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Polymers, Synthesis 769

either of the values is greater than 1, that means that the
growing chain end will homopropagate rather than cross-
initiate the other monomer. On the other hand, if the reac-
tivity ratio is very small, for example, if it approaches 0,
this implies that the growing chain end will cross-initiate
the other monomer rather than add to its own chain end.
In the best situation the reactivity ratios are approximately
equal and their product is nearly 1. Such a system is termed
a perfectly random copolymer.
SCHEME 17 “Random free-radical chain polymerization.
The copolymerization equation can be transformed into
mole fractions, which are frequently more useful. If one
copolymers in this article, but they are discussed in some does this, it is possible to derive an expression that gener-
detail in the references. Very briefly, these copolymers ates r values by a graphical procedure. Thus, to determine
contain very long sequences joined either from the end or whether two monomers will copolymerize, it is necessary
from the sides of the chain. We shall limit our discussion to perform a series of experiments in which one varies the
here mostly to random copolymers and only very briefly monomer feed ratios and, at low conversions, assesses the
touch on alternating copolymers. The simplest reaction concentration of the two species in the formed copolymer;
sequence for random free-radical chain copolymerization there are basically three possibilities (Table XIII). If one
is given in Scheme 17. Here, four possible reactions may has similar reactivity ratios or if one limits the polymer-
lead to either a copolymer unit or a homopolymer unit ization to a low conversion, it is possible to make a rather
being formed. uniform random copolymer.
In each case cross-initiation of the other monomer by By this we mean that the distribution of the monomer
a different macroradical chain end will produce elements units may be considered to be relatively random. Nonuni-
of a copolymer. Copolymers of this type are usually of form copolymers of this type are usually undesirable
interest because they can display a number of desirable since one may exceed the lifetime of the growing radi-
averaged properties. One usually attempts to relate the cal and thus generate homopolymers. This occurs if one
rate of depletion of the two monomers with their rate of has widely different reactivity ratios and if the reaction is
entry into the copolymer chain. It is possible to derive a carried to high conversion. Clearly, as the faster reacting
copolymer composition that yields the molar ratio of the monomer becomes consumed, it becomes apparent that
two units that are formed in the copolymer to the reaction the composition of the chain will be heterogeneous. In-
copolymerization kinetics. By assuming a steady state and deed, in later stages of such a reaction, homopolymer is
by making further manipulations it is possible to derive a derived from the slower reacting monomer in the system.
so-called copolymer equation that relates the mole ratio This is to be avoided because the homopolymer will tend
of the two units that are found in the copolymer to the to be incompatible with the copolymer and the resulting
respective monomer molar charge ratios through the use material characteristics will usually be rather poor. If the
of reactivity ratios or coefficients. reactivity ratios do not differ by too great a margin, it may
The reactivity ratios are basically the ratio of the homo- be possible slowly to add the faster reacting monomer to
propagation rate constants to the copolymerization rate the system and hence to maintain a more or less constant
constants for each of the monomer species under investi- comonomer composition. By this method, it is possible to
gation. The values of the reactivity ratios (r 1 and r 2 ) have produce a relatively uniform copolymer, even though the
considerable significance. As indicated in Table XII. r reactivity ratios may be somewhat different.
values of between 0 and 1 imply that two monomers will
probably be copolymerized in a fairly random fashion. If TABLE XIII Three Possibilities of Formed Copolymers

1. Uniform copolymer
TABLE XII Reactivity Ratios Same reactivity ratios, or
Low conversion, or
r values of 0 ≤ 1 Imply monomers will copolymerize
Constant comonomer composition
r 1 > 1 Prefers to homopropagate 2. Nonuniform copolymer
∼
r 1 = 0 Prefers to alternate Different reactivity ratios carried to high conversion
∼
∼
r 1 = r 2 = 1 Perfectly random 3. Alternating copolymer
=
(r 1 )(r 2 ) ∼ 1 Termed “ideal” system, by analogy Reactive radical accepting comonomer that will not homopolymerize
r 1 = 1/r 2 With vapor–liquid equilibria Charge transfer complex