RUSSELL J. HANNA Development Department, Carbide and Carbon Chemicals Co., South Charleston, W. Va.
Synthesis of Chemically Uniform Copolymers Rapid Calculation o f Monomer Addition Equations offer a rapid method of calculation for computing the amount of monomer to be added to produce a chemically uniform copolymer in a free radical batch copolymerization
A
RAPID METHOD is outlined here for calculation of monomer addition during a free radical copolymerization, so that a chemically uniform copolymer results as copolymerization proceeds. Calculation of monomer addition is encountered in practical work; and, although the computation of monomer addition is not particularly involved, it has almost always been laborious. The proposed method applies to the usual batch process in which the copolymerization of a given ratio of monomer I to monomer I1 forms a copolymer that has a different ratio of these components. As an example, under certain conditions a 35 to 65 weight ratio of vinyl chloride to vinyl acetate gives approximately a 58 to 42 proportion of these components in the copolymer. This difference in rates of monomer reaction causes a shift in the original monomer-monomer ratio unless continuously corrected. Such a shift would cause formation of a chemically different copolymer as copolymerization progressed. The proposed method, then, applies specifically to the batch production of a chemically uniform copolymer by maintenance of the original monomer-monomer ratio. The monomer-monomer ratio is held constant by the addition of the more reactive monomer. The purpose of the calculation is to construct a curve showing the amount of monomer I to be added as conversion proceeds.
catalyzed copolymerization may usually be expressed by (7) :
where W , is the initial charge weight of monomer I ( w ’ ~ ) , the more reactive
where m i l and w’2 are parts by weight of two different monomers, and M1 and Mz are their molecular weights. Constants rl and r2 are ratios of reaction rates of the two monomers. If the ratio of w‘1 to W ’ Z is held to a constant R, Equation 1 may be expressed as :
of the two monomers; W Zis the initial charge weight of monomer I1 ( w ’ ~ ) ; and W , is the weight of monomer I added as reaction proceeds. T o keep the copolymer composition constant, the ratio of w’1 to w J 2is kept constant and is the same as the original monomer ratio:
dw‘1 ~- - k -w’l dw’z W’P
Monomer I in copolymer monomer I =k Monomer I1 in copolymer monomer I1
(21
where k =
rlRM2
RMz
+ Mi
+
(3)
rpiM1
which is a constant for a particular isothermal conversion at a constant monomer-monomer ratio.
+
For the conditions of copolymerization which resulted in Equation 2 (constant monomer to monomer ratio; constant monomer ratio in the copolymer; isothermal reaction), Equation 2 becomes:
Amount of Monomer Addition. The relation between monomers and copolymer in an isothermal free-radicalINDUSTRIAL AND ENGINEERING CHEMISTRY
w1
+ W, W2
- w’1 - w’2 S
If “solids” are defined as copolymer plus anv other nonvolatile nonreactants added, the fraction of solids in the reaction mixture is expressed by:
copolymer nonvolatile nonreactants nonreactants f residual monomers copolymer formed
Fraction of solids =
Derivation
208
(5)
or more simply :
=
m ( W n
k
