Nonadditivity of nanoparticle interactions

Solutions for nanoparticle solutions Nanoparticle interactions in solution affect their binding to biomolecules, their electronic properties, and their packing into larger crystals. However, the theories that describe larger colloidal particles fail for nanoparticles, because the interactions do not add together linearly. Nanoparticles also have complex shapes and are closer in size to the solvent molecules. Silvera Batista et al. review approaches that can treat the nonadditive nature of nanoparticle interactions, resulting in a more complete understanding of nanoparticles in solution. Science, this issue p. 10.1126/science.1242477 BACKGROUND Interactions between inorganic nanoparticles (NPs) are central to a wide spectrum of physical, chemical, and biological phenomena. An understanding of these interactions is essential for technological implementation of nanoscale synthesis and engineering of self-organized NP superstructures with various dimensionalities, collective properties at the nanoscale, and predictive biological responses to NPs. However, the quantitative description of NP forces encounters many obstacles not present, or not as severe, for microsize particles (µPs). These difficulties are revealed in multiple experimental observations that are, unfortunately, not fully recognized as of yet. Inconsistencies in the accounting of NP interactions are observed across all material platforms that include ceramic, semiconductor, and metallic NPs; crystalline and amorphous NPs; as well as dispersions of inorganic, organic, and biological nanomaterials. Such systematic deviations of theoretical predictions from reality point to the generality of such phenomena for nanoscale matter. Here we analyze the sources of these inconsistencies and chart a course for future research that might overcome these challenges. ADVANCES Nanoparticle interactions are often described by classical colloidal theories developed for µPs. However, several foundational assumptions of these theories, while tolerable for microscale dispersions, fail for NPs. For example, the sizes of ions, solvent molecules, and NPs can be within one order of magnitude of each other, which inherently disallows continuum approximations. Fluctuations of ionic atmospheres, ion-specific effects, enhanced NP anisometry, and multiscale collective effects become essential for accurate accounting of NP interactions. The nonuniformity of the stabilizing layer adds another essential contradistinction. When the particle size becomes smaller than a few tens of nanometers and the gaps between particles become smaller than a few nanometers, nonadditivity of electrostatic (Vel), van der Waals (VvdW), hydrophobic (Vhph), and other potentials (V′) emerges. In fact, it becomes impossible to cleanly decompose the potential of mean force (PMF) for the interaction of two NPs into separate additive contributions from these interactions—as in, e.g., classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory [V(r) = Vel(r)+ VvdW(r)+ Vhph(r)+ V′(r)]—due to the coupled structural dynamics of neighboring NPs and surrounding media. Experimentally, the nonadditivity of NP interactions was observed long ago as an unusually high colloidal stability of NP dispersions, defying all reasonable predictions based on DLVO and other classical theories. It also manifests itself in paradoxical phase behavior, self-assembly into sophisticated superstructures, complex collective behavior, enigmatic toxicology, and protein-mimetic behavior of inorganic NPs. Molecular dynamics simulations of PMFs computed for NP pairs confirm the nonadditivity of van der Waals and electrostatic interactions for nanometer-scale separations. OUTLOOK Further work in the field of NP interactions should perhaps embrace NPs as strongly correlated reconfigurable systems with diverse physical elements and multiscale coupling processes, which will require new experimental and theoretical tools. Meanwhile, several heuristic rules identified in this Review can be helpful for discriminating between the systems in which mean-field theories can and cannot be applied. These precepts can guide qualitative thinking about NP interactions, stimulate further research into NP interactions, and aid in their design for applications. Though it is the crux of nonadditivity, the similarity in size between the ions and molecules composing the solvent medium and the NP offers a silver lining: it makes atomic simulations of their interactions increasingly practical as computer speed increases. The direct determination of the PMF by atomistic simulation bypasses the enumeration of individual forces and therefore resolves the nonadditivity problem. In fact, NPs present a favorable system for atomistic simulations because solid inorganic cores have many fewer degrees of freedom than flexible organic chains. Improvements in force fields are necessary to adequately account for intermolecular interactions, entropic contributions, dispersion interactions between atoms, high polarizability of inorganic materials, and quantum confinement effects. Evolving experimental tools that can accurately examine interactions at the nanoscale should help to validate the simulations and stimulate improvement of relevant force fields. In fact, new opportunities for better understanding of the electronic origin of classical interactions are likely as the rapidly improving capabilities in synthesis, simulations, and imaging converge at the scale of NPs. Schematics of hydrated ions, a NP, and a µP, demonstrating the structural uniqueness and discreteness of NPs. Nonadditivity of NP interactions stems from the size similarity of reconfigurable structural elements of NPs (i.e., surface ligands, ionic atmosphere, adsorbed molecules, etc.) and the surrounding media, leading to their strongly coupled dynamics. The high polarizability and faceting that are typical of NPs—as well as collective multibody effects at atomic, molecular, and nanometer scales—lead to the enhancement of nonadditivity and result in interdependence of electrostatic, van der Waals, hydrophobic, and other forces. Understanding interactions between inorganic nanoparticles (NPs) is central to comprehension of self-organization processes and a wide spectrum of physical, chemical, and biological phenomena. However, quantitative description of the interparticle forces is complicated by many obstacles that are not present, or not as severe, for microsize particles (μPs). Here we analyze the sources of these difficulties and chart a course for future research. Such difficulties can be traced to the increased importance of discreteness and fluctuations around NPs (relative to μPs) and to multiscale collective effects. Although these problems can be partially overcome by modifying classical theories for colloidal interactions, such an approach fails to manage the nonadditivity of electrostatic, van der Waals, hydrophobic, and other interactions at the nanoscale. Several heuristic rules identified here can be helpful for discriminating between additive and nonadditive nanoscale systems. Further work on NP interactions would benefit from embracing NPs as strongly correlated reconfigurable systems with diverse physical elements and multiscale coupling processes, which will require new experimental and theoretical tools. Meanwhile, the similarity between the size of medium constituents and NPs makes atomic simulations of their interactions increasingly practical. Evolving experimental tools can stimulate improvement of existing force fields. New scientific opportunities for a better understanding of the electronic origin of classical interactions are converging at the scale of NPs.