Kinetics of solid-state polymerization—II

European Polymer Journal, 1969, Vol. 5, pp. 219-229. Pergamon Press. Printed in England.

KINETICS

OF SOLID-STATE

POLYMERIZATION--II*

E. BOROS-GYEVIand F. T~2D6S Central Research Institute for Chemistry of the Hungarian Academy of Sciences, Budapest (Received 17 June 1968)

Abstract--We investigated the decomposition kinetics of AIBN during the solid-state polymerization of N-vinyl-carbazole. We found that the decomposition of AIBN is much affected by the physical condition of the solid system. The rate of decomposition increases with the progress of polymerization and reaches the rate measured in the liquid phase only when the polymer formed in a large amount (20--40 per cent) has sut~ciently loosened the solid structure. We established that the rate of decomposition of AIBN in the solid state can be expressed by the following equation: -- -_.L.: = k t ( x ) y dt

where y stands for the concentration of the initiator and x for the conversion of the monomer. The rate constant of decomposition is an unambiguous function (of a saturation curve type) of conversion.

INTRODUCTION I~ SVITEof the substantial efforts made in recent years in the field of solid-state polymerization, several problems regarding the kinetics and mechanism of this process are still unsolved. The dependence of the ability for polymerization in the solid state on the chemical and physical structure may be interpreted only with knowledge of the exact relationship between the different elementary processes and the overall reaction rate. For the elucidation of these relations, the polymerization of N-vinyl earbazole with chemical initiators (AIBN) was investigated. By using radical initiators, the mechanism of the process is rendered unambiguous; furthermore, this method makes it possible to perform a direct and exact investigation of the initiation process which is an important elementary step of polymerization. To the best of our knowledge, only three previous publications deal with the use of radical initiators in solid-state polymerization. R. Sehultz e t al., m when investi~ting the possibilities of initiating acrylamide polymerization, observed that the reaction may be carried out in the solid state also with AIBN. Acrylamide was melted with 5 per cent AIBN and, after solidifying, the mixture was kept for 2 rain at 80°C (m.p. : 84°C); a 70 per cent polymer formation was observed. In the ease of methaerylamide, the same could be observed on maintaining the substance for 3-5 rain at 10°C below the melting point. In the two other publications, the use of chemical initiators as sensitizers was mentioned. C. H. Bamford e t al. ~2) polymerized a methacrylic acidAIBN system by u.v. irradiation; C. S. Hsia ChenC3~initiated the polymerization of an acrylamide-methylene blue system by visible light. As no detailed investigations were carried out up till now in the field of the kinetics of solid-state polymerization initiated with AIBN, we first investigated the kinetics of the decomposition of initiator in the solid state. In this paper, we present results * Part I.: Acta chim. hung. 56, 67-85 (1968). VOLV~R 5!1---~

219

220

E. BOROS-GYEVI and F. T1DDOS

obtained in these investigations, It has to be noted that our first results concerning the kinetics of polymerization have been published briefly/*~ EXPERIMENTAL Prior to polymerization, the monomer was treated according to the method outlined in the previous publication(*) Three and a half mole per cent AIBN was used as initiator. Polymerizations were carried out at 49°C and 54°C. The polymer contents of the samples being polymerized for different periods were determined gravimetrically; the initiator contents were found by the polarographic method. The polarographic measurements were carried out with a Radelkisz OH 102 type recording polarograph. The potentials were related to a mercury electrode. A 1 : 1 mixture of methanol-benzene was used as solvent, which contained 2 per cent lithium chloride as basic electrolyte. Before use, the p.a. solvents were purified by shaking with sulphuric acid and by subsequent distillation. From the reaction mixture, solutions of 4- 8 g/l concn were prepared with the above solvent mixture. (This is equivalent to a concentration of AIBN of about 10 -3 mole/1 in the case ofa non-polymerized sample.) To eliminate oxygen, purified nitrogen saturated with benzene and methanol was passed through the solution for 15 min before measurement and afterwards led over the solution during measurement. Under such conditions, AIBN gives a well defined wave for which the halfwave potential is --1" 52 V. Thus, in the course of the measurement, the two-electron reduction of the N = N double bond takes place.

2

/ / -0"8

I -I'0

-I12

/

-i4

gJ

-I'6

-l'-8"

-2 3

v FIG. 1. Polarogram of a sample with 3.5 mole per cent AIBN content. As the monomer present in the system does not give rise to a polarographic wave in the particular voltage range, its presence does not interfere with the measurement. EXPERIMENTAL RESULTS T h e c o n v e r s i o n - t i m e relation o f the m o n o m e r s was found, in accordance with our previous investigations, to give a n S-shaped, autocatalytic curve. I n Table 1 the serial n u m b e r s of samples, the reaction time, the value of the conversion i n per

Kinetics of Solid-State Polymerization--II

6o°f

221

o o °°°

¢0

ZO~

o/O

0

200

1

1

400

600 f,

I 8(3,9

I ~ooo

hr

Fro. 2. Conversion-time relation of the monomer in the polymerization of N-vinyl carbazole initiated with AIBN (3-5 mole per cent AIBN, 49°). TABLE I. No.

t (hr)

10~.~

104 y (mole/l)

1 2 3 4

5"0 7-5 12"5 12-8

1"4 2"1 2"6 2"2

8"66 8"78 8"85 8"78

5 6 7 8

15.0 15.7 17"3 18.0

2"0 5"6 3"I 3"8

8"66 8"59 8"57 8"41

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

19"5 20.5 22"0 23"5 24'5 25.5 27-0 27-0 28"0 29" 0 29-0 30"0 30"2 32"4 35"0 36" 0 38.9 39" 5 44.7 45"2 51"0 54"5 65"2 75-0 100-0 115"0

5"6 10"4 8"1 10"7 19"2 12"5 14"8 14"8 16"1 29" 7 29"7 41 "9 20"8 23" 8 33"7 39" 8 49" 9 45"2 57"3 66"4 63"4 65"8 66"0 67-4 69"7 70"I

8'66 8"59 8"72 8"59 8"12 8"47 8"22 8"47 8"35 7" 29 7"35 7"03 8" 10 7" 97 7" 72 7.35 6- 97 6.98 6" 11 5"61 5"42 4-61 4-05 3" 11 2.12 1"68

222

E. BOROS-GYEVI and F. T ~ D 6 S

cent (10 2 ~) and the concentration of the initiator (y) are given; this latter was measured in the way described. One of the polarographic measurements is shown in Fig. 3. Here the AIBN concentrations, calculated from the wave heights with the aid of the calibration curve, are shown as a function of the polymerization time. From Fig. 3, it appears that the ]'C

--

O~ ;

o

-

• ~0,~

~"

.

0.4,-

o'~

"% 0

200

400 f,

600 hr

800

I000

Fro. 3. Change of concentration of initiator in the function of time (49~).

curves describing the change of polymer and initiator concentrations are, roughly speaking, mirror images. DISCUSSION The investigation of the decomposition kinetics of AIBN in the solid state was of interest from the point of view of studying the effect of phase. In the liquid phase, the decomposition of AIBN has been thoroughly examined. Several authors c5-8) have investigated effect of the medium and conditions (concentration, temperature). Investigations have shown unanimously that AIBN decomposition is a strictly firstorder reaction independent of the reaction conditions. A small change could be observed for the effect of the medium on the reaction only in the value of the rate constant (calculating from the extreme values of Lewis and Matheson c5~ 20 per cent, Overberger e t al. c6~ 20 per cent, Olive c~) 70 per cent and Moroni c8) 40 per cent). A greater change in the liquid phase was observed only recently by Rafykov e t al. c9~ in the system dimethyl formamide-glycerine. According to their measurements, if the viscosity of the medium increases from 0.5 cP to 20 cP (that is, a 40-fold increase), the rate constant decreases to about its one-fourth. The following conclusion can be drawn: if, in the ease of decomposition of the initiator in solid vinyl carbazole, greater deviations are observed, they must be due to changes taking place in the phase relations of the matrix. Analyzing the decomposition mechanism of the AIBN molecule, it must be coneluded that the substantial change in the mechanism of the decomposition, depending on the state of the matrix, is very improbable. From this, it follows that the initiator decomposition in a solid matrix has to be considered as a unimoleeular chemical process. Accordingly, when investigating the decomposition rate of the initiator, the

Kinetics of Solid-StatePolyrnerization--lI

223

unimolecular rate equation was used as a first approximation and the experimental data plotted according to the relation log Yo _ t. Y Contrary to the results obtained in the liquid phase, the experimental points did not fall on a straight line in the first stage of the reaction. The obtained curve tends asymptotically to a straight line but reaches it only at relatively high concentrations (20-40 per cent). I0-8-6 o

4

2

t

J

0.8 --

06

54°C

~

K~'= 3-4 IO"4rnin"t tln~ -- 27 h

S I

20

I

,~0

I

!

60

80

f,

f

I00

I

120

hr

Fio. 4. Determinationof the rate constant of the decompositionof the initiator. The rate constant of the decomposition calculated from the slope of the straight line (1 "2.10~ rain -1 at 49 °, 3.4.10 ~ rain -I at 54°) is practically in agreement with the rate constant measured in the liquid phase. As mentioned above, AIBN decomposes in the liquid phase in all cases according to unimolecular kinetics and the rate constant of its decomposition is approximately independent of the medium at a given temperature. By the fact that in the solid state this constant value could be obtained only at higher conversion, it is established that at the beginning of the polymerization the solid matrix is so rigid that most of the initiator molecules cannot decompose because of the lack of mobility. This phenomenon can be interpreted as if the molecule is forced into an extremely rigid "cage" which does not even allow the slight movement necessary for the breaking of an R-N bond. The decomposition of the initiator reaches the usual extent of that of the liquid phase, only when sufficient polymer has been formed to loosen the solid system. By the above result, we succeeded in proving by direct experiments the earlier assumption that the rate constants of the different elementary reaction steps in the solid state are essentially affected by the physical state of the solid system. Accordingly, a limitation has to be accepted when using the unimolecular equation for describing the decomposition rate of AIBN in the solid state, namely: kl is a

224

E. BOROS-GYEVIand F. T~D6S

constant depending on the physical conditions of the system which may be characterized by the amount of the formed polymer. Thus, kt is an unambiguous function of the polymer content of the system. The following discussion will show that the exact kinetic interpretation of the problem is extremely di~cult; therefore, at present, two approximate solutions are given. As first approximation, the change ofk~ is written in the form of k~ = k°x ~ where k ° is the limiting value of the rate constant of the decomposition (x stands for the conversion and in the case of total conversion x = 1). Accordingly, the rate equation can be written as follows:

__ dy__= kOx,y dt

(1)

log Y__2= k°Ix,dt. Y

(2)

Thus, to solve the problem, the explicit form of the x -----x(t) function is needed. With regard to the accelerating character of the kinetic curves of polymerization, we tried to express the amount of the formed polymer with the simplest equation relating to autocatalytic processes. (With a more detailed consideration, it may be shown that no great error is made if, instead of the exact dependence of x upon t such a rougher approximation is used.) Thus

log =kgf[ y

1 xoe*'

dt,

(3)

and, substituting e ~®t = z log O _

y

cLC~J(1/xo + z~/~) ~

(4)

Assuming that the ct = 1/2 integration may be performed easily, the following expression will be obtained for the change of initiator concentration:

E{

'

"'}

Assuming that z 2 >>1/Xo the equation of the asymptote may be given as follows: log { z + (

1 .-t-z2)\x/2"~ f,,,log2z

(6)

and so log/\/Y~ = 2k___LOlog 2a/Xo + k°lt. q~ ky!

(7)

At the same time, by using the simplifying assumption z 2 ~ 1/Xo for the initial period of the curve, the expression log Yo _ 2k ° log (1 + zV'Xo) y can be derived.

(8)

Kinetics of Solid-State Polymerization--II

225

For the length of the induction period the expression lind = 62 log 2 ~ X0

(9)

can be derived. To check the correctness of the solution, the k, values calculated theoretically were compared with the experimental values obtained by graphical differentiation. The comparison shows that the above equation system is only a rough approximation. The investigations were carried out for a few further values of a also (e.g. ~ = 1/3, a = 1/4 etc.). Nevertheless, this method proved to be rather difficult because of further integration problems and the experimental data, if calculated with other values, cannot be described better by this approximation. Concerning the exact form of the kl = f ( x ) relation, a theoretical a priori assumption is not available. Therefore other function forms may be also used for the approximate description of the relation. In the given case, for example, much better results can be obtained when using a Langmuir isotherm-like expression for the description of the conversion dependence of the rate constant. Accordingly k~ = k° a ~ x

(10)

(1 + a)

and the decomposition rate of the initiator is dy dt

kO

x a Tx

y(l + a).

(11)

Substituting the value of x and introducing a

¢--

(12)

(1 + a)Xo

we obtain logY° = k of ~ e~ t tit. y c + e ®'

•

(13)

Performing the integration, the following relation is obtained for the change of initiator concentration: log Yo y

-

k° log • ;2°7

"(14)

The equation of the asymptote can be obtained by using the e°t>~ c assumption: log Yo = kO t _ k 3° log (1 -b e). y ~5

(15)

The length of the induction period is according to this interpretation: rind = l l o g (1 + C). q9

(16)

226

E. BOROS-GYEVI and F. TI~DOS

To check the correctness of the equations, the value of constant a was determined from knowledge of the experimental k~ values. These were for 49 ° and 54°, 0.3 and 1-27 respectively. The curves calculated theoretically with the aid of the "a" values, mainly in the initial period, agree reasonably with the experimental results. I-4--

, 2 -

o

m

jof_ I0

_

/o

/o/,o'°

//e/e/o.O/

/o

JC

~

o.s

--

////

0.6

./

L~ oz 0

r 2.0

I

',

40

Conversion,

60

%

8o

FIG. 5. Dependence of the rate constant of the decomposition of the initiator on conversion (49°); O--experimental data, O---calculated data by Eqn. (10) (a ----0.3).

The above curves, as shown in Fig. 5, follow over a long period the linear course of the respective experinaental curves. In the second period, a definite (although relatively not very great) deviation may be observed. However, this approximation describes quite well the experimental data because it is exact in the first period which has a long duration. The second period, where the approximation is worse, is significantly shorter (about 70 hr, while the whole reaction time is 800 hr).* According to Fig. 5, an important conclusion may be drawn concerning the mechanism of the process. By the fact that the experimental kl values change linearly with the conversion of monomer, up to a relatively high conversion, it is shown that the initiator is evenly distributed (probably in a random way) in the monomer and the formation of the polymer takes place simultaneously in a great number of independent centres. On the other hand, the linear character of the initial period of the kl =f(x) dependence is connected with the circumstance that the lattice loosening effect of the polymer is proportional to the quantity of the polymer already formed, until the polymer chains do not interfere with one another. In the second period, when this already has * It can be stated that, with a more complicated expression, an even more precise approximation can be obtained; however, this would raise difficulties in connection with the integration. The moderate reproducibility of the experimental data does not merit too precise an approximation.

Kinetics of Solid-State Polymerization--II

227

occurred, the polymer subsequently formed cannot cause a proportional change in those physico--mechanical properties of the monomer which actually determine the mobility. As a consequence, the kt = f ( x ) curve shows a limiting character. The trend of this function can be followed much better by the Langmuir isotherm-like expression. Up till now, two unproved assumptions were used for the interpretation of the phenomena. One of the assumptions is that the initiator is in fact molecularly dispersed in the monomeric crystal. Actually, the preparation method itself does not give a suificient guarantee. This problem can be settled by crystallographic examinations. For this purpose, the X-ray diffractogram of the monomer, the initiator and the finely dispersed mixture of the two components (3-5 per cent AIBN), in particular the sample used for polymerization, were examined. The most important data (the 2 0 angles of the most intensive lines of diffractograms and the intensities) of measurements are summarized in Table 2. TABLE

N-vinyl carbazole

AIBN

2.

VC + AIBN mixture

VC + 3 ~. AIBN-rnelt

20

Intensity

20

Intensity

20

Intensity

20

Intensity

10.25

Very strong --

--

--

10-26

I0-16

Very strong

13.47

65.8 3.4 55.8 55.0 40-5 32-0 --

-19- 52 20.40 ---27.14

Very strong -91.1 20-1 --~ 50-6

13"40 13.50 17.12 19-40 20.58 20.68 22.66 23.48 27.16

Very strong 7"4 14.4 49.20 7" 1 56" 9 38.9 35.0 5-6

13.29 17.11 19- 30 20" 57 22"58 23"47 --

2"1 52-2 4" 5 29- 8 43.7 37-7 --

-17"20 19' 37 20.42 20- 51 22.65 23.44 --

It is evident from the data that the diffractogram of the mechanical mixture is practically the superposition of the diffractograms of components. At the same time, in the diffractogram of the melted sample essential changes can be observed. With the exception of one (2 0 = 13 "47°), all lines of the A I B N disappear and the remaining line, originally that of greatest intensity, appears only very faintly. A rough estimation from the intensities showed that a maximum of about I0 per cent of the initiator may be present in the form of individual crystals; the other part is incorporated into the crystal lattice of the monomer. This can be concluded also from the observation that the intensities of two lines of the monomer (2 0 = 17.20 ° and 2 0 = 20.51 °) show some change too. The other essential point which, in the discussion up till now, has been implicitly assumed is the fact that at a given temperature the A I B N molecules cannot decompose in their own crystal lattice. Actually, if the initiator decomposed under such conditions, we would not have the right to interpret the observed kinetic behaviour on the basis of the physico-mechanical properties of the monomer/initiator/polymer ternary

228

E. BOROS-GYEVI and F. TI~D(3S

system. To elucidate this problem, detailed measurements were performed with crystalline AIBN at 54°. Although in the course of these investigations, the reproducibility of polarographic measurements was somewhat worse than previously, it can be definitely stated that the initiator does not decompose in its own lattice (as shown in Fig. 6). These studies give further proof concerning the practically complete incorporation

7 1,,-

'

1'"

/ .... .. ....

_~

b

...,_..~._~

o.j 0

R/

i=

10._o ,

20

,

40

, f,

,

60

80

100

120

ht

FIo. 6. (a) change of the initiator concentration as a function of time in N-x;inyl carbazole (54 °); (b) Constancy of the concentration of crystalline AIBN as a function of time (54°).

of the initiator. If only a fraction of the initiator were incorporated in a molecularly dispersed form (quasi as an "impurity") in the crystal lattice of the monomer and the remaining fraction of the initiator separated during the cooling to form individual crystals (eutectic), the kinetics of decomposition would be of a different character. In a crystal mixture of such rough dispersity, the initiator fraction separated in the crystalline form would remain unchanged at the end of the reaction. Nevertheless, measurements show that the decomposition of the initiator is practically complete and not even a change in the slope is observed during the unimolecular period of the decomposition curve. Consequently, an important fraction of the initiator is molecularly dispersed in the monomeric crystal. This conclusion, drawn from the kinetic data, is in good agreement with the results of crystallographic investigations. AcknowledgementsmWe wish to express our thanks to the X-ray Spectroscopic Group for having carded out the crystallographic investigations, to Mr. Bdla Turcs~nyi, for his helpful cooperation in the polarographie measurements and to Miss Borb~ila Tak~ies for her participation in the experimental work.

REFERENCES (1) R. Schulz, G. Renner, A. Henglein and W. Kern, Makromolek. Chem. 12, 20 (1954). (2) C. H. Bamford, A. D. Jenkins and J. C. Ward, J. Polym. Sci. 48, 37 (1960). (3) C. S. Hsia Chela, J. Polym. Sci. B2, 891 (1964). (4) F. Tfid6s and E. Boros-Gyevi, Magy. k~m. Foly. 73, 60 (1967). F. Tfid6s and E. Boros-Gyevi, Proceedings of the Second Tihany Symposium on Radiation Chemistry, Akad~miai Kiad6, Budapest, 557 (1967). (5) F. M. Lewis and M. S. Matheson, J. Am. chem. Soc. 71, 747 (1949). (6) C. G. Overberger, M. T. O'Shaughessy and H. Shalit, J. Am. chem. Soc. 71, 2664 (1949).

Kinetics of Solid-State Polymerization--I[

229

(7) G. Hen_rici-Oliv6 and S. Oliv6, Makromolek. Chem. 58, 188 (1962). (8) A. F. Moroni, M a k r o m o l e k . Chem. 105, 43 (1967). (9) S. R. Rafikov, P. E. Messerle, G. P. Gladyshev and I. B. Shafranskaya, J. Polym. Sci. BS, 715 (1967). R~a~a6---.-On a examin6 la cin6tique de la d6composition de I'AIBN au cours de la polym6risation ~t l'6tat solide du N-vinylcarbazole. On a constat6 que la r6action de d&:omposition de I'AIBN est essentiellement influenc~e par les propri6t~s physiques du syst6me ~t l'6tat solide. La vitesse de la d~eomposition augmente ave¢ l'avancement de la polymdrisation et elle atteint la valeur mesur6e ~t l'6tat liquide lorsque 1¢ polym6re accumul6 repr~sente 20--40 pour cent ce qui a pour cons6quence une destruction de la structure eristalline. On a &abli que la vitesse de d6composition de I'AIBN h l'dta solide peut 6tre exprim6e par la relation suivante: vl"[

-

=." = k~(x)y dt

oh y repr~sente la concentration de l'amorceur et x le rendement du polym6re. La constante de vitesse de la d6composition est une fonction univoque (pr6sentant une saturation) du rendement. Sommario---Abbiamo studiato la cinetica di decomposizione delI'AIBN, durante la polimerizzazione allo stato solido dell'N-vinil-carbazolo. Abbiamo trovato c h e l a decomposizione delI'AIBN 6 molto irtfluenzata dalle condizioni fmiche del sistema solido. La velocith di decomposizione aumenta con il progredire della polimerizzazione e raggiunge la velocit~t misurata in fase liquida solo quando il polimero formato in glande quantith (20--40 per cent) ha sufficientemente perduto la struttura solida. Abbiamo stabilito the la velocit~ di decomposizione deII'AIBN allo stato solido pu6 essere espresso dalla seguente equazione: - d-ZY -~ k l (x)y dt

dove y indica la concentrazione dell'irtiziatore e x la conversione del monomero. La costante della velocit~ di decomposizione 6 una funzione non ambigua (del tipo di una eurva di saturazione) di conversione. Zasammenfassung--Die Kinetik der Zersetzung yon AIBN wurde bei der Polymerisation von Vinylcarbazol in fester Phase untersucht. Es wurde beobachtet, dab die Zersetzungsreaktion des AIBN durch den physikalischen Zustand des festen Systems wesentlich beeinflul]t wird. Die Zersetzungsgeschwiudigkeit nimmt im Lauf der Polymerisation zu und erreicht den Wert der in der fliissigen Phase gemessenen Geschwindigkeit erst, wenn das in grSBerer Menge entstandene Polymere (20--40 Prozent) die feste Struktur genfigend aufgelockert hat. Es wurde festgestellt, dab die Zersetzungsgeschwindigkeit des AIBN in der festen Phase durch folgende Gleichu~g wiedergegeben werden kann: dy

- - d-7 --- k t ( x ) y

wobei y die Initiatorkonzentration trod x den Umsatz des Monomeren bezeichnen. Die Geschwindigkeitskonstante der Zersetzung kann als die eindeutige Funktion des Umsatzes (mit dem Charakter einer Sittigungskurve) betrachtet werden.