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

Liquid-state theory of charged colloids

A simple theory of the fluid state of a charged colloidal suspension is proposed. The full free energy of a polyelectrolyte solution is calculated. It is found that the counterions condense onto the polyions forming clusters composed of one polyion and n counterions. The distribution of cluster sizes is determined explicitly. In agreement with the current experimental and Monte Carlo results, no liquid-gas phase separation was encountered.Comment: 4 pages, 2 Postscript figures, uses multicol.sty; changed conten

Donnan equilibrium and the osmotic pressure of charged colloidal lattices

We consider a system composed of a monodisperse charge-stabilized colloidal suspension in the presence of monovalent salt, separated from the pure electrolyte by a semipermeable membrane, which allows the crossing of solvent, counterions, and salt particles, but prevents the passage of polyions. The colloidal suspension, that is in a crystalline phase, is considered using a spherical Wigner-Seitz cell. After the Donnan equilibrium is achieved, there will be a difference in pressure between the two sides of the membrane. Using the functional density theory, we obtained the expression for the osmotic pressure as a function of the concentration of added salt, the colloidal volume fraction, and the size and charge of the colloidal particles. The results are compared with the experimental measurements for ordered polystyrene lattices of two different particle sizes over a range of ionic strengths and colloidal volume fractions.Comment: 8 pages, 4 Postscript figures, uses multicol.sty, to be published in European Physical Journal

Seedtime and Harvest: The Establishment of the Hawaiian Reformed Catholic Church, 1855-1870.

M.A. Thesis. University of Hawaiʻi at Mānoa 2018

Multicritical behavior of the ferromagnetic Blume-Emery-Griffiths model with repulsive biquadratic couplings

CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOCAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL E NÍVEL SUPERIORThe ferromagnetic (J gt; 0) version of the Blume-Emery-Griffiths model in the region of repulsive biquadratic couplings (K < 0) is considered on a Cayley tree of coordination z, reducing the statistical problem to the analysis of a two-dimensional nonlinear discrete map. In order to investigate the effect of the coordination z on the system multicritical behavior, we study the particular case K/J = -3.5 with the inclusion of crystal fields (D not equal 0), but vanishing external magnetic fields (H = 0), for two distinct lattice coordinations (z = 4 and z = 6). The thermodynamic solutions on the Bethe lattice (the central region of a large Cayley tree) are associated with the attractors of the two-dimensional map. The phase diagrams display several thermodynamic phases (paramagnetic, ferromagnetic, ferrimagnetic, and staggered quadrupolar). In some cases, there are regions of numerical co stability of two different attractors of the map, associated with discontinuous phase transitions between the corresponding phases. To verify the thermodynamic stability of the phases and to locate the first-order boundaries, the analytical expression of the Gibbs free energy was obtained by the method proposed by Gujrati [Rev. Lett. 74, 809 (1995)]. For lower coordinations (z = 4) the transition between the ferrimagnetic and the staggered quadrupolar phases is always continuous, while the transition between the ferromagnetic and the ferrimagnetic phases is discontinuous at low temperatures, turning into continuous for temperatures above a tricritical point. On the other hand, for higher coordinations (z = 6), the transition between the ferromagnetic and the ferrimagnetic phases is always continuous. However, the transition between the ferrimagnetic and the staggered quadrupolar phases is continuous for higher temperatures and discontinuous for temperatures below a tricritical point, in agreement with previous results obtained in the mean-field approximation (infinity-coordination limit). In both cases, the occurrence and the thermodynamic stability of the ferrimagnetic phase is confirmed.976110CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOCAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL E NÍVEL SUPERIORCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOCAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL E NÍVEL SUPERIOR132988/2014-3158316

Phase transitions in phospholipid monolayers: statistical model at the pair approximation

CAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL E NÍVEL SUPERIORCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOA Langmuir film, consisting of a phospholipid monolayer at the air-water interface, was modeled as a two-dimensional lattice gas corresponding to a ternary mixture of water molecules (w), ordered-chain lipids (o), and disordered-chain lipids (d). The statistical problem is formulated in terms of a spin-1 model, in which the disordered-chain lipid states possess a high degenerescence omega gt;gt; 1, and was termed Doniach lattice gas (DLG). Motivated by some open questions in the analysis of the DLG model at the mean-field approximation (MFA) [phys. Rev. E 90, 052705 (2014)], we have reconsidered it at the pair-approximation level by solving the model on a Cayley tree of coordination z. The attractors of the corresponding discrete-map problem are associated with the thermodynamic solutions on the Bethe lattice (the central region of an asymptotically infinite Cayley tree). To check the thermodynamic stability of the possible phases, the grand-potential density was obtained by the method proposed by Gujrati [Phys. Rev. Lett. 74, 809 (1995)]. In general, the previous MFA results are confirmed at the pair-approximation level, but a novel staggered phase, overlooked in the MFA analysis, was found when the condition epsilon(wd) gt; 1/2(epsilon(ww) + epsilon(dd)) is satisfied, where epsilon(xy) represents the nearest-neighbor intermolecular interactions between single-site states x and y. Model parameters obtained by fitting to experimental data for the two most commonly studied zwitterionic phospholipids, 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), yield phase diagrams consistent with the phase transitions observed on Langmuir films of the same lipids under isothermal compression, which present a liquid-condensed to a liquid-expanded first-order transition line ending at a critical point.991113CAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL E NÍVEL SUPERIORCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL E NÍVEL SUPERIORCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO1186359/201388887.136373/2017-00465259/2014-6142249/2017-32014/50983-

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

Tumour necrosis factor-alpha and interleukin-8 inhibit neutrophil migration in vitro and in vivo

Pretreatment of human neutrophils with recombinant tumour necrosis factor-alpha (rTNF-α) and/or interleukin-8 (rIL-8), but not with either transforming growth factor-beta, interleukin-6 or interferon-gamma, rendered these cells less responsive to FMLP, in microchemotaxis assays. This inhibitory effect was dose dependent and more powerful when neutrophils were pretreated with a mixture of both cytokines. Intravenous injection of human rIL-8 (hrIL-8) and/or murine rTNF-α (mrTNF-α) also significantly reduced in vivo neutrophil migration into peritoneal cavities of rats stimulated with carrageenan. These data suggest that the defect in neutrophil migration during septicaemia or endotoxaemia may be the result of the continuous release of IL-8 and TNF-α into the circulation. Thus, either the selective control or blockade of releasing of these cytokines as well as of its effects on neutrophils may be clinically useful in reestablishing the cell defence mechanisms

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