Diffusion in inhomogeneous fluids: Hard spheres to polymer coatings.

We investigate diffusion in fluids near surfaces that may be coated with polymer films. We first consider diffusion in hard sphere fluids near a planar hard wall. We specifically consider color diffusion, where hard spheres are labeled A or B but are otherwise identical in all respects. In this inhomogeneous fluid, we consider a surface reaction-diffusion problem. At the left wall, a particle of species A is converted to one of species B upon a wall collision. At the opposing wall, the reverse reaction takes place: B → A. Using molecular dynamics simulation, we study the steady state of this system. We demonstrate that in the homogeneous region, a diffusing particle is subject to an equilibrium oscillatory force, the solvation force, that arises from the interfacial structuring of the fluid at the wall. For the hard sphere/hard wall system, the solvation force can be determined in various ways. We use the solvation force [the potential of mean force (PMF)] to solve the continuum diffusion equation. This provides an adequate and accurate description of the reaction-diffusion problem. The analysis is then extended to consider both color diffusion in the presence of a slowly varying one-body field such as gravity and a more applied problem of diffusion of free species through a surface film consisting of tethered chains. In both cases, the PMF experienced by the free particles is affected, but the diffusion problem can be treated in the same way as for the simpler hard sphere color diffusion case.

Electric Double Layers with Surface Charge Regulation Using Density Functional Theory.

Surprisingly, the local structure of electrolyte solutions in electric double layers is primarily determined by the solvent. This is initially unexpected as the solvent is usually a neutral species and not a subject to dominant Coulombic interactions. Part of the solvent dominance in determining the local structure is simply due to the much larger number of solvent molecules in a typical electrolyte solution.The dominant local packing of solvent then creates a space left for the charged species. Our classical density functional theory work demonstrates that the solvent structural effect strongly couples to the surface chemistry, which governs the charge and potential. In this article we address some outstanding questions relating double layer modeling. Firstly, we address the role of ion-ion correlations that go beyond mean field correlations. Secondly we consider the effects of a density dependent dielectric constant which is crucial in the description of a electrolyte-vapor interface.

Solution Structure Effects on the Properties of Electric Double Layers with Surface Charge Regulation Assessed by Density Functional Theory.

The structure of electrolyte solutions in electric double layers is primarily determined by the solvent, despite the fact that it is usually neutral and not subject to Coulombic interactions. The number of solvent molecules in a typical electrolyte solution may be significantly greater that the number of ions. Hence, the charged species compete for space with a much larger number of neutral molecules, which has a strong effect on the density distributions near charged surfaces. Even for very dilute electrolyte solutions, the density profiles resemble liquidlike structure, which is entirely due to the presence of the dense solvent. Our work demonstrates that the solvent structural effect strongly couples to the surface chemistry, which governs the charge and potential. We argue that a comprehensive statistical-mechanical approach, such as classical density functional theory that explicitly includes all solution species, in combination with a surface charge regulation condition at the interface, provides an excellent approach for describing charged interfaces. It allows for revealing important physical features and includes non-Coulombic contributions such as ionic and surface solvation.

Solvent Role in the Formation of Electric Double Layers with Surface Charge Regulation: A Bystander or a Key Participant?

The charge formation at interfaces involving electrolyte solutions is due to the chemical equilibrium between the surface reactive groups and the potential determining ions in the solution (i.e., charge regulation). In this Letter we report our findings that this equilibrium is strongly coupled to the precise molecular structure of the solution near the charged interface. The neutral solvent molecules dominate this structure due to their overwhelmingly large number. Treating the solvent as a structureless continuum leads to a fundamentally inadequate physical picture of charged interfaces. We show that a proper account of the solvent effect leads to an unexpected and complex system behavior that is affected by the molecular and ionic excluded volumes and van der Waals interactions.

Tuning structure and mobility of solvation shells surrounding tracer additives.

Molecular dynamics simulations and a stochastic Fokker-Planck equation based approach are used to illuminate how position-dependent solvent mobility near one or more tracer particle(s) is affected when tracer-solvent interactions are rationally modified to affect corresponding solvation structure. For tracers in a dense hard-sphere fluid, we compare two types of tracer-solvent interactions: (1) a hard-sphere-like interaction, and (2) a soft repulsion extending beyond the hard core designed via statistical mechanical theory to enhance tracer mobility at infinite dilution by suppressing coordination-shell structure [Carmer et al., Soft Matter 8, 4083-4089 (2012)]. For the latter case, we show that the mobility of surrounding solvent particles is also increased by addition of the soft repulsive interaction, which helps to rationalize the mechanism underlying the tracer's enhanced diffusivity. However, if multiple tracer surfaces are in closer proximity (as at higher tracer concentrations), similar interactions that disrupt local solvation structure instead suppress the position-dependent solvent dynamics.

Charge regulation at semiconductor-electrolyte interfaces.

The interface between a semiconductor material and an electrolyte solution has interesting and complex electrostatic properties. Its behavior will depend on the density of mobile charge carriers that are present in both phases as well as on the surface chemistry at the interface through local charge regulation. The latter is driven by chemical equilibria involving the immobile surface groups and the potential determining ions in the electrolyte solution. All these lead to an electrostatic potential distribution that propagate such that the electrolyte and the semiconductor are dependent on each other. Hence, any variation in the charge density in one phase will lead to a response in the other. This has significant implications on the physical properties of single semiconductor-electrolyte interfaces and on the electrostatic interactions between semiconductor particles suspended in electrolyte solutions. The present paper expands on our previous publication (Fleharty et al., 2014) and offers new results on the electrostatics of single semiconductor interfaces as well as on the interaction of charged semiconductor colloids suspended in electrolyte solution.

Manipulating semiconductor colloidal stability through doping.

The interface between a doped semiconductor material and electrolyte solution is of considerable fundamental interest, and is relevant to systems of practical importance. Both adjacent domains contain mobile charges, which respond to potential variations. This is exploited to design electronic and optoelectronic sensors, and other enabling semiconductor colloidal materials. We show that the charge mobility in both phases leads to a new type of interaction between semiconductor colloids suspended in aqueous electrolyte solutions. This interaction is due to the electrostatic response of the semiconductor interior to disturbances in the external field upon the approach of two particles. The electrostatic repulsion between two charged colloids is reduced from the one governed by the charged groups present at the particles surfaces. This type of interaction is unique to semiconductor particles and may have a substantial effect on the suspension dynamics and stability.

Statistical mechanics of two-dimensional shuffled foams: geometry-topology correlation in small or large disorder limits.

Bubble monolayers are model systems for experiments and simulations of two-dimensional packing problems of deformable objects. We explore the relation between the distributions of the number of bubble sides (topology) and the bubble areas (geometry) in the low liquid fraction limit. We use a statistical model [M. Durand, Europhys. Lett. 90, 60002 (2010)] which takes into account Plateau laws. We predict the correlation between geometrical disorder (bubble size dispersity) and topological disorder (width of bubble side number distribution) over an extended range of bubble size dispersities. Extensive data sets arising from shuffled foam experiments, surface evolver simulations, and cellular Potts model simulations all collapse surprisingly well and coincide with the model predictions, even at extremely high size dispersity. At moderate size dispersity, we recover our earlier approximate predictions [M. Durand, J. Kafer, C. Quilliet, S. Cox, S. A. Talebi, and F. Graner, Phys. Rev. Lett. 107, 168304 (2011)]. At extremely low dispersity, when approaching the perfectly regular honeycomb pattern, we study how both geometrical and topological disorders vanish. We identify a crystallization mechanism and explore it quantitatively in the case of bidisperse foams. Due to the deformability of the bubbles, foams can crystallize over a larger range of size dispersities than hard disks. The model predicts that the crystallization transition occurs when the ratio of largest to smallest bubble radii is 1.4.

The effect of surface charge regulation on conductivity in fluidic nanochannels.

The precise electrostatic potential distribution is very important for the electrokinetic transport in fluidic channels. This is especially valid for small nanochannels where the electric double layers formed at the walls are comparable to the channel width. It can be expected that due to the large surface to volume ratio in such systems, they will exhibit properties that are not detectable in larger channels, capillaries and pores. We present a detailed numerical analysis of the current transport in fluidic nanochannels. It is based on solving the Poisson-Boltzmann equation with charge regulation boundary conditions that account for the surface-aqueous solution chemical equilibria. The focus is on studying the effect of the pH on the current transport. The pH is varied by adding either HCl or KOH. The analysis predicts non-monotonous and sometimes counterintuitive dependence of the conductivity on the pH. The channel conductivity exhibits practically no change over a range of pH values due to a buffering exerted by the chemical groups at the walls. An unexpected drop of the conductivity is observed around the wall isoelectric point and also in the vicinity of pH=7 even though the concentration of ions in the channel increases. These observations are explained in the framework of charge regulation theory.

A thermodynamic perspective of the metastability of holey sheets: the role of curvature.

Producing nanostructures with high surface area that are stable is important to accomplish sustained use of catalytic materials in practical settings. Avoiding the processes of ripening and sintering that typically hinder stability has long been recognized as a significant challenge and much research is focused on addressing these issues. In this article, we investigate a Pt nanostructure-a holey nanosheet-that exhibits high surface area and stability. The findings from lattice gas simulations produce a stability diagram that relates a critical hole diameter to sheet thickness. The stability is now addressed from a thermodynamic point of view, and, in particular, the crucial role of curvature is considered. We find that the stability of certain sized holes is due to the near zero mean curvature of the surface of the holes and of the surrounding flat sheet. Molecular dynamics simulations of Pt (using an embedded atom potential) are reported for small nanoclusters and model holes in sheets to illustrate the strong effects of curvature on thermodynamic properties such as the lowering of melting and surface melting temperatures.

Hierarchical cooperative binary ionic porphyrin nanocomposites.

Cooperative binary ionic (CBI) solids comprise a versatile new class of opto-electronic and catalytic materials consisting of ionically self-assembled pairs of organic anions and cations. Herein, we report CBI nanocomposites formed by growing nanoparticles of one type of porphyrin CBI solid onto a second porphyrin CBI substructure with complementary functionality.

Binary ionic porphyrin nanosheets: electronic and light-harvesting properties regulated by crystal structure.

Crystalline solids self-assembled from anionic and cationic porphyrins provide a new class of multifunctional optoelectronic micro- and nanomaterials. A 1 : 1 combination of zinc(II) tetra(4-sulfonatophenyl)porphyrin (ZnTPPS) and tin(IV) tetra(N-methyl-4-pyridiniumyl)porphyrin (SnTNMePyP) gives porphyrin nanosheets with high aspect ratios and varying thickness. The room temperature preparation of the nanosheets has provided the first X-ray crystal structure of a cooperative binary ionic (CBI) solid. The unit cell contains one and one-half molecules of aquo-ZnTPPS(4-) (an electron donor) and three half molecules of dihydroxy-SnTNMePyP(4+) (an electron acceptor). Charge balance in the solid is reached without any non-porphyrinic ions, as previously determined for other CBI nanomaterials by non-crystallographic means. The crystal structure reveals a complicated molecular arrangement with slipped π-π stacking only occurring in isolated dimers of one of the symmetrically unique zinc porphyrins. Consistent with the crystal structure, UV-visible J-aggregate bands indicative of exciton delocalization and extended π-π stacking are not observed. XRD measurements show that the structure of the Zn/Sn nanosheets is distinct from that of Zn/Sn four-leaf clover-like CBI solids reported previously. In contrast with the Zn/Sn clovers that do exhibit J-aggregate bands and are photoconductive, the nanosheets are not photoconductive. Even so, the nanosheets act as light-harvesting structures in an artificial photosynthesis system capable of reducing water to hydrogen but not as efficiently as the Zn/Sn clovers.

Templated growth of platinum nanowheels using the inhomogeneous reaction environment of bicelles.

Novel platinum nanowheels were synthesized by the reduction of aqueous platinum complex with ascorbic acid in the presence of disk-like bicelles. The platinum nanowheels possess thickened centers and flared edges that are connected by dendritic platinum nanosheets. This structural complexity can be attributed to the inhomogeneous micro-environment of the templating bicelles consisting of a central bi-layer region and a high curvature rim. The formation mechanism of the nanowheels was investigated by imaging nanostructures at different stages of the reaction. The templating bicelles were also imaged by TEM with the aid of negative staining. The variation of reaction parameters including platinum concentration, temperature, and total concentration of surfactants (CTAB + FC7) led to other types of platinum nanostructures, such as circular dendritic nanosheets with a tunable diameter and rectangular dendritic nanosheets. Interestingly, under irradiation by a TEM electron beam, the dendritic nanosheet portion of the nanowheels transforms into a metastable holey sheet. In addition, the platinum nanowheels have an electrochemical active surface area comparable to that of ETEK platinum black and thus are expected to have potential applications in catalysis.

Evolution of dendritic platinum nanosheets into ripening-resistant holey sheets.

Under electron-beam irradiation, dendritic platinum nanosheets structurally evolve into metastable "holey" nanosheets. Monte Carlo simulations of this structural transformation agree well with electron microscope images detailing the ripening process. The experiments and simulations show that nanoscale holes of a critical size are persistent and give holey sheets their morphological stability and sustained high surface area. Platinum nanostructures composed of these holey nanosheets exhibit improved durability in electrocatalytic reactions due to their remarkable ripening resistance.

Synthesis of platinum nanowheels using a bicellar template.

Disk-like surfactant bicelles provide a unique meso-structured reaction environment for templating the wet-chemical reduction of platinum(II) salt by ascorbic acid to produce platinum nanowheels. The Pt wheels are 496 +/-55 nm in diameter and possess thickened centers and radial dendritic nanosheets (about 2-nm in thickness) culminating in flared dendritic rims. The structural features of the platinum wheels arise from confined growth of platinum within the bilayer that is also limited at edges of the bicelles. The size of CTAB/FC7 bicelles is observed to evolve with the addition of Pt(II) complex and ascorbic acid. Synthetic control is demonstrated by varying the reaction parameters including metal salt concentration, temperature, and total surfactant concentration. This study opens up opportunities for the use of other inhomogeneous soft templates for synthesizing metals, metal alloys, and possibly semiconductors with complex nanostructures.

Light-driven synthesis of hollow platinum nanospheres.

Hollow platinum nanospheres that are porous and have uniform shell thickness are prepared by templating platinum growth on polystyrene beads with an adsorbed porphyrin photocatalyst irradiated by visible light.

Superhydrophobicity: drying transition of confined water.

Long-range hydrophobic interactions operating underwater are important in the mediation of many natural and synthetic phenomena, such as protein folding, adhesion and colloid stability. Here we show that rough hydrophobic surfaces can experience attractive forces over distances more than 30 times greater than any reported previously, owing to the spontaneous evaporation of the intervening, confined water. Our finding highlights the importance of surface roughness in the interaction of extended structures in water, which has so far been largely overlooked.

Drag reduction on a patterned superhydrophobic surface.

We present an experimental study of a low-Reynolds number shear flow between two surfaces, one of which has a regular grooved texture augmented with a superhydrophobic coating. The combination reduces the effective fluid-surface contact area, thereby appreciably decreasing the drag on the surface and effectively changing the macroscopic boundary condition on the surface from no slip to limited slip. We measure the force on the surface and the velocity field in the immediate vicinity on the surface (and thus the wall shear) simultaneously. The latter facilitates a direct assessment of the effective slip length associated with the drag reduction.

Molecular simulations of lubrication and solvation forces.

We report on molecular-dynamics simulations of the drag force experienced by a smooth sphere as it approaches a smooth planar surface to test the predictions of classical hydrodynamic theory. We use a simple repulsive Lennard-Jones-like model to represent the fluid interactions, and calculate the total force on the sphere as a function of its radius, velocity, and distance from the surface. We find that the presence of static solvation forces complicates the testing of hydrodynamic theory which predicts a divergent repulsive lubrication force as the gap vanishes. The solvation force contribution is most prominent at small gaps and small velocities. For a smooth wall its presence can lead to a total force that is oscillating between positive and negative, quite different from the hydrodynamic prediction. To enable an improved test of the lubrication predictions, we propose a different approach that measures the total force for approaching as well as receding spheres. We suggest a simple general analysis that decouples the dynamic and static force contributions on the sphere. The new decoupling method is applicable to simulations and laboratory experiments alike. We illustrate its power by applying it to the molecular-dynamics data.