Manning ratio

This short discussion shows that despite significant progress in the analytical theories, there are still many unsolved issues. The situation gets even more complicated if one allows for added salt and/or multivalent counterions [58] or varies the Manning ratio in the system. 

A is called the Manning ratio. The dimensionless Coulomb pair interaction is then... 

The multiloop controller contains a variety of func tion blocks (for example, PID, totalizer, lead/lag compensator, ratio control, alarm, sequencer, and Boolean) that can be soft-wired together to form complex control strategies. The multiloop controller, as part of a DCS, communicates with other controllers and man/machine interface (MMI) devices also on the DCS network. 

Serelis and Solomon108 found that primary radical termination of oligo(MAN) radicals (16) with 15 also gives predominantly combination. The ratio kllt/klc was found to have little, if any, dependence on the oligomer chain length (n<4). As with PMMA, disproportionation involves preferential abstraction of a methyl... 

For copolymerizations between non protie monomers solvent effects are less marked. Indeed, early work concluded that the reactivity ratios in copolymerizations involving only non-protic monomers (eg. S, MMA, AN, VAe, etc.) should show no solvent dependence.100101 More recent studies on these and other systems (e.g. AN-S,102-105 E-VAc,106 MAN-S,107 MMA-S,10s "° MMA-VAc1" ) indicate small yet significant solvent effects (some recent data for AN-S copolymerization are shown in Table 8.5). However, the origin of the solvent effect in these cases is not clear. There have been various attempts to rationalize solvent effects on copolymerization by establishing correlations between radical reactivity and various solvent and monomer properties.71,72 97 99 None has been entirely successful. 

The effects of solvent on reactivity ratios and polymerization kinetics have been analyzed for many copolymerizations in terms of this theory.98 These include copolymerizations of S with MAH,"7 118 S with MAA,112 S with MMA,116 117 "9 121 S with HEMA,122 S with BA,123,124 S with AN,103415 125 S with MAN,112 S with AM,11" BA with MM A126,127 and tBA with HEMA.128 It must, however, be pointed out that while the experimental data for many systems are consistent with a bootstrap effect, it is usually not always necessary to invoke the bootstrap effect for data interpretation. Many authors have questioned the bootstrap effect and much effort has been put into finding evidence both for or against the theory.69 70 98 129 "0 If a bootstrap effect applies, then reactivity ratios cannot be determined by analysis of composition or sequence data in the normal manner discussed in Section 7.3.3. 

Studies on the reactions of small model radicals with monomers provide indirect support but do not prove the bootstrap effect.111 Krstina et ahL i showed that the reactivities of MMA and MAN model radicals towards MMA, S and VAc were independent of solvent. However, small but significant solvent effects on reactivity ratios are reported for MMA/VAc111 and MMA S 7 copolymerizations. For the model systems, where there is no polymer coil to solvate, there should be no bootstrap effect and reactivities are determined by the global monomer ratio [Ma0]/[Mb0].1j1... 

The highly branched GaM of Mimosa seeds, isolated by a scaled-up process [186] at a yield of 20% of seed weight, showed a Man Gal ratio of 1.1 1 and structural features of the gum obtained on a laboratory scale [ 183]. Based on C-NMR spectroscopy of GaM from Cassia angustifolia [179], with a Man Gal ratio of 2.9 1, a blockwise pattern of the galactosyl branches was suggested. 

The slightly galactosylated mannans are essentially linear polymers. As a result of their cellulose-like (1 4)-/3-D-mannan backbone, they tend towards self-association, insolubility, and crystallinity. Crystallographic study of C. spectabilis seed GaM [180] with a Man Gal ratio 2.65 1 suggested an orthorhombic unit cell with lattice constants of a = 9.12, b = 25.63, and c = 10.28 the dimension b was shown to be sensitive to the degree of galactose substitution and the hydration conditions [180 and references therein, [191]]. 

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