Substitution effectiveness function

The last topic to be treated is unequal reactivity by substitution effects. As a first example, the effect of an infinitely negative substitution effect in C due to a reaction with an h group (so I CD Kqj = 0) is compared with the case of equal (random) reactivity of the two functional groups in C for formulation F40. This is suggested as an example of polyesterification with an anhydride and a carboxylic acid, respectively. Figure 15 gives the dramatic effect on... 

Monomers employed in a polycondensation process in respect to its kinetics can be subdivided into two types. To the first of them belong monomers in which the reactivity of any functional group does not depend on whether or not the remaining groups of the monomer have reacted. Most aliphatic monomers meet this condition with the accuracy needed for practical purposes. On the other hand, aromatic monomers more often have dependent functional groups and, thus, pertain to the second type. Obviously, when selecting a kinetic model for the description of polycondensation of such monomers, the necessity arises to take account of the substitution effects whereas the polycondensation of the majority of monomers of the first type can be fairly described by the ideal kinetic model. The latter, due to its simplicity and experimental verification for many systems, is currently the most commonly accepted in macromolecular chemistry of polycondensation processes. 

Substitution effects have been observed for both the homogeneously and heterogeneously base-catalyzed Claisen-Schmidt condensation of ketones and aldehydes with functional groups substituted in the para-position [5 -12], In this... 

Changes in reactivities of functional groups of hard components (substitution effect). 

Branching and crosslinking processes can be treated as a combinatorial problem which is not too complicated when the functionalities are equally reactive and unreacted functionalities are considered as the only kind of defects. If loop formation (intra-molecular cyclization) is involved, the complexity increases considerably. The same holds if the monomers contain groups of unequal reactivity or if the reactivity is influenced by substitution effects. 

Finally, the applicability of the cascade theory to rather complicated systems with unequal functional groups, substitution effect, vulcanization of chains and long rang correlation as a result of directed chain reactions is shown. The limitation of the theory to essentially tree-like molecules and their unperturbed dimensions is outlined and the consequence of this error for the prediction of reed systems is discussed. 

Fig. 59. a First shell substitution effect the probability for a reaction of functionality x depends on whether y or z or both had already reacted, b Second shell substitution effect the probability of reaction for a unit Xi and x2 depends on how many of the functional groups in y and z had reacted... 

We have now to take care that the various generations are properly connected. This is achieved as usual by introducing labels Si, S2, and s3 to the auxiliary variables. Furthermore, there may be reasons to assume that there will be a certain hindrance in the reaction if adjacent functionalities are already occupied. (First shell substitution effect.) Taking all these requirements together, Gordon and Parker were led to set up the generating functions as follows ... 

The above equation suggests that the benzoic acid series are much more insensitive to substitution effects due to the negatively charged benzoic functional group [-COO ]. In other words, it is much more difficult to add an additional electron to benzoic series than to benzene series furthermore, the higher the rate constant of the nonsubstituted parent compound, the lower the T values of the series will be. This is because the more reactive series have the rate constants approaching the diffusion-controlled limit of 1010 M 1 s 1, where a further increase in rate cannot occur. 

For simplicity, we start with a single tri-functional monomer RA3, the functional groups of which react with each other with the first shell substitution effect. It is now convenient to write down six types of reactions [44], one for each pair of reacting units of substitution degree 0,1, and 2. They are presented in Table 6 together with the appropriate rate constants. Similarly as in previous sec-... 

Table 6. The types of reactions in model polymerization of RA3 monomer with functional groups reacting with the first shell substitution effect. The subscripts at the symbols of reagents correspond to the codes of molecules (i,j-mers, see the text) and those at the rate constants indicate the degrees of substitution of reacting units. The left and right column corre-...

It is not difficult to extend the reasoning to the general case of RAf polymerization with the first shell substitution effect approximation. By defining the function... 

It is not very difficult to extend formally the treatment presented in Sect. 8, namely the Smoluchowski-like equation (Eq. 88), to model, besides the substitution effect, the ability of functional groups to react intramolecularly. For the simplest case of RA3 homopolymerization, a crude method [63] is to code the molecules with four indices two of which count the units with two or three reacted functional groups that are engaged in cycles. The Smoluchowski-like equation reads then... 

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. 

The polymerization temperature, often called the cure temperature, affects both transitions in different ways. In Chapter 3 it was shown that the gel conversion does not depend on temperature for ideal stepwise polymerizations but may show a small dependence on temperature for the case where unequal reactivity of functional groups or substitution effects vary... 

Figure 5.18 shows the overall conversion of NCO groups as a function of time for uncatalyzed samples cured at three different temperatures. Points are experimental values, while full curves are predicted results using the kinetic parameters derived in the adiabatic analysis. The predictive capability of the rate equation is very good, in spite of the strong hypothesis regarding the absence of substitution effects. 

Since black C has a highly aromatic structure with a low level of substitution with functional groups, it is highly recalcitrant and therefore contributes to the stable fraction of soil C. At the global scale, formation of black C rapidly transfers fast-cyclable C from the biosphere to much slower-cyclable forms that may persist in the soil for millennia. It therefore represents an effective pathway for C sequestration. 

---