Abstract
Statistical distribution models of multi-site binding equilibria have potential applicability in the study of acid-base and metal complexation chemistry of humic substances in soils, sediments, and natural waters. A mathematical derivation is presented for the general continuous model for the case of proton binding; computational methods are described for fitting numerically the parameters in such models. Among models considered are those based on nontruncated, truncated, and bimodal (mixed) distributions. Specific emphasis is placed on Gaussian distribution models.
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References
Abramowitz, M. and Stegun, I.A., 1972, Handbook of Mathematical Functions: National Bureau of Standards, Washington, D.C., 1046 p.
Bard, Y., 1974, Nonlinear Parameter Estimation: Academic Press, New York, 341 p.
Cabaniss, S. E., Shuman, M. S., and Collins, B. J. 1984, Metal-Organic Binding: A Comparison of Models: p. 165–179in C. J. M. Kramer and J. C. Duinker (Eds.), Complexation of Trace Metals in Natural Waters: Junk Publishers, The Hague.
Dempsey, B. A. and O'Melia, C. R. 1983, Proton and Calcium Complexation of Four Fulvic Acid Fractions: p. 239–273in R. F. Christman and E. T. Gjessing (Eds.), Aquatic and Terrestrial Humic Materials: Ann Arbor Science, Ann Arbor.
Ertel, J. R., Hedges, J. I., and Perdue, E. M., 1984, Lignin Signature of Aquatic Humic Substances: Science, v. 223, p. 485–487.
Fletcher, R. and Powell, M. J. D., 1963, A Rapidly Convergent Descent Method for Minimization: Comput. J., v. 6, p. 163–168.
Gamble, D. S., 1970, Titration Curves of Fulvic Acid: The Analytical Chemistry of a Weak Acid Polyelectrolyte:Can. J. Chem., v. 48, p. 2662–2669.
Gamble, D. S. 1972, Potentiometric Titration of Fulvic Acid: Equivalence Point Calculations and Acidic Functional Groups: Can. J. Chem., v. 50, p. 2680–2690.
Hamming, R. W., 1973, Numerical Methods for Scientists and Engineers: McGraw-Hill, New York, 721 p.
Lytle, C. R. and Perdue, E. M., 1981, Free, Proteinaceous, and Humic-Bound Amino Acids in River Water Containing High Concentrations of Aquatic Humus: Environ. Sci. Technol., v. 15, p. 224–228.
Parrish, R. S., 1983, On an Integrated Approach to Member Selection and Parameter Estimation for Pearson Distributions: Comput. Stat. Data Anal., v. 1, p. 239–255.
Parrish, R. S., 1987, Evaluation and Approximation of Multivariate Cumulative Joint Probabilities: J. Stat. Comput. Simul., v. 27, p. 1–33.
Parrish, R. S. and Bargmann, R. E., 1981, A Method for Evaluation of Cumulative Probabilities of Bivariate Distributions Using the Pearson Family: p. 241–257in C. Taillie, G. P. Patil, and B. Baldessari (Eds.), Statistical Distributions in Scientific Work, v. 5: Reidel, Dordrecht.
Perdue, E. M., 1985, Acidic Functional Groups of Humic Substances: p. 493–526in G. R. Aiken, D. M. McKnight, R. L. Wershaw, and P. MacCarthy (Eds.), Humic Substances in Soil, Sediment, and Water: Geochemistry, Isolation, and Characterization: Wiley-Interscience, New York.
Perdue, E. M., and Lytle, C. R., 1983, A Distribution Model for Binding of Protons and Metal Ions by Humic Substances: Environ. Sci. Technol. v. 17, p. 654–660.
Perdue, E. M. and Parrish, R. S., 1987, Fitting Multi-Site Binding Equilibria to Statistical Distribution Models: Turbo PASCAL Program for Gaussian Models: Comp. Geosci., v. 13, p. 587–601.
Perdue, E. M.; Reuter, J. H.; and Parrish, R. S., 1984, A Statistical Model of Proton Binding by Humis: Geochim. Cosmochim. Acta, v. 48, p. 1257–1263.
Posner, A. M., 1964, Titration Curves of Humic Acid: p. 161–173in Proceedings of the 8th International Congress of Soil Science, Part II: Bucharest, Romania.
Shuman, M.S.; Collins, B. J.; Fitzgerald, P. J.; and Olson, D. L.; 1983, Distribution of Stability Constants and Dissociation Rate Constants Among Binding Sites on Estuarine Copper-Organic Complexes; Rotated Disk Electrode Studies and an Affinity Spectrum Analysis of Ion-Selective Electrode and Photometric Data: p. 349–370in R. F. Christman and E. T. Gjessing (Eds.), Aquatic and Terrestrial Humic Materials: Ann Arbor Science, Ann Arbor.
Sposito, G., 1986, Sorption of Trace Metals by Humic Materials in Soils and Natural Waters: CRC Crit. Rev. Environ. Control, v. 16, p. 193–229.
Sweet, M. S. and Perdue, E. M., 1982, Concentration and Speciation of Sugars in River Water: Environ. Sci. Technol., v. 16, p. 692–698.
Turner, D. R., Varney, M. S.; Whitefield, M.; Mantoura, R. F. C.; and Riley, J. P. 1983, Electrochemical Studies of Copper and Lead Complexation by Fulvic Acid: I. Potentiometric Measurements and a Critical Comparison of Metal Binding Models: Geochim. Cosmochim. Acta, v. 50, p. 289–297.
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Parrish, R.S., Perdue, E.M. Computational methods for fitting statistical distribution models of multi-site binding equilibria. Math Geol 21, 199–219 (1989). https://doi.org/10.1007/BF00893215
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DOI: https://doi.org/10.1007/BF00893215