Books
in black and white
Main menu
Share a book About us Home
Books
Biology Business Chemistry Computers Culture Economics Fiction Games Guide History Management Mathematical Medicine Mental Fitnes Physics Psychology Scince Sport Technics
Ads

Polymer Chemistry. The Basic Concepts - Himenz P.C.

Himenz P.C. Polymer Chemistry. The Basic Concepts - Copyright, 1984. - 736 p.
Download (direct link): polymerchemistry1984.djvu
Previous << 1 .. 182 183 184 185 186 187 < 188 > 189 190 191 192 193 194 .. 312 >> Next

(7 .A) becomes
kin
-MjMj' + Mi--------> -MjMjMi-
(7.E)
^211
-+ -----* -
(7.F)
and Eq. (7.1) becomes
Rp.m = k.nlM.lMlM,]
(7.5)
Rp ,211 " k211 [M2 Mj ] [Mj ]
(7.6)
when the effect of the next-to-last, or penultimate, unit is considered.
For now we shall restrict ourselves to the simpler case where only the
terminal unit determines behavior, although systems in which the
penultimate effect is important are well known.
426
Polymers with Microstructure
It is the magnitude of the various values in Eqs. (7.1)-(7.4) that
describes the intrinsic kinetic differences between the various modes of
addition, and the k's plus the concentrations of the different species
determine the rates at which the four kinds of additions occur. It is the
proportion of different steps which determines the composition of the
copolymer produced.
Monomer Mi is converted to polymer by reactions (7.A)and (7.C);
therefore the rate at which this occurs is the sum of Rp n and Rp 21:
Likewise, reactions (7.B) and (7.D) convert M2 to polymer, and the rate
at which this occurs is the sum of Rp 12 and Rp 22 :
The ratio of Eqs. (7.7) and (7.8) gives the relative rates of the two
monomer additions and, hence, the ratio of the two kinds of repeat units
in the copolymer:
We saw in the last chapter that the stationary-state approximation is
applicable to free-radical homopolymerizations, and the same is true of
copolymerizations. Of course, it takes a brief time for the stationary-
state radical concentration to be reached, but this period is
insignificant compared to the total duration of a polymerization
reaction. If the total concentration of radicals is constant, this means
that the rate of crossover between the different types of terminal units
is also equal, or that Rp 21 = Rp 12 :
Combining Eqs. (7.9) and (7.11) yields the important copolymer
composition equation:

(7.7)

(7.8)
d[Mj _ knlMrHMj +k21[M2-] [MJ d[M2] 12[][2] + k22 [M2 ] [M2]
(7.9)
k12[Mr][M2] = ^-
(7.10)
or
[M,] = kai[M.] [MH k12[M2]
(7.11)
d[Mi] = [MJ (k j j / i2) [M t ] + [M2] d[M2] [M2] (k22/k21
)[M2 ] + [MJ
(7.12)
Copolymer Composition
427
Although there are a total of four different rate constants for
propagation, Eq. (7.12) shows that the relationship between the relative
amounts of the two monomers incorporated into the polymer and the
composition of the monomer feedstock involves only two ratios of
different pairs of these constants. Accordingly, we simplify the notation
by defining
r.
(7.13)
i2
and
k2o
r2 = -i!
(7.14)
k2i
With these substitutions, Eq. (7.12) becomes
d[Mj] _ [MJ rJMj+IMa] _ 1 +r1[M1]/[M2] d[M2] [M2] r2[M2] + [Mj]
1+r2[M2]/[M!]
(7.15)
Mayo and collaborators were among the earliest workers to clarify the
relationship between copolymer and monomer solution compositions.
The ratio d [Mi ] /d [M2 ] is the same as the ratio of the numbers of
each kind of repeat unit in the polymer formed from the solution
containing Mj and M2 at concentrations [M^ and [M2], respectively.
Henceforth we shall designate this ratio as nj/n2. Since the composition
of the monomer solution changes as the reaction progresses, Eq. (7.15)
applies to the feedstock as prepared only during the initial stages of
the polymerization. Subsequently, the instantaneous concentrations in the
prevailing mixture apply unless monomer is added continuously to replace
that which has reacted and maintain the original composition of the
feedstock. We shall assume that it is the initial product formed that we
describe when we use Eq. (7.15) so as to remove uncertainty as to the
monomer concentrations.
As an alternative to the ratios n1/n2 and [Mj]/[M2] in Eq. (7.15), it
is convenient to describe the composition of both the polymer and the
feedstock in terms of the mole fraction of each monomer. Defining F; as
the mole fraction of the ith component in the polymer and fj as the mole
fraction of component i in the monomer solution, we observe that
d[Mj]
Fj = 1 - F2 = -------------------
(7.16)
d[Mj]+d[M2]
and
[MJ ! ' [M i ] + [Mj]
(7.17)
428
Polymers with Microstructure
Combining Eqs. (7.15) and (7.16) into (7.17) yields rjfj2 + fjf2
Previous << 1 .. 182 183 184 185 186 187 < 188 > 189 190 191 192 193 194 .. 312 >> Next