Relative diffusion constant

In such a case the caged pair [A B]c are in thermodynamic equilibrium with A-B, and the last slow step is the diffusion step 3. Such a reaction can be described as a diffusion-controlled reaction even though it contains a far slower chemical step, reaction 1. The rate will now be sensitive to the relative diffusion constant Dab in the given solvent, and the over-all rate should be lower than the rate in the gas phase. There have been a number of attempts to observe this diffusion control. 

The ratio of the relative diffusion constants of brine and oil in the microemulsion phase was found to be very important. Figure 19 shows the effect of varying this ratio. When oil diffusion is less than that of brine, as would be expected in an oil-in-water microemulsion, the fraction of liquid crystal at the dispersion front Increases over that in the bulk dispersion. This situation corresponds to diffusion path 1 in Figure 19. Essentially, brine diffuses out of the dispersion faster than oil can diffuse in, causing a decrease in overall brine concentration at the interface and hence the formation of additional liquid crystal, the phase having the lower brine content. As mentioned previously, this buildup of liquid crystal was observed experimentally. 

Model systems are described in Table 2, and both numerical results from UHBD and analytical results are given. i The first model system is the diffusion of two uncharged spheres in water. The analytical diffusion-controlled rate constant for this was derived many years ago by Smoluchowski and is equal to 4TrDo(fli + <32) where a and are the hydrodynamic radii for spheres 1 and 2, respectively, and Dq is the relative diffusion constant. 

For diffusion measurements, the bipolar LED sequence with water suppression gives the best results [36], While an absolute comparison between different proteins is generally difficult, the relative diffusion constants for one particular protein at different buffer conditions are good measures for its oligomeric state or aggregated state, respectively. Furthermore, the concentration dependence of the diffusion constant is a practical indicator of the aggregation tendency. Figure 15.2-4 shows an example of what can be achieved by proper optimization of buffer conditions for MAPKAP-2. 

A chemist can evaluate two molecules and make estimates of their relative diffusion constants. The linear 1-hexanone, for example, will diffuse relatively quickly, whereas the relatively rigid chair conformation of cyclohexanone makes it notoriously slow to diffuse out of the many polymers for which it is a good solvent. Similarly, 1-butanol will diffuse... 

The second contribution to paramagnetic relaxation is the outer-sphere relaxation. It is explained by dipolar interactions at longer distances between the spins of the paramagnetic center and the nuclear spin. This intermolecular mechanism is modulated by the translational correlation time Tp, which takes into account the relative diffusion constant (D) of the Gd center and of the solvent molecule and their distance of closest approach (d). The outer-sphere contribution has been described by Freed and is given by equations (10) and (11) ... 

Fig. 27. Relative diffusion constant of the surface and inner chains in the PE particle of 6000 atoms with chain length of a 100 beads and b 50 beads. The closed circles and triangles show the diffusion for the surface and inner chains of the particle...

FRIES - The rate constant k for proton tunnelling given by Eqs. (1 ) and nir is inversely proportional to the relative diffusion constant D of the spherical potential wells. As the temperature decreases, so does D and thus k increases. This effect is easily interpreted by the fact that the reactants, i.e. the wells, stay longer in close contact where the proton can effectively tunnel. 

The relative displacement of two paxticles is given by and so the relative diffusion constant by... 

An alternative to the common device of determining relative intensities is a study of the fine structure of the scattered beam. This entails resolving the spectrum of scattered light into its three peaks, viz. a central peak and two side ones. The need is thus obviated to refer to I0 or, according to the apparatus, the scattering power of a standard calibration material. The method is used mainly for determining diffusion constants and thermodynamic properties of liquids. 

Figure 14 (a) Time-dependent behavior of cation radicals in liquid -dodecane monitored at 790 nm. The dotted and the solid lines represent the experimental curve and the simulation curve, respectively. The parameters of the electron dilfusion coefficient (De) = 6.4 x 10 " cm /sec, the cation radical diffusion coefficient (D + ) = 6.0 x 10 cm /sec, the relative dielectric constant e = 2.01, the reaction radius R = 0.5 nm, and the exponential function as shown in Eq. (19) with ro = 6.6 nm were used, (b) Time-dependent distribution function obtained from fitting curve of (a), r indicates the distance between the cation radical and the electron. The solid line, dashed line, and dots represent the distribution of cation radical-electron distance at 0, 30, and 100 psec after irradiation, respectively. 

It can be seen from the relative rate constants shown in Sch. 1 that the products formed will depend on the reaction conditions [26]. The production of formate, as shown by the right-hand reaction in Sch. 1, will be enhanced in protic solvents or in more acidic solutions. In water, formic acid is the main product. The production of CO, as shown by the left-hand reaction in Sch. 1, will be enhanced in rapidly stirred solutions in which locally high concentrations of the "C02 radical anion cannot buildup. This will decrease the probability of a bimolecular reaction between 02 radical anions. In quiet solutions and high current densities, the C02 radical anion concentration should be high in the diffusion layer, favoring formation of oxalate. 

The rate constant of the second reaction is clearly proportional to the membrane diffusion constant D. For this dependence on the diffusion constant to be detected, it is necessary that the lifetimes of IgGH2 and (IgGH2)Cl be sufficiently long and the lifetime of (IgGH2)2Cl be sufficiently short (relative to the formation of (IgGH2)2Cl) so that the overall rate is limited by reaction (17). 

The concentration gradient. This is normally in the direction external to internal relative to the cell or organism. The rate of diffusion is affected by certain factors it is proportional to the concentration gradient across the membrane the area and thickness of the membrane and a diffusion constant, which depends on the physicochemical characteristics of the compound in question. This relationship is known as Fick s Law ... 

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