The Process of Crosslink Structure Formation

In tree radical polymerization, unlike for the random crosslink polymers discussed in the previous section, primary polymer chains are formed during polymerization. The crosslink points are also formed as the polymers propagate. Furthermore, flee radical polymerization is a typical example of classic kinetically controlled systems. It is impossible to disconnect the formed bonds even by accident. Therefore, it can be easily seen that the resultant structure will not necessarily conform to the maximum probability given the primary polymer chains and crosslink density. 

In a tree radical copolymerization conducted in a homogeneous batch reactor, its crosslink structure formation process will be quite complex as compared with random crosslinking, because both the composition and degree of polymerization of the primary polymer change simultaneously. Here, we will consider kinetically the inhomo- 

These two types of crosslink density, p iO) and pjfi, ij/), can be derived by a simple mass balance equation with respect to the crosslink point on the primary polymer molecule formed at each instance [22, 23, 45, 46]. 

As a natural consequence of the crosslinking reaction process, the density of the primary polymer differs depending on the time of this primary polymer formation. That is, in the case of the copolymerization of vinyl and divinyl monomers, the generally formed inhomogeneous crosslink formation can be regarded as a natural consequence of the mechanism of crosslink formation. This is true except for die special reaction conditions by favorable timing of the incorporation of divinyl monomer in the polymer chain (formation of pendant double bonds) and consumption of pendant double bonds (formation of crosslinks). These special reaction conditions are used by Flory as simplified conditions when the Flory-Stockmayer theory is applied to the copolymerization of vinyl and divinyl monomers. Flory s simplified conditions include die following three assumptions (1) the reactivities of the monomer and die double bonds in the polymer are all equal (2) any double bond reacts independently and (3) there will be no intramolecular reactions (cyclization) within the finite size molecules (sols). 

Under Flory s simplification conditions, it can be proven that (the probability of) the crosslink density of all the primary polymers is equal by using the kinetic model shown here [47]. That is, under Flory s simplified conditions, the kinetic model that considers the change of the crosslink structure and the model based on random crosslinking become identical. Even for the system under kinetic control, the model that is based on random crosslinking will be strictly applicable. Of course in real systems an inhomogeneous crosslink structure will be formed because of (1) the difference in reactivity as expressed in copolymerization reactivity ratio between the double bonds of the monomers (2) the reactivity of the pendant double bonds with the double bonds in the monomers and the 

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