Computer Modeling of Ionic Micelle Structuring in Thin Films

Foam film stratification studies probe intermicellar interactions

Ultrathin foam films containing supramolecular structures like micelles in bulk and adsorbed surfactant at the liquid-air interface undergo drainage via stratification. At a fixed surfactant concentration, the stepwise decrease in the average film thickness of a stratifying micellar film yields a characteristic step size that also describes the quantized thickness difference between coexisting thick-thin flat regions. Even though many published studies claim that step size equals intermicellar distance obtained using scattering from bulk solutions, we found no reports of a direct comparison between the two length scales. It is well established that step size is inversely proportional to the cubic root of surfactant concentration but cannot be estimated by adding micelle size to Debye length, as the latter is inversely proportional to the square root of surfactant concentration. In this contribution, we contrast the step size obtained from analysis of nanoscopic thickness variations and transitions in stratifying foam films using Interferometry Digital Imaging Optical Microscopy (IDIOM) protocols, that we developed, with the intermicellar distance obtained using small-angle X-ray scattering. We find that stratification driven by the confinement-induced layering of micelles within the liquid-air interfaces of a foam film provides a sensitive probe of non-DLVO (Derjaguin-Landau-Verwey-Overbeek) supramolecular oscillatory structural forces and micellar interactions.

Microfluidic thin film pressure balance for the study of complex thin films

Investigations of free-standing liquid films enjoy an increasing popularity due to their relevance for many fundamental and applied scientific problems. They constitute soap bubbles and foams, serve as membranes for gas transport or as model membranes in biophysics. More generally, they provide a convenient tool for the investigation of numerous fundamental questions related to interface- and confinement-driven effects in soft matter science. Several approaches and devices have been developed in the past to characterise reliably the thinning and stability of such films, which were commonly created from low-viscosity, aqueous solutions/dispersions. With an increasing interest in the investigation of films made from strongly viscoelastic and complex fluids that may also solidify, the development of a new generation of devices is required to manage reliably the constraints imposed by these formulations. We therefore propose here a microfluidic chip design which allows for the reliable creation, control and characterisation of free-standing films of complex fluids. We provide all technical details and we demonstrate the device functioning for a larger range of systems via a selection of illustrative examples, including films of polymer melts and gelling hydrogels.

Experimental evaluation of additional short ranged repulsion in structural oscillation forces

The paper addresses additional short ranged repulsion in structural oscillation forces between silica surfaces across a suspension of silica nanoparticles. Fit and prediction of the structural oscillation forces usually involve an exponentially decreasing harmonic as introduced by Israelachvili [Israelachvili, Intermolecular & surface forces, Academic Press, San Diego, USA, 1985]. Recently we demonstrated, for aqueous suspensions of silica nanoparticles at various concentrations, that this fit equation is insufficient to describe the structural oscillation forces in its whole range [Schön et al., Beilstein J. Nanotechnol., 2018, 9, 1095-1107]. An additional force acting on short separations leads to the fit parameters scattering widely as well as being dependent on each other and the starting point of the fit. An additional repulsive term was introduced to solve these problems. The additional repulsive force has also been observed by others, in ionic liquids and polyelectrolyte solutions at high ionic strength. It was attributed to the diffusive double layer forces. The rise of the additional repulsion with increasing particle concentration seems to conflict with this interpretation. In this work, colloidal probe atomic force microscopy is used in aqueous suspensions of silica nanoparticles to investigate other contributing factors such as the increasing hydrodynamic drag in the normal direction to the confining surface with increasing particle concentration. A kinetic component to the structural oscillation forces is observed. Furthermore, sodium chloride is used to adjust the ionic strength of two different concentrated silica nanoparticle suspensions. For these systems the additional decay length is compared to the Debye length in the range from low to high ionic strength. A master curve of the additional decay length over Debye length at different ionic strengths, approach speed and particle concentration is produced. It affirms the link between the two and the connection between the additional force and the diffusive double layer forces. The increasing trend for the additional repulsion with increasing particle concentration reveals a synergistic effect of diffusive double layer forces and structural oscillation forces at low to medium ionic strength, which cannot be observed at high ionic strength.

A simple extension of the commonly used fitting equation for oscillatory structural forces in case of silica nanoparticle suspensions

Background: The ordering of molecules or particles in the vicinity of a confining surface leads to the formation of an interfacial region with layers of decreasing order normal to the confining surfaces. The overlap of two interfacial regions gives rise to the well-known phenomenon of oscillatory structural forces. These forces are commonly fitted with an exponentially decaying harmonic oscillation as introduced by Israelachvili (Israelachvili, J. N. Intermolecular & surface forces; Academic Press: San Diego, CA, USA, 1985). From the fit three important parameters are obtained, namely wavelength, amplitude and decay length, which are related to the period, the strength and the correlation length of the oscillatory structural forces, respectively. The paper addresses structural forces between a silica microsphere and a silicon wafer across silica nanoparticle suspensions measured with a colloidal probe AFM. Using the simple fitting procedure with three parameters often leads to underestimation of actually measured forces. The deviation of the fit from the experimental data is especially pronounced at small distances of the confining surfaces and at high concentrations of silica nanoparticles. As a consequence, the parameters of the common fit equation vary with the starting point of the fit. Although the wavelength is least affected and seems to be quite robust against the starting point of the fit, all three parameters show distinct oscillations, with a period similar to the wavelength of the oscillatory structural forces themselves. The oscillations of amplitude and decay length, which are of much higher magnitude, show a phase shift of 180° implying not only a dependence on the starting point of the fit but also on each other. The range affected by this systematic deviation of the fit parameters is much larger than the optically perceived mismatch between fit and experimental data, giving a false impression of robustness of the fit. Results: By introducing an additional term of exponentially decaying nature the data can be fitted accurately down to very small separations and even for high silica nanoparticle concentrations (10 wt %). Furthermore wavelength, amplitude and decay length become independent of the starting point of the fit and in case of the latter two of each other. The larger forces at small separations indicate a more pronounced ordering behavior of the particles in the final two layers before the wall. This behavior is described by the proposed extension of the common fit equation. Conclusion: Thus, the extension increases the accessible data range in terms of separation and concentration and strongly increases the accuracy for all fitting parameters in the system studied here.

Ionic liquids-mediated interactions between nanorods

Surface forces mediated by room-temperature ionic liquids (RTILs) play an essential role in diverse applications including self-assembly, lubrication, and electrochemical energy storage. Therefore, their fundamental understanding is critical. Using molecular simulations, we study the interactions between two nanorods immersed in model RTILs at rod-rod separations where both structural and double layer forces are important. The interaction force between neutral rods oscillates as the two rods approach each other, similar to the classical structural forces. Such oscillatory force originates from the density oscillation of RTILs near each rod and is affected by the packing constraints imposed by the neighboring rods. The oscillation period and decay length of the oscillatory force are mainly dictated by the ion density distribution near isolated nanorods. When charges are introduced on the rods, the interaction force remains short-range and oscillatory, similar to the interactions between planar walls mediated by some protic RTILs reported earlier. Nevertheless, introducing net charges to the rods greatly changes the rod-rod interactions, e.g., by delaying the appearance of the first force trough and increasing the oscillation period and decay length of the interaction force. The oscillation period and decay length of the oscillatory force and free energy are commensurate with those of the space charge density near an isolated, charged rod. The free energy of rod-rod interactions reaches local minima (maxima) at rod-rod separations when the space charges near the two rods interfere constructively (destructively). The insight on the short-range interactions between nanorods in RTILs helps guide the design of novel materials, e.g., ionic composites based on rigid-rod polyanions and RTILs.

Film and membrane-model thermodynamics of free thin liquid films

In spite of over 7 decades of effort, the thermodynamics of thin free liquid films (as in emulsions and foams) lacks clarity. Following a brief review of the meaning and measurement of thin-film forces (i.e., conjoining/disjoining pressures), we offer a consistent analysis of thin-film thermodynamics. By carefully defining film reversible work, two distinct thermodynamic formalisms emerge: a film model with two zero-volume membranes each of film tension γ(f) and a membrane model with a single zero-volume membrane of membrane tension 2γ(m). In both models, detailed thermodynamic analysis gives rise to thin-film Gibbs adsorption equations that allow calculation of film and membrane tensions from measurements of disjoining-pressure isotherms. A modified Young-Laplace equation arises in the film model to calculate film-thickness profiles from the film center to the surrounding bulk meniscus. No corresponding relation exists in the membrane model. Illustrative calculations of disjoining-pressure isotherms for water are presented using square-gradient theory. We report considerable deviations from Hamaker theory for films less than about 3 nm in thickness. Such thin films are considerably more attractive than in classical Hamaker theory. Available molecular simulations reinforce this finding.

Exponential approximation for one-component Yukawa plasma

A theory based on the exponential approximation of the liquid-state theory is applied to study properties of several models of one-component Yukawa plasma characterized by different values of the screening parameter z. The results of the new theory are compared to the results of a conventional theory, which is based on the first-order mean spherical approximation, and to the results of a Monte Carlo simulation. The new theory shows improvements in the predictions for the thermodynamic and structural properties of Yukawa plasmas with high and intermediate values of the screening parameter, z, and coupling parameter, Γ. For low values of z and Γ, the new theory is comparable in accuracy to the conventional theory, which in turn agrees well with the results of the Monte Carlo simulation.

Stabilization of weakly charged microparticles using highly charged nanoparticles

An experimental study was performed to understand the ability of highly charged nanoparticles to stabilize a dispersion of weakly charged microspheres. The experiments involved adding either anionic (sulfate) or cationic (amidine) latex nanoparticles to dispersions of micrometer-sized silica particles near the silica isoelectric point (IEP). Although both types of nanoparticles increased the zeta potential of the silica microspheres above the value at which dispersions containing only silica spheres remained stable, only with the amidine nanoparticles was stability obtained. Adsorption tests with flat silica slides showed that the amidine nanoparticles deposited in much greater numbers onto the silica, producing multilayer coverage with adsorbed particle densities that were roughly three times that obtained with the sulfate nanoparticles. A model calculating the DLVO interaction between the silica spheres in which the adsorbed nanoparticle layers were treated as a continuous film with dielectric properties between those of polystyrene and water predicted stability for both systems. It is hypothesized that the relatively low adsorption of the sulfate nanoparticles (fractional surface coverages ≤ 25%) led to patches of bare silica on the microspheres that could align during interaction due to Brownian motion. These results indicate that highly charged nanoparticles can be effective stabilizers provided the level of adsorption is sufficiently high. It was also found that the zeta potential alone is not a sufficient parameter for predicting stability of these binary systems.

Determination of the aggregation number and charge of ionic surfactant micelles from the stepwise thinning of foam films

The stepwise thinning (stratification) of liquid films, which contain micelles of an ionic surfactant, depends on the micelle aggregation number, N(agg), and charge, Z. Vice versa, from the height of the step and the final film thickness one can determine N(agg), Z, and the degree of micelle ionization. The determination of N(agg) is based on the experimental fact that the step height is equal to the inverse cubic root of the micelle concentration. In addition, Z is determined from the final thickness of the film, which depends on the concentration of counterions dissociated from the micelles in the bulk. The method is applied to micellar solutions of six surfactants, both anionic and cationic: sodium dodecylsulfate (SDS), cetyl trimethylammonium bromide (CTAB), cetylpyridinium chloride (CPC), sodium laurylethersulfates with 1 and 3 ethylene oxide groups (SLES-1EO and SLES-3EO), and potassium myristate. The method has the following advantages: (i) N(agg) and Z are determined simultaneously, from the same set of experimental data; (ii) N(agg) and Z are determined for each given surfactant concentration (i.e. their concentration dependence is obtained), and (iii) N(agg) and Z can be determined even for turbid solutions, like those of carboxylates, where the micelles coexist with acid-soap crystallites, so that the application of other methods is difficult. The results indicate that the micelles of greater aggregation number have a lower degree of ionization, which can be explained with the effect of counterion binding. The proposed method is applicable to the concentration range, in which the films stratify and the micelles are spherical. This is satisfied for numerous systems representing scientific and practical interest.

Hydrodynamic force on a microparticle approaching a wall in a nanoparticle dispersion: observation of a separation-dependent effective viscosity

Colloid probe atomic force microscopy was used to measure the hydrodynamic force exerted on a 30-μm-diameter silica particle being moved toward or away from a silica plate in aqueous dispersions of 22-nm-diameter silica nanoparticles (6 or 8 vol %). Upon comparing the measured force to predictions made using the well-known expression of Cox and Brenner (Cox, R. G.; Brenner, H. Chem. Eng. Sci.1967, 22, 1753-1777) assuming a constant viscosity equal to that of the bulk dispersion, the measured drag force was found to become significantly less than that predicted at smaller particle-plate separation distances (e.g., <500 nm). A recent theoretical paper by Bhattacharya and Blawzdziewicz (Bhattacharya, S.; Blawzdziewicz, J. J. Chem. Phys.2008, 128, 214704) predicted that in a solution of dispersed nanoparticles the effective viscosity characterizing the hydrodynamic force on the particle should vary from that of the solvent at contact to that of the bulk dispersion at large separations. By adjusting the viscosity in the Cox and Brenner expression to make the predicted hydrodynamic force match that measured (i.e., the effective viscosity), a curve showing these exact characteristics was obtained. The effective viscosity profile was not a function of particle speed, and changes in the effective viscosity extended to separation distances of as large as 2 μm (nearly 100 times the hard diameter of the nanoparticles). These results suggest that in the range of typical colloidal forces (on the order of 100 nm), the dynamics of particle motion in such systems are determined by the viscosity of the solvent and not that of the bulk dispersion.

The metastable states of foam films containing electrically charged micelles or particles: experiment and quantitative interpretation

The stepwise thinning (stratification) of liquid films containing electrically charged colloidal particles (in our case - surfactant micelles) is investigated. Most of the results are applicable also to films from nanoparticle suspensions. The aim is to achieve agreement between theory and experiment, and to better understand the physical reasons for this phenomenon. To test different theoretical approaches, we obtained experimental data for free foam films from micellar solutions of three ionic surfactants. The theoretical problem is reduced to the interpretation of the experimental concentration dependencies of the step height and of the final film thickness. The surface charges of films and micelles are calculated by means of the charge-regulation model, with a counterion-binding (Stern) constant determined from the fit of surface tension isotherms. The applicability of three models was tested: the Poisson-Boltzmann (PB) model; the jellium-approximation (JA), and the cell model (CM). The best agreement theory/experiment was obtained with the JA model without using any adjustable parameters. Two theoretical approaches are considered. First, in the energy approach the step height is identified with the effective diameter of the charged micelles, which represents an integral of the electrostatic-repulsion energy calculated by the JA model. Second, in the osmotic approach the step height is equal to the inverse cubic root of micelle number density in the bulk of solution. Both approaches are in good agreement with the experiment if the suspension of charged particles (micelles) represents a jellium, i.e. if the particle concentration is uniform despite the field of the electric double layers. The results lead to a convenient method for determining the aggregation number of ionic surfactant micelles from the experimental heights of the steps.

Wetting and spreading of nanofluids on solid surfaces driven by the structural disjoining pressure: statics analysis and experiments

The wetting and spreading of nanofluids composed of liquid suspensions of nanoparticles have significant technological applications. Recent studies have revealed that, compared to the spreading of base liquids without nanoparticles, the spreading of wetting nanofluids on solid surfaces is enhanced by the structural disjoining pressure. Here, we present our experimental observations and the results of the statics analysis based on the augmented Laplace equation (which takes into account the contribution of the structural disjoining pressure) on the effects of the nanoparticle concentration, nanoparticle size, contact angle, and drop size (i.e., the capillary and hydrostatic pressure); we examined the effects on the displacement of the drop-meniscus profile and spontaneous spreading of a nanofluid as a film on a solid surface. Our analyses indicate that a suitable combination of the nanoparticle concentration, nanoparticle size, contact angle, and capillary pressure can result not only in the displacement of the three-phase contact line but also in the spontaneous spreading of the nanofluid as a film on a solid surface. We show here, for the first time, that the complete wetting and spontaneous spreading of the nanofluid as a film driven by the structural disjoining pressure gradient (arising due to the nanoparticle ordering in the confined wedge film) is possible by decreasing the nanoparticle size and the interfacial tension, even at a nonzero equilibrium contact angle. Experiments were conducted on the spreading of a nanofluid composed of 5, 10, 12.5, and 20 vol % silica suspensions of 20 nm (geometric diameter) particles. A drop of canola oil was placed underneath the glass surface surrounded by the nanofluid, and the spreading of the nanofluid was monitored using an advanced optical technique. The effect of an electrolyte, such as sodium chloride, on the nanofluid spreading phenomena was also explored. On the basis of the experimental results, we can conclude that a nanofluid with an effective particle size (including the electrical double layer) of about 40 nm, a low equilibrium contact angle (<3°), and a high effective volume concentration (>30 vol %) is desirable for the dynamic spreading of a nanofluid system with an interfacial tension of 0.5 mN/m. Our experimental observations also validate the major predications of our theoretical analysis.

Oscillatory structural forces due to nonionic surfactant micelles: data by colloidal-probe AFM vs theory

Micellar solutions of nonionic surfactants Brij 35 and Tween 20 are confined between two surfaces in a colloidal-probe atomic-force microscope (CP-AFM). The experimentally detected oscillatory forces due to the layer-by-layer expulsion of the micelles agree very well with the theoretical predictions for hard-sphere fluids. While the experiment gives parts of the stable branches of the force curve, the theoretical model allows reconstruction of the full oscillatory curve. Therewith, the strength and range of the ordering could be determined. The resulting aggregation number from the fits of the force curves for Brij 35 is close to 70 and exhibits a slight tendency to increase with the surfactant concentration. The last layer of micelles cannot be pressed out. The measured force-vs-distance curve has nonequilibrium portions, which represent "jumps" from one to another branch of the respective equilibrium oscillatory curve. In the case of Brij 35, at concentrations <150 mM spherical micelles are present and the oscillation period is close to the micelle diameter, slightly decreasing with the rise of concentration. For elongated micelles (at concentration 200 mM), no harmonic oscillations are observed anymore; instead, the period increases with the decrease of film thickness. In the case of Tween 20, the force oscillations are almost suppressed, which implies that the micelles of this surfactant are labile and are demolished by the hydrodynamic shear stresses due to the colloidal-probe motion. The comparison of the results for the two surfactants demonstrates that in some cases the micelles can be destroyed by the CP-AFM, but in other cases they can be stable and behave as rigid particles. This behavior correlates with the characteristic times of the slow micellar relaxation process for these surfactants.

The colloid structural forces as a tool for particle characterization and control of dispersion stability

Knowing the size and interactions of colloid particles, one can predict the stepwise thickness transitions and the contact angles of particle-containing liquid films. Here, we consider the inverse problem, viz. how to determine the particle properties by measurements with liquid films. We carried out experiments with films formed from aqueous solutions of two nonionic surfactants, Brij 35 and Tween 20, which contain spherical micelles of diameters in the range 7-9 nm. From the measured contact angles, we determined the micelle aggregation number and volume fraction. In addition, from the measured disjoining-pressure isotherms we determined the micelle diameter. In other words, the liquid-film measurements give information about the micelles, which is analogous to that obtainable by dynamic and static light scattering. Furthermore, we investigate the predictions of different quantitative criteria for stability-instability transitions, having in mind that the oscillatory forces exhibit both maxima, which play the role of barriers to coagulation, and minima that could produce flocculation or coalescence in colloidal dispersions (emulsions, foams, suspensions). The interplay of the oscillatory force with the van der Waals surface force is taken into account. Two different kinetic criteria are considered, which give similar and physically reasonable results about the stability-instability transitions. Diagrams are constructed, which show the values of the micelle volume fraction, for which the oscillatory barriers can prevent the particles from coming into close contact, or for which a strong flocculation in the depletion minimum or a weak flocculation in the first oscillatory minimum could be observed.

Sedimentation in nano-colloidal dispersions: effects of collective interactions and particle charge

This is a review paper summarizing the progress of the development of colloidal sedimentation models for monodisperse, bidisperse, and polydisperse nanoparticle dispersions. This topic is of considerable interest because the sedimentation behavior of nanoparticles plays an important role in many practical systems, such as industrial coatings, optical products, ceramics, paints, dyes, and cosmetics. The limitations of various models are discussed. Multi-particle systems are highlighted, with a focus on the collective thermodynamic interactions resulting in the attractive depletion and repulsive structural forces. The effects of the particle concentration, particle charge, polydispersity in size, and electrolyte concentration on the sedimentation process are briefly summarized. Our contributions to this subject are reviewed.

Simple correlation-corrected theory of systems described by screened coulomb interactions

We present a simple correlation-corrected density functional treatment of dispersions containing macroions, where these are assumed to interact via screened Coulomb potentials, as given by Debye-Hückel theory. A straightforward mean-field description even fails to qualitatively capture important correlation effects displayed by such systems. However, if an effective, correlation-corrected potential is adopted at short range, then the predictions are in qualitative and semiquantitative agreement with simulated results. The correlation corrections are evaluated in a manner that is completely analogous to those recently presented in correlation-corrected Poisson-Boltzmann theory (Forsman, J. J. Phys. Chem. B 2004, 108, 9236). The accuracy of the theory is evaluated by comparison with simulation data on systems displaying correlation-generated packing effects and stratification forces.

A disjoining pressure study of foam films stabilized by mixtures of nonionic and ionic surfactants

Studying the disjoining pressure Pi as a function of the film thickness h (Pi-h curves) of foam films stabilized by ionic and nonionic surfactants, one finds that the surface charge density q0 of films stabilized by ionic surfactants increases with increasing surfactant concentration, while the opposite holds true for nonionic surfactants. Thus, it should be possible to tune the surface charge density with mixtures of nonionic and ionic surfactants. To address this question, we studied foam films stabilized by aqueous solutions of surfactant mixtures. The mixtures consisted of the nonionic beta-dodecylmaltoside (beta-C12G2) and the cationic dodecyl trimethylammonium bromide (C12TAB) with mixing ratios of beta-C12G2/C12TAB = 1:0, 50:1, 1:1, 1:50, 0:1. The addition of small amounts of C12TAB to beta-C12G2 first neutralizes the negative surface charge of the beta-C12G2 films and finally leads to a charge reversal from negatively to positively charged surfaces. On the other hand, by adding small amounts of beta-C12G2 to C12TAB, one observes the formation of stable CBFs which was also observed for the pure C12TAB. However, in contrast to the pure C12TAB, the resulting Pi-h curves for the mixtures cannot be described with the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory; the slope of the curves is too steep, and it barely changes with changing electrolyte concentration. A possible explanation for this observation will be given and discussed.

Simulation study of charged nanoparticles confined in a rectangular tube with discrete wall charges

The development of novel nanomaterials has been a subject of intense interest in recent years. An interesting structure among these materials is the so-called "pea pods" (i.e., nanoparticles confined in nanotubes). To facilitate the development and commercialization of these materials, it is important that we have an in-depth understanding of their behavior. The study of confined charged particles is particularly challenging because of the long-ranged nature of electrostatic interaction, and both interparticle and particle-confinement interactions are likely to play a role in determining the system behavior. The primary objective of this study is to develop a better understanding of the behavior of charged nanoparticles in a charged tubular confinement using Monte Carlo simulation, with particular focus on the effect of electrostatic interactions on the structure of the particles. Simulation results have shown that (i) the structuring of confined particles is associated with the asymmetry of the long-ranged interaction and (ii) factors such as confinement geometry and particle charge and size asymmetry can be manipulated to produce different particle structures. The present study represents the first step in an attempt to gain further insight into the behavior of confined nanosystems, with the ultimate objective of exploiting these characteristics, particularly the interactions between the confined particles and their external environment, in developing novel nanomaterials.

Structuring of macroions confined between like-charged surfaces

We investigate the structuring of charged spherical nanoparticles and micelles (i.e., "macroions") between two surfaces as a function of bulk macroion concentration. Structuring is deduced from measured force profiles between a silica particle and a silica plate in the presence of an aqueous macroion (Ludox silica nanoparticle or sodium dodecyl sulfate micelle) solution, obtained with an atomic force microscope. We observe oscillatory force profiles that decay with separation. We find that the wavelength of the force profiles scales with the bulk number density as rho(-)(1/3), rather than with the effective macroion size. Only at very high silica nanoparticle concentration (above 10 vol %) in a low ionic strength solution does the wavelength become smaller than that predicted by the simple rho(-)(1/3) scaling; however, the original scaling is recovered upon the addition of a small amount of electrolyte. A comparison between the measured wavelength and the predicted spacing between the macroions in the bulk shows that the two variables differ in both magnitude and bulk density scaling. This finding suggests that confined macroions are more ordered than those in the bulk and the nature of this ordering is maintained over a relatively wide range of bulk concentration.

Computer simulation of macroion layering in a wedge film

The layering of macroions confined to a wedge slit formed by two uncharged hard walls is studied using a canonical Monte Carlo method combined with a simulation cell that contains both wedge-shaped slit and bath regions. The macroion solution is modeled within a one-component fluid approach that in an effective way incorporates the double layer repulsion due to simple electrolyte ions as well as the discrete nature of an aqueous solvent. The layer formation under a wedge confinement is analyzed by carrying out separate simulation runs for a set of consecutive wedge segments designed to represent a single wedge slit. As the wedge thickness progressively increases, the sequence of regions along the wedge film with distinct features of macroion layering has been established. This sequence comprises (i) a wedge region of the thickness smaller than the macroion diameter that is free of macroions; (ii) a region with a one-dimensional macroion chain along the wedge corner at a wedge thickness of a one macroion diameter; (iii) a region comprising a low-ordered macroion monolayer that extends until the wedge thickness slightly above two macroion diameters; (iv) a region comprising a pair of well-defined two-dimensional configurations of macroions segregated on each of the wedge walls; and (v) a free-of-macroions wedge region between two surface monolayers that now originates from an electrostatic repulsion imposed by the surface macroions, which is followed by (vi) a well-defined macroion monolayer film between two surface monolayers, a less defined bilayer film, a three-layer film, and so on up to the bulk solution. Once formed, the macroion surface monolayers persist for all remaining wedge thicknesses up to the bulk, forming in such a way effective charged wedge boundaries. Such a formation of the macroion surface monolayers on the uncharged confining walls is related to the haloing mechanism for regulating the stability in colloidal suspensions [Tohver et al. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 8951] and is discussed as well. Finally, the estimated boundary of the free of macroion region between surface monolayers correlates well with the location of the boundary of the so-called "vacuum" phase that has been observed experimentally in an aqueous suspension of charged polystyrene spheres bounded by electrostatically repulsive glass walls [Pieransky et al. Phys. Rev. Lett. 1983, 50, 900].

A simulation study of electrostatic effects on mixed ionic micelles confined between two parallel charged plates

Confined colloidal systems have been the subject of extensive theoretical and experimental research, and the recent observation of long-range like-charge attraction in such systems has only highlighted their peculiar behavior. On the other hand, surfactant solutions are often used in small confined space, yet their behavior in confinement has received relatively little attention. A distinct feature of confined self-assembling systems is that the aggregates are capable of adjusting their composition, size, and shape in response to their external environment, which may lead to very different phase characteristics compared to bulk solutions. The primary objective of this study is to explore the effects of varying micelle composition on the structural behavior of a confined mixed ionic micellar solution. Mesoscale canonical Monte Carlo simulations were used to probe the structure of the confined solution, while a molecular-thermodynamic model was used to systematically account for the change in micelle size as we varied its composition. Significant micelle ordering was found under certain conditions, which implies that large deviations from the minimum-energy micelle configuration may not be entropically favorable. Accumulation of micelles along the midplane was observed when the confining walls are weakly charged, suggesting that micelle shape transformation should be considered in more detail. On the other hand, with high wall charge density, apparent attraction was found between like-charged micelles and wall. These findings point to the need for a more quantitative theoretical treatment in describing surfactant self-assembly in confined geometries.