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Polymers 2018, 10(8), 811; https://doi.org/10.3390/polym10080811

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

1
Physical Chemistry Unit, Department of Materials Science and Physical Chemistry & Research Institute of Theoretical and Computational Chemistry (IQTCUB) of Barcelona University (UB), 08028 Barcelona, Catalonia, Spain
2
Department of Chemistry, Technical School of Agricultural Engineering & Agrotecnio of Lleida University (UdL), 25003 Lleida, Catalonia, Spain
*
Authors to whom correspondence should be addressed.
Received: 15 June 2018 / Revised: 17 July 2018 / Accepted: 23 July 2018 / Published: 24 July 2018
(This article belongs to the Special Issue Polymers: Design, Function and Application)
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Abstract

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. View Full-Text
Keywords: polyelectrolytes; charge regulation; long-range interactions; Debye–Hückel interactions; transfer matrix; Ising models; semi-grand canonical ensemble; Monte Carlo simulations; conformational equilibria; variational methods polyelectrolytes; charge regulation; long-range interactions; Debye–Hückel interactions; transfer matrix; Ising models; semi-grand canonical ensemble; Monte Carlo simulations; conformational equilibria; variational methods
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Blanco, P.M.; Madurga, S.; Mas, F.; Garcés, J.L. 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. Polymers 2018, 10, 811.

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