Polymerization average degree

The number average degree of polymerization for these mixtures is easily obtained by recalling the definition of the average from Sec. 1.8. It is given by the sum of all possible n values, with each multiplied by its appropriate weighting factor, provided by Eq. (5.24) ... 

The number average degree of polymerization is given by dividing the number of repeat units by the number of chains, or... 

The above mechanism, together with the assumptions that initiator decomposition is rate controlling and that a steady state in chain radicals exists, results in the classical expressions (eqs. 8 and 9) for polymerization rate, and number-average degree of polymerization, in a homogeneous,... 

The concept of functionaUty and its relationship to polymer formation was first advanced by Carothers (15). Flory (16) gready expanded the theoretical consideration and mathematical treatment of polycondensation systems. Thus if a dibasic acid and a diol react to form a polyester, assumiag there is no possibihty of other side reactions to compHcate the issue, only linear polymer molecules are formed. When the reactants are present ia stoichiometric amouats, the average degree of polymerization, follows the equatioa ... 

D. Molecular Weight/Degree of Polymerization Average Values and Distributions... 

Components of a highly short chain branched (scb) waxymaize and a more long chain branched (Icb) amylomaize were separated on the semipreparative Sephacryl S-1000 system. Both samples contained high dp components that eluted in the exclusion volume, but the percentage of these components was quite different 90% for the scb waxymaize starch and approximately 10% for the Icb amylomaize starch (Fig. 16.6). The degree of polymerization averages for these samples was determined utilizing the previously established linear... 

Briefly summarized, S-1000 shows better resolution in the high dp range, whereas the CL 2B system resolves low dp components better. Due to these differences in separation performance, the degree of polymerization distribution and degree of polymerization average values for the same sample obtained from broad scb— nb/lcb-transformed dextran calibration yielded dp = 29,900 glucose units for the S-1000 system and dp = 21,100 glucose units for the CL 2B system (Fig. 16.18). 

FIGURE 16.24 Inulin isolated from mature Topinambur tubers sparated on Bio-Gel P-6 (140 X I. Scm) flow rate 0.33 ml/min eluent H20(dest) + 0.002% NaNs detection Waters 403 R differential refractive index detector, sensitivity 8X applied sample I ml of a 20-mg/ml aqueous solution weight average degree of polymerization dp = 9 number average degree op polymerization dp = 2 polydisper-sity dp /dp = 4.5. 

Figure I 6.34 Degree of polymerization distribution molar distribution ( ) with number average degree of polymerization (dp = 140 glucose unimers) mass distribution ( ) with weight average degree of polymerization dp = 1242 glucose unimers.

Reaction conditions should usually be chosen such that the fraction of initiator-derived chains (should be greater than or equal to the number of chains formed by radical-radical termination) is negligible. The expressions for number average degree of polymerization and molecular weight (eqs. 13 and 14) then simplify to eqs. 15 and 16 ... 

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