Volumetric and Viscosimetric Measurements for Methanol + CH 3 –O–(CH 2 CH 2 O) n –CH 3 ( n = 2, 3, 4) Mixtures at (293.15–303.15) K and Atmospheric Pressure: Application of the ERAS Model

Densities, $$\rho$$, and kinematic viscosities, $$\nu$$, have been determined at atmospheric pressure and at 293.15–303.15 K for binary mixtures formed by methanol and one linear polyether of the type CH3–O–(CH2CH2O)n–CH3 (n = 2, 3, 4). Measurements on $$\rho$$ and $$\nu$$ were carried out, respectively, using an Anton Paar DMA 602 vibrating-tube densimeter and an Ubbelohde viscosimeter. The $$\rho$$ values were used to compute excess molar volumes, $$V_{{\text{m}}}^{{\text{E}}}$$, and, together with the $$\nu$$ results, dynamic viscosities ($$\eta$$). Deviations from linear dependence on mole fraction for viscosity, $$\Delta \eta$$, are also provided. Different semi-empirical equations have been employed to correlate viscosity data. Particularly, the equations used are the: Grunberg–Nissan, Hind, Frenkel, Katti–Chaudhri, McAllister and Heric. Calculations show that better results are obtained from the Hind equation. The $$V_{{\text{m}}}^{{\text{E}}}$$ values are large and negative and contrast with the positive excess molar enthalpies, $$H_{{\text{m}}}^{{\text{E}}}$$, available in the literature, for these systems. This indicates that structural effects are dominant. The $$\Delta \eta$$ results are positive and correlate well with the difference in volumes of the mixture compounds, confirming the importance of structural effects. The temperature dependences of $$\eta$$ and of the molar volume have been used to calculate enthalpies, entropies and Gibbs energies, $$\Delta G^{*}$$, of viscous flow. It is demonstrated that $$\Delta G^{*}$$ is essentially determined by enthalpic effects. Methanol + CH3–O–(CH2CH2O)n–CH3 mixtures have been treated in the framework of the ERAS model. Results for $$H_{{\text{m}}}^{{\text{E}}}$$ are acceptable, while the composition dependence of the $$V_{{\text{m}}}^{{\text{E}}}$$ curves is poorly represented. This has been ascribed to the existence of strong dipolar and structural effects in the present solutions.     

Determination of ferrous and ferric iron from total iron content and thermogravimetric analysis

Journal of Thermal Analysis and Calorimetry - Ferrous ( $$\hbox {Fe}^{2+}$$ ) and ferric ( $$\hbox {Fe}^{3+}$$ ) iron content in mineral samples was determined from total iron (as obtained, for...     

Electrostatic-thermodynamic-kinetic (ELTHEKI) modeling of the coupled $$\text {Ni}$$ / $$\text {Ni}\text {O}$$ /water system,under physico-chemical conditions of pressurized water reactors

Journal of Solid State Electrochemistry - In the present paper, we develop an electrostatic-thermodynamic-kinetic (ELTHEKI) model for studying the behavior of the specific $$\text {Ni}$$ / $$\text...     

High-rate Deposition of Polycrystalline Diamond Film Using Time-series Exposure of Modulated/Non-modulated Induction Thermal Plasmas at Different Flow Rates of Carbon Source Gas

Plasma Chemistry and Plasma Processing - In this paper $$\hbox {CH}_4$$ / $$\hbox {H}_2$$ gas flow rate effect on polycrystalline diamond deposition was studied using a time-series exposure...     

Identifiability of chemical reaction networks

We consider the dynamics of chemical reaction networks under the assumption of mass-action kinetics. We show that there exist reaction networks for which the reaction rate constants are not uniquely identifiable, even if we are given complete information on the dynamics of concentrations for all chemical species of . Also, we show that there exist reaction networks such that their dynamics are identical under appropriate choices of reaction rate constants, and present theorems that characterize the properties of , , that make this possible. We use these facts to show how we can determine dynamical properties of some chemical networks by analyzing other chemical networks.     

Mathematical relations between codon bias indexes and their applications

Codon Adaptation Index (CAI), Effective Number of Codons as well as its modifications , can be used to measure gene codon bias. In this article, we prove is more efficient and unbiased than and by revisiting correlations of them with CAI in the level of individual amino acid’s codon bias. Correlations are studied by mathematical expressions rather than statistic methods, because the latter unavoidably depend on the data set used. Additionally, the immediate cause of correlations of with CAI (as well as those of RSCU with CAI) are also described in mathematical language. Perhaps, mathematics provides us a new way to study correlations between biological indexes.     

Electrokinetically-driven flow mixing in microchannels with wavy surface

This paper investigates the mixing characteristics of electrokinetically-driven flow in microchannels with different wavy surface configurations. Numerical simulations are performed to analyze the influence of the wave amplitude and the length of the wavy section on the mixing efficiency within the microchannel. Typically, straight channels have a poor mixing performance because the fluid flow is restricted to the low Reynolds number regime, and hence mixing takes place primarily as a result of diffusion effects. However, the wavy surfaces employed in the current microchannels increase the interfacial contact area between the two species in the microchannel and therefore improve the mixing efficiency. The mixing performance is further enhanced by the application of a heterogeneous charge pattern on the wavy surfaces. The numerical results show that the heterogeneous charge pattern generates flow circulations near the microchannel walls. These circulations are shown to provide an effective enhancement in the mixing performance. Overall, the present results show that the mixing performance is improved by increasing the magnitude of the heterogeneous surface zeta potential upon the wavy surface or by increasing the wave amplitude or the length of the wavy section in the microchannel.     

Physico-Chemical Characterization of Binary and Ternary Mixtures of Imidazolium Based Cation and Common Anion Ionic Liquids with Lactams

Journal of Solution Chemistry - Excess molar volumes, $$V_{{}}^{{\text{E}}}$$ , excess isentropic compressibilities, $$\kappa_{{\text{S}}}^{{\text{E}}}$$ of binary 1-butyl-2,3-dimethylimidazolium...     

Interaction of a finite quantum system with an infinite quantum system that contains a single one-parameter eigenvalue band

Interaction of a finite quantum system that contains ρ eigenvalues and eigenstates with an infinite quantum system that contains a single one-parameter eigenvalue band is considered. A new approach for the treatment of the combined system is developed. This system contains embedded eigenstates with continuous eigenvalues , and, in addition, it may contain isolated eigenstates with discrete eigenvalues . Two ρ × ρ eigenvalue equations, a generic eigenvalue equation and a fractional shift eigenvalue equation are derived. It is shown that all properties of the system that interacts with the system can be expressed in terms of the solutions to those two equations. The suggested method produces correct results, however strong the interaction between quantum systems and . In the case of the weak interaction this method reproduces results that are usually obtained within the formalism of the perturbation expansion approach. However, if the interaction is strong one may encounter new phenomena with much more complex behavior. This is also the region where standard perturbation expansion fails. The method is illustrated with an example of a two-dimensional system that interacts with the infinite system that contains a single one-parameter eigenvalue band. It is shown that all relevant completeness relations are satisfied, however strong the interaction between those two systems. This provides a strong verification of the suggested method.     

Sodium and Potassium tert-Butyl Peroxide Hydrates: Crystal Structure and Properties

Russian Journal of Coordination Chemistry - Sodium and potassium tert-butyl peroxide hydrates 2Na+·2C4H9 $${\text{O}}_{2}^{ - }$$ ·7H2O (I) and 2K+· 2C4H9 $${\text{O}}_{2}^{ - }$$...     

Numerically Calculating the Concentration and Temperature Dependences of the Electrical Conductivity of Aqueous Electrolyte Solutions

Russian Journal of Physical Chemistry A - Kinetic equations are used to find analytical expressions for dynamic electrical conductivity $$\sigma (\omega )$$ and electroelasticity modulus $$ {\in}...     

Interaction of an isolated state with an infinite quantum system containing several one-parameter eigenvalue bands: I. Time-independent case

A new method for the exact solution of the interaction of an isolated state with an infinite dimensional quantum system §_∞ ^b containing several one-parameter eigenvalue bands is developed. Unlike standard perturbation expansion approach, this method produces correct results however strong the interaction between the state and the system . It is shown that in the case of the weak interaction this method correctly reproduces standard results obtained within the formalism of the perturbation expansion method. In particular, due to the interaction with the system , eigenvalue E of the state shifts to a new position. In addition, if this eigenvalue is embedded inside the range of the unperturbed eigenvalues, this shifted eigenvalue broadens and spectral distribution of the state has the shape of the universal resonance curve. However, if the interaction is strong, one finds much more complex and much more complicated behavior     

A class of orthogonal polynomials suggested by a trigonometric Hamiltonian: Antisymmetric states

This is the second in a series of papers dealing with the sets of orthogonal polynomials generated by a trigonometric Hamiltonian. In the first of this series, a subclass of the Jacobi polynomials denoted by and referred to as the -polynomial of the first kind, which arises in the investigation of the symmetric state eigenfunctions of the Hamiltonian under consideration, was examined. Another subclass of the Jacobi polynomials denoted by is introduced here representing the antisymmetric states, and is called in accordance the -polynomial of the second kind. Moreover, by the derivation of the ultraspherical polynomial wavefunctions, interrelations between the -polynomials of the first and second kinds as well as the other orthogonal polynomial systems are also emphasized.AMS subject classification: 33C45, 81Q05, 33C05     

Unified treatment of complete orthonormal sets for exponential type vector orbitals of particles with spin 1 in coordinate, momentum and four-dimensional spaces

The new formulas are obtained for complete orthonormal sets of exponential type vector orbitals of a particle with spin 1 in coordinate, momentum and four-dimensional spaces using the properties of spherical vectors and complete orthonormal scalar basis sets of -exponential type orbitals ( -ETO), -momentum space orbitals ( -MSO) and -hyperspherical harmonics ( -HSH) introduced by the author for particles with spin s = 0, where These vector orbitals are complete without the inclusion of the continuum and, therefore, their group of transformation is the four-dimensional rotation group of O(4). For overlap integrals over vector Slater orbitals with the same screening constant the analytical relations in coordinate space are also derived. It should be noted that the new idea presented in this study is the combination of spherical vectors with complete orthonormal scalar sets for radial parts of -orbitals.     

On minimal energies of trees of a prescribed diameter

The energy of a graph is defined as the sum of the absolute values of all the eigenvalues of the graph. Let denote the set of trees on n vertices and diameter d, . Yan and Ye [Appl. Math. Lett. 18 (2005) 1046–1052] have recently determined the unique tree in with minimal energy. In this article, the trees in with second-minimal energy are characterizedAMS Subject Classification: 05C50, 05C35     

Modeling the Processes of the Dissolution of Chromium(III) and Copper Oxides in an Acidic Environment

Based on the experimental studies of the dissolution of Cr2O3 and CuO in an acidic environment, as well as investigation of the effect of acids, pH, and concentration of anions on the rate of dissolution of the oxides, the nature of the limiting stage is determined which consists in the formation of surface compounds (depending on the acidity of the environment) of the $${\text{MeOH}}_{s}^{{x + }}$$ and $${\text{MeHSO}}_{{4s}}^{{x + }}$$ types and their subsequent transition into the solution of the electrolyte. The comparative analysis of the dissolution of the oxides of two d metals is performed.     

On the Laplacian spectral radii of trees with perfect matchings

Denote by the set of trees of order 2k with perfect matchings. GUO [Guo, Linear Algebra Appl. 368:379–385, 2003.] determined the largest value of Laplacian spectral radii μ(T) of the trees T in and gave the corresponding tree T in whose μ(T) reaches this largest value. In this paper, we determine the second to the sixth largest values of μ(T) of the trees T in and also give the corresponding trees T in whose μ(T) reach these values.     

Direct and exchange contributions to inner and outer radii in many-electron atoms

Within the Hartree-Fock framework, the spinless two-electron density function Γ (r ₁, r ₂) consists of direct Γ_di (r ₁, r ₂) and exchange Γ_ex (r ₁, r ₂) parts. Accordingly, the inner and outer radii in many-electron systems are rigorously separated into the direct and exchange contributions, i.e., and . It is generally shown that and , where is the usual average radius of an electron. Numerical examinations of the direct and exchange contributions for the 102 atoms from He to Lr in their ground states find that the electron exchange works to decrease and increase . However, the exchange parts are very small and the direct parts essentially govern the inner and outer radii.     

Densities and Volumetric Properties of Binary Mixtures of Formamide with 1-Butanol, 2-Butanol, 1,3-Butanediol and 1,4-Butanediol at Temperatures between 293.15 and 318.15 K

The densities of binary mixtures of formamide (FA) with 1-butanol, 2-butanol, 1,3-butanediol, and 1,4-butanediol, including those of the pure liquids, over the entire composition range were measured at temperatures (293.15, 298.15, 303.15, 308.15, 313.15 and 318.15) K and atmospheric pressure. From the experimental data, the excess molar volume, V _m ^E, partial molar volumes, and , at infinite dilution, and excess partial molar volumes, and , at infinite dilution were calculated. The variation of these parameters with composition and temperature of the mixtures are discussed in terms of molecular interactions in these mixtures. The partial molar expansivities, and , at infinite dilution and excess partial molar expansivities, and , at infinite dilution were also calculated. The V _m ^E values were found to be positive for all the mixtures at each temperature studied, except for FA + 1-butanol which exhibits a sigmoid trend wherein V _m ^E values change sign from positive to negative as the concentration of FA in the mixture is increased. The V _m ^E values for these mixtures follow the order: 1-butanol < 2-butanol < 1,3-butanediol < 1,4-butanediol. It is observed that the V _m ^E values depend upon the number and position of hydroxyl groups in these alkanol molecules.     

The variance of a consensus

In proficiency tests the consensus of the participants' results is often used as the assigned value to calculate z-scores. Where the consensus is quantified as the robust mean of n results, the standard error of the assigned value is often taken to be , where is the robust standard deviation estimated from the same data ¹ . As some of the results are downweighted in robust estimation, is too large a denominator, so that tends to have a somewhat low bias. This bias is shown to be inconsequential for proficiency testing purposes. However, an unbiased estimate can be obtained by using the bootstrap.

---