122

Kolloid-Zeitschrift und Zeitschrift fiiv Polymere, Band 195 9Heft 2

der komplexen Dielektrizit/itskonstante abgeleitet. Die Aktivierungsenergie wurde ebenfalls nach der Methode von FrShlich bereehnet. Die l~bereinstimmung zwischen theoretischen Ergebnissen und den Beobachtungen scheint quantitativ gut. ])as dfirfte zeigen, dal~ der Mechanismus der dielektrischen Dispersion tatsi~chlich yon dieser Art ist. Die bisherigen Beobachtungsdaten geben jedoch tg 6 als Funktion der Temperatur, so dab Sti~kturiinderungen wie z. B. solche durch Rekristallisation eingeschlossen sind. Untersuchungen bei Variation der Frequenz und konstanten Temperatuven w~ren zum Vergleich mit der vorgelegten Theorie erwiinscht. Re]erences l) An example of the theories of the dielectric ua-dispersion is given by Kirkwood, J. E. and R. M. Fuoss, J. Chem. Phys. 9, 329 (1941). 2) Yama/ufi, K., J. Phys. Soc. Japan 15, 2295 (1960). 3) Yama/u]i, K. and Y. Ishida, Kolloid-Z. u. Z. Polymere 183, 15 (1962). 4) Saito, N., K. Okano, S. Iwayanagi and T. Hideshima, Molecular Motion in Solid State Polymer in; Solid State Physics (edited by F. Seitz and D. Turnbull) (Vol. 14). 5) Oakes, W. G. and D. W. Robinson, J. Polymer Sci. 14, 505 (1954). 6) Mikhailov, G. K., Zhur. Fiz. 27, 2050 (1957).

7) Okamoto, S. and K. Takeuchi, J. phys. Soc. Japan 14, 378 (1959). 8) Kr~imer, H. and K. E. Hel/, Kolloid-Z. u. Z. Polymere 180, 114 (1962). 9) Krum, F., Kolloid-Z. 165, 77 (1959). 10) Slichter, W. P., J. Appl. Phys. 32, 2339 (1961). ll) Peterlin, A., J. Appl. Phys. 31, 1934 (1960); Peterlin, A. and E. W. Fischer, Z. Physik 159, 272 (1960); Peterlin, A., E. W. Fischer and Chr. Reinhold, J. Chem. Phys. 37, 1403 (1962). 12) Rempel, R. C., H. E. Weaver, R. H. Sands and R. L. Miller, J. Appl. Phys. 28, 1082 (1957). 13) Glasstone, S., K. J. Laidler and H. Eyring, The Theory of Rate Process (New York 1941). 14) Gross, E. P., Phys. Rev. 07, 395 (1955). 15) Fr6hlich, H., Proc. Phys. Soe. 54, 422 (1942). 16) Natta, G., J. Polymer Sci. 16, 143 (1955). 17) Onsager, L., J. Amer. Chem. Soc. 58, 1486(1936). 18) Ishida, Y. (private communications). 19) Chandrasekhar, S., Rev. Mod. Phys. 15, 1 (1943). 20) Urey, H. C. and C. A. Bradley, Phys. Rev. 38, 1969 (1931). 21) Szigeti, B., Trans. Faraday Soc. 48, 400 (1952). 22) Shimanouchi, T. and S. Mizushima, J. Chem. Phys. 23, 707 (1955). 23) Tadokoro, H. (private communications). Authors' address: Dr. Kaoru Yama]u]i, Department of Metallurgy, Carnegie Institute of Technology,Pittsburgh (USA}

From the Illrd Institute o/Physics, University, GSttingen

Dielectric Relaxation of PMMA as F u n c t i o n of Pressure, Temperature and Frequency By P. Heydemann With 8 figures in 9 details and 3 tables

(Received November 25, 1963)

I. Shifting factors and free volume O n l y r e c e n t l y t h e h y d r o s t a t i c pressure w a s i n t r o d u c e d as a t h i r d v a r i a b l e into t h e i n v e s t i g a t i o n of r e l a x a t i o n s in p o l y m e r s (1, 2, 3 4, 5, 6, 7). T w o c h a r a c t e r i s t i c q u a n t i t i e s derived f r o m such m e a s u r e m e n t s are t h e shifting f a c t o r s (dT/dP)~, a n d (d lgeo/dP)~. T h e att e m p t s to derive these shifting f a c t o r s f r o m other physical properties of the respective p o l y m e r s are manifold. I t was e v e n assum e d t h a t t h e shifting f a c t o r ( d T / d P ) ~ is a u n i v e r s a l c o n s t a n t for all p o l y m e r s . This is c e r t a i n l y n o t t h e case; b u t t h e differences b e t w e e n t h e shifting f a c t o r s of t h e glass t r a n s i t i o n of different p o l y m e r s are g e n e r a l l y small (table 1). A larger v a r i a t i o n is f o u n d in t h e shifting f a c t o r s r e l a t e d to s e c o n d a r y rel a x a t i o n r a n g e s a n d t h e d e t e r m i n a t i o n of t h e shifting f a c t o r s for these ranges will e v e n t u a l l y lead to interesting conclusions on t h e molecular r e a r r a n g e m e n t processes i n v o l v e d (5, 6).

S e c o n d a r y r e l a x a t i o n r a n g e s were o m i t t e d f r o m the studies of W i l l i a m s , L a n d e l a n d F e r r y (9) on t h e influence of free v o l u m e on r e l a x a t i o n s a n d t h e resulting m e t h o d s to o b t a i n r e d u c e d f r e q u e n c y or t e m p e r a t u r e curves. Because of the g r e a t significance of the shifting factors of s e c o n d a r y r e l a x a t i o n r a n g e s a n d in t h e absence of a b e t t e r theoretical c o n c e p t a s t r i c t l y empirical e x p l a n a tion of the shifting factors of m a i n a n d sec o n d a r y t r a n s i t i o n s m i g h t t h e r e f o r e be of interest. One e x p l a n a t i o n of the shifting f a c t o r s in t e r m s of free v o l u m e is b a s e d on t h e a s s u m p tion t h a t c o n s t a n t r e l a x a t i o n t i m e ( j u m p rate) requires c o n s t a n t free v o l u m e . T h e definition of t h e t e r m ,,free v o l u m e " still p r e s e n t s s o m e difficulties, hence F e r r y (10) calls it " a p a r a m e t e r w i t h a q u a l i t a t i v e m e a n i n g b u t no e x a c t o p e r a t i o n a l definition". F o r a m o r e detailed t r e a t m e n t of t h e free v o l u m e c o n c e p t

Heydemann, Dielectric Relaxation of P M M A as Function of Pressure, Temperature and Frequency

the reader is referred to the study by Marvin and McKinney (11). A definition of the relative free volume / which includes the effects of temperature and pressure was proposed by Marvin (12) and McKinney and Belcher (2). / = t o + ~I (T -- To) -- flI P " [1] The definition is very similar to t h a t used by Williams, Landel and Ferry (9) and, to a limited extent, t h a t of O'Reilly (3). I f for a given molecular rearrangement process constant relaxation time requires constant relative free v o l u m e / , then differentiation of [1] leads to ( dT) fit Aft - ~ ~ = --~t ~ - - ' ~ [2]

where Aft and A~ are the differences between the compressibilities and expansivities above and below the transition temperature. These are generally believed to be quite close to fl: and as. For the shift of the glass transition temperature Tg equation [2] was deduced by Ehren/est (13) more than 30 years ago. Equation [2] was checked by various authors with both mechanic and dielectric measurements. Some of the available data are collected in table 1. The agreement is often satisfactory, but here are some cases with a disagreement t h a t can not be explained by experimental error. The data for Aa and Aft used in table 1 hold for atmospheric pressure. They are, however, not independent of pressure (1, 3, 8). The same holds for Afl/Aa. In the case of PVC + 10% DOP Afl/Aa calculated from the values at 1000 arm. is 31 9 10 -a ~ This reduces but certainly not removes the discrepancy between the measured and the calculated shifting factors. Table 1 dTr dP PVC P V C + 10% D O P PVC+20% DOP PVAe

14 14 13 21

[8] [8] [8] [3]

( dT) -dP ~

Aft Au

17 [6, 7] 46 [8] 17 [7] 47 [8] -36 [8] 22 [3] 50 [3]

Ve

const 24 26 ---

20 [2] 24 [2] PMMA

18 [8]

20

71 [8]

29

Shifting factors of various polymers in 10 3 ~ N u m b e r s in b r a c k e t s refer to t h e references.

Table 1 contains also the temperature differences between states of equal excess volume Ve (fig. 2). None of these quantities agrees with the observed shifting factors, although the free volume or hole volume is probably proportional to the excess volume (14). Here and in the rest of this paper the term excess

123

volume Ve with the dimension cm3/g is used instead of the free volume. The excess volume Ve is a measurable quantity. It is defined as the specific volume produced additionally above each transition temperature as illustrated in fig. 2. The excess volume VTg produced above Tg is available for the a-relaxation process. From our experimental results it seems t h a t for a fl-relaxation process both the excess volume produced above T 1 and at higher temperature also t h a t produced above T o is available. An empirical method to deduce the shifting factors was proposed by Singh and Nolle (4). It is based on the fact t h a t because of kT (~lH+2~_) ~Orel ~ e x p - - ~ + [3] constant jump rate requires constant AH+/T. Here ~rel is the relaxation frequency, AH + is the apparent energy of activation and AS + is the apparent entropy of activation. The temperature dependence of the factor kT/2~h can usually be neglected against the exponential function (15). Furthermore AS + should either be constant or small compared to AH+/T. Eby (16) finds AS+/AH+~ 4 ~ in good agreement with the experiment. With ~ 10 -3 AS+ is smaller than AH+/T but usually not neglectable. From our own measurements with PMMA (see section III) follows =/IS+. T/AH + = 0,09 for sidegroup r o t a t i o n = 0,57 for r o t a t i o n of a larger combination == 0,9 for t h e r u b b e r to glass transition.

The last value agrees closely with the value given by Eby for mechanical measurements above the glass transition. Our small value for the side group rotation is confirmed by the very small and even negative entropy of activation reported by Levi (17). For an explanation of this phenomenon see M~ller and Schmelzer (18). According to Singh and Nolle (4) for const ant AH+/T dAH+ dT ~/~.~: ....... ~ .

[4]

I f AH + is a function of the free volume, then = [ dAH+~ V , dart' \ ~ l , V ] ( - VfildP + o:ldT) [5] where a / a n d fl refer to the free volume. For dP = 0 follows:
124

Kolloid-Zeitschrifl u n d Zeitschrifl f i i r Polymere, B a n d 1 9 5 . H e f t 2

quency or j u m p rate

(d'~-),~= ,6! [l--( c~T ~ "~1- 1,

[7]

Singh and Nolle assume t h a t the apparent activation energy A H + is a linear function of the t e m p e r a t u r e (19) AH + :

a -

[8]

bT .

T h e y furthermore replaee ~I a n d fll by ~ and ft. Whence follows for P I B with a, fl, a and b t a k e n from literature ~p

,o = - - 9 - - ~

~ 18. ]0-3 ~

[9]

for t e m p e r a t u r e s well above T 0 in good agreement with the observed value of 17,5 9 10 -a ~ at 5 mops. As stated above both/3 a n d ~ are functions of the hydrostatic pressure a n d so is/3/o~. Generally AH+ is n o t a linear function of the temperature. Beclcer plots lg A H + as a linear function of l I T for small T a n d reports constant values for A H + at high t e m p e r a t u r e s (20), whereas Williams, Landel, and Ferry (9) propose a more complicated function of (T-To) and T. Usually A H + is n o t known at all as an analytical function of the temperature. Our own evaluation is therefore based on the experimentally determined plot of the a p p a r e n t energy of activation vs. temperature (fig. 1) for atmospheric pressure and on the specific volume plotted as function of the t e m p e r a t u r e with hydrostatic pressure as

l~~ Z~H

I~"" "=V %

I

~

~

:I~~2 .

8.7

,oo%1 :

2

,~

c,

.5

" 7o40-2

0.3k

PVC

z~T~.~ I . . ~ ; - , . . . ~ 4

6

v,

8[~,,,~/g]Ibl-O-2

Fig. 1. Apparent energy of activation for dielectric relaxation and excess volume of PVC as function of temperature

parameter. We assume t h a t the free volume is equal or at least proportional to the excess volume produced above Tg or T1, T 2 a.s.f. (as defined in fig. 2). W i t h an additional scale at the abscissa the plot of AH+ vs. T is readily converted into a plot o f A H + vs. V e, according to our assumption t h a t A H + is a function of the excess volume rather t h a n of T. The plot of A H + vs. Ve is assumed to hold for all pressures within reasonable limits, b u t the temperatures corresponding to certain values of AH+ v a r y with pressure. A third plot is therefore necessary presenting AH+/T as a function of the excess volume with the hydrostatic pressure as a p a r a m e t e r (lower p a r t of fig. 1). In this plot horizontal lines intersect the curves at those excess volumes for which c o n s t a n t j u m p rate is expected. v

a

v,,

J m

r,

r,

T

Fig. 2. Definition of the excess volume Ve

At 30 kcps a n d atmospheric pressure the m a x i m u m of t a n ~ for PVC was found at 380 ~ corresponding to an excess volume of 8,7 9 l0 -a cm3/g. At this excess volume the value AH+/T is slightly above 0.2 kcal/mole degree. At 1000 at the same value of AH+/T is found at an excess volume of 6,3 9 10 3 cma/g corresponding to a t e m p e r a t u r e of 397 ~ The resulting shifting factor is 17 9 10 -3 ~ The same value was actually observed in our own measurements (7) a n d in those of Koppelmann and Gielessen (5). As also indicated in fig. 1 states of equal excess volume are about 30 ~ apart, t h u s the shifting factor (dT/dP)v~ = 30.10 -3 ~ As mentioned above A S + is not necessarily small compared to AH+/T. However from our d a t a for PMMA it seems t h a t A S + varies a p p r o x i m a t e l y in proportion to A H + and will therefore exert no essential influence on the above evalution. This is different, if the shifting factor (d lg w/dP)T is deduced. F r o m equ. [3] follows for the ratio of the frequencies of m a x i m u m

Heydemann, Dielectric Relaxation of P M M A as Function of Pressure, Temperature and Frequency

absorption measured at two pressures P1 and

P2 lg ~ol 1 (AS+2 --/IS+~) [10] o92 -- R1T (AH+ 2 __ AH+I ) __ --~

and AS + must either be known or very small compared to AH+/T. We will show later t h a t a good value of lg ml/% is obtained for PMMA if AS + ~ AH+/T. II. Specific volume measurements

The data of the specific volume of PMMA used in this paper are taken from an earlier study made in this laboratory (8) with the same type of commercial PMMA. In the specific volume versus temperature curves three distinct breaks were observed at the temperatures indicated in table 2. Breaks at Tg = 383 ~ and T 1 = 340 ~ were reported by Becket (20), one at Tg = 378 ~ by Tobolslcy and coworkers (21). More references are found in (8). The break at Tq = 376 ~ is undoubtedly the glass transition. The break at T 2 = 264 ~ which is hardly affected by pressure is related with the onset of sidegroup rotation (22). It will be shown in section I I I t h a t the break at T 1 = 335 ~ corresponds to a type of molecular motion not previously reported for PMMA. The glass temperature shift determined from our isobaric measurements is 18 ~ atm, while Hellwege and coworkers (23) report 22,6 ~ atm from

--T f~ Fig. 3. Excess volume produced in PMMA above Tg, Tj and T 2 at 1 and 1000 at.

125

isothermal measurements. Gielessen and Koppelmann (24) find A V / V o = 22,5- l0 -4 for isothermal compression to 1000 atm 20 ~ while our own value under the same conditions is 22,0. l0 4. Table 2 Transition temperatures observed in PMMA in OK

1 arm 1000 atm

Tg

T1

T2

376 394

335 336

264 266

The excess specific volume of PMMA is plotted in fig. 3. The figures at the curves indicate above which temperature in degrees centigrade under the given pressure this volume is produced. III. Dielectric measurements

The complex dielectric constant of PMMA (commercial sample by RShm and Haas, Darmstadt) was measured as function of the temperature at 46 frequencies in the range from 40 cps to 300 kcps at atmospheric pressure and at a reduced number of frequencies at 1000 at. All measurements with elevated pressure were made under the same isobaric conditions as the corresponding specific volume measurements. From plots of tan ~ vs. temperature T and s" vs. temperature T the sets of values (lg/, T)+.m~x and (lg/, T)tg~max were evaluated. At frequencies below 3 kcps two relaxation processes overlap, e" vs. Tcurves were used to separate these two processes and to determine the position of their loss peaks independently. In fig. 4 our data for the position of the loss peaks in the lg l-Tplane are compared with those of other authors. Most of the data refer to maxima of tan ~ ; only those of Reddish and of Mead et al. refer to e", while the basis for the value quoted by Tuckett is unknown. The maxima of e" and tan de are usually not identical. Some of the dielectric data reported in literature were obtained as function of the frequency. These results cannot be compared with those shown in fig. 4. However the results reported by von Hippel (33), Mikhailov (26), Koppelmann and Gielessen (except the one at 55,5 ~ (6) agree quite closely with the contour maps of the complex dielectric constant of Heijboer (22) and satisfactory agreement is therefore also expected for our data. Saito (34) has reported measurements of the a-maximum of PMMA between lg T = - 3 and + 1, but we have no way of comparing his data with ours, although with respect to the rather few available data

126

KoUoid-Zeitschrift und Zeitschrifl fi~r Polymere, Band 195 9 Heft 2

for the a-maximum Saito's data are of great interest. Fig. 5 shows our data of (Ig/, T) for e"max at 1 and 1000 arm together with the apparent oC 200

T

9

120 /00 86 60

f

40

~

*/

9

+ Oeutsch el.ol. [27] z~ W~rstlin [2$] 9 Tucketl [29]

9 Plfijt~oer

9

~4,oa et..L

relfair g Mikhoilov o

20

--

Ihe outhora own

[22] [30]

[M] [32]

rl,~ults

0

-----

Ig f

Fig. 4. (T, lg 1) for tg (~emaxof PMMA activation energies. Interesting enough we find three rather distinct processes. The short steep lines at the right represent the glass ~f

Hx

5H I mainehai~[~)

i

6 5 150

Hr

) [

c~

\

I

t

\\..,u

4 I00

~

kirmtian

3 2

I

,~ \

VCS.

,0

I

0 -1

,,o

//

mined from specific volume measurements at a much longer time scale. Towards higher frequencies #'max is rapidly decreasing and at lg / = 3,5 the main loss peak is hardly detectable. At the left side of the diagram the relaxational process now generally attributed to the sidegroup rotation (22) is found. It has a low and within the experimental range almost constant apparent energy of activation. Here the shifting factor is smaller. It starts at about 6.10-a~ at l g / = 1,5 and rises to more than 15.10-3 OK/at m at lg / = 3, 5. The extrapolation of the experimental curves towards lower frequencies leads to the transition temperature T 2 as observed in the specific volume measurements. These are only about 2 ~ apart [for the accuracy of measurement see (8)]. At the high frequency end these curves are rather rapidly, although continuously changing their slope. Here a third type of rearrangement process is found. Extrapolation of this part of the curves towards lower frequencies leads to the third set of transition temperatures T 1. We can at the moment nothing but speculate on the type of motion taking place at frequencies above 3 keps. We do not know of any previous detailed report on this phenomenon in PMMA, but clearly the results of Tel/air (31) and of Hei]boer (22) show this break although it is not mentioned in their texts. A curvature towards higher frequencies was observed b y Deutseh et al. (27) for the fl-maximum of the a-chlormethylester of polymethacrylic acid. Hei]boer and Schwarzl (in 15) attribute the curvature of the curve T (tan (~max) VS. lg / for PMMA at high temperatures to the influence of the approaching c~-maximum. B u t as our measurements show the #'max for the a-process is reduced to zero before the two curves meet. I t is therefore probable that the two processes interfere only b y simple superposition of their #'-cur-

I/

" =

Ii

I

i ,

I I I I !

Fig. 5. (T, l g / ) for e"max of PMMA at 1 a n d 1000 at. Energy of activation AH + (T) at 1 at.

transition with a high apparent energy of activation and a shifting factor of about 19,5.10 -a ~ Extrapolation of the measured curves towards lower frequencies (35, 36) leads to the glass temperatures as deter-

In his explanation of the reversal of the frequency shift of the fl-process in PVC at high temperatures Koppelmann (5) supposes that the fl-process is influenced b y the onset of the main chain mobility. A similar effect might be found here: Under the influence of the external a. c. field the dipoles in the polymer tend to orient themselves parallel to the field. Below 380 ~ only sidegroup rotation leads to dipole orientation. Above 380 ~ the coordinate movement of large chain segments becomes possible and contributes to the total dipole orientation. As the temperature is increased rotating sidegroups

Heydemann, Dielectric Relaxation of P M M A as Function of Pressure, Temperature and Frequency

start moving small segments of the main chain as these get more and more mobility. This e v e n t u a l l y leads to higher losses (as observed) a n d to a higher energy of a c t i v a t i o n due to the larger masses to be moved. At the same time less large segment r o t a t i o n takes place since the o r i e n t a t i o n of the dipoles is m a d e quicker and easier with the sidegroup plus small segment r o t a t i o n (~fl-maximum, combination). This phenomenological explanation is necessarily incomplete and will need more consideration.

a n d the a p p r o p r i a t e value of AH+/T is 0,432 kcal/mole ~ A t 1000 a r m this AH+/T value is related to an excess v o l u m e of 3 9 l0 -s cm3/g corresponding to T = 408,2 ~ The resulting shifting factor is 18,2 9 10 -3 ~ a t m in good a g r e e m e n t with the measured value of 20 9 10 -3 ~

x I0 -~

/=fat

~ = =lVote

v. / V21

k:--:/

:Zo,,

\\

laMMA

x 10-21 V. ' - I

IV. Determination of the Shifting Factors Figs. 6 to 8 present examples for the det e r m i n a t i o n of the shifting factors (dT/dP)~, for the a, fl, and aft-processes in PMMA using the results discussed in sections I I a n d I I I and the m e t h o d explained in section I. Plott e d in these figures are the excess v o l u m e vs. t e m p e r a t u r e and the excess v o l u m e vs. appar e n t energy of a c t i v a t i o n divided b y absolute t e m p e r a t u r e . B o t h curves are shown for 1 and 1000 atm. F o r the ~-process (main chain motion) shown in fig. 6 a m a x i m u m of ~" is f o u n d at 390~ l g / = 2,5, P - 1 atm. T h e corresponding excess v o l u m e Ve is 3,55. l0 -a cma/g

127

\p=,ot "r=~kcos

A.,o t

\N--/

.

'~

~'~l

a;~o a60 a~o 400 420 T P K1 Off'/ 0.08 0,09 O[lO O,'ll 0112 0.'13~

Fig. 8. D e t e r m i n a t i o n of (dT/dP).~ for t h e eft-process in P N N A . Dielectric relaxation

The same procedure is used in figs. 7 and 8 for the fl-maximum and the ~fl-maximum. table 3 summarizes the shifting factors of PMMA e v a l u a t e d f r o m figs. 6 to 8 t o g e t h e r with the shifting factors for c o n s t a n t excess v o l u m e and with Afl/da. The table clearly shows the merits of our straight forward method. Table 3 Shifting factors of P M M A a n d PVC in 10 -a ~

/I From :

,:mo~/ 0

,,~

9

1

I

89

a~o 3?0 3~0 390 400 4)0 T ~ K ]

~3 o:~ o.s 0.6

AH'Lk~ol 7

T l~l Fig. 6. D e t e r m i n a t i o n of (dT/dP)~ for t h e ~-proeess

in PMMA. Dielectric relaxation x I06

vo

PMMA

20

18,2

21

71

18

6,5

18

--

(1)

19

19,5

30

29

(2)

17,2

17

30

46

14

7,5

-maximum

f : 200cps

lg J 4

PMMA c~-process PMMA fl-process PMMA :(fl-process PVC ~-process

p:lat Ve vs. ~

2

p: lot VET2(T)

I I 310 320 N

340 3.r

360

T~~

Fig. 7. D e t e r m i n a t i o n o f (dT/dP).~ for t h e fl-proeess in P N N A . Dielectric relaxation

F o r the fl-process we can also calculate (d lg co/dP)T since the e n t r o p y of a c t i v a t i o n ~ S + is v e r y small c o m p a r e d to AH+/T. F r o m fig. 7 follows for the excess v o l u m i n a at 1 and 1000 a t m and 340 ~ 3 , 7 . 1 0 -a and 2,65. 10 -a cma/g. The corresponding values for AH+/T are 4,81 9 10 -a and 4,95 9 10 -a kcal/ mole degree. These d a t a i n t r o d u c e d into equation [10] yield lg col = 0,306; (D 2

e~ - 2,0 OJ 2

9*

128

Kolloid-Zeitschr~ft und Zeitschrift fiir Polymere, Band 195 9Heft 2

in s a t i s f a c t o r y a g r e e m e n t w i t h the v a l u e of w l / w 2 = 1,8 t a k e n f r o m fig. 5 b u t in c o n t r a s t to t h e results of K o p p e l m a n n (6) who s t a t e s t h a t t h e s e c o n d a r y r e l a x a t i o n process in P M M A is h a r d l y affected b y pressure. F r o m equ. [9] follows t h a t the shifting fact o r ( d T / d P ) ~ increases w i t h t e m p e r a t u r e , t h a t m e a n s t h a t a t high frequencies the influence of pressure is larger t h a n a t low frequencies. This effect follows also f r o m our own m e t h o d of e v a l u a t i o n e x c e p t for t h e a-process (fig. 8), where t h e shifting f a c t o r remains almost constant. These observations are in a g r e e m e n t w i t h the e x p e r i m e n t a l d a t a r e p o r t e d in t a b l e 3 a n d in fig. 5. Also O ' R e i l l y o b e r s e r v e d this effect (3) b u t a t t r i b u t e s it to s c a t t e r of his d a t a . T h e results of t h e dielectric m e a s u r e m e n t s discussed a b o v e seem to confirm t h a t t h e app a r e n t e n e r g y of a c t i v a t i o n is in f a c t prim a r i l y a f u n c t i o n of the excess v o l u m e a n d t h u s also of t h e free v o l u m e a n d t h a t this r e l a t i o n c a n easily be used to e x p l a i n a n u m b e r of effects of h y d r o s t a t i c pressure on relaxa t i o n processes. T h e a u t h o r wishes to t h a n k Prof. Dr. Dr.Ing. E . h. E . M e y e r for his s t e a d y interest in this s t u d y . T h e i n v e s t i g a t i o n was carried out as p a r t of one i t e m of a research c o n t r a c t w i t h t h e D e p a r t m e n t of P h y s i c a l R e s e a r c h , Admiralty, London. Summary

It is shown that the influence of pressure on dielectric relaxation in polymers is easily predicted from the apparent energy of activation and the specific volume, if the energy of activation is known as function of the free (or excess) volume at atmospheric pressure. This is demonstrated for polyvinylchloride (PVC) and for three types of dielectric relaxation in polymethylmethacrylate (PMMA). Zusammen[assung

Es wird gezeigt, dab sich der Einflul~ des Drucks auf dielektrische Relaxation in Polymeren leieht aus der scheinbaren Aktivierungsencrgie und dem spezifischen Volumen ermitteln l~]~t, wenn die Aktivierungsenergie als Funktion des freien Volumens bei Normaldruck bekannt ist. Dies wird am Beispiel der a-Relaxation in Polyvinylchlorid (PVC) und an drei Relaxationstypen in Polymethylmethacrylat (PMMA) demonstriert.

2) McKinney, J. E., H. V. Belcher, J. Research Natl. Bur. Standards 67A, 43 (1963). 3) O'Reilly, J. M., J. Polymer Sci. 57, 429 (1962). 4) Singh, H. u. A. W. Nolle, J. Appl. Phys. 39, 337 (1959). 5) Koppelmann, J. u. J. Gielessen, Z. Elektroehem. 65, 689 (1961). 6) Koppelmann, J. u. J. Gielessen, Kolloid-Z. 175, 97 (1961). 7) Heydemann, P., Friihjahrstagung der Deutsch. Physik. Ges. (Bad Pyrmont 1963). 8) Heydemann, P. and H. D. Guicking, Kolloid-Z. 193, 16 (1963). 9) Williams, M. L., R. F. Landel u. J. D. Ferry, J. Amer. Chem. Soc. 77, 370 (1955). 10) Ferry, J. D. u. R. A. Stratton, Kolloid-Z. 171, 107 (1960). ll) Marvin, R. S. and J. E. MeKinney (to be published). 12) Marvin, R. S., J. Japan. Soc. Testing Materials 11, 303 (1962). 13) Ehren/est, P., Commun. Kammerlingh Onnes Lab., University Leiden, Suppl. 75b (Leiden 1933). 14) Hirai, N. and E. Eyring, J. Appl. Phys. 29, 810 (1958). 15) Nitsche, R. and K. A. Wol/, Kunststoffe, Bd. I (Heidelberg 1962). 16) Eby, R. K., Bull. Amer. Phys. Soc. 6, 143 (1961). 17) Levi, D. L., Trans. Farad. Soe. 42A, 152 (1946). 18) Miiller, F. H. and Chr. Schmelzer, Erg. exakten Naturwiss. 25, 359 (1951). 19) Ferry, J. D., L. D. Grandine, and E. R. Fitzgerald, J. Appl. Phys. 24, 911 (1953). 20) Beeker, G. W., Kolloid-Z. 146, 1 (1955). 21) Bischo~, J., E. Catsi~, and A. V. Tobolsky, J. Amer. Chem. Soc. 74, 3378 (1952). 22) Heijboer, J., Kolloid-Z. 148, 36 (1956). 23) K. H. Hellwege, W. Knappe, and P. Lehmann. Kolloid-Z. 183, 110 (1962). 24) Gielessen, J. and J. Koppelmann, Kolloid-Z. 172, 162 (1960). 25) Reddish, W., Chemistry and Industry 1951, 1077. 26) Mikhailov, G. P., J. Polymer Sci. 30, 605 (1958). 27) Deutsch, K., E. A. W. Ho~, and W. Reddish, J. Polymer Sci. 13, 565 (1954). 28) Thurn, H. and F. Wi~rstlin, Kolloid-Z. 145, 133 (1956). 29) Tuekett, R. F., Trans. Farad. Soc. 40, 448 (1944). 30) Mead, D. J. and R. M. Fuoss, J. Amer. Chem. Soc. 64, 2389 (1942). 31) Tel[air, D., J. Apph Phys. 25, 1062 (1954). 32) Mikhailov, G. P., Makromol. Chemic 35, 26 (1960). 33) von Hippel, A. R., Dielectric Materials and Applications (New York 1954). 34) Saito, S., Kolloid-Z. 189, 116 (1963). 35) Kauzmann, W., Chem. Rev. 43, 219 (1948). 36) Williams, G., Polymer 4, 27 (1963).

Re[erences

Anschrift des Verfassers:

1) McKinney, J. E., H. V. Belcher, R. S. Marvin, Trans. Soe. Rheol. 4, 347 (1960).

Dr. P. Heydemann, III. Phys. Inst,.

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