Length of a chain

Most systems of interest in combustion include numerous chain steps. Thus it is important to introduce the concept of a chain length, which is defined as the average number of product molecules formed in a chain cycle or the product reaction rate divided by the system initiation rate [1]. For the previous... 

End to end distribution function of a chain length with n segments... 

In PB networks, the variation of the line shape as a function of the applied stress was interpreted in terms of a chain length distribution. Shorter chains may be more oriented than longer ones, at a given elongation [18], which may lead to a non-affine behaviour at the chain scale. The question of the spatial scale to which the deformation is affinely transmitted, has been investigated intensively by small angle neutron scattering [64]. However, it may happen as well that the chain portions close to junction points are more oriented (have a more restricted mobility) than those in the middle of the chains [19]. 

Further details about the molecular weight distribution of the polymer chains can be obtained by simple probability arguments. If the probability of adding another monomer unit to a chain is p, the probability of a chain length P (number distribution) with random addition is... 

The lattice-controlled diyne polymerization can occur in lipid bilayers only, if the amphiphiles are present in the solid-condensed state. Several studies dealt with the characterization of the monolayer properties of diyne surfactants. Fatty acids, for example, were investigated concerning influences of a chain length variation and headgroup ionization on the Glm stability (Fig. 9a) sv.eo. 62-64,70) number of... 

The ratio of the weight-average and the number-average degree of polymerization, Pvi/Pn, describes the polydispersity of a chain length distribution. It becomes unity if all chains have the same length—called a monodisperse distribution— and values greater than one, if the distribution exhibits a broader shape. 

Most of the methods employed to deduce and kp are based on the assumption of a chain-length-independent termination rate coefficient and yield and in some combination (kp/kt or kp /kt, respectively). In the past, before could be determined directly, the usual procedure was to use two different ratios of p and kt and to split them into their individual components via combination. In view of the chain length dependence of it is clear that any (single) experiment aiming at the determination of will render only an average value kt, which is defined by the method used and the experimental conditions chosen (eg, monomer and initiator concentration, type of initiation). Combination of kp/kt and k /kt ratios, which are invariably taken from different experiments, therefore always involves averages of which are not consistent with each other. 

This kinetic analysis, however, has two disadvantages (i) the obtained kinetic parameters kp and kt are determined as combined fit parameters and their accuracy is dependent upon the determination of either [i ]o or kp from (mostly) independent experiments and (ii) a constant value of kt is used instead of a chain-length dependent one. The first disadvantage is inherent to non-stationary experiments and is difficult to overcome. Conversion is inextricable linked to radical concentrations and propagation rate coefficients. The latter disadvantage, however, can be overcome in several ways and is discussed below. 

Because of the shape of the /F plots in the upper range of values for the pristine materials the increase of effective conjugation is undoubtely revealed by the electronic spectra in a more relevant way than by the Raman spectra. Evidence has been found of an effective conjugation length > 9-10 units and of a chain length 8 units. 

SCHEME 47.8. Stereoselectivity in the Pudovik reaction as a function of a chain length and configuration in the carbohydrate... 

---