Charged Membranes: Poisson-Boltzmann theory, DLVO paradigm and beyond

In this chapter we review the electrostatic properties of charged membranes in aqueous solutions, with or without added salt, employing simple physical models. The equilibrium ionic profiles close to the membrane are governed by the well-known Poisson-Boltzmann (PB) equation. We analyze the effect of different boundary conditions, imposed by the membrane, on the ionic profiles and the corresponding osmotic pressure. The discussion is separated into the single membrane case and that of two interacting membranes. For one membrane setup, we show the different solutions of the PB equation and discuss the interplay between constant-charge and constant-potential boundary conditions. A modification of the PB theory is presented to treat the extremely high counter-ion concentration in the vicinity of a charge membrane. For two equally-charged membranes, we analyze the different pressure regimes for the constant-charge boundary condition, and discuss the difference in the osmotic pressure for various boundary conditions. The non-equal charged membranes is reviewed as well, and the crossover from repulsion to attraction is calculated analytically. We then examine the charge-regulation boundary condition and discuss its effects on the ionic profiles and the osmotic pressure for two equally-charged membranes. In the last section, we briefly review the van der Waals (vdW) interactions and their effect on the free energy between two planar membranes. We explain the simple Hamaker pair-wise summation procedure, and introduce the more rigorous Lifshitz theory. The latter is a key ingredient in the DLVO theory, which combines repulsive electrostatic with attractive vdW interactions, and offers a simple explanation for colloidal or membrane stability. Finally, the chapter ends by a short account of the limitations of the approximations inherent in the PB theory.Comment: 57 pages, 19 figures, From the forthcoming Handbook of Lipid Membranes: Molecular, Functional, and Materials Aspects. Edited by Cyrus Safinya and Joachim Radler, Taylor & Francis/CRC Press, 201

Working Close to Home: WIRE-Net's Hire Locally Program

Hire Locally is an employment program that matches Cleveland's west side residents with industrial jobs employers would otherwise have searched far and wide to fill. The program is part of the nonprofit Westside Industrial Retention and Expansion Network, or WIRE-Net. This report documents the program's innovation in developing a sectoral strategy to meet labor market demands while also setting a broad agenda for community improvement. It also shares key program elements and recommendations to ensure that future programs are more effective

New Minkowski type inequalities and entropic inequalities for quantum states of qudits

The two-parameter Minkowski like inequality written for composite quantum system state is obtained for arbitrary Hermitian nonnegative matrix with trace equal to unity. The inequality can be used as entropic and information inequality for density matrix of noncomposite finite quantum system, e.g., for a single qudit state. The analogs of strong subadditivity condition for the single qudit is discussed in context of obtained Minkowski like inequality.Comment: 9 pages, 4 figures. It is material of poster at the conference "Advances in Foundations of Quantum Mechanics and Quantum Information with atoms and photons". It will be sent to International Journal of Quantum Informatio

Charge regulation: a generalized boundary condition?

The three most commonly-used boundary conditions for charged colloidal systems are constant charge (insulator), constant potential (conducting electrode) and charge regulation (ionizable groups at the surface). It is usually believed that the charge regulation is a generalized boundary condition that reduces in some specific limits to either constant charge or constant potential boundary conditions. By computing the disjoining pressure between two symmetric planes for these three boundary conditions, both numerically (for all inter-plate separations) and analytically (for small inter-plate separations), we show that this is not, in general, the case. In fact, the limit of charge regulation is a separate boundary condition, yielding a disjoining pressure with a different characteristic separation-scaling. Our findings are supported by several examples demonstrating that the disjoining pressure at small separations for the charge regulation boundary-condition depends on the details of the dissociation/association process.Comment: 6 pages, 3 figure