Molecular exchange

Section 13 12 Splitting resulting from coupling to the O—H proton of alcohols is not normally observed because the hydroxyl proton undergoes rapid inter molecular exchange with other alcohol molecules which decouples it from other protons in the molecule... 

The situation is completely different for mass transfer within the pore network of monolithic compounds. Here mass transfer can occur both on the pore surface or in the pore volume and molecular exchange between these two states of mobility can occur anywhere within the pore system, being completely uncorrelated with the respective diffusion paths. As a consequence, Eq. (3.1.11) is applicable, without any restrictions, to describing long-range diffusion in the pore space. Equation (3.1.14) is thus obtained,... 

SPAN module. It was mentioned at the beginning that the special polyacrylonitrile fibers of SPAN have a wall thickness of 30 gm, which is considerably thicker than the 8 gm wall thickness of the SMC modules [19]. As a consequence, the presence of stronger capillary effects from the special porous fiber material of the SPAN module would be a reasonable conclusion. Furthermore, the texture of the special polyacrylonitrile fibers is expected to have better surface properties, supporting the permeation of molecules as compared with synthetically modified cellulose. In conclusion, both convection and diffusion effectively contribute to the filtration efficiency in a SPAN module, whereas for the SMC membrane, diffusion is the driving force for molecular exchange, the efficiency of which is also considerable and benefits from the large surface-to-volume ratio. 

Gritsenko, O. V., R. van Leeuven, and E. J. Baerends. 1996. Molecular exchange-correlation Kohn-Sham potential and energy density from ab initio first- and second-order density matrices Examples for XH (X = Li, B, F). J. Chem. Phys. 104, 8535. 

SANS has been recently used to study problems related to micelle preparation and kinetics, as reported by Bates and coworkers who have used time-resolved SANS to study molecular exchange and micelle equilibration for PEO-PB diblocks in water [71]. The authors have shown that the micellar structures initially formed upon dissolution were completely locked in up to 8 d after preparation. Fluorometry and DLS have also been used to monitor micelle equilibration [72],... 

This model qualitatively explains the deviation of isotopic compositions away from the Meteoric Water Line because molecular diffusion adds a non-equilibrium fractionation term and the limited isotopic enrichment occurs as a consequence of molecular exchange with atmospheric vapor. It is mainly the humidity which controls the degree of isotope enrichment. Only under very arid conditions, and only in small water bodies, really large emichments in D and are observed. For example, Gonfiantini (1986) reported a 5 0-value of +31.3%c and a 8D-value of +129%c for a small, shallow lake in the western Sahara. 

Now we know that the asymptotic decay of the density far from atom B (but not so far that ps still dominates the molecular density p ) is determined by the ionization energy Ib- The asymptotic decay of the density pa is however also determined by the highest occupied Kohn-Sham orbital Kohn-Sham potential cannot go to zero in the asymptotic region of atom B otherwise the density decay around atom B would be determined by 1a- As the Hartree and the external potential go to zero in the outer asymptotic region it follows from Eq. (145) that the only possibility is that the molecular exchange-correlation potential around atom B is given by... 

Figure 1.30 EXSY spectrum (CD2CI2, 176 K) showing cross-peaks for the intra- and inter-molecular exchange between nuclei of the monomeric, 107, and dimeric, 108, fo rms of [Rh(dppb)2](BPh4).

The gap junctions are communicating junctions, kinds of tunnels enabling the molecular exchanges between neighboring cells. They are spread in an anarchic way on the lateral and basal faces. 

In mixtures in which sodium chloride occurs together with ammonium nitrate, there is a possibility of molecular exchange and of the formation of the more stable system sodium nitrate-ammonium chloride ... 

For T = 298 K (25°C) and M( = 78 g mol-1 (benzene), this velocity is 7 x 103 cm s-1. Even if only a small fraction of the molecules, say one out of every thousand, actually penetrates into the other phase and stays there, the molecular exchange velocity is still of the order of 10 cm s. This is much larger than the largest transfer velocities viaAv shown in Fig. 20.1. Hence, the molecular transfer right at the interface is not the limiting step. At the interface equilibrium conditions can be assumed, indeed. 

The co-existence of at least two modes of ethylene adsorption has been clearly demonstrated in studies of 14C-ethylene adsorption on nickel films [62] and various alumina- and silica-supported metals [53,63—65] at ambient temperature and above. When 14C-ethylene is adsorbed on to alumina-supported palladium, platinum, ruthenium, rhodium, nickel and iridium catalysts [63], it is observed that only a fraction of the initially adsorbed ethylene can be removed by molecular exchange with non-radioactive ethylene, by evacuation or during the subsequent hydrogenation of ethylene—hydrogen mixtures (Fig. 6). While the adsorptive capacity of the catalysts decreases in the order Ni > Rh > Ru > Ir > Pt > Pd, the percentage of the initially adsorbed ethylene retained by the surface which was the same for each of the processes, decreased in the order... 

With alumina-supported palladium, platinum and rhodium and silica-supported platinum [65,66] in the temperature range 20—200°C, no molecular exchange between adsorbed 14C-ethylene and gaseous ethylene is observed, whilst with hydrogen, small quantities of methane are formed at 100°C and above with platinum and rhodium and at 200° C withpallad-... 

C-Tracer studies of acetylene adsorption on alumina- and silica-sup-ported palladium [53,65], platinum [66] and rhodium [53] show the coexistence of at least two adsorbed states, one of which is retained on the surface, the other being reactive undergoing molecular exchange and reaction with hydrogen. Acetylene adsorption exhibits the same general characteristics as those observed with ethylene (see Sect. 3.2). However, there are important differences. The extent of adsorption and retention is substantially greater with acetylene than with ethylene. Furthermore, the amounts of acetylene retained by clean and ethylene-precovered sur-... 

NMR studies of the Zn2+-HN(CH2C02H)2 system have shown that 2 1 complexes are formed in aqueous solution, and that a variety of intra- and inter-molecular exchange processes occur.1214. 

The Free Volume and the Rate a of Particles Participating in Molecular Exchange Processes... 

The deformation y or A decreases with increasing density of the cross-links (e.g.) an increase of the sulphur bridges in vulcanized caoutchouc). Moreover the saturation stress omax increases with the temperature. A better reproduction of the experimental values can be obtained by using. <4 = const a2 in the molecular exchange theory or with the empirical Mooney-Rivling equation... 

Kinetic processes have been shown by NMR and other spectral data to involve both intra- and inter-molecular exchange for 1 1 complexes of alkaline earth metal ions and (52a) (Scheme 7).190 The internal exchange between the two monocycles occurs at a faster rate than the intermolecular process, however. 

After a discussion of the fundamental concepts in Section II, we present, in Section III, an approach to the lineshape theory of dynamic NMR spectra which comprises the most general case, namely that of a multi-component system where various intra- and inter-molecular exchange processes take place. We believe that a fully correct NMR theory of such an equilibrium has not been put forward yet. Section IV is concerned with the methods of simulation and analysis of complicated dynamic spectra. In Section V, we present our views on solving the numerous practical problems which usually appear upon the application of the theory to the analysis of dynamic spectra. 

In our further considerations we assume that the components of the relaxation matrix are known in advance. This is a realistic assumption provided that unsaturated NMR spectra are being dealt with. One should note that equation (35) can be used for the description of motion of the system during time spans which are much longer than the typical correlation times for molecular rotation in liquids (about 10-11—10—12 sec). The processes of intra- and inter-molecular exchange which are considered here are characterized by half-life times longer than 10 5 sec. It seems justified to consider these processes independently of molecular rotations, in spite of the fact that they all participate in the relaxation. 

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