Polyelectrolyte-colloid complexes: polarizability and effective interaction

We theoretically study the polarizability and the interactions of neutral complexes consisting of a semi-flexible polyelectrolyte adsorbed onto an oppositely charged spherical colloid. In the systems we studied, the bending energy of the chain is small compared to the Coulomb energy and the chains are always adsorbed on the colloid. We observe that the polarizability is large for short chains and small electrical fields and shows a non-monotonic behavior with the chain length at fixed charge density. The polarizability has a maximum for a chain length equal to half of the circumference of the colloid. For long chains we recover the polarizability of a classical conducting sphere. For short chains, the existence of a permanent dipole moment of the complexes leads to a van der Waal's-type long-range attraction between them. This attractive interaction vanishes for long chains (i.e., larger than the colloidal size), where the permanent dipole moment is negligible. For short distances the complexes interact with a deep short-ranged attraction which is due to energetic bridging for short chains and entropic bridging for long chains. Exceeding a critical chain length eventually leads to a pure repulsion. This shows that the stabilization of colloidal suspensions by polyelectrolyte adsorption is strongly dependent on the chain size relative to the colloidal size: for long chains the suspensions are always stable (only repulsive forces between the particles), while for mid-sized and short chains there is attraction between the complexes and a salting-out can occur.Comment: 13 pages, 14 figure

In memoriam: Celso-Ramon Garcia, M.D. (1922–2004), reproductive medicine visionary

This article traces the career of Celso-Ramon Garcia (1922–2004), noted physician, educator, and internationally renowned pioneer in the field of reproductive endocrinology. His work helped to formulate oral contraceptives used by millions of women throughout the world. Garcia's research collaborators included Gregory Pincus and John Rock, who together finalized the landmark clinical data needed to secure initial FDA approval for "the pill" in 1960. In addition to Garcia's monumental work in contraceptive endocrinology, his scholarly interests encompassed physiology of the menopause, minimally invasive reproductive surgery, as well as psychological aspects of infertility. Closely identified with the University of Pennsylvania, Garcia was instrumental in establishing the first formal clinical program in reproductive biology and influenced countless young scientists whose training he supervised and mentored. His distinguished career was emblematic of the best of the medical profession, characterized by compassion, intellect, and a sincere desire to help others. Our manuscript outlines Garcia's wide range of interests, acknowledges his superior fund of knowledge, and honors his humanitarian spirit – all of which contributed to an impressive legacy of medical discoveries. The impact of Prof. Garcia's work will continue to be felt for many years

Counterion density profiles at charged flexible membranes

Counterion distributions at charged soft membranes are studied using perturbative analytical and simulation methods in both weak coupling (mean-field or Poisson-Boltzmann) and strong coupling limits. The softer the membrane, the more smeared out the counterion density profile becomes and counterions pentrate through the mean-membrane surface location, in agreement with anomalous scattering results. Membrane-charge repulsion leads to a short-scale roughening of the membrane.Comment: 4 pages, 4 figure

Singularity results for functional equations driven by linear fractional transformations

We consider functional equations driven by linear fractional transformations, which are special cases of de Rham's functional equations. We consider Hausdorff dimension of the measure whose distribution function is the solution. We give a necessary and sufficient condition for singularity. We also show that they have a relationship with stationary measures.Comment: 14 pages, Title changed, to appear in Journal of Theoretical Probabilit