Mixing Functions, Excess Functions, and Sample Problems

2020 ◽  
pp. 243-257
Author(s):  
Daniel Blankschtein
Keyword(s):  
Excess Functions ◽  
Mixing Functions

Thermodynamische Interpretation der Schmelzdiagramme binärer Systeme aus Methylchlorsilanen und Pyridazin bzw. Pyrazin

1987 ◽  
Vol 42 (4) ◽  
pp. 341-351
Author(s):  
Karl Hensen ◽  
Jens Gaede
Keyword(s):  
Melting Point ◽  
Thermodynamic Functions ◽  
Liquidus Curve ◽  
Optical Measurements ◽  
Miscibility Gap ◽  
Excess Functions ◽  
Cooling Curves ◽  
Acid Base ◽  
Thermodynamic Excess Functions ◽  
Thermodynamic Excess

By analyzing the cooling curves and the resulting melting point diagrams of the chloromethylsilane- pyridazine and pyrazine systems the existence of the incongruently melting addition compounds CH3SiCl3 • Pyridazine, (CH3)2SiCl2 • (Pyridazine)2, (CH3)3SiCl • (Pyridazine)2, CH3SiCl3 • (Pyrazine)2, (CH3)2SiCl2 • (Pyrazine)2 , (CH3)3SiCl • (Pyrazine)2 was proved. By electro-optical measurements of the turbidity point it was proved that the system (CH3)3SiCl- Pyridazine exhibits a miscibility gap which intersects the liquidus curve of the amine. Based on certain approximations it was possible to fit thermodynamic functions to the experimental results to obtain the excess data of mixing of the corresponding systems. These data allow for a more profound understanding of the Lewis-acid base behaviour of the silanes and amines.Chloromethylsilanes, Pyridazine, Pyrazine, Phase Diagrams, Addition Compounds, Thermodynamic Excess Functions

Flory theory and excess thermodynamic properties of liquid mixtures containing one polar component

1978 ◽  
Vol 31 (10) ◽  
pp. 2145 ◽  
Author(s):  
KS Reddy ◽  
PR Naidu
Keyword(s):  
Thermodynamic Properties ◽  
Interaction Parameter ◽  
Energy Parameter ◽  
Liquid Mixtures ◽  
Polar Component ◽  
Excess Functions ◽  
Diethyl Ketone ◽  
Flory Theory ◽  
Excess Thermodynamic Properties ◽  
Modified Forms

Excess volumes of the binary mixtures, benzene + benzonitrile, benzene+ diethyl ketone and toluene+diethyl ketone, were determined at 303.15 K. The VE data and HE data of the mixtures reported in the literature were analysed in the light of both the original and modified forms of the Flory theory. The analysis showed that the modified Flory theory correctly predicts the sign of the excess functions over the whole range of composition when the single interaction parameter of the theory is treated as an energy parameter.

Thermodynamic Excess Functions of Binary Liquid Mixtures with Chain Association of One Component*. Part I: The Excess Gibbs Free Energy GE/RT

1976 ◽  
Vol 31 (12) ◽  
pp. 1651-1660 ◽  
Author(s):  
F. Becker ◽  
M. Kiefer ◽  
P. Rhensius ◽  
H. D. Schäfer
Keyword(s):  
Free Energy ◽  
Gibbs Free Energy ◽  
Chain Length ◽  
Liquid Mixtures ◽  
Binary Liquid Mixtures ◽  
Excess Gibbs Free Energy ◽  
Component Part ◽  
Excess Functions ◽  
Binary Liquid ◽  
Self Association

Abstract In this paper equilibrium models for the calculation of the excess Gibbs free energy of binary liquid mixtures are developed, the component A of which undergoes chain-forming self-association whilst the component B acts as an 'inert' solvent. It is shown that the extension of the well-known chain-association model of Mecke and Kempter, in which the probability of chain prolongation is assumed to be independent of chain length, is unable to establish satisfactory results because it does not exhibit sufficient unsymmetry. Reduction of the probability of chain growth with in-creasing chain length leads to an improved model with the geometric series replaced by the exponential series. This model, in which only two parameters are used, i. e. the equilibrium constants K for mutual solvation of A and B, and ρ for self-association of A, allows fitting of isothermal experimental GE /R T literature data on cycloalkanol-cycloalkane, alkanol-alkane, and NMF -CCl4 systems within the limits of experimental error. Compared with the two-parameter Wilson equation which gives equally small standard deviations, our equilibrium model has the advantage of allowing passage from GE to HE data and of being applicable to liquid-liquid equilibria.

scholarly journals Axiomatic results and dynamic processes for two weighted indexes under fuzzy transferable-utility behavior

2022 ◽  
Vol 12 (1) ◽  
pp. 1
Author(s):  
Yu-Hsien Liao
Keyword(s):  
Dynamic Processes ◽  
Excess Functions ◽  
Transferable Utility ◽  
Transferable Utility Games

<p style='text-indent:20px;'>By considering the supreme-utilities and the weights simultaneously under fuzzy behavior, we propose two indexes on fuzzy transferable-utility games. In order to present the rationality for these two indexes, we define extended reductions to offer several axiomatic results and dynamics processes. Based on different consideration, we also adopt excess functions to propose alternative formulations and related dynamic processes for these two indexes respectively.</p>

Thermodynamics of mixtures: Functions of mixing and excess functions

1999 ◽  
Vol 67 (12) ◽  
pp. 1096-1099 ◽  
Author(s):  
R. Nieto ◽  
M. C. González ◽  
F. Herrero
Keyword(s):  
Excess Functions ◽  
Thermodynamics Of Mixtures

Molar excess enthalpies for some systems containing the OH and (or) O groups in the same or in different molecules

2002 ◽  
Vol 80 (3) ◽  
pp. 292-301 ◽  
Author(s):  
Jose Carlos Cobos ◽  
Isaias Garcia de la Fuente ◽  
Juan Antonio Gonzalez
Keyword(s):  
The Self ◽  
Excess Functions ◽  
Excess Enthalpies ◽  
Effective Dipole Moment ◽  
Group Interactions ◽  
Molar Excess ◽  
Dipole Interactions ◽  
Eras Model ◽  
Self Association ◽  
Molar Excess Volumes

In this work, HmE data at 298.15 K for the systems 1-nonanol + n-C12; 1-nonanol + n-C14; 1-hexanol + 3,6,9-trioxaundecane; and 2-(2-butoxyethoxyethanol) + n-C7 are reported. Measurements were carried out with a standard Calvet-type microcalorimeter. Molar excess functions, including enthalpies and entropies, are carefully examined to report on the main features of the studied solutions. Dipole–dipole interactions between ether molecules are, therefore, of great importance in both 1-alkanols + polyoxaalkanes mixtures and between hydroxyether molecules in alkoxy ethanols + n-alkanes systems. In the second case, it has been attributed to the existence of intramolecular H-bonds in alkoxy ethanols as well as to their higher effective-dipole moment in comparison to that of homologous 1-alkanols. DISQUAC is the only model that can be used to accurately represent thermodynamic functions (except molar excess volumes, VmE) of all of the solutions under study. UNIFAC underestimates dipole–dipole interactions in 1-alkanols + polyoxaalkanes and alkoxyethanols + n-alkanes systems. In exchange, the self-association of the alcohol is overestimated in mixtures of 1-nonanol with n-alkanes. Currently, the ERAS model can only be used to examine these solutions. The variation of the VmE with the size of the n-alkanes is well described. Key words: excess functions, OH group, O group, interactions, models.

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