Solvent Isotherms and Structural Transitions in Nanoparticle Superlattice Assembly.

We introduce a Molecular Theory for Compressible Fluids (MOLT-CF) that enables us to compute free energies and other thermodynamic functions for nanoparticle superlattices with any solvent content, including the dry limit. Quantitative agreement is observed between MOLT-CF and united-atom molecular dynamics simulations performed to assess the reliability and precision of the theory. Among other predictions, MOLT-CF shows that the amount of solvent within the superlattice decreases approximately linearly with its vapor pressure and that in the late stages of drying, solvent-filled voids form at lattice interstitials. Applied to single-component superlattices, MOLT-CF predicts fcc-to-bcc Bain transitions for decreasing vapor pressure and for increasing ligand length, both in agreement with experimental results. We explore the stability of other single-component phases and show that the C14 Frank-Kasper phase, which has been reported in experiments, is not a global free-energy minimum. Implications for precise assembly and prediction of multicomponent nanoparticle systems are discussed.

Molecular Theory: A Tool for Predicting the Outcome of Self-Assembly of Polymers, Nanoparticles, Amphiphiles, and Other Soft Materials.

The supramolecular organization of soft materials, such as colloids, polymers, and amphiphiles, results from a subtle balance of weak intermolecular interactions and entropic forces. This competition can drive the self-organization of soft materials at the nano-/mesoscale. Modeling soft-matter self-assembly requires, therefore, considering a complex interplay of forces at the relevant length scales without sacrificing the molecular details that define the chemical identity of the system. This mini-review focuses on the application of a tool known as molecular theory to study self-assembly in different types of soft materials. This tool is based on extremizing an approximate free energy functional of the system, and, therefore, it provides a direct, computationally affordable estimation of the stability of different self-assembled morphologies. Moreover, the molecular theory explicitly incorporates structural details of the chemical species in the system, accounts for their conformational degrees of freedom, and explicitly includes their chemical equilibria. This mini-review introduces the general ideas behind the theoretical formalism and discusses its advantages and limitations compared with other theoretical tools commonly used to study self-assembled soft materials. Recent application examples are discussed: the self-patterning of polyelectrolyte brushes on planar and curved surfaces, the formation of nanoparticle (NP) superlattices, and the self-organization of amphiphiles into micelles of different shapes. Finally, prospective methodological improvements and extensions (also relevant for related theoretical tools) are analyzed.

Scission energies of surfactant wormlike micelles loaded with nonpolar additives.

HYPOTHESIS: The previously observed effects of nonpolar additives on the scission energy and rheological properties of surfactant wormlike micelles can be explained in terms of the spatial distribution of the additive within the micelles. The dependence of the scission energy with the molecular organization of the system can be analyzed with a molecular theory capable of describing the thermodynamics and structure of the micelles. THEORY: A new theoretical method to determine the scission energy of surfactant wormlike micelles is introduced. This methodology is based on a molecular theory that explicitly considers molecular details of all components of the micelles, and their inter- and intramolecular interactions without the use of fitting and/or empirical macroscopic parameters. FINDINGS: The predicted effects of the concentration, molecular structure and hydrophobicity of the additive on the scission energy of cetyltrimethylammonium bromide (CTAB) wormlike micelles are found to be in qualitative agreement with previous experimental observations. In particular, our theory captures the decrease of micellar length with increasing content of highly hydrophobic additives and the non-monotonic dependence of the viscosity with additive hydrophobicity. The latter effect arises because highly and mildly hydrophobic additives affect the scission energy of wormlike micelles via markedly different molecular mechanisms.

Molecular Basis for the Morphological Transitions of Surfactant Wormlike Micelles Triggered by Encapsulated Nonpolar Molecules.

Surfactant wormlike micelles are prone to experience morphological changes, including the transition to spherical micelles, upon the addition of nonpolar additives. These morphological transitions have profound implications in diverse technological areas, such as the oil and personal-care industries. In this work, additive-induced morphological transitions in wormlike micelles were studied using a molecular theory that predicts the equilibrium morphology and internal molecular organization of the micelles as a function of their composition and the molecular properties of their components. The model successfully captures the transition from wormlike to spherical micelles upon the addition of a nonpolar molecule. Moreover, the predicted effects of the concentration, molecular structure, and degree of hydrophobicity of the nonpolar additive on the wormlike-to-sphere transition are shown to be in good agreement with experimental trends in the literature. The theory predicts that the location of the additive in the micelle (core or hydrophobic-hydrophilic interface) depends on the additive hydrophobicity and content, and the morphology of the micelles. Based on the results of our model, simple molecular mechanisms were proposed to explain the morphological transitions of wormlike micelles upon the addition of nonpolar molecules of different polarities.

Twisting of Charged Nanoribbons to Helicoids Driven by Electrostatics.

Charged amphiphiles in solution usually self-assemble into flat nanoribbons that spontaneously twist into different shapes. The role of electrostatics in this process is still under strong debate. This work studies the electrostatic free energy of twisting a nanoribbon at the level of the nonlinear Poisson-Boltzmann approximation. It is shown that helicoid-shaped ribbons are more stable than flat ribbons, while other shapes under consideration (cylindrical helixes and bent ribbons) are always less stable than the flat ribbon. The unexpected electrostatics-driven twisting of the ribbon into a helicoid is ascribed to the increase in its perimeter with increasing degree of twisting, as charges near the edge of the ribbon are electrostatically more stable than those near its center. This argument successfully explains the effects of salt concentration and the width of the ribbon on the optimal twisting period and allows us to approximately describe the problem of ribbon twisting in terms of two dimensionless variables that combine the helicoid twisting period, the Debye length of the solution, and the width of the ribbon. The magnitude of the electrostatic twisting energy predicted by our calculations is comparable to that of restoring elastic forces for typical ribbons of self-assembled amphiphiles, which indicates that electrostatics plays an important role in determining the equilibrium shape of charged nanoribbons.

Layer-by-Layer Self-Assembly of Polymers with Pairing Interactions.

A molecular theory is introduced to model the layer-by-layer self-assembly (LbL-SA) of polymers with pairing interactions. Our theory provides a general framework to describe nonelectrostatic LbL-SA as the pairing interactions generically describe the formation of bonds between two complementary chemical species, for example, hydrogen donor and acceptor in hydrogen-bonding-LbL or host and guest in host-guest-LbL. The theory predicts fundamental observations related to LbL-SA: (i) phase separation of a mixture of polymers with pairing interactions in bulk solution, (ii) linear increase in film thickness with the number of LbL adsorption steps, (iii) stoichiometry overcompensation after each adsorption step, and (iv) interpenetration of polymer layers. Importantly, this study shows that the minimal requirement for nonelectrostatic LbL is the competition of a pairing interaction and an excluded-volume repulsion. A simple analytical model based on this competition predicts the volume fraction of the layers in good agreement with the numerical predictions of the molecular theory.

Lithium solvation in dimethyl sulfoxide-acetonitrile mixtures.

We present molecular dynamics simulation results pertaining to the solvation of Li(+) in dimethyl sulfoxide-acetonitrile binary mixtures. The results are potentially relevant in the design of Li-air batteries that rely on aprotic mixtures as solvent media. To analyze effects derived from differences in ionic size and charge sign, the solvation of Li(+) is compared to the ones observed for infinitely diluted K(+) and Cl(-) species, in similar solutions. At all compositions, the cations are preferentially solvated by dimethyl sulfoxide. Contrasting, the first solvation shell of Cl(-) shows a gradual modification in its composition, which varies linearly with the global concentrations of the two solvents in the mixtures. Moreover, the energetics of the solvation, described in terms of the corresponding solute-solvent coupling, presents a clear non-ideal concentration dependence. Similar nonlinear trends were found for the stabilization of different ionic species in solution, compared to the ones exhibited by their electrically neutral counterparts. These tendencies account for the characteristics of the free energy associated to the stabilization of Li(+)Cl(-), contact-ion-pairs in these solutions. Ionic transport is also analyzed. Dynamical results show concentration trends similar to those recently obtained from direct experimental measurements.