Living Radical Polymerization - American

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Chapter 2 Criteria for Livingness and Control in NitroxideMediated and Related Radical Polymerizations Hanns Fischer Physikalisch-Chemisches Institut, University of Zuerich, Winterthurerstrasse 190, C H 8059 Zuerich, Switzerland

In nitroxide mediated radical polymerizations large living and controlled polymer fractions at high conversions require equilibrium constants of the polymeric alkoxyamine dissociation-coupling cycle Κ =kd/k that are smaller than K kp[I]0/21n(10)k. Perfect livingness is reached if Κ ~ Kmax/100. These conditions imply minimum monomer conversion times. Small polydispersity indices at moderate to large conversions result if k k is close to or above a limit kdkcperf = 9(kp/2ln(10))3[M]02[I]0kt. The limits depend on the propagation and termination constants (kp, kt), that is, on the monomer, and on the initiator concentration [I]0. Five cases with different time evolutions of conversion, livingness and molecular weight distribution are distinguished. They explain the course of reported polymerizations. Effects o f initially present persistent radicals, self- and external initiation and reaction temperature are discussed. Further, the criteria are translated to apply also to atom transfer radical polymerizations. max

c

=

t

d

c

© 2003 American Chemical Society

In Advances in Controlled/Living Radical Polymerization; Matyjaszewski, Krzysztof; ACS Symposium Series; American Chemical Society: Washington, DC, 2003.

i l

Introduction

Living and controlled radical polymerizations are presently of high academic and industrial interest. Several reviews are available. " One successful process is based on the reactions shown in Scheme 1. Dormant polymeric alkoxyamines dissociate with the rate constant Ad into persistent nitroxide and propagating radicals. The latter recouple with the nitroxide (£ ), add to monomer (Ap) and undergo termination (k ) to unreactive polymer. In several cases polymers have been obtained with high nitroxide endgroup functionalities, molecular weights that are inversely proportional to the initial alkoxyamine concentration and that increase with monomer conversion, and polydispersity indices that decrease with increasing conversion to values close to unity.


1

5

c

t

Unreactive Polymer

t fc

+ Radical

t

• R' / R—(M)/

Ρ—Ν w

l

\

' =5F^

R"

Dormant Alkoxyamine

/

R—(Μ) .-Μ·

+

η

·0

Ν V

k

(χ)

Persistent Nitroxide

Scheme 1 6

Theoretical formulations have been developed by Fukuda et. al. and by this author and coworkers both for the reactions of Scheme 1 and for systems involving the initial presence of nitroxide, self- or conventional initiation, the concurrent formation of hydroxylamines and polymeric alkenes and for a limited stability of the nitroxide. They agree with experimental data and have recently been tested rigorously by absolute comparisons. Here, we use the theoretical results to derive criteria for livingness and control in the form of easy to apply equations. The reactions follow Scheme 1 and start from a dormant alkoxyamine that contains one or more monomer units in the initial absence of nitroxide. Usually, after a short time a quasi-equilibrium of the reversible alkoxyamine decay is established. It is characterized by slowly growing nitroxide and slowly decreasing propagating radical concentrations, and 5,7,8

9

10


12 it ends when termination has converted most of the alkoxyamine to unreactive products and nitroxide. " The criteria extend previous ones, and they appear quite natural. They explain many features of reported nitroxide mediated polymerizations. Also, we present numerical predictions and mention strategies for improvement. Finally, the criteria are formulated for atom transfer radical polymerizations (ATRP). Throughout, chain length independent rate constants are implied. 5

8


5,8a,n

Results and Discussion

Livingness. The polymers are called living when a large fraction of chains carries nitroxide endgroups. Hence, the decay-addition-recoupling cycle of Scheme 1 must be dominant during monomer conversion, and this implies (a) the existence of the quasi-equilibrium, (b) negligible monomer conversion before its establishment and (c) large conversion before its end. Condition (a) holds i f the rate constants obey ' 7 88

K~k /k «k [l) /k d

c

c

0

(1)

t

where [I] is the initial alkoxyamine concentration, and condition (b) requires 0

*, « 3 *

(2)

c

%&

for k < k . Insertion of known rate constants (Tables 3, 4) shows that these conditions are fulfilled in most cases. Condition (c) means that the time for large monomer conversion is smaller than the approximate time at which the quasiequilibrium ends, that is, smaller than ' c

t

7

8 a

(3) 2

3K k ' t

In the quasi-equilibrium regime the monomer concentration [M] obeys',5-8


13 2/3

ln[M], /[Μ] = ± * ,

(4)


Taking 90% as a large monomer conversion, equations (3) and (4) yield

aax

K = ^- 90% monomer conversion before 10% of the alkoxyamine I is converted to nitroxide Y «and unreactive products. The nitroxide concentration obeys " 5

2

[Y.] = ( 3 * K [ I ] o ) (

, / 3

'

1 / 3

8

.

(6)

Combination with equation (4) shows that perfect livingness requires

MI]Q

(7)

2001n(10)ifc, 1

A T * is smaller than KT by a factor of 100. The time for a given monomer conversion depends inversely on the square root of the equilibrium constant (eq. (4)). Therefore, A "*" and A ? lead to the times required for 90% monomer conversion 1

H 21n(10)

erf

and PI.


(8)

14 \2

10 21n(10) k

V

p

(9) [Ilo

J

The limiting values of the equilibrium constant and of the conversion time are determined by the monomer specific propagation and termination constants and the applied initial initiator concentration. Table 1 shows t and f* * as calculated for different propagation constants, a common termination constant k = 5 10 M ' V and [I] = 5 ΙΟ" M which corresponds to a final molecular weight of about 20Ό00 g/mol. For small propagation constants the times are long. They will be shorter in the presence of self- or additional conventional initiation but at the expence of livingness. The fast conversions calculated for large kp will lead to overheating. This can be avoided by a retarding initial addition of nitroxide. ' ' mn

1


x

8

1

2

0

2 5,80 9

Table 1. Times for 90% Monomer Conversion for a Monomer/Initiator Ratio of 200 and 510* Μ " 1 1

n

r /h

200 500 5Ό00

500 78 780

rooo 20 200

2Ό00 5 50

5Ό00 48 min 8

1

10Ό00 12 min 2

20Ό00 3 min 30 min

50Ό00 30 sec 5 min

Control. Polymerizations are usually called controlled when (a) the number average degree of polymerization DP (and the molecular weight) increases linearly with increasing monomer conversion Z)P=([M]o-[M])/[I] ,

(10)

0

and (b) the polydispersity index decreases in time and approaches PDI = 1 at high monomer conversion. Since DP =m lm , where m = [ M ] - [M] and m denote the first and zeroths moments of the polymer molecular weight distribution, equation (10) implies that m , the concentration of alkoxyamine chains with one or more monomer units, is constant during the polymerization and equals the initial initiator concentration. This is not the case i f most of the conversion occurs at the end of the quasi-equilibrium regime because then the alkoxyamine concentration decreases sharply. Consequently, control also requires that condition (5) holds. If this is fulfilled, equation (10) will always be obeyed i f one uses a (macro)-initiator which contains monomer units. For a monomer deficient initiator it will hold only i f this is transformed to a polymeric alkoxyamine in a x

Q

x

0

Q

0

7,8a


15 time which is very short compared to the time for large, say 90%, conversion, that is, ifk «(t )" . The desired properties o f the polydispersity index PDI require many dissociation-propagation-recoupling cycles before a large conversion is reached. Supported by simulations we suggest [M]o/[I] cycles, the ideal DP^ for 100% conversion. This gives 1

d

90


0

k

d

>

[

^ ± .

(11)

Calculation of tgo with equation (4) provides condition (12) which is similar to a relation given earlier. " 8

nk

D /

>2

(

1

2

)

l21n(10)J

Livingness versus Control In logarithmic forms the conditions (5), (7) and (12) read

log(* ) < - log(21n(10)) + log (*,) + log([I]o/* ) + log(* ) d

t

(13)

c

log(* ) < - log(2001n(10)) + log (kp) + log([iy*t) + log(A ) d

(14)

c

log(A ) > -31og(21n(10)/3) + 31og (kp) + log([iy*t) + 2\og(DP„) - log(* ). d

c

(15)

In a log(£ ) vs. log(£ ) plot they are represented by straight lines with locations depending on kp, k and the concentrations. Figure 1 shows these lines, denoted by K K? and k k in experimentally established * ranges of k and k for kp = 2Ό00 M' s\ k, = 5 10 M " V , [I] = 0.05 M and DP^ « 200. For pairs of rate constants (k ,k ) above K?™* in region X condition (5) does not hold so that high livingness and control at large conversions are prohibited. Pairs (k ,k ) below i ^ provide different degrees of livingness and control. The space of useful parameters is divided by the orthogonal lines representing equations (14) and (15) into four sections: A for both perfect livingness and control at > 90% conversion in times > f***, Β for perfect livingness but less d

c

t

aaax

td

ped

9

d

l

c

5

d

8

c

11

9

1

0

d

c

m a x

d

c



16

Table 2. Times, Polydispersity Indices and Alkoxyamine End Group Fractions at 90% Monomer Conversion for * = 2000 M ' V , * = 510 M ' Y , Oligomeric (MC, DP - 3) and Low Molecular Weight Model (MD) Initiators (Initial Ratio IMIo/fflo = 200) and Different k and k . %NO-gn Case Rate Constants Initiator i9o/h 1

p

8

A

A

-3

1

Ad= ΙΟ s A = 210 M- s 7

1

1

c

Β

4

* 6.2 1 0 erf

DEPN/nBuA

88Ό00

17

10

6

kj^vs. kik^/M's 9.010 3.210 6

1.2 10 > 8.1 10

3

3

10

TEMPO/wBuA

88Ό00

i2

5

3.510 < 2.510"

8

TEMPO/Sty

2Ό50

TEMPO/MMA

2*800

4

3

8

7.610 >3.210

8

6.0 10 > 8.1 10

5

3

10

Case isx/h Β 0.35 D 9.0 Χ 0.28 Β 3.0 Α 270 D 16

Effects ofL and Initiator Concentration. According to equations (5), (7) and (12) Κ™*, Κ ** and k k increase with increasing propagation constant Ap. A l l lines in Figure 1 move up, the line for k k three times more than the others. Hence, regarding livingness, the ranges of useful parameters (k ,k ) are wider for monomers with large kp than for monomers with small kp. On the other hand, low polydispersities are more difficult to achieve for fast propagating monomers. 9

pcri

a

c

pfiT{

d

c

d

c


21 With increasing attempted final degrees of polymerization [M]o/[I]o> that is, decreasing initiator concentrations, IC™* and K?** move down whereas £ £ moves up. Consequently, it is generally more difficult to achieve livingness and control for high than for low to moderate final molecular weights. Temperature Effects. The activation energies of the dissociation constants k are close to the alkoxyamine bond dissociation energies, and are typically larger than about 110 kJ/mol. This causes a large temperature dependence. On the other hand, the coupling constants k are only weakly temperature dependent. Therefore, the temperature dependence of Κ and kjcç is determined by that of k . The propagation and termination rate constants on the right hand sides of equations (5), (7) and (12) have smaller activation energies below about 40 kJ/mol. ' Hence, k increases more with increasing temperature than K™**, K? and k k . This means that the point (k ,k ) for a system representing the cases A to D may shift up in Figure 1 into the unfavourable region X . On the other hand, i f (k ,k ) is in region X at high temperatures it may fall into a more favourable region at lower temperature. In fact, D E P N / M M A seems to be such a case. perf

d

c

d

21

22


c

a

17

19,23

d

cri

per{

d

c

d

a

c

c

24

Unreactive Polymer

A + Radical

R—(M)„—Hal

+ Cat

x+

-

-

R

d e a c t

(M) _fM» n

\

u)

Dormant Chain

+ Cat

( x + 1 )

1ial

Persistent

Scheme 3 Relations for ATRP. Atom transfer radical polymerizations differ from those treated above because the activation reaction is bimolecular instead of monomolecular. The basic mechanism is shown in Scheme 3. Cat denotes a transition metal complex catalyst which reacts reversibly with a dormant halogen terminated polymer with rate constant £ . The reaction kinetics is very similar to that of nitroxide mediated polymerizations and has also been tested quite rigorously. In the equations presented above, the rate constant of alkoxyamine cleavage k has thus to be replaced by & t[Cat]o, *c by the rate constant £ ct f ° act

25

r

d

ac

dea


22 the reverse atom transfer reaction, and A'by £ [Cat]o/£deact whereas the notation I can be kept for the dormant chains. act


Concluding Remark

Even i f detrimental side reactions are absent, living and controlled polymerizations of a given monomer to high conversion are impossible i f the equilibrium constant for decay and reformation of the dormant polymeric chains exceeds an upper limit. This limit is imposed by the monomer specific propagation and termination constants and the applied initiator concentration. If the above condition is fulfilled imperfections may still occur because high livingness and high control are not correlated. A polymerization can be called living and controlled only i f both features are experimentally proven. In general, optimal living and controlled polymerizations of a specific monomer demand the use o f a tailor made nitroxide or another persistent radical which leads to the appropriate rate constants of the dormant chains. In addition, it must show little propensity for disproportionation. Acknowledgement. The author thanks P. Tordo and D . Bertin, University of Marseille, for their hospitality in the period when most of the presented ideas were developed and C. Jablon, TotalFinaElf, Paris, for financial support. 26

References and Notes

1.

2. 3. 4. 5. 6.

7. 8.

(a) Matyjaszewski, K . Ed. ACS Symp. Ser. 1998, 685; 2000, 768. (b) Matyjaszewski, K . ; Davis, T. P., Eds. Handbook of Radical Polymerization; Wiley, New York, 2002. Hawker, C. J.; Bosman, A . W.; Harth, E . Chem. Rev. 2001, 101, 3661. Kamigato,M.;Ando, T.; Sawamoto, M. Chem. Rev. 2001, 101, 3689. Matyjaszewski, K . ; Xia, J. Chem. Rev. 2001, 101, 2921. Fischer, H. Chem. Rev. 2001, 101, 3581. (a)Fukuda, T.; Goto, Α.; Tsujii, Y . in Handbook of Radical Polymerization; Matyjaszewski, K . ; Davis, T. P., Eds. Wiley, New York, 2002. (b) Fukuda, T.; Goto, Α.; Tsujii, Y . ACS Symp. Ser. 2000, 768, 27. (a) Fischer, H . Macromolecules 1997, 30, 5666. (b) Fischer, H . J. Polym. Sci. Part Α.: Polym. Chem. 1999, 37, 1885. (a) Souaille, M; Fischer, H . Macromolecules 2000, 33, 7378. (b) Souaille, M; Fischer, H . Macromolecules 2001, 34, 2830. (c) Souaille, M ; Fischer, H . Macromolecules 2002, 35, 248.


23


9.

10.

11.

12. 13. 14. 15. 16. 17. 18.

19.

20. 21. 22. 23. 24. 25. 26.

(a) Ohno, Κ. Tsujii, Y . ; Miyamoto, T. ; Fukuda, T.; Goto, M.; Kobayashi, K . Akaike, T. Macromolecules 1998, 31, 1064. (b) Lutz, J.F.; Lacroix-Desmazes, P.; Boutevin, B . Macromol Rapid Commun 2001, 22, 189. (c) Le Mercier, C.; Lutz, J.-F.; Marque, S.; Le Moigne, F.; Tordo, P., Lacroix-Desmazes, P.; Boutevin, B . ; Couturier, J.-L.; Guerret, O.; Martschke, R.; Sobek, J.; Fischer, H . ACS Symp. Ser. 2000, 768, 108. (a) Yoshikawa, C.; Goto, Α.; Fukuda, T. Macromolecules 2002, 353, 5081. (b) Fukuda, T.; Yoshikawa, C.; Kwak, Y.; Goto, Α.; Tsujii, Y . ACS Symp. Ser. This Volume. (a) Ananchenko, G . S.; Fischer, H . J. Polym. Sci. Part Α.: Polym. Chem. 2001, 39, 3604. (b) Ananchenko, G . S.; Souaille, M.; Fischer, H . ; Le Mercier, C.; Tordo, P. J. Polym. Sci. Part Α.: Polym. Chem. 2002, 40, 3264, and references therein. Using M A T L A B Version 6.1, The MathWorks Inc. 2001. Chauvin, F., PhD Thesis University of Marseille III, 2002. Goto, Α.; Fukuda, T.; Macromol. Chem. Phys. 2000, 201, 2138. From simulations of data kindly provided by D. Bertin and O. Guerret, Marseille. Greszta, D.; Matyjaszewski, K . Macromolecules 1996, 29, 7661 Van Herk, A . M. Macromol. Chem. Phys. 1997, 37, 633. Buback, M.; Gilbert, R. G . ; Hutchinson, R. Α.; Klumperman, B.; Kuchta, F. D . ; Manders, B . G . ; O'Driscoll, K . F.; Russell, G . T.; Schweer, J. Macromol. Chem. Phys. 1995, 196, 3267 Beuermann, S.; Buback, M.; Davies, T. P.; Gilbert, R. G.; Hutchinson, R. Α.; Olaj, O. F.; Russell, G . T.; Schweer, J.; van Herk, A . M. Macromol. Chem. Phys. 1997, 198, 1545. Listigover, Ν . Α.; Georges, M . K . ; Odell, P. G . ; Keoshkerian, B . Macromolecules 1996, 29, 8992. Marque, S.; Le Mercier, C.; Tordo, P.; Fischer, H . Macromolecules 2000, 33, 4403. Sobek, J.; Martschke, R.; Fischer, H . J. Amer. Chem. Soc. 2001, 123, 2849, and references therein. This was not recognized in our earlier work11b inspite of a thoughtful remark of a referee. D . Bertin, O. Guerret, private communication. Yoshikawa, C.; Goto, Α.; Fukuda, T. Macromolecules 2003, 36, 908. Lutz, J.-F.; Matyjaszewski, K . Maromol. Chem. Phys. 2002, 203, 1385.


Living Radical Polymerization - American

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