Pseudo thermodynamic analysis

It was suggested that a six-member chain of mannitol hexanitrate was coiled into a pseudo-ring. It is not surprising if one considers that long chain organic substances in solution have a tendency to be coiled. This is based on thermodynamical analysis, dipole measurements etc. 1124]. 

Adsorption of nonionic surfactants on porous solids has been studied by Huinink et al. in a series of p ers [ 149,150]. They elaborated a thermodynamic approach that accounts for the major features of experimental adsorption isotherms. It is a very well known fact that during the adsorption of nonionic surfactants there is a sharp step in the isotherm. This step is interpreted as a change from monomer adsorption to a regime where micelle adsorption takes place. Different surfactants produce the step in a different concentration range. The step is more or less vertical depending on the adsorbate. The thermodynamic analysis made by Huinink et al. is based on the assumption that the step could be treated as a pseudo first order transition. Their final equation is a Kelvin-like one, which shows that the change in chemical potential of the phase transition is proportional to the curvature constant (Helmholtz curvature energy of the surface). 

The development of various thermal analysis techniques over the past several decades has had a profound effect in accelerating the use of thermodynamic, kinetic and pseudo thermodynamic measurements in the analysis and characterization of materials. All of these methods have in common the use of very small samples and a means of causing the temperature to change linearly with time. 

Kinetic analysis revealed that this reaction is pseudo-first order in dienophile at low conversions (200). At higher conversions, the rate deviates from a linear relationship, suggestive of product inhibition. Indeed, addition of product to the reaction at the start resulted in a decrease in rate by 18%. A number of competitive inhibitors were identified in this study. Particularly interesting was the observation that the matched chiral dienophile product was less effective as an inhibitor than the mismatched product. The authors suggest that the sterically matched complex (where the ligand bulk and imide chirality is on the same side of the complex) is thermodynamically less stable than the mismatched complex. 

The analysis of a multiphase flow system is complex, in part because of the difficulties in assessing the dynamic responses of each phase and the interactions between the phases. In some special cases, the gas-solid mixture can be treated as a single pseudo-homogeneous phase in which general thermodynamic properties of a gas-solid mixture can be defined. This treatment provides an estimate for the bulk behavior of the gas-solid flow. The following treatment is based on the work of Rudinger (1980). 

Allylic alcohols are more easily oxidised than saturated alcohols and in this case rates are greatest for the equatorial isomers [42]. Activated manganese dioxide is commonly used for selective oxidations of allylic alcohols, although it will also attack saturated alcohols slowly under special conditions [44]. Its mechanism of action is not understood, although some relevant observations have been reported [43]. 2,3-Dichloro-5,6 dicyanobenzoquinone (DDQ) is a very mild and selective oxidant for allylic alcohols [43]. Kinetic studies [46] on 3a- and 3 9 hydroxy-A -systems (8) revealed a higher rate of oxidation of the pseudo-equatorial 3 -alcohol K jK a = 6), and a large primary isotope effect Kj)IKb ca. 1/5) when the C(3) H was replaced by deuterium. These results indicate a rate-determining hydride abstraction from C(3>, with preferred removal of the pseudo-axial 3C1-H as a result of optimum a-7i overlap in the transition state (9). However, a detailed analysis of thermodynamic parameters shows that the cause of the rate difference appears mainly in the term (A5 ) rep-... 

The adsorption up to 50 bars was carried out by means of a Tian-Calvet type isothermal microcalorimeter built in the former CNRS Centre for Thermodynamics and Microcalorimetry. For these experiments, around 2 g of sample was used which were outgassed by Controlled Rate Thermal Analysis (CRTA) [7]. The experiments were carried out at 30°C (303 K). Approximately 6 hours is required after introduction of the sample cell into the thermopile for the system to be within 1/100 of a degree Celsius. At this point the baseline recording is taken for 20 minutes. After this thermal equilibrium was attained, a point by point adsorptive dosing procedure was used. Equilibrium was considered attained when the thermal flow measured on adsorption by the calorimeter returned to the base line. For each point the thermal flow and the equilibrium pressure (by means of a 0-70 bar MKS pressure transdueer providing a sensitivity of 0.5% of the measured value) were recorded. The area under the peak in the thermal flow, Q eas, is measured to determine the pseudo-differential... 

The theoretical analysis of the thermodynamics of supercooled silicon, presented by Aptekar [14] treats the liquid as a pseudo-binary regular solution of two components, along lines explored in related contexts by Rappaport [41], Ponya-tovsky and coworkers [15,42], The two components are characterized by different local bonding environments (covalent or metallic). Correspondingly, the Gibbs free energy of the liquid is written as... 

Heidemann et al also presented a discontinuous method to calculate spinodal curves and critical points using two different versions of the Sanchez-Lacombe equation of state and PC-SAFT. Moreover, Krenz and Heidemann applied the modified Sanchez-Lacombe equation of state to calculate the phase behaviour of polydisperse polymer blends in hydrocarbons. In this analysis the polymer samples were represented by 100 pseudo-components. Taimoori and Panayiotou developed a lattice-fluid model incorporating the classical quasi-chemical approach and applied the model in the framework of continuous thermodynamics to polydisperse polymer solutions and mixtures. The polydispersity of the polymers was expressed by the Wesslau distribution. 

Such assignments are in error, however, even though one of them is based on a normal-co-ordinate calculation, and are quite unable, with or without a contribution of pseudo-rotation, to reproduce the measured heat capacity. The most accurate values of the measured thermodynamic properties require, for agreement within 0.1%, that /, = 10.59 x 10 gem a small contribution of anharmonicity was treated by equations (15). A subsequent molecular vibrational analysis led to some revision of the vibrational assignment, but excellent agreement with the measured heat capacity values is still obtained from it-provided the contribution of pseudo-rotation is included. The details of the selection rules for cyclopentane have been discussed. ... 

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