Search results for "Gibbs free energy"
showing 10 items of 88 documents
The Thermodynamics of Insertion Electrochemical Electrodes—A Team Play of Electrons and Ions across Two Separate Interfaces
2018
Insertion electrochemical electrodes exhibit simultaneous electron and ion transfer, with the two transfers proceeding across different interfaces. Herein the thermodynamics of the overall electrochemical electrode reaction is discussed with respect to the thermodynamics of these two charge-transfer equilibria. This Minireview includes insertion electrochemical systems where the redox centers are in a solid phase and the ions are transferred between that phase and a solution, and also systems where the redox centers are in a liquid phase that is immiscible with another liquid phase and ions are transferred between the two liquid phases. The Minireview is intended to spark similar studies on…
Computation of Unstable Binodals Not Requiring Concentration Derivatives of the Gibbs Energy
1998
The equilibrium of three liquid phases in a binary mixture implies the existence of tie lines and binodals that are different from the normal experimentally observable ones. First of all, there are the metastable extensions of the binodal built up by S/S tie lines. These S/S tie lines fulfill the equilibrium condition of the minimum of the Gibbs energy of the entire two-phase system. Both coexisting phases are located within the meta(stable) region. There are two additional types of tie lines: U/U (maximum of the Gibbs energy; both end points within the unstable area) and U/S tie lines (saddle point; one end point within the (meta)stable, the other within the unstable region). All types of…
Calculation of phase diagrams not requiring the derivatives of the Gibbs energy demonstrated for a mixture of two homopolymers with the corresponding…
1995
A method is presented which allows the calculation of phase diagrams (spinodal, binodal and tie lines) on the basis of the Gibbs energy of mixing ΔG. No derivatives of ΔG with respect to the composition variables are required. This method is particularly useful in cases where the composition dependence of ΔG is very complex and no analytical representation of the derivatives can be given. The method is applied to a ternary mixture of two homopolymers with a copolymer consisting of the same monomers. The sequence distribution of the copolymer is kept constant between random and purely alternating, and phase diagrams are calculated for different chemical compositions of the copolymer. The com…
Calculation of miscibility behavior of multinary polymer blends
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, δG, is presented which does not require the calculation of the derivatives with respect to the composition. The method is demonstrated for ternary mixtures of two homopolymers and the corresponding copolymer, and for quaternary and quinternary blends of five polymers exhibiting a closed miscibility gap. The advantages of the presented method become most obvious in the mathematical description of measured phase diagrams, where complex composition dependencies of the interaction parameter are observed.
Stress gradient versus strain gradient constitutive models within elasticity
2014
Abstract A stress gradient elasticity theory is developed which is based on the Eringen method to address nonlocal elasticity by means of differential equations. By suitable thermodynamics arguments (involving the free enthalpy instead of the free internal energy), the restrictions on the related constitutive equations are determined, which include the well-known Eringen stress gradient constitutive equations, as well as the associated (so far uncertain) boundary conditions. The proposed theory exhibits complementary characters with respect to the analogous strain gradient elasticity theory. The associated boundary-value problem is shown to admit a unique solution characterized by a Helling…
Modelling of thermo-chemical properties over the sub-solidus MgO–FeO binary, as a function of iron spin configuration, composition and temperature
2014
Thermo-chemical properties and T–X phase relations diagram of the (Mg,Fe)O solid solution are modelled using mixing Helmholtz energy, ΔF(T,x)mixing, calculated by quantum mechanical and semi-empirical techniques. The sub-solidus MgO–FeO binary has been explored as a function of composition, with iron either in high-spin (HS) or low-spin (LS) configuration. Only the HS model provides physically sound results at room pressure, yielding a correct trend of cell edge versus composition, whereas LS’s issues are at variance with observations. Mixing Helmholtz energy has been parametrized by the following relationship: ΔF(T,x)mixing = x × y × [U0(T) + U1(T) × (x – y) + U2(T) × (x − y)2]−T × S(x,y)c…
The conductance of lithium-7 fluoride in dioxane-water mixtures at 25�C
1990
Conductance data for lithium-7 fluoride in dioxane-water mixtures covering the range 78.35>D>36 in dielectric constant are presented. These data and other previous data on lithium-7 chloride and lithium-7 iodide were analyzed by the Fuoss 1980 conductance equation in order to find the limiting conductance Δo, the pairing distance R and the conductometric association constant Kλ. Setting Ka=Kλ/VM (where VM is the molar volume of the solvent), the thermodynamic pairing constant and the corresponding change of the free energy Δg were calculated. Correlation among the values found for R and Δg=Δh−TΔs and the properties characteristic of the ions and solvents are discussed.
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…
Calculation of shear influences on the phase separation of polymer blends exhibiting upper critical solution temperatures
1994
Calculations were performed on the basis of a generalized Gibbs energy of mixing G γ, which is the sum of the Gibbs energy of mixing of the stagnant system and E s, the energy stored in the system during stationary flow. With increasing shear rate γ, the demixing temperatures shift to lower values (shear-induced mixing; diminution of the heterogeneous area), then to higher values (shear-induced demixing), and finally to lower values again before the effects fade out. The details of the rather complex phase diagrams resulting for a given shear rate are primarily determined by a band in the T/χ plane (χ = mole fraction) within which (∂2 E s/∂χ2) T UCST where they submerge. Bound to a suitable…
Transduction of redox Gibbs free energy into modulated electrochemical work
1988
Abstract This work supplies an electrochemical model in order to account for some oscillatory phenomena. The model can be applied both to living bodies and to electrochemical cells. We suppose that one of the products of an electrochemical reaction in solution has a high vapour pressure and study the influence of its mass transfers on its oscillations and on that of the current,induced by the former ones. Mass transfers that we consider are either that from the solution to theatmosphere above it or both that due to bubble nucleation and that from the solution to the bubbles alreadynucleated. Two different oscillation conditions are determined. One derives from the resistance due to theinter…