Effective forces in colloidal mixtures: from depletion attraction to accumulation repulsion

Potential effects on effective attraction between probes diffusing in colloidal crystal

Considering the significant influence of interparticle potentials on traditional depletion forces, we here employ computer simulations to investigate how varying potentials between particles affect the effective interaction of probes diffusing freely in a 2D colloidal crystal. Our results reveal that attractive potentials between the background particles and probes significantly modify the interprobe effective interactions, whereas long-range repulsive tails among the background particles have minimal impact. Furthermore, we observe contrary temperature dependencies of the effective force for soft and stiff repulsions between the background particles. These findings provide deeper insights into how direct interparticle potentials shape entropic-dominated effective forces mediated by colloidal crystals.

Demixing in Binary Mixtures with Differential Diffusivity at High Density

Spontaneous phase separation, or demixing, is important in biological phenomena such as cell sorting. In particle-based models, an open question is whether differences in diffusivity can drive such demixing. While differential-diffusivity-induced phase separation occurs in mixtures with a packing fraction up to 0.7 [S. N. Weber et al. Binary mixtures of particles with different diffusivities demix, Phys. Rev. Lett. 116, 058301 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.058301], here we investigate whether demixing persists at even higher densities relevant for cells. For particle packing fractions between 0.7 and 1.0 the system demixes, but at packing fractions above unity the system remains mixed, exposing re-entrant behavior in the phase diagram that occurs when phase separation can no longer drive a change in entropy production at high densities. We also find that a confluent Voronoi model for tissues does not phase separate, consistent with particle-based simulations.

Freezing in two-length-scale systems: complexity, universality and prediction

Two-length-scale pair potentials arise ubiquitously in condensed matter theory as effective interparticle interactions in molecular, metallic and soft matter systems. The existence of two different bond lengths generated by the shape of potential causes complicated behavior in even one-component systems: polymorphism in solid and liquid states, water-like anomalies, the formation of quasicrystals and high stability against crystallization. Here we address general properties of freezing in one-component two-length-scale systems and argue that solidification of a liquid during cooling is essentially determined by the radial distribution function (RDF) of the liquid. We show that different two-length-scale systems having similar RDFs freeze into the same solid phases. In some cases, the similarity between RDFs can be expressed by the proximity of two dimensionless effective parameters: the ratio between effective bond lengths,λ, and the fraction of short-bonded particlesφ. We validate this idea by studying the formation of different solid phases in different two-length-scale systems. The method proposed allows predicting effectively the formation of solid phases in both numerical simulations and self-assembling experiments in soft matter systems with tunable interactions.

Structural correlations in highly asymmetric binary charged colloidal mixtures

We explore structural correlations of strongly asymmetric mixtures of binary charged colloids within the primitive model of electrolytes considering large charge and size ratios of 10 and higher. Using computer simulations with explicit microions, we obtain the partial pair correlation functions between the like-charged colloidal macroions. Interestingly the big-small correlation peak amplitude is smaller than that of the big-big and small-small macroion correlation peaks, which is unfamiliar for additive repulsive interactions. Extracting optimal effective microion-averaged pair interactions between the macroions, we find that on top of non-additive Yukawa-like repulsions an additional shifted Gaussian attractive potential between the small macroions is needed to accurately reproduce their correct pair correlations. For small Coulomb couplings, the behavior is reproduced in a coarse-grained theory with microion-averaged effective interactions between the macroions. However, the accuracy of the theory deteriorates with increasing Coulomb coupling. We emphasize the relevance of entropic interactions exerted by the microions on the macroions. Our results are experimentally verifiable in binary mixtures of micron-sized colloids and like-charge nanoparticles.

Chaining of hard disks in nematic needles: particle-based simulation of colloidal interactions in liquid crystals

Colloidal particles suspended in liquid crystals can exhibit various effective anisotropic interactions that can be tuned and utilized in self-assembly processes. We simulate a two-dimensional system of hard disks suspended in a solution of dense hard needles as a model system for colloids suspended in a nematic lyotropic liquid crystal. The novel event-chain Monte Carlo technique enables us to directly measure colloidal interactions in a microscopic simulation with explicit liquid crystal particles in the dense nematic phase. We find a directional short-range attraction for disks along the director, which triggers chaining parallel to the director and seemingly contradicts the standard liquid crystal field theory result of a quadrupolar attraction with a preferred [Formula: see text] angle. Our results can be explained by a short-range density-dependent depletion interaction, which has been neglected so far. Directionality and strength of the depletion interaction are caused by the weak planar anchoring of hard rods. The depletion attraction robustly dominates over the quadrupolar elastic attraction if disks come close. Self-assembly of many disks proceeds via intermediate chaining, which demonstrates that in lyotropic liquid crystal colloids depletion interactions play an important role in structure formation processes.

Binding potentials for vapour nanobubbles on surfaces using density functional theory

We calculate density profiles of a simple model fluid in contact with a planar surface using density functional theory (DFT), in particular for the case where there is a vapour layer intruding between the wall and the bulk liquid. We apply the method of Hughes et al (2015 J. Chem. Phys. 142 074702) to calculate the density profiles for varying (specified) amounts of the vapour adsorbed at the wall. This is equivalent to varying the thickness h of the vapour at the surface. From the resulting sequence of density profiles we calculate the thermodynamic grand potential as h is varied and thereby determine the binding potential as a function of h. The binding potential obtained via this coarse-graining approach allows us to determine the disjoining pressure in the film and also to predict the shape of vapour nano-bubbles on the surface. Our microscopic DFT based approach captures information from length scales much smaller than some commonly used models in continuum mechanics.

A Dirty Story: Improving Colloidal Monolayer Formation by Understanding the Effect of Impurities at the Air/Water Interface

Colloidal monolayers are important tools to fabricate surface structures at the nanoscale. A typical monolayer fabrication strategy involves the self-assembly of colloidal building blocks at liquid interfaces, which are subsequently deposited on a solid substrate. Even though this process is well established, the resulting order of the particles within the colloidal monolayer differs between batches of colloidal particles and can even change with the age of the dispersion. In this study, we investigate the origins of this variation of monolayer quality for polystyrene particles synthesized by surfactant-free emulsion polymerization. We correlate the interfacial behavior of the colloidal particles at the air/water interface on a Langmuir trough with the resulting quality of the monolayer after transfer to a solid substrate. We identify surface-active impurities as a major cause for a disturbed self-assembly of the colloidal particles. These impurities form during the particle synthesis and consist of copolymers of styrene, the comonomer acrylic acid, and sulfonate species from the initiator. We show that they can be removed by cleaning protocols to increase the monolayer quality. However, our experiments demonstrate that the impurities reappear over time even for cleaned dispersions, indicating desorption from the surface of the colloidal particles. We identify strategies to avoid the presence of the impurities at the air/water interface or to inhibit their effect on the self-assembly process. These simple guidelines improve the quality of the resulting colloidal monolayer, which is a prerequisite for the reliable fabrication of high-quality surface nanostructures from colloidal templates.

Amphiphile-Induced Anisotropic Colloidal Self-Assembly

Spherical colloidal particles typically self-assemble into hexagonal lattices when adsorbed at liquid interfaces. More complex assembly structures, including particle chains and phases with square symmetry, were theoretically predicted almost two decades ago for spherical particles interacting via a soft repulsive shoulder. Here, we demonstrate that such complex assembly phases can be experimentally realized with spherical colloidal particles assembled at the air/water interface in the presence of molecular amphiphiles. We investigate the interfacial behavior of colloidal particles in the presence of different amphiphiles on a Langmuir trough. We transfer the structures formed at the interface onto a solid substrate while continuously compressing, which enables us to correlate the prevailing assembly phase as a function of the available interfacial area. We observe that block copolymers with similarities to the chemical nature of the colloidal particles, as well as the surface-active protein bovine serum albumin, direct the colloidal particles into complex assembly phases, including chains and square arrangements. The observed structures are reproduced by minimum energy calculations of hard core-soft shoulder particles with experimentally realistic interaction parameters. From the agreement between experiments and theory, we hypothesize that the presence of the amphiphiles manipulates the interaction potential of the colloidal particles. The assembly of spherical colloidal particles into complex assembly phases on solid substrates opens new possibilities for surface patterning by enriching the library of possible structures available for colloidal lithography.

Evidence of electrostatic-enhanced depletion attraction in the structural properties and phase behavior of binary charged colloidal suspensions

In this paper we study the structure and phase behavior of binary mixtures of charged particles at low ionic strength. Due to the large size asymmetry between both species, light scattering measurements give us access only to the partial static structure factor that corresponds to the big particles. We observe that the addition of small charged colloids produces a decrease of the main peak of the measured static structure factor and a shift to larger scattering vector values. This finding is in agreement with theory based on integral equations with the Hypernetted-Chain Closure (HNC) relation. The effective interaction between two big particles due to the presence of small particles is obtained by a HNC inversion scheme and used in numerical simulations that adequately reproduce the experiments. We find that the presence of small particles induces an electrostatic depletion screening among the big colloids, creating around them an exclusion zone for the small charged colloids greater than that caused in the case of neutral small colloids, which in turn augments the depletion effect.

Effective electrostatic interactions in colloid-nanoparticle mixtures

Interparticle interactions and bulk properties of colloidal suspensions can be substantially modified by the addition of nanoparticles. Extreme asymmetries in size and charge between colloidal particles and nanoparticles present severe computational challenges to molecular-scale modeling of such complex systems. We present a statistical mechanical theory of effective electrostatic interactions that can greatly ease large-scale modeling of charged colloid-nanoparticle mixtures. By applying a sequential coarse-graining procedure, we show that a multicomponent mixture of charged colloids, nanoparticles, counterions, and coions can be mapped first onto a binary mixture of colloids and nanoparticles and then onto a one-component model of colloids alone. In a linear-response approximation, the one-component model is governed by a single effective pair potential and a one-body volume energy, whose parameters depend nontrivially on nanoparticle size, charge, and concentration. To test the theory, we perform molecular dynamics simulations of the two-component and one-component models and compute structural properties. For moderate electrostatic couplings, colloid-colloid radial distribution functions and static structure factors agree closely between the two models, validating the sequential coarse-graining approach. Nanoparticles of sufficient charge and concentration enhance screening of electrostatic interactions, weakening correlations between charged colloids and destabilizing suspensions, consistent with experiments.

Molecular simulations of cellular processes

It is, nowadays, possible to simulate biological processes in conditions that mimic the different cellular compartments. Several groups have performed these calculations using molecular models that vary in performance and accuracy. In many cases, the atomistic degrees of freedom have been eliminated, sacrificing both structural complexity and chemical specificity to be able to explore slow processes. In this review, we will discuss the insights gained from computer simulations on macromolecule diffusion, nuclear body formation, and processes involving the genetic material inside cell-mimicking spaces. We will also discuss the challenges to generate new models suitable for the simulations of biological processes on a cell scale and for cell-cycle-long times, including non-equilibrium events such as the co-translational folding, misfolding, and aggregation of proteins. A prominent role will be played by the wise choice of the structural simplifications and, simultaneously, of a relatively complex energetic description. These challenging tasks will rely on the integration of experimental and computational methods, achieved through the application of efficient algorithms. Graphical abstract.

Polyurethane Microgel Based Microtissue: Interface-Guided Assembly and Spreading

Colloidal gels are three-dimensional networks of microgel particles and can be utilized to design microtissues where the differential adhesive interactions between the particles and cells, guided by their surface energetics, are engineered to spatially assemble the cellular and colloidal components into three-dimensional microtissues. In this work we utilized a colloidal interaction approach to design cell-polyurethane (PU) microgel bimodal microtissues using endothelial cells (ECs) as a normal cell model and a nonmalignant breast cancer cell line (MCF-7) as a cancer cell model. PU microgels were developed from a library of segmental polyurethanes with poly(ethylene glycol) soft segment and aliphatic diisocyanate/l-tyrosine based chain extender as hard segment to modulate the interactions between PU colloidal particles and cells. The surface energies of the microgel particles and cells were estimated using Zisman's critical surface tension and van Oss-Good-Chaudhury theory (vOGCT) from liquid contact angle analysis. Binary interaction potentials between colloidal PU particles and cells and the ternary interaction between colloidal PU particle, cell, and collagen I/Matrigel were calculated to explain the formation of microtissues and their spreading in extraneous biomatrix respectively by using classical and extended DLVO theory (XDLVO). Furthermore, rheological analysis and in silico simulations were used to analyze the assembly and spreading of the PU microgel based microtissues. In vitro experiments showed that ECs and MCF-7 displayed more differentiated (EC spreading/MCF-7 lumen formation) character when mixed with microgel particles that were stable in aqueous medium and more undifferentiated character (EC nonspreading/MCF-7 spreading) when mixed with microgel particles unstable in aqueous medium.

Solvent-mediated forces in critical fluids

The effective interaction between two planar walls immersed in a fluid is investigated by use of density functional theory in the supercritical region of the phase diagram. A hard core Yukawa model of fluid is studied with special attention to the critical region. To achieve this goal a formulation of the weighted density approximation coupled with the hierarchical reference theory, able to deal with critical long wavelength fluctuations, is put forward and compared with other approaches. The effective interaction between the walls is seen to change character on lowering the temperature: The strong oscillations induced by layering of the molecules, typical of the depletion mechanism in hard core systems, are gradually smoothed and, close to the critical point, a long range attractive tail emerges leading to a scaling form which agrees with the expectations based on the critical Casimir effect. Strong corrections to scaling are seen to affect the results up to very small reduced temperatures. By use of the Derjaguin approximation, this investigation has natural implications for the aggregation of colloidal particles in critical solvents.

Encapsulation of spherical nanoparticles by colloidal dimers

We study by Monte Carlo simulation the coating process of colloidal dimers onto spherical nanoparticles. To this end we investigate a simplified mixture of hard spheres (the guest particles) and hard dimers formed by two tangent spheres of different sizes (the encapsulating agents) in an implicit-solvent representation; in our scheme, the range of effective interactions between the smaller particle in a dimer and a guest sphere depends on their relative size. By tuning the size and concentration of guests, under overall dilute conditions a rich phase behavior emerges: for small sizes and/or low concentrations, the preferred arrangement is compact aggregates (capsules) of variable sizes, where one or few guest particles are coated with dimers; for larger sizes and moderate guest concentrations, other scenarios are realized, including equilibrium separation between a guest-rich and a guest-poor phase. Our results serve as a framework for a more systematic investigation of self-assembled structures of functionalized dimers capable of encapsulating target particles, like for instance bioactive substances in a colloidal dispersion.

Binary Mixtures of Particles with Different Diffusivities Demix

The influence of size differences, shape, mass, and persistent motion on phase separation in binary mixtures has been intensively studied. Here we focus on the exclusive role of diffusivity differences in binary mixtures of equal-sized particles. We find an effective attraction between the less diffusive particles, which are essentially caged in the surrounding species with the higher diffusion constant. This effect leads to phase separation for systems above a critical size: A single close-packed cluster made up of the less diffusive species emerges. Experiments for testing our predictions are outlined.

Monte Carlo simulation of kinetically slowed down phase separation

Supercooled colloidal or molecular systems at low densities are known to form liquid, crystalline or glassy drops, which may remain isolated for a long time before they aggregate. This paper analyses the properties of this large time window, and how it can be tackled by computer simulation. We use single-particle and virtual move Monte Carlo simulations of short-range attractive spheres which are undercooled to the temperature region, where the spinodal intersects the attractive glass line. We study two different systems and we report the following kinetic behavior. A low-density system is shown to exhibit universal linear growth regimes under single-particle Monte Carlo correlating the growth rate to the local structure. These regimes are suppressed under collective motion, where droplets aggregate into a single large disordered domain. It is shown that the aggregation can be avoided and linear regimes recovered, if long-range repulsion is added to the short-range attraction. The results provide an insight into the behavior of the virtual move algorithm generating cluster moves according to the local forcefields. We show that different choices of maximum Monte Carlo displacement affect the dynamical trajectories but lead to the same kinetically slowed down or arrested states.

Computation of shear viscosity of colloidal suspensions by SRD-MD

The behaviour of sheared colloidal suspensions with full hydrodynamic interactions (HIs) is numerically studied. To this end, we use the hybrid stochastic rotation dynamics-molecular dynamics (SRD-MD) method. The shear viscosity of colloidal suspensions is computed for different volume fractions, both for dilute and concentrated cases. We verify that HIs help in the collisions and the streaming of colloidal particles, thereby increasing the overall shear viscosity of the suspension. Our results show a good agreement with known experimental, theoretical, and numerical studies. This work demonstrates the ability of SRD-MD to successfully simulate transport coefficients that require correct modelling of HIs.

Structural orderings of anisotropically confined colloids interacting via a quasi-square-well potential

We implement Brownian dynamics to investigate the static properties of colloidal particles confined anisotropically and interacting via a potential which can be tailored in a repulsive-attractive-respulsive fashion as the interparticle distance increases. A diverse number of structural phases are self-assembled, which were classified according to two aspects, that is, their macroscopic and microscopic patterns. Concerning the microscopic phases we found the quasicrystalline, triangular, square, and mixed orderings, where this latter is a combination of square and triangular cells in a 3×2 proportion, i.e., the so-called (3(3),4(2)) Archimedian lattice. On the macroscopic level the system could self-organize in a compact or perforated single cluster surrounded or not by fringes. All the structural phases are summarized in detailed phases diagrams, which clearly show that the different phases are extended as the confinement potential becomes more anisotropic.

Analytical theory of effective interactions in binary colloidal systems of soft particles

While density functional theory with integral equations techniques are very efficient tools in the numerical analysis of complex fluids, analytical insight into the phenomenon of effective interactions is still limited. In this paper, we propose a theory of binary systems that results in a relatively simple analytical expression combining arbitrary microscopic potentials into effective interaction. The derivation is based on translating a many-particle Hamiltonian including particle-depletant and depletant-depletant interactions into the occupation field language, which turns the partition function into multiple Gaussian integrals, regardless of what microscopic potentials are chosen. As a result, we calculate the effective Hamiltonian and discuss when our formula is a dominant contribution to the effective interactions. Our theory allows us to analytically reproduce several important characteristics of systems under scrutiny. In particular, we analyze the following: the effective attraction as a demixing factor in the binary systems of Gaussian particles, the screening of charged spheres by ions, which proves equivalent to Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, effective interactions in the binary mixtures of Yukawa particles, and the system of particles consisting of both a repulsive core and an attractive/repulsive Yukawa interaction tail. For this last case, we reproduce the "attraction-through-repulsion" and "repulsion-through-attraction" effects previously observed in simulations.

Cross-over between central and non-central conservative effective forces in a modulated colloidal fluid

We study by Monte Carlo simulations the effective forces between two particles dispersed in a two-dimensional colloidal fluid, modulated in one direction by a spatially periodic external potential. When the modulation strength exceeds the strength of interaction between the dispersed and dispersing particles, the anisotropic effective forces, show cross-over between central and non-central nature, although the effective forces remain conservative. The non-central nature of the effective forces depends on the orientation of the separation vector between the dispersed particles with respect to the modulation direction.

Structural ordering of trapped colloids with competing interactions

The structure of colloids with competing interactions which are confined in a harmonic external trap potential is analyzed numerically by energy minimization in two spatial dimensions. A wealth of different cluster structures is found to be stable including clusters with a fringed outer rim (reminiscent to an ornamental border), clusters perforated with voids, as well as clusters with a crystalline core and a disordered rim. All cluster structures occur in a two-dimensional parameter space. The structural ordering can therefore be efficiently tuned by changing few parameters only providing access to a controlled fabrication of colloidal clusters.

Protein-coat dynamics and cluster phases in intracellular trafficking

Clustering of membrane proteins is a hallmark of biological membranes' lateral organization and crucial to their function. However, the physical properties of these protein aggregates remain poorly understood. Ensembles of coat proteins, the example considered here, are necessary for intracellular transport in eukaryotic cells. Assembly and disassembly rates for coat proteins involved in intracellular vesicular trafficking must be carefully controlled: their assembly deforms the membrane patch and drives vesicle formation, yet the protein coat must rapidly disassemble after vesiculation. Motivated by recent experimental findings for protein-coat dynamics, we study a dynamical Ising-type model for coat assembly and disassembly, and demonstrate how simple dynamical rules generate a robust, steady-state distribution of protein clusters (corresponding to intermediate budded shapes) and how cluster sizes are controlled by the kinetics. We interpret the results in terms of both vesiculation and the coupling to cargo proteins.

Structure of colloidal sphere-plate mixtures

In addition to containing spherical pigment particles, coatings usually contain plate-like clay particles. It is thought that these improve the opacity of the paint film by providing an efficient spacing of the pigment particles. This observation is counterintuitive, as suspensions of particles of different shapes and sizes tend to phase separate on increase of concentration. In order to clarify this matter a model colloidal system is studied here, with a sphere-plate diameter ratio similar to that found in paints. For dilute suspensions, small angle neutron scattering revealed that the addition of plates leads to enhanced density fluctuations of the spheres, in agreement with new theoretical predictions. On increasing the total colloid concentration the plates and spheres phase separate due to the disparity in their shape. This is in agreement with previous theoretical and experimental work on colloidal sphere-plate mixtures, where one particle acts as a depleting agent. The fact that no large scale phase separation is observed in coatings is ascribed to dynamic arrest in intimately mixed, or possibly micro-phase separated structures, at elevated concentration.

Correlated electrolyte solutions and ion-induced attractions between nanoparticles

Simple expressions are presented for the equations of state of a correlated electrolyte solution, calculated straightforwardly within a full nonlinear Debye-Hückel approach in terms of the mean potential at contact, that predict quantitatively different phase behavior from the popular Debye-Hückel limiting law. The theory includes pair correlations accurately and may provide a basis for a quantitative theoretical study of organic or multivalent ionic solutions. As an example, cohesive effects are addressed of strong couplings between ions on the effective interactions between nanoparticles.

Binary fluid with attractions near a planar wall

It is well known that a mixture of big and small hard spheres next to a planar wall will exhibit segregation based on their size difference. The larger spheres will tend to locate next to the substrate because the overall system entropy loss per unit area is less. In the present study we determine the role of attraction between the small particles and the wall to displace the larger particles. Both fluids density-functional theory and discontinuous molecular dynamics simulations demonstrate that at a certain attractive potential, which is on the order of the thermal energy, the large particles can indeed be dislodged from the surface layer so the small particles are now the major surface component. Exploration of a range of parameters, including relative sphere size and concentration, as well as attractions between the small spheres in the bulk, shows that the phenomenon is quite robust.