Limiting diffusion coefficient

The fluid resistance experienced by a macromolecular solute moving in dilute solution depends on the shape and size of the molecule. A number of physical quantities have been introduced to express this. Typical ones are intrinsic viscosity [ry], limiting sedimentation coefficient s0, and limiting diffusion coefficient D0. The first is related to the rotation of the solute, while the last two are concerned with the translational motion of the solute. A wealth of theoretical and experimental information about these hydrodynamic quantities is already available for randomly coiled chains (40, 60). However, the corresponding information on non-randomly coiled polymers is as yet rather limited in number and in variety. 

It has been established that geometrical disorder has only a small effect on Brownian motion [S. Havlin, D. Ben Avraham (1987)]. Also, for thermally activated jumps, if the distribution of es and evv in a geometrically regular lattice is chosen to be Gaussian, as characterized by the variances as and crw, it has been ascertained [Y. Limoge, J. L. Bocquet (1990)] that there are two limiting diffusion coefficients ... 

Effect of Radiation Dose on Micellar Properties. Figure 1 shows the concentration dependence of the micellar diffusion coefficient at 40° as determined by quasi-elastic light scattering (QELS) for solutions subjected to radiation doses of up to 4.56 Mrad. Limiting diffusion coefficients, D0>were obtained by extrapolation of data for dilute solutions (<0.05%) to zero concentration, the critical micelle concentration (CMC) being negligibly low for this poloxamer ( 1 ). 

Effect of Temperature on Micellar Properties. Figure 5 compares the influence of temperature on the diffusion properties of the micelles in solutions previously irradiated with a dose of 4.56 Mrad with those not subjected to radiation treatment. Hydrated radii calculated from the limiting diffusion coefficients for micelles not treated with radiation remain independent of temperature over the range 25° to 40° (Table III). 

Where no experimental diffusion coefficient data in the polymer is available an estimation for the upper limit diffusion coefficient Dp can be made using the empirical correlation given in Eq. (15-1) (Chapter 15) ... 

Calculate the upper limit diffusion coefficient for styrene in polystyrene using Ap = -4 from Table 14-3. 

Estimate the limiting diffusion coefficient, the limiting sedimentation coefficient and the radius of gyration of poly(methyl methacrylate) (M = 2.5 x 105) in toluene. 

In Chap. 9 the limiting sedimentation coefficient s0 and the limiting diffusion coefficient D0 have been discussed. These are the values of the sedimentation coefficient s and the diffusion coefficient D, extrapolated to zero concentration. 

The limiting diffusion coefficient was determined by extrapolation of at four to five concentrations c to infinite dilution. is defined by... 

Limiting Diffusion Coefficients of Alkali Metal Halides in Methanol... 

The rate of diffusion of molecules through intact tissues in an animal is difficult to measure, so the amount of information currently available is limited. Diffusion coefficients for size-fractionated dextrans, albumin, and antibodies have been measured in granulation tissue and tumor tissue [20, 21] similar measurements have been made in slices of brain tissue [87]. In both cases, the diffusion coefficient was estimated by fitting solutions to the diffusion equation, similar to Equation 3-36, to data obtained by direct visualization of fluorescent tracers in the interstitial space. These measurements, as well as others made by a variety of techniques, are compiled in... 

Here Do is the limiting diffusion coefficient, a is a scaling prefactor, and i/ is a scaling exponent. If the probe and matrix molecular weights P and M differ, an elaborated form... 

Thus, at low frequencies a constant conductivity would be seen, but at higher frequencies a power law contribntion enters. In these equations. Do is the limiting diffusion coefficient and A and B are thermally activated constants. 

The values of the limiting diffusion coefficient, D of aqueous ions of the order of 10" m s" , at 25°C are shown in Table 2.11. The self-diffusion coefficients increase with increasing temperatures and a fivefold increase in aqueous solutions from 0 to 100°C has been noted. This is mainly because the viscosity of the solvent diminishes in this direction (Table 3.7). 

The Mandelkem and Flory constant can also be calculated from the limiting diffusion coefficient Dp and y such as... 

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