Regularized Least-Squares Methods for the Calculation of Discrete and Continuous Affinity Distributions for Heterogeneous Sorbents

From experimental isotherms, we calculate discrete and continuous affinity distribution functions for environmental sorbents. The calculation of such distributions is an ill-posed problem, which, if approached by classical solution schemes, leads to serious numerical problems and instabilities. The...

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Bibliographic Details
Published in:Environmental science & technology 1995-02, Vol.29 (2), p.413-425
Main Authors: Cernik, Miroslav, Borkovec, Michal, Westall, John C
Format: Article
Language:English
Subjects:
400201 - Chemical & Physicochemical Properties
540220 - Environment, Terrestrial- Chemicals Monitoring & Transport- (1990-)
990200 - Mathematics & Computers
ADSORBENTS
ADSORPTION ISOTHERMS
AFFINITY
Applied sciences
Chemicals
COMPUTER CALCULATIONS
DATA ANALYSIS
DISTRIBUTION FUNCTIONS
Environment
Environmental engineering
Environmental monitoring
ENVIRONMENTAL SCIENCES
Exact sciences and technology
Fitting
FUNCTIONS
GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
Global environmental pollution
INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY
ISOTHERMS
LEAST SQUARE FIT
Least squares method
Mathematical analysis
Mathematical models
MAXIMUM-LIKELIHOOD FIT
NUMERICAL SOLUTION
Pollution
Q1
Regularization
Soils
Sorbents
SORPTION
SORPTIVE PROPERTIES
Stability
Stabilization
SURFACE PROPERTIES
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Description
Summary:From experimental isotherms, we calculate discrete and continuous affinity distribution functions for environmental sorbents. The calculation of such distributions is an ill-posed problem, which, if approached by classical solution schemes, leads to serious numerical problems and instabilities. The application of regularization methods circumvents these difficulties and provides a substantial stabilization of the resulting distributions. We show that, without additional information about the affinity distribution, it is generally impossible to recover the true affinity distribution from realistic experimental data. As this information is usually not available, such data analysis remains a fitting exercise, which may however have an enormous practical value. The stability of the resulting distributions offers novel possibilities for comparison of sorption properties of environmental materials.
ISSN:0013-936X
1520-5851
DOI:10.1021/es00002a018