AmericanChemicalSociety.com

Inorganic nanoparticles (NPs) display unique size-dependent properties and have applications in many different areas such as medicine and the semiconductor industry. In order to take advantage of these properties, the organization of the NPs must be controlled, either to promote crystallization or to prevent agglomeration. This control is typically acheived by using covalently bound amphiphilic ligands. While the properties of the NPs themselves have been well-characterized, much less is known about the organic ligand coating. One of our goals is to take a theoretical and computer simulation approach to compute the surface area occupied per ligand molecule as a function of the NP radius and of the ligand hydrophilic to lipophilic balance. To do so we employ a self-consistent method which takes into account the full free energy of the NP/ligand/solvent system, which for this study is composed of hydrophobic NPs, alkyl poly(oxyethylene) ligands, and water. Our approach is fundamentally different from existing computational methods in the literature and builds a foundation for studies of the organization of colloidal NPs in solvents or at interfaces. First, we introduced a novel coarse grain force field and a novel free energy method to compute the area per molecule using molecular dynamics simulations. The area per molecule which minimizes the free energy of the system achieves a balance between steric clashes among ligand chains at too low an area per molecule and nanoparticle exposure to water at too high an area per molecule. We also computed the area per molecule chemisorbed to a flat solid surface using a surface tension criterion. In agreement with some experimental reports, we showed an order of magnitude increase in the area per molecule chemisorbed to flat surfaces versus nanoparticles. This effect is solely due to the curvature of the solid surface. Second, we computed the area per molecule by applying the predictive theory of surfactant self-assembly due to Nagarajan and Ruckenstein, which is based on thermodynamic stabilization.

These two approaches are only valid for amphiphilic ligands. However, experimental work to control NP organization, whether the goal is crystallization, interfacial assembly, or colloidal stability, typically employs amphiphilic ligands. We then compared and contrasted the two methods. The compact head group model, in which the poly(oxyethylene) polar chain is considered to not be swollen with water but rather form a sharp interface between the alkyl tails and water, is in reasonable agreement with the molecular dynamics data if we use a larger cross-sectional head group area than would seem appropriate from the molecular structure. The polymer chain head group model, in which the poly(oxyethylene) polar chain is considered to be swollen with water, is in poor agreement with the molecular dynamics data in the uniform concentration limit, and in reasonable agreement with the molecular dynamics data in the uniform deformation limit. A uniform head group concentration is only possible if the poly(oxyethylene) chains deform nonuniformly along the nanoparticle radial coordinate, whereas a uniform head group deformation along this coordinate allows for a water concentration gradient as one approaches the alkane core. Analysis of the molecular dynamics data clearly shows such a concentration gradient, but water and poly(oxyethylene) units are even seen to penetrate (with low probability) to the nanoparticle surface, which is not considered in the theory. The reason for this penetration is that the ligand chains tend to cluster instead of spreading out uniformly over the nanoparticle surface.

A detailed analysis of the non-uniformity is in progress. The area per molecule computed here may be considered as the optimal coverage of nanoparticles by ligands in the sense it minimizes the free energy of the system. Normally in the literature optimal coverage is defined to be the ligand coverage which prevents particle aggregation -- in other words the ligand coverage which imparts colloidal stability. We intend to explore the relationship between these two optimal coverages. The complementary simulation and theoretical approach taken here has significantly impacted the scientific development of the PI and the students involved in this work because it shows us the power of using a combined approach to study a problem simultaneously from two different perspectives. What we have learned is that both approaches have their strengths and weaknesses.

The simulation approach defines the inter- and intra-molecular forces and computes the free energy from these forces whereas the theoretical approach directly postulates the form of the free energy expressions. The strength of the simulation approach is that it is not necessary to account for all the different contributions to the free energy of the system; the free energy emerges from the potential energy expressions in the force field and from the configurational entropy. The weakness of this approach lies in the accuracy of the force field.  The strength of the theoretical approach is that the free energy expressions are physically motivated and offer great insight into the phenomenon under study. The weakness of this approach is that terms may be missing from the free energy expressions, or may be too simple or coupled in ways that are not accounted for.