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The nature of the mechanical degradation of polymethylmethacrylate
THE NATURE OF THE MECHANICAL DEGRADATION OF POLYMETHYLMETHACRYLATE *t P. Yg. B~ZTVAGI~ I n s t i t u t e of Chemical Physics, U.S.S.R. Academy of Sciences
(Received 26 November 1965)
THE breakdown of polymeric materials under mechanical action begins with rupture of chemical bonds in the macromolecules. In the present work a study was made of the kinetics of mechanical degradation of polymethylmethacrylate (PMMA) and the nature of the process of bond rupture is discussed. Degradation, i.e. rupture of bonds in the main polymer chain, is indicated b y a fall in molecular weight. The process of formation of a new surface during dispersion has previously been studied b y the adsorption method [1]. Samples of the polymer were dispersed in a laboratory eccentric mill [2]. Three grammes of polymer and 110 g of steel balls were placed in the mill chamber, of capacity 60 cm a. The amplitude of vibration was varied between 5 and 2 ram. At an amplitude of 5 mm it was found ealorimetrically that the rate of supply of mechanical energy was 700 cal.min -1, some of which is consumed unproductively in heating up the balls and the body of the mill. With water cooling the temperature in the drums varied within the limits of 10-30 ° . The molecular weight was calculated from the intrinsic viscosity of the PMMA in benzene solution at 20 °. b y means of the formula [t/]=5.5 x 10-aM °Te. The Huggins constant remained unchanged during prolonged dispersion of the polymer. In one experiment the molecular weight was determined both viscomctrically and ebullioscopically and the results coincided within the limits of accuracy of the methods. The degree of polymerization of the original, commercial PMMA was 3 X 104 and after reprecipitation it was 6 x 104. The number of ruptured bonds, X, in the main polymer chain was determined from the formula X = ( 6 X 102a/m)(P-1--Po-1 ) (m is the molecular weight of the unit and P the degree of polymerization). The results of experiments with PM!VfA are presented in Fig. 1 and in the Table. The curves in Fig. la show the decrease in degree of polymerization on dispersion at different rates of supply of mechanical energy (J, cal. mole -1. sec-1). The rate is directly proportional to the square of the amplitude of vibration of the b o d y of the mill. * Vysokomol. soyed. A9: No. 1, 136-143, 1967. ~f V. I. Kolbanev assisted in the experimental work. 149
150
P. Y~, BUTYAGIN
Under the most vigorous conditions the degree of polymerization fell by a factor of 200, from 3 x 104 to 1.4x 10~, in 45 min. The four curves in Fig. l a were combined by changing the scale of the abscissa. The scale factors, a, were selected individually for each curve. For experiments at amplitudes of 5.0, 4.1, 3.2 and 2.1 mm the values of a were 1.00, 0.55, 0.20 and 0.17 respectively. The scale factors indicate the extent of the fall in the rate of degradation with decrease in the rate of supply of mechanical energy. After change in the scale of the abscissa by the factors a the results of the four experiments are described by a single, general curve, plotted as X against ~/~ (Fig. lb) without any detectable, systematic deviation. The curve in :Fig. lb can be divided into two sections, namely an initial section where the rate of degradation increases, and a longer period of constant rate (linear section).
a
M
X,g -I
X,g -r
b
C o2
2,10 6
,.,q/,.,,,, o/;
t,tO 6
IoY 20
,
,
j
z
20 ~0 ~:/oc
¢0 %rain
zoou/ )
FIG. 1. Mechanical degradation of polymethylmethacrylatein a vibratory mill. Amplitude of vibration: 1--5, 2--4.1, 3--3.2, 4--2-1 ram; a, b, c--see text. The increase in rate of degradation in the first period can be explained by rupture of bonds on deformation of macromoleeules in a certain depth of surface layer of the polymer. In the beginning, while the diameter of the particles is large, the volume of this surface layer is small in comparison with the volume of the whole polymer particle, and correspondingly the rate of degradation is low. The constant, maximal rate of degradation is reached when, as a result of size reduction in the mill, the radius of the particles is reduced to the thickness of this surface layer. V A L U E S OF T H E CONSTANTS a , k 1 AND ~ FOR POLYMETHY:LM:ETHACRYLATE AND
Polymer PMMA Quartz
a,
cm~.g-l.min-1 2"5X 10-4 1.7 x 104
~
QUARTZ
'
g-l.min-2
3.3 X10 le 0.22 x 10~e
,,Vote. I n the calculation the density of PMMA w a s t a k e n
as
kl, g-X.min-1
~, cm
1.3X 1018 6 x 1016
2X10 -6 4 x 10 -e
1 cmS.g-1.
Mechanical degradation of polymethylmethacrylato
151
In the initial period the specific surface (s) increases at a constant rate: s ~ a ~ . Using the symbol 6 (cm) for the thickness of the surface layer, its volume is v = 6 s , and the rate of degradation d X / d T = k l v or d X / d v = k 1 agT, whence X - - kl 6a Ts
(1)
2 Equation (1) must be valid while 8 ~ 6 -1. When s ~ 6 -1 the entire volume of the polymer is subjected to deformation b y impact with the balls and friction within the layers of material. Under these conditions the rate of degradation is practically constant, i.e. d X / d T - ~ k 1 (see linear section of curve in Fig. lb). In Figure lc the experimental results corresponding to the initial part of the degradation curve are plotted as X against (~/~)~. The experimental results are in good agreement with equation (1), hence the thickness of the surface layer, 6, can be determined. Values of the constants a, ]Q and 6 are given in the Table. The values of a were taken from experimental data in reference [1]. For PMMA 6 = 2 0 0 A. In order to eliminate random errors associated with specific features of the method of measurement additional experiments were carried out for study of the kinetics of degradation of quartz b y the electron paramagnetie resonance
[~"J,g'~ 2,f0t~
a
L
/
-
[R'],~-t I8
0"2.10
.0.1~I0
/ 0
b
0
0
i
20 FIo.
40%rnin
5g
100¢
2. [R']-~ and [R']-~ *curves showing the accumulation of free radicals in the dispersion of quartz. Amplitude of vibration--5 mm.
(EPIC) method. E P R spectra given b y free radicals are described.in reference [3]. In Figures 2a and 2b curves of the accumulation of free radicals in quartz are plotted as [R']-v and [R']-T ~ curves. In the initial period (Fig. 2b) the formation of free radicals follows a quadratic law (equation (1)), i.e. the kinetics of the process are the same as for the degradation of polymethylmethacrylate. The thickness of the surface layer in quartz is 400/~ (see Table). This can be compared with values in the literature. Khodakov and Rebinder [5] studied the transition of crystalline to amorphous quartz during the dispersion process and found b y the thermographie method that the thickness of the layer transformed to the amorphous state was 150 •. It is difficult to represent this transition,
152
P. YIT. BlYrYAOIN
i.e. breakdown of the quartz crystal lattice, without rupture of Si--O bonds, and this is probably the reason why the two methods gave similar values for the thickness of the surface layer. The supposition that degradation of the polymer molecules occurs predominantly in the surface layers was also made in reference [5], where cutting of glassy polymers is discussed. u n d e r stationary conditions, with uniform supply of mechanical energy to the entire volume of the polymer, the rate of degradation is practically constant over a wide range of degrees of polymerization, from 104 to 109" (see linear section of Fig. lb). A constant rate of bond rupture was also disclosed by analysis of the experimental results of references [6] and [7] in which studies of the degradation of various polymers in ball mills is described. These results are shown in Fig. 3 as P - l - - z and X - - z curves. The rate of degradation can be constant ff the probability of rupture is the same for all bonds in the main polymer chain (with the obvious exclusion of the terminal segments), or, in other words, if the degradation rate constant is directly proportional to the chain length [8]. In this case the concentration of probable points of rupture in 1 g of polymer is C~=2N (P--2Pt)/mP, and the rate of degradation dX/dT--=KC~ or ln(~
Po--2PtjP--2Pt~ =4PtKz.
To the first approximation, when
1 1 ....
P
Po
2Kv
Pt is small in comparison with P, we obtain or
2NK
X= -m
~,
(2)
where N is the Avogadro number, Pt the number of terminal units not undergoing degradation, K the degradation rate constant (see-1) and m the molecular weight of the unit. Knowing the value of the degradation rate constant the efficiency of the process can be determined, the efficiency being given by (2KQ/J). 100N0.04% (Q is the energy for rupture of bonds in the main chain in cal/mole). The quantity of mechanical energy supplied was determined calorimetrically and no account was taken of the unproductive consumption of energy in heating the balls and the body of the mill. Moreover degradation is accompanied by recombination of some of the radicals and the true rate of bond rupture is possibly higher than the experimental figure. Those two corrections act in the same direction and the calculated efficiency is obviously lower than the true value. In explaining the nature of bond rupture in mechanically stressed macromolecules Zhurkov [9] suggested that under the action of a stress F the bond energy Q decreases by the energy of deformation EF, and the rate constant for
Mechanical degradation of polymethylmethacrylato
153
bond rupture K increases according to the equation
Q~TF)
K----Koexp(
(3)
where K o is a constant close in order of magnitude to the frequency of vibration ( ~ 1013 see-l), R the gas constant, T the absolute temperature and e a coefficient taking into account the nonuniformity of stress distribution. Equation (3) has been verified in numerous studies of the permanent strength of polymers at moderate temperatures [10]. This equation is not, however, applicable to study of pure mechanical degradation, the rate of which is either independent of temperature or has a negative temperature coefficient [11].
~K
I00,
x,g~ ~
b
2O
I0
~Z(
b
0"4 -5"0
-60 ~x~ I
30
80
~ n e , hp
FIG. 3
30
80
I
2
[
I
4
I
i
6
-04 I
J
8
lO_[OOjmo/o. 3ec ca[
I
[
r
I
I
I
J
I
O2 04 O6 O8 1000 mole,,~ec I ' caZ
Fro. 4
Fro. 3. Mechanical degradation: a - - o f cellulose, from ref. [6]; b - - p o l y s t y r e n e (1) and polyvinylacetate (2), from ref. [7]. Fro. 4. Dependence of degradation rate constant {K) on the rate of supply of mechanical energy: a - - P M M A , b--ultrasonic degradation of polystyrene, from ref. [12].
It m a y be assumed that under these conditions degradation passes through a nonequilibrium stage. In dispersion of the elastic energy the energy of bond deformation E d is converted to thermal energy and is liberated in a given section of the chain. After a time ~* the liberated energy is redistributed over all the bonds of the system. In sections of the chain with an excess vibrational energy E d the rate constant for bond rupture is approximately equal to 1/% exp (--Q/Ed), where To-----K0-1~10 -13 see, and moreover it is assumed that Ed>>RT. Whence the probability of bond rupture in time ~* will be ~*/% exp (--Q/Ed). The quantity E~=Q/(ln v*--ln %) is a critical ,value. When Ed>E*~ the probability of bond rupture in time ~* is greater than unity. It is therefore evident that there is a threshold value of the deformation energy, E~. When Edge ~ degradation of polymer molecules occurs in the process of conversion of elastic to thermal energy. The energy E~ must be con-
154
P. Yu. BUTYAGIN
siderably smaller than the bond strength Q, thus when T*----102r0, Ed~0.2 Q 104 cal. mole -1. In the dispersion of polymers the rate of absorption of mechanical energy must, to the first approximation, be directly proportional to the rate of supply, and the rate of relaxation must be proportional to the mean level of excess energy, AE~. Under stationary conditions the rates of the two processes are equal, i.e.
7J--]c~ AEm-~O
and
AEm=TJ/k r
where 7 is a dimensionless coefficient taking account of the efficiency of absorption of mechanical energy b y the polymer (efficiency ~ 1 ) , and k t is the rate constant of stress relaxation (see-l). The mechanical energy is unevenly distributed among the bonds of the main chain and the shape of the distribution function is unknown. If it is assumed that the distribution is such that the fraction of bonds with energy E~ and above is proportional to exp (Em/AEm) the degradation rate constant will be
K----A exp (E*/AEm)
or
K-~A exp (
]c~E~ ~J ] ,
(4)
where A is a coefficient taking account of the rate of redistribution of mechanical energy in the system and E m is the minimal mechanical energy necessary for bond rupture. Figure 4 shows the dependence of the rate constant of mechanical degradation on the rate of supply of mechanical energy, plotted as log K - - J -1 curves. In the dispersion of PMMA the experimental results are in satisfactory agreement with equation (4) over the entire range: Kp~Mx~--4 × 10 -5 exp (--700/J) , sec -1
(5)
In the ultrasonic degradation of polystyrene (from the results of reference [ 12]): Kps=3-5 exp (--3700/J) , sec -1
(6)
the latter formula being valid only when J ~ 2 0 0 0 cal-mole-l"sec -1. For PMMA at a high rate of supply of mechanical energy the absolute magnitude of the exponent in equation (4) is close to unity, i.e. under these experimental conditions E * ~ AE m. The mean level of absorption of mechanical energy AE,, cannot be much greater than the energy of intermolecular interaction, which for most polymers is 2-5 cal.mole -1. I t m a y therefore be assumed also that E* can scarcely be greater than 1 0 cal. mole -1, and this means that the limiting deformation energy giving rise to bond rupture is several times lower than the bond energy, Q. In unimolecular, thermal decomposition reactions the pre-exponential factor K o is about 10 a sec -1. In mechanical degradation the coefficient A in equation (4) is associated with redistribution of mechanical energy, and in order of magnitude (for PI~IMA A----4× 10-Ssec -1) is close to the stress relaxation rate constant.
Mechanical degradation of polymethylmethacrylate
155
From equations (4) and (5) it follows that 7 0 0 / J : k r Era~TJ, where E : ~ 104 and l ~ y ~ 1 0 -a, i.e. kr~ 10-1--10 -4 sec -1. The coefficients k, and A in equation (4) are, as would be expected, close to one another in order of magnitude. Thus the nonequilibrium state hypothesis satisfactorily explains the kinetics of mechanical degradation, including the orders of magnitude of the constants A, /¢~ and E ~ . A number of consequences follow from this hypothesis and in order to verify these two series, A and B, of model, experiments were carried out. A. The mean level of excess energy AE,,, was determined from the ratio of the rates of absorption of mechanical energy and of stress relaxation. The relaxation rate constant k ~ 10-1--10 -4 sec -1, i.e. relaxation occurs in a period of time measured roughly in hundreds of seconds. Whence it follows that if degradation is periodically interrupted for lengths of time of this magnitude the rate of bond rupture must be sharply reduced. Figures 5a and b show the results of measurement of the rate of interrupted degradation of PMMA at the temperature of liquid nitrogen. The mechanical treatment routines were, in experiment 1 a sequence of 5 see dispersion and 5 see at rest and in experiment 2 a sequence of 5 see dispersion and 5 min at rest. The degradation was followed in two ways, b y the change in molecular weight with subsequent calculation of the number of ruptured bonds (Fig. 5a), and b y the increase in concentration of free radicals in the powdered polymer (Fig. 5b), electron paramagnetic resonance method, see reference [13] for the method of measurement and the nature of the free radicals). The abscissa (Fig. 5) represents the total time of dispersion and each point corresponds to a separate experiment. Increase in the rest period from 5 see to 5 min causes the rate of degradation to fall b y 30-40%, which is well beyond the limit of error due to possible temperature variation. This effect was confirmed b y the two independent methods of measurement of the rate of degradation. S milar experiments were conducted with PMMA at room temperature and with polystyrene at the boiling point of nitrogen. When degradation was alternated with short periods at rest (up to 10 rain) the rate of bond rupture fell b y one third to one half. B. Excited vibrational states of bonds can be detected either b y direct spectroscopic measurements or b y a number of purely chemical indications. Spectroscopic measurement is obviously the method of the future. This complex problem requires the creation of special apparatus. Of the chemical methods the most convenient is measurement of the rate of decomposition of the free radicals formed at the sites of ruptured bonds. R u p t u r e of vibrationally excited chain segments must be accompanied b y the formation of hot macroradicals, possessing a large reserve of excess vibrational energy. The most probable path of decomposition of such radicals is liberation of monomer. The energy of activation for radical depolymerization of vinyl polymers is comparatively high (16-18 kcal.mole -1 or more), therefore at temperatures of - - 3 0 ° and below purely thermal depolymerization can be neglected. Experiments were conducted with polyisobutylene and polyformaldehyde, which were chosen
156
P. Y u . BUTYAGII~
because the volatility of their monomers at low temperatures is sufficiently high. The polymers were dispersed at --78 ° in a glass micromil], integrally sealed to a vacuum measuring system (for a discription of the apparatus see reference [1]). During the dispersion process the monomer was frozen in a trap cooled by liquid nitrogen. The composition of the volatile matter was determined by the mass spectroscopic method after the experiment. The rate of formation of radicals in polyisobutylene under these experimental conditions did not exceed 5 x 10i~ g-1 per hour, and for polyformaldehyde the rate was still lower. X .10-zz
/ [R ],/Sta
EL
b
6
2
4 2"5f
2 i
i
i
I
1
2
3
4
I hme, rain
Fro. 5
2
3
4
/20 240 360 480 120 240 360 480 Z-~me,min
FIG. 6
lq'm. 5. Mechanical degradation of PMMA in a vibratory mill at the boiling point of nitrogen. Milling routine: 1--5 see dispersion alternating with 5 see at rest, 2--5 see dispersion alternating with 5 rain at rest; a--molecular weight variation, b--increase in free radical concentration. FIG. 6. Formation of volatile products in the dispersion of polyisobutylono (a) and polyformaldehyde (b) at --78 ° in a glass micromill. The curve of the yield of monomer is shown in Fig. 6. When the mill was opened the formation of monomer ceased, despite the fact t h a t at --78 ° free radicals remain for days in both polymers. T h e quantity of monomer liberated is several times grater t h a n the concentration of radicals in the degradation products. The formation of monomer in the mechanical degradation of PMMA and other polymers was first reported in references [14] and [15]. I t has been shown [16] t h a t monomer is liberated in the decomposition of radicals with a free valency in the middle or at the end of the chain, and also in the decay of peroxide radicals. The results of experiments at low temperatures (--78 °) (Fig. 6) indicate the possibility of depolymerization at the moment of degradation, when each rupture of a bond is accompanied by the expulsion of several monomer units. I t is evident t h a t the free radicals formed by rupture of the chain possess excess vibrational energy and the liberation of monomer at --78 ° is due to decomposition of these hot radicals. The existence of excited vibrational states of long duration in the chemistry of polymers was first suggested by Tyudesh [17] to explain the kinetics of radical polymerization. I n this case the excess energy is small in comparison with R T . In mechanical degradation terminal chain segments with a large store of excess
Mechanical degradation of polymethylmethacrylate
157
e n e r g y are f o r m e d anew a n d this also is c o n s u m e d in expulsion of several m o n o m e r units. T h e results o f t h e model e x p e r i m e n t s , i.e. t h e decrease in the r a t e degradation in a n i n t e r r u p t e d r o u t i n e a n d t h e fact t h a t d e p o l y m e r i z a t i o n occurs a t low t e m p e r a t u r e s , s u p p o r t the h y p o t h e s i s o f the nonequilibrium n a t u r e o f mechanical degradation. CONCLUSIONS
(1) I n dispersion of p o l y m e t h y l m e t h a c r y l a t e u n d e r conditions o f u n i f o r m s u p p l y o f mechanical e n e r g y to t h e entire v o l u m e o f t h e p o l y m e r the r a t e o f mechanical d e g r a d a t i o n is c o n s t a n t over a wide r a n g e of degrees o f polymerization (from 104 to 10~). T h e d e g r a d a t i o n r a t e c o n s t a n t is d e p e n d e n t on the r a t e of s u p p l y of mechanical e n e r g y according to t h e law K = A exp (--E*~/zIEm). T h e p r e e x p o n e n t i a l f a c t o r (A) characterizes t h e r a t e of redistribution o f mechanical e n e r g y a n d coincides in order of m a g n i t u d e with the r a t e of stress rel a x a t i o n (10-1-10 -4 sec-~). T h e d e f o r m a t i o n e n e r g y required for b o n d r u p t u r e ( " m e c h a n i c a l a c t i v a t i o n e n e r g y " E~) does n o t exceed 104 eal.mole -1, i.e. it is several t i m e s less t h a n the b o n d energy. (2) I n order to explain t h e n a t u r e o f mechanical d e g r a d a t i o n it is suggested t h a t t h e e n e r g y r e q u i r e d for r u p t u r e is a c c u m u l a t e d on t h e b o n d s o f the m a i n p o l y m e r chain t h r o u g h conversion of elastic d e f o r m a t i o n to heat. T h e possibilit y o f creation of nonequilibrium states w i t h excess mechanical a n d t h e r m a l (vibrational) e n e r g y is confirmed e x p e r i m e n t a l l y . Translated by E. O. PHILUPS REFERENCES
1. P. Yu. BUTYAGIN, Vysokomol. soyed. 5: 1829, 1963 (Translated in Polymer Science U.S.S.R. 5: 6, 958, 1964) 2. M. I. ARONOV, Pribory i tckhnika eksperim. 1: 153, 1959 3. P. Yu. BUTYAGIN, Dokl. Akad. Nauk SSSR 140: 145, 1961 4. G. S. KHODAKOV and P. A. R E B I N D E R , Kolloid. zh. 23: 482, 1961 5. M. P. VERSHININA and Ye. V. KUVSHINSKII, Vysokomo1. soyed. 2: 1484, 1960 (Translated in Polymer Science U.S.S.R. 9: 3, 382, 1962) 6. H. GROHN and O. DETERS, Plaste und Kautschuk 7: 1862, 1962 7. N. K. BARA_MBOIM, Mekhanokhimiya polimerov (Mechanoehemistry of Polymers). Gostekhizdat, 1961 8. B. V. PAVLOV, Vysokomo1. soyed. 1: 1227, 1959 (Not translated in Polymer Science U.S.S.R.) 9. S. N. ZHURKOV, Vestnik Akad. Nauk SSSR, 1957, No. 11, 78 10. S. N. ZHURKOV and S. A. ABBASOV, Vysokomol. soyed. 4: 1485, 1962 (Not translated in Polymer Science U.S.S.R.) 11. N. K. BARAMBOIM, Zh. fiz. k_him. 32: 1248, 1958 12. A. A. BERLIN and B. S. EL'TSEFON, Vysokomol. soyed. 1: 688, 1959 (Translated in Polymer Science U.S.S.R. 1: 2, 241, 1960) 13. P. Yu. BUTYAGIN, I, V. KOBANEV and V. A. RADTSIG, Fizika tverdogo tela 5: 2257, 1963
158
T. P. VISHNYAKOVA e$ a~.
14. V. R. REGEL', T. M. MUSINOV and O. F. POZDNYAKOV, Fizika tverdogo tela 4: 2468, 1962 15. N. A. PLATE and V. A. KARGIN, International Symposium on Macromolecular Chemistry, Paris, 1963 16. P. Yu. BUTYAGIN, Dokl. Akad. Nauk SSSR 165: 103, 1965 17. F. TYUDESH, Rassmotreniye kinetiki radikal'noi polimerizatsii s tochki zreniya gipotezy o goryachikh radikalakh (Discussion of the Kinetics of Radical Polymerization from the Point of View of the Hot Radical Hypothesis). Izd. "Mir", 1966
HETEROPOLYCONDENSATION OF CARBAMYLFERROCENE WITH ALDEHYDES * T. P, VISH~YAKOVA,I. h. GOLU~EVA and R. P. S~A~XSHOVA I. i~I. Gubkln Institute of the Petrochemical and Gas Industry (Received 27 November 1965)
POLYMERS with conjugated double bonds, containing ferroeene and nitrogen in the conjugated system possess interesting properties, such as high electrical conductivity, high thermal stability and magnetic and catalytic properties. Three polymers with a conjugated system containing ferrocene and nitrogen are known, namely polyazophenylene-ferrocene obtained b y reacting diphenyl-4,4'-bisdiazonium salts and salts of diphenyl-4,4'-bisdiazonium-3,3'-dicarboxylie acid with ferrocene [1], a polyazine obtained b y polycondensation of 1,1'-diaeetylferrocene with hydrazine hydrate [2] and polyferrocenenitrile obtained b y polycondensation of earbamylferrocene [3]. The authors have synthesized new conjugated polymers containing ferrocene and nitrogen b y heteropolycondensation of earbamyfferrocene with acetaldehyde and butyraldehyde (the physicochemieal constants of the aldehydes were in good agreement with the published figures). The reaction, catalysed b y zinc chloride, was carried out in an autoclave provided with a sampling system. Carbamylferrocene (CF) was prepared b y reacting ferrocene with carbamyl chloride, used in the form of a complex with aluminium chloride [3]; b.p. 168-171 °, in good agreement with the figure quoted in reference [4]. The polymer was treated as described in reference [3]. In the synthesis of polyferrocenylnitrilevinylene from CF and acetaldehyde a study was made of the effect of temperature, reaction time and ratio of the reactants on the yield of polymer. I t is seen from Table 1 that the optimal reaction conditions are, temperature 250 °, time 5 hr and molar ratio ofZnCl~ : CF : acetal* Vysokomol. soyod. A9: No. 1, 144-149, 1967.
(Received 26 November 1965)
THE breakdown of polymeric materials under mechanical action begins with rupture of chemical bonds in the macromolecules. In the present work a study was made of the kinetics of mechanical degradation of polymethylmethacrylate (PMMA) and the nature of the process of bond rupture is discussed. Degradation, i.e. rupture of bonds in the main polymer chain, is indicated b y a fall in molecular weight. The process of formation of a new surface during dispersion has previously been studied b y the adsorption method [1]. Samples of the polymer were dispersed in a laboratory eccentric mill [2]. Three grammes of polymer and 110 g of steel balls were placed in the mill chamber, of capacity 60 cm a. The amplitude of vibration was varied between 5 and 2 ram. At an amplitude of 5 mm it was found ealorimetrically that the rate of supply of mechanical energy was 700 cal.min -1, some of which is consumed unproductively in heating up the balls and the body of the mill. With water cooling the temperature in the drums varied within the limits of 10-30 ° . The molecular weight was calculated from the intrinsic viscosity of the PMMA in benzene solution at 20 °. b y means of the formula [t/]=5.5 x 10-aM °Te. The Huggins constant remained unchanged during prolonged dispersion of the polymer. In one experiment the molecular weight was determined both viscomctrically and ebullioscopically and the results coincided within the limits of accuracy of the methods. The degree of polymerization of the original, commercial PMMA was 3 X 104 and after reprecipitation it was 6 x 104. The number of ruptured bonds, X, in the main polymer chain was determined from the formula X = ( 6 X 102a/m)(P-1--Po-1 ) (m is the molecular weight of the unit and P the degree of polymerization). The results of experiments with PM!VfA are presented in Fig. 1 and in the Table. The curves in Fig. la show the decrease in degree of polymerization on dispersion at different rates of supply of mechanical energy (J, cal. mole -1. sec-1). The rate is directly proportional to the square of the amplitude of vibration of the b o d y of the mill. * Vysokomol. soyed. A9: No. 1, 136-143, 1967. ~f V. I. Kolbanev assisted in the experimental work. 149
150
P. Y~, BUTYAGIN
Under the most vigorous conditions the degree of polymerization fell by a factor of 200, from 3 x 104 to 1.4x 10~, in 45 min. The four curves in Fig. l a were combined by changing the scale of the abscissa. The scale factors, a, were selected individually for each curve. For experiments at amplitudes of 5.0, 4.1, 3.2 and 2.1 mm the values of a were 1.00, 0.55, 0.20 and 0.17 respectively. The scale factors indicate the extent of the fall in the rate of degradation with decrease in the rate of supply of mechanical energy. After change in the scale of the abscissa by the factors a the results of the four experiments are described by a single, general curve, plotted as X against ~/~ (Fig. lb) without any detectable, systematic deviation. The curve in :Fig. lb can be divided into two sections, namely an initial section where the rate of degradation increases, and a longer period of constant rate (linear section).
a
M
X,g -I
X,g -r
b
C o2
2,10 6
,.,q/,.,,,, o/;
t,tO 6
IoY 20
,
,
j
z
20 ~0 ~:/oc
¢0 %rain
zoou/ )
FIG. 1. Mechanical degradation of polymethylmethacrylatein a vibratory mill. Amplitude of vibration: 1--5, 2--4.1, 3--3.2, 4--2-1 ram; a, b, c--see text. The increase in rate of degradation in the first period can be explained by rupture of bonds on deformation of macromoleeules in a certain depth of surface layer of the polymer. In the beginning, while the diameter of the particles is large, the volume of this surface layer is small in comparison with the volume of the whole polymer particle, and correspondingly the rate of degradation is low. The constant, maximal rate of degradation is reached when, as a result of size reduction in the mill, the radius of the particles is reduced to the thickness of this surface layer. V A L U E S OF T H E CONSTANTS a , k 1 AND ~ FOR POLYMETHY:LM:ETHACRYLATE AND
Polymer PMMA Quartz
a,
cm~.g-l.min-1 2"5X 10-4 1.7 x 104
~
QUARTZ
'
g-l.min-2
3.3 X10 le 0.22 x 10~e
,,Vote. I n the calculation the density of PMMA w a s t a k e n
as
kl, g-X.min-1
~, cm
1.3X 1018 6 x 1016
2X10 -6 4 x 10 -e
1 cmS.g-1.
Mechanical degradation of polymethylmethacrylato
151
In the initial period the specific surface (s) increases at a constant rate: s ~ a ~ . Using the symbol 6 (cm) for the thickness of the surface layer, its volume is v = 6 s , and the rate of degradation d X / d T = k l v or d X / d v = k 1 agT, whence X - - kl 6a Ts
(1)
2 Equation (1) must be valid while 8 ~ 6 -1. When s ~ 6 -1 the entire volume of the polymer is subjected to deformation b y impact with the balls and friction within the layers of material. Under these conditions the rate of degradation is practically constant, i.e. d X / d T - ~ k 1 (see linear section of curve in Fig. lb). In Figure lc the experimental results corresponding to the initial part of the degradation curve are plotted as X against (~/~)~. The experimental results are in good agreement with equation (1), hence the thickness of the surface layer, 6, can be determined. Values of the constants a, ]Q and 6 are given in the Table. The values of a were taken from experimental data in reference [1]. For PMMA 6 = 2 0 0 A. In order to eliminate random errors associated with specific features of the method of measurement additional experiments were carried out for study of the kinetics of degradation of quartz b y the electron paramagnetie resonance
[~"J,g'~ 2,f0t~
a
L
/
-
[R'],~-t I8
0"2.10
.0.1~I0
/ 0
b
0
0
i
20 FIo.
40%rnin
5g
100¢
2. [R']-~ and [R']-~ *curves showing the accumulation of free radicals in the dispersion of quartz. Amplitude of vibration--5 mm.
(EPIC) method. E P R spectra given b y free radicals are described.in reference [3]. In Figures 2a and 2b curves of the accumulation of free radicals in quartz are plotted as [R']-v and [R']-T ~ curves. In the initial period (Fig. 2b) the formation of free radicals follows a quadratic law (equation (1)), i.e. the kinetics of the process are the same as for the degradation of polymethylmethacrylate. The thickness of the surface layer in quartz is 400/~ (see Table). This can be compared with values in the literature. Khodakov and Rebinder [5] studied the transition of crystalline to amorphous quartz during the dispersion process and found b y the thermographie method that the thickness of the layer transformed to the amorphous state was 150 •. It is difficult to represent this transition,
152
P. YIT. BlYrYAOIN
i.e. breakdown of the quartz crystal lattice, without rupture of Si--O bonds, and this is probably the reason why the two methods gave similar values for the thickness of the surface layer. The supposition that degradation of the polymer molecules occurs predominantly in the surface layers was also made in reference [5], where cutting of glassy polymers is discussed. u n d e r stationary conditions, with uniform supply of mechanical energy to the entire volume of the polymer, the rate of degradation is practically constant over a wide range of degrees of polymerization, from 104 to 109" (see linear section of Fig. lb). A constant rate of bond rupture was also disclosed by analysis of the experimental results of references [6] and [7] in which studies of the degradation of various polymers in ball mills is described. These results are shown in Fig. 3 as P - l - - z and X - - z curves. The rate of degradation can be constant ff the probability of rupture is the same for all bonds in the main polymer chain (with the obvious exclusion of the terminal segments), or, in other words, if the degradation rate constant is directly proportional to the chain length [8]. In this case the concentration of probable points of rupture in 1 g of polymer is C~=2N (P--2Pt)/mP, and the rate of degradation dX/dT--=KC~ or ln(~
Po--2PtjP--2Pt~ =4PtKz.
To the first approximation, when
1 1 ....
P
Po
2Kv
Pt is small in comparison with P, we obtain or
2NK
X= -m
~,
(2)
where N is the Avogadro number, Pt the number of terminal units not undergoing degradation, K the degradation rate constant (see-1) and m the molecular weight of the unit. Knowing the value of the degradation rate constant the efficiency of the process can be determined, the efficiency being given by (2KQ/J). 100N0.04% (Q is the energy for rupture of bonds in the main chain in cal/mole). The quantity of mechanical energy supplied was determined calorimetrically and no account was taken of the unproductive consumption of energy in heating the balls and the body of the mill. Moreover degradation is accompanied by recombination of some of the radicals and the true rate of bond rupture is possibly higher than the experimental figure. Those two corrections act in the same direction and the calculated efficiency is obviously lower than the true value. In explaining the nature of bond rupture in mechanically stressed macromolecules Zhurkov [9] suggested that under the action of a stress F the bond energy Q decreases by the energy of deformation EF, and the rate constant for
Mechanical degradation of polymethylmethacrylato
153
bond rupture K increases according to the equation
Q~TF)
K----Koexp(
(3)
where K o is a constant close in order of magnitude to the frequency of vibration ( ~ 1013 see-l), R the gas constant, T the absolute temperature and e a coefficient taking into account the nonuniformity of stress distribution. Equation (3) has been verified in numerous studies of the permanent strength of polymers at moderate temperatures [10]. This equation is not, however, applicable to study of pure mechanical degradation, the rate of which is either independent of temperature or has a negative temperature coefficient [11].
~K
I00,
x,g~ ~
b
2O
I0
~Z(
b
0"4 -5"0
-60 ~x~ I
30
80
~ n e , hp
FIG. 3
30
80
I
2
[
I
4
I
i
6
-04 I
J
8
lO_[OOjmo/o. 3ec ca[
I
[
r
I
I
I
J
I
O2 04 O6 O8 1000 mole,,~ec I ' caZ
Fro. 4
Fro. 3. Mechanical degradation: a - - o f cellulose, from ref. [6]; b - - p o l y s t y r e n e (1) and polyvinylacetate (2), from ref. [7]. Fro. 4. Dependence of degradation rate constant {K) on the rate of supply of mechanical energy: a - - P M M A , b--ultrasonic degradation of polystyrene, from ref. [12].
It m a y be assumed that under these conditions degradation passes through a nonequilibrium stage. In dispersion of the elastic energy the energy of bond deformation E d is converted to thermal energy and is liberated in a given section of the chain. After a time ~* the liberated energy is redistributed over all the bonds of the system. In sections of the chain with an excess vibrational energy E d the rate constant for bond rupture is approximately equal to 1/% exp (--Q/Ed), where To-----K0-1~10 -13 see, and moreover it is assumed that Ed>>RT. Whence the probability of bond rupture in time ~* will be ~*/% exp (--Q/Ed). The quantity E~=Q/(ln v*--ln %) is a critical ,value. When Ed>E*~ the probability of bond rupture in time ~* is greater than unity. It is therefore evident that there is a threshold value of the deformation energy, E~. When Edge ~ degradation of polymer molecules occurs in the process of conversion of elastic to thermal energy. The energy E~ must be con-
154
P. Yu. BUTYAGIN
siderably smaller than the bond strength Q, thus when T*----102r0, Ed~0.2 Q 104 cal. mole -1. In the dispersion of polymers the rate of absorption of mechanical energy must, to the first approximation, be directly proportional to the rate of supply, and the rate of relaxation must be proportional to the mean level of excess energy, AE~. Under stationary conditions the rates of the two processes are equal, i.e.
7J--]c~ AEm-~O
and
AEm=TJ/k r
where 7 is a dimensionless coefficient taking account of the efficiency of absorption of mechanical energy b y the polymer (efficiency ~ 1 ) , and k t is the rate constant of stress relaxation (see-l). The mechanical energy is unevenly distributed among the bonds of the main chain and the shape of the distribution function is unknown. If it is assumed that the distribution is such that the fraction of bonds with energy E~ and above is proportional to exp (Em/AEm) the degradation rate constant will be
K----A exp (E*/AEm)
or
K-~A exp (
]c~E~ ~J ] ,
(4)
where A is a coefficient taking account of the rate of redistribution of mechanical energy in the system and E m is the minimal mechanical energy necessary for bond rupture. Figure 4 shows the dependence of the rate constant of mechanical degradation on the rate of supply of mechanical energy, plotted as log K - - J -1 curves. In the dispersion of PMMA the experimental results are in satisfactory agreement with equation (4) over the entire range: Kp~Mx~--4 × 10 -5 exp (--700/J) , sec -1
(5)
In the ultrasonic degradation of polystyrene (from the results of reference [ 12]): Kps=3-5 exp (--3700/J) , sec -1
(6)
the latter formula being valid only when J ~ 2 0 0 0 cal-mole-l"sec -1. For PMMA at a high rate of supply of mechanical energy the absolute magnitude of the exponent in equation (4) is close to unity, i.e. under these experimental conditions E * ~ AE m. The mean level of absorption of mechanical energy AE,, cannot be much greater than the energy of intermolecular interaction, which for most polymers is 2-5 cal.mole -1. I t m a y therefore be assumed also that E* can scarcely be greater than 1 0 cal. mole -1, and this means that the limiting deformation energy giving rise to bond rupture is several times lower than the bond energy, Q. In unimolecular, thermal decomposition reactions the pre-exponential factor K o is about 10 a sec -1. In mechanical degradation the coefficient A in equation (4) is associated with redistribution of mechanical energy, and in order of magnitude (for PI~IMA A----4× 10-Ssec -1) is close to the stress relaxation rate constant.
Mechanical degradation of polymethylmethacrylate
155
From equations (4) and (5) it follows that 7 0 0 / J : k r Era~TJ, where E : ~ 104 and l ~ y ~ 1 0 -a, i.e. kr~ 10-1--10 -4 sec -1. The coefficients k, and A in equation (4) are, as would be expected, close to one another in order of magnitude. Thus the nonequilibrium state hypothesis satisfactorily explains the kinetics of mechanical degradation, including the orders of magnitude of the constants A, /¢~ and E ~ . A number of consequences follow from this hypothesis and in order to verify these two series, A and B, of model, experiments were carried out. A. The mean level of excess energy AE,,, was determined from the ratio of the rates of absorption of mechanical energy and of stress relaxation. The relaxation rate constant k ~ 10-1--10 -4 sec -1, i.e. relaxation occurs in a period of time measured roughly in hundreds of seconds. Whence it follows that if degradation is periodically interrupted for lengths of time of this magnitude the rate of bond rupture must be sharply reduced. Figures 5a and b show the results of measurement of the rate of interrupted degradation of PMMA at the temperature of liquid nitrogen. The mechanical treatment routines were, in experiment 1 a sequence of 5 see dispersion and 5 see at rest and in experiment 2 a sequence of 5 see dispersion and 5 min at rest. The degradation was followed in two ways, b y the change in molecular weight with subsequent calculation of the number of ruptured bonds (Fig. 5a), and b y the increase in concentration of free radicals in the powdered polymer (Fig. 5b), electron paramagnetic resonance method, see reference [13] for the method of measurement and the nature of the free radicals). The abscissa (Fig. 5) represents the total time of dispersion and each point corresponds to a separate experiment. Increase in the rest period from 5 see to 5 min causes the rate of degradation to fall b y 30-40%, which is well beyond the limit of error due to possible temperature variation. This effect was confirmed b y the two independent methods of measurement of the rate of degradation. S milar experiments were conducted with PMMA at room temperature and with polystyrene at the boiling point of nitrogen. When degradation was alternated with short periods at rest (up to 10 rain) the rate of bond rupture fell b y one third to one half. B. Excited vibrational states of bonds can be detected either b y direct spectroscopic measurements or b y a number of purely chemical indications. Spectroscopic measurement is obviously the method of the future. This complex problem requires the creation of special apparatus. Of the chemical methods the most convenient is measurement of the rate of decomposition of the free radicals formed at the sites of ruptured bonds. R u p t u r e of vibrationally excited chain segments must be accompanied b y the formation of hot macroradicals, possessing a large reserve of excess vibrational energy. The most probable path of decomposition of such radicals is liberation of monomer. The energy of activation for radical depolymerization of vinyl polymers is comparatively high (16-18 kcal.mole -1 or more), therefore at temperatures of - - 3 0 ° and below purely thermal depolymerization can be neglected. Experiments were conducted with polyisobutylene and polyformaldehyde, which were chosen
156
P. Y u . BUTYAGII~
because the volatility of their monomers at low temperatures is sufficiently high. The polymers were dispersed at --78 ° in a glass micromil], integrally sealed to a vacuum measuring system (for a discription of the apparatus see reference [1]). During the dispersion process the monomer was frozen in a trap cooled by liquid nitrogen. The composition of the volatile matter was determined by the mass spectroscopic method after the experiment. The rate of formation of radicals in polyisobutylene under these experimental conditions did not exceed 5 x 10i~ g-1 per hour, and for polyformaldehyde the rate was still lower. X .10-zz
/ [R ],/Sta
EL
b
6
2
4 2"5f
2 i
i
i
I
1
2
3
4
I hme, rain
Fro. 5
2
3
4
/20 240 360 480 120 240 360 480 Z-~me,min
FIG. 6
lq'm. 5. Mechanical degradation of PMMA in a vibratory mill at the boiling point of nitrogen. Milling routine: 1--5 see dispersion alternating with 5 see at rest, 2--5 see dispersion alternating with 5 rain at rest; a--molecular weight variation, b--increase in free radical concentration. FIG. 6. Formation of volatile products in the dispersion of polyisobutylono (a) and polyformaldehyde (b) at --78 ° in a glass micromill. The curve of the yield of monomer is shown in Fig. 6. When the mill was opened the formation of monomer ceased, despite the fact t h a t at --78 ° free radicals remain for days in both polymers. T h e quantity of monomer liberated is several times grater t h a n the concentration of radicals in the degradation products. The formation of monomer in the mechanical degradation of PMMA and other polymers was first reported in references [14] and [15]. I t has been shown [16] t h a t monomer is liberated in the decomposition of radicals with a free valency in the middle or at the end of the chain, and also in the decay of peroxide radicals. The results of experiments at low temperatures (--78 °) (Fig. 6) indicate the possibility of depolymerization at the moment of degradation, when each rupture of a bond is accompanied by the expulsion of several monomer units. I t is evident t h a t the free radicals formed by rupture of the chain possess excess vibrational energy and the liberation of monomer at --78 ° is due to decomposition of these hot radicals. The existence of excited vibrational states of long duration in the chemistry of polymers was first suggested by Tyudesh [17] to explain the kinetics of radical polymerization. I n this case the excess energy is small in comparison with R T . In mechanical degradation terminal chain segments with a large store of excess
Mechanical degradation of polymethylmethacrylate
157
e n e r g y are f o r m e d anew a n d this also is c o n s u m e d in expulsion of several m o n o m e r units. T h e results o f t h e model e x p e r i m e n t s , i.e. t h e decrease in the r a t e degradation in a n i n t e r r u p t e d r o u t i n e a n d t h e fact t h a t d e p o l y m e r i z a t i o n occurs a t low t e m p e r a t u r e s , s u p p o r t the h y p o t h e s i s o f the nonequilibrium n a t u r e o f mechanical degradation. CONCLUSIONS
(1) I n dispersion of p o l y m e t h y l m e t h a c r y l a t e u n d e r conditions o f u n i f o r m s u p p l y o f mechanical e n e r g y to t h e entire v o l u m e o f t h e p o l y m e r the r a t e o f mechanical d e g r a d a t i o n is c o n s t a n t over a wide r a n g e of degrees o f polymerization (from 104 to 10~). T h e d e g r a d a t i o n r a t e c o n s t a n t is d e p e n d e n t on the r a t e of s u p p l y of mechanical e n e r g y according to t h e law K = A exp (--E*~/zIEm). T h e p r e e x p o n e n t i a l f a c t o r (A) characterizes t h e r a t e of redistribution o f mechanical e n e r g y a n d coincides in order of m a g n i t u d e with the r a t e of stress rel a x a t i o n (10-1-10 -4 sec-~). T h e d e f o r m a t i o n e n e r g y required for b o n d r u p t u r e ( " m e c h a n i c a l a c t i v a t i o n e n e r g y " E~) does n o t exceed 104 eal.mole -1, i.e. it is several t i m e s less t h a n the b o n d energy. (2) I n order to explain t h e n a t u r e o f mechanical d e g r a d a t i o n it is suggested t h a t t h e e n e r g y r e q u i r e d for r u p t u r e is a c c u m u l a t e d on t h e b o n d s o f the m a i n p o l y m e r chain t h r o u g h conversion of elastic d e f o r m a t i o n to heat. T h e possibilit y o f creation of nonequilibrium states w i t h excess mechanical a n d t h e r m a l (vibrational) e n e r g y is confirmed e x p e r i m e n t a l l y . Translated by E. O. PHILUPS REFERENCES
1. P. Yu. BUTYAGIN, Vysokomol. soyed. 5: 1829, 1963 (Translated in Polymer Science U.S.S.R. 5: 6, 958, 1964) 2. M. I. ARONOV, Pribory i tckhnika eksperim. 1: 153, 1959 3. P. Yu. BUTYAGIN, Dokl. Akad. Nauk SSSR 140: 145, 1961 4. G. S. KHODAKOV and P. A. R E B I N D E R , Kolloid. zh. 23: 482, 1961 5. M. P. VERSHININA and Ye. V. KUVSHINSKII, Vysokomo1. soyed. 2: 1484, 1960 (Translated in Polymer Science U.S.S.R. 9: 3, 382, 1962) 6. H. GROHN and O. DETERS, Plaste und Kautschuk 7: 1862, 1962 7. N. K. BARA_MBOIM, Mekhanokhimiya polimerov (Mechanoehemistry of Polymers). Gostekhizdat, 1961 8. B. V. PAVLOV, Vysokomo1. soyed. 1: 1227, 1959 (Not translated in Polymer Science U.S.S.R.) 9. S. N. ZHURKOV, Vestnik Akad. Nauk SSSR, 1957, No. 11, 78 10. S. N. ZHURKOV and S. A. ABBASOV, Vysokomol. soyed. 4: 1485, 1962 (Not translated in Polymer Science U.S.S.R.) 11. N. K. BARAMBOIM, Zh. fiz. k_him. 32: 1248, 1958 12. A. A. BERLIN and B. S. EL'TSEFON, Vysokomol. soyed. 1: 688, 1959 (Translated in Polymer Science U.S.S.R. 1: 2, 241, 1960) 13. P. Yu. BUTYAGIN, I, V. KOBANEV and V. A. RADTSIG, Fizika tverdogo tela 5: 2257, 1963
158
T. P. VISHNYAKOVA e$ a~.
14. V. R. REGEL', T. M. MUSINOV and O. F. POZDNYAKOV, Fizika tverdogo tela 4: 2468, 1962 15. N. A. PLATE and V. A. KARGIN, International Symposium on Macromolecular Chemistry, Paris, 1963 16. P. Yu. BUTYAGIN, Dokl. Akad. Nauk SSSR 165: 103, 1965 17. F. TYUDESH, Rassmotreniye kinetiki radikal'noi polimerizatsii s tochki zreniya gipotezy o goryachikh radikalakh (Discussion of the Kinetics of Radical Polymerization from the Point of View of the Hot Radical Hypothesis). Izd. "Mir", 1966
HETEROPOLYCONDENSATION OF CARBAMYLFERROCENE WITH ALDEHYDES * T. P, VISH~YAKOVA,I. h. GOLU~EVA and R. P. S~A~XSHOVA I. i~I. Gubkln Institute of the Petrochemical and Gas Industry (Received 27 November 1965)
POLYMERS with conjugated double bonds, containing ferroeene and nitrogen in the conjugated system possess interesting properties, such as high electrical conductivity, high thermal stability and magnetic and catalytic properties. Three polymers with a conjugated system containing ferrocene and nitrogen are known, namely polyazophenylene-ferrocene obtained b y reacting diphenyl-4,4'-bisdiazonium salts and salts of diphenyl-4,4'-bisdiazonium-3,3'-dicarboxylie acid with ferrocene [1], a polyazine obtained b y polycondensation of 1,1'-diaeetylferrocene with hydrazine hydrate [2] and polyferrocenenitrile obtained b y polycondensation of earbamylferrocene [3]. The authors have synthesized new conjugated polymers containing ferrocene and nitrogen b y heteropolycondensation of earbamyfferrocene with acetaldehyde and butyraldehyde (the physicochemieal constants of the aldehydes were in good agreement with the published figures). The reaction, catalysed b y zinc chloride, was carried out in an autoclave provided with a sampling system. Carbamylferrocene (CF) was prepared b y reacting ferrocene with carbamyl chloride, used in the form of a complex with aluminium chloride [3]; b.p. 168-171 °, in good agreement with the figure quoted in reference [4]. The polymer was treated as described in reference [3]. In the synthesis of polyferrocenylnitrilevinylene from CF and acetaldehyde a study was made of the effect of temperature, reaction time and ratio of the reactants on the yield of polymer. I t is seen from Table 1 that the optimal reaction conditions are, temperature 250 °, time 5 hr and molar ratio ofZnCl~ : CF : acetal* Vysokomol. soyod. A9: No. 1, 144-149, 1967.