Vinyl and Divinyl Monomers of Equal Reactivity

Consider the copolymerization of a vinyl monomer X with a divinyl monomer YY where all of the vinyl groups (i.e., the X group and both Y groups) have the same reactivity. [Methyl methacrylate (MMA)-ethyleneglycol dimethacrylate (EGDMA), vinyl acetate-divinyl adipate (DVA), and to an extent styrene-p- or m-divinylbenzene (DVB) are examples of this type of polymerization system (Odian, 1991). In MMA-EGDMA system. 

Let the initial molar concentrations of vinyl monomer and monomeric Y groups be [X]o and [Y]o, respectively, and that of divinyl YY be [YYJq. Thus, [Y]o = 2[YY]o. Since the X and Y double bonds are equally reactive, i.e., r = V2 = I, one obtains from the copolymer equation [Eq. (7.17)], F = f. Thus the molar ratio of Y and X groups in the copolymer is simply equal to [Y]/[X]. 

At the extent of reaction p (defined as the fraction of X and Y groups reacted). 

The number of crosslinks can be taken to be the number of YY molecules in which both Y groups are reacted and the number of polymer chains is derived in terms of the degree of polymerization DP as  

It can be generally shown (Rudin, 1982) by probability considerations that a sufficient condition for gelation occurs when a polymer sample contains one crosslink-ed unit per weight average molecule or one crosslink per two weight average polymer chains. Thus, at the critical extent of reaction pc for the onset of gelation, the number of crosslinks per chain is and the gel point is obtained as 

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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). 

In the FRC of vinyl and multivinyl monomers, a drift in the instantaneous copolymer composition throughout the reaction will be undergone due to the different reactivities of the vinyl groups. This compositional drift is caused by the fact that the more reactive monomer will be consumed faster than the less reactive ones. In the simplest instance, assuming equal reactivity of the vinyl groups in mono-and divinyl monomers present in the reaction system, the reactivity of the crosslinker would be twice that of the monovinyl monomer, and therefore, the polymer chain... 

There exist several attempts to describe the chain crosslinking (co)polymerization using an analytical mean field theory. Thus, Gordon and Malcolm treated chain crosslinking copolymeri2ation of a monovinyl and a divinyl monomer with equal and independent reactivity of vinyl groups and for the ring-free case only. 

An example of this case is a vinyl (A2 ) - divinyl (A4) polymerization. The assumption of an ideal polymerization means that we consider equal initial reactivities, absence of substitution effects, no intramolecular cycles in finite species, and no phase separation in polymer- and monomer-rich phases. These restrictions are so strong that it is almost impossible to give an actual example of a system exhibiting an ideal behavior. An A2 + A4 copolymerization with a very low concentration of A4 may exhibit a behavior that is close to the ideal one. But, in any case, the example developed in this section will show some of the characteristic features of network formation by a chainwise polymerization. 

Disulfide Formation in Polystyrene Networks. Polymer-bound thiols were prepared by copolymerizations of bis -vinylbenzyl)disulfide with other divinyl monomers followed by diborane reduction (Scheme 5) (fiS). The initially formed thiols were juxtaposed for reoxidation to disulfides. Polymer-bound thiols were prepared also by copolymerization of p-vinylbentyl thiolacetate with divinyl monomers followed by hydrolysis (Scheme 6). llie latter thiols were distributed randomly throughout the polymer network. The copolymer reactivity ratios for p-vinylbenzyl thiolacetate and styrene are unknown, but should be similar to those of styrene (Mi) and p-vinyl-bentyl chloride (M2) ri = 0.6, r2 = 1.1 (fifi). Copolymeiizations with equal volumes of monomers and 1/1 acetonitrile/toluene product macroporous 40-48% DVB-cross-linked networks (651. 

At this point, the copolymerization reactivity ratio of an ideal monomer pair that fulfills Flory s simplified condition, which states that the reactivity of every double bond is equal, will be briefly mentioned. In many cases, the copolymer reactivity ratio is determined by the composition of the polymer based on the monomer units or the remaining monomers. In this case, the obtained copolymer reactivity ratio is given by the monomer units. The situation is simple for copolymerization between vinyl monomers. However, it requires caution when divinyl monomers are included. Now, we will use subscript 1 for the vinyl monomer and subscript 2 for the divinyl monomer. Divinyl monomers possess two vinyl groups in the molecule... 

Assuming that classical chemical kinetics are valid and that the crosslinking reaction rate is proportional to the concentrations of polymer radicals and pendant double bonds, it was shown theoretically that the crosslinked polymer formation in emulsion polymerization differs significantly from that in corresponding bulk systems [270,316]. To simplify the discussion, it is assumed here that the comonomer composition in the polymer particles is the same as the overall composition in the reactor, and that the weight fraction of polymer in the polymer particle is constant as long as the monomer droplets exist. These conditions may be considered a reasonable approximation to many systems, as shown both theoretically [316] and experimentally [271, 317]. First, consider Flory s simplifying assumptions for vinyl/divinyl copolymerization [318] that (1) the reactivities of all types of double bonds are equal, (2) all double bonds... 

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