Where the linearized Poisson-Boltzmann cell model fails: (I) spurious phase separation in charged colloidal suspensions

We perform a linearization of the Poisson-Boltzmann (PB) density functional for spherical Wigner-Seitz cells that yields Debye-H\"uckel-like equations agreeing asymptotically with the PB results in the weak-coupling (high-temperature) limit. Both the canonical (fixed number of microions) as well as the semi-grand-canonical (in contact with an infinite salt reservoir) cases are considered and discussed in a unified linearized framework. In the canonical case, for sufficiently large colloidal charges the linearized theory predicts the occurrence of a thermodynamical instability with an associated phase separation of the homogeneous suspension into dilute (gas) and dense (liquid) phases. In the semi-grand-canonical case it is predicted that the isothermal compressibility and the osmotic-pressure difference between the colloidal suspension and the salt reservoir become negative in the low-temperature, high-surface charge or infinite-dilution (of polyions) limits. As already pointed out in the literature for the latter case, these features are in disagreement with the exact nonlinear PB solution inside a Wigner-Seitz cell and are thus artifacts of the linearization. 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 and osmotic pressure, may be traced back to the non-fulfillment of the underlying assumptions of the linearization.Comment: 32 pages, 3 PostScript figures, submitted to J. Chem. Phy

Organized condensation of worm-like chains

We present results relevant to the equilibrium organization of DNA strands of arbitrary length interacting with a spherical organizing center, suggestive of DNA-histone complexation in nucleosomes. We obtain a rich phase diagram in which a wrapping state is transformed into a complex multi-leafed, rosette structure as the adhesion energy is reduced. The statistical mechanics of the "melting" of a rosette can be mapped into an exactly soluble one-dimensional many-body problem.Comment: 15 pages, 2 figures in a pdf fil

Polymer reptation and nucleosome repositioning

We consider how beads can diffuse along a chain that wraps them, without becoming displaced from the chain; our proposed mechanism is analogous to the reptation of "stored length" in more familiar situations of polymer dynamics. The problem arises in the case of globular aggregates of proteins (histones) that are wound by DNA in the chromosomes of plants and animals; these beads (nucleosomes) are multiply wrapped and yet are able to reposition themselves over long distances, while remaining bound by the DNA chain.Comment: 9 pages, including 2 figures, to be published in Phys. Rev. Let

Polyelectrolyte Bundles

Using extensive Molecular Dynamics simulations we study the behavior of polyelectrolytes with hydrophobic side chains, which are known to form cylindrical micelles in aqueous solution. We investigate the stability of such bundles with respect to hydrophobicity, the strength of the electrostatic interaction, and the bundle size. We show that for the parameter range relevant for sulfonated poly-para-phenylenes (PPP) one finds a stable finite bundle size. In a more generic model we also show the influence of the length of the precursor oligomer on the stability of the bundles. We also point out that our model has close similarities to DNA solutions with added condensing agents, hinting to the possibility that the size of DNA aggregates is under certain circumstances thermodynamically limited.Comment: 10 pages, 8 figure

Semi-classical buckling of stiff polymers

A quantitative theory of the buckling of a worm like chain based on a semi-classical approximation of the partition function is presented. The contribution of thermal fluctuations to the force-extension relation that allows to go beyond the classical Euler buckling is derived in the linear and non-linear regime as well. It is shown that the thermal fluctuations in the nonlinear buckling regime increase the end-to-end distance of the semiflexible rod if it is confined to 2 dimensions as opposed to the 3 dimensional case. Our approach allows a complete physical understanding of buckling in D=2 and in D=3 below and above the Euler transition.Comment: Revtex, 17 pages, 4 figure

Stationarity-conservation laws for certain linear fractional differential equations

The Leibniz rule for fractional Riemann-Liouville derivative is studied in algebra of functions defined by Laplace convolution. This algebra and the derived Leibniz rule are used in construction of explicit form of stationary-conserved currents for linear fractional differential equations. The examples of the fractional diffusion in 1+1 and the fractional diffusion in d+1 dimensions are discussed in detail. The results are generalized to the mixed fractional-differential and mixed sequential fractional-differential systems for which the stationarity-conservation laws are obtained. The derived currents are used in construction of stationary nonlocal charges.Comment: 28 page

Thermodynamics and Fractional Fokker-Planck Equations

The relaxation to equilibrium in many systems which show strange kinetics is described by fractional Fokker-Planck equations (FFPEs). These can be considered as phenomenological equations of linear nonequilibrium theory. We show that the FFPEs describe the system whose noise in equilibrium funfills the Nyquist theorem. Moreover, we show that for subdiffusive dynamics the solutions of the corresponding FFPEs are probability densities for all cases where the solutions of normal Fokker-Planck equation (with the same Fokker-Planck operator and with the same initial and boundary conditions) exist. The solutions of the FFPEs for superdiffusive dynamics are not always probability densities. This fact means only that the corresponding kinetic coefficients are incompatible with each other and with the initial conditions

Attractive Interactions Between Rod-like Polyelectrolytes: Polarization, Crystallization, and Packing

We study the attractive interactions between rod-like charged polymers in solution that appear in the presence of multi-valence counterions. The counterions condensed to the rods exhibit both a strong transversal polarization and a longitudinal crystalline arrangement. At short distances between the rods, the fraction of condensed counterions increases, and the majority of these occupy the region between the rods, where they minimize their repulsive interactions by arranging themselves into packing structures. The attractive interaction is strongest for multivalent counterions. Our model takes into account the hard-core volume of the condensed counterions and their angular distribution around the rods. The hard core constraint strongly suppresses longitudinal charge fluctuations.Comment: 4 figures, uses revtex, psfig and epsf. The new version contains a different introduction, and the bibliography has been expande

On the fluid-fluid phase separation in charged-stabilized colloidal suspensions

We develop a thermodynamic description of particles held at a fixed surface potential. This system is of particular interest in view of the continuing controversy over the possibility of a fluid-fluid phase separation in aqueous colloidal suspensions with monovalent counterions. The condition of fixed surface potential allows in a natural way to account for the colloidal charge renormalization. In a first approach, we assess the importance of the so called ``volume terms'', and find that in the absence of salt, charge renormalization is sufficient to stabilize suspension against a fluid-fluid phase separation. Presence of salt, on the other hand, is found to lead to an instability. A very strong dependence on the approximations used, however, puts the reality of this phase transition in a serious doubt. To further understand the nature of the instability we next study a Jellium-like approximation, which does not lead to a phase separation and produces a relatively accurate analytical equation of state for a deionized suspensions of highly charged colloidal spheres. A critical analysis of various theories of strongly asymmetric electrolytes is presented to asses their reliability as compared to the Monte Carlo simulations

Counterion Penetration and Effective Electrostatic Interactions in Solutions of Polyelectrolyte Stars and Microgels

Counterion distributions and effective electrostatic interactions between spherical macroions in polyelectrolyte solutions are calculated via second-order perturbation (linear response) theory. By modelling the macroions as continuous charge distributions that are permeable to counterions, analytical expressions are obtained for counterion profiles and effective pair interactions in solutions of star-branched and microgel macroions. The counterions are found to penetrate stars more easily than microgels, with important implications for screening of bare macroion interactions. The effective pair interactions are Yukawa in form for separated macroions, but are softly repulsive and bounded for overlapping macroions. A one-body volume energy, which depends on the average macroion concentration, emerges naturally in the theory and contributes to the total free energy.Comment: 15 pages, 5 figure