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Encyclopedia of Physical Science and Technology EN008C-602 July 25, 2001 20:31

Macromolecules, Structure 877

2
initiated polymer (b) is almost exclusively a pair of dou- [mm] = P ,
m
blets; quantitative assessment shows that this polymer
is 95% isotactic. The methylene spectrum of the free [mr] = 2P m (1 − P m ),
radical polymer (a) is more complex, but the principal 2
[rr] = (1 − P m ) .
resonance—at 1.9 ppm—is a singlet, showing that this
polymer is predominantly syndiotactic but more irregular
than (b). This is generally the case for free radically initi- The heterotactic sequence must be given double weight-
ated vinyl polymers. (The other resonances are discussed ing because both directions, mr and rm—observationally
later in this section.) indistinguishable—must be counted. A plot of these re-
We see that proton NMR can provide absolute stereo- lationships is shown in Fig. 20. Note that the propor-
chemical information concerning polymer chains without tion of mr (heterotactic) units rises to a maximum when
recourse to X-ray or other methods. Somewhat more de- P m is 0.5, corresponding to a strictly random or atactic
tailed,butnotabsolute,informationcanbegainedfromthe configuration for which [mm]:[mr]:[rr] will be 1:2:1.
methyl proton resonances near 1.2 ppm. [The ester methyl For any polymer, if Bernoullian, the [mm], [mr], and [rr]
resonance at ∼3.6 ppm (not shown) is less sensitive to sequence intensities will lie on a single vertical line in
stereochemistry.] In both spectra we note three peaks— Fig. 20, corresponding to a single value of P m . Spec-
or, more correctly, groups of peaks—appearing in similar trum (a) in Fig. 19 corresponds to these simple statis-
positions but with greatly different intensities. These cor- tics, P m being 0.25 ± 0.01; the polymer corresponding to
respond to the α-methyl groups in the center monomer spectrum (b) does not. The propagation statistics in this
unit of the three possible triad sequences:isotactic, syn- case can be interpreted to indicate that the probability of
diotactic, and heterotactic. These may be more simply and isotactic placement is dependent on the stereochemical
appropriately designated by the m and r terminology, as configuration of the growing chain and cannot properly
indicated. Measurement of the relative intensities of the be expressed by a single parameter such as P m . Free-
mm, mr, and rr α-methyl peaks, which appear from left radical and cationic propagations always give predomi-
to right in both spectra in this order, gives a valid statistical nantly syndiotactic chains. Anionic initiators may also do
representation of the structure of each polymer.

O OCH 3 O OCH 3 O OCH 3 O OCH 3 O OCH 3
C H C H C C H CH H C

H H H C H
CH 3 CH 3 CH 3 CH 3 CH 3
ISOTACTIC, mm O OCH 3
SYNDIOTACTIC, rr
O OCH 3 O OCH 3
C H C H CH 3
H H
CH 3 CH 3 C
O OCH 3
HETEROTACTIC, mr [or rm]

From the triad data we may gain considerable insight
into the mechanism of propagation. This is one of the
principal uses of such information. Let us designate by P m
the probability that the polymer chain will add a monomer
unit to give the same configuration as that of the last unit
at its growing end (i.e., that an m dyad will be generated).
We assume that P m is independent of the stereochemical
FIGURE 20 The probabilities of isotactic [mm], heterotactic [mr],
configuration of the growing chain. The generation of the and syndiotactic [rr] triads as a function of P m , the probability
chain is a Bernoulli trial process; it is like reaching into of m placement. The points on the left-hand side are for methyl
a large jar of balls marked m and r and withdrawing a methacrylate polymers prepared with free-radical initiators and
ball at random. The proportion of m balls in the jar is P m . those on the right-hand side are for polymers prepared with an-
ionic initiators. For polymer (a) the points for [rr] have been arbi-
Since two monomer additions are required to form a triad
trarily placed on the [rr] curve and the others fall where they may
sequence, it is readily evident that the probabilities of their and for polymer (b) the [mm] points have been placed on the [mm]
formation are curve.