Diffusion steric hindrance

The rat constant k,, is a function of reaction temperature, functionality and environmental factors which include molecular diffusion. Steric hindrance may be significant with these chemically complex monomers. These functions likely are separable. To address functionality, consider the number average molecular weight of the polymeric phase... 

Johnson et al. [186] measured diffusion of fluorescein-labeled macromolecules in agarose gels. Their data agreed well with Eq. (85), which combined the hydrodynamic effects with the steric hindrance factors. Gibbs and Johnson [131] measured diffusion of proteins and smaller molecules in polyacrylamide gels using pulsed-field gradient NMR methods and found their data to fit the stretched exponential form... 

The rate of a catalytic reaction depends on the rate of diffusion of both substrates and products to and from the catalytic sites. Therefore it is of outmost importance that the catalytically active sites are freely accessible for reactions. Only dendrimers of low generation number can possibly be expected to be suitable carriers for catalytically active sites, especially when these are located in the interior. In high-generation dendrimers with crowded surfaces catalytic activity of an internal site would be prevented. On the other hand, a crowded surface will not only hinder access to an interior ligand site but will also cause steric hindrance between groups attached to it and thus prevent high reactivity of sites at the periphery. 

In filtration, the particle-collector interaction is taken as the sum of the London-van der Waals and double layer interactions, i.e. the Deijagin-Landau-Verwey-Overbeek (DLVO) theory. In most cases, the London-van der Waals force is attractive. The double layer interaction, on the other hand, may be repulsive or attractive depending on whether the surface of the particle and the collector bear like or opposite charges. The range and distance dependence is also different. The DLVO theory was later extended with contributions from the Born repulsion, hydration (structural) forces, hydrophobic interactions and steric hindrance originating from adsorbed macromolecules or polymers. Because no analytical solutions exist for the full convective diffusion equation, a number of approximations were devised (e.g., Smoluchowski-Levich approximation, and the surface force boundary layer approximation) to solve the equations in an approximate way, using analytical methods. 

The rate also decreases with an increase in the chain length of the alkene molecule (hex-l-ene > oct-1-ene > dodec-l-ene). Although the latter phenomenon is attributed mainly to diffusion constraints for longer molecules in the MFI pores, the former (enhanced reactivity of terminal alkenes) is interesting, especially because the reactivity in epoxidations by organometallic complexes in solution is usually determined by the electron density at the double bond, which increases with alkyl substitution. On this basis, hex-3-ene and hex-2-ene would be expected to be more reactive than the terminal alkene hex-l-ene. The reverse sequence shown in Table XIV is a consequence of the steric hindrance in the neighborhood of the double bond, which hinders adsorption on the electrophilic oxo-titanium species on the surface. This observation highlights the fact that in reactions catalyzed by solids, adsorption constraints are superimposed on the inherent reactivity features of the chemical reaction as well as the diffiisional constraints. 

The alcohols are intermediates in the formation of ketones. Isomerization of the products is not observed. Hydroxylation at the 2-position is favored over that at the 3-position, and the latter is preferred over hydroxylation at the 4-position. Solubility and concentration in the reaction medium, intrazeolite diffusion of the reactants, steric hindrance at the reactive carbon center, and C-H bond strength influence the reactivity and H202 selectivity (Table XXIV). The advantage of the large-pore Ti-beta over TS-1 in the oxidation of bulky alkane molecules is shown by the results in Table XXV. 

The amplitude and correlation time tc of the libration in the stacked state were estimated by using the diffusion in a cone model. The semiangle of the cone 6c at 20° C were obtained to be 22° and 26° for the TiL component and PBG- d2 and PBLG- d2, respectively. The tc values were obtained to be about 10 12 s at 19°C in both states. The 6C of r1L component is 4° smaller than that of PBLG- d2, showing that the amplitude of the libration in the stacked state is smaller than that in the free state due to the steric hindrance between the adjacent side chains forming the stacking... 

Alternatively, one can make the reactivity of groups dependent on the size and shape of the reacting molecule. In such a way, for instance, the effect of steric hindrances, cyclization, and diffusivities of the molecules can be modeled using generalized Smoluchowski coagulation differential equations. 

When the kinetics of a sorption process do appear to separate according to very small and very large time scales, the almost universal inference made is that pure adsorption is reflected by the rapid kinetics (16,21,22,26). The slow kinetics are interpreted either in terms of surface precipitation (20) or diffusion of the adsorbate into the adsorbent (16,24). With respect to metal cation sorption, "rapid kinetics" refers to time scales of minutes (16,26), whereas for anion sorption it refers to time scales up to hours TT, 21). The interpretation of these time scales as characteristic of adsorption rests almost entirely on the premise that surface phenomena involve little in the way of molecular rearrangement and steric hindrance effects (16,21). 

Reactions analogous to reaction (27) for methyl radicals were observed for a variety of complexes. The product of these reactions is ethane. Table IV presents a summary of their rates of reaction. As can be seen these rates are often fast, approaching the diffusion-controlled limit. The results for the homolytic decomposition of L2Cun-CH2CH2C02 suggest that steric hindrance slows down reaction (27) considerably (92). 

The rate of complex formation of dimethylsilylene with a variety of Lewis bases was found to be close to the diffusion limit in cyclohexane at room temperature.33,34 The results of Yamaji et al.34 indicate that the rate of this reaction is governed not so much by electronic factors such as the HOMO energy of the Lewis base as by steric hindrance around the heteroatom center. In contrast, Baggott et al.35 found a satisfying correlation between rate constants and ionization energies of the nucleophile for the reaction of dimethylsilylene with various oxygen-containing substrates in the gas phase. 

There are circumstances in which the simple rules for the partition of intermediates break down. If the acceptor nucleophile reacts with the acylenzyme before the leaving group has diffused away from the enzyme-bound intermediate, the partition ratio could depend on the nature of the leaving group (e.g., due to Steric hindrance of attack, etc.). Also, the measurement of rate constants for the attack of the nucleophiles on the intermediate could be in slight error due to the nonspecific binding effects mentioned above. 

Choride ion is considerably less reactive than the azide ion. Thus, although values of kc 1/ kn2o have been quite widely available from mass law effects of chloride ion on the solvolysis of aralkyl halides, normally the reaction of the chloride ion cannot be assumed to be diffusion controlled and the value of kn2o cannot be inferred, except for relatively unstable carbocations (p. 72). Mayr and coworkers251 have measured rate constants for reaction of chloride ion with benzhydryl cations in 80% aqueous acetonitrile and their values of logk are plotted together with a value for the trityl cation19 in Fig. 7. There is some scatter in the points, possibly because of some steric hindrance to reaction of the trityl cations. However, it can be seen that chloride ion is more... 

When subject to an external field, the rods will become aligned and the steric hindrance on the rotation will decrease. Using the general result in equation (7.84) to calculate ac, the rotational diffusivity of a rod of orientation u in a concentrated solution described... 

The permeability Ps is a measure of the transport of a molecule by diffusion. The reflection coefficient a of a given component is the maximal possible rejection for that component (at infinite solvent flux). Various models have been proposed for the reflection coefficient [75-77]. In the lognormal model [78], a lognormal distribution is assumed for the pore size. No steric hindrance in the pores or hydrodynamic lag is taken into account, but it is assumed that a molecule permeates through every pore that is larger than the diameter of the molecule. Moreover, the diffusion contribution to the transport through the membrane is considered to be negligible. Therefore, the reflection curve can be expressed as ... 

Micropore diffusion Diffusion within the small micropores of the adsorbent which are of a size comparable with the molecular diameter of the sorbate. Under these conditions the diffusing molecule never escapes from the force field of the solid surface and steric hindrance is important. For zeolites the terms micropore diffusion and intracrystalline diffusion are synonymous. Raffinate Product stream containing the less strongly adsorbed species. 

---