Flory most probable chain length distribution

Figure 7.4 Flory most-probable chain length distribution at a conversion of 0.99. The locations of niunber and weight averaged chain lengths are noted. Polydispersity is 1.99.

Fig. 1. Flory-Schultz s most probable chain length distributions for ATn = 1000. fn (-----)...

Polymers made by a mechanism where the chain can either grow by propagation or terminate by transfer reactions, as quantified by Eqs. (1)-(14), follow Flory s most probable chain length distribution [33] [Eq. (15)]. 

The molecular weight distribution can be calculated by solving the mass balance equations for monomer(s), initiator (catalytic sites), and polymeric species with different chain lengths. When quasisteady state assumption is applied to live polymers or propagating active centers, the molecular weight distribution of live polymers is often represented by the Schultz-Flory most probable distribution. However, the calculation of the chain length distribution of dead polymers is in general quite complicated. For some special cases such as... 

Anionic polymerization. If one assumes rapid initiation, and no termination or chain transfer, the steady state number chain length distribution follows the Flory or Most Probable Distribution [7]. 

For instance, the instantaneous chain-length distribution of many polymers is given by Flory-Schultz s most probable distribution (1),... 

Therefore, the chain length distributions of linear binary (or multicomponent) copolymers also follow Flory s most probable distribution and have, instantaneously, a polydispersity of 2. 

Therefore, in the absence of LCB formation, t = l/r , and Eq. (30) reduces to Flory s most probable distribution, Eq. (15). Figure 8.28 shows the chain length distribution for several polymer populations with increasing numbers of LCBs per chain. As expected, the chain length average increases with an increasing number of LCBs per chain. 

Most Probable (Flory) Distribution The most probable or Rory distribution is described by the following equations. For polymerization problems. Equation 16.53 is appropriate, since chains of length zero are not considered Equation 16.52 is included for completeness only. It is a single-parameter distribution, with the shape of the distribution dependent only on the value of a. The Rory distribution describes the NCLD for a number of kinetic schemes, including batch condensation polymerization and anionic polymerization in a CSTR ... 

Provided that there is a most probable distribution (a Flory distribution) of chain lengths in the linear part of the equilibrate, Eq. (2) reduces to... 

This is called the Flory, or most probable, distribution and often arises in polymerizations where reaction rates are independent of chain length. X is the fractional conversion of the limiting end group as previously defined. The mean of/(/) is... 

Flory was also from the Midwest and attended Ohio State University (Ph.D. 1934). His class notebooks reveal a hvely and inquiring mind. He wrote his thesis on the photochemical decomposition of nitric oxide. A thorough grounding in chemical kinetics was the perfect preparation for his work with Carothers at DuPont. It was known that condensation polymerization produced a broad distribution of molecular weights. Flory was able to calculate from first principles the distribution of chain lengths for a system of reacting molecules as a function of extent of reaction, p. This paper appeared in JACS in 1936 [6]. The most probable distribution law for the distribution of x-mers is one of the foundations of polymer science ll c = xp (l — p), where x is the number of monomer units in the polymer. 

Fig. 2.8 Weight-fraction Poisson distribution of chain lengths for various values of x in a polymerization without termination. For comparison, the broken line represents the most probable distribution of molar mass when x = 11 (after Flory).

Equations that describe several types of molecular weight distribution were presented in Chapter 2. One of these is the most-probable or Schulz-Flory distribution that is derived assuming that each catalyst site is equally active and that the probability of termination does not depend on chain length. This distribution has a polydispersity index of two, and... 

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