Mechanical relaxation effects in glassy polymethyl-methacrylate in stressed states of differing types

2632

Yr. V. ZET.~.~V and A. G. NOVlXOV

10. M. Sh. YAGFAROV and V. S. IONKIN, Yysokomol. soyed. A10: 1613, 1968 (Translated in Polymer Sci., 1O: 1867, 1968). 11. Yu. S. LIPATOV, Fiziko-khimiya napolnennykh polimerov (Physicochemistry of Filler Polymers). p. 166, Izd. "Naukova dumka", 1967 12. A. A. TAHER, Fiziko-khimiya polimerov, p. 481, Izd. :Nauchno-tekhn. lit., 1963 13. N. P. A.PUKHTINA, A. I. MAREI, G. E. NOVIKOVA and B. E. MYULLER, Vysokomol. soyed. 7: 117, 1965

MECHANICAL, RELAXATION EFFECTS IN GLASSY POLYMETHYLMETHACRYLATE IN STRESSED STATES OF DIFFERING TYPES* YII. V. ZELElgEV and A. G. NOVlKOV V. I. Lenin State I~stitute of Pedagogics, Moscow (Received 1 October 1968)

I~TEaEST in the effect of the t y p e and extent of deformation and stress on the mechanical relaxation properties of polymers has considerably increased recently. I t has been pointed out [1, 2] that the effect of shear stress in causing asymmetry of the potential barrier [1] and hindering molecular motion m a y result in considerable variation in the energy of molecular interaction [2], thus altering the relaxation spectrum. Compressive (or tensile) stress, in contrast to shear stress, has an additional effect due ~o volumetric variation of the sample (causing a change in the free volume of the polymer), which is typical of t h e glassy physical state, in which Poisson's ratio is considerably less than 0.5 [3]. It is assumed that when this effect predominates relaxation spectra are displaced along the time scale without any shape variation. I t is well known that relaxation time spectra and mechanical loss maxima on the frequency dependence of t a n g for polymethylacrylate (PMMA) in the glassy state do not undergo marked change (plane shape) within a limited time range; this m a y apparently be due to the superimposition of several relaxation mechanisms. Mechanical loss in glassy PMMA is normally due to the motion of lateral methylester groups. It is also well known that amorphous glassy polymers are structurally not in equilibrium. The presence of a certain proportion of free volume in glassy PMMA suggests that some limited segmental motion (mobility of a combination of atomic groups of main chains) is possible, which is confirmed b y the relatively high forced elastic deformations in polymers under the effect of high mechanical stress. I f the free volume remains constant the conditions of relaxation remain unchanged, like the most probable relaxation times z which * Vysokomol. soyed. All: No. 10, 2312-2316, 1969.

Mechanical relaxation effects in glassy polymethylmethacrylate

2633

c h a r a c t e r i z e t h e s e processes. A b o v e Tu v o l u m e t r i c r e l a x a t i o n t i m e s a r e s h o r t a n d t h e i r v a l u e w i t h s i m p l e c o m p r e s s i o n , w i t h i n f a i r l y low d e f o r m a t i o n s , n o l o n g e r d e p e n d s o n t h e c o m p r e s s i v e stress. I n t h e g l a s s y s t a t e v o l u m e t r i c t h e r e l a x a t i o n times are c o m p a r a b l e w i t h the e x p e r i m e n t a l time, a n d the r e l a x a t i o n time, with simple compression, depends on pressure, resulting in more frequent interparticle reactions. The i n s t r u m e n t developed and described in detail by the authors [4] enables dynamic mechanical measurement to be made with considerable static compression. Great effect can be exerted on the free volume variation of the glassy polymer and therefore on the restricted segmental motion. We investigated the mechanical realxation properties of ST-1 organic glass made of PMMA in the glassy state at 35 °. The tensometric system of measuring strees and deformation ensured an accuracy of measurement of the order of 5 ~o. The accuracy of measurement of the tangent of the mechanical loss angle is within this range, the absolute error of measurement being of the order of 0-002 ~o. To study the effect of the variation of polymer volume on the relaxation mechanical properties, two kinds of mechanical deformation were applied: shear a n d compressive. Investigations were carried out under static (stress relaxation) and dynamic (with constant stress amplitude) conditions. I n the first case the samples were deformed to relative deformations el = 7 x 10 4 and ca = 7 x 10 -3 in the case of compression and 71 =7 x 10 -4 and y~ = 7 × 10 -3 in the case of shear. I n the latter case the static compression reached stress values G~tl= 1-4 × 10 v dyne/cm 2 and ast~ = 1.4 x 10 s dyne/cm ~ for compression, T s t i - 1'4 X l07 dyne/era 2 and V s t 2 : l . 4 × l0 s dyne/cm 2 for shear with a constant amplitute of periodic stress % -- 1.4 x 10 ~ dyne/cm 2 for compression and v0 = 1.4 x 107 dyne/cm 2 for shear. Thus, the selected ranges of stress and deformation variation are within the range of applicability of the laws of linear visco-elasticity. I t may be assumed that no effects due to orientation or rupture of chemical bonds were clearly observed. Cylindrical polymer samples of diameter d--0.8 cm and height h = 2 cm were used for investigating compression. Young's modulus F was determilled from the formula E =--bE, where F is the force acting on the sample, x X

is the deformation of the sample and b~ is the shape factor of compression, 4e/ud ~. A "sandwich" type equipment was used for the study of shear deformation. The shear modulus F was determined from the formula a = - - ' b , , where b~ is the shape factor of shear, a/2bh X

(here the area of shear bh = 1 cm ~ and the thickness of the specimen a = 1 cm). F r o m static m e a s u r e m e n t s the t i m e d e p e n d e n c e s of the elastic shear m o d u l u s w e r e c a l c u l a t e d a n d p l o t t e d for s h e a r deferma~io]] (Fig. l a ) a n d ¥ o u n g ' s m o d u l u s for c o m p r e s s i v e d e f o r m a t i o n (Fig. lb). F o r t h e c o n v e n i e n c e o f f u r t h e r a n a l y s i s , t h e r e s u l t s are s h o w n a s t h e d e p e n d e n c e o f t h e e l a s t i c i t y m o d u l u s o n t h e l o g a r i t h m of t i m e (Fig. lc, d). S p e c t r a o f r e l a x a t i o n t i m e s were o b t a i n e d b y u s i n g t h e A n d r e w s m e t h o d o f s e c o n d a p p r o x i m a t i o n [5], a n d t h e f o r m u l a :

H

(~)=

2.303 [_c/log(t)

t_

+0.109 Ldlog (t)'.Jt=

w h e r e H (~) is t h e d i s t r i b u t i o n f u n c t i o n ( s p e c t r u m ) of r e l a x a t i o n t i m e s ; G (t) is t h e r e l a x a t i o n s h e a r m o d u l u s . T h i s m e t h o d w a s u s e d for c a l c u l a t i n g t h e spect r u m f r o m t h e d e p e n d e n c e o f Y o u n g ' s m o d u l u s o n t h e l o g a r i t h m o f t i m e , b u t G (t)

Yr. V. Z~.LE~rEV and A. G. Nowxov

2634

was replaced b y ¥oung's relaxation modulus E(t). Results are shown in Fig. 2. From dynamic mechanical measurements the frequency dependences of the tangent of the mechanical loss angle tan 5 (Fig. 3) were plotted. G, 107~ dyne/cm z

6 5

I

a

L

J

E,lO-g dyne/cm z (

b

2#' 22 2O 18

~ -

I

0

#0

I

80 T i m e , sec

2

I

120

-2

-1

0

1

2

3

log "k , sec

FIG. 1. Dependences of the elastic shear modulus G and Young's modulus E on time (a, b) and the logarithm of time (0, d) obtained from experiments on stress relaxation under conditions of shear (a, c) and compressive (b, d) deformation and changed according to the logarithm of time (c, d) at 35°: a,c: e--yl=7×10-4; © --y~ =7 ×10-8; b, d: 1--81=7 X10-4; 2--e2 =7 × 10-a. Figure 2a indicates that the spectra of relaxation times for different shear deformations, and consequently different stresses, are combined in practice, which indicates a single relaxation mechanism. Owing to the superimposition of processes due to the motion of segments and side groups in certain frequency ranges of a given width, in the relaxation spectrum of the segmental mechanism times can be the same, or even shorter than in the relaxation spectrum of a local mechanism. Dynamic mechanical measurements for shear deformation (Fig. 3a) qualitatively confirm the results of static measurements. Results of similar measurements in compression deformation are different in nature. Thus, an increase in compressive deformation in static measurements produces two relaxation mechanism (Fig. 2b), which also agrees with dynamic mechanical measurements (Fig. 3b). In the glassy state with increase of temperature the height of the mechanical loss maximum increases much less than when T > Tg, when kinetic units with a large mass (segments) are involved in motion. The half-width of the maximum decreases with increase of temperature and in the glass transition range the rate of this variation suddenly becomes higher. I f with shear deformation (for any stress value) and compressive deformation (low stress values) the spectra of relaxation times and the frequency dependences

Mechanical relaxation effects in glassy polymethylmethacrylate

2635

o f the tan g en t of mechanical loss angle are more or less plane in certain time and frequency ranges, with high stress in the case of compressive deibrmation two cleaxly expressed relaxation mechanisms are observed. F o r segmental mobility distorted dependences are normally obtained ~----f(T, v) on the t em perat u r e - f r e q u e n c y curves both on increasing compressive stress, the specimen volume remaining constant, and on increasing the relative volume with constant stress, which can be determined by the free volume variation, intensity of t h e r m a l ton ~ , 102 10

H('~')'lO-~d,.,une/cm2 (2

CL

2

8 6

3

#

I

b

5

I

I

I

i

b

8

3 1 -2

I

-f

I

l

0

1

F~G.

2

I

I

2 3 Zog (~:) , sec

4

-3

I

-2

I

•

-f Fic.

I

0

i

I

1 2 log ~ , c/s

3

FIG. 2. Spectra of relaxation times obtained from stress relaxation values under conditions of shear (a) and compressive (b) deformation at 35°: a: 1--71=7×10-4; 2--72=7X10 -3 (value of divisions along the abscissa axis: --3; --2; - - h 0; 1; 2); b: 1--e1=7× 10-~; 2-e~=7X l0 -a. FIG. 3. Frequency dependences of the tangent of meehan/cal loss angles obtained with dynamic loading under conditions of shear (a) and compressive (b) deformation at 35°; a: 1--Zstl-l'4x107; T0=1'4×107; 2--rst2=l'4><10s; v0=l'4×10 ? dYne/era2; b: 1--astl =1.4× 107; a0 =1-4× 10? dyne/cm2; 2--ast2=l'4 × 10s; a0--1"4× 10? dyne/cm2. motion of macromolecular segments and by the joint motion of kinetic units, this motion being of f u n d a m e n t a l imporbance. On reducing the free volume the combined effect increases, because the particle mobility will have more effect on environment. Higher temperatures also result in increased combined effects. Hence, it m a y be concluded t h a t the appearance of a mechanical loss m a x i m u m in glassy PMMA is determined by the cooperative m o v e m e n t of side groups and macromolecular segments. For glassy PMMA the motion of side groups determines the macroscopic properties, which however is closely related to the mobility of main chain sections, which accounts for the complex nat ure of the whole relaxation process. Within a certain t e m p e r a t u r e - t i m e range t he mobility of the macromolecular segments and side groups closely related to the main chains appear jointly, which results in the merging of macroscopic ranges

2636

Yu. V. ZELENEV and A. G. NOVIKOV

of relaxation. Separation of the mechanical loss maximum in the range of the so-called fl-relaxation, as shown previously, takes place with the superimposition on the polymer sample of compression stress, which considerably reduces the free volume and thus hinders segmental motion, displacing the corresponding maximum in the relaxation spectrum in the direction of longer times. At the same time compressive stress has no marked effect on the motion of side groups. The results obtained are in qualitative agreement with the conclusions drawn by Koppelman [6], who made a comparative study of the dielectric relaxation of glassy polymers of different structures (PMMA and polyvinylchloride). Quantitative differences in the dependences of tan J=f(v), obtained by the authors [6] for PMMA, are due to the fact t h a t in mechanical measurements the height of the maximum tan g is determined by the mass of corresponding kinetic urrits, and in dielectric measurements by their polarity. CONCLUSIONS

A study was made of the effect of different types of stress (shear and compression) on the relaxation properties of polymethylmethacrylate in the glassy state. I t is noted t h a t with relatively high compression stresses two relaxation mechanism exist, determined by the correlated interaction of motion of lateral groups and macromolecular segments. Translated by E. SEMERE REFERENCES

1. F. SCHWARZL, Kolloid. Z. 165: 88, 1959 2. G. L. SLONIMSKII, A. A. ASKADSKII, V. V. KORSHAK, S. V. VINOGRADOVA, Ch. S.

3.

4. 5. 6.

VYGODSKII and S. N. SALAZKIN, Vysokomol. soyed. A9: 1706, 1967 (Translated in Polymer Sci. U.S.S.R. 9: 1921, 1967) J. D. FERRY and R. A. STRATTON, Kolloid. Z. 171: 107, 1960 Yu. V. ZELENEV and A. G. NOVIKOV, Zavodsk. lab. 34: 1260, 1968 R. D. ANDREWS, Industr. Engng. Chem. 44: 705, 1952 J. KOPPELMANN, Physics of Non-crystalline Solids, p. 255, Amsterdam, 1965