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

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

Aging Reduces The Primary Humoral Response And The In Vitro Cytokine Production In Mice.

Aging is accompanied by a decrease in several physiological functions that make older individuals less responsive to environmental challenges. In the present study, we analyzed the immune response of female BALB/c mice (N = 6) of different ages (from 2 to 96 weeks) and identified significant age-related alterations. Immunization with hapten-protein (trinitrophenyl-bovine serum albumin) conjugates resulted in lower antibody levels in the primary and secondary responses of old mice (72 weeks old). Moreover, young mice (2, 16, and 32 weeks old) maintained specific antibodies in their sera for longer periods after primary immunization than did old mice. However, a secondary challenge efficiently induced memory in old mice, as shown by the increased antibody levels in their sera. The number of CD4+ and CD8+ T cells in the spleen increased until 8 weeks of age but there was no change in the CD4+/CD8+ ratio with aging. Splenic T cells from old mice that had or had not been immunized were less responsive to concanavalin-A and showed reduced cytokine production compared to young mice (IL-2: 57-127 vs 367-1104 pg/mL, IFN-gamma: 2344-12,836 vs 752-23,106 pg/mL and IL-10: 393-2172 vs 105-2869 pg/mL in old and young mice, respectively). These data suggest that there are significant changes in the organization of the immune system throughout life. However, the relevance of these alterations for the functioning of the immune system is unknown.401111-2

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

Dynamical coherent-potential approximation approach to excitation spectra in 3d transition metals

First-principles dynamical CPA (Coherent-Potential Approximation) for electron correlations has been developed further by taking into account higher-order dynamical corrections with use of the asymptotic approximation. The theory is applied to the investigations of a systematic change of excitation spectra in $3d$ transition metals from Sc to Cu at finite temperatures. It is shown that the dynamical effects damp main peaks in the densities of states (DOS) obtained by the local density approximation to the density functional theory, reduce the band broadening due to thermal spin fluctuations, create the Mott-Hubbard type bands in the case of fcc Mn and fcc Fe, and create a small hump corresponding to the `6 eV' satellite in the case of Co, Ni, and Cu. Calculated DOS explain the X-ray photoelectron spectroscopy data as well as the bremsstrahlung isochromat spectroscopy data. Moreover, it is found that screening effects on the exchange energy parameters are significant for understanding the spectra in magnetic transition metals.Comment: To be published in Phys. Rev.

Field theoretical representation of the Hohenberg-Kohn free energy for fluids

To go beyond Gaussian approximation to the Hohenberg-Kohn free energy playing the key role in the density functional theory (DFT), the density functional \textit{integral} representation would be relevant, because field theoretical approach to perturbative calculations becomes available. Then the present letter first derives the associated Hamiltonian of density functional, explicitly including logarithmic entropy term, from the grand partition function expressed by configurational integrals. Moreover, two things are done so that the efficiency of the obtained form may be revealed: to demonstrate that this representation facilitates the field theoretical treatment of the perturbative calculation, and further to compare our perturbative formulation with that of the DFT.Comment: 5 pages, revtex, modified on 13 April 2000 [see eqs. (3), (6), and (13)

Extracting Structural Information of a Heteropolymer from Force-Extension Curves

We present a theory for the reverse analysis on the sequence information of a single H/P two-letter random hetero-polymer (RHP) from its force-extension(f-z) curves during quasi static stretching. Upon stretching of a self-assembled RHP, it undergoes several structural transitions. The typical elastic response of a hetero-polymeric globule is a set of overlapping saw-tooth patterns. With consideration of the height and the position of the overlapping saw-tooth shape, we analyze the possibility of extracting the binding energies of the internal domains and the corresponding block sizes of the contributing conformations.Comment: 5 figures 7 page

Poisson -- Boltzmann Brownian Dynamics of Charged Colloids in Suspension

We describe a method to simulate the dynamics of charged colloidal particles suspended in a liquid containing dissociated ions and salt ions. Regimes of prime current interest are those of large volume fraction of colloids, highly charged particles and low salt concentrations. A description which is tractable under these conditions is obtained by treating the small dissociated and salt ions as continuous fields, while keeping the colloidal macroions as discrete particles. For each spatial configuration of the macroions, the electrostatic potential arising from all charges in the system is determined by solving the nonlinear Poisson--Boltzmann equation. From the electrostatic potential, the forces acting on the macroions are calculated and used in a Brownian dynamics simulation to obtain the motion of the latter. The method is validated by comparison to known results in a parameter regime where the effective interaction between the macroions is of a pairwise Yukawa form

Reversible stretching of homopolymers and random heteropolymers

We have analyzed the equilibrium response of chain molecules to stretching. For a homogeneous sequence of monomers, the induced transition from compact globule to extended coil below the $\theta$-temperature is predicted to be sharp. For random sequences, however, the transition may be smoothed by a prevalence of necklace-like structures, in which globular regions and coil regions coexist in a single chain. As we show in the context of a random copolymer, preferential solvation of one monomer type lends stability to such structures. The range of stretching forces over which necklaces are stable is sensitive to chain length as well as sequence statistics.Comment: 14 pages, 4 figure