Investigation of the dependence of parameters of dielectric relaxation processes in polymers on their structure

0032-305017810501-1260507.50]0

.:Pol¥1ncrScienceU;S.S.R.VeX.20, pp. 1260-1268, t ~ Pergamon Press Ltd. 1979.Printedin Poland

INVESTIGATION OF THE DEPENDENCE OF PARAMETERS OF DIELECTRIC RELAXATION PROCESSES IN POLYMERS ON THEIR STRUCTURE * _A. p . STETSOVSKII a n d L. V. TARASOVA ~eKtral Research I n s t i t u t e for Technical Information a n d Commercial-Engineering Studi~s

(Received 25 July 1977) The results of an analysis of experimental data on the dielectric relaxation prec. esses in 78 polymers show that the dependence of the relaxation time of cooperative dielectric polarization processes on temperature and[ pressure is described by the equation:

The value of the preoxponential factor r0 depends on the polar group structure a n d on t h e mode of its a t t a c h m e n t to a macromolecule. The activation energy Uc is determined b y the energy of intra- and intermotoculax interaction, and T , is the structural glass transition temperature.

IT IS now known that dielectric relaxation processes take place in liquids and in solid amorphous polymers in the temperature region above the glass transition temperature. A characteristic feature of such processes appears in the nonlinearity of the log T----q(l/T) plots, which is generally held to stem from the cooperative character of molecular transitions underlying these cooperative relaxation processes [1-3]. Attempts to give a theoretical description of kinetic regularities in cooperative processes of dielectric relaxation have on a few occasions been made, b u t in so far as the relations obtained are consistent with the available experimental data in [2, 3] this is solely from a quantitative standpoint, and within a limited range of temperature and frequencies. It was shown in [4] t h a t t h e temperature dependence of relaxation times for cooperative processes of dielectric polarization can in the case of some polymers be described satisfactorily b y the empirical equation T~--ro

exp . . . . In 2RT~ T - - TgJ

(1)

where Uc is the activation energy for cooperative processes; Tg -- the glass-transi* Vysokomoi. soyed. A20: No. 5, 1116-1123, 1978. 1260

Dielectric relaxation processes in polymers

1261

t?ion temperature; R -- the gas constant and r0, the preexponential factor. We thought it might well be of interest to veri~" the validity of equation (1) as a means of describing the dielectric behaviour of polymers with a variety of structures; in addition, an attempt could b e made to shed light on the dependence of parameters r 0 and Uc on the molecular structure of polymers, which could be conducive to a better une[erstanding of the mechanisms of dipole relaxation processes in polymers. To do so we analyzed a large number of experimental log T--~0(1/T) plots published in literature for polymers with various structures, as it seemed that values of r0, Uc and Tg might be cahmlated from the plots in question. The calculations were done with a computer, using a program that would ensure computation of the latter parameters while minimizing the mean square deviations a of theoretical values of log rt, calculated in accordance with equation (l), from the experimental values of log r~ at temperatures identical to those cited in the original sources of information. Similarly, we analyzed data on the temperature dependence of relaxation times for dipele-group processes on the assumption t h a t the curves in question obey the Arrhenius equation

l/g r=r,j exp R T

(2)

The principal results of the calculations are given in Table l, and the following conclusions were reached in the light of these findings. Within the limits of experimental accuracy the experimental data are in all cases described by equations (1) or (2) for the cooperative and group processes respectively, given the values of the coefficients in Tal)le l, as is evidenced b y the fac,t that the values of a(, and as do not. exc(~ed 0.3--0.4. (liven these values of a, the curves in Fig. 1 illustrate the degree of agreement between theoretical plots of log r==0(l/T ) and the experimental findings. It was f(mnd that the lowest values of ae and as correspond to values of the pre-(,xi)onential factors %° and %,, whi~,h differ fi'om the foregoing values by less than one order. Since these differences are within the limits of accuracy for the calculations, one may assume that To values for the dipole-group processes of dMectric relaxation coincide with those for the cooperative processes. Values ef the pre-exponential factors r 0 and of the activation energies Uc and Ug calculated fi)r identical substances on the basis of experimental findings of different authors (PVA, PERYP, PVC, PCTPE, .PVDP) coincide, within the limits of accuracy for the calculations, (differences of from 1-1.5 kcal/mole in the values of Uc and U~ being attributable to experimental errors), which means that the parameters in question are reasonably stable characteristics of the polymers, and relate to their structure and composition. It must be said t h a t the found values of the pre-exponential factors are within the limits of 10-~4-10 -~6 see, although the values in question relate to infinitely large temperature values (I/T----0). At temperatures of the order of 500-1000°K relaxation times found in accordance with equations (1) and (2) are 10-1=-10-nsec.

1262

T~LZ

A.P.

l, V~m

S ~ r r s o v s x M a n d L. V. T t n ~ . o v A

OF P*--,~rZRS OF Dr~LEOT~0 m ~ n T X O N

N a m e of p o l y m e r

log Te

Aetiva. tion energy, kcal/ /mole

OI-J~_ trarmition temp., OK

~SSm

n~ POLYMER8

Re.royce8

Polar groups

uolv, PVA tt

tt tt

14 14 14 14 14 14

9.8 10.3 9"9 9"7 9"8

9"5 309

9.4

0.25 o.oe 0.37 0.23 0.15 0-04 ode O.lS 0.19 0.19

[5] [6] [7] [8] [9] [i0] [10]

301 0.22 0.38

[35]

328 0.17 0-0~

[8]

298 301 298 296 311

10"5

Polyvinylpropionate

14

10.4

Polydiansebacate

16

Polyvinylbenzoate

15

Polyacrylates

15 8"5-

9"2

9"3 299

12.8 10.7

o --4jH,I - . ~ H I

O IJ --CH,--C--O---~ O o

[4]

8"0 Polymethacrylates

15

Polycyclohexylmethacrylate Polyparaethyleneoxybenzoate (crystalline) (amorphous) P E T P (crystalline) Ditt~

15

t~

P E T P (amorphous) Ditto t~

Dibutylphthalate

l

1112 14"6

[4] [4]

o II CHjA--C--O--CH, I 0 il I

15 15 15 15 15 15 15 15 15 14

9.7 8.8 11.4 10.7 9.6 14.6 9.3 9.0 11.6 5.4

I1.9

362 353 13.0 357 360 11.7 361 12.9 358 351 344 342 338 183 178

0.33 0.15 0.44 0.09 0-43 0.03 0.19 0.23 0.37 0.26

0.34 0-07 0.37 0.02

[11] [11] [12] [13] [11] [12] [12] [13] [14]

I

O

~--~--0 ---CH~ o II

\

C--C--O--CH.-II

C--C--O--CH,-Hexamethylenesebacyamide Polyvinylformal Polyvinylethylal

14 16 16

8-6 18.0 15.3 13.5

318 0.14 195 0.52 374 0.17 0.21

[15] [7] [7]

o I

Dielectric relaxation processes in polymers

1263

TABL~ 1. (cont.)

Name of polymer

log

Activation energy, kcal/

"'1 /mole

Glass transition temp.,

I

oK

[

~'e

References

O'f

Polar groups

I

I uo I u----~l[---~-~' T. T~/ Polyvinylpropional Polyvinylbutyral Ditto Polyvinyloctylal Polyvinylhexylal Polyvinylcyclohexylal Polyvinylfurfural Polymethyleneoxide PEO Tetraothylene glycol Polytetramothylenooxide Ditto Polyadipate Polypropyleneoxido Polyphenylmethylsiloxano Polyepichlorohydrin Polyepibromhydrin PVC

Chlorinated polyethylene with chlorine contents of: 50%

40°;, 30%

20% PCTPE ,, PV DP

(amorphous) (crystalline)

16 16 16 16

I 1.0 14"0

14.2[ 13.4 12.4 12.5 15.1 15.0 7.0 6"7 6"1

3781 0.13 0.15 302 2841 0.28 322 I 0.12 0.39 13.6 3041 0.11 13.6[ 313i 16"4[3981 3781 0.08 14.4[ 347 3991 0.00 9.51 186 1951 0.20 8.91 206 183l 0"I1

[7] [7]

[17] [17] [16] [18] [18]

197 I 0.11 8.61 187 196 I 0"06 0"28!

[18]

5.5 10.1 7-7

8.51 189 194 I 0"081 0"15 243 238]0"24 I 198 196 0"16

[20] [21] [22]

i

15 14 14 16 16 16 16 16

8.2 7"8

236 229 0"48 7.7 251 258 0"07 0.0l[ 246 0 05 10-3 1 350 361 0.16 0"261 10.71 348 1 1.8[ 358 356':0"09 I 323 0"O8 15'4 3.49 346 0"14 0"12:

16 16 16 16 15 15 14 14 14 14 14 14

I0"0 9-9 11"4 8"5 10'9 8'6 10-4 14"6 15.4 13'5 7-4 7.4 7.4 7"11

38210.1510.05

o/ [

--'CHs---O---CHs--

[19]

5"2

[23] [24] [24]

[25] [26] [26]

--CH--0

I ---SI--O--S[-I [ --CH--0---CH,-I CH, [ Cl

i2~]

--cII--cH,-I Cl

[27] [27]

--CF--CFs--

[27]

'

I 296 286 0.0~ 263 255 0-2c 0.1~! 260 247 0-1~ 0.14, 258 '248 0'1~ 0"071 ,!363 0'2~ 0.40 :357 0"07 2211 220 0.08 I 211 0.08 '222 0.05 224 0.16, 220 0.07 ]

22410.091

I CH,

~o

[ [

i

till'

!

[27] [27]

[28] [28] [29]

[30] [31] [32] [33] [34]

--CII,--CF,--

1264

A. P. STETSOVS~I and L. V. TARASOVA TABLE 1 (cont.)

N a m e of p o l y m e r

log T0

A c t i v a - ' Glass tion trartsienergy, tion kcalt temp., /mole i °K

~rc

¢Tg

Refer-

ences

P o l a r ,groups i

uol u,i T;Ir Copolymers of P V D P with hexafluoropropylene, c o n t e n t s of t h e l a t t e r being:

2% 10% 23% 25% 30.s% 32.5%

14 14

14 14 14 14

7"(] 6"7 6"8 7"~ 8"(] 8"4

236 248 252 255 261 269

224 253 253 255 260 259

0.14 0.15 0.10 0.11 0.03 0.03

[31]

---CH,--CFt--CF--

[31] [31]

[3U [31] [31]

I t can be seen from the data in Table 1 that there is a definite correlation between the mode of polar group attachment to a polymer molecule and the value of %. Taking as examples polymers containing the polar group - - C O O - it can be seen that v0=10 -'5 sec remains invariable in all cases when chain branching takes place on the part of a C atom (polyacrylates, polymethacrylatcs, P E T P , polyparaethyleneoxybenzoate), and where branching on the part of O atoms is of very minor significance (polyvinylbenzoate, polycyclohexylmethacrylate). However, if chain branching takes place solely on the part of O atoms (PVA, polydiansebacate), and in cases where there is close proximity between two groups (dibutylphthalate), there are changes in amounting to two orders (from 1 0 - ' ~ 1 0 -~6 sec). Similar regularities are detectable in the case of P E O homologues, polyepichlorohydrin, etc. In view of these considerations, and taking account of the constancy of 7o values for PVC and for the chlorinated polyethylene and the copolymer of P V D P with hexafluoropropylene, one may conclude that the value of T0 depends on the polar group structure and on the mode of polar group attachment to a macromolecule. The found values of Uc and Ug are within the limits of 5-18 kcal/mole, i.e. are of an order of magnitude in keeping with the energy of intra- and intermolecular interactions. On comparing the activation energies for the polymer homologues it is seen that an increase in the length of the side radical (polyacrylates, polymethacrylates, polyformals) or in the distance between polar groups in the chain (polyoxides, chlorinated polyethylene) leads to a 10-30% reduction in the activation energy, the first two or three carbon atoms accounting for the main effect. This means that the values of Uc and Ug are determined to a considerable extent b y effects of intermolecular interactions. I f on the other hand we compare U values for polymers having similar chain structures and polar group structures (e.g. PbIA and PMMA, polyhexamethacrylate and polyeyelo-

1265

Dielectric relaxation processes in polymers

hexylmethacrylate, polyvinyl- and polycyclovinylhexylal, etc.), it Can be seen t h a t changes in chain structurc giving rise to increased stiffness of the chain or limiting possibilities of intramolecular r o t a t i o n lead to higher activation energies for dielectric relaxation processes, the increase amounting to 15-25%. One m a y accordingly conclude t h a t the values of Ue and Ug are determined by effects of both intra- and intermolecular interactions.

log"C'I

-lO

000 0 2

- 5

° c~ ooo o +

0

I

J

5

/OS/T"S

Fie. 1. Temperature dependence of the relaxation time for dielectric polarization processes in polydiansebacate (1, 1') and PVA (2, 2'). Solid lines -- thcoretical dependences based on equations (1) and (2). The results of the calculations showed t h a t lhe Tg vaIues found on the basis of equation (1) coincide within the limits of experimental accuracy, with few exceptions, with structural glass transition temperatures T~ determined by DTA and by dilatometry, and accordingly there are grounds for thinking t h a t the values in question are altogether identical. The experimental results evidence the validity of equation (I) for describing cooperative dipole relaxation processes. Corroboration of this proposition could be obtained by using equation (1) to describe the effect of pressure on relaxation times for cooperative processes of dielectric polarization. To do so we will transpose the equation by using an existing empirical relation [36] q~

1

= -V"

dV

(3)

where a is the temperature coefficient of expansion, and @ is a constant that is approximately equal to 0.16; V - - volume. Integrating equation (3) over the~

~266

A.P.

Sv~rsovsKrl and L. V. T~tASOVA

T a n g e f r o m Tg to T, we o b t a i n

V--1

,

(4)

~ h e r e V a n d VB are volumes a t T a n d T 8 a t a t m o s p h e r i c pressure. S u b s t i t u t i n g f o r m u l a (4) into (1) we o b t a i n • ----T, e x p

2-R-~In

(5)

T a u s , the r e l a x a t i o n t i m e is a f u n c t i o n o f the volume, which in general is b o t h Iog~" -lY

-1o

-y t

0

.~

z

1

i'O 2"0 J.O 4.0 5"0 ?Q$/T FIe. 2. Plots of relaxation, times for cooperative processes of dielectric polarization vs. temperature and pressure in PPO under pressures of 1.0 (1), 1000 (2) and 2000 H / m s {3) and in polynonylmethacrylato under pressures of 1.0 (4), 500 (5), I000 (6) and 15,000 H / m ~ (7). t e m p e r a t u r e a n d pressure d e p e n d e n t . In this case one m a y assume t h a t to express v o l u m e in relation to pressure one m a y t h i n k in t e r m s of an exponential f u n c t i o n o f t h e t y p e of V (P) ~-- ( V0 - Vg) e-~:P--~- Vg, (6) w h e r e Vo - - t h e v o l u m e at _P= 0, and rc -- a coefficient characterizing the compressibility of a substance. :Rcplacing In (V/Vg) in formula (5) b y the first t e r m o f t h e expansion o f (V/Vg-- 1) in a series, we obtain, after s u b s t i t u t i n g (4) and (6) i n t o (5) •

(,)

Dielectric relaxation processes in polymers

1267

To verify the validity of equation (7) calculations of theoretical dependences o f z----q(P, T) were carried out for PPO and polynonylmethacrylate, substituting into (7) z0 values taken from Table 1, and x----10-' m~/H taken from the handbook [37]. Table 2 gives the calculated values of the activation parameters, and the degree of agreement between the theoretical dependences and experimental findings for the polymers is illustrated by the plots displayed in Fig. 2, from which it is clear t h a t good agreement exists between theoretical plots and the experimental data. TABLE

PPO

2.

ACTIVATION P A R A M E T E R S OF R E L A X A T I O N P R O C E S S E S IN"

AIVD

Polymer PPO Polynonylmethacrylate

POLYI~'ONYLMETHACRYLATE

AT

DIFFERENT

PRESSURES

Pressure,

~'o, sec

Uc, kcal/mole

T, °K

1.0 1000 2000 1.0 500 1000 15,000

10-18

7.75 7-7 9.0 11.4 12.1 12.9 10.0

196 216 217 258 264 272 281

H/m"

10-*' 10-'* 10-16 I0-.6

10-I. 10-,6

In the light of these considerations it appears that the empirical equation whereby the relaxation time of cooperative dielectric polarization processes (equation (7)) is related to temperature and pressure is consistent with a large a m o u n t of available experimental findings. The physical significance of parameters Uc in equation (7) seems to accord well enough with the Arrhenius activation energy of rclaxation processes and with the structural glass transition temperature. In view of this it is suggested that molecular transitions of one and the same kinetic units underlie two types of dielcctrically active relaxation processes in polymers, namely, dipole-group and dipole-segmental processes. Depending on external conditions (temperature and pressure), these transitions take place either independently of the state of the nearest neighbours (uncooperative transition), or are accompanied by corresponding changes in the positioning of the latter (cooperative transition). Accordingly, in the former case the transition probability will be proportional to the Boltzmann factor exp (U/RT), which, according to statistical mechanics, is bound to occur in a system of nonintcracting particles. In the latter case the transition probability depends on whether a change in the positioning of neighbours is feasible, and is therefore largely determined by effects of short range interaction. It is therefore possible to regard the exponential term in equation (7) as being an empirical analogue of the Boltzmann factor for cooperative processes. Trar~/a~d

by

R. J. A. HEND~Y

1268

A.P.

STETSOVSKZZand L. V. TAnAS()VA REFERENCES

1. 2. 3. 4. 5. 6.

7. 8.

9. 10. 11. 12. 13.

i

R. H. COLE, Izv. AN SSSR, seriya fiz. 24: 4, 1960 G. ADAM, J. Chem. Phys. 43: 662, 1965 Yu. Ya. GOTLIB, Fizika tverdogo tela 6: 2938, 1964 A. P. STETSOVSKII and L. V. TARASOVA, Vysokemol. soyed. A I 8 : 904, 1976 (Trans, lated in Polymer Sei. U.S.S.R. 18: 4, 1032, 1976) P. F. VESELOVSKII and A. I. SLUTSKER, Zh. teoret, fiziki 25: 1204, 1955 P. F. VESELOVSKII and I . ' A . GANDEL'MAN, Trans. Kalinln L P I 255: 148, 1965 P. F. VESELOVSKII, Izvestiya K i r o v T P I 91: 399, 1956 Y. ISHIDA, M. MATSUO and K. YAMAFUJI, Kolloid-Z. 180: 108, 1962 S. KASTNER and 5I. DITMMER, Kolloid-Z. und Z. fiir Polymere 204: 74, 1965 G . P . M I K H A I L O V a n d L . V. KRASNER, Vysokomol. soyed. 6: 1071, 1962 (Not translated in Polymer Sci. U.S.S.R.) ¥. ISH1DA, K. Y A M A F U J I , H. ITO and M. TAKAYAMAGI, Kolloid-Z. 182: 97, 1962" Y. ISHIDA, M. MATSUO, Y. UENO and M. TAKAYANAGI, Kolloid-Z. und Z. ffur Polymere 199: 69, 1964 V. I. BEKICHEV, Vysokomol. soyed. B15: 58, 1973 (Not translated in Polymer ScL

U.S.S.R.) 14. K. SAWAMURA, H. SASABE and S. SAITO, Rept. on Progr. Polymer Phys. J a p a ~ 14: 495, 1971 15. R. H. BOYD and C. H. PORTER, J. Polymer Sci. 1O: 647, 1972 16. A. I. ARTYUKHOV and P. F. VESELOVSKII, Trans. Kalinin L P I 255: 135, 1965 17. P. F. VESELOVSKII, Trans. Kalinin L P I 255: 140, 1965 18. V. V. KOCHERVINSKII, V. P. ROSHCHUPK1N, G. Ye. GOLUBKOV, V. A. TALYKO~r and G. V. KOROLEV, Vysokomol. soyed. A10: 2341, 1968 (Translated in Polymer Sci. U.S.S.R. 10: 10, 2721, 1968) 19. N. KOIZUMI and T. HANAI, Z. Phys. Chem. 60: 1496, 1956 20. R. E. WETTON and G. WILLIAMS, Trans. F a r a d a y See. 61: 2132, 1965 21. G. WILLIAMS, Trans. F a r a d a y See. 59: 1397, 1963 22. G. WILLIAMS, Trans. F a r a d a y Soc. 61: 1564, 1965 23. M. E. BAIRD and C. R. SENGURTA, J. Chem. Soc. F a r a d a y Trans. 68: 1795, 1972 24. A. R. BLYTHE and G. M. FEFFS, J. Macromolec. Sei. B3: 141, 1969 25. Y. ISHIDA, Kolloid-Z. 168: 29, 1960 26. L. V. KRASNER and A. V. SIDOROVICH, Vysokomol. soyed. A14: 1193, 1972 (Translated in Polymer Sci. U.S.S.R. 14: 5, 1337, 1972) 27. H. SASABE and S. SALT0, R ept Progr. p o l y m e r Phys. J a p a n 10: 429, 1967 28. G. P. MIKHAILOV and B. I. SAZHIN, Zh. tekhn, fiziki 26: 1723, 1956 29. H. SASABE, S. SAITO, M. A S I ~ N A and H. KAKUTANI, J. Polymer Sei. 7, A-2: 1405~ 1969 30. Y. IHIDA, M. WATANABE and K. YAMAFUJI, Kolloid-Z. 200: 48, 1964 31. N. KOIZUMI, K. TSUNASHIMA and S. YANO, J. I)olymer Sei. B7: 815, 1969 32. N. KOIZUMI, S. YANO and K. TSUNASHIMA, J. Polymer Sci. B7: 59, 1969 33. S. ¥ANO, J. Polymer Sci. 8, A-2: 1057, 1970 34. K. N A K A G A W A and Y. ISHIDA, J. Polymer Sei., Polymer Phys. Ed. 11: 1503, 1975 35. G. P. MIKHAILOV and A. M. LOBANOV, Geterotsepnye vysokomolekulyarnye soyodi. neniya (Hetorochain High-molecular Compounds). Izd. "l~lauka", p. 175, I964 36. R. F. BOYER, J. Maeromolec. Sei. B7: 487, 1973 37. I. K. KIKOIN (Ed.), Tablitsy fizieheskikh veliehin (Tables of Physical Quantities}, H a n d b o o k , Izd. Atomizdat, 1976