On the difference in ionization properties between planar interfaces and linear polyelectrolytes

Abstract

Ionizable planar interfaces and linear polyelectrolytes show markedly different proton-binding behavior. Planar interfaces protonate in a single broad step, whereas polyelectrolytes mostly undergo a two-step protonation. Such contrasting behavior is explained using a discrete-charge Ising model. This model is based on an approximation of the ionizable groups by point charges that are treated within a linearized Poisson-Boltzmann approximation. The underlying reason as to why planar interfaces exhibit mean-field-like behavior, whereas linear polyelectrolytes usually do not, is related to the range of the site-site interaction potential. For a planar interface, this interaction potential is much more long ranged if compared with that of the cylindrical geometry as appropriate to a linear polyelectrolyte. The model results are in semi-quantitative agreement with experimental data for fatty-acid monolayers, water-oxide interfaces, and various linear polyelectrolytes.Ionization of proteins, weak polyelectrolytes, or water-solid interfaces is a central theme across many disciplines. The understanding of such polyprotic systems is crucial for the assessment of various important processes, such as buffering of protons and metal ions, protein-folding mechanisms, antigenantibody interactions, formation of surfactant aggregates, particle coagulation dynamics, and crystal growth. Based on the seminal work of Tanford and Kirkwood (1, 2), much progress has been made in the development of quantitative models for the dissociation of ionizable residues in proteins. The electrostatic interactions between charged residues are treated using a Poisson-Boltzmann (or other) approximation, which provides the basis for the evaluation of the thermal statistics of protonation equilibria (3-6). Because the results of such models sensitively depend on the primary, secondary, and tertiary protein structure, the derived protonation patterns appear to be rather protein-specific. The main reasons for this behavior are the heterogeneities introduced by the different proton affinities of different amino acid residues and the specific effects due to geometrical arrangement of the ionizable groups. Any generic features in the ionization process of polyprotic protein systems are difficult to recognize.Generic features in the ionization patterns can be recognized, however, for simpler polyprotic systems such as planar ionizable interfaces and weak linear polyelectrolytes, which will be the focus of this paper. Such systems may involve a high degree of homogeneity due to the presence of identical ionizable groups and simpler geometrical structure. Moreover, such systems often contain a large number of ionizable sites, so that it is sufficient to consider the limit of an infinite number of sites. The detailed description of the ionization process for planar interfaces and linear polyelectrolytes represents an essential step in the understanding of ionization of complex polyprotic systems; a development that is not only of relevance to biochemis...

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

“…Dots represent MC simulations, while continuous lines come from eqns. (21)(22), (23) and (10), together with the transfer matrix (14). A very good agreement is again obtained.…”

“…Dots represent the values obtained from MC simulations, while continuous lines correspond to those obtained by using eqns. (21)(22)(23)(24)(25). The agreement between theory and MC simulations is excellent.…”

“…(25-27), unlike eqns. (22)(23)(24), are not accurate for the whole range of ionic strengths. [16,54].…”

“…The latter are usually mediated by the solvent and can be described by simple potentials, such as the Debye-Hückel potential, or by suitable mean field approximations [18,19,20,21]. Short range interactions, however, can produce important correlations between the binding to neighbouring sites, so that the continuous mean field approach is no longer valid [22,23]. Moreover, they are mediated by the molecular skeleton rather than by the solvent, so that they cannot in general be modelled by simple interaction potentials.…”

Effect of the surface charge discretization on electric double layers: A Monte Carlo simulation study

“…The discrete nature of the surface charge is very common in many natural systems, and it is modeled as an ionizable interface where discrete ionizable groups are treated explicitly. [6][7][8][9] This treatment was pioneered by Tandford and Kirwood for proteins 10 and was also applied to polyelectrolytes. [11][12][13] Other experimental systems studied as a planar ionizable interfaces are the titration of a variety of metal oxide and hydroxide particles, for example, goethite ͑␣-FeOOH͒, hematite ͑␣-Fe 2 O 3 ͒, and silica ͑see Ref.…”