In the past decade, classical dynamical density functional theory (DDFT) has been developed and widely applied to the Brownian dynamics of interacting colloidal particles. One of the possible derivation routes of DDFT from the microscopic dynamics is via the Mori-Zwanzig-Forster projection operator technique with slowly varying variables such as the one-particle density. Here, we use the projection operator approach to extend DDFT into various directions: first, we generalize DDFT toward mixtures of $n$ different species of spherical colloidal particles. We show that there are in general nontrivial cross-coupling terms between the concentration fields and specify them explicitly for colloidal mixtures with pairwise hydrodynamic interactions. Secondly, we treat the energy density as an additional slow variable and derive formal expressions for an extended DDFT containing also the energy density. The latter approach can in principle be applied to colloidal dynamics in a nonzero temperature gradient. For the case without hydrodynamic interactions the diffusion tensor is diagonal, while thermodiffusion -- the dissipative cross-coupling term between energy density and concentration -- is nonzero in this limit. With finite hydrodynamic interactions also cross-diffusion coefficients assume a finite value. We demonstrate that our results for the extended DDFT contain the transport coefficients in the hydrodynamic limit (long wavelengths, low frequencies) as a special case.
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 …
Bulk phase separation is responsible for the occurrence of stacks of different layers in sedimentation of colloidal mixtures. A recently proposed theory (de las Heras and Schmidt 2013 Soft Matter 9 8636) establishes a unique connection between the bulk phase behaviour and sedimentation-diffusion-equilibrium. The theory constructs a stacking diagram of all possible sequences of stacks under gravity in the limit of very high (infinite) sample heights. Here, we study the stacking diagrams of colloidal mixtures at finite sample height, h. We demonstrate that h plays a vital role in sedimentation-d…
We study a two-dimensional binary mixture of patchy colloids in sedimentation-diffusion-equilibrium using Monte Carlo simulation and Wertheim's theory. By tuning the buoyant masses of the colloids we can control the gravity-induced sequence of fluid stacks of differing density and percolation properties. We find complex stacking sequences with up to four layers and reentrant network formation, consistently in simulations and theoretically using only the bulk phase diagram as input. Our theory applies to general patchy colloidal mixtures and is relevant to understanding experiments under gravit…
Nonreciprocal effective interaction forces can occur between mesoscopic particles in colloidal suspensions that are driven out of equilibrium. These forces violate Newton's third law actio=reactio on coarse-grained length and time scales. Here we explore the statistical mechanics of Brownian particles with nonreciprocal effective interactions. Our model system is a binary fluid mixture of spherically symmetric, diffusiophoretic mesoscopic particles, and we focus on the time-averaged particle pair- and triplet-correlation functions. Based on the many-body Smoluchowski equation we develop a micr…
The self-assembly of binary nanoparticle superlattices from colloidal mixtures is a promising method for the fabrication of complex colloidal co-crystal structures. However, binary mixtures often form amorphous or metastable phases instead of the thermodynamically stable phase. Here we show that in binary mixtures of differently sized spherical particles, an excess of the smaller component can promote -- and, in some cases, may be necessary for -- the self-assembly of a binary co-crystal. Using computer simulations, we identify two mechanisms responsible for this phenomenon. First, excess smal…
Building structures with hierarchical order through the self-assembly of smaller blocks is not only a prerogative of nature, but also a strategy to design artificial materials with tailored functions. We explore in simulation the spontaneous assembly of colloidal particles into extended structures, using spheres and size-asymmetric dimers as solute particles, while treating the solvent implicitly. Besides rigid cores for all particles, we assume an effective short-range attraction between spheres and small monomers to promote, through elementary rules, dimer-mediated aggregation of spheres. St…
We develop a mesoscopic field theory for the collective nonequilibrium dynamics of multicomponent mixtures of interacting active (i.e., motile) and passive (i.e., nonmotile) colloidal particles with isometric shape in two spatial dimensions. By a stability analysis of the field theory, we obtain equations for the spinodal that describes the onset of a motility-induced instability leading to cluster formation in such mixtures. The prediction for the spinodal is found to be in good agreement with particle-resolved computer simulations. Furthermore, we show that in active-passive mixtures the spi…
We investigate theoretically the effect of gravity on a plate-sphere colloidal mixture by means of an Onsager-like density functional to describe the bulk, and sedimentation path theory to incorporate gravity. We calculate the stacking diagram of the mixture for two sets of buoyant masses and different values of the sample height. Several stacking sequences appear due to the intricate interplay between gravity, the sample height, and bulk phase separation. These include the experimentally observed floating nematic sequence, which consists of a nematic layer sandwiched between two isotropic lay…
In simulations and experiments, we study the drying of films containing mixtures of large and small colloidal particles in water. During drying, the mixture stratifies into a layer of the larger particles at the bottom with a layer of the smaller particles on top. We developed a model to show that a gradient in osmotic pressure, which develops dynamically during drying, is responsible for the segregation mechanism behind stratification.
In an attempt to quantify the role of polydispersity in colloidal suspensions, we present an efficient implementation of the renormalized jellium model for a mixture of spherical charged colloids. The different species may have different size, charge and density. Advantage is taken from the fact that the electric potential pertaining to a given species obeys a Poisson's equation that is species independent; only boundary conditions do change from a species to the next. All species are coupled through the renormalized background (jellium) density, that is determined self-consistently. The corre…
When a liquid film of colloidal solution consisting of particles of different sizes is dried on a substrate, the colloids often stratify, where smaller colloids are laid upon larger colloids. This phenomenon is counter intuitive because larger colloids which have smaller diffusion constant are expected to remain near the surface during the drying process, leaving the layer of larger colloids on top of smaller colloids. Here we show that the phenomenon is caused by the interaction between the colloids, and can be explained by the diffusion model which accounts for the interaction between the co…
Gravity can affect colloidal suspensions since for micrometer-sized particles gravitational and thermal energies can be comparable over vertical length scales of a few millimeters. In mixtures, each species possesses a different buoyant mass, which can make experimental results counter-intuitive and difficult to interpret. Here, we revisit from a theoretical perspective iconic sedimentation-diffusion-equilibrium experiments on colloidal plate-rod mixtures by van der Kooij and Lekkerkerker. We reproduce their findings, including the observation of five different mesophases in a single cuvette. …
We report on the short-time dynamics in colloidal mixtures made up of monomers and dimers highly confined between two glass-plates. At low concentrations, the experimental measurements of colloidal motion agree well with the solution of the Navier-Stokes equation at low Reynolds numbers, which takes into account the increase of the drag force on each particle due to wall-particle hydrodynamic forces. We find that the ratio of the short-time diffusion coefficients of the monomer and that of the center of mass of the dimer remains independent of both the total packing fraction and the dimer mola…
We investigate bridging and aggregation of two colloidal particles in a near-critical binary mixture when the fluid far from the particles is outside the coexistence (CX) curve and is rich in the component disfavored by the colloid surfaces. In such situations, the adsorption-induced interaction is enhanced, leading to bridging and aggregation of the particles. We realize bridging firstly by changing the temperature with a fixed interparticle separation and secondly by letting the two particles aggregate. The interparticle attractive force dramatically increases upon bridging. The dynamics is …
We give a full account of a recently proposed theory that explicitly relates the bulk phase diagram of a binary colloidal mixture to its phase stacking phenomenology under gravity [Soft Matter 9, 8636 (2013)]. As we demonstrate, the full set of possible phase stacking sequences in sedimentation-diffusion equilibrium originates from straight lines (sedimentation paths) in the chemical potential representation of the bulk phase diagram. From the analysis of various standard topologies of bulk phase diagrams, we conclude that the corresponding sedimentation stacking diagrams can be very rich, eve…
We numerically and experimentally study the segregation dynamics in a binary mixture of microswimmers which move on a two-dimensional substrate in a static periodic triangular-like light intensity field. The motility of the active particles is proportional to the imposed light intensity and they possess a motility contrast, i.e., the prefactor depends on the species. In addition, the active particles also experience a torque aligning their motion towards the direction of the negative intensity gradient. We find a segregation of active particles near the intensity minima where typically one spe…
Binary colloidal mixtures in near-critical binary solvents
Institute of Physical Chemistry, Polish Academy of Sciences（波兰科学院物理化学研究所）；H. H. Wills Physics Laboratory, University of Bristol（布里斯托大学H.H.威尔斯物理实验室）；Max-Planck-Institut für Intelligente Systeme（马克斯·普朗克智能系统研究所）
The addition of co-solutes to colloidal suspensions is often employed to induce tunable depletion interactions. In this work we investigate effective colloidal interactions arising from binary co-solute mixtures of hard spheres and patchy particles. By changing the relative concentration of the two species, we show that the resulting effective potential $V_\text{eff}$ continuously changes from the one obtained for a single-component hard sphere co-solute to that mediated by the single-component patchy particle co-solute. Interestingly, we find that, independently of the relative concentration …
We report results from the molecular dynamics simulations of a binary colloidal mixture subjected to an external potential barrier along one of the spatial directions at low volume fraction, ϕ = 0.2. The variations in the asymmetry of the external potential barrier do not change the dynamics of the smaller particles, showing Arrhenius diffusion. However, the dynamics of the larger particles shows a crossover from sub-Arrhenius to super-Arrhenius diffusion with the asymmetry in the external potential at the low temperatures and low volume fraction. Super-Arrhenius diffusion is generally observe…
Sedimentation of a two-dimensional colloidal mixture exhibiting liquid-liquid and gas-liquid phase separation: a dynamical density functional theory study
We investigate the structure of a dilute mixture of amphiphilic dimers and spherical particles, a model relevant to the problem of encapsulating globular "guest" molecules in a dispersion. Dimers and spheres are taken to be hard particles, with an additional attraction between spheres and the smaller monomers in a dimer. Using Monte Carlo simulation, we document the low-temperature formation of aggregates of guests (clusters) held together by dimers, whose typical size and shape depend on the guest concentration $χ$. For low $χ$ (less than $10\%$), most guests are isolated and coated with a la…
