Implicit Finite-Size Effects in Computer Simulations

The influence of periodic boundary conditions (implicit finite-size effects) on the anisotropy of pair correlations in computer simulations is studied for a dense classical fluid of pair-wise interacting krypton atoms near the triple point. Molecular dynamics simulation data for the pair distribution function of N-particle systems, as a function of radial distance, polar angle, and azimuthal angle are compared directly with corresponding theoretical predictions [L. R. Pratt and S. W. Haan, J. Chem. Phys. 74, 1864 (1981)]. For relatively small systems of N=60, 80, and 108 atoms, significant angular variation is observed, which is qualitatively, and in several cases quantitatively, well predicted by theory. Finite-size corrections to the spherically-averaged radial distribution function, however, are found to be comparable to random statistical errors for runs of 10^5 time steps.Comment: plain TeX, 14 pages + 16 postscript figures, to appear Z. Phys.

Thermodynamically Stable One-Component Metallic Quasicrystals

Classical density-functional theory is employed to study finite-temperature trends in the relative stabilities of one-component quasicrystals interacting via effective metallic pair potentials derived from pseudopotential theory. Comparing the free energies of several periodic crystals and rational approximant models of quasicrystals over a range of pseudopotential parameters, thermodynamically stable quasicrystals are predicted for parameters approaching the limits of mechanical stability of the crystalline structures. The results support and significantly extend conclusions of previous ground-state lattice-sum studies.Comment: REVTeX, 13 pages + 2 figures, to appear, Europhys. Let

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

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

Effective Electrostatic Interactions in Suspensions of Polyelectrolyte Brush-Coated Colloids

Effective electrostatic interactions between colloidal particles, coated with polyelectrolyte brushes and suspended in an electrolyte solvent, are described via linear response theory. The inner cores of the macroions are modeled as hard spheres, the outer brushes as spherical shells of continuously distributed charge, the microions (counterions and salt ions) as point charges, and the solvent as a dielectric continuum. The multi-component mixture of macroions and microions is formally mapped onto an equivalent one-component suspension by integrating out from the partition function the microion degrees of freedom. Applying second-order perturbation theory and a random phase approximation, analytical expressions are derived for the effective pair interaction and a one-body volume energy, which is a natural by-product of the one-component reduction. The combination of an inner core and an outer shell, respectively impenetrable and penetrable to microions, allows the interactions between macroions to be tuned by varying the core diameter and brush thickness. In the limiting cases of vanishing core diameter and vanishing shell thickness, the interactions reduce to those derived previously for star polyelectrolytes and charged colloids, respectively.Comment: 20 pages, 5 figures, Phys. Rev. E (in press

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

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

Freezing of He-4 and its liquid-solid interface from Density Functional Theory

We show that, at high densities, fully variational solutions of solid-like type can be obtained from a density functional formalism originally designed for liquid 4He. Motivated by this finding, we propose an extension of the method that accurately describes the solid phase and the freezing transition of liquid 4He at zero temperature. The density profile of the interface between liquid and the (0001) surface of the 4He crystal is also investigated, and its surface energy evaluated. The interfacial tension is found to be in semiquantitative agreement with experiments and with other microscopic calculations. This opens the possibility to use unbiased DF methods to study highly non-homogeneous systems, like 4He interacting with strongly attractive impurities/substrates, or the nucleation of the solid phase in the metastable liquid.Comment: 5 pages, 4 figures, submitted to Phys. Rev.