Equation of state of charged colloidal suspensions and its dependence on the thermodynamic route

The thermodynamic properties of highly charged colloidal suspensions in contact with a salt reservoir are investigated in the framework of the Renormalized Jellium Model (RJM). It is found that the equation of state is very sensitive to the particular thermodynamic route used to obtain it. Specifically, the osmotic pressure calculated within the RJM using the contact value theorem can be very different from the pressure calculated using the Kirkwood-Buff fluctuation relations. On the other hand, Monte Carlo (MC) simulations show that both the effective pair potentials and the correlation functions are accurately predicted by the RJM. It is suggested that the lack of self-consistency in the thermodynamics of the RJM is a result of neglected electrostatic correlations between the counterions and coions

Mixtures of Charged Colloid and Neutral Polymer: Influence of Electrostatic Interactions on Demixing and Interfacial Tension

The equilibrium phase behavior of a binary mixture of charged colloids and neutral, non-adsorbing polymers is studied within free-volume theory. A model mixture of charged hard-sphere macroions and ideal, coarse-grained, effective-sphere polymers is mapped first onto a binary hard-sphere mixture with non-additive diameters and then onto an effective Asakura-Oosawa model [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)]. The effective model is defined by a single dimensionless parameter -- the ratio of the polymer diameter to the effective colloid diameter. For high salt-to-counterion concentration ratios, a free-volume approximation for the free energy is used to compute the fluid phase diagram, which describes demixing into colloid-rich (liquid) and colloid-poor (vapor) phases. Increasing the range of electrostatic interactions shifts the demixing binodal toward higher polymer concentration, stabilizing the mixture. The enhanced stability is attributed to a weakening of polymer depletion-induced attraction between electrostatically repelling macroions. Comparison with predictions of density-functional theory reveals a corresponding increase in the liquid-vapor interfacial tension. The predicted trends in phase stability are consistent with observed behavior of protein-polysaccharide mixtures in food colloids.Comment: 16 pages, 5 figure

Charge Renormalization, Effective Interactions, and Thermodynamics of Deionized Colloidal Suspensions

Thermodynamic properties of charge-stabilised colloidal suspensions depend sensitively on the effective charge of the macroions, which can be substantially lower than the bare charge in the case of strong counterion-macroion association. A theory of charge renormalization is proposed, combining an effective one-component model of charged colloids with a thermal criterion for distinguishing between free and associated counterions. The theory predicts, with minimal computational effort, osmotic pressures of deionized suspensions of highly charged colloids in close agreement with large-scale simulations of the primitive model.Comment: 15 pages, 7 figure

Electroneutrality and Phase Behavior of Colloidal Suspensions

Several statistical mechanical theories predict that colloidal suspensions of highly charged macroions and monovalent microions can exhibit unusual thermodynamic phase behavior when strongly deionized. Density-functional, extended Debye-H\"uckel, and response theories, within mean-field and linearization approximations, predict a spinodal phase instability of charged colloids below a critical salt concentration. Poisson-Boltzmann cell model studies of suspensions in Donnan equilibrium with a salt reservoir demonstrate that effective interactions and osmotic pressures predicted by such theories can be sensitive to the choice of reference system, e.g., whether the microion density profiles are expanded about the average potential of the suspension or about the reservoir potential. By unifying Poisson-Boltzmann and response theories within a common perturbative framework, it is shown here that the choice of reference system is dictated by the constraint of global electroneutrality. On this basis, bulk suspensions are best modeled by density-dependent effective interactions derived from a closed reference system in which the counterions are confined to the same volume as the macroions. Linearized theories then predict bulk phase separation of deionized suspensions only when expanded about a physically consistent (closed) reference system. Lower-dimensional systems (e.g., monolayers, small clusters), depending on the strength of macroion-counterion correlations, may be governed instead by density-independent effective interactions tied to an open reference system with counterions dispersed throughout the reservoir, possibly explaining observed structural crossover in colloidal monolayers and anomalous metastability of colloidal crystallites.Comment: 12 pages, 5 figures. Discussion clarified, references adde

Poisson-Boltzmann Theory of Charged Colloids: Limits of the Cell Model for Salty Suspensions

Thermodynamic properties of charge-stabilised colloidal suspensions are commonly modeled 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 solution of the nonlinear PB equation, the cell model neglects microion-induced correlations between macroions, precluding modeling of macroion ordering phenomena. An alternative approach, avoiding artificial constraints of cell geometry, maps a macroion-microion mixture onto a one-component model of pseudo-macroions governed by effective interactions. In practice, effective-interaction models are usually based on linear screening approximations, which can accurately describe 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 over a range of concentrations. By comparing predictions with primitive model simulation data for salt-free suspensions, and with predictions of nonlinear PB theory for salty suspensions, we chart the limits of both the cell model and linear-screening approximations in modeling bulk thermodynamic properties. Up to moderately strong electrostatic couplings, the cell model proves accurate in predicting osmotic pressures of deionized suspensions. With increasing salt concentration, however, the relative contribution of macroion interactions grows, leading predictions of 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 soft materials.Comment: 27 pages, 5 figures, special issue of Journal of Physics: Condensed Matter on "Classical density functional theory methods in soft and hard matter

Stability of Colloidal Quasicrystals

Freezing of charge-stabilized colloidal suspensions and relative stabilities of crystals and quasicrystals are studied using thermodynamic perturbation theory. Macroion interactions are modelled by effective pair potentials combining electrostatic repulsion with polymer-depletion or van der Waals attraction. Comparing free energies -- counterion terms included -- for elementary crystals and rational approximants to icosahedral quasicrystals, parameters are identified for which one-component quasicrystals are stabilized by a compromise between packing entropy and cohesive energy.Comment: 6 pages, 4 figure

Field line distribution of density at \u3ci\u3eL\u3c/i\u3e=4.8 inferred from observations by CLUSTER

For two events observed by the CLUSTER space- craft, the field line distribution of mass density ρ was inferred from Alfve ́n wave harmonic frequencies and compared to the electron density ne from plasma wave data and the oxy- gen density nO+ from the ion composition experiment. In one case, the average ion mass M≡ρ/ne was about 5amu (28 October 2002), while in the other it was about 3 amu (10 September 2002). Both events occurred when the CLUSTER 1 (C1) spacecraft was in the plasmatrough. Nevertheless, the electron density ne was significantly lower for the first event (ne =8 cm−3 ) than for the second event (ne =22 cm−3 ), and this seems to be the main difference leading to a dif- ferent value of M. For the first event (28 October 2002), we were able to measure the Alfve ́n wave frequencies for eight harmonics with unprecedented precision, so that the er- ror in the inferred mass density is probably dominated by factors other than the uncertainty in frequency (e.g., mag- netic field model and theoretical wave equation). This field line distribution (at L=4.8) was very flat for magnetic lati- tude |MLAT|20◦ but very steeply increasing with respect to |MLAT| for |MLAT|40◦. The total variation in ρ was about four orders of magnitude, with values at large |MLAT| roughly consistent with ionospheric values. For the second event (10 September 2002), there was a small local maxi- mum in mass density near the magnetic equator. The in- ferred mass density decreases to a minimum 23% lower than the equatorial value at |MLAT|=15.5◦, and then steeply in- creases as one moves along the field line toward the iono- sphere. For this event we were also able to examine the spa- tial dependence of the electron density using measurements of ne from all four CLUSTER spacecraft. Our analysis in- dicates that the density varies with L at L∼5 roughly like L−4, and that ne is also locally peaked at the magnetic equa- tor, but with a smaller peak. The value of ne reaches a den- sity minimum about 6% lower than the equatorial value at |MLAT|=12.5◦, and then increases steeply at larger values of |MLAT|. This is to our knowledge the first evidence for a local peak in bulk electron density at the magnetic equa- tor. Our results show that magnetoseismology can be a useful technique to determine the field line distribution of the mass density for CLUSTER at perigee and that the distribution of electron density can also be inferred from measurements by multiple spacecraft

Density-Functional Theory of Quantum Freezing: Sensitivity to Liquid-State Structure and Statistics

Density-functional theory is applied to compute the ground-state energies of quantum hard-sphere solids. The modified weighted-density approximation is used to map both the Bose and the Fermi solid onto a corresponding uniform Bose liquid, assuming negligible exchange for the Fermi solid. The required liquid-state input data are obtained from a paired phonon analysis and the Feynman approximation, connecting the static structure factor and the linear response function. The Fermi liquid is treated by the Wu-Feenberg cluster expansion, which approximately accounts for the effects of antisymmetry. Liquid-solid transitions for both systems are obtained with no adjustment of input data. Limited quantitative agreement with simulation indicates a need for further improvement of the liquid-state input through practical alternatives to the Feynman approximation.Comment: IOP-TeX, 21 pages + 7 figures, to appear, J. Phys.: Condens. Matte

Phase Separation in Charge-Stabilized Colloidal Suspensions: Influence of Nonlinear Screening

The phase behavior of charge-stabilized colloidal suspensions is modeled by a combination of response theory for electrostatic interparticle interactions and variational theory for free energies. Integrating out degrees of freedom of the microions (counterions, salt ions), the macroion-microion mixture is mapped onto a one-component system governed by effective macroion interactions. Linear response of microions to the electrostatic potential of the macroions results in a screened-Coulomb (Yukawa) effective pair potential and a one-body volume energy, while nonlinear response modifies the effective interactions [A. R. Denton, \PR E {\bf 70}, 031404 (2004)]. The volume energy and effective pair potential are taken as input to a variational free energy, based on thermodynamic perturbation theory. For both linear and first-order nonlinear effective interactions, a coexistence analysis applied to aqueous suspensions of highly charged macroions and monovalent microions yields bulk separation of macroion-rich and macroion-poor phases below a critical salt concentration, in qualitative agreement with predictions of related linearized theories [R. van Roij, M. Dijkstra, and J.-P. Hansen, \PR E {\bf 59}, 2010 (1999); P. B. Warren, \JCP {\bf 112}, 4683 (2000)]. It is concluded that nonlinear screening can modify phase behavior but does not necessarily suppress bulk phase separation of deionized suspensions.Comment: 14 pages of text + 9 figure

Effective Interactions and Volume Energies in Charge-Stabilized Colloidal Suspensions

Charge-stabilized colloidal suspensions can be conveniently described by formally reducing the macroion-microion mixture to an equivalent one-component system of pseudo-particles. Within this scheme, the utility of a linear response approximation for deriving effective interparticle interactions has been demonstrated [M. J. Grimson and M. Silbert, Mol. Phys. 74, 397 (1991)]. Here the response approach is extended to suspensions of finite-sized macroions and used to derive explicit expressions for (1) an effective electrostatic pair interaction between pseudo-macroions and (2) an associated volume energy that contributes to the total free energy. The derivation recovers precisely the form of the DLVO screened-Coulomb effective pair interaction for spherical macroions and makes manifest the important influence of the volume energy on thermodynamic properties of deionized suspensions. Excluded volume corrections are implicitly incorporated through a natural modification of the inverse screening length. By including nonlinear response of counterions to macroions, the theory may be generalized to systematically investigate effective many-body interactions.Comment: 13 pages (J. Phys.: Condensed Matter, in press