Number-average chain lengths

The inlet monomer concentration was varied sinusoidally to determine the effect of these changes on Dp, the time-averaged polydispersity, when compared with the steady-state case. For the unsteady state CSTR, the pseudo steady-state assumption for active centres was used to simplify computations. In both of the mechanisms considered, D increases with respect to the steady-state value (for constant conversion and number average chain length y ) as the frequency of the oscillation in the monomer feed concentration is decreased. The maximum deviation in D thus occurs as lo 0. However, it was predicted that the value of D could only be increased by 10-325S with respect to the steady state depending on reaction mechanism and the amplitude of the oscillating feed. Laurence and Vasudevan (12) considered a reaction with combination termination and no chain transfer. 

If the reaction goes to completion, the polymer molecules will have the form B B, and the final concentration of B endgroups will be [B]o-[A]q. The number average chain length is... 

TABLE 13 1 Number Average Chain Lengths for Binary Polycondensations Going to Completion... 

The ratio of weight-to-number average chain lengths is the polydispersity,... 

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. 

A binary polycondensation of AMA and BNB is to be performed in a batch reactor. A number average chain length of at least 100 is required. What minimum accuracy is required for weighing the two components ... 

Number-Average Chain Length of the Primary Molecules which Belong to the Gel Fraction. 

As there is one functional group of each type per chain, one can write for Xn (number average chain length or degree of polymerisation)... 

Here a is a parameter that determines how broad or peaked the distribution is it is conventionally denoted by a, but we choose a different notation here to prevent confusion with the phase index used in the general discussion so far. The chain number density of the parent is pg° and the normalized first moment mf = pfVPo is simply the (number) average chain length... 

In general a solution will contain a distribution of chain lengths, characterized by the reduced chain length distribution p(y) (Eq, (5.36)) and the number averaged chain length N. As pointed out in Sect. 11.6, p(y) is invariant under the renormalization group. The other physical variables characterizing the solution can be expressed in terms of N. From Eqs. (11.38), (11.83) we recall the definitions... 

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]. 

The first moment divided by the zeroth moment gives the number-average chain length (NACL), u ... 

The number-average chain length, Equation (7-47), can be rearranged as... 

Figure E7-5.I Moments of live polymer chain lengths (a) number-average chain length (b> weight-average chain length (c) polydispersity.

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