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.

Evaporation effect on two-dimensional wicking in porous media.

We analyze the effect of evaporation on expanding capillary flow for losses normal to the plane of a two-dimensional porous medium using the potential flow theory formulation of the Lucas-Washburn method. Evaporation induces a finite steady state liquid flux on capillary flows into fan-shaped domains which is significantly greater than the flux into media of constant cross section. We introduce the evaporation-capillary number, a new dimensionless quantity, which governs the frontal motion when multiplied by the scaled time. This governing product divides the wicking behavior into simple regimes of capillary dominated flow and evaporative steady state, as well as the intermediate regime of evaporation influenced capillary driven motion. We also show flow dimensionality and evaporation reduce the propagation rate of the wet front relative to the Lucas-Washburn law.

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.

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.

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.

Microfluidic synthesis of monodisperse nanoporous oxide particles and control of hierarchical pore structure.

Particles with hierarchical porosity can be formed by templating silica microparticles with a specially designed surfactant micelle/oil nanoemulsion mixture. The nanoemulsion oil droplet and micellar dimensions determine the pore size distribution: one set of pores with diameters of tens of nanometers coexisting with a second subset of pores with diameters of single nanometers. Further practical utility of these nanoporous particles requires precise tailoring of the hierarchical pore structure. In this synthesis study, the particle nanostructure is tuned by adjusting the oil, water, and surfactant mixture composition for the controlled design of nanoemulsion-templated features. We also demonstrate control of the size distribution and surface area of the smaller micelle-templated pores as a consequence of altering the hydrophobic chain length of the molecular surfactant template. Moreover, a microfluidic system is designed to process the low interfacial system for fabrication of monodisperse porous particles. The ability to direct the assembly of template nanoemulsion and micelle structures creates new opportunities to engineer hierarchically porous particles for utility as electrocatalysts for fuel cells, chromatography separations, drug delivery vehicles, and other applications.

The targeted delivery of multicomponent cargos to cancer cells by nanoporous particle-supported lipid bilayers.

Encapsulation of drugs within nanocarriers that selectively target malignant cells promises to mitigate side effects of conventional chemotherapy and to enable delivery of the unique drug combinations needed for personalized medicine. To realize this potential, however, targeted nanocarriers must simultaneously overcome multiple challenges, including specificity, stability and a high capacity for disparate cargos. Here we report porous nanoparticle-supported lipid bilayers (protocells) that synergistically combine properties of liposomes and nanoporous particles. Protocells modified with a targeting peptide that binds to human hepatocellular carcinoma exhibit a 10,000-fold greater affinity for human hepatocellular carcinoma than for hepatocytes, endothelial cells or immune cells. Furthermore, protocells can be loaded with combinations of therapeutic (drugs, small interfering RNA and toxins) and diagnostic (quantum dots) agents and modified to promote endosomal escape and nuclear accumulation of selected cargos. The enormous capacity of the high-surface-area nanoporous core combined with the enhanced targeting efficacy enabled by the fluid supported lipid bilayer enable a single protocell loaded with a drug cocktail to kill a drug-resistant human hepatocellular carcinoma cell, representing a 10(6)-fold improvement over comparable liposomes.

Convective assembly of 2D lattices of virus-like particles visualized by in-situ grazing-incidence small-angle X-ray scattering.

The rapid assembly of icosohedral virus-like particles (VLPs) into highly ordered (domain size > 600 nm), oriented 2D superlattices directly onto a solid substrate using convective coating is demonstrated. In-situ grazing-incidence small-angle X-ray scattering (GISAXS) is used to follow the self-assembly process in real time to characterize the mechanism of superlattice formation, with the ultimate goal of tailoring film deposition conditions to optimize long-range order. From water, GISAXS data are consistent with a transport-limited assembly process where convective flow directs assembly of VLPs into a lattice oriented with respect to the water drying line. Addition of a nonvolatile solvent (glycerol) modified this assembly pathway, resulting in non-oriented superlattices with improved long-range order. Modification of electrostatic conditions (solution ionic strength, substrate charge) also alters assembly behavior; however, a comparison of in-situ assembly data between VLPs derived from the bacteriophages MS2 and Qß show that this assembly process is not fully described by a simple Derjaguin-Landau-Verwey-Overbeek model alone.

The impact of multivalent counterions, Al3+, on the surface adsorption and self-assembly of the anionic surfactant alkyloxyethylene sulfate and anionic/nonionic surfactant mixtures.

The impact of multivalent counterions, Al(3+), on the surface adsorption and self-assembly of the anionic surfactant sodium dodecyl dioxyethylene sulfate, SLES, and the anionic/nonionic surfactant mixtures of SLES and monododecyl dodecaethylene glycol, C(12)E(12), has been investigated using neutron reflectivity, NR, and small angle neutron scattering, SANS. The addition of relatively low concentrations of Al(3+) counterions induces a transition from a monolayer to well-defined surface bilayer, trilayer, and multilayer structures in the adsorption of SLES at the air-water interface. The addition of the nonionic cosurfactant, C(12)E(12), partially inhibits the evolution in the surface structure from monolayer to multilayer interfacial structures. This surface phase behavior is strongly dependent upon the surfactant concentration, solution composition, and concentration of Al(3+) counterions. In solution, the addition of relatively low concentrations of Al(3+) ions promotes significant micellar growth in SLES and SLES/C(12)E(12) mixtures. At the higher counterion concentrations, there is a transition to lamellar structures and ultimately precipitation. The presence of the C(12)E(12) nonionic cosurfactant partially suppresses the aggregate growth. The surface and solution behaviors can be explained in terms of the strong binding of the Al(3+) ions to the SLES headgroup to form surfactant-ion complexes (trimers). These results provide direct evidence of the role of the nonionic cosurfactant in manipulating both the surface and solution behavior. The larger EO(12) headgroup of the C(12)E(12) provides a steric hindrance which disrupts and ultimately prevents the formation of the surfactant-ion complexes. The results provide an important insight into how multivalent counterions can be used to manipulate both solution self-assembly and surface properties.

Brownian dynamics of emulsion film formation and droplet coalescence.

We analyze the evolution in thickness and radius of the film formed during the collision of two deformable emulsion Brownian droplets. These variables exhibit random fluctuations due to thermal disturbances from the continuous liquid phase. As a result, the system probes a random trajectory in the configurational space until it reaches a critical film thickness, at which point the droplets coalesce. Therefore, the film is modeled as a disk with thicknesses and radi that can fluctuate. Our analysis is based on a Langevin-Brownian dynamics approach, which accounts for the thermodynamic and hydrodynamic interactions in the lubrication approximation. We examine the effect of parameters such as droplet size, interfacial mobility, and electrolyte concentration on the coalescence of small Brownian droplets. The results suggest that the coalescence times depend on a complex interplay between the thermodynamic and hydrodynamic interactions.

Imbibition in porous membranes of complex shape: quasi-stationary flow in thin rectangular segments.

The sustained liquid flow of a typical lateral flow assay can be mimicked by two-dimensional shaped, thin porous membranes, specifically rectangular membranes appended to circular sectors. In designing these fan-shaped devices, we have been aided by analytical equations and finite-element simulations. We show both mathematically and experimentally how a continuous increase in unwetted pore volume causes a deviation from traditional imbibition, and leads to quasi-stationary flow in the rectangular element. These results are both theoretically and practically important because they indicate how medical diagnostic test strips may be fabricated without incorporating an absorbent pad.

Microparticles with bimodal nanoporosity derived by microemulsion templating.

Oil, water, and surfactant liquid mixtures exhibit very complex phase behavior. Depending on the conditions, such mixtures give rise to highly organized structures. A proper selection of the type and concentration of surfactants determines the structuring at the nanoscale level. In this Article, we show that hierarchically bimodal porous structures can be obtained by templating silica microparticles with a specially designed surfactant micelle/microemulsion mixture. Tuning the phase state by adjusting the surfactant composition and concentration allows for the controlled design of a system where microemulsion droplets coexist with smaller surfactant micellar structures. The microemulsion droplet and micellar dimensions determine the two types of pore sizes. We also demonstrate the fabrication of carbon and carbon/platinum replicas of the silica microspheres using a "lost-wax" approach. Such particles have great potential for the design of electrocatalysts for fuel cells, chromatography separations, and other applications.

Preface to special topic: papers from the 82nd american chemical society colloid and surface science symposium, raleigh, north Carolina, 2008.

This Special Topic section of Biomicrofluidics contains original contributions that were presented at the 82nd Colloid and Surface Science Symposium, which took place on 15-18 June 2008 at North Carolina State University. The Symposium covered a wide range of topics that are relevant to the fundamentals of fluidics and their application to biological systems.

Effect of wall-molecule interactions on electrokinetic transport of charged molecules in nanofluidic channels during FET flow control.

The interactions between charged molecules and channel surfaces are expected to significantly influence the electrokinetic transport of molecules and their separations in nanochannels. This study reports the effect of wall-molecule interactions on flow control of negatively charged Alexa 488 and positively charged Rhodamine B dye molecules in an array of nanochannels (100 nm wx 500 nm dx 14 mm l) embedded in fluidic field effect transistors (FETs). For FET flow control, a third electrical potential, known as a gate bias, is applied to the channel walls to manipulate their zeta-potential. Electroosmotic flow of charged dye molecules is accelerated or reversed according to the polarity and magnitude of the gate bias. During FET flow control, we monitor how the electrostatic interaction between charged dye molecules and channel walls affects the apparent velocity of molecules, using laser-scanning confocal fluorescence microscopy. We observe that the changes in flow speed and direction of negatively charged Alexa 488 is much more pronounced than that of positively charged Rhodamine B in response to the gate bias that causes either repulsive or attractive electrostatic interactions. This observation is supported by calculations of concentration-weighted velocity profiles of the two dye molecules during FET flow control. The velocity profile of negatively charged Alexa 488 is much more pronounced at the center of each nanochannel than near its walls since Alexa 488 molecules are repelled from negatively charged channel walls. This pronounced center velocity further responds to the gate bias, increasing the average velocity by as much as 23% when -30 V is applied to the gate (zeta-potential = -80.6 mV). In contrast, the velocity profile of positively charged Rhodamine B is dispersed over the entire channel width due to dye-wall attraction and adsorption. Our experimental observations and calculations support the hypothesis that valence-charge-dependent electrostatic interaction and its manipulation by the gate bias would enhance molecular separations of differentially charged molecules in nanofluidic FETs.

Electric field control and analyte transport in Si/SiO2 fluidic nanochannels.

This article presents an analysis of the electric field distribution and current transport in fluidic nanochannels fabricated by etching of a silicon chip. The channels were overcoated by a SiO2 layer. The analysis accounts for the current leaks across the SiO2 layer into the channel walls. Suitable voltage biasing of the Si substrate allows eliminating of the leaks or using them to modify the potential distribution of the fluid. Shaping the potential in the fluid can be utilized for solute focusing and separations in fluidic nanochannels.

Droplet-based microfluidics for emulsion and solvent evaporation synthesis of monodisperse mesoporous silica microspheres.

A novel method for the fabrication of monodisperse mesoporous silica particles is suggested. It is based on the formation of well-defined equally sized emulsion droplets using a microfluidic approach. The droplets contain the silica precursor/surfactant solution and are suspended in hexadecane as the continuous oil phase. The solvent is then expelled from the droplets, leading to concentration and micellization of the surfactant. At the same time, the silica solidifies around the surfactant structures, forming equally sized mesoporous particles. The procedure can be tuned to produce well-separated particles or alternatively particles that are linked together. The latter allows us to create 2D or 3D structures with hierarchical porosity.

Monitoring FET flow control and wall adsorption of charged fluorescent dye molecules in nanochannels integrated into a multiple internal reflection infrared waveguide.

Using Si as the substrate, we have fabricated multiple internal reflection infrared waveguides embedded with a parallel array of nanofluidic channels. The channel width is maintained substantially below the mid-infrared wavelength to minimize infrared scattering from the channel structure and to ensure total internal reflection at the channel bottom. A Pyrex slide is anodically bonded to the top of the waveguide to seal the nanochannels, while simultaneously enabling optical access in the visible range from the top. The Si channel bottom and sidewalls are thermally oxidized to provide an electrically insulating barrier, and the Si substrate surrounding the insulating SiO(2) layer is selectively doped to function as a gate. For fluidic field effect transistor (FET) control, a DC potential is applied to the gate to manipulate the surface charge on SiO(2) channel bottom and sidewalls and therefore their zeta-potential. Depending on the polarity and magnitude, the gate potential can accelerate, decelerate, or reverse the flow. Here, we demonstrate that this nanofluidic infrared waveguide can be used to monitor the FET flow control of charged, fluorescent dye molecules during electroosmosis by multiple internal reflection Fourier transform infrared spectroscopy. Laser scanning confocal fluorescence microscopy is simultaneously used to provide a comparison and verification of the IR analysis. Using the infrared technique, we probe the vibrational modes of dye molecules, as well as those of the solvent. The observed infrared absorbance accounts for the amount of dye molecules advancing or retracting in the nanochannels, as well as adsorbing to and desorbing from the channel bottom and sidewalls.