Depletion forces in bulk and in confined domains: From Asakura–Oosawa to recent statistical physics advances

Foam film stratification, viscosity, and small-angle X-ray scattering of micellar SDS solutions over an extended concentration range (1< c/CMC < 75)

Ultrathin foam films (thickness, h < 100 nm) containing micelles undergo drainage via stratification manifested as coexisting thick-thin flat regions, nanoscopic non-flat topography, and the stepwise decrease in film thickness that yields a characteristic step-size. Most studies characterize the variation in step size and stratification kinetics in micellar foam films in a limited concentration range, c/CMC < 12.5 (c < 100 mM). Likewise, most scattering studies characterize micelle dimensions, intermicellar distance, and volume fraction in bulk aqueous SDS solutions in this limited concentration range. In this contribution, we show drainage via stratification can be observed for concentrations up to c/CMC < 75 (c < 600 mM). Understanding the stratification behavior of freely draining micellar films with sodium dodecyl sulfate (SDS) concentration varying in the range 10 mM ≤ cSDS ≤ 600 mM is essential for molecular engineering, consumer product formulations, and controlling foaming in industrial processes. Here, we visualize and analyze nanoscopic thickness variations and transitions in stratifying foam films using Interferometry Digital Imaging Optical Microscopy (IDIOM) protocols. We compare step size obtained from foam stratification to micelle dimension, micelle volume fraction, and intermicellar distance obtained from small angle X-ray scattering studies. Even though the volume fraction increases and approaches 25% at c = 600 mM, the solution viscosity only increases by a factor of four compared to the solvent, consistent with the findings from both stratification and scattering studies. These comparisons allow us to explore the effect of micelle size, morphology, and intermicellar interactions on supramolecular oscillatory structural disjoining pressure, which influences the stratification behavior of draining foam films containing micelles under confinement.

DLVO surface forces in liquid films and statistical mechanics of colloidal oscillatory structural forces in dispersion stability

This paper focuses on the theory of the dispersion stability considering two models. In the classical DLVO model of surface forces, the interactions between two particles consist of two terms: the London-van der Waals attractive interaction and the electrostatic repulsive interaction in the frame of the Debye-Hückel theory. The solvent, the aqueous solution of the electrolyte, was considered the continuous phase. The film stability criteria are P_γ > Π and dP_γ/dh > 0. Henderson and Lozada-Cassou (HC) applied the statistical mechanics approach to calculate the film free energy to predict the dispersion stability by considering two large hard spheres as colloidal particles immersed in a fluid of dispersed small particles (the solvent). HC applied the radial distribution function g(r) to calculate the free oscillatory structural energy using W(r) = - kT ln g(r). HC's theoretical approach was also applied to the particle collective interactions in the film and explains the stability of film formed from complex fluids (e.g., micellar and colloidal dispersions). The differences between the solvation oscillatory layering forces and colloidal oscillatory structural forces are discussed. The application of the DLVO model to the dispersion stability is critically reviewed. The role of nanobubbles in the dispersion stability is discussed.

Salt Weakens Intermicellar Interactions and Structuring in Bulk Solutions and Foam Films

Drainage via stratification in micellar foam films formulated with ionic surfactants shows dramatic changes on salt addition: both the step size and the number of steps in their stepwise thinning diminish. As the stratification process is governed by supramolecular oscillatory structural forces that arise due to confinement-induced structuring of micelles, it is apparent that salt addition reduces the magnitude, periodicity, and decay length of the oscillatory forces. In this contribution, we characterize the changes in micellar size, shape, and interactions on salt addition in bulk solutions using small-angle X-ray scattering (SAXS) to understand and elucidate the influence of salt on stratification in micellar foam films and, more broadly, on the oscillatory structural forces. Adding salt leads to a significant reduction in long-range correlations between micelles and smaller intermicellar distances. These effects manifest as a weakening of the primary peak of the structure factor, ascertained from SAXS spectra, accompanied by its shift to higher wave vectors. Weakened long-range correlations diminish the magnitude and periodicity of the oscillatory disjoining pressure leading to smaller step sizes, fewer steps, and a rich nanoscopic topography, due to the influence of disjoining pressure on the deformable interfaces. The step sizes in stratifying thin films and intermicellar distances in bulk solutions present incongruous values, implying an imperfect analogy with studies on charged nanoparticles with matched and salt concentration-independent values of measured interparticle distances that equal the periodicity of force-distance curves. We anticipate that our findings are significant for multicomponent soft and biological matter containing self-assembled supramolecular structures wherein screened Coulomb interactions govern the self-assembly, interfacial adsorption, interactions, dynamics, and stability.

Impact of Inert Crowders on Host-Guest Recognition Process

Biological environments typically contain high concentrations (300-400 mg/mL) of different macromolecules at volume fractions as large as 30%-40%. Biomolecular recognition processes, a ubiquitous biological phenomena, occurring in such crowded heterogeneous media would differ significantly compared to the dilute buffer solutions. Here we quantify the potential impact of inert crowders on prototypical host-guest recognition process by explicit-solvent molecular dynamics (MD) simulations in atomic resolution. We demonstrate that the crowders, when smaller in size, would facilitate the binding process of the guest molecule by decreasing the free energy barrier for binding via excluded volume effect and desolvation of the host receptor. However, the extent of crowder-induced stabilization of a host-guest complex is found to be significantly higher when the guest molecule is sterically constricted to approach the host along a centrosymmetric direction, compared to its unrestricted, freely diffusive movement. A kinetic analysis of the recognition process reveals that the origin of a relatively stronger crowder impact during constricted movement of guest molecule lies in the relatively enhanced residence time of the guest inside the host by crowders. Together, our results suggest that the extent of impact of crowding on recognition processes would be contingent upon the presence or absence of constriction on ligand movement.

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.

Biomolecular interactions of ultrasmall metallic nanoparticles and nanoclusters

The use of nanoparticles (NPs) in biomedicine has made a gradual transition from proof-of-concept to clinical applications, with several NP types meeting regulatory approval or undergoing clinical trials. A new type of metallic nanostructures called ultrasmall nanoparticles (usNPs) and nanoclusters (NCs), while retaining essential properties of the larger (classical) NPs, have features common to bioactive proteins. This combination expands the potential use of usNPs and NCs to areas of diagnosis and therapy traditionally reserved for small-molecule medicine. Their distinctive physicochemical properties can lead to unique in vivo behaviors, including improved renal clearance and tumor distribution. Both the beneficial and potentially deleterious outcomes (cytotoxicity, inflammation) can, in principle, be controlled through a judicious choice of the nanocore shape and size, as well as the chemical ligands attached to the surface. At present, the ability to control the behavior of usNPs is limited, partly because advances are still needed in nanoengineering and chemical synthesis to manufacture and characterize ultrasmall nanostructures and partly because our understanding of their interactions in biological environments is incomplete. This review addresses the second limitation. We review experimental and computational methods currently available to understand molecular mechanisms, with particular attention to usNP-protein complexation, and highlight areas where further progress is needed. We discuss approaches that we find most promising to provide relevant molecular-level insight for designing usNPs with specific behaviors and pave the way to translational applications.

Smaller molecules crowd better: Crowder size dependence revealed by single-molecule FRET studies and depletion force modeling analysis

The cell is an extremely crowded environment, which is known to have a profound impact on the thermodynamics, functionality, and conformational stability of biomolecules. Speculations from recent theoretical molecular dynamics studies suggest an intriguing size dependence to such purely entropic crowding effects, whereby small molecular weight crowders under constant enthalpy conditions are more effective than larger crowders on a per volume basis. If experimentally confirmed, this would be profoundly significant, as the cellular cytoplasm is also quite concentrated in smaller molecular weight solutes such as inorganic ions, amino acids, and various metabolites. The challenge is to perform such studies isolating entropic effects under isoenthalpic conditions. In this work, we first present results from single-molecule FRET spectroscopy (smFRET) on the molecular size-dependent crowding stabilization of a simple RNA tertiary motif (the GAAA tetraloop-tetraloop receptor), indeed providing evidence in support of the surprising notion in the crowding literature that "smaller is better." Specifically, systematic smFRET studies as a function of crowder solute size reveal that smaller molecules both significantly increase the RNA tertiary folding rate and, yet, simultaneously decrease the unfolding rate, predicting strongly size-dependent stabilization of RNA tertiary structures under crowded cellular conditions. The size dependence of these effects has been explored via systematic variation of crowder size over a broad range of molecular weights (90-3000 amu). Furthermore, corresponding temperature dependent studies indicate the systematic changes in the folding equilibrium to be predominantly entropic in origin, i.e., consistent with a fundamental picture of entropic molecular crowding without additional enthalpic interactions. Most importantly, all trends in the single-molecule crowding data can be quantitatively recapitulated by a simple analytic depletion force model, whereby excluded volume interactions represent the major thermodynamic driving force toward folding. Our study, thus, not only provides experimental evidence and theoretical support for small molecule crowding but also predicts further enhancement of crowding effects for even smaller molecules on a per volume basis.

Untangling superposed double layer and structural forces across confined nanoparticle suspensions

The description of forces across confined complex fluids still holds many challenges due to the possible overlap of different contributions. Here, an attempt is made to untangle the interaction between charged surfaces across nanoparticle suspensions. Interaction forces are measured using colloidal-probe atomic force microscopy. The experimental force profiles are considered as a superposition of double layer and structural forces. In order to independently describe the decay of the double layer force, the ionic strength of the suspension is determined by electrolytic conductivity measurements. Jellium approximation is used to define the impact of the fluid on screening the surface potential. There, the nanoparticles are considered homogeneously distributed across the fluid and screening is only carried out via the particles counterions and added salt. The structural force follows a damped oscillatory profile due to the layer-wise expulsion of the nanoparticles upon approach of both surfaces. The description of the oscillatory structural force is extended by a depletion layer next to the confining surfaces, with no nanoparticles present. The thickness of the depletion layer is related to the electrostatic repulsion of the charged nanoparticles from the like-charged surfaces. The results show that the total force profile is a superposition of independent force contributions without any mutual effects. Using this rather simple model describes the complete experimentally determined interaction force profiles very well from surface separations of a few hundred nanometres down to the surfaces being almost in contact.

Confinement-induced alternating interactions between inclusions in an active fluid

In a system of colloidal inclusions suspended in an equilibrium bath of smaller particles, the particulate bath engenders effective, short-ranged, primarily attractive interactions between the inclusions, known as depletion interactions, that originate from the steric depletion of bath particles from the immediate vicinity of the inclusions. In a bath of active (self-propelled) particles, the nature of such bath-mediated interactions can qualitatively change from attraction to repulsion, and they become stronger in magnitude and range of action as compared with typical equilibrium depletion interactions, especially as the bath activity (particle self-propulsion) is increased. We study effective interactions mediated by a bath of active Brownian particles between two fixed, impenetrable, and disk-shaped inclusions in a planar (channel) confinement in two dimensions. Confinement is found to strongly influence the effective interaction between the inclusions, specifically by producing alternating interaction profiles with possible attractive and repulsive regions in sufficiently narrow channels. We study the dependence of the ensuing interactions on different system parameters and the orientational (parallel versus perpendicular) configuration of the inclusion pair relative to the channel walls. The confinement effects are largely regulated by the layering of active particles next to the surface boundaries, both of the inclusions and the channel walls that counteract one another in accumulating the active particles in their own proximities. In narrow channels, the combined effects due to the channel walls and the inclusions lead to peculiar structuring of active particles (reminiscent of wavelike interference patterns) within the channel.

Bridging the gap between two different scaling laws for structuring of liquids under geometrical confinement

Structural forces are a phenomena obtained in liquids of one-component (e.g. for organic solvents) and two-components (colloidal dispersions), alike. So far, those two systems were discussed separately, using two different scaling laws. In this review article, an attempt is made to bridge the gap between both scaling laws by defining the scaling limit for two-component systems. Colloidal probe atomic force microscopy (CP-AFM) is used to measure structural forces in suspensions of silica nanoparticles (NPs) of three different sizes. In these two-component systems (solid NPs suspended in water), oscillatory behaviour can be obtained in the force vs. separation profiles. The wavelength λ is larger than the actual particle diameter d and rather depends on the particles' volume fraction ϕ following the inverse cubic root law λ∝ϕ^-13. It is shown that the real particle diameter d can be determined by a gedankenexperiment by extrapolating the fitted wavelength λ from the structural force measurements at a specific particle concentration to a particle volume fraction ϕ of 52% - the packing factor for simple cubic packing - using the well-known inverse cubic root scaling law. This extrapolation can be interpreted as a transition from a two-component system towards a one-component-like problem. In this case, particles are in contact and the wavelength λ is equal to the particle diameter d, λ = d as for one-component systems. The determined diameters d of the different silica nanoparticles agree well with independent measurements using transmission electron microscopy (TEM), validating the used approach. The proposed method can be extended to numerous dispersions of spherical nano-sized objects, for which structural forces can be measured.

Influence of Salt on Supramolecular Oscillatory Structural Forces and Stratification in Micellar Freestanding Films

Freestanding films of soft matter containing micelles, nanoparticles, polyelectrolyte-surfactant complexes, bilayers, and smectic liquid crystals exhibit stratification. Stepwise thinning and coexisting thick-thin regions associated with drainage via stratification are attributed to the confinement-induced structuring and layering of supramolecular structures, which contribute supramolecular oscillatory structural forces. In freestanding micellar films, formed by a solution of an ionic surfactant above its critical micelle concentration, both interfacial adsorption and the micelle size and shape are determined by the concentration of surfactant and of added electrolytes. Although the influence of surfactant concentration on stratification has been investigated before, the influence of added salt, at concentrations typically found in water used on a daily basis, has not been investigated yet. In this contribution, we elucidate how the addition of salt affects stepwise thinning: step size, number of steps, as well as the shape and size of nanoscopic nonflat structures such as mesas in micellar foam films formed with aqueous solutions of anionic surfactant (sodium dodecyl sulfate (SDS)). The nanoscopic thickness variations and transitions are visualized and analyzed using IDIOM (Interferometry Digital Imaging Optical Microscopy) protocols with exquisite spatiotemporal resolution (thickness ∼1 nm, time <1 ms). In contrast to nanoparticle dispersions that show no influence of salt on step size, we find that the addition of salt to micellar freestanding films results in a decrease in step size as well as the number of stepwise transitions, in addition to changes in nucleation and growth of mesas, all driven by the corresponding change in supramolecular oscillatory structural forces.

Effect of Glucose on the Mobility of Membrane-Adhering Liposomes

Enclosed lipid bilayer structures, referred to as liposomes or lipid vesicles, have a wide range of biological functions, such as cellular signaling and membrane trafficking. The efficiency of cellular uptake of liposomes, a key step in many of these functions, is strongly dependent on the contact area between a liposome and a cell membrane, which is governed by the adhesion force w, the membrane bending energy κ, and the osmotic pressure Δp. Herein, we investigate the relationship between these forces and the physicochemical properties of the solvent, namely, the presence of glucose (a nonionic osmolyte). Using fluorescence microscopy, we measure the diffusivity D of small (∼50 nm radius), fluorescently labeled liposomes adhering to a supported lipid bilayer or to the freestanding membrane of a giant (∼10 μm radius) liposome. It is observed that glucose in solution reduces D on the supported membrane, while having negligible effect on D on the freestanding membrane. Using well-known hydrodynamic theory for the diffusivity of membrane inclusions, these observations suggest that glucose enhances the contact area between the small liposomes and the underlying membrane, while not affecting the viscosity of the underlying membrane. In addition, quartz crystal microbalance experiments showed no significant change in the hydrodynamic height of the adsorbed liposomes, upon adding glucose. This observation suggests that instead of osmotic deflation, glucose enhances the contact area via adhesion forces, presumably due to the depletion of the glucose molecules from the intermembrane hydration layer.

Entropic depletion in colloidal suspensions and polymer liquids: role of nanoparticle surface topography

We employ a hybrid Monte Carlo plus integral equation theory approach to study how dense fluids of small nanoparticles or polymer chains mediate entropic depletion interactions between topographically rough particles where all interaction potentials are hard core repulsion. The corrugated particle surfaces are composed of densely packed beads which present variable degrees of controlled topographic roughness and free volume associated with their geometric crevices. This pure entropy problem is characterized by competing ideal translational and (favorable and unfavorable) excess entropic contributions. Surface roughness generically reduces particle depletion aggregation relative to the smooth hard sphere case. However, the competition between ideal and excess packing entropy effects in the bulk, near the particle surface and in the crevices, results in a non-monotonic variation of the particle-monomer packing correlation function as a function of the two dimensionless length scale ratios that quantify the effective surface roughness. As a result, the inter-particle potential of mean force (PMF), second virial coefficient, and spinodal miscibility volume fraction vary non-monotonically with the surface bead to monomer diameter and particle core to surface bead diameter ratios. A miscibility window is predicted corresponding to an optimum degree of surface roughness that completely destroys depletion attraction resulting in a repulsive PMF. Variation of the (dense) matrix packing fraction can enhance or suppress particle miscibility depending upon the amount of surface roughness. Connecting the monomers into polymer chains destabilizes the system via enhanced contact depletion attraction, but the non-monotonic variations with surface roughness metrics persist.

Analysis of the size dependence of macromolecular crowding shows that smaller is better

The aqueous milieu inside cells contains as much as 30-40% dissolved protein and RNA by volume. This large concentration of macromolecules is expected to cause significant deviations from solution ideality. In vivo biochemical reaction rates and equilibria might differ significantly from those measured in the majority of in vitro experiments that are performed at much lower macromolecule concentrations. Consequently crowding, a nonspecific phenomenon believed to arise from the large excluded volume of these macromolecules, has been studied extensively by experimental and theoretical methods. However, the relevant theory has not been applied consistently. When the steric effects of macromolecular crowders and small molecules like water and ions are treated on an equal footing, the effect of the macromolecules is opposite to that commonly believed. Large molecules are less effective at crowding than water and ions. There is also a surprisingly weak dependence on crowder size. Molecules of medium size, ∼5 Å radius, have the same effect as much larger macromolecules like proteins and RNA. These results require a reassessment of observed high-concentration effects and of strategies to mimic in vivo conditions with in vitro experiments.