Equations weight chain length distribution

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... 

Flory Statistics of the Molecular Weight Distribution. The solution to the complete set (j - I to j = 100,000) of coupled-nonlinear ordinary differential equations needed to calculate the distribution is an enormous undertaking even with the fastest computers. However, we can use probability theory to estimate the distribution. This theory was developed by Nobel laureate Paul Floty. We have shown that for step ipolymeiization and for free radical polymerization in which termination is by disproportionation the mole fraction of polymer -with chain length j is... 

The proper knowledge of the functional form of followed by every polymerization scheme would be the key factor for describing the evolution of gel content according to Equation 9.B.I. For a conventional free radical polymerization, the weight length distribution for primary chains that are formed at x = 6> is given by [110] ... 

The weight distribution of chain length for polymer populations containing i LCBs per chain, w(r, i) is given by the following equation [45] ... 

As can be seen from the numerical example (Table 18-5) for a kinetic chain length V = 10, the degree of polymerization distribution is exceptionally narrow. Since the weight-average degree of polymerization is obtained from X = Y, iXi, this gives, with equation (18-100) and X = v + 1 with the notation Xi = X,... 

In this equation, kp is the long-chain propagation rate coefficient, Ci = (kp-kp)l kp and iia is the chain length at which k -kp halves in value (i.e., a sort of half-life ). Available data thus far suggest Ci 10-50 and ii/2 0.5-1.5 t for MMA polymerization we found values of Ci = 15.8 and i/2 = 1.12. These latter values were obtained by fitting pulsed laser polymerization data obtained by Van Herk and co-workers and were found to describe well our (independently obtained) experimental steady state data (both rates and molecular weight distributions)... 

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