Diffusion branched chains

The rate of solvent diffusion through the film depends not only on the temperature and the T of the film but also on the solvent stmcture and solvent-polymer iuteractions. The solvent molecules move through free-volume holes iu the films and the rate of movement is more rapid for small molecules than for large ones. Additionally, linear molecules may diffuse more rapidly because their cross-sectional area is smaller than that of branched-chain isomers. Eor example, although isobutyl acetate (IBAc) [105-46-4] has a higher relative evaporation rate than -butyl acetate... 

Note 2 Semi-interpenetrating polymer networks may be further described by the process by which they are synthesized. When an SIPN is prepared by a process in which the second component polymer is formed or incorporated following the completion of formation of the first component polymer, the SIPN may be referred to as a sequential SIPN. When an SIPN is prepared by a process in which both component polymers are formed concurrently, the SIPN may be referred to as a simultaneous SIPN. (This note has been changed from that which appears in ref [4] to allow for the possibility that a linear or branched polymer may be incorporated into a network by means other than polymerization, e.g., by swelling of the network and subsequent diffusion of the linear or branched chain into the network.). 

We have seen previously shape-selective catalysis by ZSM-5 in the conversion of methanol to gasoline (Chapter 15).-7 Other commercial processes include the formation of ethylbenzene from benzene and ethylene and the synthesis of p-xylene. The efficient performance of ZSM-5 catalyst has been attributed to its high acidity and to the peculiar shape, arrangement, and dimensions of the channels. Most of the active sites are within the channel so a branched chain molecule may not be able to diffuse in, and therefore does not react, while a linear one may do so. Of course, once a reactant is in the channel a cavity large enough to house the activated complex must exist or product cannot form. Finally, the product must be able to diffuse out. and in some instances product size and shape exclude this possibility. For example, in the methylu-uon of toluene to form xylene ... 

This is of the same form as Equation 30, but involves the mixed diffusion coefficient, Jci9, instead of the thermal conductivity of the mixture. However, as seen from the kinetic theory of gases, the thermal conductivity is proportional to the diffusion coefficient. Therefore agreement of experimental results with either Equation 30 or 53a is not an adequate criterion for distinguishing between first explosion limits in branching chain reactions and purely thermal limits. It has been reported (52), that, empirically,... 

Figure 7.2. Change of the thermal diffusion ratio /CT1 with the alkane concentrations xx at 30°C and ambient pressure (a) straight chain alkanes, (—) /7-hexane, (—), /7-heptane, (—) n-octane (b) branched-chain alkanes, (—) 3-methylpentane, (—) 2,2-dimethylpentane, (—) 2,2,4-trimethylpentane. Reprinted with the permission from Elsevier, Y. Demirel and S.l. Sandler, Int. J. Heat Mass Transfer, 43 (2002) 75.

C. Tanford and R. N. Pease, J. Cham, Phys.y 16, 861 (1947), have developed a model in which propagation occurs by diffusion of radicals. Since wall initiation of chains is not possible in most flames, it seems quite reasonable to expect that initiation by diffusion of chain carriers may be a necessary condition for propagation. It is difficult, however, to see this as a limiting or controlling condition even in fast flames, particularly for branching chain reactions in which, because of the rapid multiplication of centers, even cosmic rays can act as initiations once ignition temperatures have been reached. 

The above butyl-branched alkane was studied by solid-state 13C NMR, alongside its linear analogue C198H398, to establish the solid-state diffusion coefficient.150 Both alkanes were in the once-folded form. The progressive saturation experiments have shown that the longitudinal relaxation of magnetization is consistent with a solid state chain diffusion process. Reptation and one-dimensional diffusion models were demonstrated to satisfactorily represent the data. The addition of the branch to the alkane chain was shown to result in a decrease in the diffusion coefficient, which ranged from 0.0918 nm2 s 1 for the linear chain to 0.016 nm2 s 1 for the branched chain. These diffusion coefficients are consistent with those of polyethylene. 

Erionite and the related zeolite T exclude branched chain paraffins, so that n-paraffins are selectively cracked or hydrocracked over these catalysts. However, even n-paraffins have diffusities several orders of magnitude lower than in large pore zeolites. Earlier work on hydrocracking over erionite catalysts gave unexpected product distributions, with maxima at C4 and C12 and essentially no Cg product. Gorring measured diffusion coefficients for migration of n-paraffins in KT zeolite. An unexpected phenomenon, termed the window... 

In contrast, see the right side of the plot, low density polyethylene, as produced by a high-pressure process, shows the expected correspondence of Tc and Tm, because the abundant presence of side groups in LDPE effectively hinders sliding diffusion of the branched chains throu the crystallites and, because of that much less reorganization occurs. 

Thus, analysis of hydrodynamic properties of native lignins reveals that their behaviour in dilute solutions is different from that of linear polymers, both flexible- and rigid-chain, in any of the known conformations. Apparently, the macromolecules of soluble lignins are randomly branched chains. Branchings in a chain are known to reduce the hydrodynamic dimensions, (i.e., reduce [q]), and increase the diffusion mobility compared to the linear analog, theoretical value of b, in a 0-solvent is 0.25. The branching of the polymer also reduces the hydrodynamic invariant by 15-20% compared to the standard value 3.2 x 10 erg/(K mol ) and results in anomalous values of the Huggins parameter. 

NMR self-diffusion measurements indicated that all microemulsions consisted of closed water droplets and that the structure did not change much during the course of reaction. Hydrolysis was fast in microemulsions based on branched-chain anionic and nonionic surfactants but very slow when a branched cationic or a linear nonionic surfactant was employed (Fig. 11). The cationic surfactant was found to form aggregates with the enzyme. No such interactions were detected with the other surfactants. The straight-chain, but not the branched-chain, alcohol ethoxylate was a substrate for the enzyme. A slow rate of triglyceride hydrolysis for a Ci2E4-based microemulsion compared with formulations based on the anionic surfactant AOT [61,63] and the cationic surfactant cetyltrimethylammonium bromide (CTAB) [63] was observed in other cases also. Evidently, this type of lipase-catalyzed reaction should preferably be performed in a microemulsion based on an anionic or branched nonionic surfactant. Nonlipolytic enzymes such as cholesterol oxidase seem to function well in microemulsions based on straight-chain nonionic surfactants, however [64]. CTAB was reported to cause slow inactivation of different types of enzymes [62,64,65] and also, in the case of Chromobacterium viscosum lipase [66], to provide excellent stability. 

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