Radical copolymerization of maleic anhydride, styrene and vinyltriethoxysilane

Radical copolymerization of maleic anhydride, styrene and vinyltriethoxysilane

RADICAL COPOLYMERIZATION OF MALEIC A N H Y D R I D E , STYRENE AND VINYLTRIETHOXYSILANE* Z. M. RzA¥~v, L. V. BRYKSINA, SK. K. KY~zI~ov and S. I. SADYK...

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RADICAL COPOLYMERIZATION OF MALEIC A N H Y D R I D E , STYRENE AND VINYLTRIETHOXYSILANE* Z. M. RzA¥~v, L. V. BRYKSINA, SK. K. KY~zI~ov and S. I. SADYKH-ZADE Sumgait Branch of the Institute of Petrochemical Processes, Azerb. S.S.R. Academy of Sciences (Received 15 Jauuary 1970)

IT IS known that maleic anhydride (MA) copolymerizes with many electrondonating monomers such as styrene (St) [1, 2], n-dioxene [3], vinyl esters [4], vinylcyclohexane [5], dihydropyran [6], acrylic acid [7] etc., with formation of a charge-transfer complex (CTC) as an intermediate stage. It has been suggested by some authors [3] that copolymerization of MA with these monomers occurs at a stage that is virtually homopolymerization of these complexes. We have reported previously [8] that it is possible to bring about radical, ternary copolymerization of MA and St with organic, organotin and organolead maleates, vinyltriethoxysilane (VTES), vinyl chloride and other vinyl monomers. The purpose of the present work was to determine the reactivity ratios and some other kinetic parameters of the radical polymerization of the I~IA-St-VTES system. EXPERIMENTAL Starting materials. Maleie ~nhydride was recrystallized from chloroform and then sublimed in vacuo, m.p. 52"8°. Styrene and VTES were purified by conventional methods a n d had the following characteristies: St: n ~ 1-5462, d~° 0-9060, m.p. 25-5°; VTES: n~5 1.3960, d~~ 0.9027, b.p. 62"7°/20 toni. Benzoy] peroxide was prepared by the method of Bartlett and Nozaki [1] and purified b y precipitation by methanol from solution in chloroform. Copolymerization was carried out in sealed glass tubes or in a dilatometer, in aI1 atmosphere of pure nitrogen, in solution in benzene or toluene. The kinetics of copolymerization were studied by the dilatometric method. The monomers and initiator were placed in the dilatometer, degassed b y freezing a n d thawing three times in vacuo, the system was then swept out with pure nitrogen and ~he dilatometer was sealed and placed in an ultrathermostat. To determine the final yield of eopolymer hydroquinone was added to the reaction mixture and the product, which was in powder form, was filtered off, purified by washing with several por~iiolm of benzene in a centrifuge, and by precipitation by ether from solution in dimethylforraamide. The copolymer was dri(:d to constant weight in vacuo.

* Vysokomol. soyed. A14: No. 2, 259-267, 1972. 287

288

Z.M.

RZAYEV et al.

The concentrations of the monomers before and after the reaction wore determined with sufficient accuracy in a K~L-SM chromatograph, with a stationary phase of poly(ethylene glycol adipate) (10%) on INZ-600 as carrier. The yield and composition of the copo]ymer were found from the quantities of unreacted St, VTES and MA.* The composition of the copolymer was also found by elementary analysis. DISCUSSION The M A - S t - V T E S s y s t e m studied differs f r o m others in certain features o f the chemical affinity of t h e monomers, a n d is interesting because in it complex f o r m a t i o n occurs between the monomers, a n d this has a substantial effect on their copolymerization. I n references [9] a n d [10] an a t t e m p t was m a d e to d e t e r m i n e the equilibrium constants for f o r m a t i o n of complexes between MA a n d electron-donating monomers. I n m a n y instances this was n o t possible, e v i d e n t l y because o f the r a t h e r low c o n c e n t r a t i o n of complex in t h e original mixture. T h e f o r m a t i o n o f a complex in M A - S t m i x t u r e s has been confirmed b y a n u m b e r o f a u t h o r s [9, 11]. D

0"75

0"25 I

0"5 HA, mole fraction

1"0

FIG. 1. Dependence of the optical density of MA-VTES mixtures on composition, in chloro. form at 360 (1), 365 (2), 390 (3), 450 (g) and 610 m/~ (5). W e f o u n d t h a t when MA and V T E S are m i x e d a coloured solution is formed, e v i d e n t l y also as a result of c o m p l e x - f o r m a t i o n between the monomers. T o v e r i f y this t h e ultraviolet spectra were recorded o f different ratios o f t h e m o n o m e r s in chloroform (Fig. 1). I t is seen t h a t absorption m a x i m a occur only a t t h e equim o l a r ratio of t h e monomers, which gives grounds for a t t r i b u t i n g t h e following s t r u c t u r e to the 1 : 1 complex

* The qantity of unreacted MA was found by potentiometric titration of an aqueous extract of the reaction mixture.

289

Radical copolymerization of maleic anhydride

The complex-formation constants (k) and the extinction coefficients (8) given below were determined from the well known Benesi-Hfldebrand equation [12], with the condition D>>A (determined in chloroform at 184-0.5 °, concentration of MA 4.4× 10-3 and of VTES 0.5 mole/1.) ~, m/~ 420 k, l./mole 0.384 ~, 1./mole-1/cm-1 200

480 0.360 464

570 0.303 1333

We were unable to determine k and s for M_A-St systems under similar conditions, probably because of a very low concentration of the complex in themixture, due to a comparatively high mobility of the migrating electrons resulting in shift of the equilibrium toward dissociation of the complex. With regard to the special features of the chemical affinity of this system, it is well known that MA and St readily copolymerize with formation of an intermediate CTC, resulting in formation of a copolymer with a regularly alternating composition. Maleic anhydride also copolymerizes with VTES [13]. This yields products of low molecular weight, apparently because these monomers have a great tendency to form a stable adduct. Vinyltriethoxysflane undergoes radical polymerization under more rigorous conditions [13] and copolymerizes with difficulty with styrene. Maleie anhydride does not polymerize under the conditions of the ternary copolymerization, though under certain conditions it can homopolymerize. A special feature of the ternary copolymerization of MA, St and VTES is. that the reaction can occur either as a binary copolymerization of the complexomer MA-St (MI--M~) with VTES (M3) CO--SH ill--Celia 1 CH~=CH O/ + I -* ~CO--CH CH2 ] Si(OCzHs)s

I

I

I

I

I

/

!

I

or by copolymerization of the two complexomers NA-St (MI~M2) and ~ - V T E S

(M1--M3)

~C~---Si{OC.Hs), -* CH~

J

290

Z. •. RZAYEV et al.

l\

o

L

o

depending on the initial ratio of the monomers. Data on the ternary copolymerization of MA, St and VTES under conditions of excess of the donors and of the accepter are given in Table 1. TABLE 1. COPOLYMERIZATIONOF MA, St AND VTES (80 °, time 2 hr, solvent--toluene, initiator--0.1% of bonzoyl peroxide calculated on the weight of monomers) Starting mixture, mole % St VTES MA

Yield of copolyrnor,

48.8 45.2 40-0 34.5 5.0 8.8

87'5 71"3 67"2 47"0 36"5 28"3

48"8 49"8 40"0 34"5 50"0 8"8

2-4 5.0 20.0 31-0 45.0 82.4

o/ /o

Found, %

C

H

Si

70.36 69.77 69-68 69.58 64.65 57.32

4"92 5"11 5"38 5"57 6"27 5"84

0"22 0'51 0"54 0.72 4.27 6"58

Copolymer composition, mole % MA VTES St 49.25 48.25 48 "05 47-38 35"50 25.35

49.25 1"50 48.25 3-50 48-05 3"90 47.381 5"24 35.50 29"00 25.35 49"30

These monomers form an accepter (MA)-donor (St)-donor (VTES) system, to which the Mayo-Lewis theoretical equation taking account of k between the monomers is applicable. For binary copolymerization of the complexomer M~--M2 with M 3 (with excess of donor) the equation takes the form:

d[Ms]

[Ma]

[ [M~--M21+(r2/kO[M3]

}'

a n d for copolymerization of the two complexomers M~--M~ and M~--M 3 (with excess of accepter) d[Mx--M,]

[M1--M~].~r~'kl/k~" [M1--M~]-F[M1--Ms]~

d[M1--M3] = [M1--Ma] ( [Ma--M2] +r2(k~/kO[M~--M3]J We n e x t examined the possibility of determining the reactivity ratios and the parameters Q and e for the pairs of monomers and eomplexomers making up this sytesm, by the chromatographic method of Jaacks [14]. In view of the fact t h a t MA and VTES copolymerize to form products of low molecular weight [8, 13] and t h a t ethylsilyl groups are susceptible to hydrolyric splitting, it did not prove possible to isolate the copolymer with sufficient accuracy for analysis and determination of r 1 and r 2. Moreover, chromatographic

0.259 0.062 0.295 0.036

5.950 0"036

M 1

O.044 4.480 0.018 0.204

0.269 2.590

M~

0.195 0.052 0.216 0.014

5.130 0.025

M 1

0'037 4.260 0.014 0.189

0.236 2.540

M~

after copolymorization

Monomer mixture*

before copolymorization

* Concentration of monomers determined chromatographically. Figures from ref. [2]. Calculated from H a m ' s equation for t e r n a r y copolymerization [15].

(MA-St)-(MA-VTES)

St-MA* MA-VTES* (MA-St)-VTES

St-VTES

System

Q A_~D e SYSTEM

1.240

0.043 0.035 1.630

1.130

rl

0"081

0-018 0-004 0.290

0-056

~2

0-100

0.473

1 - 4 7 × 10 -4

7-74 × 10 -4

0.063

r 1•r 2

0.384

1.000 0.180 0.384

1.000

Q1

--0"012

--0.800 --2.650 --0.012

--0.800

el

Q~

0.309

0"180 0.002 0.235

-}-0-318

- - 2. 650 +0.318 --1.528

+0-858

e2

MA-St-VTES

0.235

F O R P O S S I B L E C O M ~ I ~ A T I O N OF M O N O M E R S I N T H E

(Solvent--benzene, initiator-benzoyl peroxide (0.1 ~o calculated on monomers), 70 °)

T A B L E 2. T H E R E A C T I V I T Y R A T I O S ~"x A N D ~"2 A N D T H E P ~ T E R S

O

O

N

3

c~ 0

292

Z.M.

RZAYEV et al.

analysis of the monomer mixture before and after polymerization also gave unsatisfactory results. For this reason the reactivity ratios for St and VTES were found first, then by means of Ham's theoretical equation [15] applied to the ternary copolymerization of HA, St and VTES, r 1 and r~ for HA and VTES respectively were calculated, using the known values of r 1 and r~ for St and HA. The results are presented in Fig. 2, which shows the dependence of copolymer composition on the composition of the monomer mixture, and in Table 2. It is seen from Fig. 2 that the reaction of HA with St (curve 1) and with YTES (curve 2) occurs at a stage close to homopolymerization of the correspond° ing complexomers of 1 : 1 composition. On the other hand the HA-St complexomer behaves as an individual, copolymerizable monomer with respect to VTES {curve 3) when the donors are in excess, and to its complex with HA (curve 4) (with excess of accepter). In the copolymerization of St with VTES (curve 5) no deviation from the ideal radical reactivity is observed. From the results presented in Table 2 it is seen that St and VTES are monomers that copolymerize with difficulty. The active centre of the St radical reacts very much more readily with its own monomer, but the VTES radical reacts about twenty times more easily with St than with its own monomer. In copolymerization of the HA-St complexomer with VTES the reactivity of the VTES radical is considerably changed. The copolymerization curves (Fig. 2) and the values of rl and r~ found for the complexomers HA-St and HA-VTES, which differ considerably from the corresponding data for the system HA-St and VTES, suggest that in excess of the acceptor (HA) the effect of complex formation on the radical process is enhanced. Corresponding changes occur in the values of the "specific activity" and "polarity" of the complexomers (Table 2). From the found and calculated values of the reactivity ratios for the binary systems (Table 2) the probabilities of formation of various structures in the copolymers for different compositions of the monomer mixture were calculated from the theoretical equations of ternary copolymerization [16] (Table 3). Although the experimental facts presented above explain satisfactorily some of the correlation in copolymerization involving charge-transfer complexes, they nevertheless do not show whether complex formation precedes copolymerization and whether all of the monomer molecules add to the growing chain in the form of complexomers, and they also do not provide the possibility of judging the effect of complex formation on the over-all mechanism of radical copolymerization. In order to make some sort of approach to the solution of these problems ~ve carried out some kinetic studies of radical copolymerization in the systems ,(MA-St)-VTES and (MA-St)-(MA-VTES). The results of dilatometric study of the kinetics of copolymerization are presented in Fig. 3. It is seen from the graphs that the relationship is linear at low conversions and the onset of copolymerization is preceded by an induction

0.050

0.010

0-025

0-002

0-050

0.010

0.025

0.020

St

I

0.018

0.050

0-010

0.045

0.025

VTES

m i x t u r o , molos

0-050

[

,,

0.050

MA

Initial

f (M). I

0.014 0.040 0-002 0-012 0.040 0.003 0.012 0"040 0.004 0"009 0.038 0.007 0.031 0.004 0"003

,~=2 0-000 0-001 0.000 0.000 0-001 0.000 0.000 0.001 0.000 0-000 0.001 0.000 0.000 0-000 0.000

n~3

0.172

0.328

0.393

0.405

0-440

0.964

0.894

0-924

0.929

0.942

0.800

0.503

0.342

0.315

0.202

fMA--V~

0-989

0.926

0.928

0.929

0.930

.t'Wm-MA

Probability of formation of struoturos

0.444

0.068

0.036

0.032

0.018

~ t - VTEfl

T A B L E 3. P R O B A B I L I T I E S OF F O R M A T I O N OF V A R I O U S S T R U C T U R E S I N T H E T E R N A R Y C O P O L Y M E R

0.007

0.066

0.066

0.066

0.066

fVTES-St

¢¢

O

O

o

*0

o O

0

294

Z. ~ . I~ZAYEV e t a l .

period, which decreases as the temperature is raised. The latter can be explained by formation of complexes between monomer molecules reacting in the initial mixture. The over-all energies of activation for the above systems of monomers were calculated from the experimentally found initial rates of reaction at different m2

1"0

//" /1

×]

fO | !

Z z3 $

/

5 8

06

0"2 v

I

I

0.2

I

O.g FIG. 1

I

M2

1.0

20

60

100

T/me, m/n FIG. 2

FIG. 2. Copolymerization curves of the sysbems: 1--MA-St; 2--MA-VTES; 3--St-VTES; 4---(MA-St)-VTES; 5--(MA-St)-(MA-VTES). 1K2 and m2 are the mole fractions of St, VTES and the MA-VETS complexomer in the initial monomer mixture and in the copolymer respectively. FIG. 3. Copolyrnerization rate curves: 2, g, 5, 7--(MA-St)-VTES; 1, 3, 6--(M_~-St)-(MAVTES); 1, 2--75°; 3, 4--70°; 5, 6--65 ° and 7--60% temperatures (60, 65, 70 and 75°). The values found were 20.7 keal/mole for the (MA-St)-VTES system and 26.2 keal/mole for the (MA-St)-(MA-VTES) system. The considerably higher activation energy in the second system is probably due to a greater effect of complex formation, because in this system (with excess of acceptor) there is a greater probability of formation of complexes between the acceptor and two donors than in the first system (with the donors in excess). Determination of the dependence of the rate of copolymerization on the concentration of benzoyl peroxide showed t h a t copolymerization of MA-St with VTES is a reaction of the first order with respect to initiator (Fig. 4a), but the order of reaction in the (MA-St)-(MA-VTES) system is 0.53 (Fig. 4b). This suggests t h a t in the first instance chain transfer to VTES occurs to a considerable extent, but in the second the reactivity of the monomers is increased by complex formation of ]VIA with St and VTES, whereby the rate of reaction becomes proportional to the square root of the initiator concentration.

295

Radical copolymerization of maleic anhydride

I n both instances the rate of copolymerization increases as the initial eoneent'ration of the monomers in solution in benzene is increased. The order of reaction with respect to the monomers was found from the slopes of the log-log graphs, the figures being 1.57 for the (MA-St)-VTES system and 2.25 for the (MA-St)(MA-VTES) system (Fig. 5).

lo3 w÷5 2

30

looqw+6

b

¢o

2

!

! 0-02

0"0¢

[BPO],

0.06

I

I

I

2

,

i

3

0.8

loj [BPc].,

me/eft.

f'O

log [M]

FIG. 4

Fro.

1.~ +I

5

FIG. 4. Dependence of the rate of copolymerization on initiator concentration. (MA-St)VTES (a) and (MA-St)-(MA-VTES) (b). FIG. 5. Log-log graphs of the dependence of copolymerization rate on monomer concentration. (MA-St)-VTES (1) and (MA-St)-(MA-VTES) (2). Hence the equations for the rates of copolymerization are: for (MA-St)VTES w=/c[I] [M]r57 and for (MA-St)-(MA-VTES) w=k[I]0'53[M]2"~5. From the general reactivity of the monomers it m a y be assumed t h a t in the first instance there is no effect of complex formation between MA and VTES, "~ 2.0-

8.O

~.'.

"~

2-0'.~ i.o

20

I

I

ziO

80

I

80

[M], mole %

Fro. 6. Dependence of the rat~ of copolymerization on concentration of MA (1) and of VTES (2) in initial mixture. or it is very weak because of the higher rate of interaction of MA with St t h a n with VTES. This assumption is supported by the fact t h a t MA copolymerizes with St at a high rate, whereas it does not copolymerize with VTES under similar conditions.

296

Z . M . RzAY~V e~ al.

T h e results of s t u d y of t h e effect of t h e c o n t e n t of t h e a c c e p t o r (MA) a n d d o n o r (VTES) in t h e initial m o n o m e r m i x t u r e were v e r y interesting (Fig. 6). W h e n t h e MA c o n t e n t is increased t h e r a t e of c o p o l y m e r i z a t i o n increases a n d reaches a m a x i m u m a t a n MA c o n c e n t r a t i o n of 65-70 moles ~ , b u t t h e r a t e decreases as t h e c o n t e n t o f V T E S in t h e initial m i x t u r e is increased. T h e o b s e r v e d changes in t h e kinetic p a r a m e t e r s in t h e studied s y s t e m s m a d e u p f r o m MA, St a n d V T E S show t h a t c o m p l e x f o r m a t i o n b e t w e e n t h e m o n o m e r s exerts a s u b s t a n t i a l effect on t h e kinetics of t e r n a r y c o p o l y m e r i z a t i o n . CONCLUSIONS

(1) F r o m t h e results o f u l t r a v i o l e t spectroscopic analysis a n d of kinetic s t u dies it is s h o w n t h a t f o r m a t i o n o f c h a r g e - t r a n s f e r complexes occurs in c o p o l y m e r ization of maleic a n h y d r i d e (MA), s t y r e n e (St) a n d v i n y l t r i e t h o x y s i l a n e (VTES). (2) I t is s h o w n t h a t t h e t e r n a r y s y s t e m M A - S t - V T E S undergoes r a d i c a l p o l y m e r i z a t i o n as a b i n a r y c o p o l y m e r i z a t i o n , either o f t h e M A - S t c o m p l e x o m e r w i t h V T E S , or of t h e t w o c o m p l e x o m e r s M A S t a n d M A - V T E S , a n d t h e theoretical equations o f b i n a r y c o p o l y m e r i z a t i o n are applicable t o this s y s t e m . (3) T h e r e a c t i v i t y ratios a n d s o m e kinetic p a r a m e t e r s o f t h e r e a c t i o n h a v e been d e t e r m i n e d a n d it is suggested t h a t c o m p l e x f o r m a t i o n affects t h e kinetics of t h e t e r n a r y c o p o l y m e r i z a t i o n . T~m.s/a~ed by E. O. PH*LL*PS

REFERENCES

1. P. D. BARTLETT and K. NOZ~Kr~ J. Amer. Chem. Soc. 68: 1495, 1946; g. H. BAMFORD and W. G. BARB, Disc. Faraday Soc. 14: 208, 1953 2. M. C. WILDE and G. SMETS, J. Polymer Sci. 5: 253, 1950 3. S. IWATSUKI, J. TANAKA and J. JAMACHITA, J. Chem. Soc. Japan, Ind. Chem. Sect. 67: 1467, 1964 4. U. KAKU, M. TOSINM~I(A, K. JUSIMAKA and M. NIR0, J. Chem. Soe. Japan, Ind. Chem. Sect. 70: 1945, 1967 5. S. T. BASHKATOVA, V. I. KLEINER, L. L. STOTSKAYA and B. A. KRENTSEL', Vysokomol. soyed. Al1: 2603, 1969 (Translated in Polymer Sei. U.S.S.R. 11: 12, 2957, 1969) 6. R. D. KINEBROUGH and W. DICKSON, J. Polymer Sei. B2: 85, 1964 7. A. A. EL SAID, S. Ya. MIRLINA and V. A. KARGIN, Dokl. Akad. Nauk SSSR 177: 380, 1967 8. D. A. KOCHKIN, P. I. ZUBOV, Z. M. RZAYEV, I. N. AZERBAYEV, V. I. VASHKOV, I. I. KOVALEVA and G. V. SHCHEGLOVA, Vestnik Akad. Nauk K~zak.SSR 10: 45, 1966; Z. M. RZAYEV, D. A. KOCI~gIN and P. I. ZUBOV, Dokl. Akad. Nauk SSSR 172: 364, 1967; Z. M. RZAYEV, Sh. K. KYAZIMOV and S. I. SADYKH-ZADE, International Symposium o~1 Maeromolecular Chemistry, p. 31, Budapest, 1969; I. N. AZERBAYEV, Z. M. RZAYEV, D. A. KOCH~IN and S. G. MAMEDOVA, Vestnik Akad. Nauk Kazak.SSR 9: 14, 1970; S.I. SADYIgH-ZADE, Z. M. RZAYEV, L. V. BRYKSINA, Sh. K. KYAZIMOV and F. Ya. KASUMOV, Vysokomol. soyed. B15: 481, 1971 (Not translated in Polymer ScL U.S.S.R.) 9. W . G. BARB, Trails. Faraday Soc. 49: 143, 1953

Time-temperature relationship of the strength of polymers

297

10. W. KAWAI, J. Polymer Sei. A-l, 6: 1945, 1968; O. TAKAYUKI and J. HIROCHI, Makromolek. Chem. 128: 31, 1969 11. K. B. WOLFSTIRN and F. R. MAYO, J. Amer. Chem. Soc. 68: 1538, 1948; P. S. SHANTOROVICH and L. N. SOSNOVSKAYA, Izv. A k ~ . Nauk SSSR, set. khhn., 358, 1970 12. H. A. BENESI and J. H. HILDEBRAND, J. Amer. Chem. Soc. 71: 2703, 1949 1 3 . G. H. WAGNER, D. L. BAILEY, A. N. PINES, M. L. DUNHAM and D. B. MELTIRE, Ind. Engng. Chem. 45: 367, 1953 14. V. V. JAACKS, Makromolek. Chem. 105: 289, 1967 15. G. E. HAM, J. Polymer Sei. A2: 2735, 1964 16. H. J. HARWOOD and W. M. RITCHEY, J. Polymer Sci. B2: 601, 1964; S. TOSI, European Polymer J. 6: 161, 1970

THE POLE S H I ~ OF THE TIME-TEMPERATURE RELATIONSHIP OF THE STRENGTH OF POLYMERS* K. V. NEL'SON and D. SA~DOV S. V. Lebedev All-Union Research Institute of Synthetic Rubber

(Received 27 April 1970) THE logarithmic dependence of the durability of polymers on temperature is represented according to the formula ~=T0 exp [(Uo--ya)/kT ] by a family of straight lines at a = c o n s t , intersecting at a pole whose coordinates, according to the thermal fluctuation theory of the strength of materials, should have the value z0=10 -18 sec at l / T = 0 [1, 2]. On the other hand in some instances the pole is found to be shifted along the reciprocal temperature axis [3-7]. In this connection there are two, diametrically opposed points of view. Some authors consider t h a t when this pole shift occurs U 0 loses its physical meaning as the energy of activation for rupture and it cannot be determined from graphs of log z=f(1/T) [5]. Others suggest the introduction of an empirical correction for the pole shift and determination of U o in the usual way. Since in the physics of the strength of materials fundamental importance is attached to the coordinates of the pole, study of the physical nature of the factors causing the shift is of considerable value. I t is shown in this paper t h a t the position of the pole is related to a certain value of the intermolecular interaction of the polymer chains. In an unfilled vulcanizate (Fig. lb) the pole is shifted along the reciprocal temperature axis by the q u a n t i t y 1 / T = 3 x 10 -8 deg -1. When an active filler is introduced the pole is displaced to the left from this point, and for an SKN vulcanizate containing 32 ~/o of Aerosil the pole lies on the ordinate in conformity with theory (Fig. 2b). * Vysokomol. soyod. A14: No. 2, 268-273, 1972.