Julio Benegas

Limiting-laws of polyelectrolyte solutions. Ionic distribution in mixed-valency counterions systems. I: The model.

An extension of the counterion-condensation (CC) theory of linear polyelectrolytes has been developed for the case of a system containing a mixture of counterions of different valency, i and j. The main assumption in the derivation of the model is that the relative amount of the condensed counterions of the type i and j is strongly correlated and it is determined by the overall physical bounds of the system. The results predicted by the model are consistent, in the limiting cases of single species component, with those of the original CC theory. The most striking results are obtained for the cases of low charge density and excess of counterion species: in particular, an apparent positive binding cooperativity of divalent ions is revealed for small, increasing additions of M2+ ions to a solution containing a swamping amount of monovalent salt and a polyelectrolyte of low charge density. Apparent competitive binding of mono- and divalent ions derives as a bare consequence of the electrostatic interactions. Theoretical calculations of experimentally accessible quantities, namely single-(counter) ion activity coefficients, confirm the surprising predictions at low charge density, which qualitatively agree with the measured quantities.

Polyelectrolytic effects in semi-flexible carboxylate polysaccharides. Part 2

A statistical model is presented in which an ionic polymer is taken as a linear arrangement of flexible segments (similar to the spring-bead model). This model is used to represent semi-flexible linear ionic polysaccharides in solution. The distribution of end-to-end distances is taken from Monte Carlo calculations of the amylosic chain conformation and combined with Mannings counterion condensation theory of linear polyelectrolytes. The excess thermodynamic properties are then calculated as a function of the degree of ionization and of a number of physical variables. The results show that the statistical average of thermodynamic functions taken over the conformational states is not equivalent to the thermodynamic function of the average conformation. This has important implications for the correct comparison of theoretical prediction with the experimental results.

Potentiometric titration of poly(acrylic acid) in mixed counterion systems: Chemical binding of Cd ions

Abstract Potentiometric titration curves of various Cd/poly(acrylic acid) systems have been obtained in order to study the cadmium poly(acrylic acid) interaction. The experimental data, in terms of pKa versus α, is well described by taking into account chemical binding of the cadmium ions with the polymer and electrostatically bound potassium counterions as calculated by the counterion condensation approach. In this way, the speciation of both divalent and monovalent counterions in solution is readily calculated.

Complexation of heavy metals by humic acids: analysis of voltammetric data by polyelectrolyte theory

The complexation of heavy metals by humic acids has been studied by voltammetry for a number of different cases, including (a) different metal ions; (b) various concentrations of the supporting salt; (c) different total metal concentrations and (d) different charge densities of the humic acid. The voltammetric speciation data are compared with predictions of a theoretical model which, besides polyelectrolytic interactions, takes into account: (i) chemical binding of metal ions; (ii) ionic strength effects; (iii) entropic effects; and (iv) competitive interactions between counterions of different valences. All experimentally obtained speciation data agree well with theoretical predictions by considering a single value of the intrinsic free energy of binding, which appeared to be the same for the Cd and Zn metal ions. This means that under the presently applied experimental conditions the interactions between the humate ion and the metal ions is similar. It is furthermore shown that with the present experimental-theoretical procedure a very consistent and precise behavior of the stability constant of the complex is reached in the wide range of the physico-chemical solution variables reported in this work.

Analysis of potentiometric titrations of heterogeneous natural polyelectrolytes in terms of counterion condensation theory: application to humic acid

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.

Polyelectrolytic aspects of the titration curve : pH-induced conformational transition of poly(L-glutamic acid) : the semi-flexible model

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.

Chemical bonding of divalent counterions to linear polyelectrolytes: Theoretical treatment within the counterion condensation theory

Chemical bonding of counterions to a linear polyelectrolyte is addressed within the framework of the counterion condensation theory of linear polyelectrolytes. The model allows for the proper identification of the kind of counterion association to a linear polyelectrolyte when it is in solution with two different types of counterions (of equal or different valences). Two extreme modes of counterion association to the polyelectrolyte are considered: loose territorial (“classical” condensation) and a coalent bonding at a specific site on the polyion. The model provides analytical expressions for calculating the fraction of counterions in each type of association. Any thermodynamic function of interest can also be readily computed through the appropriate function of the calculated excess Gibbs energy of the system. The concentrations of the different types of associated counterions, for a few particular solution conditions, are presented and discussed in order to provide tools not only for analyzing experimental results, but also for planning suitable experiments aimed at discriminating between the two types of counterion association proposed.

Innovative Training of In-service Teachers for Active Learning: A Short Teacher Development Course Based on Physics Education Research

In this contribution we describe a short development course for in-service physics teachers. The course structure and materials are based on the results of educational research, and its main objective is to provide in-service teachers with a first contact with the active learning strategy “Tutorials in Introductory Physics,” developed by the Physics Education Research Group at the University of Washington. The course was organized in a constructivist, active learning environment, so that teachers have first to experience, as regular students, the whole Tutorial sequence of activities: Tutorial pre-test, Tutorial, and Tutorial Homework. After each Tutorial, teachers reflect on, and recognize their own students’ learning difficulties, discussing their teaching experiences with their colleagues in small collaborative groups first and the whole class later. Finally they read and discuss specific Physics Education Research literature, where these learning difficulties have been extensively studied by researchers. At the beginning and at the end of the course the participants were given the conceptual multiple-choice test Force Concept Inventory (FCI). The pre-/post-instruction FCI data were presented as a practical example of the use of a research-based test widely used in educational research and in formative assessment processes designed to improve instruction.

Affinity interactions in counterion‐polyelectrolyte systems: Competition between different counterions

Non-bonding, specific interactions between linear polyelectrolytes and different species of counterions (of equal or different valence) are considered in the framework of the counterion condensation theory. It is assumed that these interactions are of short distance nature and that, within our theoretical approach, they apply only to the counterions territorially associated (condensed) to the polyion, which are free to move within the condensation volume V p around it. It is found that a simple additive term in the total free energy is sufficient to account for this interaction, resulting in a modulation of the polyelectrolytically determined population of territorially bound counterions. The distribution of free and condensed counterions as well as its variation with the physicochemical variables of the solution can be readily calculated. Analysis of literature data on titrations of poly(methacrylic acid) and dextran sulfate in aqueous solution with different species of monovalent and divalent counterions show that both polyanions appear to have a modest affinity free energy (of about RT) for Ca ++ counterions when compared with Na + . On the other hand, polyion interactions with the Mg ++ /Na + pair are well described by bare polyelectrolytic interactions.

Insight into the Molecular Properties of Chitlac, a Chitosan Derivative for Tissue Engineering

Chitlac is a biocompatible modified polysaccharide composed of a chitosan backbone to which lactitol moieties have been chemically inserted via a reductive N-alkylation reaction with lactose. The physical-chemical and biological properties of Chitlac that have been already reported in the literature suggest a high accessibility of terminal galactose in the lactitol side chain. This finding may account for its biocompatibility which makes it extremely interesting for the production of biomaterials. The average structure and the dynamics of the side chains of Chitlac have been studied by means of NMR (nuclear Overhauser effect and nuclear relaxation) and molecular dynamics to ascertain this hypothesis. A complete assignment of the (1)H and (13)C NMR signals of the modified polysaccharide has been accomplished together with the determination of the apparent pKa values of the primary and secondary amines (6.69 and 5.87, respectively). NMR and MD indicated a high mobility of Chitlac side chains with comparable average internuclear distances between the two techniques. It was found that the highly flexible lactitol side chain in Chitlac can adopt two distinct conformations differing in the orientation with respect to the polysaccharide chain: a folded conformation, with the galactose ring parallel to the main chain, and an extended conformation, where the lactitol points away from the chitosan backbone. In both cases, the side chain resulted to be highly hydrated and fully immersed in the solvent.