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Determination of the change in the rate constant for mutual chain termination by the inhibitor method
1198
M . P . B~.~EZlN e t a l .
rate (curve 1), which m a y be explained by the fact that under the conditions corresponding to the rising branch of curve 1 there is an increase in catalyst molecules to which a molecule of 2,6-dimethylphenol is coordinated as an additional ligand. The reducing properties of the complex thus rise and, at the same time, one coordination location remains for the coupling of oxygen. As the concentration of 2,6-dimethylphenol is further increased, the number of catalyst molecules to which two molecules of 2,6-dimethylphenol are coordinated as additional ligands begins to increase, and, as a result of this, the possibility of oxygen being coordinated is reduced and, although the reducing properties of the complex continue to increase, the reaction rate falls. The electron donor properties of methanol and pyridine as additional ligands are less clearly expressed and their inhibiting effect therefore appears at higher concentrations. Translated by G. F. lYIODLE~ REFERENCES 1. I. S. FILATOV, B. I. YUDKIN, B. M. KHLEBNIKOV, O. P. KUKLIN, K. N. OLEINIKOVA, V. P. GRITSEV and V. Ya. FILATOVA, Elektrichestvo 11: 84, 1972 2. W. HANHART and C. K. INHOLD, J. Chem. See., 997, 1927 3. F. BASOLO and R. G. PEARSON, Mekhanizmy neorganicheskikh reaktsii (Mechanisms of Inorganic Reactions). p. 369, Izd. "Mir", 1971 (Russian translation)
DETERMINATION OF THE CHANGE IN THE RATE CONSTANT FOR MUTUAL CHAIN TERMINATION BY THE INHIBITOR METHOD * M. P. BE~Ezr~, L. I. MAKHOI~II~Aand G. V. KOROLEV Chemical Physics Institute, ~.S.S.R.~Academy of Sciences
(Received 7 January 1974) The thermometric method has been used to study the polymerization kinetics of methyl mcthacrylate (MMA) inhibited by trinitrotoluene, at constant initiation rate, wi, and various inhibitor concentrations [X] at 60°C. The inhibition rate constant, /¢inh, has been determined from the Xice equation by two methods: by changing the parameter ~5 that characterizes the ratio of the reduced rate of inhibited polymerization to that of inhibited polymerization, by altering IX] (at zero extent of polymerization), and b y using our proposed change in ~ with extent of polymerization, which involves a change in the rate constant for m u t u a l chain termination, kt, with con* Vysokomol. soyed. A17: No. 5, 1043-1048, 1975.
Change in rate constant for m u t u a l chain termination
1199
version at constant IX] and wx (35.5 and 33.9 1./mole-sec respectively). The values obtained b y us for binh agree satisfactorily b o t h between themselves and also with the d a t a in the literature (bmh----23 1./mole .sec at 44.5°C). A method is proposed for determining the change in kt with extent of polymerization b y altering the parameter ~ as conversion continues. The change in bt with the extent of polymerization of ~ has been measured for the first time (2.5 × 107 at zero degree of conversion to 2.2 × 1051./mole.see. at 500/0 conversion).
THE METHODS at present in existence for determining the change in the rate coustant for mutual chain termination, kt, during polymerization are very laborious [1, 2]. Clearly one m a y determine the change in kt with extent of polymerization by the inhibitor method: one assumes as a basis the Kice equation [3] which the author himself proposed for determining the rate constant for inhibition, k~h, at zero degrees of conversion. I n our view, this method of determining kt with conversion is of additional interest since the study of the change in kt with conversion in inhibited polymerization is generally not carried out. Kice proposes the following equation for the determination of kinh : ¢2 I X ]
kt
1 - - ¢ 2 - - 2kpkin ~
Winh
]~reg kt [M]
[M] -b k¢
kinh '
(1)
which he obtained on the basis of a steady state approximation to the following kinetic scheme: I-~2R" (initiation) 2kuf[I] (2) M~-R'-~I~" (chaitl propagation)
kp[1%']. [M]
(3)
R'A-X-*Z" (transfer or coupling)
~h[1%'] [x]
(4)
Z'A-M-~R' (copolymerization) Z'A- 1%" Z'-~Z" •
R+R"
~ inactive / products
kr0g [z'] [M] kc[z']'[1%] 2k~[z'32 2k~ [1%']2•
(5) (6) (7) (s)
I n equation (1), X is the inhibitor and ¢ is a parameter characterizing the ratio of the reduced rate of inhibited polymerization to that of unhibited polymerization, Winh/W (the notation for the constants may be seen from the kinetic scheme presented above). By changing the parameter ¢ (by changing the inhibitor concentration at a constant initiation rate, or, with the inhibitor concentration [X] held constant, changing wi, or by changing both simultaneously) and by solving equation ( l ) graphically with the coordinates ¢2 [X]/(1 -- ¢2) _ Winh/ /[M], kinh may be determined with known Yalucs of k t and kp from the slope, which is equal to kJ£'pki~h. We propose to use equation (1) to determine kt, drawing attention to the * 2k~Pkt.
1200
M.P. B~.~zi~ et al.
following points. With the inhibited polymerization of oligoesterarylates as an example, it was shown previously [4] that the parameter ¢ changes during polymerization because of a change in the rate constant for mutual chain termination with degree of conversion. Consequently, having determined the parameter experimentally for varying degrees of conversion (~c) and using equation (1), one m a y Mso determine k t at the corresponding degrees of conversion. B u t one m a y evidently determine the change in kt with extent of polymerization from equation (1) up to conversions such that the propagation constant I% remains practically constant. In order that the consumption of [X] with extent of polymerization could be neglected in comparison with the consumption of the monomer, it was necessary to select an inhibitor with a low value of 1%h (as compared with ]%) and a regeneration constant, kreg, close to zero. In using equation (1) to determine the change in kt with extent of polymerization, the second term m a y be neglected since it is considerably smaller than the first [3].* I t is desirable to exclude I% from equation (1) b y substituting, instead of the rate of inhibited polymerization wl~/[M], its value which is equal to
¢-w [M]-=
Ok,w! /ct
(9)
Hence, in order to determine kt with extent of polymerization, equation (1) m a y be written in the final form which we will use hereinafter /~t-- (1-¢X)2w~ '
(10)
where k ~ [X]2/wI is a constant, because of what has been stated above. I t is also desirable to take advantage of the change in the parameter # with extent of polymerization to determine kmh , b y using the following rearrangement of equation (1): ¢~
Wikp¢ c
(I-¢~) [HI
2~h[X] w
@
kro~ .
]ct
ko
k~h[X]
(ll)
I f the graphical solution of this equation in the coordinates
and (1--¢~) [M]. w is represented b y a straight line, on the one hand this will be an indication of the applicability of the Kiee equation when the parameter ~ at constant [X] and wI changes with conversion because of a change in kt, and on the other hand it will be confirmation of the fact that k [X]2/wI in equation (1 O) as a constant * We have also derived the complete equation for the determination of the change in kt with dega'ee of conversion. The contribution of the second term was found to be negligibly small and amounted to only 0.025 %.
C h a n g e i n r a t e c o n s t a n ~ for m u t u a l c h a i n t e r m i n a t i o n
1201
a n d t h a t kp also remains practically unchanged with extent of polymerization. kmh m a y be determined from the slope of the line from the known values of kp, wI and [X]. The polymerization of methyl methaerylate (MMA) was carried out in bulk at 60°0, at a constant initiation rate and a variable inhibitor concentration, in an MK-2 differential calorimetric [5, 6], the sensitivity of the thermopile being 5 × 102 roW. The treatment of the experimental data was carried out by the usual method [5]. The accuracy in the determination of the rates was ?-200/0 . CHA-~GE
IIq TIKE P A ~ & M [ E T E R
(ib W I T H
EXTENT
OF POLY1KERIZ&TIO~
&IqD W I T H
IN'HIBITOR
C O l q C E N T R A . T I Olq
Wtnh . ×
Winh
× l0 s
[M], i x 10 5,
C~
mole/1.
wt.%
Winh
SO0-1
Winh --×
--X
--X
[~
[M7
X 10 s
X 10 5,
I X 105,
see-1
[M7
× l0 s
cp × 10"
× 105, sec-1
SOC-1
]
C o n c e n t r a t i o n of t r i n i t r o t o l u e n e , mole tl. 1 × 10 - I
2.5 × 10 -~
I
5 × 10 -s
I
10 × 10 - t
i
0 i 9"36 5 9"00 10 8"64 12"5 8-45 15"0 8"27 17-5 I 8.07
20
i7.88
22.5 7.69 25 7'49 27.5 7.29 30 "7.08 32.5 6.88 35 6-67 37 "5 6"45 40 6.24 45 5.80 50 i 5"35
4"59 4.70 4-70 4"75 4-80 5"00 5"20 5"50 6"00 6"60 7 "40 8"50 9"40 10"42 11"4 13"4 15'2
!
i
i
87"1 81 "75 80-00 79"61 79"45 79"25 79"28 79"43 77-42 74"16 70'67 66"34 59"37 53"19 47"03 35"31 26.52
3"73 3"80 3"80 3"85 3'87 3"90 4"00 4.13 4.30 4-50 4"75 5"06 5-35 5"60 5.86 6"30 6"60
l ! i
I i !
70.78 66.86 65.25 64"52 61"70 62-77 61"76 59"33 55"38 50"37 45"06 39"67 33"79 28"64 24"24 16"64 11-48
3-16 3.23 3.23 3"24 3"25 3.26 3"27 3"32 3"37 3"42 3"42 3"60 3"72 3"82 3"93 4"13 4"33
59"96 56.64 55.03 54.33 53.42 51.99 50"26 47.61 43.44 38.34 33.20 28.30 23.47 19.53 16.28 10.89 7-54
1.95 1 "94 1-92 1-92 1.92 1.91 1.90 1.88 1-87 1.86 1.85 1.84 1.83 1.83 1.82 1-77 1.62
37.00 33"96 32.64 32.12 31-51 30.45 29.15 27.03 24-19 20-80 17.55 14.44 11"58 9.36 7.55 4"68 2.97
MM_A was subjected to purification and further prepolymerization [7]. I n order to carry out an experiment, the pure monomer was over-frozen in a vacuum installation from the ampoule containing the "syrup" (the solution of the polymer, formed during prepolymerization, in the monomer) into the working ampoule where the initiator and inhibitor were introduced. The solution was vacuum treated and the ampoule sealed off. The degree of purification was monitored kinetically. The initiator, azo-bis-isobutyronitrile (ABIN), was purified by reerystallization from ethanol, benzene and acetonate, melting point, 103°C; ,trinitrotoluene was purified by recrystallization from ethanol, melting point, 80.5-81°C.
1202
M . P . BEm~zIy, et al.
The experimental data obtained are shown in the Table* and in Fig. 1-4. The rate constants for mutual termination during the course of polymerization were determined from equation (10) by using the experimental data in the Table. B u t it follows from equation (10) that, in order to determine kt with extent o f polymerization, it is necessary to know the value of the constant term k~nh [X]2/wI.
A ',I) .% ~
¢e [xJ 10_e,~oze/l. l_¢Z
1 /
0"2~-10
a
'
4 15
03 o o
0"15 7
O.l
0.2
;
3
10
OO5
04
--0.1
0.3
0.5 [MJ ,~ec
]~IG, 1
05
0.5 1
1.0
1.5(z,2,3) 7(~/w)qa-2&)
q I~IG. 2
FIG. 1. Dependence of ¢*[X]/1--¢2 on wl~h/[M]in the case of trinitrotoluene. FIo. 2. Dependence of ¢*/(1--¢ 2) [Mr] (A, L/mole) on ¢/w (1.-sec/mole).Concentration of trinitrotoluene: 1 - - 1 × 10-s; 2 - - 2.5 × 10-2; 3 - - 5 × 10-2; 4 - - 10 × 10-2 mole/1. It is shown on the axes to which curves the various scales relate. I t is always desirable t h a t the values introduced into an equation should be determined (if this is possible) under the conditions of the experiment performed. The determination of kl~h for the polymerization of MMA inhibited by trinitrotoluene is presented below (kxnh for this case is equal to 23 1./mole. sec at 44.5°C
D]). The inhibition rate constant for the polymerization of MMA inhibited by trinitrotoluene was determined by two methods: from equation (1) by altering the parameter ¢ (at zero extent of polymerization) by changing the trinitrotoluene concentration from 1 × 10 -2 to 10X 10 -2 mole/1, with a constant rate of initiation; and from equation (11) by using the change in ~ with degree of con* The current monomer concentration in the Table is calculated to take account of the contraction of the polymerizing mixture.
Change in rate constant for mutual chain termination
1203
version caused b y the change in the rate constant for m u t u a l chain t e r m i n a t i o n during polymerization [2, 4] at constant [X] and w I. For example, w i t h [X] 1 × 10-2 mole/1, the parameter ¢ is equal to 0.87 at zero degree of conversion but, at C = 5 0 % , it falls to 0.26 (see Table). The value of kinh, determined from t h e slope of the line in Fig. 1, is equal to 35.5 1./mole • see at zero degree of conversion (kt and kp are equal to 2-4× 10 -7 and 573 respectively [8]). I t follows from Fig. 1 t h a t , under the conditions of our experiment, the intercept was equal to 4.4X 10 -a mole/1, in satisfactory agreement w i t h the d a t a of other work [3].
Io~ J ti.h -z; M]
7
-
2"5
i
2"0 ~6
×
1"5
1.0
5
1 lO
I
I 30 Fro. 3
I
I 50 0,%
0"8
I 10
t 30
I 50 0,%
Fro. 4
FIO. 3. Dependence of log kt OI1 C, %. Concentration of trinitrotoluene: 1--0 (plotted from the data in [2]); 2 q l × 10-~; 3--2.5)< 10-2; 4--5X 10-2; 5--10X 10 -3 mole/1. Fro. 4. Dependence of log wtnh/[M'] on C, %. Concentration of trinitrotoluene; 1 -- 0; 2-- 1 × 10-s; 3--2.5 × 10-~; 4--5 × 10-3; 5--10 X 10-~ mole/1. I n solving equation (11) graphically w i t h the coordinates q~c/(1--~2) [5I] a n d ¢P¢/w, a series of straight lines was obtained passing t h r o u g h the coordinate origin (each concentration [X] gives rise to its own slope) (Fig. 2). The values of kinh, d e t e r m i n e d from the slopes of the lines (Fig. 2), are equal to 38.4, 38.0, 29 a n d 30 1./mole. sec for trinitrotoluene concentrations of 1 X 10 -2, 2.5 x 10 -2, 5 × 10 -2 a n d 10 × 10 -2 mole/1. I t m a y be considered t h a t , in the region of concentrations [X] investigated, there is satisfactory agreement between these various values of k~,h, a n d the average value o f k ~ , 33.9 1./mole • see, agrees well with the value of k ~ , 35-5 1./mole.see, determined from equation (1) a t zero degree of conversion.
1204
M . P . BE~EZr~ et al.
The initiation rate in the polymerization of ~ M A by azo-bis-isobutyronitrile, determined by the inhibitor method (in this case the iminoxyl free radical was used for this purrose as inhibitor) was equal to 2 × 10-7 mole/1..sec. Determination of the change in k t with extent of polymerization. Having data determined experimentally from the change in the parameter ~b with degree of conversion and substituting them, together with the values of k~h and wi, determined under the conditions of our experiment, into equation (10), we found the corresponding value of kt (Fig. 3) for each ¢ (and consequently for each degree of conversion as well). I t follows from Fig. 3 that the values of kt are practically the same during the course of the polymerization within the region of trinitrotoluene concentrations investigated, varying from 2.5 × 107 (at zero extent of polymerization) to 2-2X 105 1./mole.sec (at 50% extent of polymerization). Two sections are found on the curves: up to a degree of conversion, C, of approximately 23% (in our case, the conversion corresponding to the start of autoacceleration), the decrease in k t with conversion is smooth, but after a value of C of approximately 23%, more abrupt. The same Figure also gives (curve 1) the change in kt for the uninhibited polymerization of MMA (plotted from the data in [2]). It follows from a comparison of curve 1 (for uninhibited polymerization of ]MMA) with curves 2-5 (for inhibited polymerization) t h a t the characteristics of the decrease in kt, and even the values themselves, are practically the same in two cases at the same values of conversion. The fact t h a t the values of k t are the same, independently of the inhibitor concentration at a specified degree of conversion, m a y appear strange at first sight, since there are statements in the literature to the effect that the rate constant for mutual chain termination depends on molecular weight [2]. But as we introduce a greater inhibitor concentration, a polymer must be formed with a progressively lower molecular weight as compared with, for example, the polymer at the same conversion in uninhibited polymerization. But let us refer to Fig. 4 which shows t h e dependence of the reduced rate on extent of polymerization plotted in logarithmic coordinates. I t has been shown [9] that a change in slope of the curve in these coordinates is evidence that the gel effect begins at this conversion. This change in slope denotes the gel point. I t follows from a consideration of the curves in Fig. 4 that, in all cases independently of the inhibitor concentration, t h e gel point sets in at practically the same degree of conversion, namely, approximately 23%, a fact which m a y be explained in the following way. The facts at present accumulated enable it to be suggested that, in processes limited by the progressive diffusion of macromolecules, the true molecular weight of the polymeric chains m a y not be apparent but rather the molecular weight of aggregates, ff the forces of aggregation are sufficiently strong (if, as it were, cross]lulling occurs through strongly localized intermoleeular interactions, for example, through strong polar interactions between fragments of the trinitrotoluene inhibitor incorporated into the polymeric chains). Thus the decrease in the true molecular weight as the inhibitor concentration is increased will be comport-
Reactions of TMT with alkyl(aryl)dimethoxysilanes
1205
sated for by an increase in the number of "crosslinks" (since the number of trinitrotoluene fragments incorporated into the chain will increase as the concentration is increased because of the occurrence of chain regeneration), so that the "effective molecular weight" will remain approximately constant. Translated by G. F. MODLEN REFERENCES
1. G. E. HAM (Ed.), Polimerizatsiya vinilovykh monomerov (Polymerization of Vinyl Monomers). p. 161, Izd. "Khimiya", 1973 (Russian translation) 2. P. HAYDEN and H. W. MELVILLE, J. Polymer Sci. 43: 201, 1960 3. J. L. KICE, J. Amer. Chem. Soc. 76: 2674, 1954 4. G. V. KOROLEV and L. I. MAKHONINA, Vysokomol. soyed. A1O: 1245, 1968 (Translated in Polymer Sei. U.S.S,R. 10: 2, 288, 1968) 5. E. CALVET and A. PRATT, Mikrokalorimetriya (Microcalorimetry) Izd. inostr, lit., 1963 (Russian translation) 6. O. S. GALYUK, Yu. I. RUBTSOV, G. F. MALINOVSKAYA and G. B. MANELIS, Zh. fiz. khimii 39: 2319, 1965 7. C. H. BAMFORD and P. R. MORRIS, Makromolek. Chem. 7: 73, 1965 8. Kh. S. BAGDASAR'YAN, Teoriya radikal'noi polimerizatsii (Theory of Radical Polymerization), p. 119, Izd. "Nauka", 1967 9. O. A. EDEL'SHTEIN, B. R. SMIRNOV, V. P. GRACHEV and G. V. KOROLEV, Sb. Khimiya aromaticheskikh i nepredel'nykh soyedinenii (Collection: Chemistry of Aremated and Unsaturated Compounds), Izd. Irkutskogo Un-ta, 1971
THE REACTIONS OF TETRAKIS(TRIMETHYLSILOXY)TITANIUM WITH ALKYL(ARYL)DIMETHOXYSILANES AND a,co-DIHYDROXYPOLYDIMETHYLSILOXANES* K.A. ANDRIANOV, •. A. KURASHEVA, L. I. KUTEINIKOVA and B. D. LAVRUKHIN Organometal Compounds Institute, TJ.S.S.R. Academy of Sciences
(Received 11 January 1974) The reactions of tetrakis-(trimethylsiloxy)titanium with vinyl methyl-, methyl phenyl-, diphenyl methoxysilanes, and ~,co-dihydroxypolydimethylsiloxanes (DHPDMSiO) of general formula HO[Si(ClCI3)~OJ~H, in which n = 15, 60 or 100, were studied at ratios of 1 : 1 and 1 : 2 of the components; some of the properties of the resulting polymers have been examined. * Vysokomol. soyed. A17: No. 5, 1049-1053, 1975.
M . P . B~.~EZlN e t a l .
rate (curve 1), which m a y be explained by the fact that under the conditions corresponding to the rising branch of curve 1 there is an increase in catalyst molecules to which a molecule of 2,6-dimethylphenol is coordinated as an additional ligand. The reducing properties of the complex thus rise and, at the same time, one coordination location remains for the coupling of oxygen. As the concentration of 2,6-dimethylphenol is further increased, the number of catalyst molecules to which two molecules of 2,6-dimethylphenol are coordinated as additional ligands begins to increase, and, as a result of this, the possibility of oxygen being coordinated is reduced and, although the reducing properties of the complex continue to increase, the reaction rate falls. The electron donor properties of methanol and pyridine as additional ligands are less clearly expressed and their inhibiting effect therefore appears at higher concentrations. Translated by G. F. lYIODLE~ REFERENCES 1. I. S. FILATOV, B. I. YUDKIN, B. M. KHLEBNIKOV, O. P. KUKLIN, K. N. OLEINIKOVA, V. P. GRITSEV and V. Ya. FILATOVA, Elektrichestvo 11: 84, 1972 2. W. HANHART and C. K. INHOLD, J. Chem. See., 997, 1927 3. F. BASOLO and R. G. PEARSON, Mekhanizmy neorganicheskikh reaktsii (Mechanisms of Inorganic Reactions). p. 369, Izd. "Mir", 1971 (Russian translation)
DETERMINATION OF THE CHANGE IN THE RATE CONSTANT FOR MUTUAL CHAIN TERMINATION BY THE INHIBITOR METHOD * M. P. BE~Ezr~, L. I. MAKHOI~II~Aand G. V. KOROLEV Chemical Physics Institute, ~.S.S.R.~Academy of Sciences
(Received 7 January 1974) The thermometric method has been used to study the polymerization kinetics of methyl mcthacrylate (MMA) inhibited by trinitrotoluene, at constant initiation rate, wi, and various inhibitor concentrations [X] at 60°C. The inhibition rate constant, /¢inh, has been determined from the Xice equation by two methods: by changing the parameter ~5 that characterizes the ratio of the reduced rate of inhibited polymerization to that of inhibited polymerization, by altering IX] (at zero extent of polymerization), and b y using our proposed change in ~ with extent of polymerization, which involves a change in the rate constant for m u t u a l chain termination, kt, with con* Vysokomol. soyed. A17: No. 5, 1043-1048, 1975.
Change in rate constant for m u t u a l chain termination
1199
version at constant IX] and wx (35.5 and 33.9 1./mole-sec respectively). The values obtained b y us for binh agree satisfactorily b o t h between themselves and also with the d a t a in the literature (bmh----23 1./mole .sec at 44.5°C). A method is proposed for determining the change in kt with extent of polymerization b y altering the parameter ~ as conversion continues. The change in bt with the extent of polymerization of ~ has been measured for the first time (2.5 × 107 at zero degree of conversion to 2.2 × 1051./mole.see. at 500/0 conversion).
THE METHODS at present in existence for determining the change in the rate coustant for mutual chain termination, kt, during polymerization are very laborious [1, 2]. Clearly one m a y determine the change in kt with extent of polymerization by the inhibitor method: one assumes as a basis the Kice equation [3] which the author himself proposed for determining the rate constant for inhibition, k~h, at zero degrees of conversion. I n our view, this method of determining kt with conversion is of additional interest since the study of the change in kt with conversion in inhibited polymerization is generally not carried out. Kice proposes the following equation for the determination of kinh : ¢2 I X ]
kt
1 - - ¢ 2 - - 2kpkin ~
Winh
]~reg kt [M]
[M] -b k¢
kinh '
(1)
which he obtained on the basis of a steady state approximation to the following kinetic scheme: I-~2R" (initiation) 2kuf[I] (2) M~-R'-~I~" (chaitl propagation)
kp[1%']. [M]
(3)
R'A-X-*Z" (transfer or coupling)
~h[1%'] [x]
(4)
Z'A-M-~R' (copolymerization) Z'A- 1%" Z'-~Z" •
R+R"
~ inactive / products
kr0g [z'] [M] kc[z']'[1%] 2k~[z'32 2k~ [1%']2•
(5) (6) (7) (s)
I n equation (1), X is the inhibitor and ¢ is a parameter characterizing the ratio of the reduced rate of inhibited polymerization to that of unhibited polymerization, Winh/W (the notation for the constants may be seen from the kinetic scheme presented above). By changing the parameter ¢ (by changing the inhibitor concentration at a constant initiation rate, or, with the inhibitor concentration [X] held constant, changing wi, or by changing both simultaneously) and by solving equation ( l ) graphically with the coordinates ¢2 [X]/(1 -- ¢2) _ Winh/ /[M], kinh may be determined with known Yalucs of k t and kp from the slope, which is equal to kJ£'pki~h. We propose to use equation (1) to determine kt, drawing attention to the * 2k~Pkt.
1200
M.P. B~.~zi~ et al.
following points. With the inhibited polymerization of oligoesterarylates as an example, it was shown previously [4] that the parameter ¢ changes during polymerization because of a change in the rate constant for mutual chain termination with degree of conversion. Consequently, having determined the parameter experimentally for varying degrees of conversion (~c) and using equation (1), one m a y Mso determine k t at the corresponding degrees of conversion. B u t one m a y evidently determine the change in kt with extent of polymerization from equation (1) up to conversions such that the propagation constant I% remains practically constant. In order that the consumption of [X] with extent of polymerization could be neglected in comparison with the consumption of the monomer, it was necessary to select an inhibitor with a low value of 1%h (as compared with ]%) and a regeneration constant, kreg, close to zero. In using equation (1) to determine the change in kt with extent of polymerization, the second term m a y be neglected since it is considerably smaller than the first [3].* I t is desirable to exclude I% from equation (1) b y substituting, instead of the rate of inhibited polymerization wl~/[M], its value which is equal to
¢-w [M]-=
Ok,w! /ct
(9)
Hence, in order to determine kt with extent of polymerization, equation (1) m a y be written in the final form which we will use hereinafter /~t-- (1-¢X)2w~ '
(10)
where k ~ [X]2/wI is a constant, because of what has been stated above. I t is also desirable to take advantage of the change in the parameter # with extent of polymerization to determine kmh , b y using the following rearrangement of equation (1): ¢~
Wikp¢ c
(I-¢~) [HI
2~h[X] w
@
kro~ .
]ct
ko
k~h[X]
(ll)
I f the graphical solution of this equation in the coordinates
and (1--¢~) [M]. w is represented b y a straight line, on the one hand this will be an indication of the applicability of the Kiee equation when the parameter ~ at constant [X] and wI changes with conversion because of a change in kt, and on the other hand it will be confirmation of the fact that k [X]2/wI in equation (1 O) as a constant * We have also derived the complete equation for the determination of the change in kt with dega'ee of conversion. The contribution of the second term was found to be negligibly small and amounted to only 0.025 %.
C h a n g e i n r a t e c o n s t a n ~ for m u t u a l c h a i n t e r m i n a t i o n
1201
a n d t h a t kp also remains practically unchanged with extent of polymerization. kmh m a y be determined from the slope of the line from the known values of kp, wI and [X]. The polymerization of methyl methaerylate (MMA) was carried out in bulk at 60°0, at a constant initiation rate and a variable inhibitor concentration, in an MK-2 differential calorimetric [5, 6], the sensitivity of the thermopile being 5 × 102 roW. The treatment of the experimental data was carried out by the usual method [5]. The accuracy in the determination of the rates was ?-200/0 . CHA-~GE
IIq TIKE P A ~ & M [ E T E R
(ib W I T H
EXTENT
OF POLY1KERIZ&TIO~
&IqD W I T H
IN'HIBITOR
C O l q C E N T R A . T I Olq
Wtnh . ×
Winh
× l0 s
[M], i x 10 5,
C~
mole/1.
wt.%
Winh
SO0-1
Winh --×
--X
--X
[~
[M7
X 10 s
X 10 5,
I X 105,
see-1
[M7
× l0 s
cp × 10"
× 105, sec-1
SOC-1
]
C o n c e n t r a t i o n of t r i n i t r o t o l u e n e , mole tl. 1 × 10 - I
2.5 × 10 -~
I
5 × 10 -s
I
10 × 10 - t
i
0 i 9"36 5 9"00 10 8"64 12"5 8-45 15"0 8"27 17-5 I 8.07
20
i7.88
22.5 7.69 25 7'49 27.5 7.29 30 "7.08 32.5 6.88 35 6-67 37 "5 6"45 40 6.24 45 5.80 50 i 5"35
4"59 4.70 4-70 4"75 4-80 5"00 5"20 5"50 6"00 6"60 7 "40 8"50 9"40 10"42 11"4 13"4 15'2
!
i
i
87"1 81 "75 80-00 79"61 79"45 79"25 79"28 79"43 77-42 74"16 70'67 66"34 59"37 53"19 47"03 35"31 26.52
3"73 3"80 3"80 3"85 3'87 3"90 4"00 4.13 4.30 4-50 4"75 5"06 5-35 5"60 5.86 6"30 6"60
l ! i
I i !
70.78 66.86 65.25 64"52 61"70 62-77 61"76 59"33 55"38 50"37 45"06 39"67 33"79 28"64 24"24 16"64 11-48
3-16 3.23 3.23 3"24 3"25 3.26 3"27 3"32 3"37 3"42 3"42 3"60 3"72 3"82 3"93 4"13 4"33
59"96 56.64 55.03 54.33 53.42 51.99 50"26 47.61 43.44 38.34 33.20 28.30 23.47 19.53 16.28 10.89 7-54
1.95 1 "94 1-92 1-92 1.92 1.91 1.90 1.88 1-87 1.86 1.85 1.84 1.83 1.83 1.82 1-77 1.62
37.00 33"96 32.64 32.12 31-51 30.45 29.15 27.03 24-19 20-80 17.55 14.44 11"58 9.36 7.55 4"68 2.97
MM_A was subjected to purification and further prepolymerization [7]. I n order to carry out an experiment, the pure monomer was over-frozen in a vacuum installation from the ampoule containing the "syrup" (the solution of the polymer, formed during prepolymerization, in the monomer) into the working ampoule where the initiator and inhibitor were introduced. The solution was vacuum treated and the ampoule sealed off. The degree of purification was monitored kinetically. The initiator, azo-bis-isobutyronitrile (ABIN), was purified by reerystallization from ethanol, benzene and acetonate, melting point, 103°C; ,trinitrotoluene was purified by recrystallization from ethanol, melting point, 80.5-81°C.
1202
M . P . BEm~zIy, et al.
The experimental data obtained are shown in the Table* and in Fig. 1-4. The rate constants for mutual termination during the course of polymerization were determined from equation (10) by using the experimental data in the Table. B u t it follows from equation (10) that, in order to determine kt with extent o f polymerization, it is necessary to know the value of the constant term k~nh [X]2/wI.
A ',I) .% ~
¢e [xJ 10_e,~oze/l. l_¢Z
1 /
0"2~-10
a
'
4 15
03 o o
0"15 7
O.l
0.2
;
3
10
OO5
04
--0.1
0.3
0.5 [MJ ,~ec
]~IG, 1
05
0.5 1
1.0
1.5(z,2,3) 7(~/w)qa-2&)
q I~IG. 2
FIG. 1. Dependence of ¢*[X]/1--¢2 on wl~h/[M]in the case of trinitrotoluene. FIo. 2. Dependence of ¢*/(1--¢ 2) [Mr] (A, L/mole) on ¢/w (1.-sec/mole).Concentration of trinitrotoluene: 1 - - 1 × 10-s; 2 - - 2.5 × 10-2; 3 - - 5 × 10-2; 4 - - 10 × 10-2 mole/1. It is shown on the axes to which curves the various scales relate. I t is always desirable t h a t the values introduced into an equation should be determined (if this is possible) under the conditions of the experiment performed. The determination of kl~h for the polymerization of MMA inhibited by trinitrotoluene is presented below (kxnh for this case is equal to 23 1./mole. sec at 44.5°C
D]). The inhibition rate constant for the polymerization of MMA inhibited by trinitrotoluene was determined by two methods: from equation (1) by altering the parameter ¢ (at zero extent of polymerization) by changing the trinitrotoluene concentration from 1 × 10 -2 to 10X 10 -2 mole/1, with a constant rate of initiation; and from equation (11) by using the change in ~ with degree of con* The current monomer concentration in the Table is calculated to take account of the contraction of the polymerizing mixture.
Change in rate constant for mutual chain termination
1203
version caused b y the change in the rate constant for m u t u a l chain t e r m i n a t i o n during polymerization [2, 4] at constant [X] and w I. For example, w i t h [X] 1 × 10-2 mole/1, the parameter ¢ is equal to 0.87 at zero degree of conversion but, at C = 5 0 % , it falls to 0.26 (see Table). The value of kinh, determined from t h e slope of the line in Fig. 1, is equal to 35.5 1./mole • see at zero degree of conversion (kt and kp are equal to 2-4× 10 -7 and 573 respectively [8]). I t follows from Fig. 1 t h a t , under the conditions of our experiment, the intercept was equal to 4.4X 10 -a mole/1, in satisfactory agreement w i t h the d a t a of other work [3].
Io~ J ti.h -z; M]
7
-
2"5
i
2"0 ~6
×
1"5
1.0
5
1 lO
I
I 30 Fro. 3
I
I 50 0,%
0"8
I 10
t 30
I 50 0,%
Fro. 4
FIO. 3. Dependence of log kt OI1 C, %. Concentration of trinitrotoluene: 1--0 (plotted from the data in [2]); 2 q l × 10-~; 3--2.5)< 10-2; 4--5X 10-2; 5--10X 10 -3 mole/1. Fro. 4. Dependence of log wtnh/[M'] on C, %. Concentration of trinitrotoluene; 1 -- 0; 2-- 1 × 10-s; 3--2.5 × 10-~; 4--5 × 10-3; 5--10 X 10-~ mole/1. I n solving equation (11) graphically w i t h the coordinates q~c/(1--~2) [5I] a n d ¢P¢/w, a series of straight lines was obtained passing t h r o u g h the coordinate origin (each concentration [X] gives rise to its own slope) (Fig. 2). The values of kinh, d e t e r m i n e d from the slopes of the lines (Fig. 2), are equal to 38.4, 38.0, 29 a n d 30 1./mole. sec for trinitrotoluene concentrations of 1 X 10 -2, 2.5 x 10 -2, 5 × 10 -2 a n d 10 × 10 -2 mole/1. I t m a y be considered t h a t , in the region of concentrations [X] investigated, there is satisfactory agreement between these various values of k~,h, a n d the average value o f k ~ , 33.9 1./mole • see, agrees well with the value of k ~ , 35-5 1./mole.see, determined from equation (1) a t zero degree of conversion.
1204
M . P . BE~EZr~ et al.
The initiation rate in the polymerization of ~ M A by azo-bis-isobutyronitrile, determined by the inhibitor method (in this case the iminoxyl free radical was used for this purrose as inhibitor) was equal to 2 × 10-7 mole/1..sec. Determination of the change in k t with extent of polymerization. Having data determined experimentally from the change in the parameter ~b with degree of conversion and substituting them, together with the values of k~h and wi, determined under the conditions of our experiment, into equation (10), we found the corresponding value of kt (Fig. 3) for each ¢ (and consequently for each degree of conversion as well). I t follows from Fig. 3 that the values of kt are practically the same during the course of the polymerization within the region of trinitrotoluene concentrations investigated, varying from 2.5 × 107 (at zero extent of polymerization) to 2-2X 105 1./mole.sec (at 50% extent of polymerization). Two sections are found on the curves: up to a degree of conversion, C, of approximately 23% (in our case, the conversion corresponding to the start of autoacceleration), the decrease in k t with conversion is smooth, but after a value of C of approximately 23%, more abrupt. The same Figure also gives (curve 1) the change in kt for the uninhibited polymerization of MMA (plotted from the data in [2]). It follows from a comparison of curve 1 (for uninhibited polymerization of ]MMA) with curves 2-5 (for inhibited polymerization) t h a t the characteristics of the decrease in kt, and even the values themselves, are practically the same in two cases at the same values of conversion. The fact t h a t the values of k t are the same, independently of the inhibitor concentration at a specified degree of conversion, m a y appear strange at first sight, since there are statements in the literature to the effect that the rate constant for mutual chain termination depends on molecular weight [2]. But as we introduce a greater inhibitor concentration, a polymer must be formed with a progressively lower molecular weight as compared with, for example, the polymer at the same conversion in uninhibited polymerization. But let us refer to Fig. 4 which shows t h e dependence of the reduced rate on extent of polymerization plotted in logarithmic coordinates. I t has been shown [9] that a change in slope of the curve in these coordinates is evidence that the gel effect begins at this conversion. This change in slope denotes the gel point. I t follows from a consideration of the curves in Fig. 4 that, in all cases independently of the inhibitor concentration, t h e gel point sets in at practically the same degree of conversion, namely, approximately 23%, a fact which m a y be explained in the following way. The facts at present accumulated enable it to be suggested that, in processes limited by the progressive diffusion of macromolecules, the true molecular weight of the polymeric chains m a y not be apparent but rather the molecular weight of aggregates, ff the forces of aggregation are sufficiently strong (if, as it were, cross]lulling occurs through strongly localized intermoleeular interactions, for example, through strong polar interactions between fragments of the trinitrotoluene inhibitor incorporated into the polymeric chains). Thus the decrease in the true molecular weight as the inhibitor concentration is increased will be comport-
Reactions of TMT with alkyl(aryl)dimethoxysilanes
1205
sated for by an increase in the number of "crosslinks" (since the number of trinitrotoluene fragments incorporated into the chain will increase as the concentration is increased because of the occurrence of chain regeneration), so that the "effective molecular weight" will remain approximately constant. Translated by G. F. MODLEN REFERENCES
1. G. E. HAM (Ed.), Polimerizatsiya vinilovykh monomerov (Polymerization of Vinyl Monomers). p. 161, Izd. "Khimiya", 1973 (Russian translation) 2. P. HAYDEN and H. W. MELVILLE, J. Polymer Sci. 43: 201, 1960 3. J. L. KICE, J. Amer. Chem. Soc. 76: 2674, 1954 4. G. V. KOROLEV and L. I. MAKHONINA, Vysokomol. soyed. A1O: 1245, 1968 (Translated in Polymer Sei. U.S.S,R. 10: 2, 288, 1968) 5. E. CALVET and A. PRATT, Mikrokalorimetriya (Microcalorimetry) Izd. inostr, lit., 1963 (Russian translation) 6. O. S. GALYUK, Yu. I. RUBTSOV, G. F. MALINOVSKAYA and G. B. MANELIS, Zh. fiz. khimii 39: 2319, 1965 7. C. H. BAMFORD and P. R. MORRIS, Makromolek. Chem. 7: 73, 1965 8. Kh. S. BAGDASAR'YAN, Teoriya radikal'noi polimerizatsii (Theory of Radical Polymerization), p. 119, Izd. "Nauka", 1967 9. O. A. EDEL'SHTEIN, B. R. SMIRNOV, V. P. GRACHEV and G. V. KOROLEV, Sb. Khimiya aromaticheskikh i nepredel'nykh soyedinenii (Collection: Chemistry of Aremated and Unsaturated Compounds), Izd. Irkutskogo Un-ta, 1971
THE REACTIONS OF TETRAKIS(TRIMETHYLSILOXY)TITANIUM WITH ALKYL(ARYL)DIMETHOXYSILANES AND a,co-DIHYDROXYPOLYDIMETHYLSILOXANES* K.A. ANDRIANOV, •. A. KURASHEVA, L. I. KUTEINIKOVA and B. D. LAVRUKHIN Organometal Compounds Institute, TJ.S.S.R. Academy of Sciences
(Received 11 January 1974) The reactions of tetrakis-(trimethylsiloxy)titanium with vinyl methyl-, methyl phenyl-, diphenyl methoxysilanes, and ~,co-dihydroxypolydimethylsiloxanes (DHPDMSiO) of general formula HO[Si(ClCI3)~OJ~H, in which n = 15, 60 or 100, were studied at ratios of 1 : 1 and 1 : 2 of the components; some of the properties of the resulting polymers have been examined. * Vysokomol. soyed. A17: No. 5, 1049-1053, 1975.