Search

Recent extensions of counterion condensation theory, originally developed for well-defined linear polyelectrolytes, enable us to analyze the interaction of trace metals with humic acid. In the present model, the heterogeneity of the macromolecule is taken into account as well as the chemical binding of the considered metal ions to the humic material. Experimentally, potentiometric titrations have been performed for humic acid in solution in the presence of different environmentally important (heavy) metals (Ca, Cd, Cu, Ni, and Pb) at various metal concentrations by titrating with potassium hydroxide without additional salt. From proton release data obtained for the initial point in the titration, it was estimated that the interaction of the different metals with the humic acid in terms of binding strength increased in the order Ca < Cd approximately = Ni < Pb approximately = Cu. These results were confirmed by model analysis. Experimentally obtained apparent dissociation constants were in good agreement for the humic acid systems containing Ca, Cd, and Ni at concentrations ranging from 0 up to 0.75 x 10(-3) mol L(-1) and polymer dissociation degree from about 0.1 up to approximately 0.8. Also for the Cu/humic acid and Pb/humic acid systems, the agreement between experimental data and calculated data was satisfactory atthe lowest metal concentrations over the complete titration curve. For elevated levels of Cu and Pb, the agreement between experimental data and theoretical calculations becomes less satisfactory at low degrees of dissociation of the humic acid. This distortion of the potentiometric curves is probably due to changes in the intrinsic pK of the functional groups due to metal binding. This complex process is not included in present polyelectrolytic models.

A model, developed within the framework of the counterion condensation theory of linear polyelectrolytes, is presented in this paper to describe the acid-base properties of linear polyelectrolytes, consisting of several types of functional ionizable groups. This formalism has been successfully applied to Fluka humic acid under salt-free conditions, as well as in the presence of supporting simple 1:1 salt (KNO3) at three different concentrations. As part of this approach, the charge density of the humic acid is obtained from the activity coefficient measurements of potassium counterions at different humic acid concentrations at a constant degree of dissociation of the polyelectrolyte. The humic acid average charge density was found to be 0.80 +/- 0.05. Using the present model, we are able to satisfactorily describe the experimental data obtained from acid-base potentiometric titrations. Four main functional groups making up the polymer are determined through their fractional abundances (Xi) and intrinsic pK (pK0i) values. The fractional abundances remained constant and independent of the ionic strength, indicating that the humic acid constitution does not depend on the concentration of excess salts. The pK0i values show a small change with ionic strength, which can be explained by the polyelectrolytic behavior of the solution.

A formal development of the Counterion Condensation theory (CC) of linear polyelectrolytes has been performed to include specific (chemical) affinity of condensed counterions, for polyelectrolyte charge density values larger than the critical value of condensation. It has been conventionally assumed that each condensed counterion exhibits an affinity free-energy difference for the polymer, (DeltaG(aff)). Moreover, the model assumes that the enthalpic and entropic contributions to DeltaG(aff), i.e., DeltaH(aff) and DeltaS(aff), are both independent of temperature, ionic strength and polymer concentration. Equations have been derived relative to the case of the thermally induced, ionic strength dependent, conformational transition of a biopolyelectrolyte between two conformations for which chemical affinity is supposed to take place. The experimental data of the intramolecular conformational transition of the ionic polysaccharide kappa-carrageenan in dimethylsulfoxide (DMSO) have been successfully compared with the theoretical predictions. This novel approach provides the enthalpic and entropic affinity values for both conformations, together with the corresponding thermodynamic functions of nonpolyelectrolytic origin pertaining to the biopolymer backbone change per se, i.e., DeltaH(n.pol) and DeltaS(n.pol), according to a treatment previously shown to be successful for lower values of the biopolyelectrolyte linear charge density. The ratio of DeltaH(n.pol) to DeltaS(n.pol) was found to be remarkably constant independent of the value of the dielectric constant of the solvent, from formamide to water to DMSO, pointing to the identity of the underlying conformational process., (Copyright 1999 John Wiley & Sons, Inc.)

Voltammetric speciation data for the potassium/zinc/polymethacrylate system, recently obtained for various charge densities of the polyelectrolyte (Díaz-Cruz et al., Anal. Chim. Acta, 264 (1992) 163) and for different concentrations of monovalent counterions (van den Hoop and van Leeuwen, Anal. Chim. Acta, 273 (1993) 275), are compared with theoretical predictions computed according to a new thermodynamic model developed by Paoletti et al. (Biophys. Chem., 41 (1991) 73) and recently extended by Benegas and Paoletti (in preparation). The model allows: (i) the simultaneous condensation of both monovalent and divalent counterions and (ii) can account for a certain specific affinity of the polyelectrolyte for one type of the counterion over the other. For various charge densities of the polyelectrolyte, experimentally obtained speciation data for the K/Zn/PMA system agree well with theoretical predictions by considering an extra reduced molar affinity energy of -4RT for the Zn(2+) polyelectrolyte binding. The agreement between experimental and theoretical values for the distribution of Zn(2+) ions over the free and bound state becomes less perfect for relatively high concentrations of monovalent counterions.

An analysis is given of the theoretical approach to the quantitative description of proton dissociation curves for weak polyacids. The basic model of the counterion condensation theory has been used, with the modification reported in the preceding study (S. Paoletti, A. Cesàro, C. Arce Samper and J.C. Benegas, Biophys. Chem. 34 (1989) 301). In this paper we demonstrate the effect of relaxing the hypothesis of a rigid conformation on the polyelectrolytic properties of weak polyacids. As an application of the present approach, a description is given of the titration curves for two weak polyacids, poly(DL-glutamic acid) (PDLGA) and poly(L-aspartic acid) (PLAA).

The cooperative conformational transition of poly(L-glutamic acid) induced by pH is monitored by the titration curves from literature. The polyelectrolytic approach described in the preceding article (A. Cesàro, S. Paoletti and J.C. Benegas, Biophys. Chem. 39 (1991) 1) is used to fit the experimental curves under various conditions of ionic strength and temperature, with the sole assumption that each polymeric state is characterized by a proper conformational flexibility. The helix-coil transition of the system becomes molecularly defined by the balance between the non-ionic conformational energy and the repulsive electrostatic energy of the two forms. Implications of the results of the theoretical model on the energetics of the cooperative order-disorder transition are discussed.

The charge-induced conformational transition of poly(alpha-L-glutamic acid) (PLGA) is considered in this paper from the point of view of proton dissociation. Equations for the excess electrostatic Gibbs energy of dissociation (i.e., delta pKa) are derived as a function of the degree of ionization, alpha. These analytical equations are used to describe some experimental dissociation curves at different polymer and salt concentrations. The dependence of the calculated delta pKa with respect to the ionic strength for the two conformational states, alpha-helical and extended coil, respectively, is rather satisfactorily explained. Even more interesting are the predictions which are derived from this approach for the transition point, alpha tr which is found to be ionic-strength dependent, in full agreement with the experimental results.