Langmuir 1987,3,687-695
687
Nitrogen Adsorption Isotherms on Organic and Ionic Model Surfaces’ David Amati and Ervin sz. KovZits* Laboratoire de Chimie-technique de 1’Ecole Polytechnique Fgddrale de Lausanne, CH-1015 Lausanne, Switzerland Received November 20, 1986. I n Final Form: February 25, 1987 Powders of known surface area were prepared by treating surface-hydrated, nonporous Si02samples with dimethyl(triorganylsi1yl)amines. The surface area of the starting material was supposed to be correctly known from the BET evaluation of the N2 isotherm by using ci(N,) = 16.2 A2 for the space requirement of the N2 molecule in the first adsorbed layer. Dense layers of the bulky substituents used in this study completely shielded the underlying matrix. Groups exposed at the surface were known from chemical synthesis. Surface areas of the model powders were calculated by using the uniform globular model. The model surfaces could be classed as type D and L on the basis of the BET evaluation of the N2 isotherms. On type D surfaces the first adsorbed N2 layer was dense with U(N2)= 16.2 A2, while on type L a loose first layer was formed with ci(Nz) = 20 f 1A2. It was shown that the nature of the surface determines the value of this parameter and that the form of the isotherm does not permit its prediction. Intermediate first-layer densities were found on partially silylated, heterogeneous surfaces. Surfaces with well-defined structure have been prepared by chemical modification of surface-hydrated silicon dioxide preparations.’ Reaction with monofunctional (dimethy1amino)silanes has been shown to give the densest possible layers, attached by chemical bonds at the surface silanols as anchoring points.24 By use of surface-modified acid-leached glass capillaries, the wetting properties of such layers have been studied: and it has been found that the properties of the modified surfaces are independent of the underlying matrix if the organic layer is thicker than about 6 A. By use of different silicon dioxide powders, it has been demonstrated6 that the surface area of surface modified powders can be related to that of the starting material following the ideas of Martin7 for the calculation of the specific surface area of liquids suspended on a support. Application of the uniform globular modela-” for the structure of porous and nonporous samples used in ref 6 even permits a refinement of the calculation of the specific surface area, s*, referred to unit mass Si02. After the small correction for area lost a t the contacting points of the globules, the surface area, s*, of the treated powder was nearly the same as that of the starting materiala6In these calculations it has been supposed that the specific surface area of the untreated material was correct. I t was measured by the BET evaluation of the N2isotherms by using experimental points in the domain 0.05 < p e / p o< 0.23 and the value of U(N2)= 16.2 A2 for the space requirement of the N2 molecule in the first adsorbed layer. With knowledge of the surface area of th_echemically modified powders, standard N2 isotherms [ VNTp(cm3m-2)] could be presented on well-defined surfaces. The BET evaluation12 of the standard isotherms gave a surprising result. The value for space requirement of the N2 molecule was either near 16.2 or around 20 A*. By accepting the BET model as physical reality, this observation would suggest two possible structures for the first adsorbed layer. The looser layer was found on powders covered with organic substituents, the denser layer on hydrated or partially dehydrated Si02 samples. The constant C of the BET equation is a measure of the adsorption energy in the first layer. A plot of the.space requirement, U(Nz),as a function of the constant C gave Presented at the “Kiselev Memorial Symposium”, 60th Colloid and Surface Science Symposium, Atlanta, GA, June 15-18,1986; K. S. W. Sing and R. A. Pierotti, Chairmen. 0743-7463/87/2403-0687$01.50/0
a plot which did not suggest a simple correlation between adsorption energy and density of the first adsorbed layer as found by Buyanova et al.13914 On the other hand, the plot did not exclude a discontinuous change of the space requirement a t around C = 60. Such a change has also been suggested by a work of Aristov and Kiselev;16these authors found d(N2) = 21 A2 on a thermally dehydrated SiOz sample. The objective of the present project was an extension of the work of ref 6 in order to ascertain the nature of the correlation between the space requirement of the N2 molecule and the constant C. For this purpose isotherms were determined on a nonporous silicon dioxide sample (Aerosil 0x50)covered with substituents depicted in Figure 1. Samples where methyl (DM.M and DMB) phenyl (DM.Ph) and trifluoromethyl groups (BTF) are exposed at the surface were examined in ref 6. It has been shown that DMB-covered layers completely shield the underlying m a t r i ~ Following .~ this observation, surfaces covered with derivatives of the DMB substituent, i.e., surfaces covered with (5-R-3,3-dimethylpentyl)dimethyldoxy groups (DMP.R), should be completely shielded and the surface properties should be uniquely determined by the exposed polar group, R. Surfaces covered by methoxy (DMP.MO), dimethylamino (DMP.A), and cyano groups (DMP.CN) are representatives of slightly basic and polar organic surfaces. Ionic surfaces were prepared by quaternizing the dimethylamino-covered surface to give the (1) Gobet, J.; sz. KovHts, E. Adsorpt. Sci. Technol. 1984, 1 , 77. (2) Szabb, K.; Ha, N. L.; Schneider, Ph.; Zeltner, P.; sz. Kovlts, E. Helu. Chim. Acta 1984, 67, 2128. (3) Lork, K. D.; Unger, K. K.; Kinkel, J. N. J . Chromatogr. 1986,352,
199. (4) Gobet, J.; sz. KovHts, E. Adsorpt. Sci. Technol. 1984, 1, 111. (5) Korosi, G.; sz. KovHts, E. Colloids Surf.1981, 2, 315. (6) Gobet, J.; sz. Kovkts, E. Adsorpt. Sci. Technol. 1984, 1, 285. (7) Martin, R. L. Anal. Chem. 1963, 35, 116. (8) Iler, R. K. The Chemistry of Silica; Wiley Interscience: New York, 1979. (9) Ridgeway, K.; Tarbuck, K. J. Br. Chem. Eng. 1962, 12, 384. (10)Karnaukhov, A. P. In Pore Structure and Properties of Materials; Proceedings of the IUPAC Conference, Prague, 1973; p A3. (11)Rumpf, H. Agglomeration 1962 379. (12) Brunauer, S.; Emmett, P. H.; Teller, E. J. Am. Chem. SOC.1938, 60, 309. (13) Buyanova, N. E.; Zagrafskaya, R. V.; Karnaukhov, A. P.; Shepah a , A. S. Kinet. Katal. 1983, 24, 1187. (14) Karnaukhov, A. P. J. Colloid Interface Sci. 1985, 103, 311. (15) Aristov, B. G.; Kiselev, A. V. Zh. Fiz. Khim. 1963, 37, 2520.
0 1987 American Chemical Society
688 Langmuir, Vol. 3,No. 5, 1987
Amati and 82. Koudts
Table I. Adsorption Properties of Silicon Dioxide Samples Used i n This W o r P samples Aerosil OX50 SiO2/8.0 , Si02/3.5 Si02/2.4
treatment received RP 500 'C (1V2torr), 5 h 1000 'C (l0-l torr), 72 h as
8 , mz g-' 45.9 + 0.6 42.7 + 0.6
d , A'
c
L,g ax-'
ref 16.3 16.3
96 133 86 50
0.17 0.33 0.33 0.33
Cab-0-Sil-M5 as received 207 + 3 92 0.09 Cah/S.O RP 174 i 2 ref 109 0.15 500 OC (lo-? torr), 16 h 16.2 96 0.15 Cab/no. 1 Cab/no. 2 700 "C (lo-? torr), 5 h 16.3 80 0.15 Cab/no. 3 700 "C ( W Etorr), 120 h 16.2 15 0.15 Cab/no. 4 1000 "C torr), 48 h 16.2 53 0.15 Cab/no. 5 1100 "C (lo-, torr), 48 h 16.3 47 0.15 CWp Cab/no. 4 in water vapor, 4.6 torr for 2 h 16.3 72 0.15 'The symbol 8 (average of three determinations) is for specific surface area determined hy the BET method with d(N2)= 16.2 AP: d is the space requirement of the Nz molecule on thermally dehydrated samples; C is the constant in eq 9; d,w is for the apparent density of the powder samples. The starting materials for dehydrated samples waa SiO,/O.8 and Cab/8.0. RP is for the recommended procedure of ref 1. chloride and the bromide form of t h e trimethylammonio substituent (DMP.QA.CI and .Br). Furthermore, it was also intended to acquire standard i s o t h e r m o n dehydratpd silicon dioxide preparations in order to control the results of Aristov and Kiselev.lS Finally, t h e value of d(N,) should be controlled on heterogeneous surfaces, modeled by silicon dioxide preparations Dartiallv covered with oreanic suhstituents.
Experimental Section General. Silicon dioxide samples were stored and handled in a drybox from Mecaplex AG (Grenchen, Switzerland; Model GB-801 in an argon atmosphere containing 0.9998). Using points i? this domain slope ( = l / r ) and the value of the function [In (a'I'Vmm)] at p e / p o= e-1 were calculated by linear regression. Results are shown in Table IV where evaluation of results from ref 6 are also included. P a r t i a l l y Surface-Modified Samples. A. Samples with Low S u r f a c e Coverage. A sample with 96.7% DMB coverage was obtained in an experiment used for the preparation of dense layers but silylation time was only 4 h. For lower coverages, Si02/8.0 was treated in cyclohexane with the silylating agent. In a typical experiment, 3.01 g of sio2/8.0 was weighed in a Pyrex vessel of 100 mL in the drybox. Outside the drybox, 50 mL of absolute cyclohexane was added under argon protection. The vessel was cooled to 10 "C and a quantity of 7.2
Langmuir, Vol. 3, No. 5, 1987 691
Nitrogen Adsorption Isotherms on Model Surfaces Table V. Properties of SiO2/8.O Samples with Low DMB Calculated from the and DM.Ph Surface Coverage, rBOx, Carbon Content P,”
Table VI. Adsorption Properties of Mixtures of SiO2/8.O with Densely Covered DMB and DM.Ph Samples” BET
surface coverage sample
DMB
DM.Ph
no. 1 2 3 4 5 6 7 1 2
3 4 5 6
PCYb %
0.07 0.40 0.61 0.96 1.28 1.54 1.59 0.13 0.39 0.76 1.00
1.35 1.68
rsom
rmol m-2 0.17 0.98 1.50 2.37 3.18 3.84 3.97 0.32 0.96 1.87 2.47 3.35 4.19
e 0.043 0.247 0.378 0.597 0.801 0.967 1.000 0.076 0.229 0.446 0.590 0.800 1.000
BET C a, A2 80 40 28 24 18 16 16 73 50 39 36 34 30
16.2 16.7 17.2 17.7 18.3 19.5 19.8 16.2 16.8 17.4 17.8 18.5 19.4
“Also are given the relative surface coverage, 0, and the con: stants of the BET evaluation of the N2 isotherm: the constant C and a, the space requirement of a N2 molecule. Average of three
a,
Si02/8.0 DMB
ec&d
C
0.000
133 118 85 58 42 27 22 16 133
0.041 0.182 0.315 0.487 0.699 0.823 1.000
DM.Ph
0.000 0.102 0.449 0.649 1.000
112
64 50 30
A2 16.2 16.3 16.9 17.3 18.1 18.8 19.4 19.8 16.2 16.3 17.6 18.4 19.4
aLCt
C, 136 119.9 82.4 61.0 42.9 28.5 22.4 15.6 136 111.4
65.6 48.1 30.3
A2
16.20 16.37 16.95 17.51 18.25 19.03 19.57 19.80 16.20 16.51 17.60 18.25 19.40
“The relative surface coverage, 6&dr was calculated with eq 12. Symbols of the BET evaluation on the N2 isotherms as in Table V; constants of the evaluation of the isotherm calculated by linear combination,LC, are also listed (eq 13).
determinations.
mg of dimethyl[(3,3-dimethylbutyl)dimethylsilyl]amine(38.4pmol of 4, corresponding to 0.3 pmol m-2) was added to the stirred suspension. After 1.5 h at room temperature, 200 mL of absolute
diethyl ether was added. The powder was washed and dried as described under A. After elemental analysis and determination of the N2 isotherm, the same powder was treated as described, with a further quantity of (dimethy1amino)silaneto give a sample with higher surface coverage. Surface coverage and relative surface coverage of the samples is listed in Table V. In the BET evaluation of the N2 isotherms it was supposed that the surface area of the sample is equal to that of the Si02contained in the powder. The surface requirement of the N2 molecule, ci, compatible with this hypothesis was calculated as explained before. B. Mixtures of SiOZ/8.0with Densely Covered DMB and DM.Ph Samples. A weighed amount of Si02/8.0,m(Si02/8.0), and a weighed amount of fully treated sample, m(X) (X is for DMB or DM.Ph), were dispersed in cyclohexane by ultrasonic irradiation. After sedimentaiton the clear supernatent is pipetted, , then the wet paste solidified at 0 O C and the solid cyclohexane evaporated at this temperature at 0.01 torr. The relative surface coverage, Bcded, of the mixture is calculated with eq 10 in order to give an analogous number to that as in the case of partially treated samples. m(X)w(Si021X) (12) = m(X)w(SiO&) + m(SiO2/8.0) The compositionof the mixtures in terms of Odd and the constants of the BET evaluation of the N2 isotherms are summarized in Table VI. With the aid of the standard isotherms of the Si02/8.0 and that of the X-covered samples, isotherms were calculated by linear combination as shown in eq 13. Constants of the BET vNW(mixture)= Bvmp(X) + (1-B)vmp(Si02/8.0) (13) evaluation of this “synthetic”isotherm are also shown in Table VI.
Results and Discussion The choice of the substituent was incited by successful experiences with surface coverages of dense (3,3-dimethylbuty1)dimethylsiloxy(DMB) layers. Actually, most of the substituents applied in this study, the (3,3-dimethylpenty1)dimethylsiloxy groups substituted in the 5-position of the pentyl chain, are derivatives of this group (DMP.R). The DMB group doubly shields the surface. A first protective layer is formed by the base of the substituent (methylenedimethylsilane),the size of which determines its limiting surface concentration. The size of the trimethyl “umbrella” is slightly smaller but forms a nearly compact second protective layer above the base
layer. In wetting experiments the surface of acid-leached glass capillaries covered by a dense DMB layer was shown to be less polar than that covered by the thin trimethyld o x y layer (DM.M).5 This observation is in accordance with results of Zisman,22namely, that the effect of a polar bond is “felt” by the wetting agent to a depth of about 8 A. Therefore, it could be expected that adsorption properties of surfaces covered by DMP.R substituents will be determined only by the groups exposed at the surface. For a complete shielding of the underlying polar silicon dioxide the chemically bonded layer must have the maximum density. The limiting surface concentration of the DMB layer was shown to be rDMB = 3.86 f 0.10 pmol m-z on nonporous silicon dioxide preparation^.^ Data listed in Table I11 indicate that this value was attained on our fully hydrated, nonporous SiOz/8.0 and Cab/8.0 samples, not only for DMB coverages, but also for all DMP.R layers. Let us mention at this point that surface coverages should be considered to be correct only on a relative basis. Actually, they refer to the BET surface area of the untreated sample calculated by using d(Nz) = 16.2 A2 for the space requirement of the nitrogen molecule. For the time being, this figure seems to be correct on hydrated anatase (Ti02)surfaces as was shown by Harkins and Juraz3(heat of immersion) and by Pickering and Ecstromz4(electron microscopy). Being currently used also for silicon dioxide, we will accept this value throughout this work. Nitrogen isotherms were measured on samples of SiOz/8.0 covered with dense layers of substituents depicted in Figure 1, except those already examined in ref 6, furthermore on a thermally dehydrated sample Si02/2.4. The isotherms did not show hysteresis on desorption and were reproducible up to p e / p o= 0.88. The coefficients of the polynomial representation of the dimensionless a,-curve (eq 6) are listed in Table 111. The specific surface area of the surface-modified powders of the sample Si02/8.0 referred to unit mass SiOz in the sample, s*, is nearly (f0.170) the same as that of the nontreated SiOz as calculated with the uniform globular model. Actually, the coordination number of the globules is such (CN = 4.0) that the increase of surface area due to the increase of the diameter of the globules by the coating layer just compensates surface lost a t the con(22) Shafrin, E. G.; Zisman, W. A. J. Phys. Chem. 1957, 61, 1046. (23) Harkins, W. D.; Jura, G. J.Am. Chem. SOC.1944,66,1362,1366. (24) Pickering, H. L.; Ecstrom, H. C. J. Am. Chem. SOC.1952,74,4775.
Amati and sz. Koucits
692 Langmuir, Vol. 3, No. 5, 1987 i 22
t
I
1
I
I
I
I
0
P. /P.
1
Figure 3. Examples of isotherms having the same constant C but different space requirement of the.Nzmolecule (Si02/2.4,C = 50, U(N2) = 16.3 A'; DMP.QA.CI, C = 53, U(Nz) = 19.2 A'). I
!c f
22
2.6 3.0 Figure 2. Space requirement of a Nzmolecule as a function of the constant C of the BET equation and as that of the constant r of the FHH equation. Data from Table IV. Open symbols refer to thermally dehydrated Cab/8.0 samples (see Table I).
tacting points.6 Knowledge of the specific surface area allows the calculation of the constants necessary lp convert the a,-curves to the areal adsorption isotherms (VNTp(cm3 m-2); eq 4). These constants, ua,are also given in Table 111. Evaluation of the areal adsorption isotherm by the BET method in the domain 0.05 < p e / p o4 0.23 gave the constant C and the space requirement of the Nz molecule, ci(N2),as listed in Table IV. In order to calculate the constants of the FHH equ_ation,the logarithm of the areal adsorption isotherm, In VNTP,was plotted as a function of -In [-ln (pe,po)]. The plot is linear in the multilayer region. From points in the region 0.50 4 p e / p o< 0.85, the value_ of the exponent r and that of the constant (ul/rVmNTP)were calculated from the linear regression and listed in Table IV. The constant C of the BET equation is characteristic of the curvature of the adsorption isotherm a t low coverages, it characterizes the form of the isotherm in this region. Similarly, the constant r of the FHH equation is characteristic of the form of the isotherm in the multilayer region. Both constants are independent of the amplitude of the adsorption. The plot of the space requirement of the Nzmolecule as a function of these constants is shown in Figure 2. From this plot it can be concluded that the adsorbents examined can be divided into two groups with U ( N 2 )= 16 and 20 A2 but there .is no correlation between space requirement U ( N z ) and C or r; thus prediction of a(NJ from data given by the isotherm is not possible. Properties of the partially dehydrated adsorbent Si02/2.4 are important to support this conclusion. It was observed that thermal treatment of fume silicas in vacuo did not result in a decrease of the specific surface area.27
Therefore, a dehydrated sample was prepared by heating a sample of SiOz/8.0with a surface hydroxyl concentration roH= 8.0 pmol m-z25926to 1000 "C in vacuo torr) for 72 h. Treatment with dimethyl(trimethylsily1)amine resulted in a surface concentration of r D M , M = 2.4 pmol m-2, supposed to be equal to the residual silanol concentration on the sample. Results on this surface are in contradiction with data reported by Aristov and Kiselev,15on a thermally treated sample where a space requirement of ci(Nz)= 21 A2 was found. This result was used by Karnaukhov14in order to prove correlation between ci(Nz)and the constant C . Therefore, further partially dehydrated samples were prepared. Samples of Cabl8.0 were heated in vacuo a t different temperatures: no. 1at 500 "C; no. 2 and 3 at 700 "C; no. 4 at IO00 "C; no. 5 at 1100 OC for periods indicated in Table I. Finally, Cablno. 4 was rehydrated in water vapor of 4.6 torr for 2 h to give a partially rehydrated sample similar to Si02/3.5. Surface hydroxyl concentrations were not determined, but it is obvious that the surface hydroxyls decreased in the series 1 5. Points of ci(Nz)obtained on these samples are included in the plot vs. C, proving that the space requirement of the Nz molecule remains 16.2 A2 on hydrated and partially dehydrated silicon dioxide surfaces. A n important conclusion can be drawn by comparing the isotherm on SiOz/2.4 and that measured on the surface exhibiting the chloride of the trimethylammonio substit: uent, DMP.QA.Cl. In Figure 2, it is seen that constant C and exponent r are the same on both surfaces, but the space requirement of the nitrogen molecule is different. Figure 3 shows that the isotherms are very similar. Indeed, by plotting points of the Ly,-curve of Si02/2.4as a function of the a,-curve of the DMP-QA.Cl-covered sample, points are on the 45O line. This experimental fact leads to the important conclusion that N2 isotherms can in every respect be similar but the actual surface concentrations of the molecules are different. This same argument expressed in another way allows the conclusion that the form of the
-
(26) Davidov, V. Ya.; Kiselev, A. V.; Zhuravlev, L. T. Trans. Faraday
SOC.1964, 60,2254.
(25) Hockey, J. A,; Pethica, B. A. Trans. Faraday SOC.1961,57, 2247.
(27) Amati, D.; sz. Kovlts, E., unpublished results.
Langmuir, Vol. 3, No. 5, 1987 693
Nitrogen Adsorption Isotherms on Model Surfaces Table VII. Surface Pressure (erg cm-2) of
Nzat 77 K Calculated with the BET Equation, from the Polynomial (Eq 4), and by Extrapolation with the FHH Equation”
sample DM.H DM.M DM.Ph DMB DMP.MO DMP.CN DMP.A DMP.QA.Br DMP.QA.Cl BTF Si02/8.0 Si02/3.5 sio2/2.4
r from BET,b
erg cm-2 2.61 2.65 5.23 3.23 4.66 5.91 3.32 8.71 7.35 6.22 13.77 11.18 8.39
A r e x ppolynomial: erg cm-2
A r FHH,d erg cm-2
28.89 16.82 20.36 18.02 16.15 19.39 17.81 21.67 21.54 20.56 25.77 25.24 25.52
3.67 3.97 4.13 3.80 4.78 3.73 3.93 3.85 3.95 4.15 3.82 3.83 4.77
#,e
7% erg cm-* 45.8 47.7 63.3 51.5 52.8 61.5 51.6 75.9 71.9 66.6 104.8 94.5 89.4
erg cm-2 22.61 23.44 29.72 25.05 25.59 29.03 25.06 34.23 32.84 30.93 43.36 40.25 38.68
The symbol ro is for the surface pressure at p e = p o and ys is for the surface energy of the solid calculated with the approximation given in eq 23. b p e / p o= 0.05. C p e / p o= 0.05-0.88. d p e / p o= 0.88-1. ‘ p e / p 0 = 0-1.
experimental isotherm does not give information about the question of whether a surface belongs to the U(N,) = 16.2 or to the 20-A2 class either in the low-pressure (BET) region or in the domain of multilayer adsorption (FHH). Inside of the 20-A2 class there seems to be correlation between ci(N,) and the constant C or the constant r. Pierce advanced the seducing idea that once the first layer is completed, the adsorption law in the multilayer region is independent of the adsorbent, thus a universal isotherm can be given, for which the FHH equation with r = 2.75 was proposed.28 This method was used by Karnaukhov14for the determination of the parameter a(N,) on different adsorbents. The use of two “master isotherms” was proposed by Z e t t e l m ~ y e r . A ~ ~value of r = 2.12 was measured on Teflon, polypropylene, and polyethylene powders. Therefore, it was suggested that an FHH isotherm with r = 2.75 is valid in the multilayer region above surfaces of high energy but an isotherm with r = 2.12 describes adsorption on low-energy surfaces. Carrott et aL30believe that values of r appreciably less than 2.6 are likely to be due to the effect of capillary condensation rather than to the low-energy surface interaction. Data listed in Table IV are distributed in the range r = 2.1-2.9; they are not grouped around 2.1 and 2.8. Also, data plotted in Figure 2 contradict these proposals. A last question to be answered was whether the integral behavior of the isotherm could give any information about the value of Ci(N2)to be used in the BET evaluation. Inspite of the arguments described above, the surface pressure, TO, was determined in the following manner.21 The adsorption equation of Gibbs (eq 14) (y is the surface -dy = dT = Fdp (14) tension, .R the surface pressure, and p the chemical potential) gives eq 15 by supposing that nitrogen is an ideal
gas. The film pressure a t saturation, TO, was calculated as a sum of three terms. In the region t = 0-0.05 the film pressure was calculated by using the BET equation. Combination of eq 9 and 15 and integration give eq 16, TBET
= RTr, In [[I + (C - 1)t1/(1 - 8 1
gwrp
Y
0.0 0.0
1
I
1
hh
1.0
Figure 4. Examples of isotherms extrapolated in the region 0.88 Q p e / p o Q 1 with the FHH equation.
vm
where rm= f 22415 mol m-, is the concentration in the first adsorbed layer. In the region where the polynomial expression is valid, eq 4 can be used to arrive at the expression given in eq 17, where x = In [ and [ = a and fl are
= (RT/22415)[A’f1 - B’ln (-x) - C’x (0’/2)x2 - (E’/3)x3- (F’/4)x4 - (G’/5)x5 - (H’/6)r6]! (17) the limits of integration. Equation 17 can be used in the domain [ = 0.01-0.88. Finally, it was supposed that above 5 = 0.88 the FHH-equation describes the adsorption isotherm, by using the constants determined in the domain 5 = 0.50-0.85. The extrapolated isotherm is illustrated in Figure 4 on two examples. Combination of eq 11 with 15 and integration between the limits $. and 1give eq 18. The
(16) (18)
(28) Pierce, C. J. Phys. Chem. 1959, 63, 1076. (29) Zettlemoyer, A. C. J. Colloid Interface Sci. 1968, 28, 343. (30) Carrott, P. J. M.; McLeod, A. I.; Sing, K. S. W. In Adsorption at the Cas-Solid and Liquid-Solid Interface; RouquBrol, J., Sing, K. S.W., Eds.; Elsevier: Amsterdam, 1982; p 403.
decrease of the areal free energy on the powders was now calculated in the domain 5 = 0-0.05 with eq 16, in the domain 0.05-0.88 with eq 17, and for 0.88-1 with eq 18. The result is shown in Figure 5. Numerical values of the
694 Langmuir, Vol. 3, No. 5, 1987 0.0
Amati and sz. Koucits i
I0
P,/Po
01.
I
40
60
80
Figure 6. Space requirement of an N2 molecule on the surfaces indicated as a function of the areal surface free energy of the solid, ys,as calculated with eq 23. .#& ET:
---&L]
___-__
I
FHH
Figure 5. Decrease of the areal free energy (=-a,where r is the surface pressure) as a function of the relative pressure calculated with the BET equation in the domain 0 Q pe/poQ 0.05, with the polynomial of eq 4 in the domain 0.05 6 pe/poC 0.88 and with the FHH-equation in the domain 0.88 Q p e / p o C 1.
Table VIII. Comparison of Values of A r Calculated with the Polynomial in Eq 17 ( A r e x J n 13.lPn
0.01-0.05 Arerpt
erg cm-’
DM.H DM.M DM.Ph DMB DMP.MO DMP.CN DMP.A DMP.QA.Br DMP.QA.CI BTF Si02/8.0 sio2/3.5 Si02/2.4
2.02 2.07 4.16 2.73 3.61 4.31 2.72 5.76 5.49 4.68 8.33 7.74 6.10
0.50-0.85
- ATBET, A r e x p , erg cm-2 erg cm-2 +0.03 5.50 +0.04 5.70 6.37 +0.39 +0.29 5.96 6.52 +0.21 +0.19 5.92 5.84 +0.22 6.42 +0.12 6.44 +0.50 +0.34 6.32 7.13 +0.23 +0.65 7.11 +0.37 7.82
Arerp
- A~FHH, erg cm-2
+0.01 +0.02 -0.01 +0.01 -0.01 0.00 0.00 +0.01 0.00 -0.01 0.00
+0.01 0.00
integral between the limits indicated are given in Table VII, together with the value of the surface pressure a t saturation, TO, calculated with eq 19. In order to have an = “BET
+
AT,,^ + ATFHH
(19)
estimate of the error in this procedure, surface pressure differences were calculated in the domain of =$ = 0.014.05 with eq 16 and 17. Actually both the polynomial (eq 4) and the BET equation (eq 9) should be valid. Similarly, surface pressure differences were calculated in the domain 0 . 5 0 . 8 5 with eq 17 and 18. Results of these calculations are listed in Table VIII. In the low-pressure domain the BET isotherm always underestimates the adsorption, as discussed by McMillan and Teller.31 Examination of data listed in Table VI11 would suggest an error of about 0.5 erg cm-2 in the value of TO. The values T O listed in Table VI1 were calculated by applying surface concentrations referring to known surface (31) McMillan, W.
G.;Teller, E. J . Chem. Phys.
TO’
1951, 19, 25.
= [ d (N2)/ 16.21TO
(20)
these TO’ values would be independent of the knowledge of the surface area and could be used for the prediction whether the first adsorbed layer is of the loose or dense type. There is no correlation between TO’ and U(Nz). Surface pressures can be used to estimate the areal free surface energy of the adsorbents. All surfaces examined are wettable by liquid nitrogen, consequently eq 21 is valid,
Arenp
a Values obtained by using the BET and FHH equations (eq 16 and 18) in the domains pe/po = 0.01-0.05 and 0.50-0.85, respectively.
TO
area. If the surface area would have been determined from the isotherm applying d(N2)= 16.2 A2 for all surfaces the resulting TO’ values would be as given in eq 20. Obviously
To
= Ys -
(YL
+ 7%)
(21)
where ys is the areal free surface energy of the solid, yL is the surface tension of the wetting liquid, and ysL is the interfacial tension at the liquid/solid interface. Supposing that nitrogen is a nonpolar liquid, the approximation of Girifalco and Good32can be applied for the calculation of ysL. Accepting the simplified form of this approximation proposed by F o w k e ~eq , ~22 ~ gives the relationship between YSL
= Ys +
YL -
2(YsYL)1’z
(22)
the interfacial tension ys and yL. Combination of eq 21 and 22 gives eq 23.34 Areal free surface energy of the
Ys = (a0+ 2YLI2/4YL
(23)
surfaces studied was calculated by using yL = 8.95 erg cm-2 for the liquid nitrogen at 77 K. Results are listed in Table VII. Dependence of the space requirement of the nitrogen molecule on the free surface energy of the solid estimated a t 77 K with eq 23 is shown in Figure 6. As already mentioned this correlation cannot be used to predict d(N2) because knowledge of this same parameter‘was supposed in the calculations giving ys. From the foregoing discussion we can conclude that the first adsorbed layer of nitrogen can have a “loose” and a “dense” structure. The density of the layer is primarily determined by the nature of the surface and not by the adsorption energy of the first layer or by the force of the potential field near the surface. Dense layers were observed on hydrated or partially dehydrated silicon dioxide surfaces. Loose layers were observed on nonpolar surfaces (32) Girifalco, L. A.;Good, R. J. J . Phys. Chem. 1957, 61, 904. (33) Fowkes, F. M. In Recent Adoances in Adhesion; Lee, L. H., Ed.; Gordon & Breach London, New York, Paris: 1973; p 39. (34)Fowkes, F. M. In Chemistry and Physics oflnterfaces;American Chemical Society: Washington, DC, 1965; p 1.
Langmuir 1987,3,695-699 c i
i-!
!
!
1
4
RMB
M.Ph
0
OJ
a
10
0.0
a
l.8
Figure 7. Constant C of the BET equation and the space requirement of an N2 molecule on partially DMB- and DM.Phcovered surfaces (fullsymbols)and on those of mixtures of densely
covered and untreated Si02/8.0 samples (open symbols) as a function of the relative coverage, 8. Full lines are traces of the evaluation of the isotherm obtained by linear combination of the individual isotherms; dashed lines are drawn by eye.
with exposed methyl groups (DM.H, DM.M, DMB), on slightly polar surfaces with exposed phenyl groups (DM.Ph), on medium polar surfaces with exposed methoxy, dimethylamino, and cyano groups (DMP.MO, DMP.A, DMP.CN), and finally also on ionic surfaces (DMP.QA.Br and Cl).
695
We put now forward the question of U(Nz)on surfaces that are mixtures of the two classes. In a first series of experiments N2 isotherms were determined on mixtures of treated and untreated sio2/8.0 samples. As anticipated, the properties of the isotherms on these mixtures were the same as the properties of isotherms calculated by linear combination of the individual isotherms as shown in Figure 7. In a second series of experiments heterogeneous surfaces were prepared by partidy covering Si02/8.0 samples with DMB or DM.Ph. On such adsorbents intermediate values between U(N2)= 20 and 16 A2 were observed. Kiselev et al.35 found similar values on partially trimethylsilylated surfaces. In conclusion, on homogeneous surfaces the first adsorbed layer of Nz can have two structures. Loose layers are formed on polar or nonpolar organic surfaces as well as on ionic surfaces, whereas dense layers were observed on surfaces where hydroxyl groups are exposed. Intermediate densities were found on heterogeneous surfaces.
Acknowledgment. This paper reports on part of a project financed by the Fonds National Suisse de la Recherche Scientifique. We thank Dr. Ph. Schneider for help in organic syntheses and Dr. F. PB1 for discussions. Registry No. N,, 7727-37-9. (35) Kiselev, A. V.; Korolev, A. Ya.; Petrova, R. S.; Shcherbakova, K.
D.Kolloidn. Zh. 1960,22,671.
Heterogeneous Adsorption on Microporous Carbons? B. McEnaney,* T. J. Mays, and P. D. Causton School of Materials Science, University of Bath, Claverton Down, Bath BA2 7AY, U.K. Received October 21, 1986. I n Final Form: February 23, 1987 The influence of heterogeneity in microporous carbons on adsorption of gases is studied by using the as a model. Adsorption of Ar at 77 K on two poly(vinylidene chloride) generalized adsorption isotherm (GAI) based carbons activated to 28 wt 70 (PVDC-28) and 80 w t % (PVDC-80) burn-off is measured by using a McBain spring-type balance over a pressure range from 6.7 X lo4 to 23 kPa, corresponding to a relative pressure range of (2.3 X 106)-0.79. The GAI comprises three functions: (i) the total isotherm (determined experimentally), (ii) the local isotherm (assumed), and (iii) the adsorption energy distribution (unknown). Problems of computing the energy distribution are considered. Two previously published analytic solutions of the GAI (Sircar's equation and the condensation approximation) and one numerical method (regularization, incorporating a new smoothing algorithm) are applied to the adsorption data. For all three methods the Langmuir equation is assumed for the local isotherm function. For both carbons the energy distributions obtained from the three methods are similar, but the dispersions of the distributions obtained from regularization are wider than those obtained from Sircar's equation. The distribution functions obtained from the condensation approximation are similar to those obtained from regularization, suggesting that it is a good approximation for adsorption of Ar at 77 K on these carbons. When the two carbons are compared, although PVDC-80 gives a slightly wider dispersion than PVDC-28 for all three methods, the energy distributions do not change a great deal with burn-off. The similarity in shape of the energy distributions is probably a reflection of the similarity in shape of the experimentally determined total isotherms. It is concluded that, although activation from 28 wt % to 80 wt % burn-off increases adsorptive capacity substantially, there is no significant increase in the mean width of micropores. 1. Introduction Microporous carbons are disordered solids with a structure consisting of a twisted network of defective carbon layer planes, cross-linked by an array of aliphatic *To whom correspondence should be addressed. Presented at the "Kiselev Memorial Symposium", 60th Colloid and Surface Science Symposium, Atlanta, GA, June 1518,1986; K. S. W.Sing and R. A. Pierotti, Chairmen. 0743-7463/87/2403-0695$01.50/0
bridging groups, and incorporating heteroatoms, for example, €3 and 0.Micropores are the spaces between the layer Planes whose widths are less than 2 nm.' It is highly likely that adsorption on such a material is strongly influenced by the heterogeneity of the structure. It is therefore of interest to explore the application of the (1) Sing, K. S. W.; Everett, D. H.; Haul,R. A. W.; Moscou, L.; Pierotti, R. A.; Rouquerol, J.; Siemieniewska, T. Pure Appl. Chem. 1985,57,603.
0 1987 American Chemical Society
