Molecular Schultz-Flory

This distribution is known as the Schultz-Flory or most probable distribution.2S The moments of the molecular weight distribution are ... 

While the catalysts and conditions are very different than in ZN (water is a severe poison for ZN but is a product in FT), both produce linear polymers, and the molecular weight distributions are very similar because they are controlled by relative rate coefficients of propagation kp and termination k. If these are nearly independent of molecular weight one obtains the Schultz Flory size distribution in both processes. 

When the mass fraction of the long-chain hydrocarbon products of the F-T synthesis (W) is plotted against the carbon number (TSf) it is found that W decreases approximately monotonically with molecular size. Thus the major product is the Ci, methane, followed by the C2 hydrocarbons (ethylene and ethane), the C3 hydrocarbons, and so forth, as shown in Figure 15. This distribution follows Schultz-Flory statistics for a polymerization involving the sequential addition of Ci units to a chain, given by the dotted line in Figure 15. Further and more detailed consideration of the mechanisms is in Annex 1. 

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... 

Most data concerns ethylene oligomerization on the TiCl2/Et Al3 systems. The influence of reaction conditions on selectivity, Schultz-Flory molecular weight oligomer distribution, and yields has been investigated. These factors are catalyst composition—Ti/Al ratio, catalyst concentration, reaction time, and kind of the titanium and aluminum ligand. 

Schultz and Flory have developed, starting from the FH model and Equation 16.41, the following expression, which relates the critical solution temperature (CST), with the theta temperature and the polymer molecular weight ... 

Triangular phase equilibrium for two polymers with a low molecular weight substance/solvent was first presented in some detail by Dobry and Boyer-Kawenoki [22]. A subsequent study was by Schultz and Flory [23]. Typical phase diagrams are shown in Fig. 6.2. 

Molecular weight distribution of oligomers in the range between the narrow (Poisson) and the most probable (Flory) distribution can be described by the G -distribution of Schultz, which can be analytically expressed by equation... 

SO that a plot of l/T versus [(1/2tw) + (1/ ] should be a straight line with a slope of 1 /Oil/ and an intereept of 1 /6. These are, in fact, the results obtained by Schultz and Flory [9], and this allows for easy determination of ij/ and 6. Clearly, X equals 0.5 when T equals 0 and, therefore, the parameter 0 is the theta temperature referred to earUer and is the maximum in the cloud point ciuve for an infinite-molecular-weight polymer. It can be shown that at the theta temperature, the effect of attraction between polymer segments exactly cancels the effect of the excluded volume and the random coil described in the next chapter exactly obeys Gaussian statistics. Also, the Mark-Houwink exponent equals under theta conditions. 

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