Thermodynamic non-ideality

To obtain a correct form of Eq. (22) allowing for thermodynamic non-ideality of the solution, fluctuation theory originally developed by Einstein, Zernicke, Smoluchowski and Debye has been adapted to polymer solutions. 

The quantity (op2/Bm2)TiP can be expressed in terms of thermodynamic non-ideality coefficients A2 and A3 8) such that, when combined with Eq. (12), gives... 

Thermodynamic non-idealities are considered both in the transport equations and in the equilibrium relationships at the phase interface. If electrolytes are present, the liquid-phase diffusion coefficients should be corrected to account for the specific transport properties of electrolyte systems. 

Thermodynamic non-idealities are taken into account while calculating necessary physical properties such as densities, viscosities, and diffusion coefficients. In addition, non-ideal phase equilibrium behavior is accounted for. In this respect, the Elec-trolyte-NRTL model (see Section 9.4.1) is used and supplied with the relevant parameters from Ref. [50]. The mass transport properties of the packing are described via the correlations from Refs. [59, 61]. This allows the mass transfer coefficients, specific contact area, hold-up and pressure drop as functions of physical properties and hydrodynamic conditions inside the column to be determined. 

Correlations for the determination of the dissociation equilibrium constants and solubility values for SO2 and CO2 as functions of temperature as well as the equations for activity coefficients are given in Ref. [70], Thermodynamic non-idealities are taken into account depending on whether species are charged, or not. For uncharged species, a simple relationship from Ref. [102] is applied, whereas for individual ions, the extended Debye-Hiickel model is used according to Ref. [103]. 

Horton, J. C., Harding, S. E., Mitchell, J. R., and Morton-Holmes, D. F. (1991). Thermodynamic non-ideality of dilute solutions of sodium alginate studied by sedimentation equilibrium ultracentrifugation. Food Hydrocoll. 5 125-127. 

It has long been a mystery why diffusion coefficients of polymer-diluent systems, especially when the diluent is a good solvent for a given polymer, exhibit so pronounced a concentration dependence that it looks extraordinary. Several proposals have been made for the interpretation of this dependence. Thus Park (1950) attempted to explain it in terms of the thermodynamic non-ideality of polymer-diluent mixtures, but it was found that such an effect was too small to account for the actual data. Fujita (1953) suggested immobilization of penetrant molecules in the polymer network, which, however, was not accepted by subsequent workers. Recently, Barrer and Fergusson (1958) reported that their diffusion coefficient data for benzene in rubber could be analyzed in terms of the zone theory of diffusion due to Barrer (1957). Examination shows, however, that their conclusion is never definitive, since it resorted to a less plausible choice of the value for a certain basic parameter. 

Consequently, new investigations dealing with reactions in micellar solutions composed of functional surfactants, or mixtures of inert and functional surfactants, continue to appear in the literature. An interesting study of acid-catalyzed hydrolysis of 2-(p-tetradecyloxyphenyl)-l,3-dioxolane (p-TPD) in aqueous sodium dodecyl sulfate (SDS) solutions has been reported [13]. In this case,/ -TPD behaves as a non-ionic functional surfactant and apparently forms non-ideal mixed micelles with the anionic surfactant (SDS). Based on the observed kinetic data, the authors propose that, at elevated temperatures, the thermodynamic non-ideality results in the manifestation of two populations of micelles, one rich in SDS and the other rich in/>-TPD. 

For non-ideal systems, on the other hand, one may use either D12 or D12 and the corresponding equations above (i.e., using the first or second term in the second line on the RHS of (2.498)). In one interpretation the Pick s first law diffusivity, D12, incorporates several aspects, the significance of an inverse drag D12), and the thermodynamic non-ideality. In this view the physical interpretation of the Fickian diffusivity is less transparent than the Maxwell-Stefan diffusivity. Hence, provided that the Maxwell-Stefan diffusivities are still predicable for non-ideal systems, a passable procedure is to calculate the non-ideality corrections from a suitable thermodynamic model. This type of simulations were performed extensively by Taylor and Krishna [96]. In a later paper, Krishna and Wesselingh [49] stated that in this procedure the Maxwell-Stefan diffusivities are calculated indirectly from the measured Fick diffusivities and thermodynamic data (i.e., fitted thermodynamic models), showing a weak composition dependence. In this engineering approach it is not clear whether the total composition dependency is artificially accounted for by the thermodynamic part of the model solely, or if both parts of the model are actually validated independently. 

The TST is viewed here mainly as a tool for the calculation of rate coefficients, an endeavor that has now become possible with dedicated software and powerful computers. Before that it has also been used to explain the observed behavior of reacting media, e.g., under thermodynamically non ideal conditions (high pressure, strong electrolyte solutions) and to correctly express the rate in terms of fugacities or activities [Boudart, 1968]. 

As mentioned above, the assvunption of a pixrely entropic elasticity leads to the prediction, Eq. (1.14), that the stress should be directly proportional to the absolute temperature at constant a (and V). The extent to which there are deviations from this direct proportionality may therefore be used as a measure of the thermodynamic non-ideality of an elastomer [9, 68-74]. In fact, the definition of ideality for an elastomer is that the energetic contribution /e to the elastic force / be zero. This quantity is defined by... 

The thermodynamic non-ideality of these systems are stressed, because some authors are still tending to determine what they are calling the thermodynamic quantities (like AH° and AS°) on the basis of simpler relationships, holding onlyPfor the ideal systems. 

The presence of solutions (cpi < cpcr ) in the area of flat maximum on the curve of dependence Dv on cpi is determined by the competition of two factors on the one hand, it is the increase of amenability of matrix during dissolution of oligomer in it (as the consequence of plasticization). It results in decrease of resistibility of diffusion environment and in the growth of the diffusion rate correspondingly. On the other hand, thermodynamic non-ideality of solutions, caused by aggregation of diffiisant molecules, becomes stronger at spontaneous mixture of components. This evidently reduces the speed of translational diffusion. Therefore, the character of concentration dependence Dv for every... 

Figure 5 shows the 3D (A, q, /s) compositional space representation of the behaviour of the electroactive film mobile species (ion and solvent). This representation has been extended to combine thermodynamic non-ideality (attractive or repulsive interaction... 

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