Monte Carlo studies on potentiometric titration of poly(glutamic acid)

Coupling of Charge Regulation and Conformational Equilibria in Linear Weak Polyelectrolytes: Treatment of Long-Range Interactions via Effective Short-Ranged and pH-Dependent Interaction Parameters

The classical Rotational Isomeric State (RIS) model, originally proposed by Flory, has been used to rationalize a wide range of physicochemical properties of neutral polymers. However, many weak polyelectrolytes of interest are able to regulate their charge depending on the conformational state of the bonds. Recently, it has been shown that the RIS model can be coupled with the Site Binding (SB) model, for which the ionizable sites can adopt two states: protonated or deprotonated. The resulting combined scheme, the SBRIS model, allows for analyzing ionization and conformational equilibria on the same foot. In the present work, this approach is extended to include pH-dependent electrostatic Long-Range (LR) interactions, ubiquitous in weak polyelectrolytes at moderate and low ionic strengths. With this aim, the original LR interactions are taken into account by defining effective Short-Range (SR) and pH-dependent parameters, such as effective microscopic protonation constants and rotational bond energies. The new parameters are systematically calculated using variational methods. The machinery of statistical mechanics for SR interactions, including the powerful and fast transfer matrix methods, can then be applied. The resulting technique, which we will refer to as the Local Effective Interaction Parameters (LEIP) method, is illustrated with a minimal model of a flexible linear polyelectrolyte containing only one type of rotating bond. LEIP reproduces very well the pH dependence of the degree of protonation and bond probabilities obtained by semi-grand canonical Monte Carlo simulations, where LR interactions are explicitly taken into account. The reduction in the computational time in several orders of magnitude suggests that the LEIP technique could be useful in a range of areas involving linear weak polyelectrolytes, allowing direct fitting of the relevant physical parameters to the experimental quantities.

Size and charge characterization of polymeric drug delivery systems by Taylor dispersion analysis and capillary electrophoresis

In this work, Taylor dispersion analysis and capillary electrophoresis were used to characterize the size and charge of polymeric drug delivery nanogels based on polyglutamate chains grafted with hydrophobic groups of vitamin E. The hydrophobic vitamin E groups self-associate in water to form small hydrophobic nanodomains that can incorporate small drugs or therapeutic proteins. Taylor dispersion analysis is well suited to determine the weight average hydrodynamic radius of nanomaterials and to get information on the size polydispersity of polymeric samples. The effective charge was determined either from electrophoretic mobility and hydrodynamic radius using electrophoretic modeling (three different approaches were compared), or by indirect UV detection in capillary electrophoresis. The influence of vitamin E hydrophobicity on the polymer effective charge has been studied. The presence of vitamin E leads to a drastic decrease in polymer effective charge in comparison to non-modified polyglutamate. Finally, the electrophoretic behavior of polyglutamate backbone grafted with hydrophobic vitamin E (pGVE) nanogels according to the ionic strength was investigated using the recently proposed slope plot approach. It was deduced that the pGVE nanogels behave electrophoretically as polyelectrolytes which is in good agreement with the high water content of the nanogels.

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.