General equation for determining the dissociation constants of polyprotic acids and bases from additive properties. Part I. Theory

Measured additive properties of polyprotic acids and bases as functions of the pH of the solution can be used for the determination of the dissociation constants. A rigorous general equation is derived in this paper for this purpose. The equation relates the additive property of the acid or base to the dissociation constants, the limiting values and activity coefficients of the solute species, and to the pH of the solution. The equation is used to obtain the dissociation constants by fitting it to the experimental data in a nonlinear least-square fitting procedure. Overlapping dissociation constants pose no problem in this method. Applications to spectrophotometry and reversed-phase high performance liquid chromatography are presented in a following paper (Part II of this series).     

Diffusion in glassy polymers. III

The diffusion studies of several solvents in epoxy polymer reported by Kewi and Zupko in Part I of this series are explained with the solution obtained from the generalized diffusion equation which includes the internal stress contribution. The rate of permeation of a penetrant through a polymer film and the time lag needed to reach steady state are also given for the generalized diffusion equation.     

Electrochemistry of capillary systems with narrow pores III. Electrical conductivity

The extension of the Teorell–Meyer–Sievers theory of the dialysis potential to a general theory of capillary systems with narrow pores outlined in Part I of this series of publications has been applied to electroosmotic phenomena in Part II. In this Part, the electrical conductivity, including the electrical convection conductivity, will be treated in terms of the new theory. The corresponding equations already referred to in Part I are derived. In addition, results of measurements of the electrical conductivity of collodion membranes with graded porosity and graded electrochemical activity in aqueous KCl solutions of different concentrations are reported. They are used to test the new theory. It will be shown that it is possible to determine the fixed ion concentration A of the membranes by using electrical conductivity data. The theory predicts that the value of A should be identical with the ‘selectivity constant' of the Meyer–Sievers theory of the dialysis potential. This prediction will be checked in Part IV of this series of contributions.     

The electrostatic potential generated by topological atoms. II. Inverse multipole moments

Quantum chemical topology defines finite atoms, whose bounded electron density generates a well-defined electrostatic potential. A multipole expansion based on spherical tensors provides a potential that is formally convergent outside the divergence sphere. Part I of this series [P. L. A. Popelier and M. Rafat, Chem. Phys. Lett.376, 148 (2003)] showed that a continuous multipole expansion expands the convergence region, thereby allowing the electrostatic potential to be evaluated at short range. Here, we propose a different method, based on "inverse" multipole moments, enabling an expansion that converges everywhere. These moments are defined by inverse (i.e., negative) powers of the magnitude of the position vector describing the electron density inside the atom. We illustrate this technique on nitrogen in N(2), oxygen in H(2)O, and oxygen in the phenolic group of the amino acid tyrosine. The proposed method constitutes a considerable advance over the method presented in Part I.     

Polyurethane cationomers. II. Phase inversion and its effect on physical properties

The three series of polyether polyurethane cationomers based on MDI, HDI, and TDI that are the subject of Part I, undergo emulsification (or phase inversion) on addition of water to solutions in MEK. The phase inversion mechanism depends on the structure of hard segment, ionic content, and dispersion temperature. The dispersion process can be divided into three stages involving a separation of hard segment aggregates due to adsorption of water on their surface, water entering into disordered and then ordered hard domains, and finally a rearrangement of agglomerates to form microspheres. The extent of penetration of water into the disordered hard domains decreases with increasing glass transition temperature; while in ordered hard domains, penetration depends on the dissociation temperature of urethane–urethane hydrogen bonds. Thus the penetration of water into the hard domains is strongly dependent on the dispersion temperature. Films cast from the emulsions have both ordered and disordered hard segment regions, this is also true of films cast directly from solution. The dispersion can disrupt the order in hard domains, leading to an increased phase separation for the MDI system and to a slightly increased phase mixing for the HDI and TDI systems. Films cast from solutions have a morphology with soft domains as a continuous phase and hard domains as a fibrillar network dispersed in the continuous phase. After dispersion, the hard segments originally distributed in the dispersed phase can be inverted to become a hard domain network or a continuous phase.     

Dielectric spectra broadening as the signature of dipole-matrix interaction. II. Water in ionic solutions

In this, the second part of our series on the dielectric spectrum symmetrical broadening of water, we consider ionic aqueous solutions. If in Part I, dipole-dipole interaction was the dominant feature, now ion-dipole interplay is shown to be the critical element in the dipole-matrix interaction. We present the results of high-frequency dielectric measurements of different concentrations of NaCl/KCl aqueous solutions. We observed Cole-Cole broadening of the main relaxation peak of the solvent in the both electrolytes. The 3D trajectory approach (described in detail in Part I) is applied in order to highlight the differences between the dynamics and structure of solutions of salts on one hand and dipolar solutes on the other hand.     

An analysis of the siegert eigenvalue problem for autoionizing states

We show that the divergent integrals which appear in a direct matrix solution to the Siegert problem for autoionizing (or electron scattering) state energies and widths can be cancelled exactly. When this is done the Siegert problem becomes essentially a bound state problem. We also show that the resulting non-hermitian secular equation which requires several non-hermitian diagonalizations in the iterative solution for the complex energy can be exactly reduced by a partitioning technique to a single hermitian diagonalization (for a single open channel) with the subsequent iterative solution of a simple algebraic equation.     

Transformation-Governed Heating Techniques in Thermal Analysis II.

The described instrumental method makes it possible that the quasi-static heating technique, well applicable to thermogravimetric measurements, (see Part I of this paper) can be used in the case of DTA and DSC examinations, too. Based on the new type of curves the characteristic transformation temperatures, the whole course of the transformation in dependence of sample temperature, the extent of the enthalpy change caused by the transformation or by its partial processes can accurately be determined. The essentially greater accuracy of the measurements — in comparison to the conventional ones — is due to the quasi-static heating technique which ensures that the transformations should take place under quasi-equilibrium conditions.This revised version was published online in November 2005 with corrections to the Cover Date.     

The rigorous (nonvariational) solution of the Schrödinger equation for a molecular potential of arbitrary shape. II. The basis functions,discrete spectrum,and the special case of MT potential

This paper continues Part I of this paper, referred to in the following as I. The construction of a basis set is explicitly presented. The special case of MT potential is considered, and the corresponding secular equation is shown to match exactly the one resulting from the well-known scattered wave method. Finally, the bound states of a molecule are obtained as the solutions of a real-valued matrix eigenvalue problem.     

Studies of the micro-brownian motion of a polymer chain by the fluorescence polarization method. III. Fluorescent conjugates of polyethyleneimine

Fluorescent conjugates of polyethyleneimine (PEI) were prepared by conjugation of fluorescent dyes, fluorescein isocyanate (FIC), and 1-dimethylaminonaphthalene-5-sulfonyl chloride (DNS), to PEI. The degree of polarization of the fluorescence was measured as a function of temperature and solvent viscosity on aqueous solutions of the conjugates and the data thus obtained were analyzed in terms of an equation of the Perrin type to calculate the mean relaxation time of the conjugate. The mean relaxation times obtained for the two types of the conjugates, which differ in the excited lifetime by a factor of about three, practically agree with one another and are about 2.5 X 10^?8 sec. The relaxation time of the DNS conjugate increases with increasing molecular weight of the conjugate from 2 X 10^?8 to 4 X 10^?8 sec. These values are much larger than those of the PAA conjugates reported in Part I of this series. The relaxation time of this order may correspond to that for the cooperative rotary motion of about ten monomeric residues on the PEI chain, that is, for the motion of an intermediate segment of the PEI molecule in solution. Finally, relaxation time–molecular weight relationships for various types of fluorescent conjugates are compared. It is suggested that these data may serve as a basis for elucidating the mode of motion of a given molecule in solution from the polarization data.     

Electrochemistry of capillary systems with narrow pores III. Electrical conductivity

The extension of the Teorell–Meyer–Sievers theory of the dialysis potential to a general theory of capillary systems with narrow pores outlined in Part I of this series of publications has been applied to electroosmotic phenomena in Part II. In this Part, the electrical conductivity, including the electrical convection conductivity, will be treated in terms of the new theory. The corresponding equations already referred to in Part I are derived. In addition, results of measurements of the electrical conductivity of collodion membranes with graded porosity and graded electrochemical activity in aqueous KCl solutions of different concentrations are reported. They are used to test the new theory. It will be shown that it is possible to determine the fixed ion concentration A of the membranes by using electrical conductivity data. The theory predicts that the value of A should be identical with the `selectivity constant' of the Meyer–Sievers theory of the dialysis potential. This prediction will be checked in Part IV of this series of contributions.     

The adsorption of cetyltrimethylammonium bromide and propanol mixtures with regard to wettability of polytetrafluoroethylene II. Adsorption at polytetrafluoroethylene-aqueous solution interface and wettability

Measurements of contact angles (theta) of aqueous solutions of cetyltrimethylammonium bromide (CTAB) and propanol mixtures at constant CTAB concentration equal to 1x10(-5), 1x10(-4), 6x10(-4) and 1x10(-3) M on polytetrafluoroethylene (PTFE) were carried out. The obtained results indicate that the wettability of PTFE by aqueous solutions of these mixtures depends on their composition and concentration. They also indicate that, contrary to Zisman, there is no linear relationship between cos theta and the surface tension (gamma(LV)), but a linear relationship exists between the adhesional (gamma(LV)cos theta) and surface tension of aqueous solutions of CTAB and propanol mixtures. Curve gamma(LV)cos theta vs gamma(LV) has a slope equal -1 suggesting that adsorption of CTAB and propanol mixtures and the orientation of their molecules at aqueous solution-air and PTFE-aqueous solution interfaces is the same. Extrapolating this curve to the value of gamma(LV)cos theta corresponding to theta=0, the value of the critical tension of PTFE wetting equal 23.4 mN/m was determined. This value was higher than that obtained from contact angles of n-alkanes on PTFE surface (20.24 mN/m). The difference between the critical surface tension values of wetting probably resulted from the fact that at cos theta=1 the PTFE-aqueous solution of CTAB and propanol mixture interface tension was not equal to zero. This tension was determined on the basis of the measured contact angles and Young equation. It appeared that the values of PTFE-aqueous solution of the CTAB and propanol mixtures interface tension can be satisfactorily determined by modified Szyszkowski equation only for solutions in which probably CTAB and propanol molecules are present in monomeric form. However, it appeared that using the equation of Miller et al., in which the possibility of aggregation of propanol molecules in the interface layer is taken into account, it is possible to describe the PTFE-solution interfacial tension for all systems studied in the same way as by the Young equation. On the basis of linear dependence between the adhesional and surface tension it was established that the work of adhesion of aqueous solution of CTAB and propanol mixtures does not depend on its composition and concentration, and the average value of this work was equal to 46.85 mJ/m(2), which was similar to that obtained for adhesion of aqueous solutions of two cationic surfactants mixtures to PTFE surface.     

A model of ionic current densities in the vicinity of a corroding disk-shaped region

The scanning vibrating electrode technique (SVET) permits the measurement of ionic corrosion current densities in a uniform electrolyte solution adjacent to an anodic region in a corroding metal sheet. A credible model for such a corrosion experiment envisages a disk-shaped anode embedded in an infinite coplanar sheet of more noble metal, serving as the cathode. If ohmic polarization governs the corrosion rate, then Laplace's equation holds in the steady state. Two independent, but different, solutions of this equation exist, both based on the premise that the two metallic regions have distinct uniform electrical potentials. In this communication, we show these two solutions to be equivalent and thereby predictions are made about the ionic current densities at points in solution near the corrosion site. These predictions are found to be qualitatively similar to reported experimental findings.     

Polarographic investigations of benzylideneaminoguanidine

Summary 2-(Phenylmethylene)-hydrazinecarboximidamide (I) is reduced at the dropping mercury electrode in a pH-dependent wave, the diffusion-controlled limiting current is markedly influenced by surface active substances due to the adsorption of I. The pK_a1-value of I (photometrically determined) is 9.7. In acid solutions reduction occurs with consumption of 4 electrons per molecule, forming guanidine and benzylamine; thereby fission of the N-N-bond takes place at first, followed by reduction of the C-N(2)-double-bond. In alkaline solutions 2-(phenylmethyl)-hydrazine-carboximidamide (II) is formed by consumption of 2 electrons per molecule; II is not reducible in acid solution.

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Polarographische Untersuchungen von Benzylidenaminoguanidin

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A. Zeller: Part of the thesis in preparation     

Semi-ideal solution theory. 2. Extension to conductivity of mixed electrolyte solutions

Conductivities were measured for the ternary systems NaCl-LaCl(3)-H(2)O and KCl-CdCl(2)-H(2)O and their binary subsystems NaCl-H(2)O, KCl-H(2)O, CdCl(2)-H(2)O, and LaCl(3)-H(2)O at 298.15 K. The semi-ideal solution theory for thermodynamic properties of aqueous solutions of electrolyte mixtures was used together with the Eyring absolute rate theory to study conductivity of mixed electrolyte solutions. A novel simple equation for prediction of the conductivity of mixed electrolyte solutions in terms of the data of their binary solutions was established. The measured conductivities and those reported in literature were used to test the newly established equation and the generalized Young's rule for conductivity of mixed electrolyte solutions. The comparison results show that the deviation of a ternary solution from the new conductivity equation is closely related to its isopiestic behavior and that the deviations are often within experimental uncertainty if the examined system obeys the linear isopiestic relation. While larger deviations are found in the system with large ion pairing effect, the predictions can be considerably improved by using the parameters calculated from its isopiestic results. These results imply that the previous formulation of the thermodynamic properties of aqueous solutions of electrolyte mixtures has a counterpart for transport properties.     

MIBPB: A software package for electrostatic analysis

The Poisson–Boltzmann equation (PBE) is an established model for the electrostatic analysis of biomolecules. The development of advanced computational techniques for the solution of the PBE has been an important topic in the past two decades. This article presents a matched interface and boundary (MIB)‐based PBE software package, the MIBPB solver, for electrostatic analysis. The MIBPB has a unique feature that it is the first interface technique‐based PBE solver that rigorously enforces the solution and flux continuity conditions at the dielectric interface between the biomolecule and the solvent. For protein molecular surfaces, which may possess troublesome geometrical singularities, the MIB scheme makes the MIBPB by far the only existing PBE solver that is able to deliver the second‐order convergence, that is, the accuracy increases four times when the mesh size is halved. The MIBPB method is also equipped with a Dirichlet‐to‐Neumann mapping technique that builds a Green's function approach to analytically resolve the singular charge distribution in biomolecules in order to obtain reliable solutions at meshes as coarse as 1 Å — whereas it usually takes other traditional PB solvers 0.25 Å to reach similar level of reliability. This work further accelerates the rate of convergence of linear equation systems resulting from the MIBPB by using the Krylov subspace (KS) techniques. Condition numbers of the MIBPB matrices are significantly reduced by using appropriate KS solver and preconditioner combinations. Both linear and nonlinear PBE solvers in the MIBPB package are tested by protein–solvent solvation energy calculations and analysis of salt effects on protein–protein binding energies, respectively. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Corridor of existence of thermodynamically consistent solution of the Ornstein-Zernike equation

We obtain the exact equation for a correction to the Ornstein-Zernike (OZ) equation based on the assumption of the uniqueness of thermodynamical functions. We show that this equation is reduced to a differential equation with one arbitrary parameter for the hard sphere model. The compressibility factor within narrow limits of this parameter variation can either coincide with one of the formulas obtained on the basis of analytical solutions of the OZ equation or assume all intermediate values lying in a corridor between these solutions. In particular, we find the value of this parameter when the thermodynamically consistent compressibility factor corresponds to the Carnahan-Stirling formula.     

Application of a micro/macro‐homogenization procedure to the investigation of the mechanical behavior of ionomer membranes for fuel cells

A microhomogenization/macrohomogenization procedure is proposed to compute the mechanical and swelling behavior of ionomer (Nafion) membranes for fuel cells under external compression loads. The membrane is viewed as a periodic porous media composed of a charged solid phase saturated by an aqueous electrolyte solution. We establish the equation of state in a single membrane pore based on a rigorous treatment of thermodynamic, electrostatic (Poisson–Boltzmann equation) and of mechanical equilibrium. The homogenization technique is then applied to propagate the information available in the pore‐scale model to the macroscale. Numerical experiments are performed to illustrate the results in a cylindrical pore geometry. The results show that the swelling pressure can be approximated by the osmotic pressure, which depends on the charge density at the pore walls and the pore radius. The model predicts the water content of liquid equilibrated membrane under various compression loads and the results are consistent with literature data. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1496–1509     

Green's function analysis of the vibrational spectra of polymer chains. I. Several approaches to the problem

Various methods of solving the dynamical equation for defect polymers are discussed. It is shown that the Green's function (GF) can be conveniently used to reduce the order of the characteristic equation to the number of the degrees of freedom of a repeat unit in the case when the perturbation caused by each of the defects is localized within it. In the general case, the order of the reduced determinant depends on the range of the interaction forces between the defect unit and the regular chain. For a polymer chain containing one or two defect units, the Green's function method allows us to obtain the exact solution of the dynamical equation, while for a high concentration of randomly distributed defect units various approximation methods can be used. As a possible approach to the solution of the latter problem we suggest using either one of the versions of the perturbation theory (the dilute limit, the coherent potential approximation) or the cluster approximation.     

Stable drop shapes under disjoining pressure. II. Multiplicity and stability

The stability of the contact line region as affected by the disjoining pressure has been analyzed by solving the augmented Young-Laplace equation. Because of the results in Part I (Zhang, X., Neogi, P., and Ybarra, R. M., J. Colloid Interface Sci.), we have concentrated on obtaining multiple solutions for the same set of conditions. As many as five solutions were obtained: drops that end in a thin film with uniform thickness and where the film shape oscillates, drops that end with microscopic contact angles, as well as uniform thin films of two different thicknesses. The results of linear stability analysis were used to show that most cases were unstable to infinitesimal disturbances. Only two stable drop shapes for the particular disjoining pressure investigated are stable, a thin film of constant thickness and a thin drop that ends in a film of same thickness. Both multiplicity and stability have been discussed here for the first time and shed considerable light on the role of the attractive and repulsive forces.