Diffusion, anomalous dilute solution

As far as comparison with experimental data is concerned, the fractional Klein-Kramers model under discussion may be suitable for the explanation of dielectric relaxation of dilute solution of polar molecules (such as CHCI3, CH3CI, etc.) in nonpolar glassy solvents (such as decalin at low temperatures see, e.g., Ref. 93). Here, in contrast to the normal diffusion, the model can explain qualitatively the inertia-corrected anomalous (Cole-Cole-like) dielectric relaxation behavior of such solutions at low frequencies. However, one would expect that the model is not applicable at high frequencies (in the far-infrared region), where the librational character of the rotational motion must be taken... 

Quemer C, Schmidt T, Arndt K-F (2004) Oiaracterization of structural changes of poly(vinyl methyl ether) y-irradiated in diluted aqueous solutions. Langmuir 20 2883-2889 Ren SZ, Shi WF, Zhang WB, Sorensen CM (1992) Anomalous diffusion in aqueous solutions of gelatin. Phys Rev A 45 2416-2422... 

Cornel et al (1986) measured diffusion coefficients of HA in dilute solutions and found a decrease with increased molecular weight. This contradicts the above method and the anomalous behaviour was attributed to artifacts in the size measurements. Diffusivity increased with increasing ionic strength and decreasing pH. This could be attributed to the change in shape of the molecules as will be further explained in section 2.7. Diffusion coefficients were in the order of 1 to 2.5 lO" mV for 50 to 100 kDa and 0.5 10 m-s for 1 kDa UF fractions, respectively. The diffusion coefficients for Suwannee River materials are shown in Table 2.1. 

Thus, analysis of hydrodynamic properties of native lignins reveals that their behaviour in dilute solutions is different from that of linear polymers, both flexible- and rigid-chain, in any of the known conformations. Apparently, the macromolecules of soluble lignins are randomly branched chains. Branchings in a chain are known to reduce the hydrodynamic dimensions, (i.e., reduce [q]), and increase the diffusion mobility compared to the linear analog, theoretical value of b, in a 0-solvent is 0.25. The branching of the polymer also reduces the hydrodynamic invariant by 15-20% compared to the standard value 3.2 x 10 erg/(K mol ) and results in anomalous values of the Huggins parameter. 

The osmosis described by this equation is called normal osmosis and it is observed in dilute solutions and inert (noncharged) membranes. The osmosis of electrolytes solutions through charged ionic membranes is called anomalous osmosis because in this case the solute diffusion enhances (positive anomalous osmosis) or decreases (negative anomalous osmosis) the solvent transfer. The solvent transfer through a membrane under an electric current across the system is called electro-osmosis [3]. 

We report on steady-state and time-resolved fluorescence of pyrene excimer emission in sub- and supercritical C02. Our experimental results show that, above a reduced density of 0.8, there is no evidence for ground-state (solute-solute) interactions. Below a reduced density of 0.8 there are pyrene solubility complications. The excimer formation process, analogous to normal liquids, only occurs for the excited-state pyrene. In addition, the excimer formation process is diffusion controlled. Thus, earlier reports on pyrene excimer emission at rather "dilute pyrene levels in supercritical fluids are simply a result of the increased diffusivity in the supercritical fluid media. There is not any anomalous solute-solute interaction beyond the diffusion-controlled limit in C02. 

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