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The kinetics of the anionic polymerization of cyclic polydimethylsiloxanes
Anionic polymerization of cyclic polydimethylsiloxanes
535
REFERENCES
1. D. S. BRESLOW and N. R. NEWBURG, J. Amer. Chem. Soc. 81: 81, 1959; W. P. LONG and D. S. BRESLOW, J. Amer. Chem. Soc. 82: 1953, 1960; W. P. LONG, J. Amer. Chem. Soc. 81: 5312, 1959 2. J. C. W. CHIEN, J. Amer. Chem. Soc. 81: 86, 1959 3. A. K. ZEFIROVA and A. Ye. SHILOV, Dokl. Akacl. Nauk SSSR 136: 599, 1961 4. A. K. ZEFIROVA, N. N. TIKHOMIROVA and A. Ye. SHILOV, Dokl. Akad. Nauk SSSR 132.~ 1082, 1960 5. A. N. MAKI and E. W. RANDALL, J. Amer. Chem. Soc. 82: 4109, 1960 6. M. A. KIRRMANN, Bull Soc. Chim. France 39: 990, 1926 7. G. WILKINSON and J. M. BIRMINGHAM, J. Amer. Chem. Soc. 76: 4281, 1954 8. A. W. GROSSE and J. M. MAVITY, J. Org. Chem. 5: 106, 1940 9. A. Ye. SHILOV and R. D. SABIROVA, Zh. fiz. khim. 33: 1365, 1959
THE
KINETICS
OF THE
ANIONIC POLYMERIZATION
O F CYCLIC P O L Y D I M E T H Y L S I L O X A N E S * Z. LAITA and M. J E L I N E K Scientific-Research Institute of Macromolecular Chemistry, Brun (Received 12 March 1962)
A NUMBER of a u t h o r s h a v e studied the anionic p o l y m e r i z a t i o n o f cyclic polydimethylsiloxanes. T h e kinetics o f p o l y m e r i z a t i o n of o c t a m e t h y l c y c l o t e t r a s i l o x a n e (subsequently called the t e t r a m e r ) h a v e been studied t o the greatest e x t e n t [1-8]. W i t h r e g a r d t o h e x a m e t h y l c y c l o t r i s i l o x a n e (subsequently called t h e trimer) it is k n o w n only t h a t it polymerizes m u c h faster t h a n t h e t e t r a m e r [9]. T h e r e is no i n f o r m a t i o n in t h e l i t e r a t u r e on t h e higher cyclic polydimethylsiloxanes, t h o u g h a s t u d y o f the kinetics o f p o l y m e r i z a t i o n o f these cyclic c o m p o u n d s would be o f great interest for t h e t h e o r y o f anionic polymerization. T h e m a i n subject o f this c o m m u n i c a t i o n is a comparison o f the rates o f p o l y m e r i z a t i o n o f cyclic polydimethylsiloxanes with t h r e e t o nine a t o m s o f silicon in the molecule, induced b y potassium, sodium a n d lithium hydroxides. I t was f o u n d t h a t t h e over-all rate o f p o l y m e r i z a t i o n differs m a r k e d l y for different cyclic p o l y d i m e t h y l s i l o x a n e s a n d with the different catalysts, t h o u g h the e n e r g y of a c t i v a t i o n is t h e same. These facts are explained b y t h e different basicities of the catalysts a n d b y steric effects in the siloxane rings. * Vysokomol. soyed. 4: No. 11, 1739-1745, 1962.
536
Z. LAITA and M. JELINEK
EXPERIh~ENTAL The polymerization was studied b y the dilatome~ic m e t h o d described b y Ku6era and Jelinek [5]. The trimer and octamer were measured out from a thermostatically controlled burette, because the melting points of these compounds are above room temperature. The dilatometers were heated in a thermostat with a precision o f i 0 . 1 5 °. The contractions were read by means of a cathetomcter with a precision of 0.1 mm. The alkaline catalysts were added in the form of suspensions [2,5], or as the silanolate [10] when the polymerization was carried out at temperatures below 100 °, and solution of a suspension became difficult. Only an approximate investigation of the polymerization of the nonamer could be made, by following the increase in viscosity of the system, because the contraction with this compound was very small. The polymerization of the trimer at a temperature above its boiling point was carried out with sodium hydroxide in a sealed, evacuated ampoule, and the degree of conversion was determined after rapid cooling in ice-water. The relationship between contraction and conversion was found by two methods. I n the first method, after polymerization was stopped at a given contraction the contents of th') dilatometer were dissolved in toluene and the polymer was precipitated b y methanol as described in reference [5]. I n the second method the polymer was isolated by evaporation of the volatile material in vacuo(O.O05 mm). I t is necessary to carry out the evaporation at room temperature because a t higher temperatures the polymer depolymerizes. This method can be used only with the more volatile polydimethylcyclosiloxanes (up to the pentamer). Materials. We studied the polymerization of the following cyclic siloxanes: hexamethylcyclotrisiloxane (trimer), octamethyl-eyclotetrasiloxane (tetramer), decamethylcyclopentasiloxane (pentamer), dodecamethylcyclohexasiloxane (hexamer), tetradecamethylcycloheptasiloxane (heptamer), hexadecamethylcyclooetasiloxane (octamer), oetadecamethylcyclononasiloxane (nonamer). These ring compounds were obtained by fractional distillation under reduced presssure of a mixture obtained by catalytic depolymerization of linear polydimethylsiloxane in the presence of N a O H at 250 ° and a residual pressure of 10 mm. The p u r i t y of the compounds was determined chromatographically [11] a n d in all cases was higher than 95%. The remainder (to 100%) consistd of lower ring compounds t h a t could not be removed b y distillation. :No other impurities were detected and all the cyclic poliydimcthylsiloxanes gave linear polymers on polymerization.
RESULTS The two methods of determination of the relationship between concentration and conversion mentioned above did not give concordant results. In both cases a l i n e a r r e l a t i o n s h i p w i t h t h e s a m e s l o p e w a s o b t a i n e d b u t in t h e e a s e o f t h e m e t h o d of precipitation of the polymer the straight line did not pass through the origin [5], w h e r e a s i n t h e e v a p o r a t i o n m e t h o d t h e l i n e s t a r t e d f r o m t h e o r i g i n . T h e r e is o b v i o u s l y a s y s t e m a t i c e r r o r i n t h e f i r s t m e t h o d d u e t o t h e p r e s e n c e o f l o w molecular polymers soluble in the methanol-toluene mixture. We therefore considered only the slopes of the lines. The amount of contraction on polymerization decrease sharply as the number of silicon atoms in the original cyclic siloxane increases. For this reason it was not possible to follow the polymerization of the nonamer by the dilatometric m e t h o d a n d t h e r e s u l t s o b t a i n e d f o r t h e o c t a m e r a r e less a c c u r a t e t h a n t h o s e f o r the other compounds.
Anionic polymerization of cyclic polydimethylsiloxanes
537
The curves of the dependence of conversion on time are similar to the curve for the tetramer described previously [5, 6], b u t at the high rates of polymerization of the more reactive rings a maximum appears in the curves (Fig. 1). The conversion curves were reduced to the linear form b y means of the equation [M]~,- [M]'/, 1 ([M]~/~- [M]'/2)([M]V,+[M]'/0 k,K~/, [cJV, [M]:/~ + 2 ln([M]~,+[M]~h) ([M]'/,--[M]~/0 = - 2 " [M]:/,'t (1) Equation (1) is the integrated form of equation (2) dM
dt = [c]'/' {klK~'[a]l[~- l~ K 2KI-'I'[M ]-'/'} ,
(2)
which was derived b y Vese]~ and KuSera [8] from the following kinetic scheme:
/ o \ K, PnO@Mo®+Si
/o\
/ ~----2_PnOSiC-'
"-,~O/ ( a )
80
k,
wK,
] +Me®c_~_~pn. 10~ + M e ® ~ p n + 10®Me®"
~01
(~
(c)
i
x
GO
40
2O
0
I
I
20
40
lL,~eCm~n)
60
FIG. 1. Curve of conversion of the hexamer (0"01~/ KOH, 150°). where [M]o is the initial concentration of polydimethylcyclosiloxane, [M] the concentration of polydimethylcyclosiloxane, [M]~ the equilibrium concentration of polydimethylcyclosiloxane, [c] the catalyst concentration, K 1 and K 2 the
Z . LAITA a n d M . JELINEK
538
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Anionic polymerization of cyclic polydimethylsiloxanes
539
./O) equilibrium constants, k 1 and k 2 the rate constants, t the time, $1\O the polydimethylcyclosiloxane molecule, P~ the polydimethylsiloxane chain, and Me the Mkali metal atom. The slopes, tan e, of the straight lines obtained by plotting eqn. (1) were determined. From eqn. (3) it is possible to calculate the over-all rate constant of polymerization and K ' = klk~' tan "~Z-2 = ' ~[c] "[/]'/~ (3)
K' is expressed in relative units. It does not have the usual dimensions because the equilibrium concentration of the polydimethylcyclosiloxane cannot be expressed in moles/litre because of depolymerization of the polymer resulting in the formation of various ring. structures. The results are given in Table 1, which also includes energies of activation and factors, independent of temperature, for the over-all reaction rates from the equation K'=Ae-~/RT. On comparing the energies of activation for the different ring compounds and with different alkali metal hydroxides it was found that with the exception off the trimer the energies of activation were the same in all cases within the limits of experimental error, at 19-5:k0-5 keal/mole. DISCUSSION
According to the above mechanism the reaction rate is determined b y reaction (b) and the rate constant for this reaction is k r ' Reactions (a) and (c) are fh
considerably faster, because the concentration of the complex P n O S i e ~ i s constant and depends only on the value of the expression K1½ [c]½ [M]½ .K 1 depends on the nature of the metal hydroxide and increases with increasing basicity of the hydroxide. It m a y be assumed that the variation of the dissociation constant, K1, with temperature is small and will be approximately the same for all the hydroxides. Reaction (b) involves a more or less free ion and is thus independent of the counter-ion. The rate is therefore independent of the identity of the metal hydroxide. This is supported by the experimental results. On changing to another catalyst only the temperature-independent factor changes while the activation energy, determined by reaction (b), remains constant though the reaction rate changes by three orders of magnitude. The molecule of the trimer is strained and the energy involved is 3-4 kcal/mole [12]. It is therefore not surprising that the activation energy in this case is lower b y 2-3 kcal/mole. The relationship between the reactivity of the ring compounds, expressed as the temperature-independent constant, and the size of the ring is very interesting (Fig. 2). The tetramer and pentamer are least reactive. The reactivity
540
Z. LAITA a n d M. JELINEK
d togA/n 0
9
0 0 0
///. 8
o
~
// //
o
O O I
t
5 FIe. 3. Configuration of bonds of pentavalent silicon.
FIe. 2. Dependence of reactivity of cyclosiloxanes on ring size.
increases sharply for the hexamer and heptamer, after which there is little further change with increasing size of the ring. This can be explained by the effect of the structure of the ring on the thermodynamic probability of the formation of the complex with a pentavalent silicon atom. For the study of the effect of structure the following equations were used: - - A G o = R T In K c
(4)
AG o = T f l S o - f i l l o
(5)
From a consideration of the reaction PnOeMe® + s i ( O ) K2~ ~__ P n O S i e ( o0) +Me~', it m a y be assumed that for all the rings (except the trimer) A H o is the same, but the entropy change involved in this reaction is dependent on the structure of the ring. a
Me~
_
Me
Me
C
Me
19
Me
/'~00~ ~ SiO
Me
OSi
o\ ~SiO ~l~os
~~,
d FIG. 4. Possible structures for complex compounds with pen~avalent silicon.
Anionic polymerization of cyclic polydimethylsiloxanes
541
I t is assumed t h a t hybridization of the spad electrons occurs in pentavalent silicon and the valence bonds have a trigonal, bipyramidal configuration [13] (Fig. 3). There are five possibilities for the structure of the complex compound (Fig. 4). The symmetrical configuration a is the most probable. Three-dimensionM atom models were used for the study of the structure of the rings and intermediate compounds with pentavalent silicon. Since the lengths of the bonds with pentavalent silicon are not known they were taken, to the first approximation, as being equal to the lengths of the tetravalent silicon bonds (Si-O 1.65 A, Si-C 1.9 A). The results are given in Table 2. In the trimer the molecule is rigid and strained. On formation of the complex these properties do not change, consequently the entropy change due to structural changes will be zero (AS o struct~0), However on reaction of the tetramer and pentamer with the silanol atom the possibility of movement of the individual silicon and oxygen atoms falls sharply and the entropy of the molecule must decrease (AS0 struct d 0 ) . With the hexamer and larger membered rings the mobility of the atoms does not change with formation of the complex and therefore z~S struct ~-0. It follows from eqn. (4) and (5) t h a t for th~ tetramer and pentamer K e will by lower thun for the other rings, for which AS=(). T A B L E 2. P E N T A V A L E N T
SILICON COMPLEXES
Configu- r amer I~'entamer Trimer :I Tet I'Hexamer Heptamer ration !
--
o o
-
+
+ +
+
+ -- + ÷
+ 0
÷
÷
f q÷-÷ --.
+
+
-t- ÷ + ÷ +
+
+
+
Note: + + molecule of grood m o b i l i t y + molecule of l i m i t e d m o b i l i t y 0
r igid molecule
-- s t r a i n e d nmlecule -- -- c~mnot exist.
These results are only qualitative because at pres=~nt there is insufficient knowledge of pentavalent silicon. In the experimental section a curve of the polyme,ization of the hexamer, showing a maximum, is given (Fig. 1). This maximum is brought about by the fact t h a t even at low concentrations polymerization of the hexamer is faster than the simultaneous depolymerization of the polymer. As a result of depolymerization a mixture of cyclic siloxanes is formed, containing a large amount of tetramer (about 47%), which polymerizes slowly. Under equilibrium conditions the concentration of polymer is determined by the ratio of the rates of polymerization and depolymerization. Consequently at first polymerization pro-
542
Z. LAITA and M. JELINZK
ceeds until the concentration of polymer corresponds to the h e x a m e r - p o l y m e r equilibrium. However the t e t r a m e r concentration gradually increases and this is less reactive and corresponds to a lower equilibrium concentration of polymer. The concentration of polymer decreases and fina]ly reaches the value characteristic o f the system polymer-depolymerization products. This must apply to all rings with rates of polymerization higher t h a n the rate of polymerization of the equilibrium mixture of rings (virtually tetramer). However the dilatometric method is not sufficiently sensitive to enable the m axi m um to be detected in the case o f t h e hept am e r and higher membered ring compounds.
CONCLUSIONS
(1) The rate of polymerization of cyclic polydimethylcyclosiloxanes with 3-9 silicon atoms, catalysed by L i 0 H , N a 0 H and K O H , has been measured. The energy of activation was calculated from the results. (2) I t was found t h a t rings with seven or more silicon atoms are most reactive and octamethy]cyclotetrasiloxane is least reactive. F o r hexamethylcyclotrisiloxane the energy of activation is 17.5 kcal/mole and for the other ring compounds the value is 19.5 kcal/mole, and is independent of the nature of the catalyst. (3) The different rate of polymerization of the various polydimethylsiloxanes is explained b y steric effects at the pentavalent silicon atom in the transition complex. Tra,nsloted by E. O. PHILLIPS REFERENCES R. C. OSTHOFF and M. L. CORRIN, J. Amer. Chem. Soc. 76: 243, 1954 W. T. GRUBB and R. C. OSTHOFF, J. Amer. Chem. Soc. 77: 1405, 1955 T. ARAKI and K. OSUGA, J. Chem. Soc. Japan, Ind. Chem. Soc. 58: 302, 1955 T. ARAKI and K. OSUGA, Reports Govt. Chem. Ind. Res. Inst., Tokyo, 50: 161, 1955 M. KUt~ERA and M. JELtNEK, Collection Czech. Chem. Commun. 25: 536, 1960 M. KU~ERA, Collection Czech. Chem. Commun. 25: 547, 1960 M. KUI~ERA, Sbornik trudov AN, 6, 1960 K. VESELY ~nd M. KUI~ERA, Symposium tiber Makromolekfile in Wiesbaden DBR, Kurzmitteilungen IV, B3, 1959 S. W. KANTOR, W. T. GRUBB and R. C. OSTHOFF, J. Amer. Chem. Soc. 76: 5190, 1954 M. KU~ERA and M. JELINEK, Vysokomol. soyed. 2: 1860, 1960 K. OTTO and M. DOUBEK, Chem. prumysl 10: 476, 1960 W. A. PICOLI, G. G. HABERLAND and R. L. MERKER, J. Amer. Chem. Soc. 82: 1883, 1960 C. EABORN, Organosilicon compounds, London, 1960
1. D. T. H I ~ D ,
2. 3. 4. 5. 6. 7. 8. 9.
10. 11. 12. 13.
535
REFERENCES
1. D. S. BRESLOW and N. R. NEWBURG, J. Amer. Chem. Soc. 81: 81, 1959; W. P. LONG and D. S. BRESLOW, J. Amer. Chem. Soc. 82: 1953, 1960; W. P. LONG, J. Amer. Chem. Soc. 81: 5312, 1959 2. J. C. W. CHIEN, J. Amer. Chem. Soc. 81: 86, 1959 3. A. K. ZEFIROVA and A. Ye. SHILOV, Dokl. Akacl. Nauk SSSR 136: 599, 1961 4. A. K. ZEFIROVA, N. N. TIKHOMIROVA and A. Ye. SHILOV, Dokl. Akad. Nauk SSSR 132.~ 1082, 1960 5. A. N. MAKI and E. W. RANDALL, J. Amer. Chem. Soc. 82: 4109, 1960 6. M. A. KIRRMANN, Bull Soc. Chim. France 39: 990, 1926 7. G. WILKINSON and J. M. BIRMINGHAM, J. Amer. Chem. Soc. 76: 4281, 1954 8. A. W. GROSSE and J. M. MAVITY, J. Org. Chem. 5: 106, 1940 9. A. Ye. SHILOV and R. D. SABIROVA, Zh. fiz. khim. 33: 1365, 1959
THE
KINETICS
OF THE
ANIONIC POLYMERIZATION
O F CYCLIC P O L Y D I M E T H Y L S I L O X A N E S * Z. LAITA and M. J E L I N E K Scientific-Research Institute of Macromolecular Chemistry, Brun (Received 12 March 1962)
A NUMBER of a u t h o r s h a v e studied the anionic p o l y m e r i z a t i o n o f cyclic polydimethylsiloxanes. T h e kinetics o f p o l y m e r i z a t i o n of o c t a m e t h y l c y c l o t e t r a s i l o x a n e (subsequently called the t e t r a m e r ) h a v e been studied t o the greatest e x t e n t [1-8]. W i t h r e g a r d t o h e x a m e t h y l c y c l o t r i s i l o x a n e (subsequently called t h e trimer) it is k n o w n only t h a t it polymerizes m u c h faster t h a n t h e t e t r a m e r [9]. T h e r e is no i n f o r m a t i o n in t h e l i t e r a t u r e on t h e higher cyclic polydimethylsiloxanes, t h o u g h a s t u d y o f the kinetics o f p o l y m e r i z a t i o n o f these cyclic c o m p o u n d s would be o f great interest for t h e t h e o r y o f anionic polymerization. T h e m a i n subject o f this c o m m u n i c a t i o n is a comparison o f the rates o f p o l y m e r i z a t i o n o f cyclic polydimethylsiloxanes with t h r e e t o nine a t o m s o f silicon in the molecule, induced b y potassium, sodium a n d lithium hydroxides. I t was f o u n d t h a t t h e over-all rate o f p o l y m e r i z a t i o n differs m a r k e d l y for different cyclic p o l y d i m e t h y l s i l o x a n e s a n d with the different catalysts, t h o u g h the e n e r g y of a c t i v a t i o n is t h e same. These facts are explained b y t h e different basicities of the catalysts a n d b y steric effects in the siloxane rings. * Vysokomol. soyed. 4: No. 11, 1739-1745, 1962.
536
Z. LAITA and M. JELINEK
EXPERIh~ENTAL The polymerization was studied b y the dilatome~ic m e t h o d described b y Ku6era and Jelinek [5]. The trimer and octamer were measured out from a thermostatically controlled burette, because the melting points of these compounds are above room temperature. The dilatometers were heated in a thermostat with a precision o f i 0 . 1 5 °. The contractions were read by means of a cathetomcter with a precision of 0.1 mm. The alkaline catalysts were added in the form of suspensions [2,5], or as the silanolate [10] when the polymerization was carried out at temperatures below 100 °, and solution of a suspension became difficult. Only an approximate investigation of the polymerization of the nonamer could be made, by following the increase in viscosity of the system, because the contraction with this compound was very small. The polymerization of the trimer at a temperature above its boiling point was carried out with sodium hydroxide in a sealed, evacuated ampoule, and the degree of conversion was determined after rapid cooling in ice-water. The relationship between contraction and conversion was found by two methods. I n the first method, after polymerization was stopped at a given contraction the contents of th') dilatometer were dissolved in toluene and the polymer was precipitated b y methanol as described in reference [5]. I n the second method the polymer was isolated by evaporation of the volatile material in vacuo(O.O05 mm). I t is necessary to carry out the evaporation at room temperature because a t higher temperatures the polymer depolymerizes. This method can be used only with the more volatile polydimethylcyclosiloxanes (up to the pentamer). Materials. We studied the polymerization of the following cyclic siloxanes: hexamethylcyclotrisiloxane (trimer), octamethyl-eyclotetrasiloxane (tetramer), decamethylcyclopentasiloxane (pentamer), dodecamethylcyclohexasiloxane (hexamer), tetradecamethylcycloheptasiloxane (heptamer), hexadecamethylcyclooetasiloxane (octamer), oetadecamethylcyclononasiloxane (nonamer). These ring compounds were obtained by fractional distillation under reduced presssure of a mixture obtained by catalytic depolymerization of linear polydimethylsiloxane in the presence of N a O H at 250 ° and a residual pressure of 10 mm. The p u r i t y of the compounds was determined chromatographically [11] a n d in all cases was higher than 95%. The remainder (to 100%) consistd of lower ring compounds t h a t could not be removed b y distillation. :No other impurities were detected and all the cyclic poliydimcthylsiloxanes gave linear polymers on polymerization.
RESULTS The two methods of determination of the relationship between concentration and conversion mentioned above did not give concordant results. In both cases a l i n e a r r e l a t i o n s h i p w i t h t h e s a m e s l o p e w a s o b t a i n e d b u t in t h e e a s e o f t h e m e t h o d of precipitation of the polymer the straight line did not pass through the origin [5], w h e r e a s i n t h e e v a p o r a t i o n m e t h o d t h e l i n e s t a r t e d f r o m t h e o r i g i n . T h e r e is o b v i o u s l y a s y s t e m a t i c e r r o r i n t h e f i r s t m e t h o d d u e t o t h e p r e s e n c e o f l o w molecular polymers soluble in the methanol-toluene mixture. We therefore considered only the slopes of the lines. The amount of contraction on polymerization decrease sharply as the number of silicon atoms in the original cyclic siloxane increases. For this reason it was not possible to follow the polymerization of the nonamer by the dilatometric m e t h o d a n d t h e r e s u l t s o b t a i n e d f o r t h e o c t a m e r a r e less a c c u r a t e t h a n t h o s e f o r the other compounds.
Anionic polymerization of cyclic polydimethylsiloxanes
537
The curves of the dependence of conversion on time are similar to the curve for the tetramer described previously [5, 6], b u t at the high rates of polymerization of the more reactive rings a maximum appears in the curves (Fig. 1). The conversion curves were reduced to the linear form b y means of the equation [M]~,- [M]'/, 1 ([M]~/~- [M]'/2)([M]V,+[M]'/0 k,K~/, [cJV, [M]:/~ + 2 ln([M]~,+[M]~h) ([M]'/,--[M]~/0 = - 2 " [M]:/,'t (1) Equation (1) is the integrated form of equation (2) dM
dt = [c]'/' {klK~'[a]l[~- l~ K 2KI-'I'[M ]-'/'} ,
(2)
which was derived b y Vese]~ and KuSera [8] from the following kinetic scheme:
/ o \ K, PnO@Mo®+Si
/o\
/ ~----2_PnOSiC-'
"-,~O/ ( a )
80
k,
wK,
] +Me®c_~_~pn. 10~ + M e ® ~ p n + 10®Me®"
~01
(~
(c)
i
x
GO
40
2O
0
I
I
20
40
lL,~eCm~n)
60
FIG. 1. Curve of conversion of the hexamer (0"01~/ KOH, 150°). where [M]o is the initial concentration of polydimethylcyclosiloxane, [M] the concentration of polydimethylcyclosiloxane, [M]~ the equilibrium concentration of polydimethylcyclosiloxane, [c] the catalyst concentration, K 1 and K 2 the
Z . LAITA a n d M . JELINEK
538
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~
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Anionic polymerization of cyclic polydimethylsiloxanes
539
./O) equilibrium constants, k 1 and k 2 the rate constants, t the time, $1\O the polydimethylcyclosiloxane molecule, P~ the polydimethylsiloxane chain, and Me the Mkali metal atom. The slopes, tan e, of the straight lines obtained by plotting eqn. (1) were determined. From eqn. (3) it is possible to calculate the over-all rate constant of polymerization and K ' = klk~' tan "~Z-2 = ' ~[c] "[/]'/~ (3)
K' is expressed in relative units. It does not have the usual dimensions because the equilibrium concentration of the polydimethylcyclosiloxane cannot be expressed in moles/litre because of depolymerization of the polymer resulting in the formation of various ring. structures. The results are given in Table 1, which also includes energies of activation and factors, independent of temperature, for the over-all reaction rates from the equation K'=Ae-~/RT. On comparing the energies of activation for the different ring compounds and with different alkali metal hydroxides it was found that with the exception off the trimer the energies of activation were the same in all cases within the limits of experimental error, at 19-5:k0-5 keal/mole. DISCUSSION
According to the above mechanism the reaction rate is determined b y reaction (b) and the rate constant for this reaction is k r ' Reactions (a) and (c) are fh
considerably faster, because the concentration of the complex P n O S i e ~ i s constant and depends only on the value of the expression K1½ [c]½ [M]½ .K 1 depends on the nature of the metal hydroxide and increases with increasing basicity of the hydroxide. It m a y be assumed that the variation of the dissociation constant, K1, with temperature is small and will be approximately the same for all the hydroxides. Reaction (b) involves a more or less free ion and is thus independent of the counter-ion. The rate is therefore independent of the identity of the metal hydroxide. This is supported by the experimental results. On changing to another catalyst only the temperature-independent factor changes while the activation energy, determined by reaction (b), remains constant though the reaction rate changes by three orders of magnitude. The molecule of the trimer is strained and the energy involved is 3-4 kcal/mole [12]. It is therefore not surprising that the activation energy in this case is lower b y 2-3 kcal/mole. The relationship between the reactivity of the ring compounds, expressed as the temperature-independent constant, and the size of the ring is very interesting (Fig. 2). The tetramer and pentamer are least reactive. The reactivity
540
Z. LAITA a n d M. JELINEK
d togA/n 0
9
0 0 0
///. 8
o
~
// //
o
O O I
t
5 FIe. 3. Configuration of bonds of pentavalent silicon.
FIe. 2. Dependence of reactivity of cyclosiloxanes on ring size.
increases sharply for the hexamer and heptamer, after which there is little further change with increasing size of the ring. This can be explained by the effect of the structure of the ring on the thermodynamic probability of the formation of the complex with a pentavalent silicon atom. For the study of the effect of structure the following equations were used: - - A G o = R T In K c
(4)
AG o = T f l S o - f i l l o
(5)
From a consideration of the reaction PnOeMe® + s i ( O ) K2~ ~__ P n O S i e ( o0) +Me~', it m a y be assumed that for all the rings (except the trimer) A H o is the same, but the entropy change involved in this reaction is dependent on the structure of the ring. a
Me~
_
Me
Me
C
Me
19
Me
/'~00~ ~ SiO
Me
OSi
o\ ~SiO ~l~os
~~,
d FIG. 4. Possible structures for complex compounds with pen~avalent silicon.
Anionic polymerization of cyclic polydimethylsiloxanes
541
I t is assumed t h a t hybridization of the spad electrons occurs in pentavalent silicon and the valence bonds have a trigonal, bipyramidal configuration [13] (Fig. 3). There are five possibilities for the structure of the complex compound (Fig. 4). The symmetrical configuration a is the most probable. Three-dimensionM atom models were used for the study of the structure of the rings and intermediate compounds with pentavalent silicon. Since the lengths of the bonds with pentavalent silicon are not known they were taken, to the first approximation, as being equal to the lengths of the tetravalent silicon bonds (Si-O 1.65 A, Si-C 1.9 A). The results are given in Table 2. In the trimer the molecule is rigid and strained. On formation of the complex these properties do not change, consequently the entropy change due to structural changes will be zero (AS o struct~0), However on reaction of the tetramer and pentamer with the silanol atom the possibility of movement of the individual silicon and oxygen atoms falls sharply and the entropy of the molecule must decrease (AS0 struct d 0 ) . With the hexamer and larger membered rings the mobility of the atoms does not change with formation of the complex and therefore z~S struct ~-0. It follows from eqn. (4) and (5) t h a t for th~ tetramer and pentamer K e will by lower thun for the other rings, for which AS=(). T A B L E 2. P E N T A V A L E N T
SILICON COMPLEXES
Configu- r amer I~'entamer Trimer :I Tet I'Hexamer Heptamer ration !
--
o o
-
+
+ +
+
+ -- + ÷
+ 0
÷
÷
f q÷-÷ --.
+
+
-t- ÷ + ÷ +
+
+
+
Note: + + molecule of grood m o b i l i t y + molecule of l i m i t e d m o b i l i t y 0
r igid molecule
-- s t r a i n e d nmlecule -- -- c~mnot exist.
These results are only qualitative because at pres=~nt there is insufficient knowledge of pentavalent silicon. In the experimental section a curve of the polyme,ization of the hexamer, showing a maximum, is given (Fig. 1). This maximum is brought about by the fact t h a t even at low concentrations polymerization of the hexamer is faster than the simultaneous depolymerization of the polymer. As a result of depolymerization a mixture of cyclic siloxanes is formed, containing a large amount of tetramer (about 47%), which polymerizes slowly. Under equilibrium conditions the concentration of polymer is determined by the ratio of the rates of polymerization and depolymerization. Consequently at first polymerization pro-
542
Z. LAITA and M. JELINZK
ceeds until the concentration of polymer corresponds to the h e x a m e r - p o l y m e r equilibrium. However the t e t r a m e r concentration gradually increases and this is less reactive and corresponds to a lower equilibrium concentration of polymer. The concentration of polymer decreases and fina]ly reaches the value characteristic o f the system polymer-depolymerization products. This must apply to all rings with rates of polymerization higher t h a n the rate of polymerization of the equilibrium mixture of rings (virtually tetramer). However the dilatometric method is not sufficiently sensitive to enable the m axi m um to be detected in the case o f t h e hept am e r and higher membered ring compounds.
CONCLUSIONS
(1) The rate of polymerization of cyclic polydimethylcyclosiloxanes with 3-9 silicon atoms, catalysed by L i 0 H , N a 0 H and K O H , has been measured. The energy of activation was calculated from the results. (2) I t was found t h a t rings with seven or more silicon atoms are most reactive and octamethy]cyclotetrasiloxane is least reactive. F o r hexamethylcyclotrisiloxane the energy of activation is 17.5 kcal/mole and for the other ring compounds the value is 19.5 kcal/mole, and is independent of the nature of the catalyst. (3) The different rate of polymerization of the various polydimethylsiloxanes is explained b y steric effects at the pentavalent silicon atom in the transition complex. Tra,nsloted by E. O. PHILLIPS REFERENCES R. C. OSTHOFF and M. L. CORRIN, J. Amer. Chem. Soc. 76: 243, 1954 W. T. GRUBB and R. C. OSTHOFF, J. Amer. Chem. Soc. 77: 1405, 1955 T. ARAKI and K. OSUGA, J. Chem. Soc. Japan, Ind. Chem. Soc. 58: 302, 1955 T. ARAKI and K. OSUGA, Reports Govt. Chem. Ind. Res. Inst., Tokyo, 50: 161, 1955 M. KUt~ERA and M. JELtNEK, Collection Czech. Chem. Commun. 25: 536, 1960 M. KU~ERA, Collection Czech. Chem. Commun. 25: 547, 1960 M. KUI~ERA, Sbornik trudov AN, 6, 1960 K. VESELY ~nd M. KUI~ERA, Symposium tiber Makromolekfile in Wiesbaden DBR, Kurzmitteilungen IV, B3, 1959 S. W. KANTOR, W. T. GRUBB and R. C. OSTHOFF, J. Amer. Chem. Soc. 76: 5190, 1954 M. KU~ERA and M. JELINEK, Vysokomol. soyed. 2: 1860, 1960 K. OTTO and M. DOUBEK, Chem. prumysl 10: 476, 1960 W. A. PICOLI, G. G. HABERLAND and R. L. MERKER, J. Amer. Chem. Soc. 82: 1883, 1960 C. EABORN, Organosilicon compounds, London, 1960
1. D. T. H I ~ D ,
2. 3. 4. 5. 6. 7. 8. 9.
10. 11. 12. 13.