Determining Number of Moles To determine the number of moles of polymer the analysis method
must respond equally to each molecule without regard to its chain length. As the structures given
above show, the monomer molecules on the ends of the chain must in some way be different from
the chain itself. For a linear polymer (i.e., one in which there are no bonds, called crosslinks, between
the chains) every molecule has two end groups, which may be identical, as in PEG, or different, as in
Dacron. (For polymers such as PVC and polystyrene the identities of R and R’ depend on the choice
of reagent used to initiate the polymerization reaction.) Thus, if the end groups can be analyzed, the
number of polymer molecules may be calculated using simple stoichiometric relationships. This
method for determining Mn is called end group analysis.
Figure 2. Reaction of PMDA with PEG to produce ester
Some Specifics The ends
of PEG are alcohol groups,
which may be analyzed by a
reaction known
as
esterification. In an
esterification the -OH reacts
with an organic acid, or, more
commonly, with a more
reactive derivative of the acid.
In this experiment the
anhydride of 1,2,4,5
benzenetetracarboxylic acid,
known commonly as
pyromellitic dianhydride, or PMDA for short, will be used. The reaction with PEG is shown in Fig. 2.
The reaction must be conducted in a nonaqueous solvent, and, because of its low volatility and
desirable solvating properties, N,N-dimethyl formamide, DMF, is a good
choice. A catalyst is also required, and in many esterification procedures
pyridine, a rather foul-smelling organic base, is used. However, for the
reaction of alcohols with PMDA it has been found that imidazole, IMDA, a
very soluble solid with no odor, has at least equal catalyzing power. The
formulas of DMF and IMDA are shown below.
The analysis involves an indirect titration procedure. An excess of PMDA is
mixed with the weighed PEG sample, and the catalyst is added. After the
reaction is complete (at least one-half hour reaction time), water is added to
convert the unreacted anhydride groups to the acid form, and the acid is titrated with standard NaOH.
The equations in Fig. 3 show that each ester linkage to a PEG end group replaces one of the four
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