Number-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,... 

Investigation has shown that chain transfer to polymer occurs predominantly on the acetate methyl group in preference to the chain backbone one estimate of the magnitude of the predominance is 40-fold (92,93). The number of branches per molecule of poly(vinyl acetate) polymerised at 60°C is ca 3, at 80% conversion. It rises rapidly thereafter and is ca 15 at 95% conversion and 1-2 x lO" number-average degrees of polymerisation. 

The number average degree of polymerisation x is defined as the average number of monomer units per polymer chain. Therefore if termination is by disproportionation r = jc, but if by combination r = x. 

It follows immediately that the number average degree of polymerisation is given by ... 

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 ... 

Figure 5. Number average degree of polymerization vs, conversion for hatch-mass styrene polymerization (4j...

To run the residence time distribution experiments under conditions which would simulate the conditions occurring during chemical reaction, solutions of 15 weight percent and 30 percent polystyrene in benzene as well as pure benzene were used as the fluid medium. The polystyrene used in the RTD experiment was prepared in a batch reactor and had a number average degree of polymerization of 320 and a polydispersity index, DI, of 1.17. 

The styrene conversion for the continuous flow stirred tank experiments was determined utilizing the concentration of the polymer in the feed and the number average degrees of polymerization... 

Reactor Conditions for Experimental Runs. Operating conditions for the continuous, stirred tank reactor runs were chosen to study the effects of mixing speed on the monomer conversion and molecular weight distribution at different values for the number average degree of polymerization of the product polymer. 

Our theoretical studies [38] showed that the hyperbranched polymers generated from an SCVP possess a very wide MWD which depends on the reactivity ratio of propagating and initiating groups, r=kjk. For r=l, the polydispersity index where P is the number-average degree of polymerization. 

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