Polymerization number-average chain length

FIGURE 13.5 Representative profiles of viscosity versus conversion for free-radical and condensation polymerizations. The endpoint is 99.9% conversion with a number average chain length of 1000. 

The traditional method of determining the monomer transfer constant is the Mayo method [294,295], where the inverse of the number average chain length Pn is extrapolated to zero polymerization rate. To obtain reliable values, one needs to measure rather large P values to high precision that can then be extrapolated to zero polymerization rate. In addition, linear extrapolation is not guaranteed if bimolecular termination reactions are chain-length-dependent [296]. 

Example 3 (Effect of monofunctional chain stoppers or impurities) Let us suppose we have No moles of AE-type monomers and Nj moles of monofimctional impurity containing an A functional group, but no B group. Whenever this monofunctional impurity adds to the end of a molecule, that end can no longer participate in step-growth polymerization reactions. As in Equation 7.11, the number-average chain length is equal to the initial number of molecules divided by the final number of molecules, so that ... 

The easiest method for obtaining the number-average chain length for the evaporator contents, using either of the two models, is to divide the total number of molecules that have been consumed by polymerization or remain unreacted in the vessel by the final number of molecules in the vessel. For example, using the functional-group modeling approach, first solve the differential equations to obtain concentrations for aU of the spedes at the time of interest and then compute ... 

Then, the number average chain length (or degree of polymerization) is given by... 

The calculation of the condition to produce a latex with a given MWD is based on the fact that for linear polymers produced by free-radical polymerization, the polymer chains do not suffer any modification once they are formed. This opens the possibility of decomposing the desired final MWD in a series of instantaneous MWDs to be produced at different stages of the reaction [130]. When chain transfer to a CTA is the main termination event, each of those MWDs can be characterized by the number-average chain length, according to Eq. (76). 

It is usually straightforward to detect the presence of multiple-site types on a coordination catalyst because these catalysts will produce polymer with polydispersity higher than 2 even under invariant polymerization conditions. The simplest way to visualize this phenomenon is to assume that every different site type on a multiple-site catalyst produces polymers that follow a distinct Flory s distribution that is, those with a distinct number-average chain length, [38]. In this way, the chain length distribution for the whole polymer is a combination of distinct Flory s distributions weighted by the mass fraction of polymer made on each site type, mj [Eq. (24)]. 

The molar mass can be addressed using the kinetic chain length concept for free radical polymerization the instantaneous number average chain length, is given in the QSSA for the aforementioned conditions... 

FIGURE 9.5 Instantaneous and cumulative number-average chain lengths versus conversion for an isothermal, free-radical, batch polymerization (data of Example 9.10). 

As with other modes of polymerization, the number-average chain length is given by the moles of monomer polymerized over the moles of chains present. With an initiator like -BuLi, each molecule starts a single chain, therefore. 

Obtain an expression for the number-average chain length at complete conversion in a group-transfer polymerization batch that contains I, M, and RH moles of initiator, monomer, and chain-transfer agent, respectively. 

Here, GH is the catalyst and G is the gegen ion. The ionization step is assumed to be essentially instantaneous, and always at equilibrium, with K being the equilibrium constant. Obtain expressions for the rate of polymerization and the number-average chain length according to this mechanism. 

The quantity Fi, the instantaneous copolymer composition, is analogous to x , the instantaneous number-average chain length in free-radical addition polymerization. Like x , it depends on the conditions in the reactor at a particular instant. It, too, is really an average, since not all the copolymer formed at a particular instant has exactly the same composition. However, the instantaneous distribution of compositions is normally much narrower than the instantaneous distribution of chain lengths, and because the fact that it is an average is not normally of great practical importance and cannot be controlled anyhow, the overbar is left off of Fj. 

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