Determination of surface areas for supported-metal catalysts from small-angle scattering

Goodisman, Jerry; Brumberger, H.; Cupelo, R.

doi:10.1107/s0021889881009436

Cited by 33 publications

(13 citation statements)

References 9 publications

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“…* However, the meaning of the law is not always clear. It rests on some assumptions which require interpretation, main-*Porod-law analyses of experimental data are, for example, used by Brumberger, Delaglio, Goodisman & Whitfield (1986), Goodisman, Brumberger & Cupelo (1981) and Ciccariello & Benedetti (1986). ly related to passing from a continuous to a discrete description of a sample.…”

Section: Introductionmentioning

confidence: 99%

On the Porod law

Ciccariello¹,

Goodisman²,

Brumberger³

1988

J Appl Crystallogr

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The Porod law states that i(h), the intensity of Xradiation scattered by an ideal multiphase noncrystalline system, for 'large' momentum transfer values (= h) approaches C~h-4 and that ~ is linearly related to the interphase surface areas. A more general expression is obtained which relates the value of the correlation-function derivative at the origin to the integral of the discontinuity of the electron density fluctuation along the discontinuity surface. Debye's assumption, by which the continuous electron density of the sample is approximated by a discrete-valued one, is critically discussed. The validity of the approximation results in the presence of a Porod plateau [hai(h) =constant]. The momentum transfer rangewhere the plateau is observed is related to the scale of lengths where the sharp-boundary idealization remains essentially unchanged. It is argued that the scattered intensity can show more than one Porod plateau and some examples of correlation functions with this behaviour are reported. The problem of the background subtraction is discussed and the corresponding coefficients are related to the electron densities relevant to the real and to the associated sharp-boundary sample.

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Section: Introductionmentioning

confidence: 99%

On the Porod law

Ciccariello¹,

Goodisman²,

Brumberger³

1988

J Appl Crystallogr

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“…By following the terminology of the paper by Goodisman, Brumberger & Cupelo (1981), the support, the void and the metallic phase will be denoted by 1, 2 and 3. The catalysts are obtained by letting the metallic particles deposit on the support.…”

Section: Linear Constraints On Spfsmentioning

confidence: 99%

“…In contrast with Goodisman et al (1981) and with Espinat, Moraweck, Larue & Renouprez (1984), who assumed the simultaneous validity of either of (33) and (34) or of (33) and (36), respectively, we shall consider later each of conditions (33), (34), (36) separately. We underline that the use of one of these linear constraints corresponds to an assumption stronger than that relevant to the use of parameterization (31).…”

Section: P~x2)2(r) = P]~(r) + Ptl3)3(r )mentioning

confidence: 99%

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Parameterizations of scattering intensities and values of the angularities and of the interphase surfaces for three-component amorphous samples

Ciccariello¹,

Benedetti²

1985

J Appl Cryst

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Different functional parameterizations of the radiation intensity scattered by an N-component amorphous sample are considered. Each parameterization is such that (i) it depends only on the areas and on the angularities of the samples' interphase surfaces, (ii) it fulfils all the known physical constraints and (iii) it yields a rather simple algebraic expression both for the correlation function and for the scattered intensity. The parameterizations have been used for analysing the scattering data relevant to some three-component catalysts. Provided the volume fraction of the metal is not very small, the best fit yields satisfactory results only for some of the considered parameterizations. In this way, the determination of both the areas and the angularities of catalysts appears possible.

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“…A different sort of model (Goodisman, Brumberger & Cupelo, 1981;Brumberger, Delaglio, Goodisman, Phillips, Schwarz & Sen, 1985) involves the use of measurements on metallized support as well as on the catalyst. It is assumed that the addition of metal to the support, which gives the catalyst, does not change the support structure, so that, for example, the sum of the support-void and the support-metal surface areas in the catalyst is identical to the support-void surface area in the unmetallized support:…”

Section: (C) Support Subtractionmentioning

confidence: 99%

Small-angle X-ray scattering analysis of catalysts: comparison and evaluation of models

Brumberger¹,

Delaglio²,

Goodisman³

et al. 1986

J Appl Cryst

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Small-angle X-ray scattering (SAXS) can be used to obtain interphase surface areas of a system, such as a supported-metal catalyst, composed of internally homogeneous phases with sharp interphase boundaries. Measurements of SAXS for samples of porous silica, alumina, platinum on silica, and platinum on alumina are reported. A variety of models and forms for the correlation function, the Fourier transform of which gives the X-ray scattering, are considered, and theoretical and measured intensities are compared. A criterion of fit for comparing models with different numbers of parameters is proposed. For the two-phase (unmetallized) systems the 'Debye-random' model must be rejected. Modifications of the Debye (exponential) correlation function are also not particularly good compared to an exponential-plus-Gaussian form, not derivable from a physical model, and forms based on Voronoi cell models. Since intensities can be fit to experimental error with a five-parameter correlation function, it seems incorrect to ascribe significance to the result of fitting a function with six or more parameters. It is shown that values for the single interphase surface area can be obtained independently of a model. However, fitting intensities using a modelbased correlation function gives information about the structure of the system. The two-cell-size Voronoi and the correlated Voronoi cell models are useful in this regard. For the systems containing metal, fiveparameter correlation functions again suffice to fit intensities. However, for three-phase systems a model or physical assumption is necessary to obtain values for the three surface areas from X-ray scattering intensities. The area of the surface between support and void is quite insensitive to the assumptions employed and the metal-support surface area somewhat less so, but values for the metal-void surface area $23 are consistent only to one significant figure from model to model. If the support in the three-phase catalyst is known to be unchanged from support in the absence of metal, a 'support-subtraction' model can be used to obtain reliable values for $23. In the present systems, the assumption does not seem to be borne out.

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Determination of surface areas for supported-metal catalysts from small-angle scattering

Cited by 33 publications

References 9 publications

On the Porod law

On the Porod law

Parameterizations of scattering intensities and values of the angularities and of the interphase surfaces for three-component amorphous samples

Small-angle X-ray scattering analysis of catalysts: comparison and evaluation of models

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