Dealing with long‐range interactions in the determination of polyelectrolyte ionization properties. Extension of the transfer matrix formalism to the full range of ionic strengths. Issue 3 (14th November 2016)

• Record Type: Journal Article
• Authors: Garcés, Josep L.; Madurga, Sergio; Rey‐Castro, Carlos; Mas, Francesc
• Is Part Of: Journal of polymer science. Volume 55:Issue 3(2017)
• Page Start: 275
• Page End: 284
• Publication Date: 2016-11-14
• Subjects: Debye‐Hückel interactions -- heterogeneous polymers -- ionization properties -- Ising model -- long‐range interactions -- Monte Carlo simulations -- polyelectrolytes -- Potts model -- statistical mechanics -- transfer matrix; 547
• DOI: 10.1002/polb.24269
• Languages: English
• ISSNs: 0887-6266

Abstract

ABSTRACT: The ionization state of charged macromolecules in solution is usually determined by the extent of the binding processes. These processes are very sensitive to the ionic strength of the medium, which are of long‐range nature. The ionization properties of weak polyelectrolytes can be described by means of Ising‐type models, which is only feasible when long‐range interactions are neglected. Here, this formalism is extended to include long‐range interactions by introducing a modified free energy involving only effective short‐range interaction parameters. These parameters can be systematically calculated by using the Gibbs‐Bogoliubov variational principle. The technique is illustrated with the calculation of titration curves of homogeneous and heterogeneous polyelectrolytes in a wide range of ionic strengths. The correction of the site protonation free energy (first order correction) is enough to obtain an excellent agreement between theory and Monte Carlo simulations. Corrections to other cluster parameters (higher‐order corrections) are also implemented. In general, the correction to a particular parameter represents the average change in the long‐range energy when a new interaction is created in the polyelectrolyte. The method presented here represents an improvement in the description of the ionization state of polyelectrolytes that can be relevant in a wide range of areas. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys.2017, 55, 275–284 Abstract : The transfer matrix technique is a very powerful technique to solve Ising‐type models of proton binding to polyelectrolytes, but its use is restricted to short range interactions. This work extends the technique to include long range interactions. The resulting titration curves that correspond to different binding models (homogeneous, heterogeneous, polyampholytes) are extremely accurate and indistinguishable in practice from those obtained by Monte Carlo simulations.