Polymerisation number average degree

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 ... 

In the absence of any transfer, only the type of termination reaction has to be taken into account to obtain the number average degree of polymerisation (or chain length) Xn. Indeed, if the reaction terminates by addition, two radicals give one chain, while if the reaction terminates by disproportionation, one radical generates one chain. Using 0.5 < x < 1, one obtains... 

Equation (4) clearly shows that the number average degree of polymerisation Xn is inversely proportional to the reaction rate Rp, meaning that, in radical chain polymerisation high reaction rates are linked to low molecular masses and vice versa. One way to avoid this dilemma is to use emulsion polymerisation where the lifetime of a radical (i.e., the "kinetic" chain length) is independent of... 

Also used as a measure for molecular weights, especially by polymer chemists [2], are "number average degree of polymerisation" and the "weight average degree of polymerisation", Pw and Pn. Here we will use Mw and Mn. They are defined as follows ... 

The number-average degree of polymerisation of the polymer, P , is given... 

The absence of termination and of chain transfer is also demonstrated by the molecular weight of the resulting polymer, its number average degree of polymerisation being given then by the simple relation,... 

Such an expression is based on the simple kinetic model of olefin polymerisation and is valid for systems with non-supported Ziegler-Natta catalysts (of moderate activity). Some important limiting expressions can be deduced when [M] is high and when k kp km, and Cp = C, where C denotes the total concentration of active sites, and Pn denotes the number-average degree of polymerisation ... 

Micelle formation has been studied for sodium salts of fatty acids containing terminal double bonds using electrical conductivity . Here two critical micelle concentration points were observed of which the first point at 0.044 moles litres" was critical in terms of the number average degree of polymerisation of the polymers produced. At concentrations up to the second point the molecular weight change was significantly smaller. The photopolymerisation of acrylamide in reverse micelles was found to be first order with respect to monomer concentration whilst the order was found to depend upon the oil concentration in the... 

The number average degree of polymerisation (DP ) can be calculated as a function of functionality of the monomers, i.e. the number of reactive groups per monomer, and as a function of the extent of conversion. For a functionality of 2.000, i.e. corresponding to very pure difunctional monomers, and for 99.9% conversion, it can be calculated that DP = 1000, i.e. a number-average molecular weight of about 200 000. 

Quantitatively, the end-group intensity relative to the main-chain intensity gives the number-average degree of polymerisation directly. In practice, because of incomplete resolution of end-group peaks and insufficient sensitivity, this use of NMR is usually restricted to degrees of polymerisation of the order of 100 or less. 

The number average degree of polymerisation (DP ) is defined as the ratio of number of units (number of molecules initially present) to the number of molecules present after the reaction. DP can be expressed as ... 

Fig. 3.18 Simulation of polymerisation within a droplet with a diffiisimi coeffidoitZl = 10 m /s droplet radius and surface temperature over time and radial profiles of the degree of polymerisation (number average) and concentrations at times 0, 5, 10,. 50 s. Circles dtaiote results Irtnn a OD model...

In this Section the effects of undesirable transfer reactions on the number average degree of polymerisation (DP) and on the weight fraction of polymer molecules possessing undesirable functionality (0, ) will be discussed. As will be seen later DP and are not independent, nevertheless it is worth dealing with them separately. 

For the number averaged degree of polymerisation Pn of the chains that are formed at a particular point in time, the following holds Pn = number of monomer units added in the time interval dt over the number of dead chains formed in dt. Therefore, Pn = 2v for termination by combination, because two growing chains produce one dead chain and Pn = V for termination by disproportionation, because two growing chains will produce two dead chains. 

Here Vp is the volume fraction of polymer (related to the conversion), X is the number average degree of polymerisation of the polymer, x is the Flory-Huggins interaction parameter between the monomer and the polymer, R is the gas constant and T the temperature. Um is the molar volume of the monomer, y is the particle-water interfacial tension and To is the radius of the unswollen micelles, vesicles and/or latex particles. [M]a is the concentration of monomer in the aqueous phase and [M]a,sat the saturation concentration of monomer in aqueous phase. Figure 3.3 shows the contributions of the different terms of Equation 3.10 to the Vanzo equation. For a more detailed discussion see also Section 4.2 and Figure 4.5. 

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