Using mesoscopic numerical simulations and analytical theory we investigate the coarsening of the solvent structure around a colloidal particle emerging after a temperature quench of the colloid surface. Qualitative differences in the coarsening mechanisms are found, depending on the composition of the binary liquid mixture forming the solvent and on the adsorption preferences of the colloid. For an adsorptionwise neutral colloid, as function of time the phase being next to its surface alternates. This behavior sets in on the scale of the relaxation time of the solvent and is absent for colloids with strong adsorption preferences. A Janus colloid, with a small temperature difference between its two hemispheres, reveals an asymmetric structure formation and surface enrichment around it, even if the solvent is within its one-phase region and if the temperature of the colloid is above the critical demixing temperature $T_c$ of the solvent. Our phenomenological model turns out to capture recent experimental findings according to which, upon laser illumination of a Janus colloid and due to the ensuing temperature gradient between its two hemispheres, the surrounding binary liquid mixture develops a concentration gradient.
The influence of poor solvent quality on fluid demixing of a model mixture of colloids and nonadsorbing polymers is investigated using density functional theory. The colloidal particles are modelled as hard spheres and the polymer coils as effective interpenetrating spheres that have hard interactions with the colloids. The solvent is modelled as a two-component mixture of a primary solvent, regarded as a background theta-solvent for the polymer, and a cosolvent of point particles that are excluded from both colloids and polymers. Cosolvent exclusion favors overlap of polymers, mimicking the e…
We determine the solvent mediated contribution to the effective potentials for model colloidal or nano- particles dispersed in a binary solvent that exhibits fluid-fluid phase separation. Using a simple density functional theory we calculate the density profiles of both solvent species in the presence of the `colloids', which are treated as external potentials, and determine the solvent mediated (SM) potentials. Specifically, we calculate SM potentials between (i) two colloids, (ii) a colloid and a planar fluid-fluid interface, and (iii) a colloid and a planar wall with an adsorbed wetting fil…
This study reports a general scenario for the out-of-equilibrium features of collapsing polymeric architectures. We use molecular dynamics simulations to characterize the coarsening kinetics, in bad solvent, for several macromolecular systems with an increasing degree of structural complexity. In particular, we focus on: flexible and semiflexible polymer chains, star polymers with 3 and 12 arms, and microgels with both ordered and disordered networks. Starting from a powerful analogy with critical phenomena, we construct a density field representation that removes fast fluctuations and provide…
We study the effect of solvent granularity on the effective force between two charged colloidal particles by computer simulations of the primitive model of strongly asymmetric electrolytes with an explicitly added hard sphere solvent. Apart from molecular oscillating forces for nearly touching colloids which arise from solvent and counterion layering, the counterions are attracted towards the colloidal surfaces by solvent depletion providing a simple statistical description of hydration. This, in turn, has an important influence on the effective forces for larger distances which are considerab…
We study the non-equilibrium coarsening dynamics of a binary liquid solvent around a colloidal particle in a presence of a time-dependent temperature gradient that emerges after temperature quench of a suitably coated colloid surface. The solvent is maintained at its critical concentration and the colloid is fixed in space. The coarsening patterns near the surface are shown to be strongly dependent on the colloid surface adsorption properties and on the temperature evolution. The temperature gradient alters the morphology of a binary solvent near the surface of a colloid as compared to the coa…
We induce and investigate the coarsening and melting dynamics of an initially static nanoparticle colloidal monolayer at an ionic liquid-vacuum interface, driven by a focused, scanning electron beam. Coarsening occurs through grain interface migration and larger-scale motions such as grain rotations, often facilitated by sliding dislocations. The progressive decrease in area fraction that drives melting of the monolayer is explained using an electrowetting model whereby particles at the interface are solvated once their accumulating charge recruits sufficient counterions to subsume the particl…
We present a numerical study of the effective potential $V_\mathrm{eff}$ between two hard-sphere colloids dispersed in a solvent of interacting particles, for several values of temperature and solvent density, approaching the solvent gas-liquid critical point. We investigate the stability of a system of particles interacting via $V_\mathrm{eff}$ to evaluate the locus of colloidal aggregation in the solvent phase-diagram, and its dependence on the colloid size. We assess how the excluded volume depletion forces are modified by solvent attraction and discuss under which conditions solvent critic…
Using numerical simulations, we study the non-equilibrium coarsening dynamics of a binary solvent around spherical colloids in the presence of a temperature gradient. The coarsening dynamics following a temperature quench is studied by solving the coupled modified Cahn-Hilliard-Cook equation and the heat diffusion equation, which describe the concentration profile and the temperature field, respectively. For the temperature field we apply a suitable boundary condition. We observe the formation of circular layers of different phases around the colloid whereas away from the colloid patterns of s…
We determine the phase diagram of mixtures of spherical colloids and neutral nonadsorbing polymers in the thermal crossover region between the $θ$ point and the good-solvent regime. We use the generalized free-volume theory (GFVT), which turns out to be quite accurate as long as $q = R_g/R_c\lesssim 1$ ($R_g$ is the radius of gyration of the polymer and $R_c$ is the colloid radius). Close to the $θ$ point the phase diagram is not very sensitive to solvent quality, while, close to the good-solvent region, changes of the solvent quality modify significantly the position of the critical point and…
We consider an ensemble of spherical colloidal particles immersed in a near-critical solvent such as a binary liquid mixture close to its critical demixing point. The emerging long-ranged fluctuations of the corresponding order parameter of the solvent drive the divergence of the correlation length. Spatial confinements of these critical fluctuations by colloidal solute particles, acting as cavities in the fluctuating medium, restrict and modify the fluctuation spectrum in a way which depends on their relative configuration. This results in effective, so-called critical Casimir forces (CCFs) a…
Within mean field theory, we investigate the bridging transition between a pair of parallel cylindrical colloids immersed in a binary liquid mixture as a solvent which is close to its critical consolute point $T_c$. We determine the universal scaling functions of the effective potential and of the force between the colloids. For a solvent which is at the critical concentration and close to $T_c$, we find that the critical Casimir force is the dominant interaction at close separations. This agrees very well with the corresponding Derjaguin approximation for the effective interaction between the…
A gold-capped Janus particle suspended in a near-critical binary liquid mixture can self-propel under illumination. We have immobilized such a particle in a narrow channel and studied the nonequilibrium dynamics of a binary solvent around it, using experiment and numerical simulations. For the latter we consider both a purely diffusive and a hydrodynamic model. All approaches indicate that the early time dynamics is purely diffusive and characterized by composition layers traveling with a constant speed from the surface of the colloid into the bulk. Subsequently, hydrodynamic effects set in an…
We consider a simplified coarse-grained model for colloid-polymer mixtures, in which polymers are represented as monoatomic molecules interacting by means of pair potentials. We use it to study polymer-colloid segregation in the presence of a quenched matrix of colloidal hard spheres. We fix the polymer-to-colloid size ratio to 0.8 and consider matrices such that the fraction f of the volume that is not accessible to the colloids due to the matrix is equal to 40%. As in the Asakura-Oosawa-Vrij (AOV) case, we find that binodal curves in the polymer and colloid volume-fraction plane have a small…
A new method is presented for mesoscopic simulations of particle dispersions in liquid crystal solvents. It allows efficient first-principle simulations of the dispersions involving many particles with many-body interactions mediated by the solvents. Demonstrations have been performed for the aggregation of colloid dispersions in two-dimensional nematic and smectic-C* solvents neglecting hydrodynamic effects, which will be taken into account in the near future.
In colloidal suspensions, self-organization processes can be easily fueled by external fields. One particularly interesting class of phenomena occurs in monolayers of dipolar particles that are driven by rotating external fields. Here we report results from a computer simulation study of such systems focusing on the clustering behavior also observed in recent experiments. The key result of this paper is a novel interpretation of this pattern formation phenomenon: We show the clustering to be a by-product of a vapor-liquid first order phase transition. In fact, the observed dynamic coarsening p…
If colloidal solute particles are suspended in a solvent close to its critical point, they act as cavities in a fluctuating medium and thereby restrict and modify the fluctuation spectrum in a way which depends on their relative configuration. As a result effective, so-called critical Casimir forces (CCFs) emerge between the colloids. The range and the amplitude of CCFs depend sensitively on the temperature and the composition of the solvent as well as on the boundary conditions of the order parameter of the solvent at the particle surfaces. These remarkable, moreover universal features of the…
We consider depletion effects of a pear-shaped colloidal particle in a hard-sphere solvent, for two different model realisations of the pear-shaped colloidal particle. The two models are the pear hard Gaussian overlap (PHGO) particles and the hard pears of revolution (HPR). The motivation for this study is to provide a microscopic understanding for the substantially different mesoscopic self-assembly properties of these pear-shaped colloids, in dense suspensions, that have been reported in the first part of this series. This is done by determining the differing depletion attraction via MC simu…
Spatial confinement of a near-critical medium changes its fluctuation spectrum and modifies the corresponding order parameter distribution. These effects result in effective, so-called critical Casimir forces (CCFs) acting on the confining surfaces. These forces are attractive for like boundary conditions of the order parameter at the opposing surfaces of the confinement. For colloidal particles dissolved in a binary liquid mixture acting as a solvent close to its critical point of demixing, one thus expects the emergence of phase segregation into equilibrium colloidal liquid and gas phases. W…
We report a numerical investigation of two colloids immersed in a critical solvent, with the aim of quantifying the effective colloid-colloid interaction potential. By turning on an attraction between the colloid and the solvent particles we follow the evolution from the case in which the solvent density close to the colloids changes from values smaller than the bulk to values larger than the bulk. We thus effectively implement the so-called $(+,+)$ and $(-,-)$ boundary conditions defined in field theoretical approaches focused on the description of critical Casimir forces. We find that the ef…
We study an attractive version of the East model using the real-space renormalization group (RG) introduced by Stella et al. The former is a kinetically constrained model with an Ising-like interaction between excitations, and shows striking agreement with the phenomonology of attractive colloidal systems. We find that the RG predicts two nonuniversal dynamic exponents, which suggests that in the out-of-equilibrium regime the model coarsens via a two-stage mechanism. We explain this mechanism physically, and verify this prediction numerically. In addition, we find that the characteristic relax…
We calculate the ion and composition distributions around colloid particles in an aqueous mixture, accounting for preferential adsorption, electrostatic interaction, selective solvation among ions and polar molecules, and composition-dependent ionization. On the colloid surface, we predict a precipitation transition induced by strong preference of hydrophilic ions to water and a prewetting transition between weak and strong adsorption and ionization. These transition lines extend far from the solvent coexistence curve in the plane of the interaction parameter χ(or the temperature) and the aver…
We report a study of the structure of droplets of colloidal gels containing dissolved sodium chloride. The components segregate and form intricate patterns. The salt crystalizes in fractal and multi-fractal dendritic forms which are determined by the material which forms the colloidal gel. Here potato starch, gelatine and carboxymethyl cellulose have been used. The substrate also plays a role in some cases. Photographs and micrographs at different level of magnification are shown.
As first explained by the classic Asakura-Oosawa (AO) model, effective attractive forces between colloidal particles induced by depletion of nonadsorbing polymers can drive demixing of colloid-polymer mixtures into colloid-rich and colloid-poor phases, with practical relevance for purification of water, stability of foods and pharmaceuticals, and macromolecular crowding in biological cells. By idealizing polymer coils as effective penetrable spheres, the AO model qualitatively captures the influence of polymer depletion on thermodynamic phase behavior of colloidal suspensions. In previous work…
The liquid-liquid phase separation of a binary solvent can be arrested by colloidal particles trapped at the interface [K. Stratford et al., Science 309, 5744 (2005)]. We show experimentally that the colloidal network so formed can remain stable after fully remixing the liquids, creating a new type of gel in which colloids in a single-phase solvent have locally planar coordination. We argue that this structure is likely maintained by primary-minimum DLVO bonding of our charged colloids, created under strong compression by capillary forces. We present simulation evidence that the combination of…
A coarse-graining strategy, previously developed for polymer solutions, is extended here to mixtures of linear polymers and hard-sphere colloids. In this approach groups of monomers are mapped onto a single pseudoatom (a blob) and the effective blob-blob interactions are obtained by requiring the model to reproduce some large-scale structural properties in the zero-density limit. We show that an accurate parametrization of the polymer-colloid interactions is obtained by simply introducing pair potentials between blobs and colloids. For the coarse-grained model in which polymers are modelled as…
The surface tension, the adsorption, and the depletion thickness of polymers close to a single nonadsorbing colloidal sphere are computed by means of Monte Carlo simulations. We consider polymers under good-solvent conditions and in the thermal crossover region between good-solvent and $θ$ behavior. In the dilute regime we consider a wide range of values of $q$, from $q = 0$ (planar surface) up to $q\approx 30$-50, while in the semidilute regime, for $ρ_p/ρ_p^*\le 4$ ($ρ_p$ is the polymer concentration and $ρ_p^*$ is its value at overlap), we only consider $q = 0,0.5,1$ and 2. The results are …
We analyze the depletion interaction between two hard colloids in a hard--sphere solvent and pay special attention to the limit of large size ratio between colloids and solvent particles which is governed by the well--known Derjaguin approximation. For separations between the colloids of less than the diameter of the solvent particles (defining the depletion region), the solvent structure between the colloids can be analyzed in terms of an effective two--dimensional gas. Thereby we find that the Derjaguin limit is approached more slowly than previously thought. This analysis is in good agreeme…
We study theoretically and experimentally the solvent-mediated critical Casimir force acting on colloidal particles immersed in a binary liquid mixture of water and 2,6-lutidine and close to substrates which are chemically patterned with periodically alternating stripes of antagonistic adsorption preferences. These patterns are experimentally realized via microcontact printing. Upon approaching the critical demixing point of the solvent, normal and lateral critical Casimir forces generate laterally confining effective potentials for the colloids. We analyze in detail the rich behavior of the s…
The interactions between nanoparticles and solvents play a critical role in the formation of complex, metastable nanostructures. However, direct observation of such interactions with high spatial and temporal resolution is challenging with conventional liquid-cell transmission electron microscopy (TEM) experiments. Here, a windowless system consisting of polymer nanoreactors deposited via scanning probe block copolymer lithography (SPBCL) on an amorphous carbon film is used to investigate the coarsening of ultrafine (1-3 nm) Au-Pt bimetallic nanoparticles as a function of solvent evaporation. …
The growing interest in the dynamical properties of colloidal suspensions, both in equilibrium and under an external drive such as shear or pressure flow, requires the development of accurate methods to correctly include hydrodynamic effects due to the suspension in a solvent. In the present work, we generalize Multi-Particle Collision Dynamics (MPCD) to be able to deal with soft, polymeric colloids. Our methods build on the knowledge of the monomer density profile that can be obtained from monomer-resolved simulations without hydrodynamics or from theoretical arguments. We hereby propose two …
A general class of nonadditive sticky-hard-sphere binary mixtures, where small and large spheres represent the solvent and the solute, respectively, is introduced. The solute-solute and solvent-solvent interactions are of hard-sphere type, while the solute-solvent interactions are of sticky-hard-sphere type with tunable degrees of size nonadditivity and stickiness. Two particular and complementary limits are studied using analytical and semi-analytical tools. The first case is characterized by zero nonadditivity, lending itself to a Percus-Yevick approximate solution from which the impact of s…
The physical behaviour of anisotropic charged colloids is determined by their material dielectric anisotropy, affecting colloidal self-assembly, biological function and even out-of-equilibrium behaviour. However, little is known about anisotropic electrostatic screening, which underlies all electrostatic effective interactions in such soft or biological materials. In this work, we demonstrate anisotropic electrostatic screening for charged colloidal particles in a nematic electrolyte. We show that material anisotropy behaves markedly different from particle anisotropy: The electrostatic potent…
We show how to coarse grain polymers in a good solvent as single particles, interacting with density-independent or density-dependent interactions. These interactions can be between the centres of mass, the mid-points or end-points of the polymers. We also show how to extend these methods to polymers in poor solvents and mixtures of polymers. Treating polymers as soft colloids can greatly speed up the simulation of complex many-polymer systems, including polymer-colloid mixtures.
The RMPCDMD software package performs hybrid Molecular Dynamics simulations, coupling Multiparticle Collision Dynamics to model the solvent and Molecular Dynamics to model suspended colloids, including hydrodynamics, thermal fluctuations, and chemically active solvent particles and catalytic colloids. The main usage of RMPCDMD is the simulation of chemically powered nanomotors, but other setups are considered: colloids in the presence of a thermal gradients or forced flows. RMPCDMD is developed in Fortran 2008 with OpenMP for multithreaded operation and uses the HDF5-based H5MD file format for…
Anisotropic particles oriented in a specific direction can act as artificial atoms and molecules, and their controlled assembly can result in a wide variety of ordered structures. Towards this, we demonstrate the orientation transitions of uncharged peanut-shaped polystyrene colloids, suspended in a non-ionic aprotic polar solvent, near a flat surface whose potential is static or time-varying. The charged surface is coated with an insulating dielectric layer to suppress electric currents. The transition between several orientation states such as random, normal or parallel orientation with resp…
The density profile and surface tension for the interface of phase-separated colloid-polymer mixtures have been studied in the framework of the square gradient approximation for both ideal and interacting polymers in good solvent. The calculations show that in the presence of polymer-polymer excluded volume interactions the interfaces have lower widths and surface tensions compared to the case of ideal polymers. These results are a direct consequence of the shorter range and smaller depth of the depletion potential between colloidal particles induced by interacting polymers.
A mixture of solvent particles with short-range, directional interactions and solute particles with short-range, isotropic interactions that can bond multiple times is of fundamental interest in understanding liquids and colloidal mixtures. Because of multi-body correlations predicting the structure and thermodynamics of such systems remains a challenge. Earlier Marshall and Chapman developed a theory wherein association effects due to interactions multiply the partition function for clustering of particles in a reference hard-sphere system. The multi-body effects are incorporated in the clust…
Thermoresponsive microgels are polymeric colloidal networks that can change their size in response to a temperature variation. This peculiar feature is driven by the nature of the solvent-polymer interactions, which triggers the so-called volume phase transition from a swollen to a collapsed state above a characteristic temperature. Recently, an advanced modelling protocol to assemble realistic, disordered microgels has been shown to reproduce experimental swelling behavior and form factors. In the original framework, the solvent was taken into account in an implicit way, condensing solvent-po…
We study the Brownian dynamics of flexible and semiflexible polymer chains densely grafted on a flat substrate, upon rapid quenching of the system when the quality of solvent becomes poor and chains attempt collapse into a globular state. The collapse process of such a polymer brush differs from individual chains, both in its kinetics and its structural morphology. We find that the resulting collapsed brush does not form a homogeneous dense layer, in spite of all chain monomers equally attracting each other via a model Lennard-Jones potential. Instead, a very distinct inhomogeneous density dis…
We focus on understanding the influence of the two-component coupling in ferronematics, a colloidal suspension of magnetic nanoparticles in nematic liquid crystals. Using coarse-grained Landau-de Gennes free energies, we study the ordering dynamics of this complex fluid and present a range of analytical and numerical results. Our main observations are: (i) slaved coarsening for quench temperatures $T$ intermediate to the critical temperatures of the uncoupled components, (ii) slower growth similar to the Lifshitz-Slyozov law ($L \sim t^{1/3}$) for symmetric magneto-nematic coupling, (iii) sub-…
The association of ions in electrolyte solutions at very low concentration and low temperature is studied using computer simulations and quasi-chemical ion-pairing theory. The specific case of the restricted primitive model (charged hard spheres) is considered. Specialised simulation techniques are employed that lead to efficient sampling of the arrangements and distributions of clusters and free ions, even at conditions corresponding to nanomolar solutions of simple salts in solvents with dielectric constants in the range 5-10, as used in recent experimental work on charged-colloid sus- pensi…
Many low-density nanoparticles show a radial inner structure. This work proposes a novel approach to contrast variation with SAXS based on the constitution of a solvent density gradient in a glass capillary in order to resolve this internal morphology. Scattering curves of a polymeric core-shell colloid were recorded at different suspending medium contrasts at the four-crystal monochromator beamline of PTB at the synchrotron radiation facility BESSY II. The mean size and size distribution of the particles as well as an insight into the colloid electron density composition were determined using…
We combine experiments, theory, and simulations to investigate the coexistence of nonequilibrium phases emerging from interacting colloidal particles that are electrokinetically propelled in a nematic liquid crystal solvent. We directly determine the mechanical pressure within the radial assemblies and measure a non-equilibrium equation of state for this athermal driven system. A generic model combines phoretic propulsion with the interplay between electrostatic effects and liquid-crystal-mediated hydrodynamics, which are effectively cast into a long-range interparticle repulsion, while elasti…
A method for measuring the pair interaction potential between colloidal particles by extrapolation measurement of collective structure to infinite dilution is presented and explored using simulation and experiment. The method is particularly well suited to systems in which the colloid is fluorescent and refractive index matched with the solvent. The method involves characterizing the potential of mean force between colloidal particles in suspension by measurement of the radial distribution function using 3D direct visualization. The potentials of mean force are extrapolated to infinite dilutio…
Most available theoretical predictions for the self-diffusiophoretic motion of colloidal particles are based on the hydrodynamic thin boundary layer approximation in combination with a solvent body force due to a self-generated local solute gradient. This gradient is enforced through specifying boundary conditions, typically without accounting for the thermodynamic cost to maintain the gradient. Here we present an alternative thermodynamic approach that exploits a direct link between dynamics and entropy production: the local detailed balance condition. We study two cases: First, we revisit se…
We examine the translation and rotation of an uncharged spheroidal colloid in polar solvents (water) near a charged flat surface. We solve the nonlinear Poisson-Boltzmann equation outside of the colloid in two dimensions for all tilt angles $θ$ with respect to the surface normal. The colloid's size is assumed to be comparable to the Debye's length and hence field gradients are essential. The Maxwell stress tensor, including the ideal gas pressure of ions, is integrated over the colloid's surface to give the total force and torque on the colloid. From the torque we calculate the effective angul…
The ion distribution around charged colloids in solution has been investigated intensely during the last decade. However, few theoretical approaches have included the influence of variation in the dielectric permittivity within the system, let alone in the surrounding solvent. In this article, we introduce two relatively new methods that can solve the Poisson equation for systems with varying permittivity. The harmonic interpolation method (HIM) approximately solves the Green's function in terms of a spherical harmonics series, and thus provides analytical ion-ion potentials for the Hamiltonia…
Solvent evaporation in soft matter solutions (solutions of colloidal particles, polymers and their mixtures) is an important process in material making and in printing and coating industries. The solvent evaporation process determines the structure of the materials, and strongly affects their performance. Solvent evaporation involves many physico-chemical processes: flow, diffusion, crystallization, gelation, glass transition, etc., and is quite complex. In this article, we report recent progresses in this important process, with a special focus on theoretical and simulation studies.
We report simulations of a spherical Janus particle undergoing exothermic surface reactions around one pole only. Our model excludes self-phoretic transport by design. Nevertheless, net motion occurs from direct momentum transfer between solvent and colloid, with speed scaling as the square root of the energy released during the reaction. We find that such propulsion is dominated by the system's short-time response, when neither the time dependence of the flow around the colloid nor the solvent compressibility can be ignored. Our simulations agree reasonably well with previous experiments.
We present a theory to predict the structure and thermodynamics of mixtures of colloids of different diameters, building on our earlier work [J. Chem. Phys. 145, 074904 (2016)] that considered mixtures with all particles constrained to have the same size. The patchy, solvent particles have short-range directional interactions, while the solute particles have short-range isotropic interactions. The hard-sphere mixture without any association site forms the reference fluid. An important ingredient within the multi-body association theory is the description of clustering of the reference solvent …
In soft and condensed matter physics, effective interactions often emerge as a result of the spatial confinement of a fluctuating field. For instance, microscopic particles in a binary liquid mixture are subject to critical Casimir forces whenever their surfaces confine the thermal fluctuations of the order parameter of this kind of solvent, the range of which diverges upon approaching the critical demixing point. Critical Casimir forces are predicted to be nonadditive on a particular large scale. However, a direct experimental evidence of this fact is still lacking. Here, we fill in this gap …
In its original formulation, the seminal Deryaguin-Landau-Verwey-Overbeek (DLVO) theory of colloidal stability seemed like a simple but realistic description of the world of colloid interactions in electrolyte solutions. It is based on a straightforward superposition of the mean-field Poisson-Boltzmann (PB) electrostatics with the electrodynamic van der Waals (vdW) interactions driven by thermal and quantum fluctuations. However, subsequent developments continued to reveal a much richer and deeper structure of fundamental interactions on the nano- and micro-scale: the granularity and structure…
