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The Journal of Physical Chemistry, Vol. 83, No. 72, 7979
A lack of temperature information makes it impossible to judge this point. Two theoretical s t u d i e ~provide ~ * ~ no HOCl absorption bands for X/nm 1 300. It is questionable how accurate such predictions are, especially in cases where elements of the third period with unoccupied 3d orbitals such as C1 or S atoms participate. The stratospheric HOCl photodissociation rate calculated on the basis of our cross sections is about 25% smaller than the photolysis rate derived from Molina’s data, corresponding to an equally enlarged HOCl lifetime. Acknowledgment. The authors are grateful to the Manufacturing Chemists Association, Washington, D.C., for financial support and to the Hoechst AG, Frankfurt Am Main, for the gift of an 1-m quartz glass absorption cell. We also thank Professor Dr. H. Dreizler and Dr. H. Mader, Kiel, for the least-squares analysis subroutine. The computer calculations were performed at the PDP 10 of the Rechenzentrum at the University of Kiel. References and Notes (1) This research was supported by two contracts from the Manufacturing Chemists Association (MCA), Washington, D.C., Contract No. FC-77-171 and FC-77-224. Preliminary results were presented at the MCA Workshop on Fluorocarbon Research, Boukler, Coio., March 14, 1978. (2) (a) J. W. Birks et al., C. J. Howard et al., cited in ref 5 and 10. (b) B. Reimann and F. Kaufman. J . Chem. Phvs.. 89. 2925 (19781. (3) W. C. Fergusson, L. Slotin, and D. W. G. Style: Trans. Faraday Soc:, 32, 956 (1936). (4) S.Jaffe and W. B. DeMore, NASA Ref. Pubi., No. 1010 (1977). (5) L. T. Molina and M. J. Molina, J . Phvs. Chem.. 82, 2410 (1978). (6) R. B. Timmons, report to the Manufacturing Chemists Association, 1977; private communication.
F. P. J. M. Kerkhof and J. A. Mouiljn (7) J. C. Hisatsune, report to the Manufacturing Chemlsts Association, 1978; private comrnunicatlon. (8) G. Hirsch. P. J. Bruna, S. D. Peyerimhoff,and R. J. Buenker, Chem. Phys. Lett., 52, 442 (1977). (9) R. L. Jaffe and S. R. Langhoff, J . Chem. Phys., 88, 1638 (1978). (10) D. Sz6, report to the Manufacturing Chemlsts Association, 1978; private communication. (11) B. Janowski, H.-D. Knauth, and H. Martin, Ber. Bunsenges. Phys. Chem., 81, 1262 (1977). (12) C. J. Schack and C. 8. Lindhal, Inorg. Nuci. Chem. Lett., 3, 387 (1967). (13) Quartz glass column manufacturedfrom Norddeutsche Quarzschmelze GmbH, Geesthacht, according to our statement; H.-D. Knauth, Dissertation, Kid, 1970. (14) H.-D. Knauth, Ber. Bunsenges. Phys. Chem., 82, 428 (1978). (15) H. Clausen, Dissertation, Kiel, 1977; H. Clausen and H.-D. Knauth, to be submitted for publication. (16) The effective first-order constant klO,G of the gas reaction at total pressures near 1 atm may be of the same order of magnitude as klo,sfor the reaction in solution: the effective dissociation constant k,o,oat 1 atm is expected to be lower than the high-pressure rate constant k , , because the high-pressure limit is not expected to be reached d 1 atm; klOsshould also be lower than klo.. by reason of solvent cage effects.’ For example kG (1 atm) and k , for the analogous thermal CINO, decompositioni7 have indeed slmiiar values. (17) (a) M. L. Dutton, D. L. Bunker, and H. Harris, J. Phys. Chem., 78, 2614 (1972); (b) H.-D. Knauth and H. Martin, 2. Naturforsch., A , 33, 1037 (1978). (18) (a) “JANAF ThermochemicalTables”, Nafl. Stand. Ref. Data Ser., Nati. Bur. Stand., No. 37 (1971); (b) J. Phys. Chem. Ref. Data, 8. 916 (1977). (19) “Selected Vaiues of Thermodynamic Propertles”, Nati. Bur. Stand. ( U . S . ) Tech. Note, No. 270-273 (1968). (20) R. Alqasmi, H.-D. Knauth, and D. Rohiack, Ber. Bunsenges. Phys. Chem., 82, 217 (1978). (21) (a) J. C. Morris, J. phys. Chem., 70, 3798 (1966); (b) H. L. Frledman, ibid., 21, 319 (1953). (22) D. P. Stevenson, G. M. Coppinger, and J. W. Forbes, J. Am. Chem. SOC.,83, 4350 (1961). (23) Presumably room temperature. (24) H. Martin, J. Robisch, H.D. Knauth, and K.G. Russet, 2.Phys. Chem. (Frankfurt am Main), 77, 227 (1972).
Quantitative Analysis of XPS Intensities for Supported Catalysts F. P. J. M. Kerkhof” and J. A. Moulijn Institute for Chemical Technology, University of Amsterdam, fiantage Muldergracht 30, 10 18 TV Amsterdam, The Netherlands (Received October IO, 1978; Revlsed Manuscript Received February 26, 1979) Publication costs assisted by the University of Amsterdam
A model is presented to predict XPS intensities for solid catalysts. The model is compared with several models published so far. It is shown that for high surface area supports, covered with a monolayer of metal or metal oxide, the XPS intensity ratio can be predicted from the bulk ratio of the metal and support and from the relative photoelectron cross sections. A method to estimate crystallite sizes from the relative XPS intensities is presented.
Introduction It has been shown by many authors that XPS is a powerful tool in catalytic research. Mainly, binding energies have been used to obtain information on the valency and chemical environment of the atom studied. Less often the XPS intensities are calculated although from these intensities valuable information can be obtained, e.g., the concentration profile of the active material in the catalyst pellet and the size of the deposited material. In order to obtain quantitative information, a number of models have been proposed to predict XPS intensities for solid catal y s t ~ . ~In- ~this study we will present a new model from which the intensities in case of monolayer catalysts and in case of crystallite formation can be predicted. It will 0022-3654/79/2083-1612$01 .OO/O
be shown that the models presented in literature are special cases of our model.
Theory For convenience we shall use the term promoter for any kind of supported material. The relative XPS intensities of the electrons from the support (s) and of the promoter (p) will be a function of the following: the photoelectron cross sections (us,up);the bulk atomic ratio of the promoter and the support (p/s)b; the escape depths of the electrons (A); the surface area of the support (So); the promoter fraction (weight) in the final catalyst (n); the atomic densities in promoter and support (n?,nJ;and the detector , e is the kinetic energy of the elecefficiency D ( E )where @ 1979 American Chemical Society
The Journal of Physical Chemistry, Vol. 83, No. 12, 1979
XPS Intensities for Supported Catalysts
f
1
4
Is,o = AnsosAs,(l- e-01) = AnpapApp(l- P 1 ) f
We shall now calculate the fraction of the electrons from one layer of promoter or support passing through another layer of promoter or support. If we call the fraction of electrons from one support layer passing through a layer of support P,,, the fraction from one layer of promoter passing through a layer of support Ppsetc., the following equations can be derived: P,, = e+
t
4
1613
pPS = e-02
I
I t
t
+ fe-.s
Ppp= 1 - f
+
fe-.1
The electrons from the jth support sheet have to pass j - 1 support layers and 2 j - 1 promoter layers. The intensity of the electrons from the j t h support layer is therefore
Flgure 1. Model of the catalyst particle.
trons. According to our model the catalyst consists of sheets of support, with cubic crystallites with dimension c in between (Figure 1). The thickness ( t )of these sheets can be estimated from the density (p,) and the surface area of the support:
t = 2/PSSO
Psp= 1 - f
(1)
ISJ= I,,opspPsp~'-l
(4)
The total intensity of support electrons reaching the detector is obtained by summation over the layers:
I, = XI,, = I,,ocP,,J-'P,,2,-~ I
I
(5)
Straightforward algebra leads to
I t is assumed that electrons leave the sample only in a direction perpendicular to the surface and that a Lambert-Beer type law is valid:
I ( z ) = I(z=O)e-z/x where I ( z ) is the intensity of the electrons at distance z from the surface. I(z=O)is the intensity of the electrons from the first layer of atoms, which all reach the detector. In our model the following four escape depths are involved: the escape depth of electrons from the support passing through the support (A,,); the escape depth of electrons from the support passing through the promoter (Asp); the escape depth of electrons from the promoter traveling through the promoter (App); and the escape depth of electrons from the promoter traveling through the support (Aps). For one isolated layer of support the amount of electrons escaping is t
I,,o = An,a,L
e-Z/Xns
dz = AnsasA,,(l - e - t / X B a )
(2)
where A is the effective area of the sample from which electrons reach the detector. For an isolated layer of promoter the analogous equation is
Ip,o= fAnpapXpp(l- e-c/x)
The approximation is made that a catalyst particle consists of an infinite number of sheets. For the high surface area supports commonly used, this is certainly acceptable. E.g., a typical porous silica has a wall thickness of 2.6 nm and, therefore, the number of sheets in a particle mounted on tape after grinding will be between 400 and 4000. Considering the fact that the top layers contribute most to the 00 is certainly acceptable. intensity, the approximation j The calculation of the intensity of the promoter atoms is slightly more complicated. The electrons of the promoter on top of the j t h support layer have to pass j - 1 support layers and 2 j - 1 layers of promoter while the electrons of the promoter under the jth support layer have to pass j support layers and 2j - 1 layers of promoter. Therefore the total intensity of the electrons from the promoter on the j t h support layer is
-
IPJ= Ip,opp$lPppD-2+ I P8opPS' PPP2j-1
(7)
This leads to
(3)
where f is the fraction of support covered with promoter. The dimensionless crystallite size parameters are as follows:
The ratio of the number of promoter and support electrons is
a1 = m p p a2
= C/b,
and the dimensionless support thicknesses are
61 = t / h , PZ
This results in
=
t/Ap,
The intensity ratio measured is dependent on the detector efficiency D, which can be a function of' the kinetic energy E of the electrons. If this intensity ratio is (Ip/I,),,p,I D(Ep)Ip,o(l
+ PpsPpJ(1 - P a s p s p 2 )
D(%)I,,o(l- ppsPpp2)psp
(10)
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The Journal of Physical ChemWy, Vol. 83, No. 12, 1979
which generally predicts XPS intensity ratios for solid catalysts. It can easily be shown that for many practical systems Pep= Ppp= 1. This can be illustrated for a W03/Si02catalyst (So= 350 m2 g-l) where, e.g., the W 4f and Si 2p electrons are studied. The escape depth of a W 4f electron in W 0 3 has been reported by Carlson and McGuire4to be 2.63 nm (1450 eV). If a catalyst with high metal loading (20 wt % W03) and low dispersion ( c = 10 nm) is considered then al = c/A,, = 3.8, f = 0.01, and Ppp = 0.99. For a comparable catalyst with high dispersion ( c = 0.5 nm) f = 0.2 and al = 0.19 resulting in Ppp= 0.97. Thus, even for a rather high dispersion this approximation is valid. A similar calculation shows that Psp= 1. With these assumptions eq 10 reduces to
F. P. J. M. Kerkhof and J. A. MouliJn
2
0
-3
4
Figure 2. The correction term (2)as a function of the dimensionless support thickness (p).
XPS intensity of a monolayer catalyst can be predicted with a maximum error of about 10% by
Using eq 2 and 3
(;) We will now express the XPS intensity ratio as a function of the bulk composition, (p/s)b. In our model the surface coverage f can be calculated from f=-
X
(13) SBETP~C If we assume that during catalyst preparation no change in support surface area takes place, SBET = So(l- x) and X = (1 - x)S0ppc
It is easily shown that
where (p/s)b is the atomic ratio of promoter and support. From eq 1, 12, 14, and 15:
In case of a monolayer catalyst a is small and eq 16 reduces to
When electrons with small differences in kinetic energy are studied (e.g., W 4f, Si 2p, A1 2p, Re 4f, and Pt 4f) the difference in escape depth is small and thus A,, = A,, and = p2 = p. In that case D(ep) = D(e,) and the measured intensity ratio will be
In this case the mathematical result is the same as derived by Defoss6 et al.l for the prediction of the intensity of the N 1s electron of a layer of pyridine adsorbed on a silica-alumina. In Figure 2 the term z = (@/2)[(1+ e-p)/(l - e-@)]is plotted as a function of the dimensionless parameter t/A, = p. This figure shows that if p = l, z equals 1-08. This result leads to the conclusion that when the escape depth of an electron from the support has either the same or a smaller value than the support thickness the
exptl
Equation 19 shows that in this case the prediction is the same as if XPS is a bulk technique instead of a surface technique. This rather surprising result can be explained from a practical example. The escape depth of a Si 2p electron for a typical silica support is 3.8 nm (Mg K a radiation). This value can be determined from an interpolation of the data of Klasson et al.5 The sheet thickness of a typical silica support (So = 350 m2 g-l, p = 2200 kg m-3) is 2.6 nm. So in this case the escape depth is greater than the characteristic support thickness and therefore “all” of one support layer is seen by XPS. For a monolayer catalyst all promoter electrons will escape from the supported material and, having a kinetic energy on the order of the energy of the support electrons, will therefore have the same escape depth through the support. These facts result in the conclusion that electrons from the support and from the promoter have an equal chance of reaching the detector. The practical use of eq 19 was shown by Shalvoy and Reucroft2 in case of a series of coprecipitated nickelalumina catalysts. Besides the models used by Defoss6 et a1.l and Shalvoy and Reucroft2 a third model was presented by Angevine et al.3 The model of Angevine is based on only one layer of crystallites on a semiinfinite support. As we showed that the support thickness of a high-surfacearea support has a value on the order of the escape depth of an electron, this assumption of a semiinfinite support is not always valid. Therefore the prediction based on the model of Angevine will be different. Evaluation of this model in case of a monolayer catalyst leads to
(;)
exptl
=(g),:f
The difference between the model of Angevine and our model is the term 1 + e-@ 1 - e-p
For a typical silica ( p N 0.7) the term, mentioned above, equals three. Therefore, in this case, the intensity ratio predicted by the model of Angevine is too high by a factor of 3. Equation 16 also shows that, for a series of catalysts with increasing promoter content but constant crystallite size, a linear relation between the intensity ratio and bulk
The Journal of Physical Chemistry, Vol. 83, No. 12, 1979
XPS Intensities for Supported Catalysts
TABLE I: Theoretical and Experimental Mean Free Paths of Electrons in Some Materials Chandnm Pednm hexpdnm sample dmonolayer/nma e/eV Si SiO, A1203 W
wo
a
0.27 0.25 0.21 0.25 0.24
3
1180 1610 1390 1450 1450
1.9 2.0 1.5 1.9 1.8
2.2 1.9 1.8 1.9 1.9
1815
ref
3.9 4.8 1.3 (1.7) 1.3 2.6
5 5 5 (9) 4 4
Cube edge length of the average volume per atom. TABLE I1 : Comparison of Experimental and Calculated Photoelectron Cross Section Ratios Xrays core sample ( K a ) electrons calcda exptlb wo 3 Mg W 4 f / 0 Is 3.44 4.24 0.29 0.38 SiO, (Grace Mg Si 2p/O Is Davison 6 2 ) 0.18 0.20 A1,03 (Ketjen A1 A1 2 p / 0 Is Grade B)' 0.18 0.22 A1,03 (Ketjen A1 A1 2p/O Is CK300) 0.26 0.29 SiO, (ref 5) A1 Si 2p/O Is
Fraction monolayer intensity
0
5
10
ai
*
Figure 3. The intensity ratio in case of crystallite growth (fraction of the monolayer prediction) as a function of the dimensionless crystallite size (a, = c/X,,).
composition can be expected. Prediction of the Crystallite Size of Supported Materials. The monolayer intensity of a given system is predicted by eq 17 whereas eq 16 must be used when crystallites are formed. By taking the quotient of these equations the relation between the intensity in case of crystallite growth and in case of monolayer formation is given by
This relation is plotted in Figure 3. Therefore the procedure for estimation of the crystallite size is as follows: (1)Based on estimated values of ap, as (see next section), PI, Pz, and the bulk atomic ratio, the intensity ratio in case of a monolayer catalyst is calculated. (2) Based on the measured value the percentage of the monolayer value is calculated. (3) With Figure 3 an estimate is made of c / A p p and, when A,, is known, of c. We shall demonstrate this procedure for a series of Pt/SiOz catalysts measured by ScharpenS6 Evaluation of Escape Depths and Cross Sections. (1) Escape Depths. A method to estimate escape depths in elemental solids and compounds has been published by Penn.' The method gives the mean free path in freeelectron-like materials accurate to 5% whereas for nonfree-electron materials the error may be as much as 40%. In the same paper the energy dependence of electrons with different kinetic energies in free-electron and non-freeelectron materials is presented as el (In cz - 2.3) -A(€,) =(22) A(€,) cz(ln el - 2.3) with a typical error of 5% for both types of materials. So, in spite of a relatively large error in the absolute value of A, the ratio of the free paths can be calculated rather accurately. An empirical estimate of A was presented by Chang? viz. A, = 0.2d/'d, where d is the thickness of a monolayer
a Scofield. This work. Corrected for the energy dependence of h ( c ) and l l ( ~ ) . After 16 h in a fluidized bed at 820 K.
estimated as 0.25 nm. The values of A estimated by the relations of Chang and Penn are compared with experimental results in Table I. The experimental values were determined by Klasson et al.5 and Battye et al.9 from the loss of intensity of electrons of known kinetic energy through layers of known thickness. The table shows a reasonable agreement between the estimates of Chang and Penn. However, these values sometimes differ considerably from the experimental values. An example is the escape depth of an Si 2p electron in silica for which the experimental value is twice the predicted value. For alumina better agreement is found. Later it will be demonstrated that the predictions of the model are not very sensitive to errors in the estimation of the free path. (2) Photoelectron Cross Sections. One method to estimate photoelectron cross sections is based on measuring compounds of known composition. The intensity ratio of a compound M,N, is given by
(!E)
=---X: D(cM) UM exptl
y
D(EN) GN
A(")
If the core electrons of the same kinetic energy are studied then
(2)
= -X-uM
exptl y UN and the cross sections are easily estimated. When the energies are different the detector efficiency must be known as a function of t. In our study (see Experimental Procedures) D ( 4 1 / ~If. the Penn energy dependence of A is taken into account D(tp~) A ( ~ M ) - In CN - 2.3 -In CM - 2.3 D ( E ~A(€,) J) which is about one for a large range of differences between CM and Q. If, e.g., SiOz is studied with Mg K a photons then this ratio for the Si 2p and 0 1s electrons is 0.90. Obviously, if the cross sections had been determined without correcting for the energy dependence of A and D, the estimates would have been correct to within 10%. Calculated cross sections have been presented in literature.l@I2 Table I1 shows a comparison of cross sections measured by us and theoretical values calculated by
-
1616
The Journal of Physical Chemistry, Vol. 83, No. 72, 1979
Scofield.lo A reasonable agreement is observed and therefore the values of Scofield will be used in this study. However, due to a large difference in the reported cross section ratios for one silica sample,13measured on several spectrometers, it is advisable to check these values, for the apparatus used, by measuring reference samples. The best results will be obtained by measuring the intensities of core electrons with a small difference in kinetic energy because in that case the uncertainty in D(e) and A(€) is eliminated. This can be demonstrated by the data in Table 11. The estimate of a(W 4f)/a(Si 2p) calculated from W03 and Si02 is 11.2 whereas the value of Scofield is 13.2 in this case. So in spite of the large deviation in a(W 4f)/(r(O 1s) a reasonable agreement is found for the cross sections calculated from the intensities of electrons of the same kinetic energy. However, it should be kept in mind that the method is based on a known composition and it is always questionable whether the surface composition of a reference compound is equal to the bulk composition. Comparison of Predictions of t h e Model with Experimental Results In this section the following catalysts will be considered: (1) a series of Re207/A1203catalysts; (2) a series of fluorine-containing aluminas; and (3) a series of Pt/Si02 catalysts, measured by Scharpena6 Experimental Procedure. (I) Catalyst Preparation. Rhenium oxide on alumina was prepared by impregnation of Ketjen CK300 y-alumina with aqueous solutions of ammonium perrhenate and subsequently drying and calcining. Further details on the preparation and activity of these catalysts are given by Kapteijn et and Kerkhof et aI.l5 The preparation of the fluorinated alumina was based on coimpregnation of aluminum nitrate and ammonium fluoride on alumina. This is slightly different from procedures where the support is treated with solutions of NH4F or with HF. Further details are given e1~ewhere.l~ (2) Spectrometer Procedures. The XPS spectra were recorded with an AEI ES-200 spectrometer with a hemispherical detector operated in the constant pass energy mode which gives a detector efficiency varying linearly with e-l. A1 K a X rays with a source power of 180 W were used. The sample temperature varied between -15 and -35 "C. The intensity of the core electrons was determined by measuring peak areas which were corrected for scanning time and attenuation. The catalyst samples were well powdered and mounted on tape in a glove box attached to the spectrometer. Due to the differential charging of the samples rather broad peaks are obtained in this way.16 However, still the intensities can be measured and used to determine the dispersion of the promoter on the support. The binding energies were determined at the half-width of the peak measured at half-maximum height and corrected for charging. Results. ( 1 ) The Catalyst Rhenium Oxide on Alumina. From infrared spectroscopy it was concluded by Olsthoorn and Boelhouwer17 that the rhenium is monomolecularly dispersed on the alumina surface. Later on we showed that for a rhenium loading higher than 6 wt % Re207 the rhenium is present as Reo4- tetrahedra.18 For these catalysts the values of the characteristic binding energy and the widths at half-maximum peak height (in parentheses) were 531.6 (3.0) for 0 Is, 284.6 (2.7) for C Is, and 47.9 (4.9) eV for Re 4f electrons. The A1 2p binding energy at 75.0 eV was used as a reference. The measured peak areas are given in Table 111. For alumina a value of 1.3 nm has been reported for the
F. P. J. M. Kerkhof and J. A. Mouiijn
TABLE 111: XPS Intensitiesa of the Re,O,/A1,0, Catalysts [IReif / I A l z ~ l
,
% Re,O,
5.7 8.3 10.7 13.0 15.3 18.0 Peak areas.
(Re/Al),
0.013 0.019 0.025 0.032 0.038 0.046
calcd h = 1.3 h = 1.8 nm nm
0.35 0.53 0.70 0.88 1.06 1.29
0.32 0.47 0.61 0.78 0.93 1.13
exptl
0.34 0.49 0.60 0.85 0.92 1.26
1.0
05
0
0 04
0 02 (Re/Al)bulk P
Figure 4. Calculated and measured XPS intensities for Re2O7/AI2O3 catalysts.
A1 2p electrons at a kinetic energy of 1390 eVq6The kinetic energies of Re 4f and A1 2p electrons differ only 2% and, therefore, we assume that the free path of the Re 4f electrons in alumina is also 1.3 nm and that the detector efficiencies are equal. From the surface area So (190 m2 g-l) and the bulk density of y-alumina (3800 kg m-3) it follows that t = 2.77 nm and p1 = p2 = = 2.13. This results in z = 1.35. The value of u(Re 4f)/a(Al2p) of Scofield = 20.63 (A1 Ka) and, therefore, the prediction of the XPS intensity ratio is [IRe4f/IA12p]exptl = 27.85 (Re/Al)b. If in this case the Penn value of X is used (1.8 nm), p = 1.54, z = 1.19, and [IRe4f/IAlSp]exptl = 24.5 (Re/Al)b, which differs 12% from the previous value. This is demonstrated in Figure 4, which shows that the model fits the experimental data reasonably for both values of A. This will be the case for low values of 0, which means small wall thickness and large escape depth. (2) Fluorine-Containing Aluminas. The XPS spectra of a series of fluorinated aluminas have been studied by Dreiling,lg Scokart et and Kerkhof et a1.21 Here we compare recent results in a series of fluorinated aluminas with the predictions of the model and with the literature. We studied the F Is and A1 2p electrons. Because the kinetic energies are different a distinction between p1 and pz must be made. If the value of 1.3 nm of Klasson et ale5 is used for the mean free path of the A1 2p electrons a value of 0.83 nm is calculated by the method of Penn7 for the F 1s electrons. For the alumina used (So= 320 m2 g-l) t = 1.64 and, therefore, p1= 1.27 and p2 = 1.98 and z = 0.84. The cross section ratio of Scofield for the F 1s and A1 2p electrons in the case of A1 Ka photons is 8.64 and the monolayer prediction is
XPS
The Journal of Physlcal Chemistry, Vol. 83, No. 12, 1979
Intensities for Supported Catalysts
TABLE IV: XPS Intensitiesa of the Fluorine-Containing Alumina
%F
a
(F/Al)b
0.04 0.06 0.13 0.14 0.17 0.40 0.74 1.79
1.3 2.3 4.7 5.0 6.0 13.7 23.7 48.0 Peak areas.
I
[IFl J I ~ i d exptl
cdcd 0.5 0.8 1.7 1.8 2.2 5.1 9.5 22.9
0.6 1.0 1.9 1.6 1.9 4.4 7.3 14.1
15-
/(Fls)
i(AI2P)
I
lo-
05
10 W)b",k
20
15
____)
Flgure 5.
Calculated and measured XPS intensitles for F/A1203catalysts.
The experimental results are presented in Table IV and Figure 5 which show a good agreement a t . 1 0 ~fluorine contents. At higher fluorine content (>lo wt % F) a systematic deviation is observed, which can be explained by the occurrence of aluminum hydroxyfluorides and aluminum fluoride crystallites from which only part is "seen" by XPS. Dreiling studied a series of fluorinated aluminas with a fluorine content up to 5 wt % F. In this study Mg K a X rays were used and therefore the A1 2p electrons will have a slightly smaller free path than in our experiments. Using the estimation of Penn a value of 1.09 nm for the A1 2p and 0.64 nm for the F 1s electrons is found. The prediction of XPS intensities in case of the measurements of Dreiling differs slightly from the method presented in the Introduction. This is caused by the fact cannot be represented by SBET that the surface area SBET = So(l- x ) . Therefore, the surface area measured must be used instead of the approximation used in eq 14. This results in the prediction
(2)
exptl
p =
(1 - x)D(ep)-gPp1(1
D(e,)
+ e-pz)
gaP2 (1-
e-62)
For each measurement t varies and, therefore, PI and P2 are dependent on the fluorine content. Further calculations showed that a t 0.5% fluorine our model predicts a 20% higher value than was measured. A smooth increase of this deviation with the percentage of fluorine is observed. The fact that the experimental intensity is lower than predicted by the model may be explained in several ways: Crystallites formed. In samples with a fluorine content exceeding 10 wt % we find crystalline material. For aluminas impregnated with NH4F, crystallite formation
1617
at even lower contents was reported by Scokart et alez0 Fluorine was lost during preparation. Such a loss was observed by Scokart et al. and also by us. This resulted, e,g., in a fluorine content of 3.7% F for a catalyst where the expected value was 5.7% F. There was a concentration gradient of fluorine within the catalyst particle. If the preparation resulted in a higher concentration of fluorine inside the particle also a too low fluorine signal will be observed when the particles are not sufficiently well powdered. The assumption of crystallite formation is not supported by the binding energies of A1 2p and F Is electrons reported by Dreiling because the shifts corresponding to crystallite formation2I are not reported. Summarizing it can be stated that at low fluorine content a monolayer of fluorine atoms on the surface of alumina is formed. The intensity of the F Is signal in that case can be well predicted by the model presented in the Introduction. (3) Silica Supported Platinum. In this section the measurements of Scharped will be reinterpreted with our model, Scharpen has reported the XPS intensities of a number of Pt/Si02 catalysts. Some of the catalysts showed 100% dispersion, measured by hydrogen chemisorption, and some of them consisted of platinum crystallites on the support and, therefore, had a lower dispersion. One catalyst with 34% dispersion showed a relatively high XPS intensity ratio. BriggsZ2suggested that due to incomplete reduction, for this catalyst, the hydrogen uptake and, therefore, the dispersion calculated was too low. On the other hand Angevine3 suggested that, for this catalyst, prepared by impregnation, the Pt would be preferentially present on the outer surface and in larger pores. So the XPS intensity of this point is perhaps not reliable. In spite of this fact it will be shown that it fits the 100% dispersion or monolayer prediction. The analysis of the data of Scharpen is hampered further by two facts: a relatively large variation in reported surface areas which would result in large variations of /3, and the uncertainty in the value of A,,. As we showed in Table I there is a difference in the measurements of Klasson and the calculations of Penn. However, Penn concludes that his calculations will give the largest error for non-free-electron-like materials and, therefore, we preferred the measured high value of A, = 4.5 nm (A1 Ka). If we assume So is constant and equal to 276 m2 g-l (reported by Angevine et al.3) and ept4f = €siap then = 0.73 and z = 1.04. This gives for a monolayer catalyst (IPt4f/lSiPp)exptl = 19*7(Pt/Si)b The results of the measurements of the 100% dispersed catalysts and the catalysts with crystallites on it are given in Table V. In this table also the values of the crystallite sizes calculated from the dispersion and from the XPS intensities are given. For catalyst no. 5 the measured XPS intensity ratio is 0.069. With a bulk atomic ratio of 11.9 X eq 21 would predict an intensity ratio of 0.23 and therefore the fraction of the monolayer intensity is 29.4%. From Figure 3 or relation 22 a is determined as 3.3 which is the value of c/hP in the table. The monolayer prediction and the experimental values for well-dispersed catalysts are given in Figure 6 which shows an excellent agreement between the predicted and experimental values. However, if we had applied a lower value of A, e.g., 2 nm, z would be 1.22 and the prediction would be 17% higher than the one presented. In Figure 7 the crystallite sizes estimated from the dispersion and from the XPS model are correlated. Although only three points could be calculated, the figure
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The Journal of Physical Chemistry, Vol. 83,
No. 12, 1979
F. P. J.
M. Kerkhof and J. A. Mouiijn
TABLE V : XPS Intensities and Crystallite Sizes for the Pt/SiO, Catalysts [IptrflI~izp1
a
catal no,a
%Pt
(Pt/Si)b/lO-'
calcd
exptl
% dispernb
1 2 3 4 5 6 7
1.5 1.1
4.71 3.44 1.18 7.27
0.093
0.092 0.067 0.022 0.076
100 100 100
0.38 2.3 3.7 0.53
11.9 1.65 2.49
0.80
Scharpen.
0.068 0.023 0.143 0.234 0.033 0.049
Measured b y hydrogen chemisorption.
/ / /
0.019 0.047
/
0 Experimental (100% dispersion)
/ 0
))
( 34x
cd /nmc
1.4 3.3 1.2
1.6 7.1
1.8
Calculated f r o m chemisorption ( c d = 100/dispersion).
Colculated
0
62 14 56 34
0.069
c / h p p calcd
?9
8
2
"i
4 6
2
,
0 002
0 004
-
0 006
(pt~5~)bulk
Figure 6. Calculated and measured XPS intensities for silica-supported platinum.
shows that a linear correlation between these estimates can be obtained. From the slope of the line the value of in platinum is estimated to be 1.9 nm, which is in good agreement with the value of 1.63 nm calculated by Penn7 and the value of 2.2 nm reported by BriggsZ2and Br~ndle.2~ This last example shows how XPS can be used to study crystallite sizes when free paths are known or to determine free paths when crystallite sizes are known.
Concluding Remarks In this paper we showed for a number of catalysts that the relative XPS intensity can be predicted from a model which is based on sheets of the carrier with the promoter, well dispersed or as crystallites, in between. A method to estimate crystallite sizes from measured XPS intensities is presented and demonstrated for Pt/Si02. It was shown that for high-surface-area catalysts the escape depth of the electrons is on the order of the thickness of the sheets and therefore the assumption of a semiinfinite support is not valid in these cases. Important parameters are the relative photoelectron cross sections and the escape depths of the electrons. In our prediction we used the cross sections reported by ScofieldlO and showed that for a number of pure compounds these values agree with our measurements. The absolute escape depths cannot be evaluated accurately. However, reliable estimates of the ratio of the free paths in one material for different kinetic energies can be made by the formalism given by Penn.' It was shown that the model is not very sensitive to errors in the escape depth. To test our model we tried to evaluate a number of XPS intensities given in l i t e r a t ~ r e .However, ~~ in most cases the measurements for pure compounds are not given and therefore it could not be verified whether the values of Scofield can be used. In one case, the Pt/Si02 catalyst of Scharpen, the relative intensity of the support was given and agreed well with an estimate based on the cross sections of Scofield. In that case good agreement between
0
Figure 7. Comparison of the dimensionless crystallke size (a,= c / b ) calculated from the XPS model and the crystallite size (c,) calculated from hydrogen chemisorption.
the predicted and measured intensity was observed. Our own measurements for a series of Re207/A1203catalysts and for fluorinated alumina could also satisfactorily be explained by the model. Although some uncertainties still exist, the model can be used for series of catalysts with increasing promoter content. For monolayer catalysts as well as for catalysts with crystallites of constant sizes a linear relation between relative XPS intensity and bulk atomic ratio may be expected. From a deviation between monolayer catalysts and crystallite containing samples an estimate of the crystallite size can be made. A deviation of the linear correlation can be interpreted in terms of sample inhomogeneity or crystallite growth.
Acknowledgment. This study was supported by the Netherlands Foundation for Chemical Research (S.O.N.) with financial aid from the Netherlands Organization for Advancement of Pure Research (Z.W.O.). We thank Dr. G. Sawatzky and A. Heeres from the Laboratory for Physical Chemistry of the University of Groningen for their help in recording and interpreting the XPS spectra. References and Notes (1) C. Defoss6, P. Canesson, P. G. Rouxhet, and B. Delmon, J. Catal., 51, 269 (1978).
(2) R. B. Shalvoy and P. J. Reucroft, J. Electron Spectrosc. Relat. Phenom., 12, 351 (1977). ( 3 ) P.J. Angevine, J. C. Vartuli, and W. N. Delgass, Proc. Int. congr. Catal., 6th, 7976, 2 , (1977). (4) T. A. Carlson and G. E. McGuire, J. Electron Spectrosc. Relat. Phenom., 1, 161 (1972/1973). ( 5 ) M. Klasson, A. Berndtsson, J. Hedman, R. Nilsson, R. Nyholm, and C. Nordling, J. Spectrosc. Relat. Phenom., 3 , 427 (1974). (6) L. H. Scharpen, J. Electron Spectrosc. Relat. phenom., 5,369 (1974). (7) D. R. Penn, J. Electron Spectrosc. Relat. Phenom., 9, 29 (1976). (8) C. C. Chang, Surface Scl., 48, 9 (1975). (9) F. L. Battye, J. C. Jenkin, L. Liesegang, and R. C. G. Leckey, Phys. Rev. 6,9v 2887 (1974). (10) J. H. Scoflekl, J. Electron Spectrosc. Relat. Phenom., 8, 129 (1976).
Adsorptlon of Interacting Chain Molecules
(11) C. D. Wagner, Anal. Chem., 44, 1050 (1972). (12) V. I. Nefedov, N. P. Sergwhln, I. M. Band, and M. B. Trzhaskovskaya, J . Electron Spectrosc. Relat. Phenom., 2 , 383 (1973). (13) T. E. Madey, C. D. Wagner, and A. Joshl, J. Nectron Spectrosc. Relat. Phenom., 10, 359 (1977). (14) F. Kapteljn, L. H. G. Bredt, and J. C. Mol, Red. Trav. Chim. Pays-Bas, 96, 139 (1977). (15) F. P. J. M. Kerkhof, J. A. Moulijn, R. Thomas, and J. C. Oudejans, Proceedings of the 2nd Internation Symposium on "Scientific Bases for the Preparation of Heterogeneous Catalysts", in press. (16) F. P. J. M. Kerkhof, J. A. Moull~,and A. Heeres,J. Electron specbosc. Relat. Phenom., 14, 453 (1978). (17) A. A. Olsthoorn and C. Boelhouwer, J. Catal., 44, 197 (1976).
The Journal of Physical Chemistty, Vol. 83, No. 12, 1979
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(18) F. P. J. M. Kerkhof, J. A. Moulijn, and R. Thomas, J. Catal., 58, 279 (1979). (19) M. J. Drelling, Surface Sci., 71, 231 (1978). (20) P. 0. Scokart, S. A. Selim, J. P. Damon, and P. G. Rouxhet, J. colloid Interface Sci.. in Dress. (21) F. P. J. M. Kerkhoi, H. J. Reitsma, and J. A. Moulijn, React. Kinet. Catal. Lett., 7 , 15 (1977). (22) D. Briggs, J. Electron Spectrosc. Relat. Phenom., 9, 487 (1976). (23) C . R. Brundle, Surf. Scl.. 48. 99 (1975). (24) J. Grimblot, J. P. Bonnelle, and J. P.'Beadils, J. E/ectron Spectrosc. Relat. Phenom., 8, 437 (1976); J. Grimblot and J. P. Bonnelle, IbM., 9, 449 (1976); J. S. Brinen, J. L. Schmitt, W. R. Doughman, P. J. Achorn, L. A. Siegel, and W. N. Delgass, J. Catal., 40, 295 (1975).
Statistical Theory of the Adsorption of Interacting Chain Molecules. 1. Partition Function, Segment Density Distribution, and Adsorption Isotherms J. M. H. M. Scheutjens" and 0. J. Fleer Laboratory for Physical and Colloid Chemistry, De Dreljen 6, Wageningen, The Netherlands (Received July 17, 1978; Revlsed Manuscript Received December 29, 1978)
We present a general theory for polymer adsorption using a quasi-crystalline lattice model. The partition function for a mixture of polymer chains and solvent molecules near an interface is evaluated by adopting the Bragg-Williams approximation of random mixing within each layer parallel to the surface. The interaction between segments and solvent molecules is taken into account by use of the Flory-Huggins parameter x;that between segments and the interface is described in terms of the differential adsorption energy parameter xs. No approximation was made about an equal contribution of all the segments of a chain to the segment density in each layer. By differentiating the partition function with respect to the number of chains having a particular conformation an expression is obtained that gives the numbers of chains in each conformation in equilibrium. Thus also the train, loop, and tail size distribution can be computed. Calculations are carried out numerically by a modified matrix procedure as introduced by DiMarzio and Rubin. Computations for chains containing up to lo00 segments are possible. Data for the adsorbed amount r, the surface coverage 0, and the bound fraction p = O/r are given as a function of xs,the bulk solution volume fraction and the chain length r for two x values. The results are in broad agreement with earlier theories, although typical differences occur. Close to the surface the segment density decays roughly exponentially with increasing distance from the surface, but at larger distances the decay is much slower. This is related to the fact that a considerable fraction of the adsorbed segments is present in the form of long dangling tails, even for chains as long as r = 1000. In previous theories the effect of tails was usually neglected. Yet the occurrence of tails is important for many practical applications. Our theory can be easily extended to polymer in a gap between two plates (relevant for colloidal stability) and to copolymers. c#J,,
I. Introduction The adsorption of polymers at interfaces is an important phenomenon, both from a theoretical point of view and for numerous practical applications. One of the areas where polymer adsorption plays a role is in colloid science, since many colloidal systems are stabilized or destabilized by polymeric additives. In these cases, not only the adsorbed amount is an important parameter, but also the way in which the polymer segments are distributed in the vicinity of a surface. An adsorbed polymer molecule generally exists of trains (sequences in actual contact with the surface), loops (stretches of segments in the solution of which both ends are on the surface), and tails (at the ends of the chain with only one side fixed on the surface). If two surfaces are present at relatively short separations, bridges (of which the ends are adsorbed on different surfaces) may also occur. The properties of systems in which polymer is present depend strongly on the length and distribution of trains, loops, tails, and bridges. Many of the older theories1* on polymer adsorption treat the case of an isolated chain on a surface. These treatments neglect the interaction between the segments and have, therefore, little relevance for practical systems, since even in very dilute solutions the segment concen0022-365417912083- 16 19$0 1.OOlO
tration near the surface may be very high. Other theories7i8 account for the interaction between chain segments but make specific assumptions about the segment distribution near the surface which are not completely warranted, such as the presence of a surface phase with only adsorbed molecules' or the neglect of tails.* For oligomers up to four segments a sophisticated theory has been presented9 but its application to real polymer molecules is impossible due to the tremendous computational difficulties involved. The most comprehensive theory for polymer adsorption as yet has been given by Roe,lo although here also a simplifying assumption is made, namely, that each of the segments of a chain gives the same contribution to the segment density at any distance from the surface. Roe arrives at the segment density profile near the surface, but does not calculate loop, train, and tail size distributions. Recently, Helfandl' has shown that Roe's theory is also incorrect on another point, since the inversion symmetry for chain conformations is not properly taken into account. Helfand corrects this by introducing the so-called flux constraint, but his calculations apply only to infinite chain lengths. Less work has been done on the problem of polymer between two plates. DiMarzio and Rubid* give an elegant 0 1979 American Chemical Society
