Chain length, definition

Now in polymerization it is probably not so much the monomer rate, but the product polymer rate and the properties of the product polymer that are of interest. The product polymer rate follows directly from equation (1-123) since, to the extent that the pssh is valid, the initiation and termination rates must be equal. The kinetic analysis also leads to some characterization norms for the product that are useful. The number-average degree of polymerization, P , is the average number of monomer units in the polymer product. This is defined in a manner analogous to the chain length definition of equation (1-113) and is... 

The kinetic chain length has a slightly different definition in the presence of chain transfer. Instead of being simply the ratio Rp/R, it is redefined to be the rate of propagation relative to the rates of all other steps that compete with propagation specifically, termination and transfer (subscript tr) ... 

We now discuss the effects of finite chain length. The difficulties arise from the definition of a bulk free energy term, when the very nature of the chains constrains the crystal thickness to be finite. There are two different approaches to this problem the first to be considered is due to Hoffman et al. [31] and is a simple modification of the infinite chain case, but is somewhat lacking in theoretical justification the second, due to Buckley and Kovacs [23], aims to correct this deficiency and suggests that the interpretation of experimental data given by Hoffman s approach is misleading. 

Pure alkyl sulfuric acids are white crystalline solids with definite melting points but they are hygroscopic. Hygroscopicity increases as the chain length increases. Dodecyl, tetradecyl, hexadecyl, and octadecyl sulfuric acids were obtained by Maurer et al. [57] by chlorosulfation of the corresponding alcohols and the melting points obtained are shown in Table 2. 

Kinetic vs. material chain. Kinetically, a chain reaction exists throughout the "life" of the radical, that is, from the initiation of a radical up to its termination by recombination or by disproportionation. The lifetime of a radical determines the so-called kinetic chain length Lp defined as the number of monomers consumed per initiating radical. Lp, by definition, can be calculated from the ratio between the propagation rate Rp to the initiation rate R, or, using steady-state hypothesis (Equation (1)), from the ratio between propagation rate to the termination rate Rt (Equation (3)). 

Fischer-Tropsch synthesis could be "tailored by the use of iron, cobalt and ruthenium carbonyl complexes deposited on faujasite Y-type zeolite as starting materials for the preparation of catalysts. Short chain hydrocarbons, i.e. in the C-j-Cq range are obtained. It appears that the formation and the stabilization of small metallic aggregates into the zeolite supercage are the prerequisite to induce a chain length limitation in the hydrocondensation of carbon monoxide. However, the control of this selectivity through either a definite particle size of the metal or a shape selectivity of the zeolite is still a matter of speculation. Further work is needed to solve this dilemna. 

Considering that for a steady system, the termination and initiation steps must be in balance, the definition of chain length could also be defined as the rate of product formation divided by the rate of termination. Such a chain length expression would not necessarily hold for the arbitrary system of reactions (3.1)—(3.6), but would hold for such systems as that written for the H2—Br2 reaction. When chains are long, the types of products formed are determined by the propagating reactions alone, and one can ignore the initiation and termination steps. 

When it is possible to specify the chain length of a block, the appropriate Greek prefix (e.g. hecta for 100) may be used rather than poly. Although short sequence lengths are not strictly embraced within the definition of block , the same device may usefully be employed by using the general prefix oligo or the appropriate specific prefix (e.g. tri). 

In this section the group of polyphosphates with a chain length of n > 4 which undergo definite migration in paper chromatography is considered. They include compounds with (P 03,l+i)( +2) anions having chain length up to n 9. 

Fig. 1.5. The, swelling factor (Eq. (1.17)) as function of z (Eq, (1.16)). Points p o ly sty re ne- cyclohexane [MF81] [YFTY71]. Circles P-isobutvlc rio-iso amylisovalerate [MNE72]. Each set of data comprises several chain lengths. The theoretical crossover curve is also given. The precise definition of the variable used here, which later will be called i, is given in Sect. 13.3...

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