Conditional equilibrium constants in multicomponent heterogeneous adsorption: The conditional affinity spectrum

The concept of conditional stability constant is extended to the competitive binding of small molecules to heterogeneous surfaces or macromolecules via the introduction of the conditional affinity spectrum (CAS). The CAS describes the distribution of effective binding energies experienced by one complexing agent at a fixed concentration of the rest. We show that, when the multicomponent system can be described in terms of an underlying affinity spectrum [integral equation (IE) approach], the system can always be characterized by means of a CAS. The thermodynamic properties of the CAS and its dependence on the concentration of the rest of components are discussed. In the context of metal/proton competition, analytical expressions for the mean (conditional average affinity) and the variance (conditional heterogeneity) of the CAS as functions of pH are reported and their physical interpretation discussed. Furthermore, we show that the dependence of the CAS variance on pH allows for the analytical determination of the correlation coefficient between the binding energies of the metal and the proton. Nonideal competitive adsorption isotherm and Frumkin isotherms are used to illustrate the results of this work. Finally, the possibility of using CAS when the IE approach does not apply (for instance, when multidentate binding is present) is explored. © 2006 American Institute of Physics.

Adding similarity-based reasoning capabilities to a Horn fragment of possibilistic logic with fuzzy constants

PLFC is a first-order possibilistic logic dealing with fuzzy constants and fuzzily restricted quantifiers. The refutation proof method in PLFC is mainly based on a generalized resolution rule which allows an implicit graded unification among fuzzy constants. However, unification for precise object constants is classical. In order to use PLFC for similarity-based reasoning, in this paper we extend a Horn-rule sublogic of PLFC with similarity-based unification of object constants. The Horn-rule sublogic of PLFC we consider deals only with disjunctive fuzzy constants and it is equipped with a simple and efficient version of PLFC proof method. At the semantic level, it is extended by equipping each sort with a fuzzy similarity relation, and at the syntactic level, by fuzzily “enlarging” each non-fuzzy object constant in the antecedent of a Horn-rule by means of a fuzzy similarity relation.

A mechanistic approach to methylene blue sorption on two vegetable wastes: Cork bark and grape stalks

Two vegetable wastes, cork bark and grape stalks, were investigated for the removal of methylene blue from aqueous solution. The effects of contact time, dye concentration, pH, and temperature on sorption were studied relative to adsorption on a commercially-activated carbon. The highest adsorption yield was obtained within the pH range 5 to 10 for grape stalks and 7 to 10 for cork bark. The sorption kinetics of dye onto activated carbon and grape stalks was very fast. Kinetics data were fitted to the pseudo-first and second order kinetic equations, and the values of the pseudo-second-order initial rate constants were found to be 1.69 mg g-1 min-1 for activated carbon, 2.24 mg g-1 min-1 for grape stalks, and 0.90 mg g-1 min-1 for cork bark. Langmuir maximum sorption capacities for activated carbon, grape stalks, and cork bark for methylene blue estimated by the Orthogonal Distance Regression method (ODR) were 157.5 mg g-1, 105.6 mg g-1, and 30.52 mg g-1, respectively. FTIR spectra indicated that carboxylic groups and lignin play a significant role in the sorption of methylene blue. Electrostatic forces, n-p interactions, cation-p, and p-p stacking interactions contribute to methylene blue sorption onto grape stalks and cork bark. Grape stalks can be considered an efficient biosorbent and as a viable alternative to activated carbon and ion-exchange resins for the removal of methylene blue