Donnan equilibrium and the osmotic pressure of charged colloidal lattices

We consider a system composed of a monodisperse charge-stabilized colloidal suspension in the presence of monovalent salt, separated from the pure electrolyte by a semipermeable membrane, which allows the crossing of solvent, counterions, and salt particles, but prevents the passage of polyions. The colloidal suspension, that is in a crystalline phase, is considered using a spherical Wigner-Seitz cell. After the Donnan equilibrium is achieved, there will be a difference in pressure between the two sides of the membrane. Using the functional density theory, we obtained the expression for the osmotic pressure as a function of the concentration of added salt, the colloidal volume fraction, and the size and charge of the colloidal particles. The results are compared with the experimental measurements for ordered polystyrene lattices of two different particle sizes over a range of ionic strengths and colloidal volume fractions.Comment: 8 pages, 4 Postscript figures, uses multicol.sty, to be published in European Physical Journal

Kinematics of a Spacetime with an Infinite Cosmological Constant

A solution of the sourceless Einstein's equation with an infinite value for the cosmological constant \Lambda is discussed by using Inonu-Wigner contractions of the de Sitter groups and spaces. When \Lambda --> infinity, spacetime becomes a four-dimensional cone, dual to Minkowski space by a spacetime inversion. This inversion relates the four-cone vertex to the infinity of Minkowski space, and the four-cone infinity to the Minkowski light-cone. The non-relativistic limit c --> infinity is further considered, the kinematical group in this case being a modified Galilei group in which the space and time translations are replaced by the non-relativistic limits of the corresponding proper conformal transformations. This group presents the same abstract Lie algebra as the Galilei group and can be named the conformal Galilei group. The results may be of interest to the early Universe Cosmology.Comment: RevTex, 7 pages, no figures. Presentation changes, including a new Title. Version to appear in Found. Phys. Let

Influence of disordered porous media in the anomalous properties of a simple water model

The thermodynamic, dynamic and structural behavior of a water-like system confined in a matrix is analyzed for increasing confining geometries. The liquid is modeled by a two dimensional associating lattice gas model that exhibits density and diffusion anomalies, in similarity to the anomalies present in liquid water. The matrix is a triangular lattice in which fixed obstacles impose restrictions to the occupation of the particles. We show that obstacules shortens all lines, including the phase coexistence, the critical and the anomalous lines. The inclusion of a very dense matrix not only suppress the anomalies but also the liquid-liquid critical point

Cosmic microwave background constraints on the epoch of reionization

We use a compilation of cosmic microwave anisotropy data to constrain the epoch of reionization in the Universe, as a function of cosmological parameters. We consider spatially-flat cosmologies, varying the matter density $\Omega_0$ (the flatness being restored by a cosmological constant), the Hubble parameter $h$ and the spectral index $n$ of the primordial power spectrum. Our results are quoted both in terms of the maximum permitted optical depth to the last-scattering surface, and in terms of the highest allowed reionization redshift assuming instantaneous reionization. For critical-density models, significantly-tilted power spectra are excluded as they cannot fit the current data for any amount of reionization, and even scale-invariant models must have an optical depth to last scattering of below 0.3. For the currently-favoured low-density model with $\Omega_0 = 0.3$ and a cosmological constant, the earliest reionization permitted to occur is at around redshift 35, which roughly coincides with the highest estimate in the literature. We provide general fitting functions for the maximum permitted optical depth, as a function of cosmological parameters. We do not consider the inclusion of tensor perturbations, but if present they would strengthen the upper limits we quote.Comment: 9 pages LaTeX file with ten figures incorporated (uses mn.sty and epsf). Corrects some equation typos, superseding published versio