Anomalous small-angle x-ray scattering from mesoporous noble metal catalysts
Abstract
We present the analysis of a catalyst containing platinum nanoparticles supported on mesoporous MCM-41 silica by anomalous small-angle x-ray scattering (ASAXS). The analysis of this composite system by ASAXS is first studied by use of model calculation. Here, it is shown that the full analysis must proceed by decomposing the scattering data measured at different energies of the incident beam into three partial intensities. This evaluation is compared to a simplified method in which scattering curves measured at two different energies are subtracted from each other. The different methods are applied to experimental data obtained from platinum nanoparticles on an MCM-41 support material. The model calculations show that the simplified method leads to large deviations especially at low q in ordered systems. In the semi-ordered material MCM-41, these deviations are less pronounced, and the method of simple subtraction proves to be a good approximation for q values higher than 0.1 nm^{−1}.
Keywords
Small-angle x-ray scattering Catalyst Noble metal MCM-41Introduction
Matrix-supported metal systems represent an important class of catalysts. They are usually obtained by impregnation of a porous support material like SiO_{2} or γ-Al_{2}O_{3} to yield a high dispersion of the active metal [1]. In particular, ordered mesoporous silica such as MCM-41 and MCM-48 has been intensely studied as support for catalytically active noble metals [2, 3, 4]. These materials provide a high specific surface area and an ordered system of mesopores with a narrow size distribution typically in the range of 2 to 15 nm. Besides being suitable model supports, these materials can thus stabilize nanosized particles within their pore system. This is an advantage particularly for supported metals which often undergo sintering during catalytic applications, e.g. at elevated temperatures [5, 6, 7].
f_{0} is the non-resonant term given by the number of electrons of the respective element and therefore constant. f′ and f″ are the so-called anomalous dispersion corrections which depend on the energy of the incident radiation and can be calculated or taken from literature [12, 13, 14]. In the vicinity of absorption edges, f′ and f″ change markedly. In this manner, the contribution of elements exhibiting strong anomalous scattering can be dissected by determining the scattered intensity at two different energies E far and near to an absorption edge. The scattered intensity of anomalous scatterers will change under these conditions, while the one of non-anomalous scatterers will remain unchanged in good approximation.
In recent years, ASAXS has been used frequently to characterize the volume as well as spatial distribution of metal catalyst particles supported by matrix materials. Usually, the matrix is made of “light” elements with low electron density while the metals are rich in electrons and exhibit absorption edges in energy ranges available at synchrotron sources. Thus, investigations have been carried out to characterize such catalyst materials containing platinum [15, 16, 17, 18, 19, 20, 21, 22], nickel [23, 24, 25], ruthenium [26, 27, 28], palladium [29, 30], germanium [31], gold [32, 33] or copper [34]. In most cases ASAXS was utilized to obtain the volume or size distribution of the structure elements formed by the metal nanoparticles.
Two methods were used for the evaluation of the ASAXS data. In many investigations, I(q) is determined at two energies, one close to the absorption edge and one far from it, and the scattering contribution of the metal is obtained by simple subtraction of two scattered intensities I(q) [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30]. In the second approach, the anomalous scattering intensity is split up into three partial intensities as shown many years ago by Stuhrmann [11]. This decomposition proceeds without additional assumptions [35, 36, 37, 38] and has been employed in numerous studies in the last decade due to the improved accuracy of ASAXS experiments [27, 28, 38]. The third partial intensity describes the scattering intensity which is solely due to the anomalous scattering units, that is, the metal particles in case of heterogeneous catalyst. Here, the question arises under which condition the simplified method may lead to meaningful results.
In an important paper, Brumberger et al. [39] showed that for metal spheres embedded in a non-ordered, randomly oriented support phase, the simple difference I(q, E) − I(q, E′) will yield an expression with a q dependence solely depending on the shape and spatial distribution of the metal particles. In this case, the supporting material and the void space which surround the metal clusters effectively can be treated like a quasi-homogenous medium. It must be noted, however, that the approach of Brumberger et al. is based on stringent assumptions that may or may not be met by the catalyst under consideration.
Here, we present the analysis of a catalyst in which platinum nanoparticles are incorporated into a mesoporous MCM-41 silica support. We combine this analysis with a general discussion of the evaluation of ASAXS data obtained from solid catalysts consisting of a matrix of light elements (SiO_{2} or polystyrene (PS)) and metal (Pt) nanoparticles. The general goal of this study is the assessment of partial order of the matrix on the resulting anomalous scattering intensity.
Theory and model calculations
The term \( {F_0}^2(q) \) depicts the non-resonant contribution to the overall scattering measured far away from the adsorption edge. The second term is the cross term of the non-resonant and resonant scattering amplitudes F_{0}(q) and ν(q), respectively. The third term v^{2}(q) represents the resonant scattering contribution solely of the Pt particles.
i.e., the q-dependent part of I(q, E) − I(q, E′) depends only on size and distribution of the metal particles. In this case, the information about the metal nanoparticles in the system can be obtained by analysing the difference curves according to Eq. (5). A similar method of evaluation has been used by Yu et al. [22]. Here too it is assumed that the total ASAXS signal from platinum embedded in porous material consists of two parts I_{Pt}(q, E) and I_{pores}(q) which add up linearly. Thus, the scattering function is separated via subtraction of two curves I(q, E) determined at two different energies [22]. However, the discussion of Eq. (5) demonstrates that this above approach is only valid under the assumption that the combined void and support phase forms a non-ordered system throughout all relevant length scales. In order to elucidate this problem further, model calculations will be presented in the following.
The PS and Pt spheres are located at a distance of \( L={R_{\mathrm{PS}}}+{R_{\mathrm{Pt}}} \) from each other. Cross terms F_{PS}(q)F_{Pt}(q) therefore have to be multiplied by the factor sin(q L)/(q L) in order to take into account the interference between the small and the large sphere [41].
Simulation parameters for the two attached PS/SiO_{2} and Pt spheres
R_{i}/nm | f_{0,i} | ρ_{0,i}/(10^{10} cm^{−2}) | |
---|---|---|---|
PS | 500 | 56 | 9.553 |
SiO_{2} | 500 | 30 | 19.49 |
Pt | 5 | 78 | 143.1 |
Coefficients f′ and f″ for the calculation of the scattering length of Pt as function of energy of the incident radiation [14]
E_{i}/keV | f′ | f″ |
---|---|---|
9.03 | −4.304 | 5.761 |
11.03 | −7.496 | 4.109 |
11.55 | −15.102 | 3.806 |
Here, the small-volume fraction of the Pt spheres can be safely neglected, i.e. ϕ is considered to be solely occupied by support particles. Moreover, we disregard any mutual interference of the Pt spheres in the course of the model calculations. The effect of interparticle correlations between the large spheres was model by using the structure factor S(q) for a system of hard spheres given by the Percus–Yevick approximation [42]. This approximation was shown to give an excellent description of the scattering intensity of a system of randomly packed spheres [43, 44]. An algorithm as implemented in the software SASfit was used for the computation [45]. The computation of I(Q) according to the formulas outlined above was performed with the software Mathematica [46]. Polydispersity of the PS/SiO_{2} particles was introduced by the convolution of the respective radii with a normal distribution. The hard sphere repulsion radius of the structure factor S(q) was set equal to the radii of the large support particles. This procedure is of course an approximation for a polydisperse system. It will turn out, however, that this approximation is inconsequential.
Experimental section
The MCM-41-type silica was prepared according to a procedure reported earlier [47]. For incorporation of Pt, the MCM-41 powder (2 g) was loaded with [Pt(NH_{3})_{4}]Cl_{2} (Chempur, 99.5 wt%) from an aqueous solution (deionized water) by incipient wetness impregnation. The target loading was 4 wt% Pt. Subsequently, the sample was pressed (20 MPa), crushed and sieved to obtain the particle fraction of 1.1–1.6 mm. Batches of 0.5 g of the pelletized material were treated in a flow of air (150 cm^{3} min^{−1}) at 250 °C for 3 h and then, in flowing hydrogen (150 cm^{3} min^{−1}) at 280 °C for 2 h to obtain Pt nanoparticles supported on MCM-41 (Pt/MCM-41).
The platinum content of the resulting Pt/MCM-41 materials was determined by optical emission spectrometry with inductively coupled plasma (ICP-OES instrument: PerkinElmer, Plasma 400) after dissolution in 50 vol% hydrofluoric acid (Fluka, 40 wt% in water) and 50 vol% hydrochloric acid (Fluka, 37 wt% in water). Thus, a Pt loading of 3.4 wt% was obtained.
The textural properties of the Pt/MCM-41 material were characterized by nitrogen physisorption at −196 °C on a micromeritics, ASAP2010C equipment. Prior to analysis, the samples were activated at 350 °C for 12 h at a pressure <1 Pa. The same instrument was used for determination of the Pt dispersion via hydrogen chemisorption at 30 °C. In this case, the samples were activated at 350 °C for 2 h at a pressure <1 Pa.
X-ray diffractograms were recorded on a Siemens D5000 instrument using CuKα radiation (30 mA, 40 kV). For characterizing the structure of the MCM-41 material, the 2θ range of 1.5° to 7° (step size, 0.2°; 5 s/step) was scanned. The Pt particle size was estimated using the Scherrer equation using the full width at half maximum from a Gaussian fit of scanning time of 20 s/step. TEM micrographs were obtained from the Pt(111) − reflection at 2θ = 39.7°. For this, a field emission electron microscope (type Jeol, JSM-2100F) at the Institute for Physical Chemistry and Electrochemistry at the Leibniz Universität Hannover was employed.
ASAXS measurements were performed at the JUSIFA beamline [48] at HASYLAB, DESY Hamburg at three different energies in the energy range of the L_{III} absorption edge of platinum at 11.564 keV with a precision in the resolution regime 10^{−3} < ΔI/I < 10^{−2} (separated pure resonant scattering with respect to the overall scattering). Precise corrections (background, sensitivity, transmission, normalization, dead-time correction, dark current) and the calibration of the scattering curves into absolute units are mandatory and have to meet these accuracy requirements (i.e., should be better by one order in magnitude). Transmission measurements were performed with a precision of 10^{−4} using a special (windowless) photodiode (Hamamatsu S2387-1010N). The dead-time correction of the MWPC detector was measured for each exposure and corrected for in the data reduction. The normalization of the scattering pattern was performed by measurements of the primary photon flux with a sodium-iodine scintillation counter with an accuracy of better than 10^{−4}.
The scattering curves of all sample measurements have been calibrated into macroscopic scattering cross section in units of cross section per unit volume [cm^{2}/cm^{3}] = [cm^{−1}] by using the JUSIFA glassy carbon standards. The errors have been calculated via error propagation law from the statistical errors of the photon counts of all contributing measurements (i.e. measurements of sample, sensitivity, background, dark current).
Results and discussion
The 3.4 Pt/MCM-41 material (Pt loading of 3.4 wt%) shows an x-ray diffractogram typical of the ordered mesoporous MCM-41-type silica support (see Online resource, Fig. S1) [49]. Also, as expected, the nitrogen sorption isotherms are of type IV according to the IUPAC classification corresponding to a specific surface area of 1,018 m^{2} g^{−1} and a pore diameter of 2.3 nm (BJH model) (see Online resource, Fig. S2).
Assuming a spherical geometry and an fcc structure of the Pt particles, an average diameter of 16.6 nm (Pt dispersion of 7 %) was determined by XRD applying the Scherrer equation to the Pt(111) reflection at 2θ = 39.7°. From hydrogen chemisorption, a clearly lower average particle diameter of 3.3 nm (Pt dispersion, 33 %) was obtained. It should be noted, however, that Pt particles with diameters lower than 1 nm cannot be detected by XRD and that particles of low crystallinity and deviations of the fcc structure do not substantially contribute to the Pt(111) reflection [50]. XRD, therefore, may overestimate the actual average Pt particle size, especially when smaller particles are present. On the other hand, hydrogen chemisorption often underestimates the noble metal particle size as deviations of the assumed stoichiometry of H/Pt of 1 to higher values, corresponding to higher Pt dispersions than 100 %, may result [49].
From Eqs. (5) and (12), it is evident that the resonantly scattered intensity extracted by simple subtraction and the one extracted by decomposition are just separated by a constant factor and thus should exhibit the same q dependency. The difference I(q, 10.620 keV) − I(q, 11.551 keV) indeed exhibits over a broad range a similar q dependency as compared to the resonant term ν^{2}(q) obtained by decomposition of the data. However, at lowest and highest q, the latter data set follows a different pattern as compared to ν^{2}(q) (see Fig. 5, inset). The differences at low q are much more pronounced and have a considerable impact on the fitting results. The characteristic radius of 1.8 nm determined for the population of the small Pt spheres agrees well with the one obtained from fitting ν^{2}(q). Here, just the characteristic width parameter σ increases to 0.25. The characteristic radius of the population of large Pt spheres, however, changes due to the deviation of the subtracted curve from ν^{2}(q). A characteristic radius of 20 nm (σ = 0.25) instead of 27 nm is obtained which means that this value differs by more than 25 %. The tendency of the curve calculated by simple subtraction to differ especially at low q from the decomposed one has already been seen at the example of the theoretical curves (see Fig. 3). Thus, the experimental data support qualitatively the finding already obtained from the model calculations. But the simple subtraction method represents a good approximation to obtain the pure resonant scattering for high q values. It yields reliable fitting values for the small Pt particles, i.e. in the high q region. These findings are fully supported by the model calculations showing that the main problem of this method resides at low scattering angles.
Conclusions
We considered the anomalous small-angle x-ray scattering of a heterogeneous system consisting of large polydisperse spheres (PS and SiO_{2}), containing small platinum spheres. We showed that the complete extraction of the pure resonant scattering contribution requires the determination of I(q, E) at three different energies at least and the subsequent decomposition into the three partial scattered intensities. The result obtained by the simple subtraction of I(q, E) at two different energies as suggested by Brumberger et al. [39] was found to give the purely resonant contribution in good approximation for high q values but may lead to erroneous results at smaller scattering angles. This finding is supported by comparison with experimental results obtained from platinum supported on the ordered mesoporous silica MCM-41. The full decomposition into three partial intensities is the superior way inasmuch as it gives the scattering function of the metal particles without any prior assumption or condition.
Notes
Acknowledgments
The authors would like to thank Prof. Dr. Armin Feldhoff of the Leibniz Universität Hannover, Germany, for taking the TEM micrographs. Part of this work was funded by the Ministry of Science, Research and the Arts as well as the Landesstiftung foundation of Baden Wuerttemberg (Az: 23-720.431-1.8/1)
Supplementary material
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