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44645-AC7
Charge Heterogeneities in Cationic-Anionic Co-Assemblies

Monica Olvera de la Cruz, Northwestern University

In line with the goals envisioned in our proposal, we have achieved further progress in determining the surface structure of systems consisting of co-assembled cationic and anionic substructures in various ionic conditions. Specifically, we have proposed a model, based on an extension to the our prior results funded by the ACS grant [Phys. Rev. Lett. 98, 237802 (2007)], that elucidates the origin of the hitherto confounding experimental findings that only negatively charged colloids—and not their equivalently positively charged counterparts—assemble into dense lattice phase on surfaces.

It has been long known that colloidal interactions influencing the system's overall properties include Van der Waals dispersion forces, electrostatic interactions between the charge densities themselves, as well as an effective attraction of the larger particles due to depletion when the colloidal suspension contains particles of different sizes. At the mean-field level where we neglect fluctuation effects, it is well known that the Poisson-Boltzmann framework precludes long-range attraction between like-charges, in contradiction to experimental findings such as those found in confined systems. So one may account for these long-range attraction between like charges by going beyond mean-field approaches and take in account fluctuation effects. However, there have been recent experimental indications that this long-range attraction occurs only between colloidal particles of negative charge and not of the opposite kind. Depletion cannot account for this asymmetry since it is entropic in nature and should not distinguish between the two kinds of charge. On the other hand, Van der Waals forces are much smaller in magnitude by comparison to be a possible significant contributing factor.

In our submitted work, we propose a simple, mean-field analytical model that would demonstrate this asymmetric behavior between the negatively (positively) charged colloidal disks in their ability (inability) to form long-range attraction based on their interaction with water molecules. In particular, we conjecture that due to the bent-core shape and the charge distribution of the water molecule, the greatest aggregation of them —swelling—occurs between the larger-sized colloidal particles that are negatively charged and the smaller-sized counterions that are positively charged. Swelling also occurs, albeit to a lesser degree, in the opposite case where the system consists of equivalently charged positive particles with negative counterions. Therefore, this interaction with water molecules induces an effective repulsion between opposite charges and correspondingly a comparative attraction between like charges, which exactly counter-balances the effects of electrostatics. Consequently, there exists a general competition between these two types of interaction in the system. For a range of interaction parameters and densities, we have demonstrated the resulting coexistence of a low-density isotropic phase and a high-density hexagonal lattice phase in our mean-field model. Our model extends the results of our prior work to include charged species of different sizes and of different short-range repulsion strengths. Moreover, our generalized model can determine from first thermodynamics principle both coexistence densities for the dilute and periodic phases, rendering the assumption of fixed density in the periodic phase found in the previous work unnecessary.

An important aspect in understanding the highly cooperative phenomena involved in the assembly of charged macromolecules, as well as the complexation and de-complexation effects of co-assembled cationic-anionic amphiphile molecules in different ionic conditions, is the physics of ion solvation. As a first step towards the fundamental problem of determining charge heterogeneities in media with different dielectric properties, we have presented, in another work to be submitted, a mean-field formulation of the thermodynamics of ion solvation in polar binary mixtures. Assuming an equilibrium planar interface separating two semi-infinite regions of constant dielectric medium, we study the electrostatic phenomenon of differential absorption of ions at the boundary. Using general thermodynamic considerations, we construct the mean-field Ω-potential and demonstrate that the requirement of electro-neutrality and the spontaneous formation of an electric double-layer around the interface necessarily follow. In our framework, we can also relate both the bulk ion densities in the two phases and the distribution potential across the interface to the fundamental Born free energy of ion polarization.

In fine, the ACS grant has allowed my group to move into the fundamental area of how to determine charge heterogeneities in media with different dielectric properties. This is a fundamental area of electrostatic-driven co-assembly. Cationic-anionic amphiphilic molecules dissolve in water self-assemble into vesicles or cylindrical fibers. Both the hydrophobic tails and the polar headgroups on the surface with water create an environment of dielectric heterogeneity. The new visitor from the CINVESTAV in Mexico, Prof. Pedro Gonzalez Mozuelos, will collaborate with Dr. William Kung, who is funded by this ACS grant, to compare results from liquid theory approaches with our analytic results. Moreover, Dr. Dongsheng Zhang is incorporating a local electrostatics algorithm into the LAMMPS program to study the self-assembly of charged molecules on surfaces with dielectric inhomogeneities.

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