An Adsorption Isotherm from a Micro-state Model
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An Adsorption Isotherm from a Micro-state Model BARDO ERNST JOSEF BODMANN∗ Instituto de F´ısica e Matem´atica, Universidade Federal de Pelotas, Pelotas, RS, Brazil [email protected], [email protected]
DEBORAH PINHEIRO DICK AND YEDA PINHEIRO DICK Instituto de Qu´ımica, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brazil [email protected]
Received November 3, 2003; Revised August 10, 2004; Accepted September 23, 2004
Abstract. The present study is dedicated to the derivation of an alternative adsorption isotherm for liquid-solid interfaces from a micro-state model, where adsorption is predominantly of a chemical nature. We describe adsorptiondesorption on a liquid-solid interface starting from a partition function. In the new model the surface site occupation number is controlled by the Pauli principle (monolayer condition) and additional an attractive or repulsive surface potential, which depends on the overall surface coverage (nonlinearity). The effective potential represents adsorbate adsorbent interaction, as well as an influence of adsorbate adsorbate interactions on the surface potential. A Langmuir equivalent isotherm is recovered in the limit of a weak potential. The proposed model and Langmuir’s isotherm are compared using data of humic acid (HA) adsorption on Brazilian Oxisol soil samples. Both models parameterize the experimental data well, but only the new model seems to be self-consistent. Keywords: adsorption isotherm, liquid-solid interface, micro-state model, humic acid, oxisol
1.
Introduction
Adsorption is one of the main mechanisms that regulates mobility of chemical species and their geochemical cycles in the environment (Almendros, 1995; Kretschmar, 1997; Murphy et al., 1994; Senesi et al., 1997; Tipping, 1981; Wang et al., 1997). In order to understand rates of mineral phase dissolution and ion exchange processes, adsorption measurements represent a useful tool for investigating interactions with the microscopic surface structure. The question, as to which is the most appropriate isotherm equation for a given set of adsorption data, has been the principal issue in a variety of works (for a recent review see ref: Hinz, 2001). Knowing the adequate parametrization serves
∗ To
whom correspondence should be addressed.
as a phenomenological classification of the interaction between adsorbent and adsorbate. Since most adsorption equations (i.e., adsorption isotherms), as for instance the Langmuir, the van Bemmelen-Freundlich, the Frumkin-FowlerGuggenheim, the Brunauer-Emmett-Teller model and others (for a more detailed description see for instance (Sparks, 1986; Sposito, 1989; Stumm, 1992)) are derived from a gas-solid adsorption hypothesis, consequently, their usefulness for liquid-solid interfaces may only be validated by direct comparison to experimental data. The present study is dedicated to the derivation of an alternative adsorption model for liquid-solid interfaces from a micro-state model. Because of the considerable complexity of possible processes involved it seems
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