Excess thermodynamic properties of tetraalkyltin compounds with Trans-decalin and highly branched alkanes. Effect of steric hindrance

1986 ◽  
Vol 64 (4) ◽  
pp. 681-688 ◽  
Author(s):  
Hong Phuong-Nguyen ◽  
Geneviève Delmas
Keyword(s):  
Thermodynamic Properties ◽  
Steric Hindrance ◽  
Thermodynamic Quantities ◽  
Flory Theory ◽  
Excess Viscosities ◽  
Branched Alkanes ◽  
Energy Of Mixing ◽  
Excess Thermodynamic Quantities ◽  
The Difference ◽  
Free Energy Of Mixing

Molar excess thermodynamic quantities hE, [Formula: see text], and vE have been measured at 25 °C over the whole composition range for mixtures of four globular Sn(CnH2n+1)4 (SnR4) (n = 1–4) with t-decalin, and 2,2,4,4,6,8,8-heptamethylnonane (br-C16) as well as hE for the same SnR4 compounds with 2,2,4-trimethylpentane (br-C8). The excess viscosities are measured at −20, 25, and 40 °C for the t-decalin + SnR4 systems. By introducing gE in the solution activation energy, the free energy of mixing can be related to and calculated from the excess viscosities. The steric hindrance contribution, corresponding to an increase of order or diminution of mobility in solution, known to occur either with compounds having highly substituted atoms or with flat-shaped molecules, was investigated. The free volume contribution to the different thermodynamic properties is calculated from the Prigogine–Patterson–Flory theory. The difference between the experimental and calculated excess data is associated with the steric hindrance contribution. Values of hE, [Formula: see text], vE, and sE confirm the existence of a large steric hindrance contribution (hE < −200 J mol−1 and TsE < −400 J mol−1 for two systems). Another contribution, found to occur for the two smaller globular SnR4, may originate in the liberation of movement induced in solution by the second component.

Higher Order Conditional Probabilities and Thermodynamics of Binary Molten Alloys

1997 ◽  
Vol 11 (02n03) ◽  
pp. 93-106 ◽  
Author(s):  
O. Akinlade
Keyword(s):  
Free Energy ◽  
Experimental Evidence ◽  
Cluster Model ◽  
Excess Free Energy ◽  
Higher Order ◽  
Thermodynamic Quantities ◽  
Equiatomic Composition ◽  
Conditional Probabilities ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

The recently introduced four atom cluster model is used to obtain higher order conditional probabilities that describe the atomic correlations in some molten binary alloys. Although the excess free energy of mixing for all the systems studied are almost symmetrical about the equiatomic composition, most other thermodynamic quantities are not and thus, the study enables us to explain the subtle differences in their physical characteristics required to describe the mechanism of the observed strong heterocoordination in Au–Zn or homocoordination in Cu–Ni within the same framework. More importantly, we obtain all calculated quantities for the whole concentration range thus complimenting experimental evidence.

Calculation on the Free Energy of Mixing of some Silane Systems

2011 ◽  
Vol 391-392 ◽  
pp. 1017-1021
Author(s):  
Ru Zhang ◽  
Yan Fen Wu ◽  
Ping Hu
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Activity Coefficients ◽  
Influence Factors ◽  
Critical Parameters ◽  
Model Parameters ◽  
Free Energies ◽  
Wilson Model ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

Six binary silane systems were chosen to calculate the activity coefficients (γ) and free energies of mixing (ΔGm). These systems included: methyldichlorosilane + methyltrichlorosilane, methyldichlorosilane + methylvinyldichlorosilane, methyldichlorosilane + toluene, methyltrichlorosilane + methylvinyldichlorosilane, methyltrichlorosilane + toluene, methylvinyldichlorosilane + toluene. Based on the Antoine constants, critical parameters of the pure components and Wilson model parameters, γ and ΔGmwere calculated. The influence factors of these thermodynamic properties were also discussed.

scholarly journals Energetics and local order in In-based liquid alloys

BIBECHANA ◽  
2015 ◽  
Vol 13 ◽  
pp. 60-71
Author(s):  
RP Koirala ◽  
BP Singh ◽  
IS Jha ◽  
D Adhikari
Keyword(s):  
Thermodynamic Properties ◽  
Local Order ◽  
Heat Of Mixing ◽  
Liquid Alloys ◽  
Association Model ◽  
Long Wavelength ◽  
Energy Of Mixing ◽  
Self Association ◽  
Free Energy Of Mixing ◽  
Solution Behaviour

A comparative study has been carried out to understand the concentration dependence of thermodynamic properties such as, free energy of mixing, heat of mixing, entropy of mixing, activity  and microscopic properties, such as concentration fluctuation in long wavelength limit  and Warren-Cowley short range order parameter  of  In-based three liquid alloys (In-Pb , In-Tl and In-Zn) on the basis of self-association model. The analysis reveals that self-association model successfully explains the observed properties of the liquid alloys.  Positive deviation of the thermodynamic properties of the alloys from the Raoultian solution behaviour indicates that the alloys are weakly segregating in nature. The comparative assessment of the interaction energy and the microscopic properties suggests that the degree of segregation is greatest in In-Zn alloy and comparable in In-Pb and In-Tl alloys.BIBECHANA 13 (2016) 60-71

The statistical thermodynamics of multicomponent systems

1951 ◽  
Vol 205 (1081) ◽  
pp. 247-269 ◽  
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Potential Energy ◽  
Multicomponent Systems ◽  
Reference Species ◽  
Two Phase ◽  
Energy Of Mixing ◽  
Volume Of Mixing ◽  
Two Component Systems ◽  
Free Energy Of Mixing

This paper describes a new statistical approach to the theory of multicomponent systems. A ‘conformal solution’ is defined as one satisfying the following conditions: (i) The mutual potential energy of a molecule of species L r and one of species L s at a distance ρ is given by the expression u rs (ρ) = f rs u 00 ( g rs ρ ), where u 00 is the mutual potential energy of two molecules of some reference species L 0 at a distance ρ , and f rs and g rs are constants depending only on the chemical nature of L r and L s . (ii) If L 0 is taken to be one of the components of the solution, then f rs and g rs are close to unity for every pair of components. (iii) The constant g rs equals ½( g rr + g ss ). From these assumptions it is possible to calculate rigorously the thermodynamic properties of a conformal solution in terms of those of the components and their interaction constants. The non-ideal free energy of mixing is given by the equation ∆* G = E 0 ƩƩ rs x r x s d rs , where E 0 equals RT minus the latent heat of vaporization of L 0 , x r is the mole fraction of L r and d rs denotes 2 f rs — f rr — f ss . This equation resembles that defining a regular solution, with the important difference that E 0 is a measurable function of T and p , which makes it possible to relate the free energy, entropy, heat and volume of mixing to the thermodynamic properties of the reference species; and the predicted relationships between these quantities agree well with available data on non-polar solutions. The theory makes no appeal to a lattice model or any other model of the liquid state, and can therefore be applied both to liquids and to imperfect gases, and to two-phase two-component systems near the critical point.

scholarly journals Thermodynamic Properties of InNa Liquid Alloy

1970 ◽  
Vol 6 (6) ◽  
pp. 16-18
Author(s):  
SK Chakrabarti ◽  
IS Jha ◽  
BP Singh
Keyword(s):  
Thermodynamic Properties ◽  
Liquid Alloy ◽  
Heat Of Mixing ◽  
Liquid Alloys ◽  
Atomic Composition ◽  
Binary Liquid ◽  
Scientific World ◽  
Energy Of Mixing ◽  
Large Asymmetry ◽  
Free Energy Of Mixing

The large asymmetry observed in the properties of mixing of indium-sodium liquid alloy is discussed on the basis of quasi-lattice chemical model. A special attention is given to the concentration dependence of free energy of mixing, entropy of mixing and heat of mixing. The results explain the observed asymmetry in the properties of mixing of InNa liquid alloys around equi-atomic composition. Key words: Complex forming alloys; Binary liquid alloys; Quasi-lattice model; Thermodynamic properties. DOI: 10.3126/sw.v6i6.2627 Scientific World, Vol. 6, No. 6, July 2008 16-18

scholarly journals A Theoretical study of thermodynamic properties of Cd-Bi liquid alloy

BIBECHANA ◽  
1970 ◽  
Vol 8 ◽  
pp. 90-95
Author(s):  
D Adhikari
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Liquid Alloy ◽  
Theoretical Study ◽  
Energy Parameter ◽  
Heat Of Mixing ◽  
Liquid Alloys ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing ◽  
Good Agreement

Flory’s model has been used for the study of thermodynamic properties of Cd-Bi liquid alloys. Free energy of mixing, heat of mixing, entropy of mixing and activity of Cd have been determined. All of these computed quantities have been found to be in a good agreement with observed values.Keywords: Flory’s model; thermodynamic properties; Cd-Bi liquid alloy; weakly interacting system; interaction energy parameter  DOI: http://dx.doi.org/10.3126/bibechana.v8i0.5693  BIBECHANA 8 (2012) 90-95

Excess heats of tri-n-alkylamines and tetraalkyl tin compounds in linear and branched alkanes: correlations of molecular orientations and steric hindrance effect

1979 ◽  
Vol 57 (5) ◽  
pp. 517-525 ◽  
Author(s):  
R. Philippe ◽  
G. Delmas ◽  
Phuong Nguyen Hong
Keyword(s):  
Steric Hindrance ◽  
Solution Structure ◽  
The Other ◽  
Short Chain ◽  
Flory Theory ◽  
Tin Compounds ◽  
Branched Alkanes ◽  
Linear Alkanes ◽  
Chain Compounds ◽  
Long Chain

Excess heats of the following mixtures of trialkylamines and tetraalkyl tin compounds with branched and linear alkanes have been measured at 25 °C: five trialkylamines NR3 (R = C2H5, C3H7, C4H9, C10H21, C12H25) with six linear alkanes, n-C5, n-C6, n-C8, n-C10, n-C12, n-C16, and three highly branched alkanes, 2,2,4-trimethylpentane, 2,2,4,6,6-pentamethylheptane, and 2,2,4,4,6,8,8-heptamethylnonane (br-C16). Further measurements were carried out on tetrapropyl tin (SnPr4) with n-C8, n-C16, and br-C16.Measurements were made to obtain more information on the heats of disordering of long chain compounds and on an exothermic contribution to the heats coming possibly from the sterically hindered character of one of the components of the mixture. The three short-chain trialkylamines have large heats with the linear long alkanes and small heats with the branched alkanes. On the other hand, the two long-chain trialkylamines have very small heats with linear alkanes and large heats with the branched alkanes. These results are interpreted as indicating no change of liquid or solution 'structure' when two ordered compounds (long alkanes and long-chain amines) are mixed but a change of 'structure' when an ordered compound (long alkane or long-chain amine) is mixed with a non-ordered one (branched alkane or short-chain amine). The heat of disordering of n-hexadecane is obtained with many order breakers and found to depend to some extent on the expansion coefficient of the order breaker. HE values for the series of the shorter NR3 do not vary regularly with molecular weight but are smaller for the propyl (and possibly the ethyl) derivative. Similarly, HE of SnPr4 in n-C16, br-C16, and n-C8 are much lower than the corresponding heats with SnEt4 and SnBut4. This is attributed to the presence of the exothermic contribution to the heats, HE(steric hindrance). The X12 parameter of the Flory theory has been calculated and is interpreted in terms of the disorder and steric hindrance contributions to the heats.

scholarly journals Theoretical assessment on hetero-coordination of Alloys Silver-Antimony at Molten State

2020 ◽  
pp. 68-73
Author(s):  
Narayan Panthi ◽  
Indra Bahadur Bhandari ◽  
Ishwar Koirala
Keyword(s):  
Reasonable Agreement ◽  
Chemical Activity ◽  
Heat Of Mixing ◽  
Thermodynamic Quantities ◽  
Molten State ◽  
Energy Of Mixing ◽  
Interchange Energy ◽  
Free Energy Of Mixing ◽  
Experimental Values ◽  
Theoretical Assessment

The thermodynamic and structural properties of binary alloy Ag- Sb at temperature 1250K have been reported theoretically using quasi lattice model. The interchange energy has been considered a function of a temperature and thus various thermodynamic quantities are calculated at elevated temperature. The theoretical values of free energy of mixing, heat of mixing, entropy of mixing and chemical activity are reasonable agreement with experimental values in all concentrations of antimony from 0.1 to 0.9. The theoretical analysis tells that the alloy shows both ordering nature in Ag rich end and segregating nature in Sb rich end .The study reveals that the properties of alloy are asymmetric around equi-atomic composition. The Ag_3 Sn complexes are most likely to exist in the liquid state and are moderately interacting.

Some Thermodynamic Properties of High Polymers, and Their Molecular Interpretation

1948 ◽  
Vol 21 (3) ◽  
pp. 564-595
Author(s):  
Geoffrey Gee
Keyword(s):  
Thermodynamic Properties ◽  
Previous History ◽  
The Past ◽  
Quantitative Measurements ◽  
Energy Of Mixing ◽  
History Of ◽  
Molecular Interpretation ◽  
Free Energy Of Mixing ◽  
Broad Outline ◽  
Experimental Difficulty

Abstract The past decade has witnessed a rapid growth in the understanding of the thermodynamic properties of polymers and their solutions. This has been achieved largely by the development of statistical theories of rubberlike elasticity and of the free energy of mixing of polymers with liquids. A number of reviews are available dealing with portions of this field of work, but for the most part they are addressed to specialist workers. The object of this review is to survey in broad outline a number of related topics, without entering into detailed discussion of statistical theories. The emphasis is, therefore, laid on the experimental thermodynamic data which form the basis for these theories, and on their physical significance. An attempt is made to develop the argument as far as possible in physical terms, although it must be realized that this is essentially a field in which we are concerned with quantitative measurements and their mathematical interrelations. One fundamental experimental difficulty which is common to nearly all the problems to be discussed below is that of ensuring that the system under investigation has reached a state of equilibrium. The significance of the concept of equilibrium in measurements on polymers has recently been very clearly discussed by Ubbelohde. The difficulty arises from the fact that many processes in a polymer take place so slowly that they may to a good approximation be said not to occur at all during the time involved in an experiment. When this is the case, it is clear that the system cannot be assumed to reach a state of equilibrium with respect to this particular process. It is, indeed, common to find that certain properties of a polymer depend greatly on the previous history of the specimen; examples will be given later. Even when this is the case, the system may still be in equilibrium with respect to other possible changes, and it is, therefore, permissible to apply the thermodynamic criteria of equilibrium. Care is needed in relating the experimental results to theories to make sure that the theory is not based on the assumption of equilibrium with respect to changes which are so slow as to be virtually negligible. The usefulness of considering partial equilibria in this way depends on the possibility of choosing a time scale for the experimental work long enough for the rapid processes to be complete, and at the same time short enough to exclude other slower processes.

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