Ion-Size Effect at the Surface of a Silica Hydrosol

The author used synchrotron x-ray reflectivity to study the ion-size effect for alkali ions (Na$^+$, K$^+$, Rb$^+$, and Cs$^+$), with densities as high as $4 \times 10^{18}- 7 \times 10^{18}$ m$^{-2}$, suspended above the surface of a colloidal solution of silica nanoparticles in the field generated by the surface electric-double layer. According to the data, large alkali ions preferentially accumulate at the sol's surface replacing smaller ions, a finding that qualitatively agrees with the dependence of the Kharkats-Ulstrup single-ion electrostatic free energy on the ion's radius.Comment: 17 pages, 4 figure

Theory and simulations of rigid polyelectrolytes

We present theoretical and numerical studies on stiff, linear polyelectrolytes within the framework of the cell model. We first review analytical results obtained on a mean-field Poisson-Boltzmann level, and then use molecular dynamics simulations to show, under which circumstances these fail quantitatively and qualitatively. For the hexagonally packed nematic phase of the polyelectrolytes we compute the osmotic coefficient as a function of density. In the presence of multivalent counterions it can become negative, leading to effective attractions. We show that this results from a reduced contribution of the virial part to the pressure. We compute the osmotic coefficient and ionic distribution functions from Poisson-Boltzmann theory with and without a recently proposed correlation correction, and also simulation results for the case of poly(para-phenylene) and compare it to recently obtained experimental data on this stiff polyelectrolyte. We also investigate ion-ion correlations in the strong coupling regime, and compare them to predictions of the recently advocated Wigner crystal theories.Comment: 32 pages, 15 figures, proceedings of the ASTATPHYS-MEX-2001, to be published in Mol. Phy

Description beyond the mean field approximation of an electrolyte confined between two planar metallic electrodes

We study an electrolyte confined in a slab of width $W$ composed of two grounded metallic parallel electrodes. We develop a description of this system in a low coupling regime beyond the mean field (Poisson--Boltzmann) approximation. There are two ways to model the metallic boundaries: as ideal conductors in which the electric potential is zero and it does not fluctuate, or as good conductors in which the average electric potential is zero but the thermal fluctuations of the potential are not zero. This latter model is more realistic. For the ideal conductor model we find that the disjoining pressure is positive behaves as $1/W^3$ for large separations with a prefactor that is universal, i.e. independent of the microscopic constitution of the system. For the good conductor boundaries the disjoining pressure is negative and it has an exponential decay for large $W$. We also compute the density and electric potential profiles inside the electrolyte. These are the same in both models. If the electrolyte is charge asymmetric we find that the system is not locally neutral and that a non-zero potential difference builds up between any electrode and the interior of the system although both electrodes are grounded.Comment: 16 pages, 5 figures, added a new appendix B and a discussion on ideal conductors vs. good conductor

The Role of the Gouy Phase in the Coherent Phase Control of the Photoionization and Photodissociation of Vinyl Chloride

We demonstrate theoretically and experimentally that the Gouy phase of a focused laser beam may be used to control the photo-induced reactions of a polyatomic molecule. Quantum mechanical interference between one- and three-photon excitation of vinyl chloride produces a small phase lag between the dissociation and ionization channels on the axis of the molecular beam. Away from the axis, the Gouy phase introduces a much larger phase lag that agrees quantitatively with theory without any adjustable parameters.Comment: 4 pages, 4 figure

Radius of a Photon Beam with Orbital Angular Momentum

We analyze the transverse structure of the Gouy phase shift in light beams carrying orbital angular momentum and show that the Gouy radius $r_G$ characterizing the transverse structure grows as $\sqrt{2p+|\ell|+1}$ with the nodal number $p$ and photon angular momentum number $\ell$. The Gouy radius is shown to be closely related to the root-mean-square radius of the beam, and the divergence of the radius away from the focal plane is determined. Finally, we analyze the rotation of the Poynting vector in the context of the Gouy radius.Comment: 11 page

Incorporation of excluded volume correlations into Poisson-Boltzmann theory

We investigate the effect of excluded volume interactions on the electrolyte distribution around a charged macroion. First, we introduce a criterion for determining when hard-core effects should be taken into account beyond standard mean field Poisson-Boltzmann (PB) theory. Next, we demonstrate that several commonly proposed local density functional approaches for excluded volume interactions cannot be used for this purpose. Instead, we employ a non-local excess free energy by using a simple constant weight approach. We compare the ion distribution and osmotic pressure predicted by this theory with Monte Carlo simulations. They agree very well for weakly developed correlations and give the correct layering effect for stronger ones. In all investigated cases our simple weighted density theory yields more realistic results than the standard PB approach, whereas all local density theories do not improve on the PB density profiles but on the contrary, deviate even more from the simulation results.Comment: 23 pages, 7 figures, 1 tabl

X-ray Near Field Speckle: Implementation and Critical Analysis

We have implemented the newly-introduced, coherence-based technique of x-ray near-field speckle (XNFS) at 8-ID-I at the Advanced Photon Source. In the near field regime of high-brilliance synchrotron x-rays scattered from a sample of interest, it turns out, that, when the scattered radiation and the main beam both impinge upon an x-ray area detector, the measured intensity shows low-contrast speckles, resulting from interference between the incident and scattered beams. We built a micrometer-resolution XNFS detector with a high numerical aperture microscope objective and demonstrate its capability for studying static structures and dynamics at longer length scales than traditional far field x-ray scattering techniques. Specifically, we characterized the structure and dynamics of dilute silica and polystyrene colloidal samples. Our study reveals certain limitations of the XNFS technique, which we discuss.Comment: 53 pages, 16 figure

Ion-ion correlations: an improved one-component plasma correction

Based on a Debye-Hueckel approach to the one-component plasma we propose a new free energy for incorporating ionic correlations into Poisson-Boltzmann like theories. Its derivation employs the exclusion of the charged background in the vicinity of the central ion, thereby yielding a thermodynamically stable free energy density, applicable within a local density approximation. This is an improvement over the existing Debye-Hueckel plus hole theory, which in this situation suffers from a "structuring catastrophe". For the simple example of a strongly charged stiff rod surrounded by its counterions we demonstrate that the Poisson-Boltzmann free energy functional augmented by our new correction accounts for the correlations present in this system when compared to molecular dynamics simulations.Comment: 5 pages, 2 figures, revtex styl

Bargmann invariants and off-diagonal geometric phases for multi-level quantum systems -- a unitary group approach

We investigate the geometric phases and the Bargmann invariants associated with a multi-level quantum systems. In particular, we show that a full set of `gauge-invariant' objects for an $n$-level system consists of $n$ geometric phases and ${1/2}(n-1)(n-2)$ algebraically independent 4-vertex Bargmann invariants. In the process of establishing this result we develop a canonical form for U(n) matrices which is useful in its own right. We show that the recently discovered `off-diagonal' geometric phases [N. Manini and F. Pistolesi, Phys. Rev. Lett. 8, 3067 (2000)] can be completely analysed in terms of the basic building blocks developed in this work. This result liberates the off-diagonal phases from the assumption of adiabaticity used in arriving at them.Comment: 13 pages, latex, no figure

Screening of Spherical Colloids beyond Mean Field -- A Local Density Functional Approach

We study the counterion distribution around a spherical macroion and its osmotic pressure in the framework of the recently developed Debye-H"uckel-Hole-Cavity (DHHC) theory. This is a local density functional approach which incorporates correlations into Poisson-Boltzmann theory by adding a free energy correction based on the One Component Plasma. We compare the predictions for ion distribution and osmotic pressure obtained by the full theory and by its zero temperature limit with Monte Carlo simulations. They agree excellently for weakly developed correlations and give the correct trend for stronger ones. In all investigated cases the DHHC theory and its computationally simpler zero temperature limit yield better results than the Poisson-Boltzmann theory.Comment: 10 pages, 4 figures, 2 tables, RevTeX4-styl