Diffusivity Experimental

Other results also confirm the important role of internal diffusion. Experimental activation energies (67—75 kJ mol"1) of the sucrose inversion catalysed by ion exchangers [506—509] were considerably lower than those of a homogeneously catalysed reaction (105—121 kJ mol"1) [505, 506,508] and were close to the arithmetic average of the activation energy for the chemical reaction and for the diffusion in pores. The dependence of the rate coefficient on the concentration in the resin of functional groups in the H+-form was found to be of an order lower than unity. A theoretical analysis based on the Wheeler—Thiele model for a reaction coupled with intraparticle diffusion in a spherical bead revealed [510,511] that the dependence of the experimental rate coefficient on acid group concentration should be close to those found experimentally (orders, 0.65 and 0.53 for neutralisation with Na+ and K+ ions respectively [511] or 0.5 with Na+ ions [510]). 

The rate of diffusion is proportional to the concentration gradient, and the proportionality constant is defined as the diffusion coefficient (D) in Fick s first law of diffusion. Experimental determination of D is commonly performed ex vivo due to the difficulty of measuring concentration gradients in the interstitium. In vivo measurement can be performed in specific tissues, using transparent chamber preparations in combination with the FRAP technique (Berk et al., 1997 Jain et al., 1997 Pluen et al, 2001). However, the in vivo approach is limited only to fluorescent molecules or solutes whose D is not affected by labeling with fluorescent markers. 

Table 1. Oxygen diffusion experimental results for La1 ySryMn03 8...

Figure 1. The dependences of 5%-th mass loss temperature Ty, in TGA testing on Z contents Cz for compositions HDPE+Z. The calculation according to the equation (6) for slow (1) and rapid (2) diffusion experimental TGA data in air (3) and in helium atmosphere (4).

The simulated and experimental hydronium diffusivities both increase with increasing water contents. The simulated values are lower than the experimental values, presumably, due to the fact that the simulations report only the vehicular contribution to the proton diffusivity, whereas the experiment measures the total proton diffusivity. Experimentally, Nafion has higher proton diffusivity than SSC at low water contents and lower proton diffusivity than SSC at high water contents. The vehicular diffusion coefficients of the hydronium ion measured from simulation are higher for Nafion than in SSC PFSA at all water contents. Clearly a detailed understanding of the total proton diffusivity as a function of polymer architecture requires a model capable of structural diffusion. 

H-bond lifetimes tiq from ref. 46. (2) Probability pg calculated ftdlowing the procedure in Section V.A. (3) Relaxation times calculated from Eq. (6.1) with the same conditions (6.2) for H2O and D2O. (4) Experimental values of dielectric relaxation times from ref. 75 ( ) at 10°C (t) extrapolated. (5) Self-diffiision coefficients calculated from Eq. (7.5) assuming for D2O the same Dj-(ij/) used for H2O. (6) Self-diffusion experimental data from ref. 63. 

Bres, M. and Hatzfeld, C., Three Gas Diffusion—Experimental and Theoretical Studies, Pflugers Arch., 371, 227-233 (1977). 

Rebour et al. (1997) review the literature describing gas diffusion in a porous medium as a double porosity process. In this model, gas diffusion is affected by the increase in water viscosity when in the close vicinity of clay minerals. This produces an environment in which the gas diffusion rate is expected to be variable in the porous network depending on the local tortuosity and grain-size distribution. In modeling this type of system, diffusion is considered to occur along a direct pathway. These fast routes interconnect slow regions, into and out of which gas also diffuses. Experimental work by the same authors (Rebour et al. 1997) determines Rf = 200 for a clayey marl from Paris basin Callovo-Oxfordian sediments that have a porosity and permeability of 23% and 10 m, respectively. 

Dale and Eisinger have analyzed the effect of rotational mobility Stryer presents an analysis of the errors introduced by assuming = 2/3 and van der Meer et al. present a treatment on the effects of restricted rotational and translational diffusion. Experimentally, one determines the rotational mobility of the dyes by a steady-state or time-resolved fluorescence depolarization experiment. ... 

The interaction of turbulent flow containing regions of high strain rate and high shear rate with polymer molecules can involve both individual molecules and polymer structures. The results of this interaction lead to suppressions of the small scale motions and to production of some large scale motions that do not contribute to turbulent diffusion. Experimental results are interpreted in terms of the interaction of molecules near the wall and movement of the polymeric large scale structures in the center of pipe flows. 

To permit a comparison of the cell diffusion experimental results with scaling predictions of the protein partitioning behavior, the partition coefficients were correlated... 

In our calculations, two different values of a are used at for parallel irradition and 02 for diffuse radiation. We assume that the irradiation beam is parallel and that the reflected beams are more or less diffuse. Experimentally, it was determined that the fraction of reflected flux was usually greater for the diffuse irradiation then for the parallel one (16), = w ai. From the experiments... 

The diffusivity of a component in a porous solid, where the pores are filled with a fluid phase, is of course lower than the diffusivity in the fluid phase itself. If the void fraction in the particles is e, and the tortuosity factor is the effective diffusivity, related to the total cross sectional area of the solid particle, would be reduced by a factor of e. The tortuosity factor should not only account for the fact that the diffusing molecules follow a zig-zag path, but also that the individual pores do not have a constant cross section. One might attempt to describe the diffusion in the porous structure using geometrical parameters, but it is in fact simpler to measure the effective diffusivity experimentally. In the following it is assumed that the effective diffusivity of 0 of reactant A in the porous solid is known. 

Eqs. 25 and 26 differ by their dependence upon the liquid velocity. The convective term of Eq. 26 is proportional to whereas Taylor s model predicts an exponent equal to three for this dependence. Furthermore, the convective term of Eq. 26 is unaffected by molecular diffusion. Experimentally, some investigators (42) have shown that the RTD curves are nearly independent of the molecular diffusivity of the tracer used. 

In addition to the substantial literature on solvent and small-molecule translational diffusion, there is also a significant literature on small-molecule rotational diffusion. Experimental methods that report rotational diffusion behavior include VH tight scattering, as examined in different time domains with Fabry-Perot interferometry and photon correlation methods, nuclear magnetic resonance, oscillatory electrical birefringence, and time-resolved optical spectroscopy. 

From centrifugation and solvent dynamics to viscosity and diffusion, experimental measurements and their quantitative representations are the core of the discussion. The book reveals several experiments never before recognized as revealing polymer solution properties. A novel approach to relaxation phenomena accurately describes viscoelasticity and dielectric relaxation, and how they depend on polymer size and concentration. 

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