Gibbs Free Energy Expression for the System Polystyrene in Methylcyclohexane and Its Application to Microencapsulation

Langmuir ◽  
2003 ◽  
Vol 19 (13) ◽  
pp. 5240-5245 ◽  
Author(s):  
Takayuki Narita ◽  
Takao Yamamoto ◽  
Eri Hosoya ◽  
Toshiaki Dobashi
Keyword(s):  
Free Energy ◽  
Gibbs Free Energy ◽  
Energy Expression

Equations of state, phase relations, and oxygen fugacity of the Ru-RuO2 buffer at high pressures and temperatures

2020 ◽  
Vol 105 (3) ◽  
pp. 333-343
Author(s):  
Katherine Armstrong ◽  
Nicki C. Siersch ◽  
Tiziana Boffa-Ballaran ◽  
Daniel J. Frost ◽  
Tony Yu ◽  
...  
Keyword(s):  
High Pressure ◽  
Free Energy ◽  
Gibbs Free Energy ◽  
Oxygen Fugacity ◽  
Equations Of State ◽  
Experimental Studies ◽  
Phase Relations ◽  
Cubic Phase ◽  
High Pressure And Temperature ◽  
Energy Expression

Abstract Experimental studies and measurements of inclusions in diamonds show that ferric iron components are increasingly stabilized with depth in the mantle. To determine the thermodynamic stability of such components, their concentration needs to be measured at known oxygen fugacities. The metal-oxide pair Ru and RuO2 are ideal as an internal oxygen fugacity buffer in high-pressure experiments. Both phases remain solid to high temperatures and react minimally with silicates, only exchanging oxygen. To calculate oxygen fugacities at high pressure and temperature, however, requires information on the phase relations and equation of state properties of the solid phases. We have made in situ synchrotron X-ray diffraction measurements in a multi-anvil press on mixtures of Ru and RuO2 to 19.4 GPa and 1473 K with which we have determined phase relations of the RuO2 phases and derived thermal equations of state (EoS) parameters for both Ru and RuO2. Rutile-structured RuO2 was found to undergo two phase transformations, first at ~7 GPa to an orthorhombic structure and then above 12 GPa to a cubic structure. The phase boundary of the cubic phase was constrained for the first time at high pressure and temperature. We have derived a continuous Gibbs free energy expression for the tetragonal and orthorhombic phases of RuO2 by fitting the second-order phase transition boundary and P-V-T data for both phases, using a model based on Landau theory. The transition between the orthorhombic and cubic phases was then used along with EoS terms derived for both phases to determine a Gibbs free energy expression for the cubic phase. We have used these data to calculate the oxygen fugacity of the Ru + O2 = RuO2 equilibrium, which we have parameterized as a single polynomial across the stability fields of all three phases of RuO2. The expression is log10fO2(Ru – RuO2) = (7.782 – 0.00996P + 0.001932P2 – 3.76 × 10–5P3) + (–13 763 + 592P – 3.955P2)/T + (–1.05 × 106 – 4622P)/T2, which should be valid from room pressure up to 25 GPa and 773–2500 K, with an estimated uncertainty of 0.2 log units. Our calculated fO2 is shown to be up to 1 log unit lower than estimates that use previous expressions or ignore EoS terms.

Chemical equilibrium and chemical kinetics

2018 ◽  
Author(s):  
Dennis Sherwood ◽  
Paul Dalby
Keyword(s):  
Free Energy ◽  
Equilibrium Constant ◽  
Gibbs Free Energy ◽  
Chemical Kinetics ◽  
Chemical Equilibrium ◽  
First Principles ◽  
Effect Of Temperature ◽  
Total System ◽  
Free Energies

Building on the previous chapter, this chapter examines gas phase chemical equilibrium, and the equilibrium constant. This chapter takes a rigorous, yet very clear, ‘first principles’ approach, expressing the total Gibbs free energy of a reaction mixture at any time as the sum of the instantaneous Gibbs free energies of each component, as expressed in terms of the extent-of-reaction. The equilibrium reaction mixture is then defined as the point at which the total system Gibbs free energy is a minimum, from which concepts such as the equilibrium constant emerge. The chapter also explores the temperature dependence of equilibrium, this being one example of Le Chatelier’s principle. Finally, the chapter links thermodynamics to chemical kinetics by showing how the equilibrium constant is the ratio of the forward and backward rate constants. We also introduce the Arrhenius equation, closing with a discussion of the overall effect of temperature on chemical equilibrium.

Extended Gibbs Free Energy and Laplace Pressure of Ordered Hexagonal Close-Packed Spherical Particles: A Wettability Study

Langmuir ◽  
2021 ◽  
Author(s):  
Amir Bayat ◽  
Mahdi Ebrahimi ◽  
Saeed Rahemi Ardekani ◽  
Esmaiel Saievar Iranizad ◽  
Alireza Zaker Moshfegh
Keyword(s):  
Free Energy ◽  
Gibbs Free Energy ◽  
Laplace Pressure ◽  
Spherical Particles ◽  
Hexagonal Close Packed

scholarly journals First-Principles Study of Mechanical and Thermodynamic Properties of Binary and Ternary CoX (X = W and Mo) Intermetallic Compounds

Materials ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1404
Author(s):  
Yunfei Yang ◽  
Changhao Wang ◽  
Junhao Sun ◽  
Shilei Li ◽  
Wei Liu ◽  
...  
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Gibbs Free Energy ◽  
Density Functional ◽  
Vibrational Entropy ◽  
Functional Theory ◽  
Lattice Constants ◽  
The Density Functional Theory ◽  
Ductile Behavior ◽  
Pseudo Potential

In this study, the structural, elastic, and thermodynamic properties of DO19 and L12 structured Co3X (X = W, Mo or both W and Mo) and μ structured Co7X6 were investigated using the density functional theory implemented in the pseudo-potential plane wave. The obtained lattice constants were observed to be in good agreement with the available experimental data. With respect to the calculated mechanical properties and Poisson’s ratio, the DO19-Co3X, L12-Co3X, and μ-Co7X6 compounds were noted to be mechanically stable and possessed an optimal ductile behavior; however, L12-Co3X exhibited higher strength and brittleness than DO19-Co3X. Moreover, the quasi-harmonic Debye–Grüneisen approach was confirmed to be valid in describing the temperature-dependent thermodynamic properties of the Co3X and Co7X6 compounds, including heat capacity, vibrational entropy, and Gibbs free energy. Based on the calculated Gibbs free energy of DO19-Co3X and L12-Co7X6, the phase transformation temperatures for DO19-Co3X to L12-Co7X6 were determined and obtained values were noted to match well with the experiment results.

scholarly journals Kinetics and thermodynamic properties related to the drying of 'Cabacinha' pepper fruits

2016 ◽  
Vol 20 (2) ◽  
pp. 174-180 ◽  
Author(s):  
Hellismar W. da Silva ◽  
Renato S. Rodovalho ◽  
Marya F. Velasco ◽  
Camila F. Silva ◽  
Luís S. R. Vale
Keyword(s):  
Experimental Data ◽  
Activation Energy ◽  
Free Energy ◽  
Thermodynamic Properties ◽  
Gibbs Free Energy ◽  
Removal Rate ◽  
Effective Diffusion ◽  
Drying Time ◽  
Three Samples ◽  
Different Temperatures

ABSTRACT The objective of this study was to determine and model the drying kinetics of 'Cabacinha' pepper fruits at different temperatures of the drying air, as well as obtain the thermodynamic properties involved in the drying process of the product. Drying was carried out under controlled conductions of temperature (60, 70, 80, 90 and 100 °C) using three samples of 130 g of fruit, which were weighed periodically until constant mass. The experimental data were adjusted to different mathematical models often used in the representation of fruit drying. Effective diffusion coefficients, calculated from the mathematical model of liquid diffusion, were used to obtain activation energy, enthalpy, entropy and Gibbs free energy. The Midilli model showed the best fit to the experimental data of drying of 'Cabacinha' pepper fruits. The increase in drying temperature promoted an increase in water removal rate, effective diffusion coefficient and Gibbs free energy, besides a reduction in fruit drying time and in the values of entropy and enthalpy. The activation energy for the drying of pepper fruits was 36.09 kJ mol-1.

Standard Gibbs free energy of formation of ZrOS

1990 ◽  
Vol 163 (1) ◽  
pp. 109-113 ◽  
Author(s):  
Zhi-Tong Sui ◽  
Xing-Yi Xiao ◽  
Ke-Qin Huang ◽  
Chang-Zhen Wang
Keyword(s):  
Free Energy ◽  
Gibbs Free Energy ◽  
Standard Gibbs Free Energy ◽  
Free Energy Of Formation ◽  
Energy Of Formation
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