The polymerization of trioxan in cyclohexane

The polymerization of trioxan in cyclohexane

European Polymer Journal, 1965, Vol. 1, pp. 133-145. Pergamon Press Ltd. Printed in England THE POLYMERIZATION OF TRIOXAN IN CYCLOHEXANE P. F. Ore'ON...

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European Polymer Journal, 1965, Vol. 1, pp. 133-145. Pergamon Press Ltd. Printed in England

THE POLYMERIZATION OF TRIOXAN IN CYCLOHEXANE P. F. Ore'ON and K. J. TAYLOR Research Laboratories, B.I.P. Chemicals Ltd., Oldbury, Birmingham, England

(Received23 October 1964) Abstract. The polymerization of trioxan, initiated by boron trifluoride n-butyl etherate, has been studied in cyclohexane solution at 50 °, 65 ° and 70 °. Correlations have been obtained between the yields and inherent viscosities of the polymer and the main reaction variables. Increasing the concentration of initiator results in larger yields of polymer but has little effect on inherent viscosity, whereas both higher yields and higher inherent viscosities are obtained when the monomer concentration is increased. Expressions derived from kinetic considerations enable the course of the reaction to be accurately predicted over the entire conversion range, within the temperature limits studied. The importance of terminating reactions in determining the kinetics has been demonstrated but the exact nature of these reactions remains uncertain. A number of complicating features of the system, such as heterogeneity and dielectric constant effects, preclude elucidation of the mechanism on the basis of kinetic evidence alone and additional techniques must be utilized if a complete understanding of the reaction is to be achieved. ALTHOUGH various processes for the polymerization of trioxan in the presence of cationic initiators are described in patents,0) very few detailed investigations of such systems have been reported in the literature, t2-5) and satisfactory kinetic interpretations of the reaction are still lacking. The present study of trioxan polymerization in cyclohexane was undertaken with the object of correlating the course of reaction with certain reaction variables; this aim has been achieved and quantitative data have been obtained which enable the validity of assumed kinetic schemes to be tested. However, as will become apparent, consideration of a number of plausible schemes leads to the conclusion that kinetic measurements must be supplemented by other evidence if the mechanism o f the reaction is to be elucidated with any degree of certainty. At temperatures below or near its melting point, and upon addition of small amounts of Lewis acids, trioxan polymerizes readily to polyoxymethylene of high molecular weight. Polymerization may be carried out in an inert diluent, as this affords a more easily handled product and serves to moderate the exothermicity, but it is found that the course of the reaction is influenced by the nature of the diluent and also by the presence of trace contaminants. Consequently it is necessary to subject both the monomer and diluent to careful purification in order to obtain reproducible conversions. Polymer precipitates as it is formed and, with certain initiators, or if purification has not been fully effective, substantial induction periods may be observed. These and other features of the reaction, typical of many ionic polymerizations, add to the difficulties of kinetic evaluation and interpretation. Nevertheless, by means of a relatively simple gravimetric technique, the course of reaction can be followed sufficiently well to allow the influence o f the main reaction parameters to be assessed. In this work the polymerization of trioxan in cyclohexane has been investigated, mainly at 65 °, over a range of monomer and initiator concentrations using boron trifluoride dibutyletherate as initiator. The latter was chosen because it is reasonably 133

134

P.F.

O N Y O N and K. J. T A Y L O R

s t a b l e , is s o l u b l e i n t h e r e a c t i o n m i x t u r e a n d d o e s n o t n o r m a l l y give rise t o i n d u c t i o n p e r i o d s . T h e c h o i c e o f s o l v e n t w a s d i c t a t e d b y t h e f a c t t h a t it c a n b e o b t a i n e d i n a r e l a t i v e l y p u r e s t a t e a n d it is a l s o m i s c i b l e w i t h t h e m o n o m e r i n all p r o p o r t i o n s a t t e m p e r a t u r e s a b o v e 60 ° . EXPERIMENTAL Materials Trioxan (Celanese Corporation, 99 per cent Grade) was purified, first by distillation over stearylamine and then by fractionation over stearylamine and barium oxide through a 2-ft column packed with Fenske helices, the first 10 per cent of the distillate being discarded. The water content of the distilled material was less than 0.01 per cent as measured by Karl Fischer titration. Cyclohexane (Howards, Standard Grade) was distilled from barium oxide through a similar column, the product having a boiling range of 80-81 ° and a water content of less than 0-005 per cent. The initial 10 per cent cut and final 20 per cent residue were not used. BF3 di-n-butyl etherate was prepared by passing BF3 gas through the ether and purified by vacuum distillation. Polymerization procedure

Known amounts of trioxan, followed by cyclohexane, were distilled into a reaction flask fitted with a reflux condenser, a high speed stainless steel stirrer, a thermocouple pocket and a sampling inlet. Quantities were estimated by differential weighing. The flask and its contents were maintained at the reaction temperature by thermostatically controlled heating jackets. Initiator, in the form of a 50~o solution in cyclohexane, was added from a micrometer syringe. Samples of known volume were taken from the reaction mixture at timed intervals and were immediately quenched in excess acetone. The polymer was filtered off, washed with further acetone and dried to constant weight. Nominally identical runs gave conversion plots reproducible to within a few percent. Inherent viscosities Inherent viscosities, -q~,of polymer samples were measured in p-chlorophenol (containing 2 per cent alpha-pinene) at a polymer concentration of 0'5 g. d1-1, from which intrinsic viscosities were obtained by the following equation, derived in these laboratories 6:

•h = [~]-0"075['ql 2

(1)

TABLE 1. FRACTIONALCONVERSIONSAT 65 °

Run 40 39 38 37 32 31 30 29 36 35 34

103 x Initial CycloInitiator Monomer hexane Concent- Concent- Concentration, 1, ration, Mo, ration, S, (m.1. -1) (m.l. -1) (m.l. -l) 1"10 1"10 1"10 1-10 0"72 0"72 0'72 0'72 0'36 0"36 0"36

5"76 4"07 2"68 1"51 5"75 4'51 3'07 1"71 5'73 4"69 2"95

4"87 6"20 7'10 8"13 4"95 5"87 6"96 8"00 4"95 5-67 7"12

• c (50 min)

0'37 0-23 0"17 0"09 0"26 0-19 0"12 0"06 0"14 0-11 0'05

Fractional Conversions ^ c cf cf (100 min) (estimated) (calculated) 0"52 0"31 0"24 0"13 0"34 0"29 0"19 0.09 0"20 0-16 0"09

0"74 0"45 0"35-0"37 0"15 0"52-0"55 0"43-0"45 0"28-0"32 0"12 0"30-0"35 0"26 0"16--0'18

0"73 0"52 0"34 0"19 0'57 0"43 0"28 0"14 0"34 0"26 0"14

Note: The values of c at 50 min and 100 min have been interpolated from the experimental data; c/is the fractional conversion at infinite time, the calculated values of cf being derived from equation (13). Fractional conversions are defined as the ratio of weight of polymer formed to weight of monomer present initially.

The Polymerization of Trioxan in Cyclohexane

135

No reliable molecular weight-viscosity relation is available for polyoxymethylene, but some numberaverage molecular weights (J~rn) and corresponding intrinsic viscosities in dimethylformamide have been reported in a patent specification ~7). F r o m these data, and by separate experiments relating intrinsic viscosities in dimethylformamide at 150 ° and in p--chlorophenol at 60 °, the following approximate relation was obtained for the latter solvent: [~] = K / ~ n ° ' 6 2 5 d l . g - I . (2) where Klies within the range 2.0 x 10-3 to 3.5 x 10-3 dl.g -1. RESULTS T h e m a i n r e s u l t s a r e p r e s e n t e d i n T a b l e s 1-4. M o n o m e r a n d s o l v e n t c o n c e n t r a t i o n s were calculated from the weights of each added at room temperature, assuming densities o f 1.11 f o r t r i o x a n a n d 0.78 f o r c y c l o h e x a n e . E x p e r i m e n t a l p o i n t s f o r i n d i v i d u a l TABLE 2. FRACTIONAL CONVERSIONS AT 5 0 ° AND 70 °

Run

Temp. °C

47 48 46 45 54 53 50 49

70 70 70 70 70 70 50 50

103 X Initial Initiator M o n o m e r Concent- Coneentration, L ration, M0, (m.l. -1 ) (m.1. -1) 1 "44 1-44 1"44 1"44 0"72 0-72 1"46 I "46

Cyclohexane Concentration, S, (m.l. -1)

c (50 rain)

4"95 5"76 7"04 8"03 4"98 7"19 7'52 8" 12

0"48 0"39 0"26 0"13 0"27 0"14 0"13 0"08

5"74 4"66 2"97 1"63 5"70 2"78 2"32 1"52

Fractional Conversions c ct c: (100 min) (estimated) (calculated)

0.60 0"49 0"33 0"16 0"35 0"17 0"18 0" 14

0"75 0"62 0"48 0"20 0"50 0"20 0'28 0"20

TABLE 3. INHERENT VISCOSITIES FOR EXPERIMENTS AT 65 °

Run

Inherent Viscosities with Corresponding Fractional Conversions

40 c 39 c 38 c 37

1.02 0-06 0-55 0"03 0"56 0.06 0"29

1"26 0.26 I-I 1 0-25 0-82 0"21 0"42

1.18 0.54 1"09 0.37 0"88 0.30 0.44

c

0.06

0"14

0.14

1.21 0-65 1"I0 0-39 0.88 0"34

5.76 4"07 2.68 1"51

32

1"40

1-33

I'18

1"22

c 31 c 30 e 29 c 36 c 35 c 34 c

0'17 1.25 0' 14 0"69 0.06 0"47 0"08 0-67 0.05 0.90 0-06 0.42 0.04

0"34 1.23 0-30 0.99 0"19 0"47 0.10 1"41 0-14 1-13 0-15 0"73

0'45 1'15 0"43 0"96 0"28 0.48 0.11 1-37 0"19 1.14 0.23 0.70 0.16

0'50

0-15

Mo

5'75

4"51 0.96 0-31

3"07 1"71

1"22 0"31 1.10 0-25

5"73 4.69 2-95

0"76 0"66 0"40 0"22 0"50 0"21 0-32 0"21

136

P. F. ONYON and K. J. TAYLOR TABLE 4.

Run 47 e 48 c 46 c 45 c 54 c 53 c 50 c 49 c

INHERENT VISCOSITIESFOR EXPERIMENTS AT 500 AND

Temp. °C 70 70 70 70 70 70 50 50

Representative Inherent Viscosities with Corresponding Fractional Conversions 1.01 0-15 1.01 0-13 0.66 0.09 0.28 0.08 0-79 0-02 0.48 0.03 0.43 0.03 0.27 0.07

1.22 0.33 1-09 0-35 0.73 0.26 0.65 0.13 1.58 0.15 0.80 0.10 0.42 0.13 0.40 0.16

l.l I 0.65 1.02 0-56 0.72 0.39 0.46 0.18 1-47 0.24 0.76 0.13 0"69 0.23 0.45 0.19

1-11 0.73 0.99 0.55 0.69 0-43

70°

M0 5.74 4.66 2-97 1-63

1.27 0-38

5.70 2.78 2-32 1.52

runs at 65 ° are shown in Figs. 1-4, and these are c o m p a r e d with curves calculated on the basis o f the kinetic scheme discussed under case (iv) below (Eqn. (13)). The time scales o f Runs 34 and 35 have been shifted by 10 min to allow for the effect o f small induction periods observed in these two runs. Figure 5 shows the effect o f small additions o f water. DISCUSSION

Generalfeatures of the system The salient points which emerge from the results can be summarized qualitatively as follows. 1. U n d e r all conditions investigated the rate o f polymer formation decreases with time, the fractional conversion approaching asymptotically a limiting value, denoted by

92. Initial rates o f conversion increase with increasing concentrations o f m o n o m e r and catalyst and are approximately proportional to b o t h o f these quantities. Estimated values o f cf also increase with increasing m o n o m e r and initiator, but no simple p r o p o r tionality is evident in this case. 3. N o substantial induction periods are present. 4. Inherent viscosities of polymer sampled at corresponding conversions in different runs are effectively independent o f initiator concentration and increase with increasing m o n o m e r concentration. 5. Inherent viscosities o f successive samples from the same run increase rapidly with increasing conversion, reaching a m a x i m u m at a conversion less than one-third o f the final yield, and thereafter diminish gradually with increasing conversion.

Mechanism of the reaction The above facts, together with other features o f the reaction noted previously, enable some tentative conclusions to be reached concerning the mechanism o f the reaction. Evidence that the mechanism is that o f an ionic chain polymerization is provided by the

i

~

°.,k

0

,

o.6r

°' F

tOO

Time,

.~.

je

,.

rain

200

",--~'~Z',

~

~

A.

"

;



I00

,



Time,

min

200

. . .

,

......_.5-

,

,

Fro. 4. Runs 37 and 29.

FIG. 3. Runs 38, 30 and 34.

FIG. 2. Runs 39, 31 and 35.

FIG. I. Runs 40, 32 and 36.

FIGS. 1--4. Experimental conversions at 65 ° compared with conversion-time curves calculated from Eqn. (13). Initiator concentrations in m.I-L; e , l ' 1 0 x 1 0 - 3 ; v , 0.72x 10-3; A , 0 . 3 6 x 10 -3.

-..d

O ¢D

O

O

138

P . F . ONYON and K. J. TAYLOR 0.7 V o x



0"6



0-5

x

x

o O

x•









x o

~

0.4

x•

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t

o

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0"3, - -

To x

14.

0"2 +

0"1

I

I

I00

200 Time,

min

FIG. 5. Effect of added water on conversions at 65°. Initiator concentration, 1.10 x 10-3 m.l-t. Trioxan concentration 4.81 m.1-1. Concentrations of water in m.1-1.; +, nil; e, 0-35 x 10-3; A, 0.70 x 10-a; v, 1.39 x 10-3; x, 2"78x 10-3. Open circles indicate points calculated from Eqn. (13). nature of effective initiators, (2} the influence of impurities and of solvent (4) and by the fact that the highest molecular weights are obtained early in the reaction. The propagating species may be either carbonium or oxoriium ions. The absence of any marked induction period or period of acceleration suggests that all the active centres are formed within a short space of time after addition of initiator, an assumption which is reasonable on chemical grounds. If this is the case, then since the polymer chains are long, the overall rate of polymerization is equal to the rate of the growth reaction which, in turn, is directly proportional to the concentration of growing active centres. The comparatively rapid deceleration in rate, and eventual cessation of polymerization at a point far short of complete conversion, indicates that the active centres are terminated by some process which, as shown by the dependence ofcy on monomer concentration, assumes increasing importance at the higher solvent concentrations. The nature of this process will determine the kinetics and it is therefore necessary to examine, in turn, the consequences of postulating each of the more probable termination reactions that might operate. These are listed below, where X represents a growing polymer ion, P dead polymer and S the solvent, and the k's are velocity coefficients. (i) First order self-termination (for example, by recombination with the counter-ion associated with the growing end). kl X

>P

This type of termination is believed to occur in cationic polymerization of many vinyl monomers.

The Polymerization of Trioxan in Cyclohexane

139

(ii) A succession of transfer reactions with either solvent or impurity at each of which is produced a species T with considerably less reactivity towards monomer than the polymeric ions. k2 X+(S) >P+T k3

T+M

>X

(iii) Reaction of the polymer ion with an impurity Q in the solvent or, less probably, in the monomer, to give inert products X+ Q

k4

>P+ ?

(iv) Reaction of the polymer ion with the solvent itself, to give inert products. k, X+S

>P+ ?

Other processes which may contribute to an apparent termination are discussed later. Kinetic consequences o f assumed termination steps

In deriving the kinetic expressions of this section it has been assumed that the molar concentration of active centres, X, (square brackets are omitted for the sake of clarity) attains its maximum value, X0, within a very short period from the start of the reaction i.e. that chain initiation is very rapid, and faster than any of the succeeding reaction steps. In these circumstances the reaction kinetics must be of t h e " non-stationary" type (cf. the polymerization of styrene by sulphuric acid'S)). The propagation reaction is written as

X+M

>X

where M is the monomer, the initial concentration of which is M0. The fractional conversion, c, is given by ( M 0 - M ) / M o and the final conversion at infinite time is denoted by cf. The following cases are numbered to correspond with the termination steps listed above. Case (i). For first-order termination it is easily shown that ln(1 - c / ) = ~

X0

(3)

If X0 is proportional to initiator concentration alone, then Eqn. (3) is clearly inapplicable; if, however, X0 is assumed to be proportional to the product 1 M o, where I is the initiator concentration, a definite correlation is obtained when the cyvalues are plotted according to Eqn. (3) although the points show appreciable scatter. For individual experiments the corresponding relationship In(l - e ) - = 1 - exp ( - kl t), In ( 1 - cs)

(4)

where t is the time from the start of reaction, is obeyed reasonably well, although derived values of kl vary by a factor of 2.4. Case (ii). Here it is necessary to assume that k3 <~k,, but there is no real termination unless k3 = 0, when the situation becomes equivalent to cases (iii) and (iv). If k3 is not

140

P.F. ONYON and K. J. TAYLOR

zero, polymerization should continue, albeit at a low rate, to complete conversion, and as this is contrary to all the experimental indications this case can be dismissed from further consideration. This does not preclude the existence of transfer reactions in the system, which are in fact believed to occur, as will be seen below, but transfer reactions alone plainly cannot account for the experimental observations. Case (iii). Kinetic expressions derived for this case are as follows. In (1 - cl) =

[ 1 - Q0J' X°] In L

(5)

where Q0 is the initial concentration of impurity, and Q0 > X0, and

I n ( l - c ) =/c41n

Q o - Xo .] Q 0 - X0exp [ - ( Q o - X o ) k4t H

(6)

If Xo, Q0 are put proportional to IMo and S respectively, the experimental results can be fitted satisfactorily to Eqn. (5) with a value for kp/k4 of 2. (If Qo is put proportional to M0 no fit is obtained and therefore this scheme, if applicable, indicates that terminating impurities are associated with the solvent only). However, even with this simple integral value for kr/k 4 it is not possible, without excessive computation, to test Eqn. (6) for individual runs. If, however, the simplifying approximation is made that kp = k4, Eqn. (6) can be fitted, with very good agreement, to the results, all of which can be predicted from the corresponding equations (7) and (8), which contain effectively only two proportionality constants relating X0 to IMo and Q0 to S. (1 - cl)°'5 = 1-403 IMo/S

(7)

c/cf= [exp (bk 4 t) - I ]/[exp (bk4 t) - c£]

(8)

where bk4 = ( Q 0 - X0)k4 = 2 x 10-3S-0-903 IMo. The correctness of this termination mechanism can be tested by experiments in which solvent recovered from a polymerization is used for a second polymerization under the same conditions as the first. If, as vapour phase chromatography shows, impurity levels in the cyclohexane are low, and if the impurities are consumed during the reaction by being incorporated in the polymer, then termination reactions in the second polymerization should be less numerous, and the final yield of polymer correspondingly increased. However, separate experiments show that the course of polymerization is virtually unaffected by this procedure, thus providing some evidence against the hypothesis that solvent impurities are solely responsible for kinetic termination in the present system. • Case (iv). Termination by solvent alone is kinetieally similar to the previous case except that here the concentration of terminating agent remains effectively constant during the reaction ; this results in considerable simplification of the kinetic treatment. For this case -dX dt - kt XS,

(9)

-dM dt = k p M X

and since it follows that

whence X = X0 exp ( - k t St)

M, k Xo l n - ~ = - l n ( 1 - c ) = -7:---v-[1 - e x p ( - k t S t ) ] 2V/

(i0)

The Polymerization of Trioxan Cyclohexane

141

and

In (1 - c ) _ 1 - exp (kt St) ln(1 - c r )

(11)

where

In (1 - cr) = - kp Xo/kt S

(12)

I f Xo is put proportional to IMo, the observed final yields are well represented by Eqn. (12). Also a single value for k t of 1.51 x 10 -3 1. mol. -x rain. -1 in Eqn. (11) allows good agreement to be obtained between the calculated curves and most of the experimental points in all of the runs (Figs. 1-4). All curves were computed from the expression log10(1 - c ) = - 4 4 0S IMo [1 - e x p ( -

1.51 x 10 -3 St)]

(13)

Results of experiments at the other two temperatures studied obey similar relationships. At 50 ° and at 70 ° log10(1 - c l ) = - 370 IMo/S (14) and derived average values o f k t (in I. mol. -1 min. -1 units) are 1.24 x 10 -3 at 50 ° and 1.96 x 10 -3 at 70 °. These values are in accord with an activation energy for k t of about + 5 Kcal. mo1-1. The constants ofEqns. (13) and (14) indicate that the activation energy for kpis of the same order. Thus, within the range 50 ° to 70 °, rates and final conversions are relatively insensitive to temperature variation. The chemical nature of the termination reaction assumed in this case is obscure, since the only plausible reaction is that of hydride ion abstraction from the cyclohexane and there appears to be no reason why the resulting cyclhexyl cation should not be capable of reacting readily with monomer. On the basis of kinetic evidence alone case (iv) is preferable to case (i) but the latter mechanism cannot be entirely excluded because of the uncertain extent to which physical factors may influence the kinetics. Two such factors which may be of importance are the effects of dielectric constant and the heterogeneous nature of the reaction. It will have been observed that, with cases (i), (iii) and (iv), in order to obtain agreement with experimental results it was necessary to put the initial concentration of active centres proportional to the product of initial m o n o m e r concentration M0 and initiator concentration. I f the formation of active centres is virtually instantaneous on addition of initiator it would be expected that, in the presence of excess monomer, Xo = L In the rate expressions X0 is always multiplied by the quotient of the velocity coefficients for propagation and termination, and since it is known ~9~ that rates of cationic polymerizations are stongly influenced by the dielectric constant of the medium it is not unreasonable to associate the M0 term with the velocity coefficients rather than with X0. That is to say, over the range of initial monomer concentrations examined the dielectric constant of the mixture increases with Mo (for trioxan c ~ 8, for cyclohexane E ~ 2.0) and this variation m a y be sufficient to cause the ratio kp/kt to vary approximately linearly with M0. I f this is so, then it must be recognized that no allowance has been made in the kinetics for the decrease in dielectric constant which occurs during the course of each experiment, although for runs at the lower m o n o m e r concentrations this decrease would be relatively small. Without knowing the nature of the functional dependence of velocity coefficients on ~ further speculation on this point is unwarranted. The other possibly important factor is the insolubility of the polymer in the reaction medium. Because of the known ready tendency of polyoxymethylene chains to enter a

142

P.F. ONYON and K. J. TAYLOR

crystal lattice it is probable that much of the propagation reaction takes place at or near a solid-liquid interface, and some evidence has been presented 00~ in support of this. If, as is likely, the particles containing growing chains undergo aggregation, then it is possible that termination could be effected as a result of growing ends being occluded on coalescence. In the absence of experimental verification it can only be said that if such a mechanism is operative then it is unlikely that the termination reaction would be of simple first order, since the kinetics of coagulation would also enter into the rate equations. If the rate of the termination reaction is proportional to some function of P and also to X, it would be expected that the rates of polymerization and the final yields would be less dependent on initiator concentration than is found for a first order termination. A further objection to this mechanism is that for comparable values of M0 in different solvents, comparable final yields should be found, and this is not so.

Degree of polymerization Further knowledge of the reaction mechanism can, in principle, be derived from a study of the influence of reaction variables on the number-average molecular weights (~rn) of the polymer. The value of such evidence depends on the accuracy with which jt~rncan be determined and in the present work estimates of2Qn based on Eqn. (2) may be in error by as much as a factor of 2 or 3. Another serious complication is introduced by the marked changes in inherent viscosity with conversion (Tables 3 and 4). Thus it is clear that much uncertainty would attach to any attempt to distinguish between the rather similar kinetic schemes already discussed on the basis of viscosity results alone. Nevertheless, consideration of observed trends in the inherent viscosities shows that they do not conflict with proposed interpretations of the rate measurements (cases (i), (iii) or (iv) above); furthermore the data indicate that there are present in the system reactions additional to those considered so far. In all of the reported experiments, the molecular weight of polymer sampled at a sufficiently early stage ofthe reaction is lower than that of polymer formed subsequently; this behaviour is attributed to the occurrence of a facile transfer reaction with some trace impurity which is thereby consumed well before the reaction is completed. It is possible that one such impurity may be water, and it is noteworthy that in experiments in which small additions of water were deliberately made, the intensity of the OH bands in the infra-red spectra of the polymer decreased rapidly with increasing conversion, which suggests that the reactivity of water in this system is high. At the same time it was found (Fig. 5, Table 5) that addition of these amounts of water, while causing a reduction in inherent viscosity, had little or no observable effect on the overall course of reaction. The occurrence of transfer reactions can also be established with reasonable certainty by comparison of the kinetic chain length of the reaction with the degree of polymerization (DP) of the polymer. For present purposes the repeat unit of the polymer is taken to consist of three oxymethylene units, i . e . . ~ t = 90.1 x DP. The kinetic chain length (KCL) is defined as the average number of propagation steps following each act of initiation, or, assuming that each initiator molecule starts one chain, it is the ratio of total monomer units polymerized to the number of molecules of initiator reacted, that is, KCL = cfMo/l (15) Kinetic chain lengths computed in this way range from about 4000 at the highest monomer concentrations to about 200 at the lowest. By means of Eqn. (2) corresponding

The Polymerization o f Trioxan in Cyclohexane

143

values of DP are calculated to lie within the probable limits of 150-400 for experiments at highest initial monomer concentrations and of 20-50 for those at the lowest. Thus the number of transfers which take place during the lifetime of a growing chain, (KCL--DP)/DP, is at least three and can be ten or more. TABLE 5. INHERENTVISCOSITIESFOR EXPERIMENTSAT 650; THE EFFECT OF WATER

Run 70 c 41 c 43 c 51 c 52 c

10 3 x Water Concentration

I n h e r e n t Viscosities with

(m.1.-1)

Corresponding Fractional Conversions

nil 0-348 0"695 1"39 2'78

0"96 0"12 0-74 0"07 0-61 0"11 0'42 0"02 0"87 0"30

1"12 0"19 1 "08 0"30 1 "07 0.40 1 "08 0"39 0"91 0"59

M0 4.97

1 "10 0"53 1-08 0"50 1"09 0"61 0.94 0-64

4'69 1-00 0"58 0"99 0"66

4.90 4"78 4-75

The amount of water present in the system is insufficient to account for this number of transfers and it is apparent that at least one other type of transfer process is operative besides that responsible for the initial low polymer. Consequently at least two different types of end group are likely to be present in the final polymer besides end groups arising from initiation and termination processes, and since each kind of end group will have a different susceptibility to thermal breakdown this finding is of appreciable significance in regard to polymer stability. The course of the thermal degradation of these polymers at 220 ° is in fact consistent with there being more than one type of thermal initiation. If the exponent in Eqn. (2) is substantially correct, then [7/]t'6° will be directly proportional to the molecular weights, and for the experiments at 65 ° this quantity (derived from an average ofinberent viscosities of samples taken after the first 40 per cent of final yield) is plotted in Fig. 6 as a function of the initial monomer concentration. It is seen that, in spite of some scatter in the results, there is good correlation, the molecular weight of the polymer being roughly proportional to M0. A similar relationship is obtained if, instead of Mo, the average value of M during polymerization is plotted. Fig. 6 also shows that molecular weights are independent of initiator concentration. This result is in accord with any of the schemes (i), (iii) or (iv) above. For these it can easily be shown that, instantaneously, 1 rate of termination process + sum of rates of all transfer processes D--ff = rate of chain growth

(16)

The concentration of active centres appears as a first order quantity in all of the rate terms and therefore cancels out; thus the DP is independent of X and therefore, on previous assumptions, of the initiator concentration. For the general case, Eqn. (16) can be written as

kpM = K I + K 2 S + K a M DP

(17)

144

P . F . ONYON and K. J. TAYLOR

where K1 is a first o r d e r t e r m i n a t i o n constant, a n d K2 a n d K 3 are c o n s t a n t s including transfer velocity coefficients and, if associated impurities are transfer reactive, concentr a t i o n p r o p o r t i o n a l i t y factors. F r o m the a p p r o x i m a t e c o n s t a n c y o f M o / D P (Fig. 6) it can be d e d u c e d either t h a t K2 a n d K3 are zero (which, f r o m c o n s i d e r a t i o n o f kinetic chain lengths, a p p e a r s to be unlikely) or, owing to the n a t u r e o f the relation between S a n d M in the present system, t h a t solvent a n d m o n o m e r (or their associated impurities) d i s p l a y a b o u t equal reactivity in transfer processes. However, in view o f the uncertainties a l r e a d y referred to, the latter conclusion can only be tentative. A similar c o r r e l a t i o n exists between [r/] 1"6° a n d M 0 for experiments at 70 ° as for those at 65 °, a n d in general the m o l e c u l a r weights o b t a i n e d at c o r r e s p o n d i n g values o f Mo are similar, being on the whole slightly lower t h a n those at 65 ° .



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O

I

2

3

4

Id o

FIG. 6. Molecular weight as a function of initial monomer concentration. Initiator concentrations in m.1-1. ; e, 1"10 x 10-3; V, 0"72 x 10-3; A, 0"36 x 10-3. Acknowledgment--The authors wish to thank Mrs. S. A. Morgan and Messrs. A. G. Badger, C. B. Gardiner and P. B. Smith for assistance in the experimental work. Thanks are also due to the directors of British Industrial Plastics Ltd. for permission to publish this paper.

REFERENCES (1) (2) (3) (4) (5)

British Patents: (a) 877,820; (b) 878,163; (c) 914,046; (d) 921,541 ; (e) 942,745; (f) 943,684. W. Kern et aL, Angew. Chem. 73, 177 (1961). W. Kern and V. Jaacks, J. Polym. Sci. 48, 399 0960). V. Jaacks and W. Kern, MakromoL Chem. 62, 1 (1963). Okamura, Higashimura and Tomikawa, Kogyo-Kwagaku zasshi 65, 712 (1962); (Chem. Abstr. 57, 15345a (1962). (6) D. B. Partridge, private communication. (7) British Patent 796.863.

The Polymerization of Trioxan in Cyclohexane

145

(8) (a) R. E. Burton and D. C. Pepper, Proc. R. Soc., A263, 58 (1961); (b) M. J. Hayes and D. C. Pepper, Proc. R. Soc. A263, 63 (1961). (9) P. H. Plesch, ed. The Chemistry of Cationic Polymerization, p. 126. Pergamon Press (1963). (10) L. Leese and M. W. Baumber, Polymer, 5, 380 (1964). R6sum6--On a 6tudi6 la polym6risation de l'=-trioxym6thyl6ne en cyclohexane dilu6 b. 50 °, 65 ° et 70 ~, catalys6e par le trifluorure n-butyl ether borique. On a trouve des relations, d'une part entre les rendements et les viscosit6s propres du polym6re, et d'autre part les principaux facteurs de la r6action. L'augmentation de la quantit6 de catalyseur accroit les rendements en polym6re mais a peu d'action sur sa viscosit6; tandis que l'augmentation de la concentration du monom~re donne h la fois de plus hauls rendements et des viscosites plus 6levees. Dans les limites de temp6ratures 6tudi6es, des relations d6riv6es de considdrations cin6tiques permettent de pr6voir exactement le d6roulement de la r6action jusqu'h son stade d6finitif. On a d6montr6, pour la d6termination des cin6tiques, l'importance du stade final de la reaction bien que la nature exacte de ces r6actions demeure incertaine. Un certain nombre de facteurs secondaires de la reaction, tels que les effets de l'h6t6rog6n6it6 et ceux de la constante di61ectrique, emp~chent la r6solution de son m6canisme sur des bases reposant sur les cin6tiques; si 1'on recherche une connaissance compl6te de la r6action, on utilisera des techniques compl6mentaires. Somnmrio---Si 6 studiata la polimerizzazione del triossano, con catalizzazione a eterato n-butilico di trifluoruro di boro, in soluzione di cicloesano sotto temperature di 50 °, 65 ° e 70 °. Si sono ottenute correlazioni fra prodotto, relative viscositb, del polimero e principali variabili di reazione. L'aumento di concentrazione del catalizzatore ha per effetto maggiore resa di polimero ma scarsa influenza sulla viscosith propria, mentre maggiore resa e viscosit/t si ottengono aumentando la concentrazione monomerica. Espressioni derivate da considerazioni cinetiche permettono di prevedere esattamente 1o svolgimento della reazione per tutta la gamme di conversione, entro i limiti di temperatura studiati. Si 6 dimostrata l'importanza della reazione finale agli effetti della determinazione della cinetica, pure rimandendo la natura di queste reazioni incerta. Diverse caratteristiche del sistema, come l'eterogeneit/~. e gli effetti di costanti dielettriche, precludono il chiarimento del meccanismo sulla sola base di dimostrazione cinetica, dovendosi usare tecniche complementari se si vuole raggiungere la piena comprensione della reazione. Zusammenfassung--Es wurde die durch Bortrifluorid-n-Butyl~.therat eingeleitete Polymerisation yon Trioxan in einer Cyclohexani6sung bei 50 °, 65 ° und 70 ° untersucht. Es wurden Beziehungen zwischen den Ausbeuten und inneren Viskosit~ten des Polymers und den Hauptver~nderlichen der Reaktion festgestellt. Eine Konzentrationssteigerung der Ausl6severbindung liefert h6here Ausbeuten an Polymer, hat aber geringen EinfluB auf die innere Viskosit~it, w~ihrend h6here Ausbeuten und h6here inhere Viskosit~iten gleichzeitig gewonnen werden, wenn die Monomerkonzentration gesteigert wird. Aus kinetischen Betrachtungen abgeleitete Ausdrticke erm6glichen es. den Verlauf der Reaktion innerhalb der untersuchten Temperaturgrenzen tiber den gesamten Umwandlungsbereich genau vorherzusagen. Die Wichtigkeit der abschliel3enden Reaktion ftir die Bestimmung der Kinetik wurde gezeigt, doch bleibt die genaue Beschaffenheit dieser Reaktionen ungewilL Eine Anzahl komplizierender Gesichtspunkte des Systems wie Heterogenit/it und Wirkungen der Dielektrizit~itskonstanten schlieBen eine Aufkl~rung des Meehanismus auf der Grundlage von Beweisftihrungen der Kinetik allein aus, so daB, wenn eine vollst~indige Erkl~irung der Reaktion erreicht werden soll, die zus~itzlichen Verfahren rnit herangezogen weden miissen.

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