- Email: [email protected]
X-ray study of deformation of polyethylene
394
Yu. A. Z u s o v e~ a/.
REFERENCES
I. A.A. TAGER and V. Ye. DREVAL', Dokl. Akad. l~auk SSSR 145: 136, 1962; V. Ye. DREVAL', A, A, TAGER and A. S. FOMINA, Vysokomol. soyed. 5: 1404, 1963 (Translated in Polymer Sci. U.S.S.R. 5: 3, 495, 1964) 2. F. BUECHE, J. Appl. Phys. 24: 432, 1953 3. I. R. VAN WAZER e~ ed., Viscosity and Flow Measurement, Interscience, 1963 4. I. V. KONYUKI~, G. V. VINOGRADOV and A. :A. KONSTANTINOV, Plast. massy, No. 10, 45, 1963 5. V. V. SINITSYN, A. A. KONSTANTIN and G. V. VINOGRADOY, Tr. I I I Vses. konf. po kolloidnoi khimii (Trans. 3rd All-Union Conference on Colloid Chemistry), p. 113, Izd. Akad. Nauk SSSR, Moscow, 1956 6. A. I. KORETSKAYA, A. A. KONSTANTINOV and G. V. VINOGRADOV, Khim. volokna, No. 2, 36, 1960 7. G. V. YINOGRADOV and N. V. PROZOROVSKAYA, P last. massy, No. 5, 50, 1964. 8. L. V. IVANOVA-CHUMAKOVA and P. A. REBINDER, Kolloid. zh. 18: 429, 1956 9. G. V. VINOGRADOV, I. M. BELKIN, A. A. KONSTANTINOY, B. A. ROGOV, S. K. KRASHENNIKOV, A. Ya. MALKIN and I. V. KONYIFKH, Zavod. lab. 30: 864, 1964 10. Yu. F. DEINEGA, V. P. PAVLOV and G. V. VINOGRADOY, Zavod. lab. 26: 353, 1960 11. S. SHIST~[IDOand I. ITO, J. Chem. Soc. Japan (Pure Chem. Sect.) 889, 1963 12. W. A. WRIGHT and W. W. CROUSE, A New Concept in Generalizing Non-Newtonian Fluid Flow Data, ASME-ASLE Internat. Lubric. Conf., Washington D. C. Preprint 64, LCII, Oct. 1964 13. F. D. GRANDINE and F. D. FERRY, J. Appl. Phys. 24: 679, 1953 14. A. A. TAGER and V. V. ANDREYEVA, International Symposium on Macromolecular Chemistry, Prague, Preprint 125, 1965 15. F. BUECHE, J. Chem. Phys. 22: 1570, 1954; F. BUECHE and S. W. HARDING, J. Polymer Sci. 32: 177, 1958 16. G. V. VINGRADOV, A. Ira. MALKIN, N. V. PROZOROVSKAYA and V. A. KARGIN', Dokl. Akad. Nauk SSSR 150: 574, 1963; 154: 890, 1964
X-RAY STUDY OF DEFORMATION OF POLYETHYLENE* Yu. A. ZuBov, V. I. S~.LIKHOVXand V. A. KARGI~ L. Ya. Karpov Physicochomical Institute
(Received 6 January 1966) AS A RESULT of n u m e r o u s investigations o f the s t r u c t u r e o f crystalline p o l y m e r s in recent times some degree o f success has been o b t a i n e d in s t u d y o f the structure o f b o t h u n o r i e n t a t e d a n d o r i e n t a t e d p o l y m e r s [1-7]. I t has been established t h a t in the m a j o r i t y o f p o l y m e r s studied t h e m a i n morphological form in u n o r i e n t a t e d p o l y m e r s is a crystalline plate. The molecular chains are a r r a n g e d * Vysokomol. 8oyod. A9; No 2, 353-364, 1967.
X-ray study of deformation of polyethylene
395
perpendicularly or at a definite angle to the surface of the plate and are folded back on themselves. Aggregates of plates, arranged in a definite manner, form more complex supermolecular structures (bands, sheaves, spherulites etc.). In the complex, supermolecular structures, especially those obtained by crystallization from the melt, the plates are probably connected together by interpenetrating chains [2, 8]. _Another possibility that cannot be excluded is gradual growth of supermolecular structures by mutual packing of simpler structural elements (for example, bundles of chains), and here interpretation of chains is not essential [9-11]. In unorientated, crystalline polymers in a number of cases fibrillar formations are found, and it has been suggested that these consist of bundles of straightened chains arranged along the axis of the fibril [12-13]. Crystalline formations with straightened chain molecules are found in bulk polyethylene, crystallized from the melt under pressure [14, 15], and in the needle-shaped crystals of polyoxymethylcne obtained by controlled polymerization [16]. However since at the present time electron microscopic study in conjunction with electron diffraction analysis shows in most cases the presence of crystalline plates with a folded chain conformation we proceed, in discussion of the structure of an isotropic specimen, from the existence of plates with folded chains, or aggregates of plates, connected by interpenetrating molecules or bundles of molecules. It is well known that a highly orientated material has a fibrillar structure. The fibrils are ar.ranged parallel to the direction of stretching. Along the axis of the fibril, which coincides with the direction of the molecular chains, there is an alternating sequence of regions of different density, i.e. denser, highly ordered, crystalline regions and less dense, defective or amorphous regions. The combined length of the crystalline and amorphous regions gives the long period [17]. The problem of how the transition from the structure of the unorientated polymer to that of the orientated polymer is brought about during deformation is of great interest. It is suggested in references [18-20] that this transition occurs by complete breakdown of the crystalline structure of the original isotropic material and formation of a new, orientated fibre structure. This mechanism is not the only possibility however. Recently some authors, bearing in mind the complex structure of well developed supermolecular formations, especially of large spherulites, consider that structural changes on deformation proceed by a stepwise mechanism and can involve breakdown of higher structures while simpler structural elements are preserved [21, 22]. It is evident that different degrees of breakdown of the original structure can occur, depending on the conditions of deformation and on the supermolecular structure. •It was shown in references [23] and [24] than on deformation of polyethylene the average length of the crystallite in the direction perpendicular to the direction of the chain molecules decreases. Unfortunately these papers do not give information on the length of the crystallite in the direction of the chains. The possibility of fracture of blocks of folded chains into fragments and building up of
396
Yu. A. ZUBOV et a/.
t h e s e f r a g m e n t s i n t o fibrils d u r i n g u n i a x i a l d e f o r m a t i o n o f p o l y e t h y l e n e is s h o w n i n r e f e r e n c e s [7] a n d [25]. The aim of the present work was to follow the change in the dimensions of polyethylene crystallites during uniaxial deformation by means of large and small angle X-ray studies, and also to estimate change in the degree of order in the crystalline regions at different stages of stretching.
EXPERIMENTAL The linear polyethylene, Hostalen, w i t h a melting point of 130° and It/I= 1"04 in decalin at 135 ° was studied. Specimens in the form of films of thickness 2 m m were prepared b y compression moulding of granular polyethylene in a laboratory press at 220 ° and a pres-
~,,kg/cm2 200
3
2 7
b
8
$
I~G.1. Conventional stress-strain curves for polyethylene stretched a t 20 ° (a) and 110 ° (b). sure of 50 arm, with a second heat t r e a t m e n t of t h e films in t h e mould at 220 ° without pressure. Films prepared in this w a y were completely isotropic. Blade test pieces with a working section 10 rnm in length were cut from the films and stretched uniaxially at a rate of movem e n t of the lower clamp of 10 mm/min, a t 20 °, 90 ° and 110 °, in an FMPw-250 tensile t e s t machine provided with a heating chamber. W e used unstretehed fllm~ and films stretched b y 50~o at 90 ° and b y 800~/o and 900% a t 90 ° and 20 ° for X - r a y measurement of the dimensions of the crystallites, and for smallangle measurements. The stretched films were removed from the clamps (a contraction o f 3 - 5 % then occurred) and were stacked together to form specimens of optimal thickness. The optimal thickness, t, was obtained from the condition t = c o s v/~ where ~ is the linear coefficient of absorption for polyethylene. I n order to s t u d y loss of order in the crystal lattice specimens stretched at 20 ° and 110 ° were fixed in the stressed state between special clamps and after 24 hr were placed in t h e X - r a y diffTactometer. The specimens studied corresponds to points 2-5 (Fig. 1, curve a) a n d 6-8 (Fig. 1, curve b) in the stress-strain curves. I t should be noted t h a t a "neck" began to form after uniaxial stretching of the whole test piece to 30~/o a t 20 ° and to 50% a t 90 ° and 110% The elongation in the neck corresponded on the average to 900% for stretching a t 20 °, ~ 800% at 90 ° and to 7000//o at 110% Specirdens stretched through the neck stage a t 20 ° were opaque as a result of a high degree of "silvering". E x a m i n a t i o n of sections of the polyethylene films in a polarizing microscope showed t h a t t h e unstretched filru~ consist of spherulites of diameter about 10 $. The region of uniform elongation of the specimen is characterized b y uniform elongation of the spherulites in the direc-
X-ray study of deformation of polyethylene
397
tion of stretching, as we have previously observed in the stretching of polyethylene films a fine spherulitic structure [21]. The X-ray investigation, in which the procedure described in reference [2"6] was followed, showed a high degree of c-axis orientation of the crystals along the direction of stretching in films with elongations of 800% a n d 900~/o. The azimuthal half-width of the 110 reflections was in both cases 6 °. The large-angle X-radiogrRma indicated t h a t in film, stretched b y 50~/o at 90 ° the polymer chains are predominantly arranged at a n angle of 25 ° to the stretching axis. For study of the effect of annealing on structure some film, stretched at 20 ° and 90 ° were heated for 2 hr at 90 °, 110 °, 120 ° and 125° in a current of nitrogen, both under tension and in the free state. I t is noteworthy t h a t whereas annealing under tension gave n o significant change in the orientation of the crystallites, after free contraction there was considerable scatter due to textural changes, though c-axis orientation was preserved. The large angle X-ray study was carried out in a DRON-1 cli~actometer, using CuK~ radiation (Ni filter). I n order to avoid distortion of the shape of the reflection due to vertical divergence of the primary beam we used a Seller sllt. The diffracted radiation was recorded b y means of a scintillation counter with a discriminator. During the recording period the counter was moved at a rate of 0.5°/min. We selected the time constant (RG) of the integrating i n s t r u m e n t to fit the condition R G = 0.25 ~, where ¢ is the time for passage of the counter through the half-width of t~e diffraction peak [27]. The diffractograrns were obtained b y the transmission method because with the reflection method the diCDaction peaks were distorted as a result of the depth of penetration of the primary beam into the specimen, and absorption. The profile of the cllCfraction line was recorded on an EPP-09 recording strip. For determination of the instrumental line width coarsely eryst~ni,xe, powdered urotropine and lithium fluoride were used as reference standards. During the recording period the standards were rotated at a rate of 50 rev/min in order to average the intensities over the I)ebye ring. The standards and the polyethylene filma were recorded under identical conditions with, the same routine of operation of the instrument and with standards and specimens of the same thickness. For determination of the dimensions of the crystallites the integral half-wldths of the 110, 220 and 002 polyethylene reflections were measured, and also of the lines of the standards lying under Bragg angles close to the angles of the above reflections. The integral half-width of a reflection was calculated as the ratio of the area under the diffraction maxim u m to its height, after separation of the reflection from the background. The true halfwidth of the reflection, assuming Gausslan distribution of the intensities of the lines of the polyethylene specimens and the standard, was calculated b y means of the formula
where B is the true integral half-width of the reflection and B 1 and B, are the experimental reflection half-widths of the specimen and standard respectively. The dimensions of the crystallites were determined b y means of the formula based on calculation of the di~raction for a paracrystalline polymer model suggested b y Hoseman [28]: -
]'1
(2)
where 9 is the parameter of paracryst~lllae distortions giving the fluctuating paracrystallino distortions relative to the mean interatomio distance, n the order of the reflection, B(n) the integral half-width of the reflection, (in the units of reciprocal space), L the average length of the crystallite in the direction perpendicular to the given crystallographic plane with a n interplanar distance d. The values of Ll,o and g**0 for polyethylene were found from equation (2), using two orders of reflection from the (110) plane. For determination of the
398
Yv. A. ZUBOV et a/.
length of the crystalllte in the direction perpendicular to the (002) plane, L001, it was assumed that g----0. The accuracy of the determination of L and g was not less than 10%. We assessed the loss of order in the crystalline regions by the change in volume and density of the unit cell at different stages of deformation. For determination of the volume (V) we measured the a, b and c periods of the polyethylene unit cell from the position of the 200, 020 and 002 reflections. The density of the unit cell, Pk, was calculated by means o f the formula p~ ~ 2 M / V , where M is the molecular weight of the monomer unit in grammes. The factor 2 indicates the number of monomer units in the unit cell. Since the value of c changed little in highly stretched specimens in comparison with unstretchod films and because we were unable to measure this period for specimens 2, 3, 6 and 7 (Fig. 1), for calculation of V for these specimens we used the average value c=2.55/k. The position of the diffraction maximum was found as the point of intersection of the profile of the maximum with the line drawn through the centres of the lines joining points of equal intensity [27]. A zero goniometric setting was established according to the position of the same reflection on each side of the primary beam. In order to elimlnate the effect of inertia of the integrating system the counter was moved in the forward and reverse directions. Each diffraction maximum was recorded several times (usually twelve times) with three new settings of the specimen. The accuracy of setting of the specimen on the axis of the GUR-5 goniometer ~vas ±0.05 mm. When the above experimental conditions were observed the error in determination of the angle 0 was ± 1 ' for the 200 reflection, ±1.5' for the 020 reflection and ±2.5' for the 002 reflection. The lower degree of accuracy in determination of 0 for the 020 and 002 reflections was due to their low intensities. In accordance with the given accuracy of 0 the following accuracies of determination of the periods, volume and density of the unit cell were calculated: a - - ± 0 . 0 1 A, b--±0.01 A, c--±0.003 A, V--±0.03×-10 -I~ cm s and Pk-±0"003 g/cm*. The apparatus and method for small-angle recording used in this work has been described previously [29]. The density (p) of a number of samples was determined by the gradient tube method [30]. RESULTS AND DISCUSSION D a t a on change in t h e dimensions of crystallites on s t r e t c h i n g are given in T a b l e 1. I n f u t u r e we shall denote the direction along which t h e l e n g t h of t h e crystal° ]ire is d e t e r m i n e d b y the reciprocal lattice v e c t o r Hh~l, which is perpendicular t o t h e plane (hb/). I n a n u n s t r e t c h e d specimen t h e l e n g t h of the crystalline in t h e H l l 0 direction was 233 A. The long period, which, as was s h o w n in referenpe [32] is n o t perpendicular t o t h e direction o f t h e p o l y m e r chains in a n u n o r i e n t a t e d material, was 270 A. The L0o2 length was 140 A. I t should be n o t e d t h a t the a c c u r a c y o f determin a t i o n o f L0o~ in an u n o r i e n t a t e d specimen is s o m e w h a t lower t h a n for o r i e n t a t e d specimens. L e t us consider t h e s t r u c t u r e o f a specimen stretched b y 9 0 0 ~ at 20 °. I n comparison w i t h an u n s t r e t c h e d specimen the length o f the crystallite in t h e H-*~2 direction is p r a c t i c a l l y u n c h a n g e d whereas in the Hl10 direction it has decreased b y a f a c t o r of a p p r o x i m a t e l y three. I t is seen f r o m :Figure 2a t h a t the i n t e n s i t y o f t h e small-angle diffraction m a x i m u m for this specimen is v e r y low. I n a d d i t i o n
X-ray study of deformation of polyethylene
399
TABLE 1. RESULTS OF X-RAY ANALYSIS AND T~t~ DEI~SI'I'I~:S OF THE POLYETHYLENE SPECIMENS I. S t r e c h i n g a t 20 ° b y 9 0 0 %
Parameters
9~vv / o at 20 °
i
annealing temperature, °C under tension 90
"~110~ ~
Lo., A. g.o, %
D,A
p, g / c m s
I I . S t r e c h i n g a t 90 ° b y 8 0 0 %
110
t annealing temperature, °C 8q__ ,~
in t h e free state 110
120
at 90°
125
under tension 110
in t h e free state
120
110
120
125
158 146 190 233 107 142 159 139 194 2 2 0 233 171 80 1 0 6 140 168 142 157 175 143 168 175 164 189 198 1 5 1 157 1 9 3 2.6 2.4 2.1 2.8 3.0 2.8 3.0 2.3 2.2 2.3 2.9 2.8 2.6 2.6 270 200 174 174 210 210 270 313 185 203 250 210 270 313 0.921 - - 0.942 0.952 - - 0.954 0.945 - - 0.860 - - 0"907 - -
.Definition; I~1o and ~ -- average lengths of crystallite in the direction perpendicular to the (110) and (002) planes, I.e, in conformity with the structure of the polyethylene unit cell [B1], in the directions perpendicular to and parallel with the polymer chains; gxxothe parameter of paracrystalline distortions in the direction perpendicular to the 110 plane; D-long period, p-denszty. '
to this the specimen gives extraordinarily high equatorial scattering (Fig. 2b). The fact that the intensity of scattering is substantially higher in the equatorial direction than in the meridial direction means that the specimen contains asymmetrical inhomogeneities, the long dimension of which lies along the direction of stretching. Since the intensity of equatorial scattering is comparable with the intensity for substances known to be porous it may be considered that the inhomogeneities are pores formed during stretching. This conclusion is supported by the density of the specimens, which is very low in the case of those stretched at 20 °. TABLE 2. VALVES OF THE PERIODS (a, b, c) THE VOLUME (V) . ~ v THE DENSITY (Pk) OF TH~ CELL, AND THE INTEGRAL HALF-WIDTH (~) OF THE 200, 020 AND 002 REFLECTIOI~'S FOR POLYETHYLENE
P o l y e t h y l e n e film s p e c i m e n s Parameters unstreched 1
a,A b,A e,A V × 10U, c m a p~, g / e m 8 Aloe, r a d Aol o. r ~ l Aool, r~d
7"44 4"97 2"552 94"4 0"987 0"0120 0"0105 0"0142
s t r e t c h e d a t 20 ° 2
3
7"44 4"96 -94"1 94"1 0"990 I 0"990 0.0108] 0"0116 0"0130 0.0105 7"44 4"96
--
s t r e t c h e d a t 110 °
4
5
6
7
8
7"52 4"97 2"550 95"3 0'978 0"0273 0"0232 0"0138
7"53 4"97 2"548 95"3 0"978 0"0267 0"0243 0"0140
7"45 4"97
7"44 4"96
7"45 4"96 2"548 94"2 0"989 0"0170 0"0162 0"0129
94"4
0"987 0"0115 0"0105
94"1 0"990 0"0123 0.0121
0
20
a
40
v6
*5
o! A2 A3 v4
60 ~=20
0
3OO
~00
5O0
600
700
10
20
30
b
40
ol A2 "3 v4 °5 v6
50
~ = 20'
FIG. 2. S m a l l - a n g l e X - r a y s c a t t e r i n g c u r v e s for p o l y e t h y l e n e films s t r e t c h e d b y 900~o a t 20 ° a n d a n n e a l e d u n d e r t e n s i o n a n d in t h e free s t a t e : a - - a l o n g t h e t e x t u r e axis; b - - i n t h e d i r e c t i o n p e r p e n d i c u l a r t o t h e t e x t u r e axis; 1 - - s t r e t c h e d a t 20°; 2 a n d 3 - - a n n e a l e d a t 90 ° a n d 110 ° u n d e r t e n s i o n ; 4, ~ a n d 6 - - a n n e a l e d i n t h e free s t a t e a t 110 °, 120 ° a n d 125 ° r e s p e c t i v e l y .
8
12
I6
20
I, zn ~/sec
o
X-ray study of deformation of polyethylene
401
When this specimen was annealed in the stretched state Ln0 and L0os increased to some extent. The intensity of the small-angle maximum also increased a little (Fig. 2a), though it still remained rather weak even at the highest annealing temperature of 110 °. The intensity of the equatorial scattering was practically unchanged by annealing in the stretched state (Fig. 2b t. At high annealing temperatures (for example 120 °) the specimen ruptured. Characteristic differences of specimens of group I (stretched at 20 °) annealed in the free state are: 1) a marked increase in the length of the crystallites in the Hno direction, Lno coinciding, after contraction at 125 °, with the values of Lno for an unstretched specimen; 2) a relatively small increase in Leos in comparison with Lo02for specimens unstretched and stretched at 20°; S) a considerable increase in the ~long period, by a factor of about two in comparison with the specimen stretched at 20°; 4) increase in the intensity of the small-angle ma~inmm (Fig. 2a); 5) decrease in the small-angle equatorial, diffuse scattering (Fig. 2b). Specimens of group I I (stretched by 800~/o at 90°), in contrast to group I, gave a stronger small-angle reflection (Fig. 3a) and weaker equatorial scattering at small angles (Fig. Sb). The values of LI~o and L002for group I I specimens are very close to those for the crystallites in the corresponding specimens of group I. The specimens stretched st 90 ° do not break during the period of annealing under tension at 120 °, in contrast to those stretched at room temperature. Let us consider the problem of paracrystalline distortions in the crystalline structure of polyethylene. It is seen from Table 1 that the values of the parameter gn0 are fairly close for all the specimens. It is a little longer in stretched specimens in comparison with unstretched specimens. After specimens have been annealed in the free state gno decreases a little but when they are annealed in the un~tretched state it remains unchanged (within the limits of experimental error), with the exception of annealing at 120° when it again decreases. Unfortunately we were unable to calculate the parameter g in the Hoe~ direction because it was not possible to separate higher orders of reflection for the (002) plane when recording with MoKa-radiation. However since L0o2 calculated on the assumption that g ~ 0 , for orientated specimens, conforms with the long period (Loozis close to or a little less than D) and for any significant value ofg (for example g----l% ), even on contraction at 125 °, L00~ will be greater than D, it may be assumed that g0o~is considerably less than gno and close to zero. In order to follow the initial stage of deformation of polyethylene films let us examine the experimental data for specimens stretched by 5 0 ~ at 90 °. The length Lno and the value of D (in the equatorial direction) decreased by only 25~/~ in comparison with the unstretched specimen, and L0o~ and gno are close to the corresponding values for the unstretehed material. Consequently we consider that the initial stage of deformation (uniform stretching) is mainly associated with rotation of the crystallitesin the Hoe2 direction, parallel to the direction of stretching, and to a considerably smaller extent with decrease in the dimensions of t h e crystallites.
402
Yu. A. ZUBOV e~
ed.
Deformation to high degrees of elongation is accompanied, as we have shown, by a considerable decrease in the length of the crystallites along Hn0 while the length along H002 is practically unchanged. It may be suggested that at this stage of stretching the predominating process is slipping of their component parts along the [001] crystallographic direction. The folded form of the chains in the sliding parts of the crystallite is evidently preserved to a large extent. In a number of communications the behaviour of polymers on stretching has been compared with the deformational behaviour of metals [33-35]. We shall attempt to explain the difference in structure of specimens stretched at room temperature and at 90 ° by comparison of the behaviour of the polymer on stretching with the behaviour of a metal wire. It is well known that for metals cold drawing causes strengthening of a wire [36-38] and this retards the development of plastic deformation. When drawing is carried out at an elevated temperature the strengthening effect is reduced and the attainment of plastic deformation is easier. From this it may be concluded that when polyethylene is stretched at 20 ° a phenomenon analogous to the strengthening in metals arises in the crystallites. Since under these conditions deformation of the crystallites is difficult it is evident that very small parts of the crystallites (possibly at the edges) are broken off. Since these parts of the crystallite are joined to the main part by interpenetrating chains fibrils of irregular cross-section are formed in the polymer. The irregularity o f the cross-section of the fibrils leads on the one hand to marked decrease in the average size of the crystallite in the Hu0 direction and to decrease in the intensity of the small-angle reflection, and on the other hand to the occurrence of micro:pores between the fibrils, giving rise to the strong equatorial scattering under small angles (Figs. 2a and b). In stretching at 90 °, when the strengthening effect is reduced, sliding along planes parallel to the H0o~ direction occurs. The slipping process results in a more uniform cross-section of the fibrils and consequently to decrease in the intensity of the small-angle, equatorial scattering, and also to increase in the thickness of the fibrils. The greater uniformity of the cross-section of the fibrils is of course also due to recrystallization, which will be discussed below. It is well known also that the strengthening effect in the cold drawing of lnetals is associated with distortion of the unit cell. In connection with the abovementioned analogy between the deformation behaviour of metals and polymers it is interesting to follow the change in the periods of the unit cell of polyethylene at different stages of stretching at 20 ° and 110% Values of the periods a, b and c, t h e volume (V) and the density Pk of the unit cell of an unstretched specimen (specimen 1) and stretched specimens (specimens 2-8), corresponding to points 2-8 on the stress-strain curves (Fig. 1), are given in Table 2. Our values of the periods are in good agreement with those given in references [39] and [40]. For consideration of the change in dimensions of the crystallites during stretching Table 2 also gives the integral half-widths of the 200, 020 and 002 reflections (in
X-ray study of deformation of polyethylene
#no/see
i
/0-
8-
403
t7 o!
"2 A3 v4 'e 3-
.v8
ii I
0
I0
3O
40
b
50
cp= 2~)'
ol ~2 "3 ",5 t 3'
JO
20
/0
0
;0
20
30
~,0
i
'
50
~--20'
I
FIG. 3. Small-angle X-ray scattering curves of polyethylene films stretched by 800 % at 90° and ~nnealod under tenBion and in the free state: a--along the texture axis; b--in the direction perpendicular to the texture axis; 1-- stretehed at 90°, 2 and 3 -annealed at 110° and 120° under tension, 4, 5 and 6--annealed in the free state at 110°, 120° and 125° respectively. radians), with a correction for t h e i n s t r u m e n t a l half-width. W e were u n a b l e fx) calculate the average dimensions o f the crystallite in this case because it was n o t possible t o s t a c k several films t o o b t a i n the o p t i m a l specimen thickness a n d c o n s e q u e n t l y t h e i n t e n s i t y o f the diffraction m a x i m a o f t h e higher o r d e r s o f reflection was too weak.
404
Yu. A. ZUBOVe$a/.
Let us first consider the initial stage of stretching. Since for specimen 2 and 6 the unit cell periods and the line width, and hence the average dimensions of the crystallitcs, coincide (within the limits of experimental error) with the corresponding characteristics of the unstretched m~terial, it m a y be assumed that at this stage stretching involves mainly t h e defective (amorphous) regions between the crystallites. This constitutes an obvious difference between the elastic deformation of polymers and of low-moleenlar weight, crystalline bodies, in which elastic deformation is due to change in the interatomic distances in the crystals. In sections 3 and 7 of the curves in Fig. 1 the above structural parameters are again practically unchanged. However the X-radiograms of these specimens show weak texture, indicating predominant orientation of the c-axis in a direction close to the direction of stretching. Consequently at this stage deformation involves orientation of the crystallites without substantial change in their dimensions and without distortion of the crystal lattice. We shall now consider the structural changes occurring as a result of neck formation (specimens 4 and 8). It is seen from Table 2 that here there is a marked difference in the structural parameters of specimens stretched at 20 ° and 110 °. Deformation at 20 ° leads to increase in the period a and in the volume of the unit cell and consequently to a reduction in the density of the crystallites. The halfwidths of the 200 and 020 lines increase, indicating considerable decrease in the length of the crystallite in the direction perpendicular to the direction of stretching. After stretching of specimens at 110 ° the periods and volume of the unit cell remain unchanged, within the limits of experimental error, in comparison with the unstretched material. The density of the crystallites is practically the same as that of the crystallites in the original material, only their average dimensions are decreased. Thus comparison of the structural parameters of polyethylene specimens drawn through the necking stage at 20 ° and 110 ° shows that at the lower temperature the density of the crystallites decreases substantially, indicating reduction in the degree of order in the latter, whereas at the higher temperature the degree of order remains the same as in the crystallites in an unstretched specimen. The considerable distortion of the unit cell of polyethylene on stretching at 20 ° can hinder deformation as in the case of plastic deformation of metals. It m a y therefore be suggested that as a result of the formation of strengthened sites in polyethylene specimens undergoing stretching the material does not deform further in these regions until the whole specimen has passed into the neck. In our opinion stretching of polyethylene films at 100 ° follows essentially the same mechanism as at 20 °, but because of the considerably higher temperature the relaxation and recrystallization processes are accelerated. Consequently distortions of the unit cell are removed and the average dimensions of the crystallites are increased in comparison with specimens stretched at 20 ° . We did not detect any change in structure and in the dimensions of the crystallites in section 5 of the stretching curve (Fig. 1) in comparison with section 4.
X-ray study of deformation of polyethylene
405
This stage of deformation is accompanied by further orientation of the crystallites, as is indicated by decrease in the textural scattering in the X-radiograms in comparison with the X-radiogram of section 4. It is also possible that changes take place in the defective (amorphous), intercrystallite regions [41]. Like other authors [42, 43] (Table 1) we regard the annealing of stretched specimens, both under tension and in the free state, as previously [26], as a process of recrystallization by breakdown of small crystallites. The disintegrating, small crystallites, joined by interpenetrating chains to larger and possibly more perfect, stable crystallites, by crystallizing on the latter on cooling increase the size of the large crystallites. After free contraction at 125° the length of the crystallite in the ~1~'11o direction returns to the value of Ln0 in the original material, i.e. the crystallite is restored, as it were, in this direction. It is clear that the large increase in the lengths of the crystallites along ~ n o on annealing in the free state must lead to decrease and disappearance of pores between the fibrils, and hence to decrease in the intensity of equatorial, small-angle scattering (Fig. 25). It should be noted that when the annealing temperature is increased breakdown of the larger and more perfect crystallites begins. This is confirmed by the fact that the mobility of the polymer chains in the crystallites increases sharply [44, 45]. Consequently at higher temperatures recrystallization is more complete and involves a larger number of crystallites. For this reason L~z increases to some extent after annealing. The reversible nature of the deformation of spherulites in polyethylene [21] can be explained on the basis of the processes of deformation and rccrystallization during annealing analysed in the present work. The central part of the spherulite is obviously the most stable region with respect to deformation and melting. After stretching the largest and most perfect crystallites remain there, and they are also stable to heat. Moreover the centre of the stretched spherulite is still joined by interpenetrating chains to the residual particles. Consequently when the deformed spherulite is heated its centre acts as a nucleus for re-formation of the original spherulite. Thus as a result of deformation of the fibrils of the spherulites, of which most unstretched specimens consist, a new fibrillar structure is formed with a period differing from the long period of the unstretched material, and coinciding in direction with the direction of the polymer chains. The fact that deformation causes practically no change in the length of the crystaUite in the direction of the polymer chains probably indicates that the new fibrillar structure has arisen from the fibrillar structure of the unorientated specimens by rotation of the crystaUites vcith the c-axis in the direction of stretching and they deform by slipping of one part of the crystallite relative to another along the direction of the chains. Since polyethylene, especially when crystallized from the melt, has, as we assume, chains passing from one folded layer of the crystallite to another and from crystalli~ to crystallite, and while these connecting chains are preserved during defor-
40(}
Yu. A. ZUBOVeta/.
marion, deformation will be thermally reversible, in contrast to metals where plastic deformation is irreversible. Reversibility of deformation arises only when the material is heated to sufficiently high temperatures (3-5 ° below the melting point is sufficient), since the reversibility is associated with recrystallization. We express our deep gratitude to ¥ u . Malinskii, D. ¥ a . Tsvankin, G S.. Markova and Yu. K. Ovchinnikov for participation in discusion of our results and for valuable advice and suggestions, and also to T. F. Kostina for determination of the density of the specimens and measurement of the intrinsic viscosity of the polyethylene. CONCLUSIONS (1) I t is shown t h a t the first stage of deformation (before "neck" formation) is characterized mainly by a tendency for the crystallites to become orientated with the axis of the polymer chains in the direction of the field of force. In the second stage of deformation, associated with r e c k formation, the predominating process is deformation of the crystaUites, probably by slipping of one part of the crystallite relative to another along the axis of the polymer chains. (2) It is suggested that stretching at 20 ° leads to formation of fibrils of less uniform cross-section than those formed on stretching at 90 ° . (3) The periods have been measured and the volume and density of the unit cell calculated for high-density polyethylene at different stages of uniaxial deformation at room temperature and 110 °. Deformation of polyethylene to neck formation at room temperature causes a substantial increase in the period a and in the volume of the unit cell. These changes are associated with loss of order in the crystalline regions on stretching. I n specimens of polyethylene stretched to neck formation at 110 ° the periods and volume of the unit cell are not changed in comparison with unstretched specimens. I t is probable that under these conditions relaxation and recrystallization are more complete, leading to removal of distortions in the crystallites. (4) I n view of the constancy of the structural parameters of the unit cell and average dimensions of the crystallites in the elastic deformation region it is suggested that deformation of the material at this stage of stretching involves the defective, intercrystallite regions. (5) The annealing of stretched polyethylene specimens, under ~ s i o n and in the free state, is discussed in terms of recrystallization by b r e a k c l o ~ of small crystallites. Tranalat~ by E. O. PHILLIPS
REFERENCES
I. V. A. KARGIN, Sovremennye prob|emy nauki o polimerakh (Contemporary Problems in Polymer Science}, Izd. MGU, 1962 2. P. H. GELL, Polymer Single Crystals, Interscience, New York-London, 1963 3. L. MANDELKERN, Crystallization of Polymers, McGraw-Hill, New York, 1964 4. A. KELLER and S. SAWADA, Makromol. Chem. 74: 190, 1964
X-ray study of deformation of polyethylene 5. 6. 7. 8. 9. 10. 11.
12.
13.
14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32.
33. 34. 35.
407
A. P E T ~ , Mak~omol. Chem. 74: 107, 1964 V. A. ]KARGIN, International Symposium on Macromolecular Chemistry, Prague, 1965 A. PETERLIN, J. Polymer Science C8: 61, 1965 A. KETJLER, Polymer 3: 393, 1962 V. A. KARGIN and T. A. KORETSKAYA, Vysokomol. soyed. 1: 1721, 1959 (Not translated in Polymer Sci. U.S.S.R.) Vo A. KARGIN, Vestnik Akad. Nauk SSSR, No. 4, 19, 1961 M. B. KONSTANTINOPOL'SKAYA, Z. Ya. BERESTNEVA and V. A. KARGIN, ])ok]. Akad. Nauk SSSR 151: 1108, 1963; Vysokomol. soyed. 7: 420, 1965 (Translated in Polymer SCi. U.S.S.R. 7: 465, 1965) V. A. KARGIN and I. I. GORINA, Vysokomol. soyed. 7: 220; 1273; 1323; 1965; (Translated in Polymer Sci. U.S.S.R. 7: 2, 231; 7: 1, 1411; 7: 8, 1465, 1965) Dokl. Akad. Nauk. SSSR. 165: 1108, 1965 M. V. KONSTANTINOPOL'SKAYA, T. A. KORETSKAYA, Z. Ya. BEEESTNEVA and V. A. KARGIN, Vysokomol. soyed. 7: 1927, 1965 (Translated in Polymer Sei. U.S.S.R 7: 11, 2113, 1965) B. WUNDEKI,[CH and T. ARAKAWA, J. Polymer Sci. A2: 3697, 1964 P. H. GELL, F. R. ANDERSON, B. WUNDERLICH and T. ARAKAWA, J. Polymer Sci. A2: 3707, 1964 A. I. SLUTSKER, A. E. GROMOV and V. S. PSHEZHETSKH, Fizika tverdogo tela 6: 456, 1964 K. HESS and H. KIESSIG, Naturwissenschaften 31: 171, 1943; Z. Phys. Chem. 193: 196, 1944 F. H. M t ~ L E R and K. J~L~lgET~,Makromol. Chem. 9: 97, 1953 V. A. KARGIN and T. I. 80GOLOVA, Zh. fiz. khim. 27: 1039, 1953 S. N. ZHURKOV, V. A. MARIlgHT~I, L. P. MYASNEKOVAand A. I. SLUTSKER, VysokomoL soyed. 7: 1041, 1965 (Translated in Polymer Sci. U.S.S.R. 7: 6, 1145, 1965) V. A. KARGIN, V. I. SEI.TKHOVA and G. S. MARKOVA, Vysokomol. soyed. 7: 1495, 1965 (Translated in Polymer Sci. U.S.S.R. 7: 9, 1653, 1965) V. A. KARGIN, T. I. SOGOLOVA and N. Y&. RAI~PORT-MOLODTSOVA, Vysokomol. soyed. 6: 1562, 1964 (Translated in Polymer Sci. U.S.S.R. 6: 9, 1732, 1964) K. KATAYAMA, J. Phys. Soc. Japan 16: 462, 1961 N. KASAI and M. KAKUDO, J. Polymer Sci. A2: 1955, 1964 P. INGRAM, H. lgIHO and A. PETERLIN, International Symposium on Macromolecular Chemistry, Prague, 1965 Yu. A. ZUBOV and D. Y&. TSVANKIN, Vysokomol. soyed. 6: 2131, 1964 (Translated in Polymer SCi. U.S.S.R. 6: 12, 2367, 1965) D. M. ltHKkkER and A. S. ZEVIN, Rentgenovskaya difraktometriya (X-Ray Diffractometry), Fizmatgiz, 1963 R. RONART, R. HOSEMAN and R. L. Mc~ULLOUGH, Polymer 4: 199, 1963 K. Kh. RAZIK0V, Yu. A. ZUB0V, G. S. MARKOVA and V. A. KARGIN, Vysokomol. soyed. 5: 760, 1963 (Translated in Polymer Sci. U.S.S.R. 4: 6, 1471, 1963) N. V. MEgHAILOV, V. O. GORBACHEVA, N. N. ZAV'YALOVA, K_him. volokna, No. 1 19, 1960 C. W. BUNN, Trans. Faraday Soc. 35: 482, 1939 A. E. GROMOV and A. I. SLUTSKER, Sb. Karbotsepnye vysokomolekulyarnye soyedineniya (Collected papers. Carbon.chain Macromolecular Compounds). p. 247, Izd. Akad. Nauk SSSR, 1963 J. K A U F M and W. GEORGE, J. Appl. Phys. 21: 431, 1950 P. I. VINCENT, Polymer 1: 7, 1960 D. A. ZAUKELIES, J. Appl. Phys. 88: 2797, 1962
408
G. L. SLo~rr~smz e t a / .
36. S. S. SHTEINBERG, Metallovedenie, G1TL po chernoi i tsvetnoi metallurgii (Metallurgical Science, G L T L on Ferrous and Light Metallurgy). Sverdlovsk-Moscow, 1952 37. A. H. COTTRELL, Dislokatsii i plasticheskoe techenie v kristallakh (Dislocations and Plastic Flow in Crystals). Metallurgizdat, 1958 38. D. Mac CLEAN, Mekhanicheskoe svoistva metallov (Mechanical Properties of Metals). Izd. ,,Metallurgiya", 1965. 39. P. R. SWAN, J. Polymer Sci. 56: 403, 1962 40. N. KASAI and M. KAKUDO, International Symposium on Macromoleeular Chemistry, Prague, 1965 41. S. N. ZHURKOV, A. I. SLUTSKER and A. A. YASTREBINSKH, Fizika tverdogo tela 6: 3601, 1964 42. W. O. STATTON and P. H. GEIL, J. Appl. Polymer Sci. 3: 357, 1960 43. M. B. RHODES and R. S. STEIN, J. Appl. Phys. 32: 2344, 1961 44. Yu. A. ZUBOV, D. Ya. TSVANKIN, G. S. MARKOVA and V. A. KARGIN, ])old. Akad. l~auk SSSR 157: 948, 1964 45. U. SLICHTER, bS. Fizika polimerov (Collected papers. The Physics of Polymers). Foreign Literature Publishing House, 1960
INVESTIGATION OF THE EFFECT OF THE TYPE OF SUPERMOLECULAR AND CHEMICAL STRUCTURE ON THE STRENGTH AND ELASTICITY OF POLYMER GLASSES* G. L. SLOI~IMSKII, A. A. ASKADSKIIand V. I. PArLey I n s t i t u t e for E l e m e n t a r y Organic Compounds, U.S.S.R. A c a d e m y of Sciences
(Received 19 February 1966) THE objective of the present work was the quantitative investigation of the strength and relaxation properties of a number of polyarylates, differing in the chemical structure of the repeating unit, and differing in their supermoleeular structure. The method used [1] consists of the following: b y moans of thermomochanical measuremerits under conditions when a film is stretched to rupture with a non-linear regime for t h e increase in temperature T with time t, the regime complying with the equation
T=a/(b--t)
(1)
(whore a and b are constants), one m a y comparatively easily determine the parameters which characterize the strength (according to Zhurkov) and the relaxation (according to Aloksandrov-Gurevich-Lazurkin) properties of the polymer m a t e r i a l . . k s is well known [2-6] those parameters are structure-sensitive constants, as also are the activation energies for the rupture and relaxation processes. * Vysokomol. soyod. A9: No. 2, 365-369, 1967.
Yu. A. Z u s o v e~ a/.
REFERENCES
I. A.A. TAGER and V. Ye. DREVAL', Dokl. Akad. l~auk SSSR 145: 136, 1962; V. Ye. DREVAL', A, A, TAGER and A. S. FOMINA, Vysokomol. soyed. 5: 1404, 1963 (Translated in Polymer Sci. U.S.S.R. 5: 3, 495, 1964) 2. F. BUECHE, J. Appl. Phys. 24: 432, 1953 3. I. R. VAN WAZER e~ ed., Viscosity and Flow Measurement, Interscience, 1963 4. I. V. KONYUKI~, G. V. VINOGRADOV and A. :A. KONSTANTINOV, Plast. massy, No. 10, 45, 1963 5. V. V. SINITSYN, A. A. KONSTANTIN and G. V. VINOGRADOY, Tr. I I I Vses. konf. po kolloidnoi khimii (Trans. 3rd All-Union Conference on Colloid Chemistry), p. 113, Izd. Akad. Nauk SSSR, Moscow, 1956 6. A. I. KORETSKAYA, A. A. KONSTANTINOV and G. V. VINOGRADOV, Khim. volokna, No. 2, 36, 1960 7. G. V. YINOGRADOV and N. V. PROZOROVSKAYA, P last. massy, No. 5, 50, 1964. 8. L. V. IVANOVA-CHUMAKOVA and P. A. REBINDER, Kolloid. zh. 18: 429, 1956 9. G. V. VINOGRADOV, I. M. BELKIN, A. A. KONSTANTINOY, B. A. ROGOV, S. K. KRASHENNIKOV, A. Ya. MALKIN and I. V. KONYIFKH, Zavod. lab. 30: 864, 1964 10. Yu. F. DEINEGA, V. P. PAVLOV and G. V. VINOGRADOY, Zavod. lab. 26: 353, 1960 11. S. SHIST~[IDOand I. ITO, J. Chem. Soc. Japan (Pure Chem. Sect.) 889, 1963 12. W. A. WRIGHT and W. W. CROUSE, A New Concept in Generalizing Non-Newtonian Fluid Flow Data, ASME-ASLE Internat. Lubric. Conf., Washington D. C. Preprint 64, LCII, Oct. 1964 13. F. D. GRANDINE and F. D. FERRY, J. Appl. Phys. 24: 679, 1953 14. A. A. TAGER and V. V. ANDREYEVA, International Symposium on Macromolecular Chemistry, Prague, Preprint 125, 1965 15. F. BUECHE, J. Chem. Phys. 22: 1570, 1954; F. BUECHE and S. W. HARDING, J. Polymer Sci. 32: 177, 1958 16. G. V. VINGRADOV, A. Ira. MALKIN, N. V. PROZOROVSKAYA and V. A. KARGIN', Dokl. Akad. Nauk SSSR 150: 574, 1963; 154: 890, 1964
X-RAY STUDY OF DEFORMATION OF POLYETHYLENE* Yu. A. ZuBov, V. I. S~.LIKHOVXand V. A. KARGI~ L. Ya. Karpov Physicochomical Institute
(Received 6 January 1966) AS A RESULT of n u m e r o u s investigations o f the s t r u c t u r e o f crystalline p o l y m e r s in recent times some degree o f success has been o b t a i n e d in s t u d y o f the structure o f b o t h u n o r i e n t a t e d a n d o r i e n t a t e d p o l y m e r s [1-7]. I t has been established t h a t in the m a j o r i t y o f p o l y m e r s studied t h e m a i n morphological form in u n o r i e n t a t e d p o l y m e r s is a crystalline plate. The molecular chains are a r r a n g e d * Vysokomol. 8oyod. A9; No 2, 353-364, 1967.
X-ray study of deformation of polyethylene
395
perpendicularly or at a definite angle to the surface of the plate and are folded back on themselves. Aggregates of plates, arranged in a definite manner, form more complex supermolecular structures (bands, sheaves, spherulites etc.). In the complex, supermolecular structures, especially those obtained by crystallization from the melt, the plates are probably connected together by interpenetrating chains [2, 8]. _Another possibility that cannot be excluded is gradual growth of supermolecular structures by mutual packing of simpler structural elements (for example, bundles of chains), and here interpretation of chains is not essential [9-11]. In unorientated, crystalline polymers in a number of cases fibrillar formations are found, and it has been suggested that these consist of bundles of straightened chains arranged along the axis of the fibril [12-13]. Crystalline formations with straightened chain molecules are found in bulk polyethylene, crystallized from the melt under pressure [14, 15], and in the needle-shaped crystals of polyoxymethylcne obtained by controlled polymerization [16]. However since at the present time electron microscopic study in conjunction with electron diffraction analysis shows in most cases the presence of crystalline plates with a folded chain conformation we proceed, in discussion of the structure of an isotropic specimen, from the existence of plates with folded chains, or aggregates of plates, connected by interpenetrating molecules or bundles of molecules. It is well known that a highly orientated material has a fibrillar structure. The fibrils are ar.ranged parallel to the direction of stretching. Along the axis of the fibril, which coincides with the direction of the molecular chains, there is an alternating sequence of regions of different density, i.e. denser, highly ordered, crystalline regions and less dense, defective or amorphous regions. The combined length of the crystalline and amorphous regions gives the long period [17]. The problem of how the transition from the structure of the unorientated polymer to that of the orientated polymer is brought about during deformation is of great interest. It is suggested in references [18-20] that this transition occurs by complete breakdown of the crystalline structure of the original isotropic material and formation of a new, orientated fibre structure. This mechanism is not the only possibility however. Recently some authors, bearing in mind the complex structure of well developed supermolecular formations, especially of large spherulites, consider that structural changes on deformation proceed by a stepwise mechanism and can involve breakdown of higher structures while simpler structural elements are preserved [21, 22]. It is evident that different degrees of breakdown of the original structure can occur, depending on the conditions of deformation and on the supermolecular structure. •It was shown in references [23] and [24] than on deformation of polyethylene the average length of the crystallite in the direction perpendicular to the direction of the chain molecules decreases. Unfortunately these papers do not give information on the length of the crystallite in the direction of the chains. The possibility of fracture of blocks of folded chains into fragments and building up of
396
Yu. A. ZUBOV et a/.
t h e s e f r a g m e n t s i n t o fibrils d u r i n g u n i a x i a l d e f o r m a t i o n o f p o l y e t h y l e n e is s h o w n i n r e f e r e n c e s [7] a n d [25]. The aim of the present work was to follow the change in the dimensions of polyethylene crystallites during uniaxial deformation by means of large and small angle X-ray studies, and also to estimate change in the degree of order in the crystalline regions at different stages of stretching.
EXPERIMENTAL The linear polyethylene, Hostalen, w i t h a melting point of 130° and It/I= 1"04 in decalin at 135 ° was studied. Specimens in the form of films of thickness 2 m m were prepared b y compression moulding of granular polyethylene in a laboratory press at 220 ° and a pres-
~,,kg/cm2 200
3
2 7
b
8
$
I~G.1. Conventional stress-strain curves for polyethylene stretched a t 20 ° (a) and 110 ° (b). sure of 50 arm, with a second heat t r e a t m e n t of t h e films in t h e mould at 220 ° without pressure. Films prepared in this w a y were completely isotropic. Blade test pieces with a working section 10 rnm in length were cut from the films and stretched uniaxially at a rate of movem e n t of the lower clamp of 10 mm/min, a t 20 °, 90 ° and 110 °, in an FMPw-250 tensile t e s t machine provided with a heating chamber. W e used unstretehed fllm~ and films stretched b y 50~o at 90 ° and b y 800~/o and 900% a t 90 ° and 20 ° for X - r a y measurement of the dimensions of the crystallites, and for smallangle measurements. The stretched films were removed from the clamps (a contraction o f 3 - 5 % then occurred) and were stacked together to form specimens of optimal thickness. The optimal thickness, t, was obtained from the condition t = c o s v/~ where ~ is the linear coefficient of absorption for polyethylene. I n order to s t u d y loss of order in the crystal lattice specimens stretched at 20 ° and 110 ° were fixed in the stressed state between special clamps and after 24 hr were placed in t h e X - r a y diffTactometer. The specimens studied corresponds to points 2-5 (Fig. 1, curve a) a n d 6-8 (Fig. 1, curve b) in the stress-strain curves. I t should be noted t h a t a "neck" began to form after uniaxial stretching of the whole test piece to 30~/o a t 20 ° and to 50% a t 90 ° and 110% The elongation in the neck corresponded on the average to 900% for stretching a t 20 °, ~ 800% at 90 ° and to 7000//o at 110% Specirdens stretched through the neck stage a t 20 ° were opaque as a result of a high degree of "silvering". E x a m i n a t i o n of sections of the polyethylene films in a polarizing microscope showed t h a t t h e unstretched filru~ consist of spherulites of diameter about 10 $. The region of uniform elongation of the specimen is characterized b y uniform elongation of the spherulites in the direc-
X-ray study of deformation of polyethylene
397
tion of stretching, as we have previously observed in the stretching of polyethylene films a fine spherulitic structure [21]. The X-ray investigation, in which the procedure described in reference [2"6] was followed, showed a high degree of c-axis orientation of the crystals along the direction of stretching in films with elongations of 800% a n d 900~/o. The azimuthal half-width of the 110 reflections was in both cases 6 °. The large-angle X-radiogrRma indicated t h a t in film, stretched b y 50~/o at 90 ° the polymer chains are predominantly arranged at a n angle of 25 ° to the stretching axis. For study of the effect of annealing on structure some film, stretched at 20 ° and 90 ° were heated for 2 hr at 90 °, 110 °, 120 ° and 125° in a current of nitrogen, both under tension and in the free state. I t is noteworthy t h a t whereas annealing under tension gave n o significant change in the orientation of the crystallites, after free contraction there was considerable scatter due to textural changes, though c-axis orientation was preserved. The large angle X-ray study was carried out in a DRON-1 cli~actometer, using CuK~ radiation (Ni filter). I n order to avoid distortion of the shape of the reflection due to vertical divergence of the primary beam we used a Seller sllt. The diffracted radiation was recorded b y means of a scintillation counter with a discriminator. During the recording period the counter was moved at a rate of 0.5°/min. We selected the time constant (RG) of the integrating i n s t r u m e n t to fit the condition R G = 0.25 ~, where ¢ is the time for passage of the counter through the half-width of t~e diffraction peak [27]. The diffractograrns were obtained b y the transmission method because with the reflection method the diCDaction peaks were distorted as a result of the depth of penetration of the primary beam into the specimen, and absorption. The profile of the cllCfraction line was recorded on an EPP-09 recording strip. For determination of the instrumental line width coarsely eryst~ni,xe, powdered urotropine and lithium fluoride were used as reference standards. During the recording period the standards were rotated at a rate of 50 rev/min in order to average the intensities over the I)ebye ring. The standards and the polyethylene filma were recorded under identical conditions with, the same routine of operation of the instrument and with standards and specimens of the same thickness. For determination of the dimensions of the crystallites the integral half-wldths of the 110, 220 and 002 polyethylene reflections were measured, and also of the lines of the standards lying under Bragg angles close to the angles of the above reflections. The integral half-width of a reflection was calculated as the ratio of the area under the diffraction maxim u m to its height, after separation of the reflection from the background. The true halfwidth of the reflection, assuming Gausslan distribution of the intensities of the lines of the polyethylene specimens and the standard, was calculated b y means of the formula
where B is the true integral half-width of the reflection and B 1 and B, are the experimental reflection half-widths of the specimen and standard respectively. The dimensions of the crystallites were determined b y means of the formula based on calculation of the di~raction for a paracrystalline polymer model suggested b y Hoseman [28]: -
]'1
(2)
where 9 is the parameter of paracryst~lllae distortions giving the fluctuating paracrystallino distortions relative to the mean interatomio distance, n the order of the reflection, B(n) the integral half-width of the reflection, (in the units of reciprocal space), L the average length of the crystallite in the direction perpendicular to the given crystallographic plane with a n interplanar distance d. The values of Ll,o and g**0 for polyethylene were found from equation (2), using two orders of reflection from the (110) plane. For determination of the
398
Yv. A. ZUBOV et a/.
length of the crystalllte in the direction perpendicular to the (002) plane, L001, it was assumed that g----0. The accuracy of the determination of L and g was not less than 10%. We assessed the loss of order in the crystalline regions by the change in volume and density of the unit cell at different stages of deformation. For determination of the volume (V) we measured the a, b and c periods of the polyethylene unit cell from the position of the 200, 020 and 002 reflections. The density of the unit cell, Pk, was calculated by means o f the formula p~ ~ 2 M / V , where M is the molecular weight of the monomer unit in grammes. The factor 2 indicates the number of monomer units in the unit cell. Since the value of c changed little in highly stretched specimens in comparison with unstretchod films and because we were unable to measure this period for specimens 2, 3, 6 and 7 (Fig. 1), for calculation of V for these specimens we used the average value c=2.55/k. The position of the diffraction maximum was found as the point of intersection of the profile of the maximum with the line drawn through the centres of the lines joining points of equal intensity [27]. A zero goniometric setting was established according to the position of the same reflection on each side of the primary beam. In order to elimlnate the effect of inertia of the integrating system the counter was moved in the forward and reverse directions. Each diffraction maximum was recorded several times (usually twelve times) with three new settings of the specimen. The accuracy of setting of the specimen on the axis of the GUR-5 goniometer ~vas ±0.05 mm. When the above experimental conditions were observed the error in determination of the angle 0 was ± 1 ' for the 200 reflection, ±1.5' for the 020 reflection and ±2.5' for the 002 reflection. The lower degree of accuracy in determination of 0 for the 020 and 002 reflections was due to their low intensities. In accordance with the given accuracy of 0 the following accuracies of determination of the periods, volume and density of the unit cell were calculated: a - - ± 0 . 0 1 A, b--±0.01 A, c--±0.003 A, V--±0.03×-10 -I~ cm s and Pk-±0"003 g/cm*. The apparatus and method for small-angle recording used in this work has been described previously [29]. The density (p) of a number of samples was determined by the gradient tube method [30]. RESULTS AND DISCUSSION D a t a on change in t h e dimensions of crystallites on s t r e t c h i n g are given in T a b l e 1. I n f u t u r e we shall denote the direction along which t h e l e n g t h of t h e crystal° ]ire is d e t e r m i n e d b y the reciprocal lattice v e c t o r Hh~l, which is perpendicular t o t h e plane (hb/). I n a n u n s t r e t c h e d specimen t h e l e n g t h of the crystalline in t h e H l l 0 direction was 233 A. The long period, which, as was s h o w n in referenpe [32] is n o t perpendicular t o t h e direction o f t h e p o l y m e r chains in a n u n o r i e n t a t e d material, was 270 A. The L0o2 length was 140 A. I t should be n o t e d t h a t the a c c u r a c y o f determin a t i o n o f L0o~ in an u n o r i e n t a t e d specimen is s o m e w h a t lower t h a n for o r i e n t a t e d specimens. L e t us consider t h e s t r u c t u r e o f a specimen stretched b y 9 0 0 ~ at 20 °. I n comparison w i t h an u n s t r e t c h e d specimen the length o f the crystallite in t h e H-*~2 direction is p r a c t i c a l l y u n c h a n g e d whereas in the Hl10 direction it has decreased b y a f a c t o r of a p p r o x i m a t e l y three. I t is seen f r o m :Figure 2a t h a t the i n t e n s i t y o f t h e small-angle diffraction m a x i m u m for this specimen is v e r y low. I n a d d i t i o n
X-ray study of deformation of polyethylene
399
TABLE 1. RESULTS OF X-RAY ANALYSIS AND T~t~ DEI~SI'I'I~:S OF THE POLYETHYLENE SPECIMENS I. S t r e c h i n g a t 20 ° b y 9 0 0 %
Parameters
9~vv / o at 20 °
i
annealing temperature, °C under tension 90
"~110~ ~
Lo., A. g.o, %
D,A
p, g / c m s
I I . S t r e c h i n g a t 90 ° b y 8 0 0 %
110
t annealing temperature, °C 8q__ ,~
in t h e free state 110
120
at 90°
125
under tension 110
in t h e free state
120
110
120
125
158 146 190 233 107 142 159 139 194 2 2 0 233 171 80 1 0 6 140 168 142 157 175 143 168 175 164 189 198 1 5 1 157 1 9 3 2.6 2.4 2.1 2.8 3.0 2.8 3.0 2.3 2.2 2.3 2.9 2.8 2.6 2.6 270 200 174 174 210 210 270 313 185 203 250 210 270 313 0.921 - - 0.942 0.952 - - 0.954 0.945 - - 0.860 - - 0"907 - -
.Definition; I~1o and ~ -- average lengths of crystallite in the direction perpendicular to the (110) and (002) planes, I.e, in conformity with the structure of the polyethylene unit cell [B1], in the directions perpendicular to and parallel with the polymer chains; gxxothe parameter of paracrystalline distortions in the direction perpendicular to the 110 plane; D-long period, p-denszty. '
to this the specimen gives extraordinarily high equatorial scattering (Fig. 2b). The fact that the intensity of scattering is substantially higher in the equatorial direction than in the meridial direction means that the specimen contains asymmetrical inhomogeneities, the long dimension of which lies along the direction of stretching. Since the intensity of equatorial scattering is comparable with the intensity for substances known to be porous it may be considered that the inhomogeneities are pores formed during stretching. This conclusion is supported by the density of the specimens, which is very low in the case of those stretched at 20 °. TABLE 2. VALVES OF THE PERIODS (a, b, c) THE VOLUME (V) . ~ v THE DENSITY (Pk) OF TH~ CELL, AND THE INTEGRAL HALF-WIDTH (~) OF THE 200, 020 AND 002 REFLECTIOI~'S FOR POLYETHYLENE
P o l y e t h y l e n e film s p e c i m e n s Parameters unstreched 1
a,A b,A e,A V × 10U, c m a p~, g / e m 8 Aloe, r a d Aol o. r ~ l Aool, r~d
7"44 4"97 2"552 94"4 0"987 0"0120 0"0105 0"0142
s t r e t c h e d a t 20 ° 2
3
7"44 4"96 -94"1 94"1 0"990 I 0"990 0.0108] 0"0116 0"0130 0.0105 7"44 4"96
--
s t r e t c h e d a t 110 °
4
5
6
7
8
7"52 4"97 2"550 95"3 0'978 0"0273 0"0232 0"0138
7"53 4"97 2"548 95"3 0"978 0"0267 0"0243 0"0140
7"45 4"97
7"44 4"96
7"45 4"96 2"548 94"2 0"989 0"0170 0"0162 0"0129
94"4
0"987 0"0115 0"0105
94"1 0"990 0"0123 0.0121
0
20
a
40
v6
*5
o! A2 A3 v4
60 ~=20
0
3OO
~00
5O0
600
700
10
20
30
b
40
ol A2 "3 v4 °5 v6
50
~ = 20'
FIG. 2. S m a l l - a n g l e X - r a y s c a t t e r i n g c u r v e s for p o l y e t h y l e n e films s t r e t c h e d b y 900~o a t 20 ° a n d a n n e a l e d u n d e r t e n s i o n a n d in t h e free s t a t e : a - - a l o n g t h e t e x t u r e axis; b - - i n t h e d i r e c t i o n p e r p e n d i c u l a r t o t h e t e x t u r e axis; 1 - - s t r e t c h e d a t 20°; 2 a n d 3 - - a n n e a l e d a t 90 ° a n d 110 ° u n d e r t e n s i o n ; 4, ~ a n d 6 - - a n n e a l e d i n t h e free s t a t e a t 110 °, 120 ° a n d 125 ° r e s p e c t i v e l y .
8
12
I6
20
I, zn ~/sec
o
X-ray study of deformation of polyethylene
401
When this specimen was annealed in the stretched state Ln0 and L0os increased to some extent. The intensity of the small-angle maximum also increased a little (Fig. 2a), though it still remained rather weak even at the highest annealing temperature of 110 °. The intensity of the equatorial scattering was practically unchanged by annealing in the stretched state (Fig. 2b t. At high annealing temperatures (for example 120 °) the specimen ruptured. Characteristic differences of specimens of group I (stretched at 20 °) annealed in the free state are: 1) a marked increase in the length of the crystallites in the Hno direction, Lno coinciding, after contraction at 125 °, with the values of Lno for an unstretched specimen; 2) a relatively small increase in Leos in comparison with Lo02for specimens unstretched and stretched at 20°; S) a considerable increase in the ~long period, by a factor of about two in comparison with the specimen stretched at 20°; 4) increase in the intensity of the small-angle ma~inmm (Fig. 2a); 5) decrease in the small-angle equatorial, diffuse scattering (Fig. 2b). Specimens of group I I (stretched by 800~/o at 90°), in contrast to group I, gave a stronger small-angle reflection (Fig. 3a) and weaker equatorial scattering at small angles (Fig. Sb). The values of LI~o and L002for group I I specimens are very close to those for the crystallites in the corresponding specimens of group I. The specimens stretched st 90 ° do not break during the period of annealing under tension at 120 °, in contrast to those stretched at room temperature. Let us consider the problem of paracrystalline distortions in the crystalline structure of polyethylene. It is seen from Table 1 that the values of the parameter gn0 are fairly close for all the specimens. It is a little longer in stretched specimens in comparison with unstretched specimens. After specimens have been annealed in the free state gno decreases a little but when they are annealed in the un~tretched state it remains unchanged (within the limits of experimental error), with the exception of annealing at 120° when it again decreases. Unfortunately we were unable to calculate the parameter g in the Hoe~ direction because it was not possible to separate higher orders of reflection for the (002) plane when recording with MoKa-radiation. However since L0o2 calculated on the assumption that g ~ 0 , for orientated specimens, conforms with the long period (Loozis close to or a little less than D) and for any significant value ofg (for example g----l% ), even on contraction at 125 °, L00~ will be greater than D, it may be assumed that g0o~is considerably less than gno and close to zero. In order to follow the initial stage of deformation of polyethylene films let us examine the experimental data for specimens stretched by 5 0 ~ at 90 °. The length Lno and the value of D (in the equatorial direction) decreased by only 25~/~ in comparison with the unstretched specimen, and L0o~ and gno are close to the corresponding values for the unstretehed material. Consequently we consider that the initial stage of deformation (uniform stretching) is mainly associated with rotation of the crystallitesin the Hoe2 direction, parallel to the direction of stretching, and to a considerably smaller extent with decrease in the dimensions of t h e crystallites.
402
Yu. A. ZUBOV e~
ed.
Deformation to high degrees of elongation is accompanied, as we have shown, by a considerable decrease in the length of the crystallites along Hn0 while the length along H002 is practically unchanged. It may be suggested that at this stage of stretching the predominating process is slipping of their component parts along the [001] crystallographic direction. The folded form of the chains in the sliding parts of the crystallite is evidently preserved to a large extent. In a number of communications the behaviour of polymers on stretching has been compared with the deformational behaviour of metals [33-35]. We shall attempt to explain the difference in structure of specimens stretched at room temperature and at 90 ° by comparison of the behaviour of the polymer on stretching with the behaviour of a metal wire. It is well known that for metals cold drawing causes strengthening of a wire [36-38] and this retards the development of plastic deformation. When drawing is carried out at an elevated temperature the strengthening effect is reduced and the attainment of plastic deformation is easier. From this it may be concluded that when polyethylene is stretched at 20 ° a phenomenon analogous to the strengthening in metals arises in the crystallites. Since under these conditions deformation of the crystallites is difficult it is evident that very small parts of the crystallites (possibly at the edges) are broken off. Since these parts of the crystallite are joined to the main part by interpenetrating chains fibrils of irregular cross-section are formed in the polymer. The irregularity o f the cross-section of the fibrils leads on the one hand to marked decrease in the average size of the crystallite in the Hu0 direction and to decrease in the intensity of the small-angle reflection, and on the other hand to the occurrence of micro:pores between the fibrils, giving rise to the strong equatorial scattering under small angles (Figs. 2a and b). In stretching at 90 °, when the strengthening effect is reduced, sliding along planes parallel to the H0o~ direction occurs. The slipping process results in a more uniform cross-section of the fibrils and consequently to decrease in the intensity of the small-angle, equatorial scattering, and also to increase in the thickness of the fibrils. The greater uniformity of the cross-section of the fibrils is of course also due to recrystallization, which will be discussed below. It is well known also that the strengthening effect in the cold drawing of lnetals is associated with distortion of the unit cell. In connection with the abovementioned analogy between the deformation behaviour of metals and polymers it is interesting to follow the change in the periods of the unit cell of polyethylene at different stages of stretching at 20 ° and 110% Values of the periods a, b and c, t h e volume (V) and the density Pk of the unit cell of an unstretched specimen (specimen 1) and stretched specimens (specimens 2-8), corresponding to points 2-8 on the stress-strain curves (Fig. 1), are given in Table 2. Our values of the periods are in good agreement with those given in references [39] and [40]. For consideration of the change in dimensions of the crystallites during stretching Table 2 also gives the integral half-widths of the 200, 020 and 002 reflections (in
X-ray study of deformation of polyethylene
#no/see
i
/0-
8-
403
t7 o!
"2 A3 v4 'e 3-
.v8
ii I
0
I0
3O
40
b
50
cp= 2~)'
ol ~2 "3 ",5 t 3'
JO
20
/0
0
;0
20
30
~,0
i
'
50
~--20'
I
FIG. 3. Small-angle X-ray scattering curves of polyethylene films stretched by 800 % at 90° and ~nnealod under tenBion and in the free state: a--along the texture axis; b--in the direction perpendicular to the texture axis; 1-- stretehed at 90°, 2 and 3 -annealed at 110° and 120° under tension, 4, 5 and 6--annealed in the free state at 110°, 120° and 125° respectively. radians), with a correction for t h e i n s t r u m e n t a l half-width. W e were u n a b l e fx) calculate the average dimensions o f the crystallite in this case because it was n o t possible t o s t a c k several films t o o b t a i n the o p t i m a l specimen thickness a n d c o n s e q u e n t l y t h e i n t e n s i t y o f the diffraction m a x i m a o f t h e higher o r d e r s o f reflection was too weak.
404
Yu. A. ZUBOVe$a/.
Let us first consider the initial stage of stretching. Since for specimen 2 and 6 the unit cell periods and the line width, and hence the average dimensions of the crystallitcs, coincide (within the limits of experimental error) with the corresponding characteristics of the unstretched m~terial, it m a y be assumed that at this stage stretching involves mainly t h e defective (amorphous) regions between the crystallites. This constitutes an obvious difference between the elastic deformation of polymers and of low-moleenlar weight, crystalline bodies, in which elastic deformation is due to change in the interatomic distances in the crystals. In sections 3 and 7 of the curves in Fig. 1 the above structural parameters are again practically unchanged. However the X-radiograms of these specimens show weak texture, indicating predominant orientation of the c-axis in a direction close to the direction of stretching. Consequently at this stage deformation involves orientation of the crystallites without substantial change in their dimensions and without distortion of the crystal lattice. We shall now consider the structural changes occurring as a result of neck formation (specimens 4 and 8). It is seen from Table 2 that here there is a marked difference in the structural parameters of specimens stretched at 20 ° and 110 °. Deformation at 20 ° leads to increase in the period a and in the volume of the unit cell and consequently to a reduction in the density of the crystallites. The halfwidths of the 200 and 020 lines increase, indicating considerable decrease in the length of the crystallite in the direction perpendicular to the direction of stretching. After stretching of specimens at 110 ° the periods and volume of the unit cell remain unchanged, within the limits of experimental error, in comparison with the unstretched material. The density of the crystallites is practically the same as that of the crystallites in the original material, only their average dimensions are decreased. Thus comparison of the structural parameters of polyethylene specimens drawn through the necking stage at 20 ° and 110 ° shows that at the lower temperature the density of the crystallites decreases substantially, indicating reduction in the degree of order in the latter, whereas at the higher temperature the degree of order remains the same as in the crystallites in an unstretched specimen. The considerable distortion of the unit cell of polyethylene on stretching at 20 ° can hinder deformation as in the case of plastic deformation of metals. It m a y therefore be suggested that as a result of the formation of strengthened sites in polyethylene specimens undergoing stretching the material does not deform further in these regions until the whole specimen has passed into the neck. In our opinion stretching of polyethylene films at 100 ° follows essentially the same mechanism as at 20 °, but because of the considerably higher temperature the relaxation and recrystallization processes are accelerated. Consequently distortions of the unit cell are removed and the average dimensions of the crystallites are increased in comparison with specimens stretched at 20 ° . We did not detect any change in structure and in the dimensions of the crystallites in section 5 of the stretching curve (Fig. 1) in comparison with section 4.
X-ray study of deformation of polyethylene
405
This stage of deformation is accompanied by further orientation of the crystallites, as is indicated by decrease in the textural scattering in the X-radiograms in comparison with the X-radiogram of section 4. It is also possible that changes take place in the defective (amorphous), intercrystallite regions [41]. Like other authors [42, 43] (Table 1) we regard the annealing of stretched specimens, both under tension and in the free state, as previously [26], as a process of recrystallization by breakdown of small crystallites. The disintegrating, small crystallites, joined by interpenetrating chains to larger and possibly more perfect, stable crystallites, by crystallizing on the latter on cooling increase the size of the large crystallites. After free contraction at 125° the length of the crystallite in the ~1~'11o direction returns to the value of Ln0 in the original material, i.e. the crystallite is restored, as it were, in this direction. It is clear that the large increase in the lengths of the crystallites along ~ n o on annealing in the free state must lead to decrease and disappearance of pores between the fibrils, and hence to decrease in the intensity of equatorial, small-angle scattering (Fig. 25). It should be noted that when the annealing temperature is increased breakdown of the larger and more perfect crystallites begins. This is confirmed by the fact that the mobility of the polymer chains in the crystallites increases sharply [44, 45]. Consequently at higher temperatures recrystallization is more complete and involves a larger number of crystallites. For this reason L~z increases to some extent after annealing. The reversible nature of the deformation of spherulites in polyethylene [21] can be explained on the basis of the processes of deformation and rccrystallization during annealing analysed in the present work. The central part of the spherulite is obviously the most stable region with respect to deformation and melting. After stretching the largest and most perfect crystallites remain there, and they are also stable to heat. Moreover the centre of the stretched spherulite is still joined by interpenetrating chains to the residual particles. Consequently when the deformed spherulite is heated its centre acts as a nucleus for re-formation of the original spherulite. Thus as a result of deformation of the fibrils of the spherulites, of which most unstretched specimens consist, a new fibrillar structure is formed with a period differing from the long period of the unstretched material, and coinciding in direction with the direction of the polymer chains. The fact that deformation causes practically no change in the length of the crystaUite in the direction of the polymer chains probably indicates that the new fibrillar structure has arisen from the fibrillar structure of the unorientated specimens by rotation of the crystaUites vcith the c-axis in the direction of stretching and they deform by slipping of one part of the crystallite relative to another along the direction of the chains. Since polyethylene, especially when crystallized from the melt, has, as we assume, chains passing from one folded layer of the crystallite to another and from crystalli~ to crystallite, and while these connecting chains are preserved during defor-
40(}
Yu. A. ZUBOVeta/.
marion, deformation will be thermally reversible, in contrast to metals where plastic deformation is irreversible. Reversibility of deformation arises only when the material is heated to sufficiently high temperatures (3-5 ° below the melting point is sufficient), since the reversibility is associated with recrystallization. We express our deep gratitude to ¥ u . Malinskii, D. ¥ a . Tsvankin, G S.. Markova and Yu. K. Ovchinnikov for participation in discusion of our results and for valuable advice and suggestions, and also to T. F. Kostina for determination of the density of the specimens and measurement of the intrinsic viscosity of the polyethylene. CONCLUSIONS (1) I t is shown t h a t the first stage of deformation (before "neck" formation) is characterized mainly by a tendency for the crystallites to become orientated with the axis of the polymer chains in the direction of the field of force. In the second stage of deformation, associated with r e c k formation, the predominating process is deformation of the crystaUites, probably by slipping of one part of the crystallite relative to another along the axis of the polymer chains. (2) It is suggested that stretching at 20 ° leads to formation of fibrils of less uniform cross-section than those formed on stretching at 90 ° . (3) The periods have been measured and the volume and density of the unit cell calculated for high-density polyethylene at different stages of uniaxial deformation at room temperature and 110 °. Deformation of polyethylene to neck formation at room temperature causes a substantial increase in the period a and in the volume of the unit cell. These changes are associated with loss of order in the crystalline regions on stretching. I n specimens of polyethylene stretched to neck formation at 110 ° the periods and volume of the unit cell are not changed in comparison with unstretched specimens. I t is probable that under these conditions relaxation and recrystallization are more complete, leading to removal of distortions in the crystallites. (4) I n view of the constancy of the structural parameters of the unit cell and average dimensions of the crystallites in the elastic deformation region it is suggested that deformation of the material at this stage of stretching involves the defective, intercrystallite regions. (5) The annealing of stretched polyethylene specimens, under ~ s i o n and in the free state, is discussed in terms of recrystallization by b r e a k c l o ~ of small crystallites. Tranalat~ by E. O. PHILLIPS
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407
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INVESTIGATION OF THE EFFECT OF THE TYPE OF SUPERMOLECULAR AND CHEMICAL STRUCTURE ON THE STRENGTH AND ELASTICITY OF POLYMER GLASSES* G. L. SLOI~IMSKII, A. A. ASKADSKIIand V. I. PArLey I n s t i t u t e for E l e m e n t a r y Organic Compounds, U.S.S.R. A c a d e m y of Sciences
(Received 19 February 1966) THE objective of the present work was the quantitative investigation of the strength and relaxation properties of a number of polyarylates, differing in the chemical structure of the repeating unit, and differing in their supermoleeular structure. The method used [1] consists of the following: b y moans of thermomochanical measuremerits under conditions when a film is stretched to rupture with a non-linear regime for t h e increase in temperature T with time t, the regime complying with the equation
T=a/(b--t)
(1)
(whore a and b are constants), one m a y comparatively easily determine the parameters which characterize the strength (according to Zhurkov) and the relaxation (according to Aloksandrov-Gurevich-Lazurkin) properties of the polymer m a t e r i a l . . k s is well known [2-6] those parameters are structure-sensitive constants, as also are the activation energies for the rupture and relaxation processes. * Vysokomol. soyod. A9: No. 2, 365-369, 1967.