Where the linearized Poisson-Boltzmann cell model fails: (II) the planar case as a prototype study

The classical problem of two uniformly charged infinite planes in electrochemical equilibrium with an infinite monovalent salt reservoir is solved exactly at the mean-field nonlinear Poisson-Boltzmann (PB) level, including an explicit expression of the associated nonlinear electrostatic contribution to the semi-grand-canonical potential. A linearization of the nonlinear functional is presented that leads to Debye-H\"uckel-like equations agreeing asymptotically with the nonlinear PB results in the weak-coupling (high-temperature) and counterionic ideal-gas limits. This linearization scheme yields artifacts in the low-temperature, large-separation or high-surface charge limits. In particular, the osmotic-pressure difference between the interplane region and the salt reservoir becomes negative in the above limits, in disagreement with the exact (at mean-field level) nonlinear PB solution. By using explicitly gauge-invariant forms of the electrostatic potential we show that these artifacts -- although thermodynamically consistent with quadratic expansions of the nonlinear functional -- can be traced back to the non-fulfillment of the underlying assumptions of the linearization. Explicit comparison between the analytical expressions of the exact nonlinear solution and the corresponding linearized equations allows us to show that the linearized results are asymptotically exact in the weak-coupling and counterionic ideal-gas limits, but always fail otherwise, predicting negative osmotic-pressure differences.Comment: 24 pages, 3 PostScript figures, submitted to J. Chem. Phy

Liquid-state theory of charged colloids

A simple theory of the fluid state of a charged colloidal suspension is proposed. The full free energy of a polyelectrolyte solution is calculated. It is found that the counterions condense onto the polyions forming clusters composed of one polyion and n counterions. The distribution of cluster sizes is determined explicitly. In agreement with the current experimental and Monte Carlo results, no liquid-gas phase separation was encountered.Comment: 4 pages, 2 Postscript figures, uses multicol.sty; changed conten

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

High-efficiency 20 GHz traveling wave tube development for space communications

A 75 watt CW high efficiency helix TWT operating at 20 GHz was developed for satellite communication systems. The purpose was to extend the performance capabilities of helix TWTs by using recent technology developments. The TWT described is a unique design because high overall efficiency is obtained with a low perveance beam. In the past, low perveance designs resulted in low beam efficiencies. However, due to recent breakthoughs in diamond rod technology and in collector electrode materials, high efficiencies can now be achieved with low perveance beams. The advantage of a low perveance beam is a reduction in space charge within the beam which translates to more efficient collector operation. In addition, this design incorporates textured graphite electrodes which further enhance collector operation by suppressing backstreaming secondaries. The diamond supported helix circuit features low RF losses, high interaction impedance, good thermal handling capability and has been designed to compensate for the low perveance beam. One more discussed tube feature is the use of a velocity taper in the output helix that achieves low signal distortion while maintaining high efficiency

Seedtime and Harvest: The Establishment of the Hawaiian Reformed Catholic Church, 1855-1870.

M.A. Thesis. University of Hawaiʻi at Mānoa 2018

The one-component plasma: a conceptual approach

The one-component plasma (OCP) represents the simplest statistical mechanical model of a Coulomb system. For this reason, it has been extensively studied over the last forty years. The advent of the integral equations has resulted in a dramatic improvement in our ability to carry out numerical calculations, but came at the expense of a physical insight gained in a simpler analytic theory. In this paper we present an extension of the Debye-Hueckel (DH) theory to the OCP. The theory allows for analytic calculations of all the thermodynamic functions, as well as the structure factor. The theory explicitly satisfies the Stillinger-Lovett and, for small couplings, the compressibility sum rules, implying its internal self consistency.Comment: 28 pages, 5 Postscript figures, uses elsart.sty, accepted for publication in Physica