Intramolecular cycles

Serious deviations of the polymer network structure from the ideal one can have several causes. One of them is the crosslinking agent involvement in intramolecular cycle formation. The contribution of this reaction grows with the system dilution as well as when the crosslinker units in the chain are close one to the other, i.e. its fraction in the copolymer increases. All this is in good agreement with the observed trend. 

Analysis of data pertaining to the modulus of PEO gels obtained by the polyaddition reaction [90] shows that even in this simplified case the network structure substantially deviates from the ideal one. For all samples studied, the molecular weight between crosslinks (M p) exceeds the molecular weight of the precursor (MJ. With decreasing precursor concentration the M xp/Mn ratio increases. Thus, at Mn = 5650 a decrease in precursor concentration from 50 to 20% increases the ratio from 2.3 to 12 most probably due to intramolecular cycle formation. 

Some Bis reactions may lead to intramolecular cycles that will not affect the elasticity behavior of the gel, and pendant, unreacted, gronps may form where only the crosslinker reacts at one of its double bonds [315]. Tobita and Hamielec [393] found that primary cyclization, i.e., the formation of loop cycles, may consnme as much as 80% of... 

One way to reduce the intramolecular cycle formation, is to add AB2-mono-mer successively throughout the reaction in a so-called concurrent slow-addi-tion . Several authors have shown that slow addition of monomer leads to a reduction in side reactions and increased molecular weight [5], while others have studied the occurrence of cyclization in hyperbranched systems [6]. 

The ideal homopolymerization of a monomer with three functional groups (functionalities) that may react among themselves will be considered. The ideal case means that the three functionalities are equally reactive, there are no substitution effects, and there are no intramolecular cycles in finite species. 

Equation (3.23) has no physical sense for x > xgei, because intramolecular reactions in the gel cannot be neglected so, the relationship between the number of moles in the system and the conversion is no longer valid. For an actual system, the departure of the theoretical prediction of Mn and the experimental value in the pregel stage may be ascribed to the formation of intramolecular cycles. This constitutes the usual way of determining the significance of cyclization for a particular system. 

Intramolecular cycles are absent in the pregel stage (although short cycles may be introduced in the definition of fragments). 

The network structure at any conversion may be obtained by joining the different fragments at random, with a probability given by the concentration of every fragment in the mixture. This is a mean-field approach and is not valid when nonidealities are present. Unequal reactivities, substitution effects, and intramolecular cycles give place to preferred nonrandom combinations. 

The error introduced by the second assumption may be decreased by adding larger fragments to describe the system. Usually, it is verified that the mean-field approach gives a very good approximation, and it is not necessary to increase the number of fragments. In most cases the presence of intramolecular cycles is responsible for departures between experimental results and theoretical predictions. 

Several approaches can be used to obtain statistical parameters of these general systems under ideal conditions (equal reactivities, and absence of substitution effects and intramolecular cycles). In this section we will discuss some of these results. The reader is referred to the papers of Macosko and Miller (1976), Miller and Macosko (1976), and Miller et al. (1979) for the deductions of the equations used in this section. 

Equation (3.79) was obtained by dividing the total mass of the system by the total number of moles (Af and Bg represent the initial number of moles of each one of the monomers). The factor xAfAf in the denominator represents the moles of type A functionalities that have reacted, which is equal to the number of moles that are lost by reaction provided that no intramolecular cycles are formed. As 1 mole of A reacts with 1 mole of B, it must be verified that... 

Results expressed by Eqs (3.100) and (3.102) are strictly valid for ideal systems. Unequal reactivities, substitution effects and the formation of intramolecular cycles will affect them. The first two nonidealities may be conveniently taken into account using the fragment approach described in the previous sections. 

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. 

In any case, the macromolecules formed at the beginning of polymerization exhibit a large number of intramolecular cycles and are very compact. Cyclization reactions are favored by dilution with a nonreactive solvent. 

Stepwise Polymerizations For stepwise polymerizations of stoichiometric formulations of comonomers with / and g active sites per molecule exhibiting an ideal behavior (equal reactivity of functional groups, absence of both substimtion effects and intramolecular cycles), the gel conversion (Xg i) is given by ... 

Ozol-Kalnin et al. [52] showed theoretically that from the viewpoint of conformational chain statistics, the formation of a heterogeneous structure with a large number of intramolecular cycles dominates the formation of a homogeneously crosslinked polymeric network. 

Consider the polycondensation of functional monomers of the type R AB/ i. The reaction is assumed to take place between the A group and B group only [1], Nonlinear polymers with a tree structure are formed by reaction. They may have intramolecular cycles, but to find the exact solution we consider only branched tree-type polymers which have no cycles (Figure 3.6). These are sometimes called Cayley trees, named after the mathematician who studied tree-type graphs. The approximation under this assumption of no intramolecular cycles is called the tree approximation. 

We next consider the condensation reaction of polyfunctional molecules of the type R A/. The molecular weight distribution for the special case / = 3 was first studied by Flory [10], The result was later extended to the general case of / by Stockmayer [11] under the assumption of no intramolecular cycle formation. Their theories are called the classical theory of gelation reaction. 

Milton et al. have demonstrated the preparation of substrates for the Pummerer reaction by the addition of thiols to glyoxalates. Procter et al have extended this methodology to include fluorous phase tag thiols which then led to Pummerer intramolecular cyclative capture under the appropriate reaction conditions. The methodology efficiently resulted in tagged heterocyclic frameworks which could be further modified in a number of... 

---