Melting line of charged colloids from primitive model simulations

Rayleigh-Taylor instability in strongly coupled plasma

Rayleigh–Taylor instability (RTI) is the prominent energy mixing mechanism when heavy fluid lies on top of light fluid under the gravity. In this work, the RTI is studied in strongly coupled plasmas using two-dimensional molecular dynamics simulations. The motivation is to understand the evolution of the instability with the increasing correlation (Coulomb coupling) that happens when the average Coulombic potential energy becomes comparable to the average thermal energy. We report the suppression of the RTI due to a decrease in growth rate with increasing coupling strength. The caging effect is expected a physical mechanism for the growth suppression observed in both the exponential and the quadratic growth regimes. We also report that the increase in shielding due to background charges increases the growth rate of the instability. Moreover, the increase in the Atwood number, an entity to quantify the density gradient, shows the enhancement of the growth of the instability. The dispersion relation obtained from the molecular dynamics simulation of strongly coupled plasma shows a slight growth enhancement compared to the hydrodynamic viscous fluid. The RTI and its eventual impact on turbulent mixing can be significant in energy dumping mechanisms in inertial confinement fusion where, during the compressed phases, the coupling strength approaches unity.

Hunting mermaids in real space: known knowns, known unknowns and unknown unknowns

We review efforts to realise so-called mermaid (or short-ranged attraction/long ranged repulsion) interactions in 3d real space. The repulsive and attractive contributions to these interactions in charged colloids and colloid-polymer mixtures, may be accurately realised, by comparing particle-resolved studies with colloids to computer simulation. However, when we review work where these interactions have been combined, despite early indications of behaviour consistent with predictions, closer analysis reveals that in the non-aqueous systems used for particle-resolved studies, the idea of summing the attractive and repulsive components leads to wild deviations with experiment. We suggest that the origin lies in the weak ion dissociation in these systems with low dielectric constant solvents. Ultimately this leads even to non-centro-symmetric interactions and a new level of complexity in these systems.

Equilibrium fluid-crystal interfacial free energy of bcc-crystallizing aqueous suspensions of polydisperse charged spheres

The interfacial free energy is a central quantity in crystallization from the metastable melt. In suspensions of charged colloidal spheres, nucleation and growth kinetics can be accurately measured from optical experiments. In previous work, from these data effective nonequilibrium values for the interfacial free energy between the emerging bcc nuclei and the adjacent melt in dependence on the chemical potential difference between melt phase and crystal phase were derived using classical nucleation theory (CNT). A strictly linear increase of the interfacial free energy was observed as a function of increased metastability. Here, we further analyze these data for five aqueous suspensions of charged spheres and one binary mixture. We utilize a simple extrapolation scheme and interpret our findings in view of Turnbull's empirical rule. This enables us to present the first systematic experimental estimates for a reduced interfacial free energy, σ(0,bcc), between the bcc-crystal phase and the coexisting equilibrium fluid. Values obtained for σ(0,bcc) are on the order of a few k(B)T. Their values are not correlated to any of the electrostatic interaction parameters but rather show a systematic decrease with increasing size polydispersity and a lower value for the mixture as compared to the pure components. At the same time, σ(0) also shows an approximately linear correlation to the entropy of freezing. The equilibrium interfacial free energy of strictly monodisperse charged spheres may therefore be still greater.

Effective charges and virial pressure of concentrated macroion solutions

The stability of colloidal suspensions is crucial in a wide variety of processes, including the fabrication of photonic materials and scaffolds for biological assemblies. The ionic strength of the electrolyte that suspends charged colloids is widely used to control the physical properties of colloidal suspensions. The extensively used two-body Derjaguin-Landau-Verwey-Overbeek (DLVO) approach allows for a quantitative analysis of the effective electrostatic forces between colloidal particles. DLVO relates the ionic double layers, which enclose the particles, to their effective electrostatic repulsion. Nevertheless, the double layer is distorted at high macroion volume fractions. Therefore, DLVO cannot describe the many-body effects that arise in concentrated suspensions. We show that this problem can be largely resolved by identifying effective point charges for the macroions using cell theory. This extrapolated point charge (EPC) method assigns effective point charges in a consistent way, taking into account the excluded volume of highly charged macroions at any concentration, and thereby naturally accounting for high volume fractions in both salt-free and added-salt conditions. We provide an analytical expression for the effective pair potential and validate the EPC method by comparing molecular dynamics simulations of macroions and monovalent microions that interact via Coulombic potentials to simulations of macroions interacting via the derived EPC effective potential. The simulations reproduce the macroion-macroion spatial correlation and the virial pressure obtained with the EPC model. Our findings provide a route to relate the physical properties such as pressure in systems of screened Coulomb particles to experimental measurements.

Impact of single-particle compressibility on the fluid-solid phase transition for ionic microgel suspensions

We study ionic microgel suspensions composed of swollen particles for various single-particle stiffnesses. We measure the osmotic pressure π of these suspensions and show that it is dominated by the contribution of free ions in solution. As this ionic osmotic pressure depends on the volume fraction of the suspension ϕ, we can determine ϕ from π, even at volume fractions so high that the microgel particles are compressed. We find that the width of the fluid-solid phase coexistence, measured using ϕ, is larger than its hard-sphere value for the stiffer microgels that we study and progressively decreases for softer microgels. For sufficiently soft microgels, the suspensions are fluidlike, irrespective of volume fraction. By calculating the dependence on ϕ of the mean volume of a microgel particle, we show that the behavior of the phase-coexistence width correlates with whether or not the microgel particles are compressed at the volume fractions corresponding to fluid-solid phase coexistence.

Crystallization kinetics of colloidal model suspensions: recent achievements and new perspectives

Colloidal model systems allow studying crystallization kinetics under fairly ideal conditions, with rather well-characterized pair interactions and minimized external influences. In complementary approaches experiment, analytic theory and simulation have been employed to study colloidal solidification in great detail. These studies were based on advanced optical methods, careful system characterization and sophisticated numerical methods. Over the last decade, both the effects of the type, strength and range of the pair-interaction between the colloidal particles and those of the colloid-specific polydispersity have been addressed in a quantitative way. Key parameters of crystallization have been derived and compared to those of metal systems. These systematic investigations significantly contributed to an enhanced understanding of the crystallization processes in general. Further, new fundamental questions have arisen and (partially) been solved over the last decade: including, for example, a two-step nucleation mechanism in homogeneous nucleation, choice of the crystallization pathway, or the subtle interplay of boundary conditions in heterogeneous nucleation. On the other hand, via the application of both gradients and external fields the competition between different nucleation and growth modes can be controlled and the resulting microstructure be influenced. The present review attempts to cover the interesting developments that have occurred since the turn of the millennium and to identify important novel trends, with particular focus on experimental aspects.

Novel kinetic trapping in charged colloidal clusters due to self-induced surface charge organization

Colloidal clusters are an unusual state of matter where tunable interactions enable a sufficient reduction in their degrees of freedom that their energy landscapes can become tractable - they form a playground for statistical mechanics and promise unprecedented control of structure on the submicron lengthscale. We study colloidal clusters in a system where a short-ranged polymer-induced attraction drives clustering, while a weak, long-ranged electrostatic repulsion prevents extensive aggregation. We compare experimental yields of cluster structures with theory which assumes simple addition of competing isotropic interactions between the colloids. Here we show that for clusters of size 4 ≤ m ≤ 7, the yield of minimum energy clusters is much less than expected. We attribute this to an anisotropic self-organized surface charge distribution which leads to unexpected kinetic trapping. We introduce a model for the coupling between counterions and binding sites on the colloid surface with which we interpret our findings.

Poisson-Boltzmann theory of charged colloids: limits of the cell model for salty suspensions

Thermodynamic properties of charge-stabilized colloidal suspensions and polyelectrolyte solutions are commonly modelled by implementing the mean-field Poisson-Boltzmann (PB) theory within a cell model. This approach models a bulk system by a single macroion, together with counterions and salt ions, confined to a symmetrically shaped, electroneutral cell. While easing numerical solution of the nonlinear PB equation, the cell model neglects microion-induced interactions and correlations between macroions, precluding modelling of macroion ordering phenomena. An alternative approach, which avoids the artificial constraints of cell geometry, exploits the mapping of a macroion-microion mixture onto a one-component model of pseudo-macroions governed by effective interparticle interactions. In practice, effective-interaction models are usually based on linear-screening approximations, which can accurately describe strong nonlinear screening only by incorporating an effective (renormalized) macroion charge. Combining charge renormalization and linearized PB theories, in both the cell model and an effective-interaction (cell-free) model, we compute osmotic pressures of highly charged colloids and monovalent microions, in Donnan equilibrium with a salt reservoir, over a range of concentrations. By comparing predictions with primitive model simulation data for salt-free suspensions, and with predictions from nonlinear PB theory for salty suspensions, we chart the limits of both the cell model and linear-screening approximations in modelling bulk thermodynamic properties. Up to moderately strong electrostatic couplings, the cell model proves accurate for predicting osmotic pressures of deionized (counterion-dominated) suspensions. With increasing salt concentration, however, the relative contribution of macroion interactions to the osmotic pressure grows, leading predictions from the cell and effective-interaction models to deviate. No evidence is found for a liquid-vapour phase instability driven by monovalent microions. These results may guide applications of PB theory to colloidal suspensions and other soft materials.

Sedimentation of charged colloids: the primitive model and the effective one-component approach

Sedimentation-diffusion equilibrium density profiles of suspensions of charge-stabilized colloids are calculated theoretically and by Monte Carlo (MC) simulations, both for a one-component model of colloidal particles interacting through pairwise screened-Coulomb repulsions and for a three-component model of colloids, cations, and anions with unscreened-Coulomb interactions. We focus on a state point for which experimental measurements are available [C. P. Royall, J. Phys.: Condens Matter 17, 2315 (2005)]. Despite the apparently different picture that emerges from the one- and three-component models (repelling colloids pushing each other to high altitude in the former, versus a self-generated electric field that pushes the colloids up in the latter), we find similar colloidal density profiles for both models from theory as well as simulation, thereby suggesting that these pictures represent different viewpoints of the same phenomenon. The sedimentation profiles obtained from an effective one-component model by MC simulations and theory, together with MC simulations of the multicomponent primitive model are consistent among themselves, but differ quantitatively from the results of a theoretical multicomponent description at the Poisson-Boltzmann level. We find that for small and moderate colloid charge the Poisson-Boltzmann theory gives profiles in excellent agreement with the effective one-component theory if a smaller effective charge is used. We attribute this discrepancy to the poor treatment of correlations in the Poisson-Boltzmann theory.

Nonlinear screening and gas-liquid separation in suspensions of charged colloids

We calculate phase diagrams of charged colloidal spheres (valency Z and radius a) in a 1:1 electrolyte from multicentered nonlinear Poisson-Boltzmann theory. Our theory takes into account charge renormalization of the colloidal interactions and volume terms due to many-body effects. For valencies as small as Z = 1 and as large as 10(4) we find a gas-liquid spinodal instability in the colloid-salt phase diagram provided Z lambdaB/a > or similar 24+/-1, where lambdaB is the Bjerrum length.

Gas-liquid phase separation in oppositely charged colloids: Stability and interfacial tension

We study the phase behavior and the interfacial tension of the screened Coulomb (Yukawa) restricted primitive model (YRPM) of oppositely charged hard spheres with diameter sigma using Monte Carlo simulations. We determine the gas-liquid and gas-solid phase transitions using free energy calculations and grand-canonical Monte Carlo simulations for varying inverse Debye screening length kappa. We find that the gas-liquid phase separation is stable for kappasigma<or=4, and that the critical temperature decreases upon increasing the screening of the interaction (decreasing the range of the interaction). In addition, we determine the gas-liquid interfacial tension using grand-canonical Monte Carlo simulations. The interfacial tension decreases upon increasing the range of the interaction. In particular, we find that simple scaling can be used to relate the interfacial tension of the YRPM to that of the restricted primitive model, where particles interact with bare Coulomb interactions.

Layering in sedimentation of suspensions of charged colloids: simulation and theory

We study the equilibrium sediment of a multicomponent system of charged colloids using primitive model Monte Carlo simulations, which include counterions explicitly. We find separation of the different colloidal components into almost pure layers, where colloids with large charge-to-mass ratio sediment higher in the sample. This effect appears due to a competition between ionic entropy, gravitational energy, and electrostatic energy. Our simulations provide a direct confirmation of recent theoretical predictions on the sedimentation of multicomponent mixtures of charged colloids in regimes with relatively low total densities and low colloidal charges. To explore the limitations of the theory we perform simulations at higher total densities for monodisperse and multicomponent systems and at stronger electrostatic couplings by increasing the colloidal charge for monodisperse suspensions. We find good agreement between theory and simulation when the colloidal charge is increased in the monodisperse case. However, we find deviations between simulations and theory upon increasing the total densities in the monodisperse and multicomponent systems. The density profiles obtained from simulations are more homogeneous than those predicted by theory. The spontaneous formation of layered structures predicted by the theory and found by simulation can serve as a useful tool to separate different components from a mixture of charged colloids.

Phase behavior of the lattice restricted primitive model with nearest neighbor exclusion

The global phase behavior of the lattice restricted primitive model with nearest neighbor exclusion has been studied by grand canonical Monte Carlo simulations. The phase diagram is dominated by a fluid (or charge-disordered solid) to charge-ordered solid transition that terminates at the maximum density rho*(max)= sqrt 2 and reduced temperature T* approximately equal to 0.29. At that point, there is a first-order phase transition between two phases of the same density, one charge-ordered, and the other charge-disordered. The liquid-vapor transition for the model is metastable, lying entirely within the fluid-solid phase envelope.

Volume terms for charged colloids: a grand-canonical treatment

We present a study of thermodynamic properties of suspensions of charged colloids on the basis of linear Poisson-Boltzmann theory. We calculate the effective Hamiltonian of the colloids by integrating out the ionic degrees of freedom grand canonically. This procedure not only yields the well-known pairwise screened-Coulomb interaction between the colloids, but also additional volume terms that affect the phase behavior and the thermodynamic properties, such as the osmotic pressure. These calculations are greatly facilitated by the grand-canonical character of our treatment of the ions and allow for relatively fast computations compared to earlier studies in the canonical ensemble. Moreover, the present derivation of the volume terms are relatively simple, make a direct connection with Donnan equilibrium, yield an explicit expression for the effective screening constant, and allow for extensions to include, for instance, nonlinear effects.