Thermodynamic data from diffusion measurements

For a given polymer-solvent system, the sedimentation eoefficient is dependent on temperature, pressure and polymer concentration. For obtaining thermodynamic data from sedimentation eoefficients, one additionally has to measure the diffusion coefficient. This ean be made with an ultraeentrifuge in special diffusion cells or with dynamic light scattering based on the theory of Pecora. Nearly all diffusion coefficients have been measured by this method sinee it became available in 1970. The determination of sedimen-... 

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. 

For non-ideal systems the Maxwell-Stefan diffiisivities for multicomponent dense gases and liquids deviate from the Pick first law binary coefficients derived from kinetic theory and are thus merely empirical parameters [26], Hence, for non-ideal systems either Dn or Du must be fitted to experimental data. In the first approach the actual diffusivities Du are measured directly, thus this procedure requires no additional activity data. In the second approach the non-ideal effects are divided from the Maxwell-Stefan diffusivities. These are the binary Maxwell-Stefan coefficients, Du, that are fitted to experimental diffusivity data. The non-ideality corrections may be computed from a suitable thermodynamic model. These thermodynamic models generally contains numerous model parameters that have to be fitted to suitable thermodynamic data. This type of simulations were performed extensively by Taylor and Krishna [148]. The various forms of the multicomponent diffusion flux formulations are all of limited utility in describing multicomponent diffusion in non-ideal systems as they all contain a large number of empirical parameters that have to be determined experimentally. 

The non-bonded interaction energy, the van-der-Waals and electrostatic part of the interaction Hamiltonian are best determined by parametrizing a molecular liquid that contains the same chemical groups as the polymers against the experimentally measured thermodynamical and dynamical data, e.g., enthalpy of vaporization, diffusion coefficient, or viscosity. The parameters can then be transferred to polymers, as was done in our case, for instance in polystyrene (from benzene) [19] or poly (vinyl alcohol) (from ethanol) [20,21]. 

Three types of methods are used to study solvation in molecular solvents. These are primarily the methods commonly used in studying the structures of molecules. However, optical spectroscopy (IR and Raman) yields results that are difficult to interpret from the point of view of solvation and are thus not often used to measure solvation numbers. NMR is more successful, as the chemical shifts are chiefly affected by solvation. Measurement of solvation-dependent kinetic quantities is often used (<electrolytic mobility, diffusion coefficients, etc). These methods supply data on the region in the immediate vicinity of the ion, i.e. the primary solvation sphere, closely connected to the ion and moving together with it. By means of the third type of methods some static quantities entropy and compressibility as well as some non-thermodynamic quantities such as the dielectric constant) are measured. These methods also pertain to the secondary solvation-sphere, in which the solvent structure is affected by the presence of ions, but the... 

Zielinski and Hanley [AlChE J. 45,1 (1999)] developed a model to predict multicomponent diffusivities from self-diffusion coefficients and thermodynamic information. Their model was tested by estimated experimental diffusivity values for ternary systems, predicting drying behavior of ternary systems, and reconciling ternary selfdiffusion data measured by pulsed-field gradient NMR. 

Incoherent quasielastic neutron scattering measured as a function of hydration for powders of deuterated phycocyanin has been used to probe water motions (Middendorf et al., 1984). The simplest model accounting for the data was jump diffusion of water molecules between localized-sorption sites and the development of clusters of surface water at higher hydration (half-coverage of the surface, 0.15 h). This model is consistent with the picture developed from sorption thermodynamics. 

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