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.     

Ferrimagnetic coupling in oxamido-bridged Mn(II)Cu(II) compounds: a combined CASPT2 and DDCI study

Multiconfigurational perturbation theory (CASPT2) and difference dedicated configuration interaction (DDCI) are applied to study the ferrimagnetic coupling in an oxamido-bridged Mn(II)Cu(II) molecular species. CASPT2 reproduces the experimental coupling very well. From the partition of the CASPT2 energy, the most important contributions to the coupling are established. Spin populations are calculated with DDCI. The successive improvement of the N-electron wave function allows us to analyse the contributions to the spin delocalization.     

On the smoothness of the moduli space of mathematical instanton bundles

In this paper we prove that the moduli spaces MI _2n+1(k) of mathematical instanton bundles on ²ⁿ⁺¹ with quantum number k are singular for n 2 and k 3 ,giving a positive answer to a conjecture made by Ancona and Ottaviani in 1993.     

Luminescence-Based Optical Fiber Chemical Sensors

Abstract

A scheme for the simultaneous determination of temperature and analyte concentration for application in luminescence-based chemical sensors is proposed. This scheme is applied to an optical oxygen sensor, which is based on the quenching of the fluorescence of a ruthenium complex. Temperature measurement is performed using the excitation radiation and an absorption long-pass filter. Preliminary results are presented that show the viability of an oxygen measurement that is independent of temperature and optical power level. The possibility of self-referenced temperature measurements with semiconductor nanoparticles is also investigated. In order to optimize the sensor design, several different optical fiber probe geometries for oxygen sensing are tested and compared, including different methods of coupling radiation into the optical fiber system. Polyvinyl alcohol (PVA) and polyacrylamide membranes are tested as supports for sensor immobilization in fiber-optical pH sensing devices in aqueous solution. Some results are presented that show the feasibility of using fiber-optical pH indicators for remote monitoring.     

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.     

THE FLUORESCENCE OF ADENINE. THE EFFECTS OF SOLVENT AND TEMPERATURE ON THE QUANTUM YIELD

Abstract— To investigate the mechanism of the solvent and thermal quenching of fluorescence, the absolute fluorescence quantum yield of adenine has been determined in several alcoholic glasses as a function of the concentration (10^-5-10^-4M) and temperature (77°-298°K). The yield is independent of the concentration but increases with decreasing temperature and increasing bulk cohesion and rigidity of the solvent.
The environmental effects on the yield are attributed to radiationless electronic relaxation processes caused by solute-solvent interaction. Increasing the temperature and decreasing the intra-solvent cohesion cause increases in the interaction and therefore accelerate the relaxation. The rate determining step behaves like a diffusion in the limit of low viscosity.     

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.