KINETICSOF ~METHYLSILOXANE POLYMERIZATION
2213
Verification of the Flory Theory of Random Reorganization of Molecular Weight Distribution-Kinetics
of Methylsiloxane Polymerization
by Jack B. Carmichael and James Heffel Basic Polymer Research Laboratory, Dow Corning Corporation, Midland, Michigan (Received December 1 1 , 1964)
The distributions of linear and cyclic methylsiloxanes were determined by gas-liquid chromatography during acid clay catalyzed reactions of equal molar amounts of D4 [D = (CH3)2SiO]and M M [A4 = (CH3)3SiOl/,] at 80". The theoretical and experimental distributions of the h e a r s are compared as a function of time. The relatively large amounts of MD4M and MDsM present after 0.5 hr. indicate that D, initially enters the linear chains as a unit. Sufficient reorganization has occurred after 0.5 hr. that the distribution of 1MDloM through MD13M is approxiniately random. The distribution of shorter chains becomes increasingly random as the reaction proceeds toward equilibrium,
I. Introduction Kinetic studies of polymerization of dimethylsiloxanes have been performed by many workers. Grubb and Osthoff have shown that the KOH-catalyzed polymerization of D4 [D = (CH3)2SiO] is first order by following the change in vapor pressure of the polymerizing system. Illany other authors have studied the anionic polymerization of cyclodimethylsiloxanes using LiOH, NaOH, and KOH.2 In all these studies, some gross parameter of the polymerizing system (e.g., viscosity) was determined for kinetic analysis. Only Van Wazer and illoedritzer3 have reported the analysis of reactants and products obtained during polymerization of dimethylsiloxanes. By means of r1.m.r. these workers studied the AIClo-catalyzed reaction of dimethyldichlorosilane with Dq in a 4 : l molar ratio. Amounts of the molecules (CH3)2SiC12, D4,and (CH3)d3lSiDI-&3i(CH3)2Cl were reported as total silicon weight per cent. The formation of large chains or large rings was detected early in the reaction. The collected kinetic data were not analyzed in detail but are probably amenable to the statistical treatment herein applied to the D4 MM reorganization [lM= (CH3)3SiOl/,]. Britton and eo-workers first reported the use of acid clays to polymerize dimethyl siloxane^.^ Dimethyldjchlorosilane was converted to a hydrolysis mixture by reaction with water, and the hydrolysis mixture was
+
polymerized using a sulfuric acid treated clay (termed Retrol). Ishzuka and Aihara5 contributed the pioneering publication to clay-catalyzed siloxane rearrangements. A white clay, terra alba, was treated with sulfuric acid, washed, and dried. A mixture of D4 and MM was polymerized a t 80°,and the viscosity rise with time was determined. The equilibrium viscosity was found to be equivalent to the viscosity from a sulfuric acid catalyzed polymerization. A linear correlation between rate and amount of clay was established. With fixed amounts of Dd and MM no change in equilibrium viscosity was noted upon changing catalyst concentration or temperature. Simmler6 has studied the equilibration of methylsiloxanes using as catalyst sulfuric acid treated Fuller's Earth a t 80'. Via terminal group analysis he reported the relative reactivities of methylsiloxanes as D3 > (1) W. T. Grubb and (1955).
R. C. Osthoff, J . Am. Chem. SOC., 7 7 , 1405
(2) 2. Laita and M. Jelinek, Vysokomlekul. Soedin., 4, 1739 (1962). and ref. 1-8 contained therein. (3) K. Moedritzer and J. R. Van Wazer, J . A m . Chem. SOC.,86, 802 (1964). (4) E. C. Britton, H. C. White. and C. Moyle, U. S. Patent 2,460,805 (Feb. 8, 1949). (5) T. Ishauka and T. Aihara, Kogyo Kagaku Zasshi, 59, 1198 (1956). (6) W. Simmler, Makromol. Chem., 57, 12 (1962).
Volume 69. Number 7 July 1966
2214
D4 > RIM > R!IR/I’ > R4’nl’ > RI”M”, where M’ = BrCH2(CH3)2Si0,,,and 34’’ = C1CH2(CH3)i3iOl,,. In this study the distributions of cyclic and linear dimethylsiloxanes were determined during the acid clay catalyzed reaction of D4 and M A 1 a t 80’. Reactant and product analyses were by gas-liquid chroniatography. This technique was previously described for the determination of cyclic distribution in high molecular weight dimethylsiloxane polymer^.^ The fit of the data to the Flory theory*-l0 of random reorganization of the linear species was deterniined as the reaction proceeded.
11. Experimental Materials. Octamethylcyclotetrasiloxane (D4) and hexamethyldisiloxane (MM) were distilled for use as the polymerization species. Chromatographic analyses indicated each material was free of other siloxane impurities. A sulfuric acid treated Fuller’s Earth was used to catalyze the polymerization. Typical analysis: total free moisture = 1% by weight; total so3 = 2.5% by weight. Polymerization Reactions. Amounts of 59.3 g. of D4 and 32.5 g. of A1111 (1: 1 molar ratio) were added to a glass polymerization vessel. The vessel was placed in a double-boiler reactor. Refluxing benzene was maintained in the bottom portion to ensure that the temperature was constant a t 80’. Dow Corning@550 Fluid was used as a heat-transfer fluid in which the polymerization vessel was immersed. After 1 hr. of preheating reactants, 0.4687 g. of catalyst was added. Polymers were analyzed periodically after reaction times of 0.5 to 48 hr. Fractions were obtained by opening the top of the reactor arid sampling the contents with a hypodermic syringe. The fractions were cooled and filtered through no. 1 filter paper to remove the catalyst. All samples were analyzed by qualitative detection of sulfur. No detectable sulfur wa found in any sample. Analysis of Polgnaeys. A standard mixture containing accurately known quantities of toluene, D3 through D6, and M A 1 through MD&I was analyzed using gas-liquid chroniatography. The weight response factors for each cyclic and linear species in the mixture were calculated. The weight response factors for D, through D9 arid 31D,&I through MDI3Mwere obtained by extrapolation. The composition of the standard mixture and weight response factors are given in Table I. A precise amount of toluene was weigihed into each filtered polymer fraction to serve as an internal standard. Area per cents of constituents D3 through D9 and MJf through AID,& were determined from the chromatograph. Weight per cents were obtained The Journal o j Physical Chemistry
JACK B. CARMICHAEL AND JAMES HEFFEL
by multiplying the area per cent by the corresponding weight response factor. Table I : Standard Siloxane Mixture Component
Wt. %
Lineara 6.29 6.76 7.02 7.21 7.34 7.42 7.50 7.55 7.60 7.64
1.14 1.25 1.35 1.44 1.49 1.55 1.64 1.66 1.72 1.77 1.81
1
1.96
Dt Da Db
De.
Cyclics 2.75 7.10 7.89 5.57
1.20 1.35 1.55 1.74
4,367
’ 95 Extrapolated 2.11 1.000
D7
Ds Toluene a
]
Weight response factors based on toluene wt. % toluene = (wt. 70 x ) area of toluene area of x
~
Chromatography Conditions. The F & R l Model 720 linear temperature programmed gas-liquid chromatograph was used for all analyses. The 0-I-nw. Brown recorder was equipped with a Model 201B Disc integrator. Columns used were a matched set, each being 0.61 m. X 0.64 cm. stainless steel packed with 10% LP-122 (diphenylsiloxane-dimethylsiloxane copolymer) on ST-111 (60-80 mesh Chroniasorb P, nontreated). Column temperatures were programmed from 50 to 75 O a t 2O/min., then 15’/min. to 350’.
111. Experimental Results The weight percentages of each linear and cyclic species us. time are plotted in Figures 1-6. Analysis of these data makes several observations clear: (1) equilibrium is reached within 3-17 hr.; (2) good analytical (7) J. B.Carmichael and R. Winger, J . Polymer Sci., Part A, in press. ( 8 ) 1’. J. Flory, J . Am. Chem. Soc., 58, 1877 (1936). (9) P. J. Flory, ibid., 64,2205 (1942). (10) P. J. Flory, Chem. Rev.,39, 137 (1946).
KINETICSOF METHYLSILOXANE POLYMERIZATION
'i
MM
MY
/
I
0 0
+ 2D4 +MDsM
(c)
A graphic illustration of the differences between the equilibrium distribution and the kinetically controlled distribution after 0.5 hr. is depicted hi Figure 6.
40
IO
2215
l
2
4
.
/'
l
l
l
l
l
l
l
l
l
6
8
IO
I2
I4
16
18
20
22
t
24
TIME. HOURS
Figure 1. Disappearance of MM and D4as a function of time.
0
2
4
6
IO
8
I2 I4 TIME HOURS
I8
16
22
ZQ
24
Figure 4. Formation of MDs-13M as a function of time.
0 0
1
1
1
2
4
6
l 8
I
10
1
1
1
1
1
l
1
I2
I4
16
18
20
22
24
't I
TIME. HOURS
Figure 2. Formation of M D I - ~ Mas a function of time.
20
-
I5
.-
4
.
0, 0
0
2
4
6
I
I
8
10
I I I2 Ib TIME. HOURS
I
1
1
IS
18
20
1
*
22
Zb
Figure 5. Formation of D6--7 as a function of time.
WEIGHT. PER CENT
MD3M Y0.M
J Y0,Y
\ 0
0
I
I
I
I
I
2
4
6
8
10
I
I
I
I
I
I
12 I4 TIME, HOURS
16
I8
20
22
24
I
Figure 3. Formation of MDs-sM as a function of time. 0 0
precision was obtained; (3) the early and prominent maxima noted for MDqRIand, to a lesser extent, MDaM indicate that the following net reactions are initially important R'IRI Dq +MD4M (a)
+
and/or
RIDqM
+ Dq +MDsM
(b)
1 1
I 3
I 5
I
I
I
9
NUMBER OF SI A T O M IN MOLECULE
II
, AS
I I3
J
I5
YD,M
Figure 6. Comparison of equilibriiim and kinetically controlled distributions.
IV. Analysis of the Results Adaptation of the Flory
Consider a polymer wherein interchange may occur freely but in which the average chain length is fixed. Volume 69,Number 7 J u l y 1965
JACK B. CARMICHAEL AND JAMES HEFFEL
2216
.
~
~~
~~~
~~
~
~
~~
Table 11: Comparison of Theory and Experiment-Molecular Calcd. Lineara
MM MDM MDIM MDSM
MDaM MDsM MDeM MD,M MDsM MDQM
MI)& MDllM MDllM MD&l
Time! 0.5
30.7 8.2 9.0 9.2 36.3 4.4 3.6 3.1 4.8 1.0 0.7 0.7 0.5 0.2
Weight Distribution (Based on Linear Portion)
Caled.
p =
%
0.58W
diff.
Time, 1
76.4 17.4 60.2 20.6 49.4 17.8 13.80 33.3 10.00 263.0 7.00 37.1 4.70 23.4 0.0 3.10 2.00 140.0 1.30 23.1 0.85 17.6 0.55 27.3 0.35 42.9 0.20 0.0
11.09 9.39 11.14 10.40 18.32 7.54 5.59 4.65 3.43 2.31 1.75 1.30 0.88 0.58
Calcd.
p =
% ’
0.645
12.6 16.4 15.7 13.50 10.95 8.45 6.35 4.70 3.40 2.45 1.75 1.25 0.85 0.60
p =
%
diff.
0.697
diff.
Time, 2
12.0 42.7 29.0 23.0 67.3 10.8 12.0 1.1 0.9 5.7 0.0 4.0 3.5 3.3
8.5 10.48 10.99 10.22 12.19 7.82 6.89 5.52 4.48 3.41 2.68 2.31 1.80 1.10
9.05 12.80 13.40 12.50 10.80 9.10 7.35 5.90 4.60 3.60 2.70 2.10 1.60 1.15
10.0 18.1 18.0 18.2 12.9 14.1 6.3 6.4 2.6 5.3 0.7 10.0 12.5 4.3
6.04 9.76 10.42 10.03 10.36 8.33 7.23 6.25 5.17 4.26 3.44 2.72 2.34 1.71
The weight fraction of x-mer thus obtained is
w,= xp”-’(l
- p)Z
(9
where p is a parameter related to the average degree of Dq polymerization. For the reaction MM
+
p=-
YZ
1
+ yz
(ii)
where y is the average number of D groups in the molecule MD,M as determined by number-average molecular weight by the original ratio of constituents, and z is the fraction of D groups in the linear portion of the polymerizing mixture (i.e., a correction for the total weight per cent cyclics). For siloxane polymers, MM represents a 1-mer. The same equation (i) can be derived in a much simpler manner by considering the random condensation of a difunctional monomer where, once formed, the molecules cannot redistribute.8 The Flory theory assumes no cyclization. However, the theory will apply to the linear species as a separate subset of molecules if the reaction has reached equilibrium.” Here the system does not reach equilibrium for several hours, and the amounts of cyclics change with time. Therefore the weight per cents of linear species were recalculated as per cent by weight of linear species to the exclusion of cyclic constituents. Comparison of Theory and Experiment. The recalculated weight per cents of linear species appear in Table 11. The comparison of theory with experiment was obtained by arbitrarily fitting the experimental weight per cent of BIDJI to the theoretical weight per The Journal of Phyaieal Chemistry
Caled.
Time, 1.5
Theoretical values computed by arbitrarily fitting MDlaM a t each time. average degree of polymerization = (2 - p)/(l - p ) .
Run Time, Wt. %”
us.
Calcd.
p =
%
Time,
p =
%
0.735
diff.
2.9
0.747
diff.
7.05 14.3 10.35 5 . 2 8.2 11.4 11.4 12.0 10.4 0.4 9.00 7 . 4 7.70 6 . 1 6.55 4.6 5.40 4 . 3 4.40 3 . 2 3.55 3.1 2.85 4 . 6 2.25 4 . 0 1.80 5 . 0
‘ Time measured in hours.
6.64 6.40 3 . 8 8.98 9.60 6 . 5 9.73 10.65 8 . 6 9.50 10.70 11.2 8.99 9.90 9 . 2 8 . 0 1 8.90 10.0 7.14 7.80 8 . 5 6.27 6.65 5 . 7 5.26 5.60 6 . 1 4.52 4.65 2 . 8 3.72 3.85 3 . 4 3.01 3.15 2 . 5 2.49 2.50 0 . 4 2.04 2.05 0 . 5
W
=
rpr-l( 1 - p ) z where
cent. The theoretical weight per cents of MM through MDl2Mwere then obtained a t the same value of p from the curves of weight fractions of x-mer for x = 1-14 as a function of p. Curves for x = 5,10, and 20 appear in Flory’s first paper.8 The important conclusions include the following. 1. Maxima occur for the weight percentages of MDM, MD2M, MD&I, and MD4Ma t times of approximately 1.5, 2, 2.5, and 0.5 hr. The maximum at 0.5 hr. for MD4M has been ascribed to opening of D4 followed by termination. The maxima for the other species may be examined by considerations of the random theory. For random polycondensation, as the polymerization reaction proceeds, the amount of a particular polymer builds up to a maximum located at p = (x - 1)/(x 1) then falls away to approach zero as p approaches unity. For x = 2, 3, and 4 the maxima are predicted to occur at values of p = 0.35, 0.5, and 0.6, respectively. However, the values of p which best describe the experimental data are 0.70, 0.73, and approximately 0.74, respectively. The deviation between the two sets of p values is explained as follows. The initial reaction in the polymer is highly nonrandom and leads to the formation of AIDJI. Therefore p increases rapidly. Rearranged small linear species are then produced. Lesser amounts of MDM, IIIDzRI, and MD3M are formed in the early stages of the reaction than if polymerization had occurred by the condensation of (CH&Si(OH)z. 2. After 0.5 hr. a reasonable fit between theory and
+
~~
~~
(11) H. Jacobson and W. H. Stockmayer, J . Chem. Phys., 18, 1600 (1 960).
KINETICS OF METHYLSILOXANE POLYMERIZATION
experiment is obtained for MDsM through MDI3M with the exception of h/ID8RI. This fit means that these large linear species are, to a good approximation, being formed randomly, and their formation is therefore independent of the mechanism of the initiation of the reaction. The overabundance of M D 8 N is due to reactions b and c cited earlier. 3. After 1.0 hr. a good fit is obtained for MDJI through MDl3?tI. Note that by this time MD8M fits the random theory almost exactly. 4. After 1.5 hr. a reasonable fit is obtained for all species. The maximum per cent difference is 18.2. 5. After 2.9 hr. a good fit is obtained for all species. The maximum per cent difference is 11.2.
V. Conclusions The large quantities of MD4M and MD8M formed during the early stages of the reaction indicate that,
2217
when Dq is cleaved by the acid catalyst, it enters the linear molecules as a unit. Reorganization occurs rapidly, so that after 0.5 hr. the distribution of chains R/ID&f through iLlD1&l is approximately random. The distribution of shorter chains becomes increasingly more random as the reaction proceeds until, a t equilibrium, the distribution of all linear species is well explained by a random reorganization model. A corollary to the above conclusions is that the rate constant for propagation of dimethylsiloxanes appears to be approximately independent of molecular size.
Acknowledgment. We wish to acknowledge a helpful discussion with Dr. Chi-long Lee. Mr. Donald Mead distilled the octamethylcyclotetrasiloxane used in this study. We thank Dr. John Speier for crit,icizing the manuscript.
Volume 69,-Vumber 7
Julu 1966
