Search

Equilibrium conditions of droplets on deformable substrates are investigated, and it is proven using Jacobi's sufficient condition that the obtained solutions really provide equilibrium profiles of both the droplet and the deformed support. At the equilibrium, the excess free energy of the system should have a minimum value, which means that both necessary and sufficient conditions of the minimum should be fulfilled. Only in this case, the obtained profiles provide the minimum of the excess free energy. The necessary condition of the equilibrium means that the first variation of the excess free energy should vanish, and the second variation should be positive. Unfortunately, the mentioned two conditions are not the proof that the obtained profiles correspond to the minimum of the excess free energy and they could not be. It is necessary to check whether the sufficient condition of the equilibrium (Jacobi's condition) is satisfied. To the best of our knowledge Jacobi's condition has never been verified for any already published equilibrium profiles of both the droplet and the deformable substrate. A simple model of the equilibrium droplet on the deformable substrate is considered, and it is shown that the deduced profiles of the equilibrium droplet and deformable substrate satisfy the Jacobi's condition, that is, really provide the minimum to the excess free energy of the system. To simplify calculations, a simplified linear disjoining/conjoining pressure isotherm is adopted for the calculations. It is shown that both necessary and sufficient conditions for equilibrium are satisfied. For the first time, validity of the Jacobi's condition is verified. The latter proves that the developed model really provides (i) the minimum of the excess free energy of the system droplet/deformable substrate and (ii) equilibrium profiles of both the droplet and the deformable substrate. [ABSTRACT FROM AUTHOR]

The solubility of Pt in acidic chloride solutions was measured at 400-475°C and P = 0.8-1.0 kbar using an autoclave technique and the analysis of the dissolved component after quenching. The PtCl complex was identified as the main Pt species at experimental parameters, m(NaCl) = 0.1-3.0 mol/kg HO and m(HCl) ∼0.01. The thermodynamic parameters of the Helgeson-Kirkham-Flowers (HKF) model were determined for Pt and Pt-Cl complexes (PtCl n = 1-4) by analysis of literature data and their adjustment with obtained results. The solubility of Pt under supercritical P- T parameters calculated using these parameters is similar to Pd solubility. The thermodynamic properties and HKF model parameters for aqueous species determined in this study were incorporated into the on-line version of the FreeGC database (), which allows calculation of the Gibbs free energy of system components and equilibrium constants of reactions with these species. [ABSTRACT FROM AUTHOR]

The exchange of Na ions of vermiculite for Co cations is measured by sorption-analytical and microcalorimetric methods. The previously revealed growth of the equilibrium constant with a rise in the degree of filling θ of vermiculite exchange sites with Co cations is confirmed. This result is explained by the segregation of Co and Na cations being exchanged in separate interlayer regions of vermiculite. The negative heats of exchange of Na cations for Co cations are associated with the energy consumption for the rearrangement of the segregated interlayer regions in vermiculite. The positive entropy changes resulting from the exchange indicate the formation of a more disordered Co-Na-layered 'cake' in comparison with the initial Na-form vermiculite. A decrease in the integral molal free-energy change Δ G of the mixed form of the mineral is determined by the entropy factor. It is shown that, as θ increases, the Δ G(θ) dependence passes from a positive to a negative range of values. This pattern of the curve may be interpreted as a gradual phase transition from the Na-form to the mixed Co-Na-segregated form. The first derivatives of the enthalpy and entropy changes with respect to the degree of filling θ exhibit distinct maxima at θ ∼ 0.20 as a result of the transition from the ideal mixing of Co and Na cations being exchanged to their segregation. [ABSTRACT FROM AUTHOR]

Nitriles pose an interesting problem to the explanatory powers of organic chemistry because, despite the favorable overall thermodynamics of to the corresponding amides, the reactions are inherently slow. The rate determining step is of the nitrile to give the imidic acid, which quickly tautomerizes to the amide. In terms of Marcus Theory, the intrinsic barriers for acid and base-catalyzed are higher for nitriles than for amides, which are themselves slow reactions. It is remarkable that of a nitrile, for which the free energy change is close to zero except for polyhaloacetonitriles, is much slower than of an amide, which is energetically unfavorable. This can be explained by No Barrier Theory in terms of the high energetic cost of the geometrical distortions in 'one thing at a time' corner species. There are no experimental equilibrium constants for this initial step, so we have determined them computationally. The free energy change for the initial is small; it is the fast and energetically downhill second step, to the amide, which makes the overall of nitrile to amide thermodynamically favorable. Very few of the p Ka values needed in the acid and base-catalyzed mechanisms are known, so we used linear free energy relations and treat the parent p Ka values as adjustable parameters. This procedure leads to p Ka values in accord with expectation based on such data as are available and permits calculation of rate constants in satisfactory agreement with experiment. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]