AmericanChemicalSociety.com

Adsorbed layers of polyelectrolyte are important in a number of energy-related applications. For example, polyelectrolyte films have been proposed as solid electrolytes in battery and fuel cell scenarios, where they offer excellent uniformity and low resistivity, and polyelectrolyte membranes are promising in certain gas phase separations of importance to energy production, such as oxygen/nitrogen (for coal burning) and hydrogen (for fuel cells). Substrate electric potential can strongly influence the adsorption process, and thus is an important control variable in engineering polyelectrolyte films of tailored properties. In recent experiments, we have uncovered conditions where polyelectrolyte adsorption to a conducting substrate at fixed electric potential may become continuous in the sense of scaling linearly with time over hours without any apparent saturation. Continuous polyelectrolyte adsorption under an applied potential offers great opportunities (single component polyelectrolyte films of controlled mass realized in a single step), but raises many fundamental questions. To answer these questions, we are conducting a molecular simulation study of polyelectrolyte adsorption at an electrified interface.

Model

Our model system consists of polycations, small anions, and small cations placed between two smooth, parallel, impenetrable walls. In this coarse-grained description, the solvent is implicit and accounted for by a dielectric constant. The polycations are modeled as chains of tangent hard spheres, of diameter d₀, and whose charge may be 0 or +e (e being the elementary charge). Anions (cations) are modeled as hard spheres of charge -ze (+ze) and diameter d. The adsorbing wall possesses a smeared out (negative) charge density of se.

Simulation

Monte Carlo simulations are employed, subject to an overall energy composed of electrostatic interactions, hard sphere repulsion, and short-range attraction, and dependant on polymer segment charges and small anion/cation positions. Specifically, three types of moves are considered: i) cation/anion translations, ii) anion and cation insertion (deletion), and iii) polymer (de)protonation/anion deletion (insertion). Periodic boundary conditions in directions parallel to the walls, and an Ewald summation method to account for Coulombic interactions with all periodic images (in the lateral directions) of molecules within the primary simulation cell, are employed.

Results

We have conducted studies on two fully (positively) charged, fully extended, rigid, coarse-grained model polymers, parallel to each other, in bulk solution with counter-ions. The polymers span (laterally) the simulation box, so are essentially infinite in length. Simulation details are given above. We investigate the interaction free energy versus polymer separation, for various counter-ion diameters. (This is a free energy because the degrees of freedom of the counter-ions are averaged over during the simulation.) Interestingly, we find an attractive potential can result, even though the polymers are like-charged. To probe the mechanism of attraction, we consider simulation snap-shots at various chain separations. We note that at intermediate separations, where the attractive energetic minimum occurs, the counter-ions preferentially arrange in the gap between the two chains. The attraction may be understood in a simple way by assuming some of the counter-ions to cluster around a line midway between the two chains, while the others to remain diffuse around the chains. At shorter separations, the counter-ions are squeezed out from between the polymers, and the attraction disappears. For larger diameter counter-ions (see pink curve), an insufficient number is able to arrange in the zone between the polymers, and no attraction is observed.

We also consider the influence of counter-ion size and polyelectrolyte charge density. We find for small counter-ions, the increase in polymer charge density causes in increase in polymer-polymer attraction, as can be understood via charge correlations among the counter-ions. However, for larger counter-ions, the opposite is true. To understand this finding, we consider the simulation snap-shots. We find that for smaller counter-ions, the counter-ions are able to fill the gap between the polymers, and act to promote attraction. For larger counter-ions, this is not possible, and the counter-ion positions around the periphery of the central polymer pair contributes instead to their mutual repulsion.

Bibliography

[1] A. P. Ngankam and P. R. Van Tassel, Proc. Nac. Acad. Sci. 104, 1140-1145 (2007).

[2] C. Olsen and P. R. Van Tassel, J. Colloid and Interface Science 329, 222-227 (2009).