4,149 research outputs found
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.
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