Fractal analysis of physical adsorption on material surfaces

Mahnke, M.; Mögel, H.-J.

doi:10.1016/s0927-7757(02)00577-0

Cited by 73 publications

(53 citation statements)

References 7 publications

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“…The derivation [17,18] of a fractal BET equation is based upon the fact that, for a fractal surface, the area available for adsorption in the ith layer of adsorptive, A i , decreases by a factor f i , given by:…”

Section: Fractal Analysis Of Surfacesmentioning

confidence: 99%

Detection of the delayed condensation effect and determination of its impact on the accuracy of gas adsorption pore size distributions

Rigby

Hasan

Hitchcock

et al. 2017

Colloids and Surfaces A: Physicochemical and Engineering Aspect

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The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription.For more information, please contact eprints@nottingham.ac.uk 1 normally requiring assumptions about the correct model for data analysis. In this work we present a novel method to both expand the range, and obtain greater accuracy, for the information obtained from the main boundary adsorption isotherms by using a combination of data obtained for two adsorptives, namely nitrogen and argon, both before and after mercury porosimetry. The method makes use of the fact that nitrogen and argon apparently 'see' a different pore geometry following mercury entrapment, with argon, relatively, 'ignoring' new metal surfaces produced by mercury porosimetry. The new method permits the study of network and pore-pore co-operative effects during adsorption that substantially affect the accuracy of the characteristic parameters, such as modal pore size, obtained for disordered materials. These effects have been explicitly quantified, for a typical sol-gel silica catalyst support material as a case study. The technique allowed the large discrepancies between modal pore sizes obtained from standard gas adsorption and mercury thermoporometry methods to be attributed to the network-based delayed condensation effect, rather than spinodal adsorption. Once the network-based delayed condensation effect had been accounted for, the simple cylindrical pore model and macroscopic thermodynamic Kelvin-Cohan equation were then found sufficient to accurately describe adsorption in the material studied, rather than needing a more complex microscopic theory. Hence, for disordered mesoporous solids, a proper account of inter-pore interactions is more important than that of intra-pore adsorbate density distribution, to obtain accurate pore size distributions. Detection of the Delayed Condensation Effect and Determination of its

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Section: Fractal Analysis Of Surfacesmentioning

confidence: 99%

Detection of the delayed condensation effect and determination of its impact on the accuracy of gas adsorption pore size distributions

Rigby

Hasan

Hitchcock

et al. 2017

Colloids and Surfaces A: Physicochemical and Engineering Aspect

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“…Besides, another model, developed by Mahnake and Mögel based on the BET formula, is used to determine the fractal dimension of a surface from one adsorption isotherm (Mahnke and Mögel 2003). An alternate derivation is suggested to avoid the inconsistent behavior in the case of a surface fractal dimension of 3.…”

Section: Fractal Isotherm Equationmentioning

confidence: 99%

Fractal analysis in particle dissolution: a review

Bao

Long

et al. 2014

Reviews in Chemical Engineering

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Abstract:Fractal is a geometric language to describe the objects, the systems, and the phenomenon spatially and temporally. This paper reviews the literature on fractal models developed to describe the dissolution of particles. Dissolution, the process by which a solid forms a homogeneous mixture with a solution, is the behavior of a population of particles rather than a single one in most of the cases. The fractal models developed for the particle population are reviewed on the basis of two key particle surface properties, namely, the surface fractal nature and the chemical reactivity of particle surfaces. In terms of the surface fractal nature, fractals have been used to describe the change in the superficial roughness of particles, surface area-particle size relation, and particle size distribution (PSD). In terms of the reactive fractal dimensions, the models that describe the dissolution process have been developed to obtain the empirical noninteger exponent, the reactive fractal dimension that can dictate the chemical reactivity of a solid surface. The comparison between the surface fractal dimension and the reactive fractal dimension provides the dissolution mechanisms in many aspects of surface morphology. Further research is necessary to modify the current models to coincide with the real industrial processes and production and to develop the specific models for a better understanding of many processes involving the dissolution of particles encountered in many areas, including pharmaceutical and chemical applications and hydrometallurgy.

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“…On a fractal surface, the amount adsorbed in each subsequent layer above the first decreases according to a power law. This principle has been used to derive versions of the BET model for adsorption on a fractal surface, such as that derived by Mahnke and Mögel (2003):…”

Section: Multi-layer Adsorptionmentioning

confidence: 99%

Fundamental studies of gas sorption within mesopores situated amidst an inter-connected, irregular network

et al. 2008

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There has been little, or no, direct testing of theories of gas sorption within particular pores situated amidst a highly inter-connected pore network. The concept of thermodynamically independent pores within networks has also been challenged. In this work, a novel integrated nitrogen sorption and mercury porosimetry technique has been used to deconvolve the condensation and evaporation processes within a specific subset of pores contained within a larger, irregular network. The sizes and geometry of these pores were obtained completely independently of gas sorption, using mercury porosimetry and NMR cryoporometry, respectively. Hence, various theories of capillary condensation, such as the Kelvin equation, the Broeckhoff-de Boer method, Saam-Cole theory, and NLDFT could be directly tested, and the potential influence of any collective network phenomena detected. It was found that, even for a shielded pore, the Cohan equation for a cylindrical meniscus gave rise to the best prediction for the relative pressure of capillary condensation, once the effects of surface chemical heterogeneity on multi-layer build-up had been taken into account. The results were also found to be incompatible with the presence of particular collective adsorption effects, such as advanced condensation.

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Fractal analysis of physical adsorption on material surfaces

Cited by 73 publications

References 7 publications

Detection of the delayed condensation effect and determination of its impact on the accuracy of gas adsorption pore size distributions

Detection of the delayed condensation effect and determination of its impact on the accuracy of gas adsorption pore size distributions

Fractal analysis in particle dissolution: a review

Fundamental studies of gas sorption within mesopores situated amidst an inter-connected, irregular network

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