Charge renormalization of cylinders and spheres: Ion size effects

The effect of the counterion size on the degree of counterion condensation onto a cylindrical macroion and a spherical one in the absence of salt is studied theoretically within a modified Poisson–Boltzmann approach. We find that excluded volume interactions reduce the degree of condensation. Using a simple variational free energy we show that this reduction can be attributed to an effective increase in the macroion size due to the contribution of the condensed counterions. We also find that for a charged cylinder, the reduction in charge renormalization vanishes at infinite dilution because of the extended nature of the condensed layer. In contrast, excluded volume interactions can reduce the degree of charge renormalization of a sphere even at high dilutions. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3598–3615, 2004     

Strongly Invariant Subspaces of Nonautonomous Linear Periodic Systems and Solutions Whose Period Is Incommensurable with the Period of the System Itself

We introduce the notions of quasi-invariant and strongly invariant subspaces of a one-parameter family of linear operators acting on a finite-dimensional vector space. The geometric meaning of these notions is that the restrictions of all operators of the family to a quasiinvariant subspace coincide and that the restrictions to a strongly invariant subspace are, in addition, an endomorphism of that subspace. These notions are used to reduce the well-known problem on Ω-periodic solutions of an ω-periodic linear differential system with incommensurable Ω and ω to the algebraic problem on the eigenvalues and eigenvectors of some matrix constructed from the right-hand side of the system.     

Elastically driven linker aggregation between two semiflexible polyelectrolytes

The behavior of mobile linkers connecting two semiflexible charged polymers, such as polyvalent counterions connecting DNA or F-actin chains, is studied theoretically. The chain bending rigidity induces an effective repulsion between linkers at large distances while the interchain electrostatic repulsion leads to an effective short-range interlinker attraction. We find a rounded phase transition from a dilute linker gas where the chains form large loops between linkers to a dense disordered linker fluid connecting parallel chains. The onset of chain pairing occurs within the rounded transition.     

Raft instability of biopolymer gels

Following recent x-ray diffraction experiments by Wong, Li, and Safinya on biopolymer gels, we apply Onsager excluded volume theory to a nematic mixture of rigid rods and strong " pi/2" cross-linkers obtaining a long-ranged, highly anisotropic depletion attraction between the linkers. This attraction leads to breakdown of the percolation theory for this class of gels, to breakdown of Onsager's second-order virial method, and to formation of heterogeneities in the form of raftlike ribbons.