Multicomponent adhesive hard sphere models and short-ranged attractive interactions in colloidal or micellar solutions

Modulating Interfacial Properties in Pseudoternary Microemulsions via Urea Addition: Impact of Cosurfactant on the Reverse Micellar Structure and Interactions

We have studied the structural and interfacial properties of CTAB/isooctane/alcohol/aqueous urea reverse micelles (RMs) for the first time using time-resolved fluorescence and small-angle X-ray scattering techniques. The chain length of alcohol, used as cosurfactant, has been varied to design three microemulsion systems: CTAB/1-butanol, CTAB/1-hexanol, and CTAB/1-octanol/isooctane/water, at a fixed water loading ratio, w0 = 12. Time-resolved fluorescence anisotropy studies indicate that urea induces micellar aggregation in CTAB/1-butanol and CTAB/1-hexanol RMs but breaks down RM aggregates in CTAB/1-octanol RMs. Urea addition slows down solvation dynamics inside RMs at higher urea concentrations, evident from the longer lifetimes of solvent correlation decay. The underlying changes in microemulsion structure and intermicellar interactions are studied using small-angle X-ray scattering studies. The significant intermicellar interactions were modeled using the sticky hard sphere (SHS) for the CTAB/1-butanol and CTAB/1-hexanol RMs and by using the Macroion model for the CTAB/1-octanol RMs. The two different structural factors highlight the dominance of attractive and repulsive forces, respectively. Although there is no change in RM shape, the combination of urea addition and chain length variation in cosurfactants significantly alters the size and interface in these pseudoternary RMs.

Close encounters of the sticky kind: Brownian motion at absorbing boundaries

Encounter-based models of diffusion provide a probabilistic framework for analyzing the effects of a partially absorbing reactive surface, in which the probability of absorption depends upon the amount of surface-particle contact time. In this paper we develop a class of encounter-based models that deal with absorption at sticky boundaries. Sticky boundaries occur in a diverse range of applications, including cell biology, colloidal physics, finance, and human crowd dynamics. They also naturally arise in active matter, where confined active particles tend to spontaneously accumulate at boundaries even in the absence of any particle-particle interactions. We begin by constructing a one-dimensional encounter-based model of sticky Brownian motion (BM), which is based on the zero-range limit of nonsticky BM with a short-range attractive potential well near the origin. In this limit, the boundary-contact time is given by the amount of time (occupation time) that the particle spends at the origin. We calculate the joint probability density or propagator for the particle position and the occupation time, and then identify an absorption event as the first time that the occupation time crosses a randomly generated threshold. We illustrate the theory by considering diffusion in a finite interval with a partially absorbing sticky boundary at one end. We show how various quantities, such as the mean first passage time (MFPT) for single-particle absorption and the relaxation to steady state at the multiparticle level, depend on moments of the random threshold distribution. Finally, we determine how sticky BM can be obtained by taking a particular diffusion limit of a sticky run-and-tumble particle (RTP).

Baseline Comparisons of Complementary Sampling Methods for Assembly Driven by Short-Ranged Pair Potentials toward Fast and Flexible Hybridization

This work measures baseline sampling characteristics that highlight fundamental differences between sampling methods for assembly driven by short-ranged pair potentials. Such granular comparison is essential for fast, flexible, and accurate hybridization of complementary methods. Besides sampling speed, efficiency, and accuracy of uniform grid coverage, other sampling characteristics measured are (i) accuracy of covering narrow low energy regions that have low effective dimension (ii) ability to localize sampling to specific basins, and (iii) flexibility in sampling distributions. As a proof of concept, we compare a recently developed geometric methodology EASAL (Efficient Atlasing and Search of Assembly Landscapes) and the traditional Monte Carlo (MC) method for sampling the energy landscape of two assembling trans-membrane helices, driven by short-range pair potentials. By measuring the above-mentioned sampling characteristics, we demonstrate that EASAL provides localized and accurate coverage of crucial regions of the energy landscape of low effective dimension, under flexible sampling distributions, with much fewer samples and computational resources than MC sampling. EASAL's empirically validated theoretical guarantees permit credible extrapolation of these measurements and comparisons to arbitrary number and size of assembling units. Promising avenues for hybridizing the complementary advantages of the two methods are discussed.

Atlasing of Assembly Landscapes using Distance Geometry and Graph Rigidity

This Article describes a novel geometric methodology for analyzing free energy and kinetics of assembly driven by short-range pair-potentials in an implicit solvent and provides a proof-of-concept illustration of its unique capabilities. An atlas is a labeled partition of the assembly landscape into a roadmap of maximal, contiguous, nearly-equipotential-energy conformational regions or macrostates, together with their neighborhood relationships. The new methodology decouples the roadmap generation from sampling and produces: (1) a queryable atlas of local potential energy minima, their basin structure, energy barriers, and neighboring basins; (2) paths between a specified pair of basins, each path being a sequence of conformational regions or macrostates below a desired energy threshold; and (3) approximations of relative path lengths, basin volumes (configurational entropy), and path probabilities. Results demonstrating the core algorithm's capabilities and high computational efficiency have been generated by a resource-light, curated open source software implementation EASAL (Efficient Atlasing and Search of Assembly Landscapes, ACM Trans. Math. Softw. 2018 44, 1-48. 10.1145/3204472; see software, Efficient Atlasing and Search of Assembly Landscapes, 2016. https://bitbucket.org/geoplexity/easal; video, Video Illustrating the opensource software EASAL, 2016. https://cise.ufl.edu/~sitharam/EASALvideo.mpeg; and user guide, EASAL software user guide, 2016. https://bitbucket.org/geoplexity/easal/src/master/CompleteUserGuide.pdf). Running on a laptop with Intel(R) Core(TM) i7-7700@3.60 GHz CPU with 16GB of RAM, EASAL atlases several hundred thousand conformational regions or macrostates in minutes using a single compute core. Subsequent path and basin computations each take seconds. A parallelized EASAL version running on the same laptop with 4 cores gives a 3× speedup for atlas generation. The core algorithm's correctness, time complexity, and efficiency-accuracy trade-offs are formally guaranteed using modern distance geometry, geometric constraint systems and combinatorial rigidity. The methodology further links the shape of the input assembling units to a type of intuitive and queryable bar-code of the output atlas, which in turn determine stable assembled structures and kinetics. This succinct input-output relationship facilitates reverse analysis and control toward design. A novel feature that is crucial to both the high sampling efficiency and decoupling of roadmap generation from sampling is a recently developed theory of convex Cayley (distance-based) custom parametrizations specific to assembly, as opposed to folding. Representing microstates with macrostate-specific Cayley parameters, to generate microstate samples, avoids gradient-descent search used by all prevailing methods. Further, these parametrizations convexify conformational regions or macrostates. This ratchets up sampling efficiency, significantly reducing number of repeated and discarded samples. These features of the new stand-alone methodology can also be used to complement the strengths of prevailing methodologies including Molecular Dynamics, Monte Carlo, and Fast Fourier Transform based methods.

Hydrotrope-Driven Self-Assembly in CTAB/ n-Hexanol/Water/Heptane Reverse Micellar System

Self-organization of nanoparticles into one-dimensional (1D) nanochains leads to new unpredicted physiochemical properties, which are further exploited to develop photonic or electronic devices. Thus, the controlled fabrication of 1D nanochains requires nanotemplate, which acts as building blocks for the self-assembly of nanoparticles. To address this issue, we designed a hydrotrope (sodium salicylate)-based CTAB/ n-hexanol/water/heptane reverse micellar system. Hydrotrope, herein, modulates electrostatic interactions between reverse micellar droplets and paves the way for the formation of self-assembled structures. Small-angle X-ray scattering studies were performed on the CTAB/heptane reverse micellar system by varying hydrotrope concentrations and water-to-surfactant ratios (W _x)_. The aqueous content of the reverse micellar pool is determined from the W _x value, where W _x = [H₂O]/[CTAB] and [CTAB] = 0.05 M. SAXS studies were performed for CTAB/heptane reverse micellar systems at three different W _x values, that is, 6, 12, and 16 and represented by W₆, W₁₂, and W₁₆, respectively. All SAXS profiles were modeled with a spherical form factor and a Baxter sticky hard sphere structure factor. The interaction between droplets was predicted in terms of stickiness parameter. The effect of W _x on the formation of self-assembled structures and forces governing the assembly has been discussed in detail. For the W₆ system, the electrostatic repulsion between reverse micellar droplets decreases, resulting in the formation of the 1D chain-like assembly of nanodroplets. In the case of the W₁₂ system, the dual feature of the hydrotrope has been observed, it increases the size of the reverse micellar system and reduces electrostatic repulsion between droplets because of which the formation of chain-like assemblies cannot be determined with accuracy. For the W₁₆ system, the decrease in micellar size with the increase in the hydrotrope concentration has been observed. Thus, our reverse micellar templates may provide a comprehensive method for the fabrication of high aspect ratio 1D nanochains of a variety of materials and harnessing their collective properties for magnetic, catalytic, and opto-electronic applications.

Statistical-thermodynamic model for light scattering from eye lens protein mixtures

We model light-scattering cross sections of concentrated aqueous mixtures of the bovine eye lens proteins γB- and α-crystallin by adapting a statistical-thermodynamic model of mixtures of spheres with short-range attractions. The model reproduces measured static light scattering cross sections, or Rayleigh ratios, of γB-α mixtures from dilute concentrations where light scattering intensity depends on molecular weights and virial coefficients, to realistically high concentration protein mixtures like those of the lens. The model relates γB-γB and γB-α attraction strengths and the γB-α size ratio to the free energy curvatures that set light scattering efficiency in tandem with protein refractive index increments. The model includes (i) hard-sphere α-α interactions, which create short-range order and transparency at high protein concentrations, (ii) short-range attractive plus hard-core γ-γ interactions, which produce intense light scattering and liquid-liquid phase separation in aqueous γ-crystallin solutions, and (iii) short-range attractive plus hard-core γ-α interactions, which strongly influence highly non-additive light scattering and phase separation in concentrated γ-α mixtures. The model reveals a new lens transparency mechanism, that prominent equilibrium composition fluctuations can be perpendicular to the refractive index gradient. The model reproduces the concave-up dependence of the Rayleigh ratio on α/γ composition at high concentrations, its concave-down nature at intermediate concentrations, non-monotonic dependence of light scattering on γ-α attraction strength, and more intricate, temperature-dependent features. We analytically compute the mixed virial series for light scattering efficiency through third order for the sticky-sphere mixture, and find that the full model represents the available light scattering data at concentrations several times those where the second and third mixed virial contributions fail. The model indicates that increased γ-γ attraction can raise γ-α mixture light scattering far more than it does for solutions of γ-crystallin alone, and can produce marked turbidity tens of degrees celsius above liquid-liquid separation.

Polymer-Graft-Mediated Interactions between Colloidal Spheres

Aqueous dispersions of fluorinated colloidal spheres bearing grafted poly(ethylene glycol) (PEG) are studied as a function of salt and particle concentration with the aim of improving the understanding of interactions among polymer-grafted particles. These dispersions can sustain large concentrations of salt, but crystals nucleate in dilute dispersions when a sufficient Na2CO3 concentration is reached, which is attributed to the presence of attractions between particles. On further increasing the Na2CO3 concentration, the solvent is rapidly cleared of particles. Small-angle X-ray scattering and cryogenic transmission electron microscopy are employed in order to quantify the attractions. The former is used to extract a second virial coefficient, and the latter shows that the PEG-graft contracts as a function of increasing salt concentration. The contraction not only leads to a reduction in excluded volume but also is accompanied by attractions of moderate magnitude. In contrast, dispersion of the particles in ethanol, in which bulk PEG solutions crystallize, lead to fractal structures caused by strong attractions.

Effects of water content and chain length of n-alkane on the interaction enthalpy between the droplets in water/sodium bis(2-ethylhexyl)-sulfosuccinate/n-alkane microemulsions

The concentration-dependent enthalpies of mixing for water/sodium bis(2-ethylhexyl)-sulfosuccinate (AOT)/n-alkane microemulsions with different water contents ω0 and chain lengths n of n-alkane were determined by isothermal titration microcalorimetry (ITC) and flow-mixing microcalorimetry at 298.15 K and used to calculate the interaction enthalpies (-ΔH(C)) between the droplets. It was found that -ΔH(C) increased with ω0, and changed from negative to positive at about ω0 = 10. The investigation of the dependence of -ΔH(C) on n revealed that the values of -ΔH(C) were negative and had a minimum for ω0 = 5; while they were positive and had a maximum for ω0 = 15. These phenomena were discussed based on the competition of the overlapping contribution of the surfactant tails between two neighbouring droplets and the penetration contribution of the solvent molecules into the surfactant tails. These results indicated the important role of entropy in the stability of the microemulsion systems.

Volumetric properties of water/AOT/isooctane microemulsions

The densities of AOT/isooctane micelles and water/AOT/isooctane microemulsions with the molar ratios R of water to AOT being 2, 8, 10, 12, 16, 18, 20, 25, 30, and 40 were measured at 303.15 K. The apparent specific volumes of AOT and the quasi-component water/AOT at various concentrations were calculated and used to estimate the volumetric properties of AOT and water in the droplets and in the continuous oil phase, to discuss the interaction between the droplets, and to determine the critical micelle concentration and the critical microemulsion concentrations. A thermodynamic model was proposed to analysis the stability boundary of the microemulsion droplets, which confirms the maximum value of R being about 65 for the stable AOT/water/isooctane microemulsion droplets.

Molecular dynamics simulation of water/BHDC cationic reverse micelles. structural characterization, dynamical properties, and influence of solvent on intermicellar interactions

We report results obtained from molecular dynamics (MD) experiments of benzylhexadecyldimethylammonium chloride (BHDC) cationic reverse micelles (RMs). In particular we analyzed equilibrium and dynamical characteristics of water/BHDC RMs in pure benzene, at two different water/BHDC ratios (W0 = 5 and W0 = 10). The RMs appear as elliptical aggregates with eccentricities close to ∼0.9. Analysis of the different spatial correlations reveals three different spatial domains in the RMs: a water inner pool, the surfactant interface, and the external solvent. The calculated accessible surface areas for the aqueous inner cores suggest a strong penetration of solvent molecules within the micellar interface domains. Comparison between the density profiles of both RMs shows an increment of the broadness in the distributions of all species at the interface, along with an increasing overlap between the tail segments of the surfactant and benzene molecules as one considers larger micelles. For the dynamical side, the rotational characteristic time scale for the confined water was found to be 1 order of magnitude larger than that of the bulk water. A similar effect was also observed for hydrogen bond dynamics. Both retardation effects diminish with the size of the aggregate. To the estimate the influence of the external solvent on the intermicellar interactions, free energy profiles for the coalescence process between RMs of similar size in pure benzene and in a n-heptane/benzene mixture were also investigated. The results indicate that the association process is facilitated by the presence of n-heptane in the external nonpolar phase. Comparison with previous theoretical and experimental results is also carried out.

Interacting hard rods on a lattice: distribution of microstates and density functionals

We derive exact density functionals for systems of hard rods with first-neighbor interactions of arbitrary shape but limited range on a one-dimensional lattice. The size of all rods is the same integer unit of the lattice constant. The derivation, constructed from conditional probabilities in a Markov chain approach, yields the exact joint probability distribution for the positions of the rods as a functional of their density profile. For contact interaction ("sticky core model") between rods, we give a lattice fundamental measure form of the density functional and present explicit results for contact correlators, entropy, free energy, and chemical potential. Our treatment includes inhomogeneous couplings and external potentials.

Monte Carlo simulation of the nonadditive restricted primitive model of ionic fluids: phase diagram and clustering

We report an accurate Monte Carlo calculation of the phase diagram and clustering properties of the restricted primitive model with nonadditive hard-sphere diameters. At high density the positively nonadditive fluid shows more clustering than in the additive model and the negatively nonadditive fluid shows less clustering than in the additive model; at low density the reverse scenario appears. A negative nonadditivity tends to favor the formation of neutrally charged clusters starting from the dipole. A positive nonadditivity favors the pairing of like ions at high density. The critical point of the gas-liquid phase transition moves at higher temperatures and higher densities for a negative nonadditivity and at lower temperatures and lower densities for a positive nonadditivity. The law of corresponding states does not seem to hold strictly. Our results can be used to interpret recent experimental works on room temperature ionic liquids.

A geometrical approach to computing free-energy landscapes from short-ranged potentials

Particles interacting with short-ranged potentials have attracted increasing interest, partly for their ability to model mesoscale systems such as colloids interacting via DNA or depletion. We consider the free-energy landscape of such systems as the range of the potential goes to zero. In this limit, the landscape is entirely defined by geometrical manifolds, plus a single control parameter. These manifolds are fundamental objects that do not depend on the details of the interaction potential and provide the starting point from which any quantity characterizing the system--equilibrium or nonequilibrium--can be computed for arbitrary potentials. To consider dynamical quantities we compute the asymptotic limit of the Fokker-Planck equation and show that it becomes restricted to the low-dimensional manifolds connected by "sticky" boundary conditions. To illustrate our theory, we compute the low-dimensional manifolds for n ≤ 8 identical particles, providing a complete description of the lowest-energy parts of the landscape including floppy modes with up to 2 internal degrees of freedom. The results can be directly tested on colloidal clusters. This limit is a unique approach for understanding energy landscapes, and our hope is that it can also provide insight into finite-range potentials.

Structure of colloidosomes with tunable particle density: simulation versus experiment

Colloidosomes are created in the laboratory from a Pickering emulsion of water droplets in oil. The colloidosomes have approximately the same diameter and by choosing (hairy) particles of different diameters it is possible to control the particle density on the droplets. The experiment is performed at room temperature. The radial distribution function of the assembly of (primary) particles on the water droplet is measured in the laboratory and in a computer experiment of a fluid model of particles with pairwise interactions on the surface of a sphere.

Effects of polydispersity and anisotropy in colloidal and protein solutions: an integral equation approach

Application of integral equation theory to complex fluids is reviewed, with particular emphasis to the effects of polydispersity and anisotropy on their structural and thermodynamic properties. Both analytical and numerical solutions of integral equations are discussed within the context of a set of minimal potential models that have been widely used in the literature. While other popular theoretical tools, such as numerical simulations and density functional theory, are superior for quantitative and accurate predictions, we argue that integral equation theory still provides, as in simple fluids, an invaluable technique that is able to capture the main essential features of a complex system, at a much lower computational cost. In addition, it can provide a detailed description of the angular dependence in arbitrary frame, unlike numerical simulations where this information is frequently hampered by insufficient statistics. Applications to colloidal mixtures, globular proteins and patchy colloids are discussed, within a unified framework.

Multidensity integral-equation theory for short diblock hard-sphere-sticky-hard-sphere chains

The multidensity Ornstein-Zernike integral equation theory is applied to study a simple model of hard sphere/sticky hard sphere diblock chains. The multidensity integral equation formalism has been successfully used to model the equilibrium structure and thermodynamic properties of homonuclear chains and shorter dimer fluids; to our knowledge it has not been applied to model diblock chains. In this work, a diblock chain fluids is represented by an m-component equal molar mixture of hard spheres with species 1,2,...,mh and sticky hard spheres with species mh+1,mh+2,...,m. Each spherical particle has two attractive sites A and B except species 1 and m, which have only one site per particle. In the limit of complete association, this mixture yields a system of monodisperse diblock chains. A general solution of this model is obtained in the Percus-Yevick, Polymer Percus-Yevick and ideal chain approximations. Both structural and thermodynamic properties of this model are investigated. From this study, a microphase separation is predicted for relatively short diblock symmetric and asymmetric chains. This microphase separation is enhanced at lower temperature and higher density. When chain length increases, the phase transition changes from a microphase level to a macrophase level. The size of microdomain structure is found to be dependent on total chain length, relative ratio of block lengths, temperature, and density.

Fluids of spherical molecules with dipolarlike nonuniform adhesion: an analytically solvable anisotropic model

We consider an anisotropic version of Baxter's model of "sticky hard spheres," where a nonuniform adhesion is implemented by adding, to an isotropic surface attraction, an appropriate "dipolar sticky" correction (positive or negative, depending on the mutual orientation of the molecules). The resulting nonuniform adhesion varies continuously, in such a way that in each molecule one hemisphere is "stickier" than the other. We derive a complete analytic solution by extending a formalism [M. S. Wertheim, J. Chem. Phys. 55, 4281 (1971)] devised for dipolar hard spheres. Unlike Wertheim's solution, which refers to the "mean spherical approximation," we employ a Percus-Yevick closure with orientational linearization, which is expected to be more reliable. We obtain analytic expressions for the orientation-dependent pair correlation function g(1,2) . Only one equation for a parameter K has to be solved numerically. We also provide very accurate expressions which reproduce K as well as some parameters, Lambda1 and Lambda2, of the required Baxter factor correlation functions with a relative error smaller than 1%. We give a physical interpretation of the effects of the anisotropic adhesion on the g(1,2) . The model could be useful for understanding structural ordering in complex fluids within a unified picture.

Third-order thermodynamic perturbation theory for effective potentials that model complex fluids

We have performed Monte Carlo simulations to obtain the thermodynamic properties of fluids with two kinds of hard-core plus attractive-tail or oscillatory potentials. One of them is the square-well potential with small well width. The other is a model potential with oscillatory and decaying tail. Both model potentials are suitable for modeling the effective potential arising in complex fluids and fluid mixtures with extremely-large-size asymmetry, as is the case of the solvent-induced depletion interactions in colloidal dispersions. For the former potential, the compressibility factor, the excess energy, the constant-volume excess heat capacity, and the chemical potential have been obtained. For the second model potential only the first two of these quantities have been obtained. The simulations cover the whole density range for the fluid phase and several temperatures. These simulation data have been used to test the performance of a third-order thermodynamic perturbation theory (TPT) recently developed by one of us [S. Zhou, Phys. Rev. E 74, 031119 (2006)] as compared with the well-known second-order TPT based on the macroscopic compressibility approximation due to Barker and Henderson. It is found that the first of these theories provides much better accuracy than the second one for all thermodynamic properties analyzed for the two effective potential models.