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.

The force, power, and energy of the 100 meter sprint

At the 2008 Summer Olympics in Beijing, Usain Bolt broke the world record for the 100 m sprint. Just one year later, at the 2009 World Championships in Athletics in Berlin he broke it again. A few months after Beijing, Eriksen [Am. J. Phys. 77, 224-228 (2009)] studied Bolt's performance and predicted that Bolt could have run about one-tenth of a second faster, which was confirmed in Berlin. In this paper we extend the analysis of Eriksen to model Bolt's velocity time dependence for the Beijing 2008 and Berlin 2009 records. We deduce the maximum force, the maximum power, and the total mechanical energy produced by Bolt in both races. Surprisingly, we conclude that all of these values were smaller in 2009 than in 2008.

Resummation of infrared divergences in the free energy of spin-two fields

We derive a closed form expression for the sum of all the infrared divergent contributions to the free energy of a gas of gravitons. An important ingredient of our calculation is the use of a gauge fixing procedure such that the graviton propagator becomes both traceless and transverse. This has been shown to be possible, in a previous work, using a general gauge fixing procedure, in the context of the lowest order expansion of the Einstein-Hilbert action, describing noninteracting spin-two fields. In order to encompass the problems involving thermal loops, such as the resummation of the free energy, in the present work, we have extended this procedure to the situations when the interactions are taken into account.

Energy of the first excited state of (43)Ar

Results of proton-proton-gamma coincidence measurements using the (36)S+(9)Be reaction revealed a gamma ray of 201.27 +/- 0.16 keV that most probably corresponds to the transition between the predicted 7/2(-) first excited state to the 5/2(-) ground state of (43)Ar.

Free energy of Lorentz-violating QED at high temperature

In this paper we study the one-and two-loop contribution to the free energy in QED with Lorentz symmetry breaking introduced via constant CPT-even Lorentz-breaking parameters at the high temperature limit. We find the impact of the Lorentz-violating term for the free energy and carry out a numerical estimation for the Lorentz-breaking parameter.

Contribution of the second Landau level to the exchange energy of the three-dimensional electron gas in a high magnetic field

We derive a closed analytical expression for the exchange energy of the three-dimensional interacting electron gas in strong magnetic fields, which goes beyond the quantum limit (L=0) by explicitly including the effect of the second, L=1, Landau level and arbitrary spin polarization. The inclusion of the L=1 level brings the fields to which the formula applies closer to the laboratory range, as compared to previous expressions, valid only for L=0 and complete spin polarization. We identify and explain two distinct regimes separated by a critical density n(c). Below n(c), the per particle exchange energy is lowered by the contribution of L=1, whereas above n(c) it is increased. As special cases of our general equation we recover various known more limited results for higher fields, and we identify and correct a few inconsistencies in some of these earlier expressions.

The influence of microstructure on the maximum load and fracture energy of refractory castables

Refractory castables are composed of fractions of fine to fairly coarse particles. The fine fraction is constituted primarily of raw materials and calcium aluminate cement, which becomes hydrated, forming chemical bonds that stiffen the concrete during the curing process. The present study focused on an evaluation of several characteristics of two refractory castables with similar chemical compositions but containing aggregates of different sizes. The features evaluated were the maximum load, the fracture energy, and the ""relative crack-propagation work"" of the two castables heat-treated at 110, 650, 1100 and 1550 degrees C. The results enabled us to draw the following conclusions: the heat treatment temperature exerts a significant influence on the matrix/aggregate interaction, different microstructures form in the castables with temperature, and a relationship was noted between the maximum load and the fracture energy. (C) 2009 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Ground-state energy of a classical artificial molecule

We study the ground-state energy of a classical artificial molecule formed by two-dimensional clusters (artificial atoms) of N/2 charged particles separated by a distance d. For the small molecules of N = 2 and 4, we obtain analytical expressions for this energy. For the larger ones, we calculate the ground-state energy using molecular dynamics simulation for N up to 128. From our numerical results, we are able to find out a function to approximate the ground-state energy of the molecules covering the range from atoms to molecules for any inter-atom distance d and for particle number from N = 8 to 128 within a difference less than one percent from the MD data.

Energy of bond defects in quantum spin chains obtained from local approximations and from exact diagonalization

We study the influence of ferromagnetic and antiferromagnetic bond defects on the ground-state energy of antiferromagnetic spin chains. In the absence of translational invariance, the energy spectrum of the full Hamiltonian is obtained numerically, by an iterative modi. cation of the power algorithm. In parallel, approximate analytical energies are obtained from a local-bond approximation, proposed here. This approximation results in significant improvement upon the mean-field approximation, at negligible extra computational effort. (C) 2008 Published by Elsevier B.V.

ENERGY OF GLOBAL FRAMES

The energy of a unit vector field X on a closed Riemannian manifold M is defined as the energy of the section into T(1) M determined by X. For odd-dimensional spheres, the energy functional has an infimum for each dimension 2k + 1 which is not attained by any non-singular vector field for k > 1. For k = 1, Hopf vector fields are the unique minima. In this paper we show that for any closed Riemannian manifold, the energy of a frame defined on the manifold, possibly except on a finite subset, admits a lower bound in terms of the total scalar curvature of the manifold. In particular, for odd-dimensional spheres this lower bound is attained by a family of frames defined on the sphere minus one point and consisting of vector fields parallel along geodesics.

Ionic Recognition by 7-Nitro-1,3,5-triaza Adamantane: First Thermodynamic Study

A thermodynamic study involving 7-nitro-1,3,5-triaza adamantane, 1, and its interaction with metal cations in nonaqueous media is first reported. Solubility data of 1 in various solvents were used to derive the standard Gibbs energies of solution, Delta G(s)degrees in these solvents. The effect of solvation in the different media was assessed from the Gibbs energy of transfer taking acetonitrile as a reference solvent. (1)H NMR studies of the interaction of 1 and metal cations were carried out in CD(3)CN and CD(3)OD and the data are reported. Conductance measurements revealed that this ligand forms lead(II) or zinc complexes of 1: 1 stoichiometry in acetonitrile. It also revealed a stoichiometry of two molecules of 1 per mercury(II) and two cadmiu (II) ions per molecule of 1. The addition of silver salt to 1 led to the precipitation of the silver-1 complex which was isolated and characterized by X-ray crystallography. At variance with conductance measurements in solution, in the solid state the X-ray structure show`s a 1:1 stoichiometry in the Hg(II) complex. The themiodynamics of complexation of 1 and these cations provide a quantitative assessment of the selective behavior of this ligand for ions of environmental relevance.

Structure of (46)Ti at low excitation energy

The nucleus (46)Ti has been studied with the reaction (42)Ca((7)Li,p2n)(46)Ti at a bombarding energy of 31 MeV. Thin target foils backed with a thick Au layer were used. Five new levels of negative parity were observed. Several lifetimes have been determined with the Doppler shift attenuation method. Low-lying experimental negative-parity levels are assigned to three bands with K(pi) = 3, 0, and 4, which are interpreted in terms of the large-scale shell model, considering particle-hole excitations from d(3/2) and s(1/2) orbitals. Shell model calculations were performed using a few effective interactions. However, good agreement was not achieved in the description of either negative- or positive-parity low-lying levels.

Dissipation as a mechanism of energy gain

Some properties of the annular billiard under the presence of weak dissipation are studied. We show, in a dissipative system, that the average energy of a particle acquires higher values than its average energy of the conservative case. The creation of attractors, associated with a chaotic dynamics in the conservative regime, both in appropriated regions of the phase space, constitute a generic mechanism to increase the average energy of dynamical systems.

Quantification of MgO surface excess on the SnO(2) nanoparticles and relationship with nanostability and growth

In this work, we experimentally showed that the spontaneous segregation of MgO as surface excess in MgO doped SnO(2) nanoparticles plays an important role in the system`s energetics and stability. Using Xray fluorescence in specially treated samples, we quantitatively determined the fraction of MgO forming surface excess when doping SnO(2) with several different concentrations and established a relationship between this amount and the surface energy of the nanoparticles using the Gibbs approach. We concluded that the amount of Mg ions on the surface was directly related to the nanoparticles total free energy, in a sense that the dopant will always spontaneously distribute itself to minimize it if enough diffusion is provided. Because we were dealing with nanosized particles, the effect of MgO on the surface was particularly important and has a direct effect on the equilibrium particle size (nanoparticle stability), such that the lower the surface energy is, the smaller the particle sizes are, evidencing and quantifying the thermodynamic basis of using additives to control SnO(2) nanoparticles stability. (C) 2010 Elsevier B.V. All rights reserved.

Interface Energy Measurement of MgO and ZnO: Understanding the Thermodynamic Stability of Nanoparticles

Nanomaterials have triggered excitement in both fundamental science and technological applications in several fields However, the same characteristic high interface area that is responsible for their unique properties causes unconventional instability, often leading to local collapsing during application Thermodynamically, this can be attributed to an increased contribution of the interface to the free energy, activating phenomena such as sintering and grain growth The lack of reliable interface energy data has restricted the development of conceptual models to allow the control of nanoparticle stability on a thermodynamic basis. Here we introduce a novel and accessible methodology to measure interface energy of nanoparticles exploiting the heat released during sintering to establish a quantitative relation between the solid solid and solid vapor interface energies. We exploited this method in MgO and ZnO nanoparticles and determined that the ratio between the solid solid and solid vapor interface energy is 11 for MgO and 0.7 for ZnO. We then discuss that this ratio is responsible for a thermodynamic metastable state that may prevent collapsing of nanoparticles and, therefore, may be used as a tool to design long-term stable nanoparticles.