Diffusion Intramolecular

Typical values for p are between 0.3 and 0.6, and for tp between 2 and 5. So, a reasonable assumption for the effective diffusion De is that it is Vio of the diffusivity I). This diffusivity D can be calculated from the Knudsen (corresponding to collisions with the wall) and molecular diffusivity (intramolecular collisions). The molecular diffusivity was estimated at 10 5 m2/s, which is reasonable for the diffusion in gases. The Knudsen diffusivity depends on the pore diameter. The exact formulas for the molecular and Knudsen diffusion are given by Moulijn et at1. For zeolites, the determination of the diffusivity is more complicated. The microporous nature of zeolites strongly influences the diffusivity. Therefore, the diffusion... 

Figure C3.1.7. Time-resolved optical absorjDtion data for the Soret band of photo lysed haemoglobin-CO showing six first-order (or pseudo-first-order) relaxation phases, I-VI, on a logaritlimic time scale extending from nanoseconds to seconds. Relaxations correspond to geminate and diffusive CO rebinding and to intramolecular relaxations of tertiary and quaternary protein stmcture. (From Goldbeck R A, Paquette S J, Bjorling S C and Kliger D S 1996 Biochemistry 35 8628-39.)...

Actually the parabolas are truncated at the diffusion-controlled limit because of considerations we met in Chapter 9. We can develop this again here in an abbreviated fashion by writing a two-step scheme, the first being entirely diffusion and the second intramolecular electron transfer ... 

This simple relaxation theory becomes invalid, however, if motional anisotropy, or internal motions, or both, are involved. Then, the rotational correlation-time in Eq. 30 is an effective correlation-time, containing contributions from reorientation about the principal axes of the rotational-diffusion tensor. In order to separate these contributions, a physical model to describe the manner by which a molecule tumbles is required. Complete expressions for intramolecular, dipolar relaxation-rates for the three classes of spherical, axially symmetric, and asymmetric top molecules have been evaluated by Werbelow and Grant, in order to incorporate into the relaxation theory the appropriate rotational-diffusion model developed by Woess-ner. Methyl internal motion has been treated in a few instances, by using the equations of Woessner and coworkers to describe internal rotation superimposed on the overall, molecular tumbling. Nevertheless, if motional anisotropy is present, it is wiser not to attempt a quantitative determination of interproton distances from measured, proton relaxation-rates, although semiquantitative conclusions are probably justified by neglecting motional anisotropy, as will be seen in the following Section. 

In the present chapter we shall be concerned with quantitative treatment of the swelling action of the solvent on the polymer molecule in infinitely dilute solution, and in particular with the factor a by which the linear dimensions of the molecule are altered as a consequence thereof. The frictional characteristics of polymer molecules in dilute solution, as manifested in solution viscosities, sedimentation velocities, and diffusion rates, depend directly on the size of the molecular domain. Hence these properties are intimately related to the molecular configuration, including the factor a. It is for this reason that treatment of intramolecular thermodynamic interaction has been reserved for the present chapter, where it may be presented in conjunction with the discussion of intrinsic viscosity and related subjects. 

Similar studies have been performed for a series of nitrophenols [299], showing the ability of the A log P parameter to identify the presence of intramolecular H-bonds in a series of eongeners. This is of pharmaeeutical relevance, since, as mentioned above, it is often reeognized that the A log P parameter is a good predietor of biodistribution and passive diffusion [215,300]. This approaeh is as yet restrieted to neutral speeies, because of the diflieulty in establishing LSER for ions. It would yet be of great interest to enlarge the speetrum of LSERs to this field. 

Therefore, the sequence of reactions illustrated in Fig. 1 catalytically (the anthraquinone is regenerated) injects a radical cation into a DNA oligonucleotide that does not simultaneously contain a radical anion. As a result, the lifetime of this radical cation is determined by its relatively slow bimolecular reaction with H20 (or some other diffusible reagent such as 02- ) and not by a rapid intramolecular charge annihilation reaction. This provides sufficient time for the long distance migration of the radical cation in DNA to occur. 

Alternatively, Leung and Eichinger [51] proposed a computer simulation approach which does not assume any lattice as the classical and percolation theory. Their simulations are more realistic than lattice percolation, since spatially closer groups form bonds first and more distant groups at later stages of network formation. However, the implicitly introduced diffusion control is somewhat obscure. The effects of intramolecular reactions were more realistically quantified, and the results agree quite well with experimental observations [52,53],... 

A bottle of the dichloride exploded violently while on a bench. No cause was established, but diffusive ingress of moisture, or an intramolecular Friedel-Crafts reaction, both of which would form free hydrogen chloride, seem possible contributory factors. 

The quenching of benzophenone phosphorescence has been used by Mar and Winnik (1981) as a photochemical probe of hydrocarbon chains in solution. The bimolecular reaction for quenching the triplet state of 4-methoxy-carbonylbenzophenone [24] by 1-pentene occurs at rates which are below the diffusion limit by two to three orders of magnitude. Consequently, the intramolecular quenching reactions of to-alkenyl esters of benzophenone-4-carbo-xylic acid [25] occurs under conformational control. In [25] the point of... 

All these reactions are thermodynamically favourable in the direction of proton transfer to hydroxide ion but the rate coefficients are somewhat below the diffusion-limited values. In broad terms, the typical effect of an intramolecular hydrogen bond on the rate coefficient for proton removal is to reduce the rate coefficient by a factor of up to ca 105 below the diffusion limit. Correspondingly the value of the dissociation constant of the acid is usually decreased by a somewhat smaller factor from that of a non-hydrogen-bonded acid. There are exceptions, however. 

In this region, the equilibrium constant for the proton-transfer step in Scheme 7 has a value K2> 1 and the proton transfer step is strongly favourable thermodynamically in the forward direction. This reaction step is a normal proton transfer between an oxygen acid which does not possess an intramolecular hydrogen bond and a base (B) and will therefore be diffusion-limited with a rate coefficient k2 in the range 1 x 109 to 1 x 1010dm3mol-1 s 1. It follows from (65) that kB will have a value which is... 

In the two examples of buffer catalysis of proton transfer from an intramolecularly hydrogen-bonded acid which have been discussed, it seems reasonably certain that the mechanism in Scheme 7 applies. The reactions are of the first order with respect to the catalyst B and it therefore follows that proton removal from the non-hydrogen-bonded species is rate-limiting k j > 2[B]- If this step consists of diffusion-controlled proton removal from a low concentration intermediate, the value k2 lx 109dm3 moP s-1 will apply for proton transfer to an amine. In the case of proton removal by hydroxide ion from 4-(3-nitrophenylazo)salicylate ion, the reaction was found to be of the first order in hydroxide ion up to the highest concentrations which could be studied (0.003 mol dm-3) with a rate... 

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