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## Phase Diagrams of Binary Mixtures of Oppositely Charged Colloids

Bier, Markus; van Roij, Rene; Dijkstra, Marjolein
Tipo: Artigo de Revista Científica
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491.9877%
Phase diagrams of binary mixtures of oppositely charged colloids are calculated theoretically. The proposed mean-field-like formalism interpolates between the limits of a hard-sphere system at high temperatures and the colloidal crystals which minimize Madelung-like energy sums at low temperatures. Comparison with computer simulations of an equimolar mixture of oppositely charged, equally sized spheres indicate semi-quantitative accuracy of the proposed formalism. We calculate global phase diagrams of binary mixtures of equally sized spheres with opposite charges and equal charge magnitude in terms of temperature, pressure, and composition. The influence of the screening of the Coulomb interaction upon the topology of the phase diagram is discussed. Insight into the topology of the global phase diagram as a function of the system parameters leads to predictions on the preparation conditions for specific binary colloidal crystals.; Comment: Submitted

## Comment to "Multipolar expansion of the electrostatic interaction between charged colloids at interfaces"

Ng, Tai-Kai; Zhou, Yi
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
499.25637%
We present a comment to a recent paper by Dominguez et. al. They claimed that the electrostatic interaction between charged colloids trapped at an interface formed by a dielectric and a screening phase is always isotropic to order $d^-3$. Base on this result, they claimed that in-plane dipolar attraction of order $d^-3$ between colloids cannot exist, in contrast to previous proposals. We point out that their analysis is not completed and anisotropic (dipolar) interaction between colloids can exist up to order $d^-3$.

## Comment on "Long-range electrostatic interactions between like-charged colloids: Steric and confinement effects"

Mateescu, Eduard M.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
487.0831%
In a recent study [Phys. Rev. E 60, 6530 (1999)], Trizac and Raimbault showed that the effective pair interaction between like charged colloids immersed in a cylindrically confined electrolyte remains repulsive even when the size of the micro-ions or the finite longitudinal extension of the confining cylinder are taken into account. Contrary to their claim, we argue that the case of finite longitudinal confinement doesn't always generate repulsive interactions and to illustrate this point we also provide a simple example.; Comment: 3 pages, 1 figure. Accepted for publication in Phys. Rev. E 2001

## Charged colloids at low ionic strength: macro- or microphase separation?

Warren, Patrick B.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
491.9877%
Phase separation in charged systems may involve the replacement of critical points by microphase separated states, or charge-density-wave states. A density functional theory for highly charged colloids at low ionic strength is developed to examine this possibility. It is found that the lower critical solution point is most susceptible to microphase separation. Moreover the tendency can be quantified, and related to the importance of small ion entropy in suppressing phase separation at low added salt. The theory also gives insights into the colloid structure factor in these systems.; Comment: 4 pages, 3 figures, ReVTeX3.1

## Pickering emulsions stabilized by oppositely charged colloids: stability and pattern formation

Pushpam, Sam David Christdoss; Basavaraj, Madivala G.; Mani, Ethayaraja
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
510.70047%
Binary mixture of oppositely charged of colloids can be used to stabilize water-in-oil or oil-in-water emulsions. A Monte Carlo simulation study to address the effect of charge ratio of colloids on the stability of Pickering emulsions is presented. The colloidal particles at the interface are modeled as aligned dipolar hard spheres, with attractive interactions between unlike-charged and repulsive interaction between like-charged particles. The optimum composition (fraction of positively charged particles) required for the stabilization corresponds to a minimum in the interaction energy per particle. In addition, for each charge ratio, there is a range of compositions where emulsions can be stabilized. The structural arrangement of particles or the pattern formation at the emulsion interface is strongly influenced by the charge ratio. We find well-mixed isotropic, square and hexagonal arrangement of particles on emulsion surface for different compositions at a given charge ratio. Distribution of coordination numbers is calculated to characterize structural features. The simulation study is useful for rational design of Pickering emulsifications wherein oppositely charged colloids are used, and for the control of pattern formation that can be useful for the synthesis of colloidosomes and porous-shells derived from thereof.; Comment: 7 pages...

## Volume terms for charged colloids: a grand-canonical treatment

Zoetekouw, Bas; van Roij, Rene
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
499.25637%
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 which 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.; Comment: 16 pages, 6 figures, published in Phys.Rev.E

## Phase diagram of aggregation of oppositely charged colloids in salty water

Zhang, R.; Shklovskii, B. I.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
512.36527%
Aggregation of two oppositely charged colloids in salty water is studied. We focus on the role of Coulomb interaction in strongly asymmetric systems in which the charge and size of one colloid is much larger than the other one. In the solution, each large colloid (macroion) attracts certain number of oppositely charged small colloids ($Z$-ion) to form a complex. If the concentration ratio of the two colloids is such that complexes are not strongly charged, they condense in a macroscopic aggregate. As a result, the phase diagram in a plane of concentrations of two colloids consists of an aggregation domain sandwiched between two domains of stable solutions of complexes. The aggregation domain has a central part of total aggregation and two wings corresponding to partial aggregation. A quantitative theory of the phase diagram in the presence of monovalent salt is developed. It is shown that as the Debye-H\"{u}ckel screening radius $r_s$ decreases, the aggregation domain grows, but the relative size of the partial aggregation domains becomes much smaller. As an important application of the theory, we consider solutions of long double-helix DNA with strongly charged positive spheres (artificial chromatin). We also consider implications of our theory for in vitro experiments with the natural chromatin. Finally...

## Sedimentation of binary mixtures of like- and oppositely charged colloids: the primitive model or effective pair potentials?

Dijkstra, M.; Zwanikken, J.; van Roij, R.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
512.58953%
We study sedimentation equilibrium of low-salt suspensions of binary mixtures of charged colloids, both by Monte Carlo simulations of an effective colloids-only system and by Poisson-Boltzmann theory of a colloid-ion mixture. We show that the theoretically predicted lifting and layering effect, which involves the entropy of the screening ions and a spontaneous macroscopic electric field [J. Zwanikken and R. van Roij, Europhys. Lett. {\bf 71}, 480 (2005)], can also be understood on the basis of an effective colloid-only system with pairwise screened-Coulomb interactions. We consider, by theory and by simulation, both repelling like-charged colloids and attracting oppositely charged colloids, and we find a re-entrant lifting and layering phenomenon when the charge ratio of the colloids varies from large positive through zero to large negative values.

## Nonlinear Screening and Effective Interactions in Charged Colloids

Denton, A. R.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
491.9877%
Influences of nonlinear screening on effective interactions between spherical macroions in charged colloids are described via response theory. Nonlinear screening, in addition to generating effective many-body interactions, is shown to entail essential corrections to the pair potential and one-body volume energy. Numerical results demonstrate that nonlinear effects can substantially modify effective interactions and thermodynamics of aqueous, low-salt suspensions of highly-charged macroions.; Comment: 4 pages, 4 figures

## Extended sedimentation profiles in charged colloids: the gravitational length, entropy, and electrostatics

Royall, C. P.; van Roij, R.; van Blaaderen, A.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
499.25637%
We have measured equilibrium sedimentation profiles in a colloidal model system with confocal microscopy. By tuning the interactions, we have determined the gravitational length in the limit of hard-sphere-like interactions, and using the same particles, tested a recent theory [R.van Roij, J. Phys. Cond. Mat. 15, S3569, (2003)], which predicts a significantly extended sedimentation profile in the case of charged colloids with long-ranged repulsions, due to a spontaneously formed macroscopic electric field. For the hard-sphere-like system we find that the gravitational length matches that expected. By tuning the buoyancy of the colloidal particles we have shown that a mean field hydrostatic equilibrium description even appears to hold in the case that the colloid volume fraction changes significantly on the length scale of the particle size. The extended sedimentation profiles of the colloids with long-ranged repulsions are well-described by theory. Surprisingly, the theory even seems to hold at concentrations where interactions between the colloids, which are not modeled explicitly, play a considerable role.

## Collective thermoelectrophoresis of charged colloids

Majee, Arghya; Würger, Alois
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
495.0059%
Thermally driven colloidal transport is, to a large extent, due to the thermoelectric or Seebeck effect of the charged solution.We show that, contrary to the generally adopted single-particle picture, the transport coefficient depends on the colloidal concentration. For solutions that are dilute in the hydrodynamic sense, collective effects may significantly affect the thermophoretic mobility. Our results provide an explanation for recent experimental observations on polyelectrolytes and charged particles and suggest that for charged colloids collective behavior is the rule rather than the exception.

## Charge and Salt Driven Reentrant Order-Disorder and Gas-Solid Transitions in Charged Colloids

Mohanty, P. S.; Tata, B. V. R.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
495.0059%
Monte Carlo simulations have been performed for aqueous charged colloidal suspensions as a function of charge density on the particles and salt concentration. We vary the charge density in our simulations over a range where a reentrant solid-liquid transition in suspensions of silica and polymer latex particles has been reported by Yamanaka et al. [Phys. Rev. Lett. 80 5806 (1998)]. We show that at low ionic strengths a homogeneous liquid-like ordered suspension undergoes crystallization upon increasing charge density . Further increase in charge density resulted once again a disordered state which is in agreement with experimental observations. In addition to this reentrant order-disorder transition, we observe an inhomogeneous to homogeneous transition in our simulations when salt is added to the disordered inhomogeneous state. This inhomogeneous to homogeneous disordered transition is analogous to the solid-gas transition of atomic systems and has not yet been observed in charged colloids. The reported experimental observations on charged colloidal suspensions are discussed in the light of present simulation results.; Comment: 8 pages, 6 figures(in PS format) submitted to Physical Review E

## Simulation of Electric Double Layers around Charged Colloids in Aqueous Solution of Variable Permittivity

Fahrenberger, Florian; Xu, Zhenli; Holm, Christian
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
491.9877%
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 Hamiltonian of charged systems. The Maxwell Equations Molecular Dynamics (MEMD) algorithm features a local approach to electrostatics, allowing for arbitrary local changes of the dielectric constant. We show that the results of both methods are in very good agreement. We also found that the renormalized charge of the colloid, and with it the effective far field interaction, significantly changes if the dielectric properties within the vicinity of the colloid are changed.

## Multipolar expansion of the electrostatic interaction between charged colloids at interfaces

Dominguez, A.; Frydel, D.; Oettel, M.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
491.9877%
The general form of the electrostatic potential around an arbitrarily charged colloid at an interface between a dielectric and a screening phase (such as air and water, respectively) is analyzed in terms of a multipole expansion. The leading term is isotropic in the interfacial plane and varies with $d^{-3}$ where $d$ is the in--plane distance from the colloid. The electrostatic interaction potential between two arbitrarily charged colloids is likewise isotropic and $\propto d^{-3}$, corresponding to the dipole--dipole interaction first found for point charges at water interfaces. Anisotropic interaction terms arise only for higher powers $d^{-n}$ with $n \ge 4$.; Comment: 6 pages, mathematical details added

## A Lattice-Boltzmann method for the simulation of transport phenomena in charged colloids

Horbach, Juergen; Frenkel, Daan
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
495.0059%
We present a new simulation scheme based on the Lattice-Boltzmann method to simulate the dynamics of charged colloids in an electrolyte. In our model we describe the electrostatics on the level of a Poisson-Boltzmann equation and the hydrodynamics of the fluid by the linearized Navier-Stokes equations. We verify our simulation scheme by means of a Chapman-Enskog expansion. Our method is applied to the calculation of the reduced sedimentation velocity U/U_0 for a cubic array of charged spheres in an electrolyte. We show that we recover the analytical solution first derived by Booth (F. Booth, J. Chem. Phys. 22, 1956 (1954)) for a weakly charged, isolated sphere in an unbounded electrolyte. The present method makes it possible to go beyond the Booth theory, and we discuss the dependence of the sedimentation velocity on the charge of the spheres. Finally we compare our results to experimental data.; Comment: 18 pages, 5 figures, to appear in Phys. Rev. E

## Two-stage crystallization of charged colloids at low supersaturations

Kratzer, Kai; Arnold, Axel
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
494.61895%
We report simulations on the homogeneous liquid-fcc nucleation of charged colloids for both low and high contact energy values. As a precursor for crystal formation, we observe increased local order at the position where the crystal will form, but no correlations with the local density. Thus, the nucleation is driven by order fluctuations rather than density fluctuations. Our results also show that the transition involves two stages in both cases, first a transition liquid-bcc, followed by a bcc-hcp/fcc transition. Both transitions have to overcome free energy barriers, so that a spherical bcc-like cluster is formed first, in which the final fcc-like structure is nucleated mainly at the surface of the crystallite. This means that the bcc-fcc phase transition is a heterogeneous nucleation, even though we start from a homogeneous bulk liquid. The height of the bcc-hcp/fcc free energy barrier strongly depends on the contact energies of the colloids. For low contact energy this barrier is low, so that the bcc-hcp/fcc transition happens spontaneously. For the higher contact energy, the second barrier is too high to be crossed spontaneously by the colloidal system. However, it was possible to ratchet the system over the second barrier and to transform the bcc nuclei into the stable hcp/fcc phase. The transitions are dominated by the first liquid-bcc transition and can be described by Classical Nucleation Theory using an effective surface tension.; Comment: 9 pages...

## Effective electrostatic interactions in mixtures of charged colloids

Chung, Jun Kyung; Denton, Alan R.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
511.81695%
We present a theory of effective electrostatic interactions in polydisperse suspensions of charged macroions, generalizing to mixtures a theory previously developed for monodisperse suspensions. Combining linear response theory with a random phase approximation for microion correlations, we coarse-grain the microion degrees of freedom to derive general expressions for effective macroion-macroion pair potentials and a one-body volume energy. For model mixtures of charged hard-sphere colloids, we give explicit analytical expressions. The resulting effective pair potentials have the same general form as predicted by linearized Poisson-Boltzmann theory, but consistently incorporate dependence on macroion density and excluded volume via the Debye screening constant. The volume energy, which depends on the average macroion density, contributes to the free energy and so can influence thermodynamic properties of deionized suspensions. To validate the theory, we compute radial distribution functions of binary mixtures of oppositely charged colloidal macroions from molecular dynamics simulations of the coarse-grained model (with implicit microions), taking effective pair potentials as input. Our results agree closely with corresponding results from more computationally intensive Monte Carlo simulations of the primitive model (with explicit microions). Simulations of a mixture with large size and charge asymmetries indicate that charged nanoparticles can enhance electrostatic screening of charged colloids. The theory presented here lays a foundation for future large-scale modeling of complex mixtures of charged colloids...

## Poisson-Boltzmann cell model for heterogeneously charged colloids

Eggen, Eelco; van Roij, René
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
491.9877%
We introduce the Poisson-Boltzmann cell model for spherical colloidal particles with a heterogeneous surface charge distribution. This model is obtained by generalizing existing cell models for mixtures of homogeneously charged colloidal spheres. Our new model has similar features as Onsager's second-virial theory for liquid crystals, but it predicts no orientational ordering if there is no positional ordering. This implies that all phases of heterogeneously charged colloids that are liquid-like with respect to translational degrees of freedom are also isotropic with respect to particle orientation.; Comment: 9 pages, 3 figures

## Lamellar order, microphase structures and glassy phase in a field theoretic model for charged colloids

Tarzia, Marco; Coniglio, Antonio
Tipo: Artigo de Revista Científica