Average degree of polymerization

The average degree of polymerization, denoted X, were k represent the type of average (i.e., arithmetic, geometric), represents the dimensionless number of monomer units or residues R constitutive of a macromolecular chain. It can be defined as the ratio of the relative molar mass of the macromolecule to the relative molar mass of the monomer unit  

Depending of the degree of polymerization, it is possible to distinguish several subgroups of 

The readers may have wondered why there is such a subtle difference. Let us start by explaining the physical difference in the distribution of degree of polymerization and the average degree of polymerization based on the number and weight.  

Therefore, the weight average degree of polymerization approaches infinity at p = 1 and in the reacting system gels. 

On the other hand, the number average degree of polymerization is the value obtained by dividing the total number of chemical repeat units (in this system, it is constant) by the number of polymer molecules. As the number of molecules reduces by one as one crosslink is formed, the number average degree of polymerization can be expressed as follows  

Let us interpret the meaning of Eq. (1) once more. Equation (lb) indicates that gelation takes place when the weight average number of the crosslink point becomes one. Some readers may not expect this. One 

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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 ... 

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 ... 

Assuming that the number average degree of polymerization (DP ) is determined by chain transfer to monomer and assuming unimolecular termination relative to propagation (i.e., chain breaking due to solvent, polymer, impurities are absent), the simple Mayo equation55 ... 

The Carothers equation relates the number-average degree of polymerization to the extent of reaction and average functionality of a step-growth polymer. In the Carothers equation, the number-average degree of polymerization, X , relates to the extent of reaction, p, and average functionality, /avg, of the polymer system ... 

The instantaneous number and weight average degrees of polymerization are given by... 

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