ARTICLE pubs.acs.org/Langmuir
Calcium Mediated Polyelectrolyte Adsorption on Like-Charged Surfaces Martin Turesson,* Christophe Labbez,* and Andre Nonat ICB, UMR 5209 CNRS, Universite de Bourgogne, F-21078 Dijon Cedex, France
bS Supporting Information ABSTRACT: Monte Carlo simulations within the primitive model of calcium-mediated adsorption of linear and comb polyelectrolytes onto like-charged surfaces are described, focusing on the effect of calcium and polyion concentrations as well as on the ion pairing between polymers and calcium ions. We use a combination of Monte Carlo simulations and experimental data from titration and calcium binding to quantify the ion pairing. The polymer adsorption is shown to occur as a result of surface overcharging by Ca2+ and ion pairing between charged monomers and Ca2+. In agreement with experimental observations, the simulations predict that the polymer adsorption isotherm goes through a maximum as the calcium or the polymer concentration is increased. The non-Langmuir isotherms are rationalized in terms of chargecharge correlations.
’ INTRODUCTION Polyelectrolytes and adsorption of polyelectrolytes onto charged surfaces from aqueous salt solutions have been intensively investigated during the past decades due to their ability to control the stability and viscoelastic properties of colloidal suspensions,1 surface hydrophobicity, and colloid crystallization. The overall stability in a mixture of colloidal particles with polymers is governed by a complex interplay between forces of different origins, such as electrosteric stabilization, ionion correlations, bridging attraction, steric effects, and so forth, which in turn are regulated by factors such as ionic strength, pH, surface charge, solvent quality, polymer size, and structure, to mention a few of them. In addition, specific interactions between polymers and surfaces as well as between ions and polymers in solution make it a demanding task to treat and characterize such systems theoretically as well as experimentally. One of the most spread examples of a polymerically stabilized colloidal system is concrete (a mix of cement and gravel). In this context, anionic comb copolymers with a charged backbone and grafted hydrophilic side chains, mostly polycarboxylate esters, have proven to be very effective stabilizers and plasticizers. The anionic backbones are found to adsorb2,3 onto the highly negatively charged cement nanohydrates overcharged by calcium ions.4 The hydrophilic neutral side chains provide the required entropy2 (steric hindrance) to overcome ion correlation forces which otherwise cause the cement grains, covered by cement nanohydrates, to aggregate.5 The result is a high performance concrete with enhanced workability, durability, and mechanical properties. Calcium (sometimes magnesium) mediated polyelectrolyte adsorption on like-charged surfaces is used/studied in many other systems, for example, alumina/Ca2+/PAA,6,7 alumina/Mg2+/PAA,8 titania/Ca2+/PAA,9 CaCO3/Ca2+/PAA,10 hydroxyapatite/Ca2+/PAA,11 r 2011 American Chemical Society
kaolinite/Ca2+/PAA.12 Interestingly, the adsorption isotherm invariably shows the same behavior that deviates from the common Langmuir isotherm characterized by a well-defined plateau when the saturation is reached. Instead, the polymer adsorption first rises, reaches a maximum, and then decreases upon further increasing the polymer content. This behavior, however, is not well understood. To our knowledge, there are only a few theoretical studies in which the adsorption of linear polyelectrolytes onto like charged surfaces was investigated. Messina et al.13 used molecular dynamics simulations within the primitive model to study the complexation of a single long flexible polyelectrolyte chain with a likecharged particle in the presence of trivalent counterions varying the coupling regime of the system. The complexation was found to be mediated by adsorption of the multivalent counterions causing the substrate surface to overcharge. However, the study was restricted to the analysis of polymer configurations. Wang et al.14 used density functional theory (DFT) calculations within the mean spherical approximation to investigate polyelectrolyte adsorption (linear chains) at a like-charged surface in the presence of di- and trivalent counterions. The adsorption was found to increase with the coupling strength (surface charge density and counterion valency) and to be nearly independent of the polymerization degree. The polymer and the salt concentration were, however, not varied. The mechanisms involved in polyelectrolyte adsorption have been studied under various levels of approximations,1524 among which only a few theoretical studies deal with explicit ions.13,21,25,26 Moreover, the effect of ion pairing between polymer Received: August 8, 2011 Revised: September 19, 2011 Published: October 12, 2011 13572
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Langmuir chains and multivalent counterions on adsorption on likecharged surfaces has so far not been studied, although such counterions are known to bind strongly to polyelectrolytes and to induce important conformational transitions.27 Multivalent ions are also known to induce overcharging of the polyions.28,29 While ionion correlations have been shown to qualitatively reproduce such phenomena in highly coupled systems, nonelectrostatic contributions may also play a significant role. As an example, Ball et al. found that some monovalent anions seem equally capable to overcharge cationic polyelectrolytes.30 Such interactions, however, are far from being well understood31 and are still a matter of debate.3241 In the present paper, we will use Monte Carlo simulations within the primitive model to investigate the calcium-mediated adsorption of linear and comb polyanions on highly negatively charged surfaces upon varying the polymer and calcium concentration, as well as the ion paring, the polymer structure, and the surface charge density. In particular, we will show that the variation in surface charge reversal with increasing polymer or calcium content is not enough to explain the observed shape of the adsorption isotherms. We will use these results to address two questions: (i) What is the role played by the ion pairing between polymer chains and calcium ion in the adsorption? (ii) What are the mechanisms of the non-Langmuir polymer adsorption isotherm? To proceed, we will first use the case of poly(acrylic acid) (PAA) to illustrate the importance of the ion pairing between calcium ions and charged monomers. We will further show that a combination of simulations and experiments of titration and calcium binding is a simple and accurate method to characterize the ion pairing. Finally, the mechanisms of adsorption will be described and rationalized in terms of apparent surface and polymer charge.
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Figure 1. Polymer model for branched polymers. Following the notation in the text, this polymer will be named P431.
’ MODEL AND SIMULATIONS Ions and Polymers. The electrostatics of linear and comb polyelectrolytes near a charged surface is influenced by a number of parameters such as the surface charge density, the polyion and salt concentration, the linear charge density, the polymerization degree of the backbone, the grafting density, and the polymerization degree of the neutral side chains. As in previous works,26,42,43 we follow a primitive model for polyelectrolyte solutions. Linear polyelectrolyte chains are represented by a number of (negative) unit charges centered in hard spheres and connected with a fixed bond length, b = 4.5 Å. Simple ions are modeled as unconnected charged hard spheres, and the solvent is a dielectric continuum. In a given simulation, the same polymerization degree is assumed for all polymers; that is, no size distribution is considered. To minimize the number of parameters defining the system, we assume that the monomers are freely jointed, forming a flexible polymer chain, and furthermore that monomers and simple ions have the same size, set to a diameter of d = 4 Å. The comb (branched) polymers consist of a charged backbone, likewise described as above to which neutral side chains are grafted (see Figure 1). The side chains consist of a number of freely jointed neutral hard spheres with a diameter of 4 Å, separated by a fixed bond length of 5 Å. The grafting points, that is, the monomers in the backbone that hold the side chains are neutral, mimicking the ester link between, for example, carboxylic groups in PAA and PEO side chains. The grafting points are distributed evenly along the backbone with the first and last monomer always carrying a side chain. Throughout this paper, if not otherwise stated, the polymerization degree of the polymer backbone (denoted P) was set to 13. The following notation Pba was adopted to define a given comb copolymer,
Figure 2. Sketch of the simulation box. The slit is defined by one charged surface and one neutral surface in the z dimension. Periodic boundary conditions are applied in the lateral dimensions with respect to the surface planes. where a is the grafting density given in percent and b is the polymerization degree of the side chains. As an example, the polymer sketched in Figure 1 will be called P431. In this study, a was varied between 0 and 54%, and b between 0 and 16. Particles and Simulation Box. Highly negatively charged particles are represented by their surface, modeled as an infinite charged hard wall carrying a uniform charge density, σ, which was varied between 0.02 and 0.04 e/Å2, corresponding to the range of values found, e.g., for cement nanohydrates at high pH and high calcium concentrations.4 Neglecting the inhomogeneity of the surface charge density,44 titrating sites,45 image forces, calcium specificity to the surface and water structuring effects, may underestimate the contact energy between calcium ions and the surface as well as the magnitude of the polymer adsorption. However, these effects are highly surface specific, and the simplest surface description was therefore used to study the general trends of polymer adsorption. The particle surface is put in contact with the polyelectrolyte solution in a parallelepipedic box forming a slit of lateral dimension L and thickness h (see Figure 2). The system is assumed to be infinite (periodic boundary conditions are applied) in the two dimensions parallel to the 13573
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surface. In the perpendicular direction, z, to the charged surface, the cell is closed by a neutral impenetrable wall. Interactions. Within the framework of the restricted primitive model with a uniform dielectric response of εr = 78.3, the interaction energy, U(r), between any two species separated by a distance r can formally be described by ( zi zj e2 =4πε0 εr r , r g d ð1Þ UðrÞ ¼ ∞ , r
