A statistical associating fluid theory for electrolyte solutions (SAFT-VRE)

A general theory for electrolyte solutions is examined within the framework of the statistical associating fluid theory for potentials of variable range (SAFT-VR). A first extension of the theory (SAFT-VRE) has already been used to describe the thermodynamics and phase equilibria of aqueous solutions of alkali-halide salts [GALINDO, A., GIL-VILLEGAS, A., JACKSON, G. and BURGESS, A. N., 1999, J. phys. Chem., 103, 10272]. The approach incorporates separate contributions describing the monomer, associating and ionic interactions. In the spirit of the SAFT-VR approach the monomer contribution is written as a high-temperature perturbation expansion up to second order; the separate effects of solvent-solvent, solvent-ion and ion-ion interactions on the phase equilibria are studied. Water is taken to be the solvent throughout the study, with the same four-site model and parameters as in the previous work. The association contribution is essential to account for the hydrogen bonding interactions present in water. The effects of ion pairing and solvent-ion association are also examined. For the ionic contribution several levels of approximation are discussed. The effect of the different molecular parameters on the phase behaviour of a model aqueous solution is examined for the different choices.     

Study of the solid-liquid-vapour phase equilibria of flexible chain molecules using Wertheim's thermodynamic perturbation theory

The phase diagram of flexible molecules formed by freely-jointed tangent spheres is studied using the first-order thermodynamic perturbation theory of Wertheim for both fluid and solid phases. A mean-field term is added to the free energy of the fluid and solid phase in order to account for attractive dispersion forces. The approach is used to determine the global (solid-liquid-vapour) phase diagrams and triple points of chain molecules of increasing chain length. It is found that the triple point temperature is not affected strongly by the length of the chain, whereas the gas-liquid critical temperature increases dramatically. The asymptotic limits of the phase diagram for infinitely long chains are discussed. The reduced critical temperature of infinitely long chains as given by the mean-field theory is 2/3, and the reduced triple point temperature is 0.048 56, so that an asymptotic value of T _t/T _c = 0.07284 for the ratio of the triple to critical point temperatures is obtained. This indicates that fully-flexible tangent chains present an enormous liquid range. The proposed theory, while being extremely simple, provides a useful insight into the phase behaviour of chain molecules, showing the existence of finite asymptotic limits for the triple and critical point temperatures. However, since n-alkanes present an asymptotic limit of about T _t/T _c, = 0.40, the agreement With experiment is not quantitative. This suggests that fully flexible models may not be appropriate to model the solid phases of real chain molecules.     

A REMARK ON THE HENSELIZATION OF A REGULAR LOCAL RING

1.IntroductionThenotionofHenselizationofintegrallyclosedintegritydomainswasintroducedbyNagata[3]fromtheconceptofHenselianringwhichwasgivenfirstlybyAzumaya[1].TheHenselizationofalocalringAisacouple(A,i),whereAisalocalHenselianringandi:AAalocalmoaphism...     

THE BLOCH SPACE ON THE UNIT BALL OF A HILBERT SPACE:MAXIMALITY AND MULTIPLIERS

We prove that,as in the finite dimensional case,the space of Bloch functions on the unit ball of a Hilbert space contains,under very mild conditions,any semi-Ba...     

New types of phase behaviour in binary mixtures of hard rod-like particles

The phase behaviour of binary mixtures of hard rod-like particles has been studied using Parsons—Lee theory (Parsons, J. D., 1979, Phys. Rev. A, 19, 1225); Lee, S. D., 1987, J. Chem. Phys., 87, 4972). The stability of the isotropic-nematic (I-N) transition with respect to isotropic—isotropic (I-I), and nematic—nematic (N-N) demixing is investigated. The individual components in the mixtures are modelled as hard cylinders of diameters D_i and lengths L_i (i = 1,2). The aspect ratios k_i = L_i/D_i of the components are kept fixed (with values of k ₁ = 15 and k ₂ = 150), and the phase behaviour of the mixtures is studied for varying diameter ratios d = D ₁/D ₂. When the diameter ratio is relatively large, e.g., for values of d = 50, component 1 may be considered a large colloidal particle, while the second component plays the role of a weakly interacting solvent. This mixture exhibits only an I-N phase transition which is driven by the excluded volume interaction between the large particles (no I-I or N-N demixing is seen). A decrease in the diameter ratio enhances the contribution of the smaller component to the free energy (especially in terms of the unlike excluded volume term), and I-I as well as N-N demixing transitions are observed. The character of the N-N transition is rather unusual, a single region bounded by a lower critical point (in the pressure—composition plane) is seen for a diameter ratio of d = 3.2, while two demixed nematic regions bounded by lower and upper critical points are observed for d = 3.13. A further decrease in the diameter ratio (e.g., to d = 3) leads to systems with a phase behaviour in which the two demixed N-N regions meet, giving rise to a large demixed region with very strong fractionation in composition, and no N-N critical points. The I-I demixing transition is always accompanied by a lower critical point and occurs for systems with intermediate size (diameter) ratios. A diameter ratio of d = 4.5 corresponds to systems with significant like and unlike excluded volume interactions, and in this case the I-N transition takes place over the whole composition range with weak fractionation and one azeotropic point. Surprisingly, the coexisting nematic phase is of lower packing fraction than the isotropic phase for some of the compositions, i.e., an inversion of packing fraction takes place. In addition to this, the longer rods can be less ordered that the shorter rods for certain values of the composition.     

Understanding liquid-liquid immiscibility and LCST behaviour in polymer solutions with a Wertheim TPT1 description

The aim of the work presented in this paper is to help in the understanding of the lower critical solution temperature (LCST) fluid phase behaviour exhibited by polymer solutions. It is well recognized that the LCST in polymer solutions is a consequence of density (compressibility) effects; the solvent is much more compressible than the polymer and the increasing difference in compressibility when the temperature is increased leads to a negative volume of mixing. The separate roles that the repulsive and attractive intermolecular interactions play in this regard are less well understood. In this study we use the Wertheim first-order thermodynamic perturbation theory (TPT1) [Wertheim, M. S., 1987, J. chem. Phys., 87, 7323; Chapman, W. G., Jackson, G., and Gubbins, K. E., 1988, Molec. Phys., 65, 1057] to describe the phase equilibria of model polymer solutions of hard spheres and hard-sphere chains where the diameter of the solvent and the polymeric segments are the same (symmetrical system). The thermodynamic functions (volume, enthalpy, entropy and Gibbs function) of mixing are determined to assess the possibility of a demixing instability in such a system. No fluid-fluid phase separation is found for the purely repulsive (athermal) system, regardless of the chain length of the polymer. The role of the attractive interactions is then investigated by incorporating attractive interactions at the mean-field level; the simplest system with equivalent (symmetric) solvent-solvent, solvent-polymer segment, and polymer segment-polymer segment interaction energies is examined. The attractive interactions are found to be essential in describing the liquid-liquid phase separation; LCST behaviour is found for mixtures with ‘polymer’ chains of seven segments or more. In this case we show that the phase behaviour is driven by an unfavourable (negative) entropy of mixing due to an increase in the density of the solvent on addition of small amounts of polymer. We also determine the thermodynamic properties of mixing for a system of spherical molecules of the same size with directional interactions that give rise to LCST and closed-loop behaviour. As expected the mechanism for phase separation in such systems is very different to that in polymer solutions.     

Improved models for the phase behaviour of hydrogen fluoride: chain and ring aggregates in the SAFT approach and the AEOS model

Hydrogen fluoride presents one of the strongest hydrogen bonds known. Ring aggregates exist both in the vapour and liquid phases at low temperatures resulting in an anomalously high low-temperature vapour pressure. The effect of ring-like aggregates on the vapour—liquid phase equilibria of associating fluids is studied within the framework of the statistical associating fluid theory (SAFT) and in the chemical model of Lencka and Anderko (AEOS). The SAFT approach incorporates separate contributions to describe chain formation, association (hydrogen bonding), and long range dispersion forces. The treatment of the association interactions stems from the thermodynamic perturbation theory of Wertheim. At the first level of approximation the contribution of ring-like aggregates is neglected and only chain- and treelike structures are treated. In this work an earlier extension of the approach to incorporate ring aggregates is used to model the phase behaviour of hydrogen fluoride. The chemical model of Lencka and Anderko for associating fluids is also considered together with a modification that takes into account the formation of ring aggregates. Vapour pressures and coexistence densities are examined together with heats of vapourization, and the calculations are compared with experimental data.     

PHOTOLYSIS AND RADIOLYSIS OF PHENYL-ALANYLGLYCINE

T he P hotolysis of glycine and alanine containing peptides in oxygenated solution has been shown to result in the formation of glyoxylic and pyruvic acids, through oxidative cleavage of the peptide bond[1]. The same products were formed in the radiolysis of such peptides in the presence of oxygen[2]. In a peptide containing aromatic amino-acids the absorption of light results in the excitation of the aromatic ring and it has been postulated[3] that energy is transferred to the peptide bond, resulting in the formation of a radical on the carbon atom adjacent to the peptide bond. Radiolysis, however, involves the attack of hydroxyl radicals and other reactive species formed in the absorption of radiation by water[2]. This study compares the behavior of phenylalanylglycine to photolysis and radiolysis in aerated aqueous solution in relation to a possible energy transfer in photolysis.