Page 261 - Carrahers_Polymer_Chemistry,_Eighth_Edition

224 Carraher’s Polymer Chemistry

In the early 1930s, Nobel Laureate Staundinger analyzed the product obtained from the copo-
lymerization of equimolar quantities of vinyl chloride (VC) and vinyl acetate (VAc). He found that
the first product produced was high in VC, but as the composition of the reactant mixture changed

because of a preferential depletion of VC, the product was becoming higher in VAc. This phenom-
enon is called the composition drift.
Wall studied the composition drift and derived what is now called the Wall equation, where n
was equal to rx when the reactivity ratio r was equal to the ratio of the propagation rate constants.
Thus, r was the slope of the line obtained when the ratio of monomers in the copolymer (M /M )
1 2
was plotted against the ratio of monomers in the feed (m /m ). The Wall equation is not general.
1 2
M 1  m 
1
n = = r   = rx
M  m 
2 2 (7.5)
The copolymer equation that is now accepted was developed in the late 1930s by a group of
investigators, including Wall, Dostal, Lewis, Alfrey, Simha, and Mayo. These workers considered
the four possible extension reactions when monomers M and M were present in the feed. As shown
1 2
below, two of these reactions are homopolymerizations or self-propagating steps (Equations 7.6 and
7.8), and the other two are heteropolymerizations or cross-propagating steps (Equations 7.7 and 7.9).
The ratio of the propagating rate constants are expressed as monomer reactivity ratios (or simply
• •

reactivity ratios), where r = k /k and r = k /k . M and M are used as symbols for the macroradi-
1
2
11
21
1
22
12
2
. .
cals with M and M terminal groups, respectively.
1 2
Reaction Rate constant Rate expression
• •

M + M → M M • k R = k [M ][M ] (7.6)
1 1 1 1 11 11 11 1 1
• •

M + M → M M • k R = k [M ][M ] (7.7)
1 2 1 2 12 12 12 1 2
• •
M + M → M M • k R = k [M ][M ] (7.8)
2 2 2 2 22 22 22 2 2
• •
M + M → M M • k R = k [M ][M ] (7.9)
2 1 2 1 21 21 21 2 1

Experimentally, it is found that the specific rate constants for the various reaction steps described
above are essentially independent of chain length, with the rate of monomer addition primarily
dependent only on the adding monomer unit and the growing end. Thus, the four reactions between
two comonomers can be described using only these four equations.
As is the case with the other chain processes, determining the concentration of the active species
is difficult so that expressions that do not contain the concentration of the active species are derived.

The change in monomer concentration, that is the rate of addition of monomer to growing copoly-
mer chains, is described as follows:
•
•

1
Disappearance of M : − d[M ] = k [M ][M ] + k [M ][M ] (7.10)
1
11
1
1
2
1
21
dt
d[M ] • •
2

Disappearance of M : − = k [M ][M ] + k [M ][M ] (7.11)
22
2
12
2
1
2
2
dt
Since it is experimentally observed that the number of growing chains remains approximately
constant throughout the duration of most copolymerizations (i.e., a steady state in the number of
• • • •

growing chains), the concentrations of M and M is constant, and the rate of conversion of M to M
1
1
2
2
• • • • •

is equal to the conversion of M to M ; that is, k [M ][M ] = k [M ][M ]. Solving for M gives
1
12
1
2
1
2
2
1
21
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