Copolymerization with Depropagation - Advances in Chemistry (ACS

28 Copolymerization with Depropagation

Downloaded by NORTH CAROLINA STATE UNIV on May 3, 2015 | http://pubs.acs.org Publication Date: June 1, 1969 | doi: 10.1021/ba-1969-0091.ch028

KENNETH F. O'DRISCOLL Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, Ν. Y. 14214

For every vinyl monomer there exists a ceiling temperature above which it is thermodynamically impossible to convert monomer into high polymer because of the depropagation reaction. If two vinyl monomers are copolymerized under conditions such that one or both may depropagate, the resultant polymer will have an unusual composition and sequence distribution. Existing theoretical and experimen tal works are reviewed which treat of copolymer composi tion, rate of copolymerization, and degree of copolymeri zation.

*Tphe theory and experimental practice of addition copolymerization have been well understood for many years ( 1 ). In the simplest form, one considers that four, and only four, propagation reactions are necessary to describe copolymer composition: —

M * + M

x

-> — M - Mi*

(1)

M * + M

2

k -> — M - M *

(2)

x

x

12

x

1

2

^21

M * + M -5 — M - Mi* 2

2

1

(3)

k2 2

M * + M 2

2

-» — M - M * 2

2

(4)

Various theoretical approaches all lead to the well known composition equation: m m

x

[MJ

r IMli+1 [M ] 1

2 ~ [M ] 2

2

[MJ

439 In Addition and Condensation Polymerization Processes; Platzer, N.; Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

W

440

ADDITION

A N DCONDENSATION

P O L Y M E R I Z A T I O N

PROCESSES

where the reactivity ratios are defined as r

l

=

*ll/*12;

2

r

=

^22/^21

(

6

)

and [Mi] and [M ] are the monomer feed concentrations which produce an instantaneous copolymer containing mole fractions mi and m of the two monomers. 2


2

Variants of the above have been used to explain unusual data where it was suspected that monomer units penultimate to the chain end (or even further back) were affecting the reaction rate constants (6). Such treatments suffer from a degree of arbitrariness in that the experimental data may not provide an adequate test of the kinetic model (3). In some cases, penultimate unit effect models have been used to interpret unusual data where one might expect depropagation to be important. Although it has long been recognized (4) that homopolymerization chain reactions can and do depropagate under reaction conditions of practical importance, it was not until recently that the problem of copolymerization with depropagation was attacked. The successful ex perimental and theoretical treatment of depropagation in anionic homopolymerization (the so-called "living polymers") provided both the incentive to begin the problem of copolymerization with depropagation and a large amount of the necessary thermodynamic data. Since the details of equilibrium homopolymerization have been reviewed elsewhere (4, 9), it will suffice to present the following, oversimplified, thermody namic considerations.

Reversibility of Homopolymerization The general reaction to be considered is that of a monomer unit in some particular state s (where s is either bulk monomer, solution in a particular solvent, or gas phase ) being incorporated in a polymer of chain length η where the polymer chain is in some particular state s' (where s' represents amorphous or crystalline polymer, or polymer in solution). For theoretical purposes, s' might represent the gaseous state. If such a reaction has achieved equilibrium (Equation 7), the free-energy change for the polymerization AG will be zero ( Equation 8 ). P

nM(s) *± - (Μ)„(*') η AG = AH p

p

(7) (8)

TAS

P

Consequently, T = AH /AS = AH /(AS ° c

p

p

P

P

+ R In a ) M

In Addition and Condensation Polymerization Processes; Platzer, N.; Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

(9)

28.

ODRiscoLL

Copolymerization with Depropagation

441

where AS ° is the standard entropy change accompanying polymerization when the monomer activity, a , is unity. T is a critical temperature for polymerization: if both AS and ΔΗ are negative, T is a "ceiling" tem perature above which it is thermodynamically impossible to convert monomer into polymer of chain length n; if both are positive, it is a "floor" temperature below which it is thermodynamically impossible to convert monomer into polymer of chain length n. P

M

c

P

Ρ

c

Equation 9 suggests several points about T . Obviously, it will be affected by conditions which affect the monomer activity or the heat of polymerization. Since these terms will be affected by the reaction medium, the critical temperature obviously depends on that. It is also important to stress that for every monomer concentration (or activity) there is a corresponding critical temperature; this can be restated by noting that for every temperature there will be a corresponding equilib rium monomer concentration. In fact, the equilibrium monomer con centrations of most polymerizations are so low ( 10" to 10" M ) that they defy precise measurement. Nevertheless, in particular cases they may be sufficiently high to cause concern over potential effects on the physical or physiological proprties of the polymer. Most vinyl polymerizations exhibit ceiling temperatures of 100°-300°C. since the heats of polymeri zation are on the order of —20 kcal./mole and the entropies of poly merization are approximately —30 cal./degree/mole. Polymerizations of ring compounds to linear polymers may show ceiling temperatures as in the case of tetrahydrofuran ( 6 0 ° - 7 0 ° C . ) or floor temperatures as in the case of sulfur ( 1 6 0 ° C . ) and selenium ( 8 0 ° C ) .


c

3

9

Reversibility of Copolymerization If one applies these considerations on homopolymerization to co polymerization, it is easy to appreciate that any or all of Reactions 1 through 4 may, in a particular copolymerization, be of such a reversible character that depropagation must be considered. Lowry was the first to construct a successful theory concerning this (11). He postulated several cases, the simplest of which considered only Reaction 4 to be reversible. —

M * + M 2

2

^ — M M * 2

2

(4a)

In his kinetic analysis of the copolymer composition that would be formed, the usual steady-state assumptions were made. Lowry also made the important deduction that the rate at which Monomer 2 disappeared from the reaction (and was incorporated into the polymer) depended not simply upon the relative rates of the forward and reverse reaction (4a)


ADDITION

442

A N DCONDENSATION


PROCESSES

but rather upon the rate of Reaction 3, wherein a run of M units was "capped" by an Mi, thus preventing depolymerization of that run. 2

- ^ 1

=

S nk

21

[(m )„* [ M J

(10)

2

where [(m ) *] is the concentration of active chains ending in a run of η consecutive M units. The composition equation for this model was given as (11): 2

n


2

- = [ M ] ( l / ( l - e ) ) / ( f i [ M ] + [M ]) mi 2

«

1

(11)

2

[(m ) i ] / [ ( m ) / ] f o r 0 < n < o o

Ξ

2

ï!î

n+

2

where α is a function of the equilibrium constant for Reaction 4a, r , and the monomer concentrations. Note that copolymer composition is a func tion of the absolute monomer concentrations when depropagation occurs but only of the ratio of monomer concentration when Equation 5 applies. The second, and more physically realistic, case which Lowry con-* sidered, postulated that only Reaction 4b was reversible: 2

—

M M * + M 2

2

^ — M M M *

2

2

2

(4b)

2

i.e., depropagation occurred whenever three or more M units were at the end of an active chain. Again using steady-state assumptions and Equation 10, the copolymer composition is given by (11): 2

m

Ρ γ - ι + (i/i -β) [ Μ ι ] / [ Μ ] ) + 1] [iffy + (β/l ~

(12)

2

2

[(Ί

2

where β is defined as a above except that 1 < η < oo and γ = [(m )!*]/[(m ) *] 2

2

2

Using Κ for the equilibrium constant of Reaction 4b 0 = y{(l -

+ K[M ] + £ [ M a ] ) 2

[ ( 1 + Κ [M ] + ^ [ M , ] J 2

γ Υ

=

1

-

[Μι] _ ' [Μ ] 2

2

- 4 Κ [M,])" }2

β Κ[Μ ] 2

(13)

( V

1

4

) ;

Κ is a thermodynamic constant and is independent of mechanism, while reactivity ratios are kinetic constants and depend on mechanism. Lowry also considered a third case in which the sequence — M M M j * could depropagate whether the terminal unit was an M i 2

2


28.

O D R I S C O L L

443

Copolymerization with Depropagation

or an M . The resulting equations were too cumbersome for use since they involved series which are slow to converge. 2

Ivin and Hazell (7) extended Lowry's treatment to include a fourth case where any propagating chain ending in M could depropagate. Such a mechanism has been shown to apply in olefin-sulfur dioxide copolymerizations.


2

More recently Durgaryan derived (5) a copolymer composition equation assuming reversibility of all propagation reactions, Equations He expressed his solution as a pair of simultaneous equations in which the two unknowns (besides kinetic parameters and monomer feed) were copolymer composition and the ratio [ ( m i ) * ] / [ m i ) i * ] . At this writing no experimental tests of Durgaryan's equations have appeared. 2

Applications of Lowry Case II Ivin and Spensley (JO) tested the Lowry Case II model and equations for the anionic copolymerization of vinyl mesitylene (Mi) with a-methylstyrene at 0°C. by varying the total concentration of the two monomers while keeping their mole ratio constant. As pointed out above, theory predicts a dependence on absolute monomer concentration when depropagation occurs. Table I summarizes some of Ivin and Spensley's data. They also tested (JO) Case II for the free radical polymerization of styrene (Mi) and methyl methacrylate at 132°C. by the dilution tech nique. These data are also shown in Table I, where the good agreement between theory and experiment is apparent. The applicability of the theory to different mechanisms of polymerization is a nice verification of the statement that the composition is governed by end-state thermo dynamics rather than by mechanism. Table I.

Comparisons of Copolymer Compositions (9)

Vinylmesitylene-a-Methylstyrene

Styrene-Methyl Methacrylate

m (Mole Fraction)

m (Mole Fraction)

2

[M ],M 2

3.90 .575 .250 .240 .054

Calcd. Obsd.(±.01) .840 .750 .696 .693 .659

.841 .790 .730 .723 .660

2

[M ],M 2

1.376 1.380 0.166 0.165 0.125

Calcd. Obsd. (± .856 .857 .706 .707 .688

.860 .856 .760 .740 .704

Coincidental with Ivin and Spensley, O'Driscoll and Gasparro (12) studied the free radical copolymerization of styrene-methyl methacrylate but at 250°C. The latter workers varied monomer feed ratio over a wide


444

ADDITION

A N D CONDENSATION


PROCESSES

range at constant total concentration and found the unusual copolymer composition curve shown in Figure 1. Again the Lowry Case II gave excellent fit to the experimental data. 1.0


0.8

0.6

0.4

0.2

~0

0.2

0.4

0.6

0.8

1.0

[M]]/[M] + [M ] 2

Figure 1. Free radical bulk copolymerization of styrene (M ) with methyl methacrylate (M ) (11). Open circles represent experimental data at 250°C. t

2

Calculated from Equation 12(v = 0.8, t = 0.8, Κ = 0.105) Calculated from Equation 5(x = 0.5, x = 0.5) 1

2

t

2

OTDriscoll and Gasparro also studied the copolymerization by free radicals of «-methylstyrene ( M ) with either styrene or acrylonitrile as M i and found excellent agreement with Case II. They also showed that the limiting composition to be expected as the mole fraction of M i in the feed approached zero was accurately given by (12): 2

m = (2 - Κ [M ] )/(3 — 2 Κ [M ] ) 2

2

2

( 15)

This equation permits the calculation of equilibrium constants for polymerization-depolymerization from copolymer composition data extrapo lated to zero M i feed. The agreement between equilibrium constants calculated in this manner from free radical copolymerizations and those obtained from anionic homopolymerizations is shown in Table II, and again emphasizes the thermodynamic character of this work.


28.

ODRiscoLL

Table II.

445

Copolymerization with Depropagation Comparison of Equilibrium Constants

(11) Κ


Μ,

M

2

Styrene

a-Methylstyrene

Acrylonitrile Styrene

a-Methylstyrene Methyl methacrylate

T, °c.

Ref. 16

from homopolym.

60 100 75 250

.097 .021 .074 .102

.110 .015 .061 .079

O'Driscoll and Dickson (13) have extended the Lowry Case II to cover the rate of copolymerization as well as composition. They attribute the apparent increase in termination rate as the depropagating monomer is added to the feed to the predominance of small radicals of the type: R — ( M ) * , where R is an initiator fragment and η is a very small whole number—1, 2, or 3. Such small radicals, they postulate, would have diffusivities 1000 times greater than polymeric free radicals, and hence the diffusion-controlled, bimolecular termination rate constant would be greatly increased. Using a model for the rate of termination which involves termination reactions between two small radicals, two large radi cals, and a small radical with a large radical, it has been shown that the experimentally observed rate of copolymerization can be interpreted precisely. Figure 2 shows a plot for the system styrene-a-methylstyrene at 60 °C. The solid line in Figure 2 is calculated according to the equation 2

rt

(16)

km is the homopolymerization termination rate constant for styrene, and is determined by extrapolation to pure α-methylstyrene feed while k \2 is given by the general geometric mean

kt22 t

*«2

=

* ^

(

1

-

Λ

)

(17)

*«2*

where χ is the mole fraction of active chain ends which are small. Experimentally, it was found by extrapolation that k 2 was about 10 which is what one expects for diffusion-controlled bimolecular rate con stants for the reaction of small molecules.

10

t2



446

ADDITION

A N D CONDENSATION


PROCESSES

[Mj| / [Μ|]·+ [M ] 2

Figure 2. Revive rate of copolymerization of styrene (M ) and a-methylstyrene (M ) at 60°C. as a function of monomer composition (12) t

2

Ring Opening Copolymerizations Tobolsky and Owen (15) extended the Tobolsky-Eisenberg (16) general treatment of homopolymerization equilibria to copolymerization and applied their equations to the copolymerization data of Schenk (14) on selenium and sulfur. In this work the equilibrium degree of poly merization is measured as a function of temperature for total conversion of monomer to polymer. Equilibrium constants for initiation and propa gation are derived from homopolymerization experiments. Recently, Yamashita and co-workers (17) extended Lowrys treat ment for use on the cationic copolymerization of 3,3-bis(chloromethyl)oxacyclobutane (BCMO, Mi) with tetrahydrofuran ( T H F , M ) . They find that their data can be interpreted successfully by a model which considers a chain ending in M to add either M i or M reversibly, but chains ending in M add both monomers irreversibly. Their equation takes the simple form 2

2

2

x

^

=

(

1

- « ' (

1

+

' w )


Copolymerization with Depropagation - Advances in Chemistry (ACS

Recommend Documents