scholarly journals Estimating Free Energies of Formation of Titanate () and Zirconate () Pyrochlore Phases of Trivalent Lanthanides and Actinides

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Anpalaki J. Ragavan ◽  
Dean V. Adams
Keyword(s):  
Free Energy ◽  
First Principles ◽  
Linear Free Energy Relationship ◽  
Free Energies ◽  
Empirical Parameter ◽  
Trivalent Lanthanides ◽  
Linear Free Energy ◽  
Free Energy Of Formation ◽  
The Difference ◽  
Energy Of Formation

A linear free energy relationship was developed to predict the Gibbs free energies of formation (, in kJ/mol) of crystalline titanate (M2Ti2O7) and zirconate (M2Zr2O2) pyrochlore families of trivalent lanthanides and actinides (M3+) from the Shannon-Prewitt radius of M3+ in a given coordination state (, in nm) and the nonsolvation contribution to the Gibbs free energy of formation of the aqueous M3+ (). The linear free energy relationship for M2Ti2O7 is expressed as . The linear free energy relationship for M2Zr2O7 is expressed as . Estimated free energies were within 0.73 percent of those calculated from the first principles for M2Ti2O7 and within 0.50 percent for M2Zr2O7. Entropies of formation were estimated from constituent oxides (J/mol), based on an empirical parameter defined as the difference between the measured entropies of formation of the oxides and the measured entropies of formation of the aqueous cation.

Synthesis and characterization of a series of 1-methyl-4-[2-aryl-1-diazenyl]piperazines and a series of ethyl 4-[2-aryl-1-diazenyl]-1-piperazinecarboxylates

2004 ◽  
Vol 82 (8) ◽  
pp. 1294-1303 ◽  
Author(s):  
Vanessa Renée Little ◽  
Keith Vaughan
Keyword(s):  
Free Energy ◽  
Chemical Shifts ◽  
Linear Free Energy Relationship ◽  
Piperazine Ring ◽  
Linear Free Energy ◽  
In Series ◽  
Methylene Groups ◽  
Diazonium Coupling ◽  
The Difference

1-Methylpiperazine was coupled with a series of diazonium salts to afford the 1-methyl-4-[2-aryl-1-diazenyl]piperazines (2), a new series of triazenes, which have been characterized by 1H and 13C NMR spectroscopy, IR spectroscopy, and elemental analysis. Assignment of the chemical shifts to specific protons and carbons in the piperazine ring was facilitated by comparison with the chemical shifts in the model compounds piperazine and 1-methylpiperazine and by a HETCOR experiment with the p-tolyl derivative (2i). A DEPT experiment with 1-methylpiperazine (6) was necessary to distinguish the methyl and methylene groups in 6, and a HETCOR spectrum of 6 enabled the correlation of proton and carbon chemical shifts. Line broadening of the signals from the ring methylene protons is attributed to restricted rotation around the N2-N3 bond of the triazene moiety in 2. The second series of triazenes, the ethyl 4-[2-phenyl-1-diazenyl]-1-piperazinecarboxylates (3), have been prepared by similar diazonium coupling to ethyl 1-piperazinecarboxylate and were similarly characterized. The chemical shifts of the piperazine ring protons are much closer together in series 3 than in series 2, resulting in distortion of the multiplets for these methylenes. It was noticed that the difference between these chemical shifts in 3 exhibited a linear free energy relationship with the Hammett substituent constants for the substituents in the aryl ring. Key words: triazene, piperazine, diazonium coupling, NMR, HETCOR, linear free energy relationship.

scholarly journals Rationalisation of the activities of phenolic (vitamin E-type) antioxidants

2003 ◽  
Vol 17 (4) ◽  
pp. 753-762
Author(s):  
Christopher J. Rhodes ◽  
Thuy T. Tran ◽  
Philip Denton ◽  
Harry Morris
Keyword(s):  
Free Energy ◽  
Vitamin E ◽  
Gibbs Free Energy ◽  
State Theory ◽  
Linear Free Energy Relationship ◽  
Free Energies ◽  
Gibbs Free Energy Change ◽  
Linear Free Energy ◽  
Free Energy Of Activation ◽  
Enthalpy And Entropy

Using Transition-State Theory, experimental rate constants, determined over a range of temperatures, for reactions of vitamin E type antioxidants are analysed in terms of their enthalpies and entropies of activation. It is further shown that computational methods may be employed to calculate enthalpies and entropies, and hence Gibbs Free Energies, for the overall reactions. Within the Linear Free Energy Relationship (LFER) assumption, that the Gibbs Free Energy of activation is proportional to the overall Gibbs Free Energy change for the reaction, it is possible to rationalise, and even to predict, the relative contributions of enthalpy and entropy for reactions of interest, involving potential antioxidants.

Hardness and Adhesion Measurements of Copper Metallizations by a Continuous Indentation Approach

1990 ◽  
Vol 203 ◽  
Author(s):  
W.R. Lafontaine ◽  
Che-Yu Li
Keyword(s):  
Free Energy ◽  
Metal Oxide ◽  
Indentation Test ◽  
Silicon Substrates ◽  
Copper Films ◽  
Free Energy Of Formation ◽  
The Difference ◽  
Continuous Indentation ◽  
Energy Of Formation

ABSTRACTA continuous indentation test has been used to evaluate the difference in adhesion between copper films deposited on oxidized silicon substrates with different transition metalinterlayers. Variations in adhesion between samples with interlayers of Al,Cr,Ni,Ti and V correlated with the free energy of formation of the particular metal oxide present.

The Free Energies of Hydration of Gaseous Ions

1948 ◽  
Vol 1 (4) ◽  
pp. 480 ◽  
Author(s):  
NS Hush
Keyword(s):  
Free Energy ◽  
Water Molecule ◽  
Pure Water ◽  
Free Energies ◽  
The Real ◽  
Free Energy Of Formation ◽  
Energy Of Hydration ◽  
Free Energy Of Hydration ◽  
Molecule Interaction ◽  
Energy Of Formation

Values of hydration energies of individual ions have usually been obtained by division of sums of energies of hydration of pairs of ions, and those calculated by different authors are usually mutually inconsistent. " Experimental " figures, whenever these are quoted, have always been obtained by assuming the truth of theoretical equations whose accuracy has not been independently checked. The distinction between free energy of ion/water-molecule interaction and the real free energy of hydration of a gaseous ion is pointed out, and the importance of Klein and Lange's measurement of the Volta-potential Hg/Hg+ (soln.), which makes possible the direct calculation of real free energies of hydration of individual ions, thus providing a check on theoretical values, is emphasized. Utilizing this value, the equation - ΔFh� = - ΔFf� + ΔFi� + ΔFs�- 103.92 z kcal. (where ΔFs� is the free energy of formation of the gaseous monatomic element, ΔFi� is the free energy of ionization, ΔFf�is the free energy of formation of the aqueous ion, and ΔFh� is the real free energy of hydration of the ion, of valency z, at 298.2� K.) is derived from fundamental considerations. By means of this equation, the real free energies of hydration of 49 ions are calculated, using the most reliable data. It is proposed that these be provisionally accepted as standard values. Several subsidiary values for important ions are calculated indirectly. The difference between ΔFh� and the free energy of ion/water-molecule interaction is discussed in relation to the surface structure of water : a value of -0.30 v. is derived for the X-potential at the surface of pure water, and it is concluded that at the water/gas interface the positive poles of the surface layer are oriented towards the gas phase. The applicability of a modified Born equation in the calculation of free energies of hydration is discussed, and a modified equation is proposed which yields values of ΔFh� for gaseous ions with noble gas structure in excellent agreement with those calculated independently by the method described above.

Using Linear Free Energy Relationship to Predict the Stability Constants of Aqueous Complexes of Metal-Organic Ligands

2004 ◽  
Vol 824 ◽  
Author(s):  
Huifang Xu ◽  
Yifeng Wang
Keyword(s):  
Free Energy ◽  
Metal Complexes ◽  
Stability Constants ◽  
Metal Cation ◽  
Dissociation Constants ◽  
Natural Environments ◽  
Linear Free Energy Relationship ◽  
Free Energies ◽  
Linear Free Energy ◽  
The Stability

AbstractThe Sverjensky-Molling linear free energy relationship was originally developed to correlate the Gibbs free energies of formation of an isostrutural family of solid phases to the thermodynamic properties of aqueous cations. In this paper, we demonstrate that the similar relationship also exists between metal complexes and simple metal cations in aqueous solutions. We extend the Sverjensky-Molling relationship to predict the Gibbs free energies of formation or dissociation constants for a family of metal complexes with a given complexing ligand. The discrepancies between the predicted and experimental data are generally less than 1.5 kcal/mol (or one log unit for stability constants). The use of this linear free energy correlation can significantly enhance our ability to predict the speciation, mobility, and toxicity of heavy metals in natural environments. According the obtained results, Gibbs free energies of formation of cations (δG0f, Mn+) can be used as an indicator for the hardness/softness of a metal cation (acid). The higher negative value of a metal cation, the harder acid it will be. It is logical to postulate that the coefficient a*ML characterizes the softness of a complexing ligand (base).

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