Search results for " free energy"
showing 10 items of 137 documents
Calculation of phase diagrams not requiring the derivatives of the Gibbs energy for multinary mixtures
1996
A method for the calculation of phase diagrams (tie lines and binodal, spinodal, critical points and their stability) based exclusively on the Gibbs energy of mixing with no need of its derivatives with respect to the composition variables is extended to multinary mixtures for any number of components. The mathematical description of the (K-1)-dimensional phase diagram of a K-component mixture is presented. The method is demonstrated for a quinternary blend of five polymers exhibiting a closed miscibility gap; all binary, ternary and quaternary subsystems are completely miscible. The phase separation in the quinternary system is caused by very favorable interactions in the ternary subsystem…
High-pressure phases, vibrational properties, and electronic structure ofNe(He)2andAr(He)2: A first-principles study
2009
We have carried out a comprehensive first-principles study of the energetic, structural, and electronic properties of solid rare-gas RG-helium binary compounds, in particular, NeHe2 and ArHe2, under pressure and at temperatures within the range of 0T2000 K. Our approach is based on density-functional theory and the generalized gradient approximation for the exchange-correlation energy; we rely on total Helmholtz freeenergy calculations performed within the quasiharmonic approximation for most of our analysis. In NeHe2, we find that at pressures of around 20 GPa the system stabilizes in the MgZn2 Laves structure, in accordance to what was suggested in previous experimental investigations. In…
Equilibrium fluid-crystal interfacial free energy of bcc-crystallizing aqueous suspensions of polydisperse charged spheres
2015
The interfacial free energy is a central quantity in crystallization from the meta-stable melt. In suspensions of charged colloidal spheres, nucleation and growth kinetics can be accurately measured from optical experiments. In previous work, from this data effective non-equilibrium values for the interfacial free energy between the emerging bcc-nuclei and the adjacent melt in dependence on the chemical potential difference between melt phase and crystal phase were derived using classical nucleation theory. A strictly linear increase of the interfacial free energy was observed as a function of increased meta-stability. Here, we further analyze this data for five aqueous suspensions of charg…
Techno-economic evaluation of Reverse Electrodialysis process in different real environments
2018
Salinity Gradient Power is a promising renewable energy source based on the recovery of the chemical potential released from the mixing of solutions at different concentrations. Natural salinity gradients are extensively available worldwide in natural reservoirs. Reverse Electrodialysis is an innovative technology able to perform a direct conversion of the energy of mixing into electricity. Salinity gradients coming from natural resources or from human activities are worldwide available. In the present work a number of different scenarios, including natural resources (e.g. rivers, seas, lakes and salt ponds), industrial/urban wastes (e.g. brine and treated wastewaters) are analysed. The aim…
Thermodynamics of the spin transition in [FexZn1−x(2-pic)3]Cl2 · EtOH
1992
Abstract With a new type of calorimeter we reinvestigated the specific heat Cp of the mixed crystals [FexZni1−x(2-pic)3]Cl2 · EtOH in the temperature range from 15 to 300 K. On the basis of a phenomenological thermodynamic model the anomaly in the Cp(T) curve of the mixed crystal (x = 0.73) can be quantitatively described as a result of the spin transition (1A1(low spin, LS) → 5T2(high spin, HS)). The parameters of the Gibbs free energy were independently derived from the temperature dependence of the HS fraction γ in [FexZn1−x(2-pic)3]Cl2 · EtOH. The pure iron complex (x = 1) exhibits a two-step spin transition. In the temperature range between the two steps the entropy obtained from the C…
Unveiling the regioselectivity in electrophilic aromatic substitution reactions of deactivated benzenes through molecular electron density theory
2021
The origin of the meta regioselectivity in electrophilic aromatic substitution (EAS) reactions of deactivated benzene derivatives is herein analysed through Molecular Electron Density Theory (MEDT). To this end, the EAS reaction of benzenesulfonic acid with the nitronium NO2+ ion in H2SO4 solution has been studied at the ωB97X-D/6-311G(d,p) level. This reaction takes place through a two-step polar mechanism involving the formation of an unstable cation intermediate. The activation Gibbs free energies associated with the three competitive regioisomeric reaction paths are found in the narrow range of 15.5–18.3 kcal mol−1. By using the Eyring–Polanyi equation a relationship of 18.7 (ortho) : 8…
Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function
2009
A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of the Helmholtz Green function are split into their half advanced+half retarded and half advanced-half retarded components. Closed form solutions are given for these components in terms of a Horn function and a Kampe de Feriet function, respectively. The systems of partial differential equations associated with these two-dimensional hypergeometric functions are used to construct a fourth-order ordinary differential equation which both components satisfy. A s…
Complex miscibility behaviour for polymer blends in flow
1995
Abstract Experimental observations of the effect of shear flow on the miscibility of binary polymer blends are compared to calculations based on a generalized Gibbs energy of mixing Gγ˙. This mixing free energy characterizes the steady state established at shear rateγ˙, as the sum of G z , the equilibrium Gibbs energy and E s , the energy the system stores while flowing.
Interfacial tension between polymer-containing liquids - Predictability and influences of additives
1999
The first part of the contribution deals with the interfacial tension, σ, of phase-separated polymer solutions in single or mixed solvents and of binary polymer blends as a function of the relative distance to the critical temperature of the system, special attention being paid to the possibilities of theoretical prediction. Two methods are discussed in more detail. One is based on a realistic description of the Gibbs energy of mixing as a function of composition, the second correlates σ with the length of the measured tie line. The second part is devoted to another aspect, namely the effects of additives on the interfacial tension between the coexisting phases of demixed polymer solutions …
Phase diagrams of the system tetrahydrofuran/γ-butyrolactone/poly(ether imide) and determination of interaction parameters
1998
Abstract The thermodynamic interactions in the ternary mixture tetrahydrofuran/γ-butyrolactone/poly(ether imide) (THF/γ-BL/PEI) are investigated from 30 to 50°C. This is a membrane-forming system with a high He-selectivity. Cloud point measurements show that the two binary polymer solutions THF/PEI and γ-BL/PEI exhibit miscibility gaps which close towards the centre of the ternary phase diagram where the mixtures become homogeneous (cosolvency). Vapour pressures were determined for the subsystem THF/γ-BL. For the theoretical calculations the Gibbs energy of mixing is formulated according to the Flory-Huggins theory and the interaction parameter χ THF γ-BL calculated from the vapour pressure…