Stoichiometric imbalance

We now turn to two of the problems we have sidestepped until now. In this section we consider the polymerization of reactants in which a stoichiometric imbalance exists in the numbers of reactive groups A and B. In the next section we shall consider the effect of monomers with a functionality greater than 2. 

We define the problem by assuming the polymerization involves AA and BB monomers and that the B groups are present in excess. We define and to be the numbers of A and B functional groups, respectively. The number of either of these quantities in the initial reaction mixture is indicated by a superscript 0 the numbers at various stages of reaction have no superscript. The stoichiometric imbalance is defined by the ratio r, where... 

The parameter r continues to measure the ratio of the number of A and B groups the factor 2 enters since the monofunctional reagent has the same effect on the degree of polymerization as a difunctional molecule with two B groups and, hence, is doubly effective compared to the latter. With this modification taken into account, Eq. (5.40) enables us to quantitatively evaluate the effect of stoichiometric imbalance or monofunctional reagents, whether these are intentionally introduced to regulate or whether they arise from impurities or side reactions. 

For any value of p, n is greater for larger values of r stoichiometric imbalance lowers the average chain length of the preparation. 

Suppose the total number of carboxyl groups in the original mixture is 2 mol, of which 1.0% is present as acetic acid to render the resulting polymer inert to subsequent esterification. What value of p would be required to produce the desired polymer in this case, assuming no other stoichiometric imbalance ... 

Eig. 2. Effect of stoichiometric imbalance in polysulfone polymerization on maximum attainable polymer reduced viscosity where (x) is theoretical,... 

The molecular weight of a polymer will be reduced if either die extent of conversion or the average functionality is decreased. At 95% conversion of difunctional monomers, for example, Xn is only 20.25 The molecular weight is also related to a stoichiometric imbalance, r, which is normally defined to be less than 1.0 ... 

In order to properly control the polymer molecular weight, one must precisely adjust the stoichiometric imbalance of the bifunctional monomers or of the monofunctional monomer. If the nonstoichiometry is too large, the polymer molecular weight will be too low. It is therefore important to understand the quantitative effect of the stoichiometric imbalance of reactants on the molecular weight. This is also necessary in order to know the quantitative effect of any reactive impurities that may be present in the reaction mixture either initially or that are formed by undesirable side reactions. Impurities with A or B functional groups may drastically lower the polymer molecular weight unless one can quantitatively take their presence into account. Consider now the various different reactant systems which are employed in step polymerizations ... 

Equation 2-78 shows the variation of Xn with the stoichiometric imbalance r and the extent of reaction p. There are two limiting forms of this relationship. When the two bifunctional monomers are present in stoichiometric amounts (r = 1), Eq. 2-78 reduces to the previous discussed Carothers relationship (Eq. 2-27)... 

Figure 2-8 shows plots of Xn versus the stoichiometric ratio for several values of p in accordance with Eq. 2-78. The stoichiometric imbalance is expressed as both the ratio r and the mole percent excess of the B—B reactant over the A—A reactant. The various plots show how r and p must be controlled so as to obtain a particular degree of polymerization. However, one does not usually have complete freedom of choice of the r and p values in a polymerization. Complete control of the stoichiometric ratio is not always possible, since reasons of economy and difficulties in the purification of reactants may prevent one from obtaining r values very close to 1.000. Similarly, many polymerizations are carried out to less than 100% completion (i.e., to p < 1.000) for reasons of time and economy. The time required to achieve each of the last few percent of reaction is close to that required for the first 97-98% of reaction. Thus a detailed consideration of Fig. 2-2 shows that the time required to go fromp = 0.97 (X = 33.3) to p = 0.98 (X — 50) is approximately the same as that to reach p = 0.97 from the start of reaction. 

The term r is the ratio of A groups to B groups and has a value equal to or less than unity, r is comparable to the previously discussed stoichiometric imbalance. The term p is the fraction of all A functional groups that belong to the reactant with / > 2. 

Carothers pioneering studies were also based on aliphatic polyesters and then culminated in laying the foundations for condensation and step-growth polymerization and in establishing a relationship between molar mass and extent of reaction and the stoichiometric imbalance of functional groups. Fundamental studies relating structure to properties were carried out using these polymers. 

FIGURE 7.1 The effects of conversion and stoichiometric imbalance on the number average degree of polymerization. 

Instead of using an equimolar mixture, one may use a slight stoichiometric imbalance of one monomer. At some point in the polymerization, the deficient reactant is used up and the molecules have two end groups with the same functional groups (i.e., those of the monomer in excess). 

The importance of deviations from the structure of an ideal network due to stoichiometric imbalance or incomplete reaction was recognized in amine-epoxy curing by Bell who developed semi-empirical corrections. Their applicability was, however, limited to rather small deviations from the perfect state. The degree of approximation has never been tested against the complete theory. 

Compounds with structures related to that of fluorite, CaF2 see Fluorides Solid-state Chemistry), readily form solid solutions with other sohds containing cations of a similar size to the fluorite host cation. Invariably the foreign cation substitutes for the host cation, and stoichiometric imbalance is taken up by the anion component of the crystal. The... 

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