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Binary compositions of surface ligands are known to improve the colloidal stability and fluorescence quantum yield of nanocrystals (NCs), due to ligand-ligand interactions and surface organization. Herein, we follow the thermodynamics of a ligand exchange reaction of CdSe NCs with alkylthiols mixtures. The effects of ligand polarity and length difference on ligand packing were investigated using isothermal titration calorimetry (ITC). The thermodynamic signature of the formation of mixed ligand shells was observed. Correlating the experimental results with thermodynamic mixing models has allowed us to calculate the inter-chain interactions and infer the final ligand shell configuration. Our findings demonstrate that the small dimensions of the NCs and the subsequent increased interfacial region between dissimilar ligands, in contrast to macroscopic surfaces, allow the formation of a myriad of clustering patterns, controlled by the inter-ligand interactions. This work provides a fundamental understanding of the parameters determining the ligand shell structure and should help guide smart surface design toward NC-based applications., Comment: 28 pages, 4 figures; combines with SI file 24 pages, 14 figures, 9 tables

Solutes added to solutions often dramatically impact molecular processes ranging from the suspension or precipitation of colloids to biomolecular associations and protein folding. Here we revisit the origins of the effective attractive interactions that emerge between and within macromolecules immersed in solutions containing cosolutes that are preferentially excluded from the macromolecular interfaces. Until recently, these depletion forces were considered to be entropic in nature, resulting primarily from the tendency to increase the space available to the cosolute. However, recent experimental evidence indicates the existence of additional, energetically-dominated mechanisms. In this review we follow the emerging characteristics of these different mechanisms. By compiling a set of available thermodynamic data for processes ranging from protein folding to protein-protein interactions, we show that excluded cosolutes can act through two distinct mechanisms that correlate to a large extent with their molecular properties. For many polymers at low to moderate concentrations the steric interactions and molecular crowding effects dominate, and the mechanism is entropic. To contrast, for many small excluded solutes, such as naturally occurring osmolytes, the mechanism is dominated by favorable enthalpy, whereas the entropic contribution is typically unfavorable. We review the available models for these thermodynamic mechanisms, and comment on the need for new models that would be able to explain the full range of observed depletion forces., Comment: 18 pages, 4 figures, supplementary info included

In aqueous solutions, dissolved ions interact strongly with the surrounding water, thereby modifying the solution properties in an ion-specific manner. These ion-hydration interactions can be accounted for theoretically on a mean-field level by including phenomenological terms in the free energy that correspond to the most dominant ion-specific interactions. Minimizing this free energy leads to modified Poisson-Boltzmann equations with appropriate boundary conditions. Here, we review how this strategy has been used to predict some of the ways ion-specific effects can modify the forces acting within and between charged interfaces immersed in salt solutions., Comment: 11 pages, 2 figures

The Poisson-Boltzmann mean-field description of ionic solutions has been successfully used in predicting charge distributions and interactions between charged macromolecules. While the electrostatic model of charged fluids, on which the Poisson-Boltzmann description rests, and its statistical mechanical consequences have been scrutinized in great detail, much less is understood about its probable shortcomings when dealing with various aspects of real physical, chemical and biological systems. These shortcomings are not only a consequence of the limitations of the mean-field approximation per se, but perhaps are primarily due to the fact that the purely Coulombic model Hamiltonian does not take into account various additional interactions that are not electrostatic in their origin. We explore several possible non-electrostatic contributions to the free energy of ions in confined aqueous solutions and investigate their ramifications and consequences on ionic profiles and interactions between charged surfaces and macromolecules.

The forces between charged macromolecules, usually given in terms of osmotic pressure, are highly affected by the intervening ionic solution. While in most theoretical studies the solution is treated as a homogeneous structureless dielectric medium, recent experimental studies concluded that, for a bathing solution composed of two solvents (binary mixture), the osmotic pressure between charged macromolecules is affected by the binary solvent composition. By adding local solvent composition terms to the free energy, we obtain a general expression for the osmotic pressure, in planar geometry and within the mean-field framework. The added effect is due to the permeability inhomogeneity and nonelectrostatic short-range interactions between the ions and solvents (preferential solvation). This effect is mostly pronounced at small distances and leads to a reduction in the osmotic pressure for macromolecular separations of the order 1--2 nm. Furthermore, it leads to a depletion of one of the two solvents from the charged macromolecules (modeled as planar interfaces). Lastly, by comparing the theoretical results with experimental ones, an explanation based on preferential solvation is offered for recent experiments on the osmotic pressure of DNA solutions., Comment: 13 pages, 8 figures

We propose a model for the liquid-liquid phase transition observed in osmotic pressure measurements of certain charged lamellae-forming amphiphiles. The model free energy combines mean-field electrostatic and phenomenological non-electrostatic interactions, while the number of dissociated counterions is treated as a variable degree of freedom that is determined self-consistently. The model, therefore, joins two well-known theories: the Poisson-Boltzmann theory for ionic solutions between charged lamellae, and Langmuir-Frumkin-Davies adsorption isotherm modified to account for charged adsorbing species. Minimizing the appropriate free energy for each interlamellar spacing, we find the ionic density profiles and the resulting osmotic pressure. While in the simple Poisson-Boltzmann theory the osmotic pressure isotherms are always smooth, we observe a discontinuous liquid-liquid phase transition when Poisson-Boltzmann theory is self-consistently augmented by Langmuir-Frumkin-Davies adsorption. This phase transition depends on the area per amphiphilic headgroup, as well as on non-electrostatic interactions of the counterions with the lamellae, and interactions between counterion-bound and counterion-dissociated surfactants. Coupling lateral phase transition in the bilayer plane with electrostatic interactions in the bulk, our results offer a qualitative explanation for the existence of the phase-transition of DDABr (didodecyldimethylammonium bromide), but its apparent absence for the chloride and the iodide homologues. More quantitative comparisons with experiment require better understanding of the microscopic basis of the phenomenological model parameters., Comment: 14 pages, 9 figures