Flory-Stockmayer model

The existence of Wk related to the distribution of aggregate sizes and fulfilling the identity at Eq. (80) implies that the aggregation process leads to an equilibrium distribution. For the Flory-Stockmayer model (model 1 in Table 4) the number of assembling an acyclic k-mer from distinguishable units is [40]... 

Note that for the random case, equivalent to the Flory-Stockmayer model (model 1 in Table 4), i=2/3 and 2=1/3. 

Figure 7. Illustrations of gelation according to the classical Flory-Stockmayer model and the percolation model. In the classical model, cyclic configurations are avoided, so the unphysical situation M R4 results. As illustrated by the 29Si NMR spectrum of an acid-catalyzed TEOS sol (36), cyclic species are quite prominent sol components. (Reproduced with permission from reference 36. Copyright 1988.)...

The results above are only valid for tetrafunctional crosslinking of monodisperse polymer. However, in many thermoreversible systems the crosslinks have functionalities that are much larger than four. Moreover, the polymers used are not monodisperse in general. In order to be able to calculate network parameters the present author [39—44] extended the Flory-Stockmayer model for polydisperse polymer which is crosslinked with f-functional crosslinks. It was possible to calculate network parameters for polymers of various molecular weight distributions (monodisperse polymer with D s M, /r3 = 1, a Schulz-Flory distribution with D = 1.5, a Flory distribution with D = 2, a cumulative... 

The Flory-Stockmayer model for polyfimctional polycondensation is represented by a tree, which corresponds to ihe generating function with a dummy variable 0 as shown in Fig. 3. 

By adjusting the parametm-s of the function p = p(T) or p = p(T, 0), which corresponds experimentally to a change in the solvent, an interesting situation described by the central part of Fig. 7 results, where the sol-gel boundary meets the phase separation curve exactly at the critical consolute point. In this case, the Bethe lattice theory which corresponds to the Flory-Stockmayer model, gives classical exponents for random-bond percolation along the whole sol-gel boundary. This is true even for the special case where the critical consolute point and the end point of the gelation line coincide then, one has to use the concentration 0 and not the temperature T as a variable to define critical exponents. 

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