan and Kiselev.n Table I lists the maximum amount aAo adsorbed in the micropores and the mesopore surface area S, evaluated for the BPL and PA carbons by means of the airnethod, which is used often to determine amioand Spe for microporous activated carbon^.'^*^' Because the mesopore surface area for both carbons studied is small (cf. Table I), we assumed that for relative pressures p / p o C 0.1 adsorption occurs mainly in the micropores and that the amount adsorbed for the mesopore surface is negligible; in other words, we did not correct the benzene adsorption isotherms for adsorption on the mesopore surface. Figure 4 presents the experimental characteristic adsorption curves for benzene on the BPL (open circles) and PA (solid circles) microporous activated carbons. The relative adsorption 1 9 =~aA/ado was calculated by using the values of amiogiven in Table 11. The experimental benzene adsorption isotherms presented in Figure 4 were described by eq 31 in order to fiid the parameters that characterize the microporous structure. To reduce the number of best-fit parameters in eq 31,we represented the micropore-size distribution J(x) by (27) Isirikyan, A. A.; Kiselev, A. V. J. Phys. Chem. 1961, 65, 601.
'
0
20
40
I 0
Adsorption Potential, A(kJ/mole) Adsorption potential distributionsX i for BPL and
Figure 6. PA activated carbons calculated according to eq 33.
three constant distributions, i.e., n = 4. The values of a and K for benzene adsorbed on microporous activated carbons, which were discussed previously, are a = 0.2358 mol/(kJ.nm) and K = 0.0806. Because the sum of the f i parameters is equal to unity, the parameters fl, f2, xl,x4, and am: should be determined for n = 4 only. Table I1 contains the values of f i , f i , xl, x4, and aio calculated by fitting eq 31 to the benzene adsorption isotherms. This table contains also the values of f 3 = 1 - f l - f i and the average values f for the BPL and PA activated carbons. Using the parameters aAo, xl, x4, fl,and f i given in Table 11, we calculated the theoretical adsorption curves BJA) (solid lines in Figure 4) for benzene adsorbed on the BPL and PA activated carbons. A comparison of these solid lines with the experimental points shows that eq 31 provides a good description of the adsorption of benzene on microporous activated carbons. This description is better than that shown by the dashed lines in Figure 4, which were obtained by using the LF eq 17. Note that the am: values predicted by eq 31 (and listed in Table II) are higher than those obtained by the a,method (see Table I). It has been shown elsewhereB that the LF eq 16 predicts higher values of am: than other methods; for example, a theoretical analysis of the LF and DR equations showed that ado obtained by means of the LF eq 16 is 1.21 times higher than that predicted by DR equation.B Because eq 31 was
844
Langmuir 1989,5, 844-849
derived by an integration of the LF isotherm equation, this equation predicts values of ado similar to those obtained from the LF equation. Comparison of the ado values given in Tables I and I1 shows that eq 31 gives the am; values that are higher than those obtained by the a,method and in agreement with the theoretical predictions. Figure 5 shows the micropore-size distributions for the BPL and PA carbons plotted for the fi values that are summarized in Table 11. Comparison of these functions shows that the PA activated carbon possesses more micropores of smaller sizes than the BPL carbon. Figure 6 presents the adsorption potential distributions X f i ( A )for both activated carbons studied; these functions show a similar behavior, although the function X,(A) for the PA activated carbon has a longer tail than that for the BPL carbon. This tail indicates that PA activated carbon contains very small micropores which have high values of A. Comparing Figures 5 and 6, we can see that the micropore-size distribution J ( x ) is more useful for characterizing the structural heterogeneities of activated carbons
than the adsorption potential distribution X,(A). The difference in the structural heterogeneity of both activated carbons is more visible in Figure 5 than in Figure 6.
Conclusions Theoretical considerations indicated how to extend the Langmuir model to adsorption on heterogeneous microporous solids. The derived integral eq 24 was solved for the micropore-size distribution represented by a set of constant distribution functions. Finally, a new equation (viz., eq 31) for the adsorption isotherm on heterogeneous microporous solids was derived. Model studies and experimental verification of this equation showed that it is useful for describing benzene adsorption on microporous activated carbons and for evaluating parameters that characterize the microporous structure. Acknowledgment. This work was supported in part by the National Science Foundation under Grant No. CBT-8721495.
Wettability Effect on Stability and Breakdown of Anodic Films on Iron and Aluminum Electrodes 0. Teschke* and M. U. Kleinke Instituto de F k c a , UNICAMP, 13081-Campinas, SP, Brazil
F . Galembeck Instituto de Quimica, UNICAMP, 13081-Campinas, SP, Brazil Received September 30, 1988. In Final Form: January 25, 1989 Wettability of iron and aluminum electrodes at both hydrogen and oxygen evolution potentials was determined with a Wilhelmy-type apparatus, in which the pull exerted by the electrolyte solution on the electrode was measured at each switching of the electrode potential for a periodically reversed step potential. Bare iron electrodes have a different wettability than those in which metal is coated with oxide. The wettability of the coatings and their adhesion to metal are dependent on the dissolved oxygen concentration. On the other hand, the wettability of the passivating coating generated on iron by previous immersion in "OB is greater than that of the metal; as a result, the coating adheres to metal, and this accounts for ita passivating ability. For aluminum electrodes,wetting properties were determined and are quite different from those of iron electrodes. On these electrodes, there is always present an oxide coating even after prolonged evolution of hydrogen. Oxygen-evolving aluminum surfaces are more wettable than the oxide coating present during hydrogen evolution, and oxygen does not affect their wettability. These results show that there is a dependence between anodic film stability and its wettability, as compared to that of the adjacent-to-the-metalcoating; moreover, wettability gradients at the passivating layer are harmful to oxide film stability.
Introduction An outstanding problem in corrosion science and electrochemistry is the breakdown of passivating films on metals. A passivated metal is obtained by the coating of its surface with an insoluble oxide (or hydroxide or salt). This oxide (or other solid product) covers the metal to a greater or lesser extent and affords to it a corresponding degree of protection against corrosion; generally speaking, protection will be complete whenever the metal coating is uniformly impermeable, perfectly adherent to metal, and nonporous. In all other cases, protection will be imperfect.' These passivating films may be thin ( 10-nm) oxide-type layers. Their characteristics are difficult to discern partly N
(1) Pourbaix, M. Atlas of Electrochemical Equilibria in Aqueous Solution; Pergamon: Oxford, 1966.
because of their small thickness and partly because they have to be examined in situ, as they may change upon withdrawal from solutions wherein they are generated. Spectroscopic studies have contributed to a better understanding of the thin passive layers formed on iron. Ellipsometry,2 Auger>4 and X-ray photoelectron spectroscopy (XPS)5s6were successfully used for the characterization of passive layers on iron. In the case of some other metals, the study of wetting as a function of electrode (2) Paik, W. K.; Bockris, J. O'M.Surf. Sci. 1971, 28, 61. (3) Seo, M.; Lumsden, J. B.; Staehle, R. W. Surf. Sci. 1974,42, 337. (4) Revie, R. W.; Baker, B. G.; Bockris, J. O'M.J. Electrochem. SOC. 1975, 122, 1460. (5) Pou, T. E.; Murphy, 0. J.; Young, V.; Tongson, L. L.; Bockris, J. O'M.; J . Electrochem. SOC.1984,131, 1243. (6) Tjong, S. C.; Yeager, E. J . Electrochem. SOC.1981, 128, 2251.
0 1989 American Chemical Society 0743-7463/~9/2~05-0844~01.50/0
