Charging of weak polyelectrolytes

The site binding model is capable to capture the protonation behavior of various poly(ethylene imines) and poly(propylene imines). The main tenet of the model is that interactions between neighboring sites are taken into account, which leads to a binding isotherm that cannot be expressed in a simple algebraic form. For small molecules, on the other hand, the model reduces to the classical chemical equilibrium description of the protonation equilibria, whereby the corresponding binding constants are again influenced by the interactions between the sites. The model can be extended to other types of polyelectrolytes, although in many situations one must deal with their tacticity, which is often not known very precisely

The intrinsic view of ionization equilibria of polyprotic molecules

The intrinsic approach describing microscopic ionization equilibria is presented. This description massively reduces the number of parameters needed to characterize microequilibria. Particularly, by exploring molecular symmetries and group transferability, this approach is capable of resolving such equilibria even for rather complex molecules. Intrinsic constants are assigned to each ionizable group and interactions between these sites are introduced. These interactions involve pairs or triplets of sites. The strength of these interactions decreases rapidly with the distance between the sites. Once these parameters are known, one can obtain macroconstants, microconstants, microstate mole fractions, and overall or site-specific titration curves. These quantities provide insight into the protonation of the molecules in question. The knowledge of such properties is relevant for a wide range of phenomena, including receptor–ligand interactions, action of drugs, or geochemical processes

Resolution of Microscopic Protonation Mechanisms in Polyprotic Molecules

Microscopic ionization equilibria can be fully resolved by means of a novel site-binding model, which is based on a cluster expansion technique borrowed from statistical mechanics. This model permits a parameterization of the problem, and offers substantial advantages over the commonly used microscopic equilibrium constants. While the number of microconstants grows very rapidly with the size of the molecules, the necessary number of parameters of the site-binding model remain small, and one can even obtain common sets of such parameters within a homologous series of molecules. Based on this approach, two methods to obtain such microconstants are discussed, namely based on NMR titration data, and on the analysis of potentiometric titrations within a homologous series

Ionization Equilibria and Conformational Transitions in Polyprotic Molecules and Polyelectrolytes

The coupling between proton binding and conformational degrees of freedom in polyprotic molecules and polyelectrolytes is studied theoretically. Our approach combines the classical rotational isomeric state (RIS) model developed by Flory and the site binding (SB) model used to treat proton binding equilibria. The properties of the resulting SBRIS model, which treats conformational degrees of freedom and proton binding on equal footing, are studied with statistical mechanical techniques. Quantities of interest, such as titration curves, conformational probabilities, or macroscopic binding constants, are expressed as thermal averages and are evaluated by direct enumeration of states or by transfer matrix techniques. We further demonstrate that in the SBRIS model conformational degrees of freedom can be averaged out, leading to the contracted description within the SB model. In most cases, this contraction leads to higher order interactions, which may not be present at the SBRIS level (e.g., triplet interactions). Several examples are discussed to illustrate the concepts developed. The case of succinic acid exemplifies the situation in its simplest form. The model can further rationalize the very different titration behavior of poly(acrylic acid) (PAA) and poly(methacrylic acid) (PMAA). In particular, the characteristic “jump” in the titration curve of PMAA is described quantitatively and is interpreted in terms of a conformational transition

Light Reflectivity Study on the Adsorption Kinetics of Poly(propylene imine) Dendrimers on Glass

International audienceThe rate of adsorption of positively charged poly(propylene imine) dendrimers on glass, an oppositely charged surface, has been studied as a function of generation and charge (by systematic adjustment of pH and ionic strength) using scanning angle reflectometry and an impinging-jet cell. A comparison of the mass transport conditions for this geometry and the bulk long-time self-diffusion coefficient obtained from pulsed field gradient NMR experiments shows that a sticking probability of the order of 3% is needed to relate the diffusion toward the surface with the long-time self-diffusion in the bulk. The adsorption kinetics were mostly diffusion/convection controlled with a linear dependence on the bulk concentrations up to 10 mg/L at pH 7 and in 0.1 M NaCl. At higher bulk concentrations there is a drop in concentration dependence into a 1 /3 power law dependence. This crossover concentration shifts to higher concentrations with decreasing pH (increasing dendrimer charge)