Simulation of the adhesive-hard-sphere model

The Effects of Electric Fields on Protein Phase Behavior and Protein Crystallization Kinetics

We experimentally studied the effects of an externally applied electric field on protein crystallization and liquid-liquid phase separation (LLPS) and its crystallization kinetics. For a surprisingly weak alternating current (AC) electric field, crystallization was found to occur in a wider region of the phase diagram, while nucleation induction times were reduced, and crystal growth rates were enhanced. LLPS on the contrary was suppressed, which diminishes the tendency for a two-step crystallization scenario. The effect of the electric field is ascribed to a change in the protein-protein interaction potential.

Temperature-induced migration of electro-neutral interacting colloidal particles

Migration of colloidal particles induced by temperature gradients is commonly referred to as thermodiffusion, thermal diffusion, or the (Ludwig-)Soret effect. The thermophoretic force experienced by a colloidal particle that drives thermodiffusion consists of two distinct contributions: a contribution resulting from internal degrees of freedom of single colloidal particles, and a contribution due to the interactions between the colloids. We present an irreversible thermodynamics based theory for the latter collective contribution to the thermophoretic force. The present theory leads to a novel "thermophoretic interaction force" (for uncharged colloids), which has not been identified in earlier approaches. In addition, an N-particle Smoluchowski equation including temperature gradients is proposed, which complies with the irreversible thermodynamics approach. A comparison with experiments on colloids with a temperature dependent attractive interaction potential over a large concentration and temperature range is presented. The comparison shows that the novel thermophoretic interaction force is essential to describe data on the Soret coefficient and the thermodiffusion coefficient.

Breaking the size constraint for nano cages using annular patchy particles

Engineering structures like nanocages, shells, and containers, by self-assembly of colloids is a challenging problem. One of the main challenges is to define the shape of the individual subunits to control the radius of the closed shell structures. In this work, we have proposed a simple model for the subunit, which comprises a spheroidal or spherical hardcore decorated with an annular patch. The self-assembly of these building blocks leads to the formation of monodispersed spherical cages (close shells) or containers (curved clusters). For a spheroid with a given bonding range, the curvature of the shell is analytically related to only the patch angle of the building blocks and independent of the shape of the subunits. This model with only one control parameter can be used to engineer cages with the desired radius, which also have been verified using thermodynamic calculations. In the phase diagram of the system, 4 phases are identified which includes gas, closed shell, partially closed (containers) shell and percolated structures. When the diameters of the spherical cages formed are small, we observe an icosahedral symmetry similar to virus capsids. We also observed that the kinetics of the cage formation is very similar to the nucleation and growth kinetics of viruses and is the key factor in determining the yield of closed shells.

Modeling Interfacial Interaction between Gas Molecules and Semiconductor Metal Oxides: A New View Angle on Gas Sensing

With the development of internet of things and artificial intelligence electronics, metal oxide semiconductor (MOS)-based sensing materials have attracted increasing attention from both fundamental research and practical applications. MOS materials possess intrinsic physicochemical properties, tunable compositions, and electronic structure, and are particularly suitable for integration and miniaturization in developing chemiresistive gas sensors. During sensing processes, the dynamic gas-solid interface interactions play crucial roles in improving sensors' performance, and most studies emphasize the gas-MOS chemical reactions. Herein, from a new view angle focusing more on physical gas-solid interactions during gas sensing, basic theory overview and latest progress for the dynamic process of gas molecules including adsorption, desorption, and diffusion, are systematically summarized and elucidated. The unique electronic sensing mechanisms are also discussed from various aspects including molecular interaction models, gas diffusion mechanism, and interfacial reaction behaviors, where structure-activity relationship and diffusion behavior are overviewed in detail. Especially, the surface adsorption-desorption dynamics are discussed and evaluated, and their potential effects on sensing performance are elucidated from the gas-solid interfacial regulation perspective. Finally, the prospect for further research directions in improving gas dynamic processes in MOS gas sensors is discussed, aiming to supplement the approaches for the development of high-performance MOS gas sensors.

Comparative Study on the Models of Thermoreversible Gelation

A critical survey on the various theoretical models of thermoreversible gelation, such as the droplet model of condensation, associated-particle model, site–bond percolation model, and adhesive hard sphere model, is presented, with a focus on the nature of the phase transition predicted by them. On the basis of the classical tree statistics of gelation, combined with a thermodynamic theory of associating polymer solutions, it is shown that, within the mean-field description, the thermoreversible gelation of polyfunctional molecules is a third-order phase transition analogous to the Bose–Einstein condensation of an ideal Bose gas. It is condensation without surface tension. The osmotic compressibility is continuous, but its derivative with respect to the concentration of the functional molecule reveals a discontinuity at the sol–gel transition point. The width of the discontinuity is directly related to the amplitude of the divergent term in the weight-average molecular weight of the cross-linked three-dimensional polymers. The solution remains homogeneous in the position space, but separates into two phases in the momentum space; particles with finite translational momentum (sol) and a network with zero translational momentum (gel) coexist in a spatially homogeneous state. Experimental methods used to detect the singularity at the sol–gel transition point are suggested.

The generalized continuous multiple step (GCMS) potential: model systems and benchmarks

The generalized continuous multiple step (GCMS) potential is presented in this work. Its flexible form allows forrepulsiveand/orattractivecontributions to be encoded through adjustable energy and length scales. The GCMS interaction provides a continuous representation of square-well, square-shoulder potentials and their variants for implementation in computer simulations. A continuous and differentiable energy representation is required to derive forces in conventional simulation algorithms. Molecular dynamics simulations are of particular interest when considering the dynamic properties of a system. The GCMS potential can mimic other interactions with a judicious choice of parameters due to the versatile sigmoid form. In this study, our benchmarks for the GCMS representation include triangular, Yukawa, Franzese, and Lennard-Jones potentials. Comparisons made with published data on volumetric phase diagrams, liquid structure, and diffusivity from model systems are in excellent agreement.

Quasiequilibrium multistate cellular automata

In our effort to tackle the problem of letting nontrivial interactions, thermodynamic equilibrium, and full synchronicity coexist, and in the hope of reviving interest in cellular automata as promising tools for the quantitative, large-scale investigation of multiparticle systems, we built a fully synchronous cellular automaton rule for the simulation of occupancy-based lattice systems with multistate cells and neighboring interactions. The core of this rule, which constitutes an actual synchronous sampling scheme, is a negotiation stage; it produces cell occupancy distributions in very good agreement with their sequential Monte Carlo counterparts, and it satisfies a cellwise detailed balance principle thanks to the use of "mixed" intermediate states that allow for the computation of locally averaged acceptance probabilities. We took a square lattice (but the rule itself is not bound by dimensionality) as a basis for comparison with sequential Monte Carlo for showing that this synchronous rule leads to quasiequilibrium; the fulfillment of cellwise detailed balance is shown through results obtained for a small one-dimensional system, where the transition matrix could be computed exactly.

Simulating sticky particles: A Monte Carlo method to sample a stratification

Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their equilibrium distribution, and there are several methods to sample probability distributions subject to fixed constraints. We introduce a Monte Carlo method to handle the case when constraints can break and form. More generally, the method samples a probability distribution on a stratification: a collection of manifolds of different dimensions, where the lower-dimensional manifolds lie on the boundaries of the higher-dimensional manifolds. We show several applications of the method in polymer physics, self-assembly of colloids, and volume calculation in high dimensions.

Dynamic cluster formation determines viscosity and diffusion in dense protein solutions

We develop a detailed description of protein translational and rotational diffusion in concentrated solution on the basis of all-atom molecular dynamics simulations in explicit solvent. Our systems contain up to 540 fully flexible proteins with 3.6 million atoms. In concentrated protein solutions (100 mg/mL and higher), the proteins ubiquitin and lysozyme, as well as the protein domains third IgG-binding domain of protein G and villin headpiece, diffuse not as isolated particles, but as members of transient clusters between which they constantly exchange. A dynamic cluster model nearly quantitatively explains the increase in viscosity and the decrease in protein diffusivity with protein volume fraction, which both exceed the predictions from widely used colloid models. The Stokes-Einstein relations for translational and rotational diffusion remain valid, but the effective hydrodynamic radius grows linearly with protein volume fraction. This increase follows the observed increase in cluster size and explains the more dramatic slowdown of protein rotation compared with translation. Baxter's sticky-sphere model of colloidal suspensions captures the concentration dependence of cluster size, viscosity, and rotational and translational diffusion. The consistency between simulations and experiments for a diverse set of soluble globular proteins indicates that the cluster model applies broadly to concentrated protein solutions, with equilibrium dissociation constants for nonspecific protein-protein binding in the Kd ≈ 10-mM regime.

Scaling laws for the mechanics of loose and cohesive granular materials based on Baxter's sticky hard spheres

We have conducted discrete element simulations (pfc3d) of very loose, cohesive, granular assemblies with initial configurations which are drawn from Baxter's sticky hard sphere (SHS) ensemble. The SHS model is employed as a promising auxiliary means to independently control the coordination number z_{c} of cohesive contacts and particle volume fraction ϕ of the initial states. We focus on discerning the role of z_{c} and ϕ for the elastic modulus, failure strength, and the plastic consolidation line under quasistatic, uniaxial compression. We find scaling behavior of the modulus and the strength, which both scale with the cohesive contact density ν_{c}=z_{c}ϕ of the initial state according to a power law. In contrast, the behavior of the plastic consolidation curve is shown to be independent of the initial conditions. Our results show the primary control of the initial contact density on the mechanics of cohesive granular materials for small deformations, which can be conveniently, but not exclusively explored within the SHS-based assembling procedure.

Lattice engineering through nanoparticle-DNA frameworks

Advances in self-assembly over the past decade have demonstrated that nano- and microscale particles can be organized into a large diversity of ordered three-dimensional (3D) lattices. However, the ability to generate different desired lattice types from the same set of particles remains challenging. Here, we show that nanoparticles can be assembled into crystalline and open 3D frameworks by connecting them through designed DNA-based polyhedral frames. The geometrical shapes of the frames, combined with the DNA-assisted binding properties of their vertices, facilitate the well-defined topological connections between particles in accordance with frame geometry. With this strategy, different crystallographic lattices using the same particles can be assembled by introduction of the corresponding DNA polyhedral frames. This approach should facilitate the rational assembly of nanoscale lattices through the design of the unit cell.

Self-assembly of trimer colloids: effect of shape and interaction range

Trimers with one attractive bead and two repulsive beads, similar to recently synthesized trimer patchy colloids, were simulated with flat-histogram Monte Carlo methods to obtain the stable self-assembled structures for different shapes and interaction potentials. Extended corresponding states principle was successfully applied to self-assembling systems in order to approximately collapse the results for models with the same shape, but different interaction range. This helps us directly compare simulation results with previous experiment, and good agreement was found between the two. In addition, a variety of self-assembled structures were observed by varying the trimer geometry, including spherical clusters, elongated clusters, monolayers, and spherical shells. In conclusion, our results help to compare simulations and experiments, via extended corresponding states, and we predict the formation of self-assembled structures for trimer shapes that have not been experimentally synthesized.

Gelation of large hard particles with short-range attraction induced by bridging of small soft microgels

In this study, mixed suspensions of large hard polystyrene microspheres and small soft poly(N-isopropylacrylamide) microgels are used as model systems to investigate the static and viscoelastic properties of suspensions which go through liquid to gel transitions. The microgels cause short-range attraction between microspheres through the bridging and depletion mechanism whose strength can be tuned by the microgel concentration. Rheological measurements are performed on suspensions with the volume fraction (Φ) of microspheres ranging from 0.02 to 0.15, and the transitions from liquid-like to solid-like behaviors triggered by the concentration of microgels are carefully identified. Two gel lines due to bridging attraction under unsaturated conditions are obtained. Ultra-small angle neutron scattering is used to probe the thermodynamic properties of suspensions approaching the liquid-solid transition boundaries. Baxter's sticky hard-sphere model is used to extract the effective inter-microsphere interaction introduced by the small soft microgels. It is found that the strength of attraction (characterized by a single stickiness parameter τ) on two gel lines formed by bridging is very close to the theoretical value for the spinodal line in the τ-Φ phase diagram predicted by Baxter's model. This indicates that the nature of the gel state may have the same thermodynamic origins, independent of the detailed mechanism of the short-range attraction. The relationship between the rheological criterion for the liquid-solid transition and the thermodynamic criterion for the equilibrium-nonequilibrium transition is also discussed.

Gel transition in adhesive hard-sphere colloidal dispersions: the role of gravitational effects

The role of gravity in gelation of adhesive hard spheres is studied and a critical criterion developed for homogeneous gelation within the gas-liquid binodal. We hypothesize that gelation by Brownian diffusion competes with phase separation enhanced by gravitational settling. This competition is characterized by the gravitational Péclet number Pe(g), which is a function of particle size, volume fraction, and gravitational acceleration. Through a systematic variation of the parameters, we observe the critical Pe(g) of ∼ 0.01 can predict the stability of gels composed of adhesive hard spheres.

Dynamical arrest, percolation, gelation, and glass formation in model nanoparticle dispersions with thermoreversible adhesive interactions

We report an experimental study of the dynamical arrest transition for a model system consisting of octadecyl coated silica suspended in n-tetradecane from dilute to concentrated conditions spanning the state diagram. The dispersion's interparticle potential is tuned by temperature affecting the brush conformation leading to a thermoreversible model system. The critical temperature for dynamical arrest, T*, is determined as a function of dispersion volume fraction by small-amplitude dynamic oscillatory shear rheology. We corroborate this transition temperature by measuring a power-law decay of the autocorrelation function and a loss of ergodicity via fiber-optic quasi-elastic light scattering. The structure at T* is measured using small-angle neutron scattering. The scattering intensity is fit to extract the interparticle pair-potential using the Ornstein-Zernike equation with the Percus-Yevick closure approximation, assuming a square-well interaction potential with a short-range interaction (1% of particle diameter). (1) The strength of attraction is characterized using the Baxter temperature (2) and mapped onto the adhesive hard sphere state diagram. The experiments show a continuous dynamical arrest transition line that follows the predicted dynamical percolation line until ϕ ≈ 0.41 where it subtends the predictions toward the mode coupling theory attractive-driven glass line. An alternative analysis of the phase transition through the reduced second virial coefficient B(2)* shows a change in the functional dependence of B(2)* on particle concentration around ϕ ≈ 0.36. We propose this signifies the location of a gel-to-glass transition. The results presented herein differ from those observed for depletion flocculated dispersion of micrometer-sized particles in polymer solutions, where dynamical arrest is a consequence of multicomponent phase separation, suggesting dynamical arrest is sensitive to the physical mechanism of attraction.

Electrostatics and aggregation: how charge can turn a crystal into a gel

The crystallization of proteins or colloids is often hindered by the appearance of aggregates of low fractal dimension called gels. Here we study the effect of electrostatics upon crystal and gel formation using an analytic model of hard spheres bearing point charges and short range attractive interactions. We find that the chief electrostatic free energy cost of forming assemblies comes from the entropic loss of counterions that render assemblies charge-neutral. Because there exists more accessible volume for these counterions around an open gel than a dense crystal, there exists an electrostatic entropic driving force favoring the gel over the crystal. This driving force increases with increasing sphere charge, but can be counteracted by increasing counterion concentration. We show that these effects cannot be fully captured by pairwise-additive macroion interactions of the kind often used in simulations, and we show where on the phase diagram to go in order to suppress gel formation.

Dynamical arrest transition in nanoparticle dispersions with short-range interactions

We measure the dynamical arrest transition in a model, thermoreversible, adhesive hard sphere dispersion. At low volume fractions ϕ, below the critical point, gelation occurs within the gas-liquid phase boundary. For ϕ slightly below and above the critical concentration, the phase boundary follows the predicted percolation transition. At high ϕ, it melds into the predicted attractive-driven glass transition. Our results demonstrate that for ϕ above ∼20% physical gelation is an extension of the attractive-driven glass line and occurs without competition for macroscopic phase separation.

Dipolar sticky hard spheres within the Percus-Yevick approximation plus orientational linearization

We consider a strongly idealized model for polar fluids, which consists of spherical particles, having, in addition to a hard-core repulsion, a "surface dipolar" interaction, acting only when particles are exactly at contact. A fully analytic solution of the molecular Orstein-Zernike equation is found for this potential, within the Percus-Yevick approximation complemented by a linearization of the angular dependence on molecular orientations (Percus-Yevick closure with orientational linearization). Numerical results are also presented in a detailed analysis about the local orientational structure. From the pair correlation function g(1,2), we first derive the best orientations of a test particle which explores the space around an arbitrary reference molecule. Then some local and global order parameters, related to the polarization induced by the reference particle, are also calculated. The local structure of this model with only short-ranged anisotropic interactions turns out to be, at least within the chosen approximation, qualitatively different from that of hard spheres with fully long-ranged dipolar potentials.

A numerical test of a high-penetrability approximation for the one-dimensional penetrable-square-well model

The one-dimensional penetrable-square-well fluid is studied using both analytical tools and specialized Monte Carlo simulations. The model consists of a penetrable core characterized by a finite repulsive energy combined with a short-range attractive well. This is a many-body one-dimensional problem, lacking an exact analytical solution, for which the usual van Hove theorem on the absence of phase transition does not apply. We determine a high-penetrability approximation complementing a similar low-penetrability approximation presented in previous work. This is shown to be equivalent to the usual Debye-Hückel theory for simple charged fluids for which the virial and energy routes are identical. The internal thermodynamic consistency with the compressibility route and the validity of the approximation in describing the radial distribution function is assessed by a comparison against numerical simulations. The Fisher-Widom line separating the oscillatory and monotonic large-distance behaviors of the radial distribution function is computed within the high-penetrability approximation and compared with the opposite regime, thus providing a strong indication of the location of the line in all possible regimes. The high-penetrability approximation predicts the existence of a critical point and a spinodal line, but this occurs outside the applicability domain of the theory. We investigate the possibility of a fluid-fluid transition by the Gibbs ensemble Monte Carlo techniques, not finding any evidence of such a transition. Additional analytical arguments are given to support this claim. Finally, we find a clustering transition when Ruelle's stability criterion is not fulfilled. The consequences of these findings on the three-dimensional phase diagrams are also discussed.

Topological characteristics of model gels

The Euler characteristic of an object is a topological invariant determined by the number of handles and holes that it contains. Here, we use the Euler characteristic to profile the topology of model three-dimensional gel-forming fluids as a function of increasing length scale. These profiles act as a 'topological fingerprint' of the structure, and can be interpreted in terms of three types of topological events. As model fluids we have considered a system of dipolar dumbbells, and suspensions of adhesive hard spheres with isotropic and patchy interactions in turn. The correlation between the percolation threshold and the length scale on which the Euler characteristic passes through zero is examined and found to be system-dependent. A scheme for the efficient calculation of the Euler characteristic with and without periodic boundary conditions is described.

Structure and phase diagram of an adhesive colloidal dispersion under high pressure: a small angle neutron scattering, diffusing wave spectroscopy, and light scattering study

We have applied small angle neutron scattering (SANS), diffusing wave spectroscopy (DWS), and dynamic light scattering (DLS) to investigate the phase diagram of a sterically stabilized colloidal system consisting of octadecyl grafted silica particles dispersed in toluene. This system is known to exhibit gas-liquid phase separation and percolation, depending on temperature T, pressure P, and concentration phi. We have determined by DLS the pressure dependence of the coexistence temperature and the spinodal temperature to be dP/dT=77 bar/K. The gel line or percolation limit was measured by DWS under high pressure using the condition that the system became nonergodic when crossing it and we determined the coexistence line at higher volume fractions from the DWS limit of turbid samples. From SANS measurements we determined the stickiness parameter tau(B)(P,T,phi) of the Baxter model, characterizing a polydisperse adhesive hard sphere, using a global fit routine on all curves in the homogenous regime at various temperatures, pressures, and concentrations. The phase coexistence and percolation line as predicted from tau(B)(P,T,phi) correspond with the determinations by DWS and were used to construct an experimental phase diagram for a polydisperse sticky hard sphere model system. A comparison with theory shows good agreement especially concerning the predictions for the percolation threshold. From the analysis of the forward scattering we find a critical scaling law for the susceptibility corresponding to mean field behavior. This finding is also supported by the critical scaling properties of the collective diffusion.

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.

Adsorption of a Binary Mixture of Adhesive Fluids in Planar Pores: A Monte Carlo Study

Grand canonical Monte Carlo simulation is used to study the adsorption of a binary sticky hard-sphere fluid mixture in planar pores. The wall-component 1 and wall-component 2 contact densities are determined to calculate the pressure as a function of the composition of the mixture and the separation between the walls. From these data dependence of the solvation force between the plates on pore width is estimated. The simulation results are compared with the predictions of the Percus-Yevick approximation for planar pores. The density profiles of particular components show interesting shapes stemming from the interplay between the steric effects and the competitive adhesion among all possible species pairs. It is shown that narrowing of the pore causes selective partitioning of individual components of the mixture between the bulk phase and the interior of the pore. The agreement between the two methods is better at wider pores and for the component comprised of weakly adhesive particles.

Novel Monte Carlo scheme for systems with short-ranged interactions

We propose a Monte Carlo (MC) sampling algorithm to simulate systems of particles interacting via very short-ranged discontinuous potentials. Such models are often used to describe protein solutions or colloidal suspensions. Most normal MC algorithms fail for such systems because, at low temperatures, they tend to get trapped in local potential-energy local minima due to the short range of the pair potential. To circumvent this problem, we have devised a scheme that changes the construction of trial moves in such a way that the potential-energy difference between initial and final states drops out of the acceptance rule for the Monte Carlo trial moves. This approach allows us to simulate systems with short-ranged attraction under conditions that were unreachable up to now.

Application of the optimized Baxter model to the hard-core attractive Yukawa system

We perform Monte Carlo simulations on the hard-core attractive Yukawa system to test the optimized Baxter model that was introduced by Prinsen and Odijk [J. Chem. Phys. 121, 6525 (2004)] to study a fluid phase of spherical particles interacting through a short-range pair potential. We compare the chemical potentials and pressures from the simulations with analytical predictions from the optimized Baxter model. We show that the model is accurate to within 10% over a range of volume fractions from 0.1 to 0.4, interaction strengths up to three times the thermal energy, and interaction ranges from 6% to 20% of the particle diameter, and performs even better in most cases. We furthermore establish the consistency of the model by showing that the thermodynamic properties of the Yukawa fluid computed via simulations may be understood on the basis of one similarity variable, the stickiness parameter defined within the optimized Baxter model. Finally, we show that the optimized Baxter model works significantly better than an often used, naive method determining the stickiness parameter by equating the respective second virial coefficients based on the attractive Yukawa and Baxter potentials.

Phase separation and percolation of reversibly aggregating spheres with a square-well attraction potential

Reversible aggregation of spheres is simulated using a novel method in which clusters of bound spheres diffuse collectively with a diffusion coefficient proportional to their radius. It is shown that the equilibrium state is the same as with other simulation techniques, but with the present method more realistic kinetics are obtained. The behavior as a function of volume fraction and interaction strength was tested for two different attraction ranges. The binodal and the percolation threshold were determined. The cluster structure and size distribution close to the percolation threshold were found to be consistent with the percolation model. Close to the binodal phase separation occurred through the growth of spherical dense domains, while for deep quenches a system spanning network is formed that coarsens with a rate that decreases with increasing attraction. We found no indication for arrest of the coarsening.

How “sticky” are short-range square-well fluids?

The aim of this work is to investigate to what extent the structural properties of a short-range square-well (SW) fluid of range lambda at a given packing fraction eta and reduced temperature T* = kBT/epsilon can be represented by those of a sticky-hard-sphere (SHS) fluid at the same packing fraction and an effective stickiness parameter tau(T*,lambda). Such an equivalence cannot hold for the radial distribution function g(r) since this function has a delta singularity at contact (r = sigma) in the SHS case, while it has a jump discontinuity at r = lambda sigma in the SW case. Therefore, the equivalence is explored with the cavity function y(r), i.e., we assume that [formula: see text]. Optimization of the agreement between y(SW) and y(SHS) to first order in density suggests the choice tau(T*,lambda) = [12(e(1/T* - 1)(lambda - 1)](-1). We have performed Monte Carlo (MC) simulations of the SW fluid for lambda = 1.05, 1.02, and 1.01 at several densities and temperatures T* such that tau(T*,lambda) = 0.13, 0.2, and 0.5. The resulting cavity functions have been compared with MC data of SHS fluids obtained by Miller and Frenkel[J. Phys.: Condens. Matter 16, S4901 (2004)]. Although, at given values of eta and tau, some local discrepancies between y(SW) and y(SHS) exist (especially for lambda = 1.05), the SW data converge smoothly toward the SHS values as lambda-1 decreases. In fact, precursors of the singularities of y(SHS) at certain distances due to geometrical arrangements are clearly observed in y(SW). The approximate mapping y(SW)-->y(SHS) is exploited to estimate the internal energy and structure factor of the SW fluid from those of the SHS fluid. Taking for y(SHS) the solution of the Percus-Yevick equation as well as the rational-function approximation, the radial distribution function g(r) of the SW fluid is theoretically estimated and a good agreement with our MC simulations is found. Finally, a similar study is carried out for short-range SW fluid mixtures.

Specific ion-dependent attraction and phase behavior of polymer-coated colloids

This paper presents results demonstrating the role of temperature and specific ions in mediating attraction between polymer-coated colloids and determining their equilibrium phase behavior. In particular, theoretical predictions of continuum van der Waals attraction between poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO)-coated polystyrene colloids are used to explain measured temperature and specific ion-dependent fluid-gel transitions in dispersions of these particles. Building on previous studies of PEO-PPO-PEO-coated polystyrene colloids dispersed in aqueous NaCl media, this work reports rheologically measured fluid-gel transitions as a function of temperature and NaCl/MgSO4 composition. Adhesive-sphere predictions of percolation thresholds are fit to measured fluid-gel data by allowing the adsorbed copolymer layer thickness as a single adjustable parameter. This allows the attraction between the PEO-PPO-PEO layers to be interpreted as a function of temperature and NaCl/MgSO4 composition. Quantitative predictions of a polymeric van der Waals attraction associated with the layer collapse in diminishing solvent conditions provides a simple mechanism for explaining the measured fluid-gel data as a dynamic percolation transition. Ultimately, this work identifies the importance of continuum polymeric van der Waals attraction for explaining specific ion-dependent phenomena.

Optimized Baxter model of protein solutions: Electrostatics versus adhesion

A theory is set up of spherical proteins interacting by screened electrostatics and constant adhesion, in which the effective adhesion parameter is optimized by a variational principle for the free energy. An analytical approach to the second virial coefficient is first outlined by balancing the repulsive electrostatics against part of the bare adhesion. A theory similar in spirit is developed at nonzero concentrations by assuming an appropriate Baxter model as the reference state. The first-order term in a functional expansion of the free energy is set equal to zero which determines the effective adhesion as a function of salt and protein concentrations. The resulting theory is shown to have fairly good predictive power for the ionic-strength dependence of both the second virial coefficient and the osmotic pressure or compressibility of lysozyme up to about 0.2 volume fraction.

Analytic solutions for Baxter’s model of sticky hard sphere fluids within closures different from the Percus–Yevick approximation

We discuss structural and thermodynamical properties of Baxter's adhesive hard sphere model within a class of closures which includes the Percus-Yevick (PY) one. The common feature of all these closures is to have a direct correlation function vanishing beyond a certain range, each closure being identified by a different approximation within the original square-well region. This allows a common analytical solution of the Ornstein-Zernike integral equation, with the cavity function playing a privileged role. A careful analytical treatment of the equation of state is reported. Numerical comparison with Monte Carlo simulations shows that the PY approximation lies between simpler closures, which may yield less accurate predictions but are easily extensible to multicomponent fluids, and more sophisticate closures which give more precise predictions but can hardly be extended to mixtures. In regimes typical for colloidal and protein solutions, however, it is found that the perturbative closures, even when limited to first order, produce satisfactory results.

Phase diagram of the adhesive hard sphere fluid

The phase behavior of the Baxter adhesive hard sphere fluid has been determined using specialized Monte Carlo simulations. We give a detailed account of the techniques used and present data for the fluid-fluid coexistence curve as well as parametrized fits for the supercritical equation of state and the percolation threshold. These properties are compared with the existing results of Percus-Yevick theory for this system.

Competition of percolation and phase separation in a fluid of adhesive hard spheres

Using a combination of Monte Carlo techniques, we locate the liquid-vapor critical point of adhesive hard spheres. We find that the critical point lies deep inside the gel region of the phase diagram. The (reduced) critical temperature and density are tau(c)=0.1133+/-0.0005 and rho(c)=0.508+/-0.01. We compare these results with the available theoretical predictions. Using a finite-size scaling analysis, we verify that the critical behavior of the adhesive hard sphere model is consistent with that of the 3D Ising universality class, the default for systems with short-range attractive forces.