An extension of the Pitzer equation for the excess Gibbs energy of aqueous electrolyte systems to aqueous polyelectrolyte solutions

Pitzer`s equation for the excess Gibbs energy of aqueous solutions of low-molecular electrolytes is extended to aqueous solutions of polyelectrolytes. The model retains the original form of Pitzer`s model (combining a long-range term, based on the Debye-Huckel equation, with a short-range term similar to the virial equation where the second osmotic virial coefficient depends on the ionic strength). The extension consists of two parts: at first, it is assumed that a constant fraction of the monomer units of the polyelectrolyte is dissociated, i.e., that fraction does not depend on the concentration of the polyelectrolyte, and at second, a modified expression for the ionic strength (wherein each charged monomer group is taken into account individually) is introduced. This modification is to account for the presence of charged polyelectrolyte chains, which cannot be regarded as punctual charges. The resulting equation was used to correlate osmotic coefficient data of aqueous solutions of a single polyelectrolyte as well as of binary mixtures of a single polyelectrolyte and a salt with low-molecular weight. It was additionally applied to correlate liquid-liquid equilibrium data of some aqueous two-phase systems that might form when a polyelectrolyte and another hydrophilic but neutral polymer are simultaneously dissolved in water. A good agreement between the experimental data and the correlation result is observed for all investigated systems. (c) 2008 Elsevier B.V. All rights reserved.

Wave-activity conservation laws for the three-dimensional anelastic and Boussinesq equations with a horizontally homogeneous background flow

Wave-activity conservation laws are key to understanding wave propagation in inhomogeneous environments. Their most general formulation follows from the Hamiltonian structure of geophysical fluid dynamics. For large-scale atmospheric dynamics, the Eliassen–Palm wave activity is a well-known example and is central to theoretical analysis. On the mesoscale, while such conservation laws have been worked out in two dimensions, their application to a horizontally homogeneous background flow in three dimensions fails because of a degeneracy created by the absence of a background potential vorticity gradient. Earlier three-dimensional results based on linear WKB theory considered only Doppler-shifted gravity waves, not waves in a stratified shear flow. Consideration of a background flow depending only on altitude is motivated by the parameterization of subgrid-scales in climate models where there is an imposed separation of horizontal length and time scales, but vertical coupling within each column. Here we show how this degeneracy can be overcome and wave-activity conservation laws derived for three-dimensional disturbances to a horizontally homogeneous background flow. Explicit expressions for pseudoenergy and pseudomomentum in the anelastic and Boussinesq models are derived, and it is shown how the previously derived relations for the two-dimensional problem can be treated as a limiting case of the three-dimensional problem. The results also generalize earlier three-dimensional results in that there is no slowly varying WKB-type requirement on the background flow, and the results are extendable to finite amplitude. The relationship A E =cA P between pseudoenergy A E and pseudomomentum A P, where c is the horizontal phase speed in the direction of symmetry associated with A P, has important applications to gravity-wave parameterization and provides a generalized statement of the first Eliassen–Palm theorem.

An Overview of Abortion Laws

Since the Supreme Court handed down its 1973 decisions in Roe v. Wade and Doe v. Bolton, states have constructed a lattice work of abortion law, codifying, regulating and limiting whether, when and under what circumstances a woman may obtain an abortion. The following table highlights the major provisions of these state laws. More detailed information can be found by selecting the table column headings in blue. Except where noted, the laws are in effect, although they may not always be enforced.

Inhibitory Control is a Rate-Limiting Factor to Preschoolers' Use of Irregular Inflection

We investigated whether children’s inhibitory control is associated with their ability to produce irregular verb forms as well as learn from corrective feedback following their use of an over-regularized form. Forty-eight 3.5 to 4.5 year old children were tested on the irregular past tense and provided with adult corrective input via models of correct use or recasts of errors following ungrammatical responses. Inhibitory control was assessed with a three-item battery of tasks that required suppressing a prepotent response in favor of a non-canonical one. Results showed that inhibitory control was predictive of children’s initial production of irregular forms and not associated with their post-feedback production of irregulars. These findings show that children’s executive functioning skills may be a rate-limiting factor on their ability to produce correct forms, but might not interact with their ability to learn from input in this domain. Findings are discussed in terms of current theories of past-tense acquisition and learning from input more broadly.

Geometric Stable Laws Through Series Representations

Let (Xi ) be a sequence of i.i.d. random variables, and let N be a geometric random variable independent of (Xi ). Geometric stable distributions are weak limits of (normalized) geometric compounds, SN = X1 + · · · + XN , when the mean of N converges to infinity. By an appropriate representation of the individual summands in SN we obtain series representation of the limiting geometric stable distribution. In addition, we study the asymptotic behavior of the partial sum process SN (t) = ⅀( i=1 ... [N t] ) Xi , and derive series representations of the limiting geometric stable process and the corresponding stochastic integral. We also obtain strong invariance principles for stable and geometric stable laws.

Inhibitory Control is a Rate-Limiting Factor to Preschoolers' Use of Irregular Inflection

We investigated whether children’s inhibitory control is associated with their ability to produce irregular verb forms as well as learn from corrective feedback following their use of an over-regularized form. Forty-eight 3.5 to 4.5 year old children were tested on the irregular past tense and provided with adult corrective input via models of correct use or recasts of errors following ungrammatical responses. Inhibitory control was assessed with a three-item battery of tasks that required suppressing a prepotent response in favor of a non-canonical one. Results showed that inhibitory control was predictive of children’s initial production of irregular forms and not associated with their post-feedback production of irregulars. These findings show that children’s executive functioning skills may be a rate-limiting factor on their ability to produce correct forms, but might not interact with their ability to learn from input in this domain. Findings are discussed in terms of current theories of past-tense acquisition and learning from input more broadly.

Visual demonstration of the ionic strength effect in the classroom: the Debye-Hückel limiting law

The effects of ionic strength on ions in aqueous solutions are quite relevant, especially for biochemical systems, in which proteins and amino acids are involved. The teaching of this topic and more specifically, the Debye-Hückel limiting law, is central in chemistry undergraduate courses. In this work, we present a description of an experimental procedure based on the color change of aqueous solutions of bromocresol green (BCG), driven by addition of electrolyte. The contribution of charge product (z+|z-|) to the Debye-Hückel limiting law is demonstrated when the effects of NaCl and Na2SO4 on the color of BCG solutions are compared.

Polyelectrolyte-protein complexation driven by charge regulation

The interplay between the biocolloidal characteristics (especially size and charge), pH, salt concentration and the thermal energy results in a unique collection of mesoscopic forces of importance to the molecular organization and function in biological systems. By means of Monte Carlo simulations and semi-quantitative analysis in terms of perturbation theory, we describe a general electrostatic mechanism that gives attraction at low electrolyte concentrations. This charge regulation mechanism due to titrating amino acid residues is discussed in a purely electrostatic framework. The complexation data reported here for interaction between a polyelectrolyte chain and the proteins albumin, goat and bovine alpha-lactalbumin, beta-lactoglobulin, insulin, k-casein, lysozyme and pectin methylesterase illustrate the importance of the charge regulation mechanism. Special attention is given to pH congruent to pI where ion-dipole and charge regulation interactions could overcome the repulsive ion-ion interaction. By means of protein mutations, we confirm the importance of the charge regulation mechanism, and quantify when the complexation is dominated either by charge regulation or by the ion-dipole term.

Periodic-orbit analysis and scaling laws of intermingled basins of attraction in an ecological dynamical system

Chaotic dynamical systems with two or more attractors lying on invariant subspaces may, provided certain mathematical conditions are fulfilled, exhibit intermingled basins of attraction: Each basin is riddled with holes belonging to basins of the other attractors. In order to investigate the occurrence of such phenomenon in dynamical systems of ecological interest (two-species competition with extinction) we have characterized quantitatively the intermingled basins using periodic-orbit theory and scaling laws. The latter results agree with a theoretical prediction from a stochastic model, and also with an exact result for the scaling exponent we derived for the specific class of models investigated. We discuss the consequences of the scaling laws in terms of the predictability of a final state (extinction of either species) in an ecological experiment.

Conservation laws, integrability, and transport in one-dimensional quantum systems

In integrable one-dimensional quantum systems an infinite set of local conserved quantities exists which can prevent a current from decaying completely. For cases like the spin current in the XXZ model at zero magnetic field or the charge current in the attractive Hubbard model at half filling, however, the current operator does not have overlap with any of the local conserved quantities. We show that in these situations transport at finite temperatures is dominated by a diffusive contribution with the Drude weight being either small or even zero. For the XXZ model we discuss in detail the relation between our results, the phenomenological theory of spin diffusion, and measurements of the spin-lattice relaxation rate in spin chain compounds. Furthermore, we study the Haldane-Shastry model where a conserved spin current exists.

Third-order nonlinear spectra and optical limiting of lead oxifluoroborate glasses

We have determined two-photon absorption and nonlinear refraction spectra of the 50BO(1.5) - (50-x)PbF(2) - xPbO glasses (with x = 25, 35, 50 cationic %) at the range of the 470 and 1550 nm. The replacement of fluor atoms by oxygen leads to an increase in the third-order susceptibility, due to the formation of non-bridging oxygens (NBO). The nonlinear index of refraction is one order of magnitude higher than the one for fused silica, and it increases almost twice for the sample with x = 50. This sample has also shown promising features for all-optical switching as well as for optical limiting. (C) 2011 Optical Society of America

Multipoint covalent immobilization of lipase on chitosan hybrid hydrogels: influence of the polyelectrolyte complex type and chemical modification on the catalytic properties of the biocatalysts

This work aimed at the production of stabilized derivatives of Thermomyces lanuginosus lipase (TLL) by multipoint covalent immobilization of the enzyme on chitosan-based matrices. The resulting biocatalysts were tested for synthesis of biodiesel by ethanolysis of palm oil. Different hydrogels were prepared: chitosan alone and in polyelectrolyte complexes (PEC) with kappa-carrageenan, gelatin, alginate, and polyvinyl alcohol (PVA). The obtained supports were chemically modified with 2,4,6-trinitrobenzene sulfonic acid (TNBS) to increase support hydrophobicity, followed by activation with different agents such as glycidol (GLY), epichlorohydrin (EPI), and glutaraldehyde (GLU). The chitosan-alginate hydrogel, chemically modified with TNBS, provided derivatives with higher apparent hydrolytic activity (HA(app)) and thermal stability, being up to 45-fold more stable than soluble lipase. The maximum load of immobilized enzyme was 17.5 mg g(-1) of gel for GLU, 7.76 mg g(-1) of gel for GLY, and 7.65 mg g(-1) of gel for EPI derivatives, the latter presenting the maximum apparent hydrolytic activity (364.8 IU g(-1) of gel). The three derivatives catalyzed conversion of palm oil to biodiesel, but chitosan-alginate-TNBS activated via GLY and EPI led to higher recovered activities of the enzyme. Thus, this is a more attractive option for both hydrolysis and transesterification of vegetable oils using immobilized TLL, although industrial application of this biocatalyst still demands further improvements in its half-life to make the enzymatic process economically attractive.

Limiting factors for phytoplankton growth in subtropical reservoirs: the effect of light and nutrient availability in different longitudinal compartments

Limited information is available on the interactions between environmental factors and algal growth in tropical and subtropical aquatic systems. We investigated the relationships between algal biomass (measured as chlorophyll, Chl-a) and light, total phosphorus (TP) and total nitrogen (TN) in longitudinal zones of subtropical reservoirs. We studied the seasonal variation of water variables in Itupararanga Reservoir (Brazil) and compared the results with 16 other subtropical lakes and reservoirs. The longitudinal zones in Itupararanga Reservoir were considered statistically different (p 0.05, MANOVA). From the riverine zone to the dam region of the reservoir, Spearman Correlation Test suggested that light limitation and TP limitation tended to decrease and increase, respectively. Although nitrate concentrations were high (400 g/L), the Spearman coefficients between Chl-a and TN and the TN:TP ratios (11:1 TN:TP 35:1) indicated that nitrogen may be co-limiting algal growth in the studied water body. Putting Itupararanga in a regional context allowed assessment of potential influences of land use on trophic state. Within the subtropical dataset, TP explained a greater percentage of variance in Chl-a (R2 = 0.70) than TN (R2 = 0.17). The main land use type within the reservoirs drainage area significantly influenced the concentrations of TP, TN, and Chl-a (p 0.05, MANOVA), with different relationships between nutrients and chlorophyll in forested (R2 = 0.12-0.33), agricultural (R2 = 0.50-0.68) and urban (R2 = 0.09-0.64) watersheds. Comparisons with literature values and those from reservoirs with less altered watersheds indicated that Itupararanga Reservoir is reaching the mesotrophic-eutrophic boundary, and further nutrient enrichment could cause water quality degradation.

Concentration inequalities and laws of large numbers under epistemic and regular irrelevance

This paper presents concentration inequalities and laws of large numbers under weak assumptions of irrelevance that are expressed using lower and upper expectations. The results build upon De Cooman and Miranda`s recent inequalities and laws of large numbers. The proofs indicate connections between the theory of martingales and concepts of epistemic and regular irrelevance. (C) 2010 Elsevier Inc. All rights reserved.

Thermodynamics of aqueous solutions of polyelectrolytes: Experimental results for the activity of water in aqueous solutions of (a single synthetic polyelectrolyte and sodium chloride)

Experimental results for the activity of water in aqueous solutions of 10 single, synthetic polyelectrolytes (polysodium acrylate, polysodium methacrylate, polyammonium acrylate, polysodium ethylene sulfonate, and polysodium styrene sulfonate) and sodium chloride at 298.2 K are presented. The experimental work was performed by applying the isopiestic method with sodium chloride as a reference substance. As expected, the activity of water decreases when the concentration of a polyelectrolyte and/or sodium chloride increases. At constant concentration of a polyelectrolyte and sodium chloride, the activity of water depends on the monomer unit and the molecular mass of the polyelectrolyte. The new data are to be used in future work to develop and test models for the Gibbs excess energy of aqueous solutions of polyelectrolytes.