Using Statistical Analysis as an Additional Tool in Porous Solid Characterization

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1 381 Using Statistical Analysis as an Additional Tool in Porous Solid Characterization Christothea Attipa, Antonia Panayiotou, Rebecca Kokkinofta and Charis R. Theocharis * Porous Solids Group, Department of Chemistry, University of Cyprus, P.O. Box 20537, Nicosia 1678 Cyprus. (Received 1 November 2010; revised form accepted 15 May 2011) ABSTRACT: Analytical chemists have long used statistical methods to help them organize and interpret experimental data especially where large numbers of these are generated as well as to help them design new experiments. Recently, chemometrics has found applications in wider fields, such as the determination of the geographical origin of food and other products. During the past several years, we have carried out a systematic study of the factors affecting the pore structure and surface chemistry of cerium oxide and of mixed oxides of cerium with various transition metal or alkaline earth metal ions. INTRODUCTION Solids based on cerium chemistry have been used extensively in several industrial applications. For example, cerium dioxide (Ce ) has been used increasingly as a promoter in so-called threeway catalysts (TWCs) and also as an oxygen ion conductor in solid oxide fuel cells (SOFCs) and oxygen monitors (Matta et al. 2002). In addition, ceria is widely used for the oxidation of CO by, for the selective catalytic reduction of S by CO, as an excellent support for precious metals, as a UV absorbent and filter, as a buffer layer with silicon wafers, as a component in solid oxide fuel cells, as a catalyst in chemical-mechanical polishing (CMP) processes, etc. (Tschope et al. 1999; Chen and Chang 2005; Chang and Chen 2005). The efficiency of ceria is based on its capacity to store or release oxygen because of the lattice defects in Ce x (Matta et al. 2002; Radhika and Sugunan 2006; Cousin et al. 2001). Several metal-doped cerium oxides exhibit high oxygen ionic conductivity which makes them interesting materials for many applications (Zhao and Gorte 2003). Chemometrics is the application of mathematical (statistical) methods to the solution of chemical problems of all types where large quantities of data are produced [see, for example, Kokkinofta and Theocharis (2005)]. It is a relatively recent addition to the arsenal of chemical analysis and is applicable in those cases where many (three or more) parameters are measured for each sample, thereby making comparisons and the extraction of useful inferences difficult. This is the so-called Multivariate Analysis, which first found application in the social sciences (e.g. econometrics), but whose applicability to chemistry was recognized in the 1970s and increasingly so in the past decade. At the University of Cyprus, we have been carrying out a systematic study of the synthetic factors affecting the surface and solid-state properties of cerium oxide, and of mixed cerium/transition metal oxides (Attipa and Theocharis 2006, 2009). The aim of this work has been to enhance the surface area of these solids and to control their porosity, especially their mesoporosity. As part of this study, we have recently made use of statistical methods (chemometrics) as a means of classifying samples * Author to whom all correspondence should be addressed. charis@ucy.ac.cy.

2 382 C. Attipa et al./adsorption Science & Technology Vol. 29 No and extracting useful information about the samples not directly obtainable from raw experimental results (Theocharis et al. 2008; Attipa et al. 2009). OUTLINE OF CHEMOMETRIC METHODS Chemometric methods can be broadly classified (Kokkinofta and Theocharis 2005; Ballabio et al. 2007) into two main groups: (a) Discriminant Analysis (DA), Principal Component Analysis (PCA) and Cluster Analysis (CA), and (b) Classification of Unknown Samples and Regularized Discriminant Analysis (CART, DA), including Canonical (CDA) and Linear Discriminant Analysis (LDA). In the very recent past, neural networks have also been applied to chemometric problems (Ballabio et al. 2007). In the present study, we have made use of PCA, Cluster Analysis and CART analysis. Here, we present results based on PCA, since all analyses methods led to similar results. The uses of chemometrics lie in experimental design, signal processing, pattern recognition, calibration and the study of evolutionary signals. The work presented here can be construed as being an application of pattern recognition. Principal Component Analysis (PCA) is the most widely used technique. Quite often, PCA is applied before proceeding to other techniques, such as (hierarchical) cluster analysis or different types of Discriminant Analyses. Thus, several variables or components are measured for each sample. Then Principal Components (PC1, PC2, etc.) are found which are linear combinations of the original variables describing each sample. For n variables, n PCs are obtained for each sample. However, if the variables are correlated, as they would be where the variables are points on an adsorption isotherm, then far fewer PCs (usually only the first three) are needed than variables to fully describe the variation in the sample set. By plotting graphs of PC1 versus PC2 (usually), or PC1 versus PC3, plots are obtained that group similar samples together. Although it is possible to pre-assign samples (objects) to a specific group, the mathematical method makes no such assumptions. It is therefore possible to check the correctness or otherwise of the assignments made. EXPERIMENTAL The triple and double mixed cerium oxide samples under investigation here were prepared from the corresponding aqueous solutions by the co-precipitation method, using 1 M ammonia solution as the base. The metal precursors used were cerium(iv) ammonium nitrate, ammonium metavanadate(v) and copper(ii) nitrate or iron(iii) nitrate (Attipa and Theocharis 2006). Samples of composition Ce x V y Cu z, Ce x V y Fe z (where x y z 1) or Ce x V 1 x were synthesized. The concentrations of all the solutions used were 0.01 M throughout. To achieve the desired results, the corresponding solutions were mixed in appropriate ratios. The resulting precipitate was allowed to stand in the mother liquor for 24 h, then centrifuged and dried at 373 K for 24 h. Nitrogen adsorption isotherms were obtained at 77 K using a Micromeritics ASAP 2010 apparatus, employing a starting pressure of 0.15 Pa. Powder XRD measurements were carried out using a Shimadzu diffractometer using graphite-monochromatized Cu Kα radiation. Chemometric analysis was carried out using the Win-DAS (WINdows Discriminant Analysis Software) package. The techniques used were PCA (Principal Component Analysis) for chemometrics, and the DFT method for the calculation of pore-size distributions. The data for each sample used for chemometric analysis were the BET surface area (S BET ), the apparent pore volume (V p ) and the average pore diameter (d p ).

3 Using Statistical Analysis as an Additional Tool in Porous Solid Characterization 383 RESULTS AND DISCUSSION The statistical analyses of data for double and triple mixed oxides are discussed separately below. Previous statistical analysis (Attipa and Theocharis 2009) of these samples employing pattern recognition of the adsorption branch of the nitrogen adsorption isotherm suggested that the dominant discriminant factor was not the nature of the hetero-atoms present in the samples, but rather the number of the different cations (two or three). Double mixed oxides A discussion of the surface and solid-state properties of the triple mixed cerium oxides has been presented previously (Attipa and Theocharis 2006). Here, we will refer to the series of double mixed oxides of composition V x Ce 1 x with values of x between 0.05 and 0.9, which were synthesized and characterized. From Figure 1, it can be seen that addition of vanadium ions to ceria influenced the surface properties of the latter. The highest BET surface area for the dried samples (288 m 2 /g) was exhibited by V 0.2 Ce 0.8. As the vanadium content increased there was a marked decrease in the apparent surface area, as well as a widening of the high-pressure hysteresis loop α S BET (m 2 /g) % V Figure 1. Comparison of the BET surface area (S BET ) and the micropore area (α) for V x y samples. Data points and related lines correspond to the following:, BET: dr 100;, BET: calc. 200;, micropore area: dr. 100;, micropore area: calc X-Ray diffractometry indicated that both the double and mixed oxide samples which were only dried at 373 K after synthesis were poorly crystalline and possessed the fluorite structure of ceria. Figure 2 overleaf displays the X-ray diffractograms of the dried mixed oxides. A comparison of the X-ray diffractograms of the double mixed oxides with that of pristine ceria indicated that the former possessed displaced peaks, presumably due to the formation of a solid solution. Samples with vanadium contents up to 40% had a higher apparent surface area than pristine ceria. This observation may be explained by the relative values of the atomic radii of vanadium and cerium, with r V(V) being 68 pm compared to a value of 101 pm for r Ce(IV). Upon calcination, these samples crystallized to yield one phase, that of ceria. For samples with a vanadium content above 40%, calcination to 673 K resulted in samples containing both a ceria phase, and CeVO 4 and V 2 O 5. This therefore suggests that a solid solution only formed when the vanadium content was below 40%. Above this value, the vanadium was unevenly distributed in the uncalcined samples, which could well have contained areas where only vanadium ions were present.

4 384 C. Attipa et al./adsorption Science & Technology Vol. 29 No β θ (degrees) Figure 2. XRD patterns for various V x samples after drying at 373 K. The traces depicted correspond to samples containing the following percentage vanadium and cerium contents:, Ce ;, 10% V, 90% Ce;, 20% V, 80% Ce;, 30% V, 70% Ce;, 40% V, 60% Ce;, 50% V, 50% Ce;, 60% V, 40% Ce;, 70% V, 30% Ce;, 80% V, 20% Ce;, 90% V, 10% Ce a L % V 0 Figure 3. Comparison of the magnitude of the unit cell axis a (Å) and the particle size L (nm) for dried V x y samples. Data points correspond to the following:, a;, L. Figure 3 shows the distortion of the ceria lattice, as presented by the value of the length of the a-axis. Chemometric analysis The samples examined for this study were assigned to three groups during PCA analysis according to the transition metal they contained (V, Cu, Fe). Thus, Group A contained nine samples with the composition V x Ce 1 x, Group B contained nine samples with the composition Cu x Ce 1 x, while Group C contained nine samples with the composition Fe x Ce 1 x. In all cases, x varied between 0.1 and 0.9. Figure 4 overleaf shows the results of PCA analysis for these samples in the form of a scatter diagram of the first two principal components, which represent 72.07% and 26.77% of the variance for all samples and therefore provide a reliable classification of the samples. It can be seen from the figure that all the samples except seven could be assembled into one group. Thus, of the vanadium group, samples (β) V 0.2 Ce 0.80, (ζ) V 0.8 Ce 0.20 and (η) V 0.9 Ce 0.10 were not

5 Using Statistical Analysis as an Additional Tool in Porous Solid Characterization 385 Second principal component (α) (β) (δ) (ζ) (ε) (γ) (η) First principal component Group A Group B Group C Figure 4. Scatter plot of PCA analysis for samples V x, Cu x and Fe x. included in the grouping. Of these, the first sample had the highest S BET value, while the other two had the lowest of the set. Sample (α) Cu 0.8 Ce 0.20 was also excluded from the group, having the largest S BET value of all the samples examined, whereas samples (γ) Fe 0.8 Ce 0.20, (δ) Fe 0.7 Ce 0.30, (ε) Fe 0.9 Ce 0.10, were also excluded. These samples were characterized by a combination of a low BET surface area and the largest average pore diameter. This behaviour may be explained by the formation of a solid solution with a distorted ceria-like structure for those samples whose heteroatom content was less than 50%. Such distortion was indicated by the displacement of the characteristic ceria peaks in the corresponding XRD spectrum. For higher concentrations, two phases were formed. This presumably affected the surface texture of the samples and led to the behaviour observed during chemometric analysis. Triple mixed oxides Table 1 lists the samples used in the analysis, divided into four groups. Group A contains samples with general formula V x Cu x Ce 1 2x y ( 0.05 x 0.45 ), whose cerium content varied from 90% to 10%. Group B consists of samples again containing V and Cu but with a constant cerium content of 60%, having the general formula V x Cu 0.4 x Ce 0.6 y (0.05 x 0.4), while Group C contains samples with the general formula V x Fe x Ce 1 2x y (0.05 x 0.45). Finally, Group D contains samples with the general formula V x Fe 0.4 x Ce 0.6 y (0.05 x 0.4). Figure 5 shows the PCA scatter plot for these 39 samples. It can be seen from the figure that all the samples with the exception of four could be classified in two groups, rather than the two proposed by the model used. The two principal components represented 58.28% and 38.68% of the variance for the data set, and therefore give a reliable description of the samples. Four samples were excluded from both groups. These samples were V 0.35 Cu 0.35 Ce 0.3, V 0.4 Cu 0.4 Ce 0.20, V 0.45 Cu 0.45 Ce 0.1 and V 0.2 Cu 0.2. Of these samples, the first three had lower S BET values compared to the other samples in Group A, whereas the fourth was the one with the largest pore diameter of the samples with a vanadium content in the range 5 30%. All these samples were mesoporous with some micropores also being present, and exhibited Type IV nitrogen adsorption isotherms. The proportion of microporosity increased with decreasing vanadium content (Attipa and Theocharis 2006).

6 386 C. Attipa et al./adsorption Science & Technology Vol. 29 No TABLE 1. Classification of Triple Mixed Oxides Sample S BET (m 2 /g) V p (cm 3 /g) D p (nm) Sample S BET (m 2 /g) V p (cm 3 /g) D p (nm) Group A Group C Cu 0.05 Ce V Fe Ce Cu 0.1 Ce V Fe Ce Cu 0.15 Ce V Fe Ce V 0.2 Cu V Fe Ce V 0.25 Cu 0.25 Ce V Fe Ce V 0.3 Cu 0.3 Ce V 0.01 Fe 0.01 Ce V 0.35 Cu 0.35 Ce V 0.02 Fe 0.02 Ce V 0.4 Cu 0.4 Ce V 0.03 Fe 0.03 Ce V 0.45 Cu 0.45 Ce V 0.04 Fe 0.04 Ce Fe 0.05 Ce Group B Fe 0.1 Ce Cu Fe 0.15 Ce Cu V 0.2 Fe Cu V 0.25 Fe 0.25 Ce V 0.25 Cu V 0.3 Fe 0.3 Ce V 0.3 Cu V 0.35 Fe 0.35 Ce V 0.35 Cu V 0.4 Fe 0.4 Ce V 0.45 Fe 0.45 Ce Group D Fe Fe Fe V 0.25 Fe V 0.3 Fe V 0.35 Fe Second principal component (γ) (β) (α) Group A Group B Group C Group D (δ) First principal component Figure 5. Scatter plot of PCA analysis for samples V x Cu x Ce 1 2x y, V x Cu 0.4 x Ce 0.6 y, V x Fe x Ce 1 2x y and V x Fe 0.4 x Ce 0.6 y.

7 Using Statistical Analysis as an Additional Tool in Porous Solid Characterization 387 TABLE 2. Second Classification of Triple Mixed Oxides Group A Group B Cu 0.05 Ce 0.90, 5 Cu 0.15 Ce 0.70 Cu 0.1 Ce 0.80, Fe 0.05 Ce 0.90 V 0.25 Cu 0.25 Ce 0.50, V 0.3 Cu 0.3 Ce 0.40 Fe 0.1 Ce 0.80, 5 Fe 0.15 Ce 0.70 Cu 0.35, Cu 0.3 V 0.2 Fe 0.2, V 0.25 Fe 0.25 Ce Cu 0.25, V 0.25 Cu 0.15 V 0.3 Fe 0.3 Ce 0.40, V 0.35 Fe 0.35 Ce 0.30 V 0.3 Cu 0.1, V 0.35 Cu 0.05 V 0.4 Fe 0.4 Ce 0.2, V 0.45 Fe 0.45 Ce 0.1 V Fe Ce 0.998, V Fe Ce Fe 0.3, 5 Fe 0.25 V Fe Ce 0.994, V Fe Ce V 0.25 Fe 0.15, V 0.3 Fe 0.1 V Fe Ce 0.99, V 0.01 Fe 0.01 Ce 0.98 V 0.35 Fe 0.05 V 0.02 Fe 0.02 Ce 0.96, V 0.03 Fe 0.03 Ce 0.94 V 0.04 Fe 0.04 Ce 0.92, Fe 0.35 The aberrant behaviour of the first three of these samples may be attributed to the fact that such samples with a higher vanadium content exhibited H2-type hysteresis loops due to their poorer crystallinity (as shown by XRD) than the other more crystalline solids which exhibited H3-type loops. This was presumably linked with the type of solid solution formed, with a quasi-ideal solid solution forming for more dilute systems and non-ideal solutions forming at higher vanadium content. The exclusion of sample V 0.2 Cu 0.2 was presumably due to the simultaneous high values for both pore volume and pore diameter exhibited by this sample, which was the only sample which exhibited such behaviour. In view of this result, PCA classification was attempted a second time with a different model consisting of only two groups, and excluding the four samples that were not previously classified. Table 2 shows the second classification of the triple mixed oxides. In this classification, Group A contains samples with the composition V x Fe y, with y 0.05, and all samples of composition V x Cu y. Group B contains the samples with the composition V x Fe y, where y Samples with the composition V x Cu y may be placed in the same class because they all exhibited similar isotherms, whereas those samples with composition V x Fe y were shown to exhibit differences in particle morphology (particle size, particle shape) with Fe content (Attipa and Theocharis 2006, 2009). These differences would be expected to impact upon the surface texture. First principal component Group A Group B First principal component Figure 6. Scatter plot of PCA analysis for samples V x Fe y and V x Cu y.

8 388 C. Attipa et al./adsorption Science & Technology Vol. 29 No Figure 6 shows the results of PCA analysis using the data listed in Table 2. The first principal component contained 70.83% and the second 28.94% of the overall variance of the whole data set. It is clear from the figure that the model used in this case led to 100% success in the classification process. The division of the data set into two groups, rather than four as initially proposed, may indicate that the conclusion reached for the double mixed oxides, viz. that the nature of the doping cation was not a distinguishing factor for the samples under investigation, may well apply to the triple oxides as well, in agreement with the results of previous analyses (Attipa and Theocharis 2009). It is clear that the classification shown in Figure 6 may be related to differences in the crystal (particle) size and shape, which would, presumably, influence the surface structure (pore size, shape volume and surface area) of the solids. The Fe-containing samples were separated according to the shape of the hysteresis loop in the nitrogen adsorption isotherm, and thus differences in pore shape and size. A possible explanation for these observations may be as follows. The samples under investigation were uncalcined and therefore poorly crystalline (small crystallites), consisting of one phase with a ceria-like structure. The level of heteroatom concentration influenced both the particle size (see Figures 1 and 2) as well as the particle shape, so far as this was affected by the unit cell dimensions. Thus, whereas the nature of the heteroatoms would influence the surface chemistry of the mixed oxide, their concentration may have a deeper impact on the surface texture. However, upon calcination, and therefore crystallization of the solids, depending upon the nature and concentration of the heteroatom, more than one crystal phase is produced, and in this case both the type and concentration of the heteroatoms would be expected to have an impact upon the surface texture. It is clear that conclusions such as those presented above are difficult to make on the basis of a cursory or simple comparison of data for a large number of samples, such as in the case under investigation here. Statistical analysis (chemometrics) can help in such cases to establish patterns and similarities/differences between the samples. These inferences could be useful in better understanding the properties of the systems under investigation, as well as in assisting in the better design of further experiments ACKNOWLEDGEMENTS The University of Cyprus is thanked for financial support of this work. Partial financial support of C.A. by the Cyprus Foundation for Research is also acknowledged. REFERENCES Attipa, C. and Theocharis, C.R. (2006) Stud. Surf. Sci. Catal. 160, 615. Attipa, C. and Theocharis, C.R. (2009) Characterisation of Porous Solids VIII, Proc. 8th Int. Symp. Characterisation of Porous Solids, Edinburgh, U.K., Seaton, N., Reinoso, F.R., Llewellyn, P., Kaskel, S., Eds, Royal Society of Chemistry, London, p Attipa, C., Kokkinofta, R. and Theocharis, C.R. (2009) Characterisation of Porous Solids VIII, Proc. 8th Int. Symp. Characterisation of Porous Solids, Edinburgh, U.K., Seaton, N., Reinoso, F., Llewellyn, P., Kaskel, S., Eds, Royal Society of Chemistry, London, p. 64. Ballabio, D., Kokkinofta, R., Todeschini, R. and Theocharis, C.R. (2007) Chemom. Intell. Lab. Syst. 87, 52. Chang, H.Y. and Chen, H.I. (2005) J. Cryst. Growth 283, 457.

9 Using Statistical Analysis as an Additional Tool in Porous Solid Characterization 389 Chen, H.I. and Chang, H.Y. (2005) Ceram. Int. 31, 795. Chen, L. (2006) Mater. Lett. 60, Cousin, R., Capelle, S., Abi-Aad, E., Coursot, D. and Aboukais, A. (2001) Chem. Mater. 13, Kokkinofta, R. and Theocharis, C.R. (2005) J. Agric. Food Chem. 53, Matta, J., Coursot, D., Abi-Aad, E. and Aboukais, A. (2002) Chem. Mater. 14, Radhika, T. and Sugunan, S. (2006) J. Mol. Catal. A 250, 169. Theocharis, C.R., Attipa, C., Hapeshi, E., Tillirou, A. and Kokkinofta, R. (2008) Adsorpt. Sci. Technol. 26, 643. Tschöpe, A., Trudeau, M.L. and Ying, J.Y. (1999) J. Phys. Chem. B 103, Zhao, S. and Gorte, R.J. (2003) Appl. Catal. A 248, 9.

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