Modeling of Liquid-Liquid Demixing Curve in Lead-Zinc Binary System

2018 ◽  
Vol 18 ◽  
pp. 49-54
Author(s):  
Naceur Amel ◽  
Adjadj Fouzia
Keyword(s):  
Mathematical Model ◽  
Free Energy ◽  
Phase Separation ◽  
Binary System ◽  
Free Energies ◽  
Common Tangent ◽  
Different Temperatures ◽  
Lead Zinc ◽  
The Common ◽  
Zn Alloys

In this work we discussed the modeling of the demixing curve in the liquid state in the Lead – Zinc binary system. We are interested to recalculate the free energies relating on Pb-Zn alloys for several temperatures based on the thermodynamic data collected in the bibliography. This calculation allows us to trace the curve of phase separation from a program after obtaining the mole fractions corresponding to the common tangent to the curve of the free energy with two minima at different temperatures. To do this, we used the Matlab 7.1 as the programming language and the Redlich-Kister polynomial as a mathematical model of development. The results obtained are very satisfactory by comparing them with those of the bibliography.

scholarly journals Evaluation of Stoichiometry, Stability Constants and Gibbs Free Energies of Acetaminophen-Zn (II) complex at Different Temperatures

2020 ◽  
Vol 24 (7) ◽  
pp. 1137-1143
Author(s):  
O.V. Ikpeazu ◽  
I.E. Otuokere ◽  
K.K. Igwe
Keyword(s):  
Free Energy ◽  
Stability Constant ◽  
Gibbs Free Energy ◽  
Stability Constants ◽  
Continuous Variation ◽  
Variation Method ◽  
Ratio Method ◽  
Free Energies ◽  
Different Temperatures ◽  
Continuous Variation Method

Acetaminophen also known as paracetamol, is a drug used in the treatment of pain and fever. It is essentially used for the relief of mild to moderate pain. The presence of phenol and carbonyl oxygen atom enables acetaminophen to behave as a bidentate ligand. The stoichiometry, stability constants and Gibbs free energies of acetaminophen-Zn (II) were determined colorimetrically at 25 and 40 oC using continuous variation and mole  ratio methods. The formation of Zn (II) complex with acetaminophen was studied colorimetrically at an absorption maximum of 630 nm at different temperatures. The data showed that Zn (II) and acetaminophen combine in the molar ratio of 1:1 at pH 7.4 with ionic strength maintained using 0.1M KNO3. Calculated stability constants values were 2.70 x 103 and 2.20 x 103 using continuous variation method and 7.21 x 103 and 7.21 x 103 using mole ratio methods at 25 and 40 oC respectively. Calculated ΔGƟ for the complex were - 1.96 x 104 and -1.98 x 104 J using continuous variation method and -2.2 x 104 J and - 2.31 x 104 J using mole ratio method at 25 and 40 oC respectively. The stability constant and Gibbs free energy results suggested that acetaminophen used in the study is a good chelating agent and can be an efficient antidote in the therapy of Zn (II) overload or poisoning. Keywords: Acetaminophen, Zinc, complex, stability constant, Gibbs free energy.

SAMPL6 Octanol-Water Partition Coefficients from Alchemical Free Energy Calculations with MBIS Atomic Charges

2019 ◽  
Author(s):  
Maximiliano Riquelme ◽  
Esteban Vöhringer-Martinez
Keyword(s):  
Free Energy ◽  
Electron Density ◽  
Free Energy Calculations ◽  
Basis Set ◽  
Energetic Cost ◽  
Atomic Charges ◽  
Free Energies ◽  
Energy Calculations ◽  
Alchemical Free Energy ◽  
Alchemical Free Energy Calculations

In molecular modeling the description of the interactions between molecules forms the basis for a correct prediction of macroscopic observables. Here, we derive atomic charges from the implicitly polarized electron density of eleven molecules in the SAMPL6 challenge using the Hirshfeld-I and Minimal Basis Set Iterative Stockholder(MBIS) partitioning method. These atomic charges combined with other parameters in the GAFF force field and different water/octanol models were then used in alchemical free energy calculations to obtain hydration and solvation free energies, which after correction for the polarization cost, result in the blind prediction of the partition coefficient. From the tested partitioning methods and water models the S-MBIS atomic charges with the TIP3P water model presented the smallest deviation from the experiment. Conformational dependence of the free energies and the energetic cost associated with the polarization of the electron density are discussed.

A canonical ensemble derivation of the McMillan-Mayer solution theory

1983 ◽  
Vol 48 (10) ◽  
pp. 2888-2892 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Energy Function ◽  
Special Function ◽  
Helmholtz Free Energy ◽  
Canonical Ensemble ◽  
Free Energy Function ◽  
Solution Theory ◽  
Pure Solvent ◽  
The Common

A special free energy function is defined for a solution in the osmotic equilibrium with pure solvent. The partition function of the solution is derived at the McMillan-Mayer level and it is related to this special function in the same manner as the common partition function of the system to its Helmholtz free energy.

Photocatalytic Effect of Fe(III) on Oxidation of Two-Carbon Substrates Related to Natural Waters

1994 ◽  
Vol 59 (5) ◽  
pp. 1066-1076 ◽  
Author(s):  
Šárka Klementová ◽  
Dana M. Wagnerová
Keyword(s):  
Mathematical Model ◽  
Natural Waters ◽  
Substrate Oxidation ◽  
Quantum Yields ◽  
Ferric Ions ◽  
Photochemical Reduction ◽  
Photocatalytic Effect ◽  
Carbon Substrates ◽  
Glyoxalic Acid ◽  
The Common

The influence of ferric ions on photoinitiated reaction of dioxygen with two carbon organic acids, aldehydes and alcohols related to natural waters was demonstrated. Photocatalytic effect of ferric ions, i.e. photochemical reduction of Fe(III) as the catalyst generating step, has been found to be the common principal of these reactions. The overall quantum yields of the reactions are in the range from 0.3 to 1.2. A mathematical model designed for the mechanism of cyclic generation of catalyst in the singlet substrate oxidation by O2 was applied to the system glyoxalic acid + Fe(III); a fair agreement between the simulated and experimental kinetic curves was obtained. The experimental rate constant is 4.4 .10-4 s -1.

Molecular orientation of liquid aliphatic hydrocarbons on the surface and at the interface with water

1989 ◽  
Vol 54 (12) ◽  
pp. 3171-3186 ◽  
Author(s):  
Jan Kloubek
Keyword(s):  
Free Energy ◽  
Surface Free Energy ◽  
Molecular Orientation ◽  
Phase Changes ◽  
Aliphatic Hydrocarbons ◽  
Water Molecules ◽  
Free Energies ◽  
Dispersion Component ◽  
System Water ◽  
Orientation Of Molecules

The validity of the Fowkes theory for the interaction of dispersion forces at interfaces was inspected for the system water-aliphatic hydrocarbons with 5 to 16 C atoms. The obtained results lead to the conclusion that the hydrocarbon molecules cannot lie in a parallel position or be randomly arranged on the surface but that orientation of molecules increases there the ration of CH3 to CH2 groups with respect to that in the bulk. This ratio is changed at the interface with water so that the surface free energy of the hydrocarbon, γH, rises to a higher value, γ’H, which is effective in the interaction with water molecules. Not only the orientation of molecules depends on the adjoining phase and on the temperature but also the density of hydrocarbons on the surface of the liquid phase changes. It is lower than in the bulk and at the interface with water. Moreover, the volume occupied by the CH3 group increases on the surface more than that of the CH2 group. The dispersion component of the surface free energy of water, γdW = 19.09 mJ/m2, the non-dispersion component, γnW = 53.66 mJ/m2, and the surface free energies of the CH2 and CH3 groups, γ(CH2) = 32.94 mJ/m2 and γ(CH3) = 15.87 mJ/m2, were determined at 20 °C. The dependence of these values on the temperature in the range 15-40 °C was also evaluated.

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.

scholarly journals Automation of absolute protein-ligand binding free energy calculations for docking refinement and compound evaluation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Germano Heinzelmann ◽  
Michael K. Gilson
Keyword(s):  
Free Energy ◽  
Early Stage ◽  
Binding Free Energy ◽  
Low Cost ◽  
Free Energy Calculations ◽  
Free Energies ◽  
Energy Calculations ◽  
Drug Candidates ◽  
Binding Free Energy Calculations ◽  
Binding Free Energies

AbstractAbsolute binding free energy calculations with explicit solvent molecular simulations can provide estimates of protein-ligand affinities, and thus reduce the time and costs needed to find new drug candidates. However, these calculations can be complex to implement and perform. Here, we introduce the software BAT.py, a Python tool that invokes the AMBER simulation package to automate the calculation of binding free energies for a protein with a series of ligands. The software supports the attach-pull-release (APR) and double decoupling (DD) binding free energy methods, as well as the simultaneous decoupling-recoupling (SDR) method, a variant of double decoupling that avoids numerical artifacts associated with charged ligands. We report encouraging initial test applications of this software both to re-rank docked poses and to estimate overall binding free energies. We also show that it is practical to carry out these calculations cheaply by using graphical processing units in common machines that can be built for this purpose. The combination of automation and low cost positions this procedure to be applied in a relatively high-throughput mode and thus stands to enable new applications in early-stage drug discovery.

scholarly journals The bulk, surface and corner free energies of the anisotropic triangular Ising model

2020 ◽  
Vol 476 (2234) ◽  
pp. 20190713
Author(s):  
Rodney J. Baxter
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Partition Function ◽  
Temperature Series ◽  
Isotropic Case ◽  
Series Expansions ◽  
Exact Results ◽  
Free Energies ◽  
Bulk Surface ◽  
Bulk Free Energy

We consider the anisotropic Ising model on the triangular lattice with finite boundaries, and use Kaufman’s spinor method to calculate low-temperature series expansions for the partition function to high order. From these, we can obtain 108-term series expansions for the bulk, surface and corner free energies. We extrapolate these to all terms and thereby conjecture the exact results for each. Our results agree with the exactly known bulk-free energy and with Cardy and Peschel’s conformal invariance predictions for the dominant behaviour at criticality. For the isotropic case, they also agree with Vernier and Jacobsen’s conjecture for the 60 ° corners.

Sign in / Sign up

Export Citation Format

Share Document