Use of the Gaussian Distribution Function as a Tool to Estimate Continuous Heterogeneity in Adsorbing Systems

Bersillon, Jean-Luc; Villièras, Frédéric; Bardot, F.; Görner, Tatiana; Cases, J. M.

doi:10.1006/jcis.2001.7657

Cited by 14 publications

(17 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It has been shown that the occurrence of the cip in charging curves depends on the actual distribution of the surface sites. [103] Among the variety of methods for the quantitative estimation of the surface heterogeneity of metal oxides, [103][104][105][106] a new method based on the determination of proton-affinity distribution by plotting titration data as derivatives of the proton/hydroxy ion adsorption as a function of pH has been proposed. As illustrated in Table 1, no definite cip is obtained for γ-Al 2 O 3 samples containing 56 % of the δ-phase [49] as a result of the increase of surface and bulk heterogeneity.…”

Section: γ-Al 2 O 3 Surface Heterogeneitymentioning

confidence: 99%

γ‐Alumina as a Support for Catalysts: A Review of Fundamental Aspects

2005

View full text Add to dashboard Cite

The present review discusses the most important aspects to take into consideration to improve the properties of γ‐Al2O3 as a support for catalytic applications. We show that the synthetic route to γ‐Al2O3 is the starting point that determines the micro‐ and macrostructure of the oxide and, consequently, allows control of the support characteristics. The relevance of the adequate structural characterization of the oxide as well as of its surface sorption behavior through the proton‐affinity distributions, are considered. The usefulness of the latter during supported catalyst preparation, for catalytic active sites characterization, and for stability evaluation after calcination are discussed for the Co/γ‐Al2O3 system in particular. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2005)

show abstract

Section: γ-Al 2 O 3 Surface Heterogeneitymentioning

confidence: 99%

γ‐Alumina as a Support for Catalysts: A Review of Fundamental Aspects

2005

View full text Add to dashboard Cite

show abstract

“…The Gaussian function is often used to describe bell-shaped curves such as chromatographic peaks [36] , heterogeneity in adsorption systems [37] , and the states of a dynamic system [38] and in other fields. In our work, the Gaussian function provided the best fit (R 2 >0.9) to all the curves of v inst and v acce .…”

Section: The Gaussian Distribution Function As a Tool For Estimating mentioning

confidence: 99%

A novel approach for estimating growth phases and parameters of bacterial population in batch culture

et al. 2006

View full text Add to dashboard Cite

Using mathematical analysis, a new method has been developed for studying the growth kinetics of bacterial populations in batch culture. First, sampling data were smoothed with the spline interpolation method. Second, the instantaneous rates were derived by numerical differential techniques and finally, the derived data were fitted with the Gaussian function to obtain growth parameters. We named this the Spline-Numerical-Gaussian or SNG method. This method yielded more accurate estimates of the growth rates of bacterial populations and new parameters. It was possible to divide the growth curve into four different but continuous phases based on changes in the instantaneous rates. The four phases are the accelerating growth phase, the constant growth phase, the decelerating growth phase and the declining phase. Total DNA content was measured by flow cytometry and varied depending on the growth phase. The SNG system provides a very powerful tool for describing the kinetics of bacterial population growth. The SNG method avoids the unrealistic assumptions generally used in the traditional growth equations.

show abstract

“…It is related to Tipping's WHAM models V-VI, defining a discrete affinity distribution and introducing a particle-surface-type electrostatic model, with some similarity to the CD-MUSIC model for inorganic colloids. Besides the application of specific models, work has also been devoted to extract affinity distributions directly from experimental data, including analytical [31][32][33][34] and numerical [35][36][37][38][39][40] methods. The extraction of affinity distribution from experimental data is an ill-posed problem [35,36,41] and as such common least-squares methods lead to a nearly infinite number of oscillating solutions [41].…”

Section: Introductionmentioning

confidence: 99%