- Email: [email protected]
Mechanical relaxation in polyethylene with a different thermal prehistory
Polymer Science U.S.S.R. Vol. 23, ~To. 9, pp. 2128-2136, 1981 Printed in Poland
0032-$950]81/092128-09507.50]0 © 1982 Pergamon Press Ltd.
MECHANICAL RELAXATION IN POLYETHYLENE WITH A DIFFERENT THERMAL PREHISTORY* Yr. V. ZELENEVand L. A. DEL'TUVA •~¢£oscow Textile :Institute Voronezh Technical Institute
(Received 14 May 1980) The influence of quenching and annealing on the mechanical loss spectrum of H D P E and LDPE in the temperature range of a and fl-relaxation has be~zn studied by a low frequency dynamic method. The total damping curve was divided into components and the existence of a duplet structure of the a peak of H D P E was established. I t was shown that the observed spectrum change accords with the morphological features of the sample if the following hypothesis of the relaxation mechanism is accepted: the a-peak (high temperature component) is due to cooperative slip of helical dislocations; the a' peak (the low temperature component) to reorientation of folds on the surface of erystallites as a result of elastic mechanical twinning inside the crystallites; the fl peak to micro-Brownian movement of molecular chains in interlamellar regions. I t was shown the widths of all three maxima are significantly more than expected for a simple relaxation process. The possible sources of the relaxation time spectra is discussed. THE m a j o r i t y of t h e t e c h n i c a l l y i m p o r t a n t p r o p e r t i e s of plastic m a t e r i a l s (strength, w e a r i n g p r o p e r t i e s , resilience) are d e t e r m i n e d b y t h e possible s e g m e n t a l m o v e m e n t s o f t h e m a c r o m o l e c u l e s w i t h large r e l a x a t i o n t i m e s [1]. I n c o n n e c t i o n w i t h these, low f r e q u e n c y m e t h o d s of m e c h a n i c a l s p e c t r o m e t r y h a v e a c q u i r e d a n i m p o r t a n t role. Specific m o l e c u l a r m o v e m e n t is m a n i f e s t e d in t h e f o r m of a m a x i m u m on t h e m e c h a n i c a l loss c u r v e in a definite t e m p e r a t u r e range. F o r p u r p o s e s of identification, t h e b e h a v i o u r of t h e m a x i m u m w a s s t u d i e d in s a m p l e s w i t h r e g u l a r l y c h a n g i n g t e x t u r e . P E a p p e a r s to be t h e classical m a t e r i a l for t h e s t u d y of a r a n g e of similar species. I n spite of i n t e n s i v e studies, t h e i n t e r p r e t a t i o n of t h e r e l a x a t i o n s p e c t r a of P E r e m a i n s l a r g e l y undefined. T h e p r o b l e m is c o n n e c t e d w i t h s u p e r i m p o s i t i o n of c o m p o n e n t s of t h e s p e c t r u m . T h e i m p o s s i b i l i t y of controlling t h e r e a c t i o n of e a c h of t h e c o m p o n e n t s p e c t r a to t h e a c t i o n of different technological p a r a m e t e r s o f t e n causes discrepancies e v e n w h e n t h e question of t h e r e l a t i o n of t h e c o m p o n e n t s to t h e a m o r p h o u s or crystalline p h a s e s [2] is decided, let alone w h e n the d e t a i l e d molecular m e c h a n i s m s a r e considered. * Vysokomol. soyed. A23: No. 9, 1951-1958, 1981. 2128
Mechanical relaxation in polyethylene
2129
T h e r m a l t r e a t m e n t is one o f t h e m e t h o d s for m o d i f y i n g p o l y m e r s t r u c t u r e s . I n this work, we s t u d i e d t h e influence of q u e n c h i n g a n d a n n e a l i n g on t h e m e c h a n ical loss s p e c t r a of h i g h ( H D P E ) a n d low ( L D P E ) d e n s i t y p o l y e t h y l e n e s . Quenching of P E in t h e m o l t e n s t a t e causes p r i n c i p a l l y o r i e n t a t i o n of t h e b-axis parallel to t h e direction of t h e t e m p e r a t u r e g r a d i e n t [3]. T h e influence of the text u r e of quenching on m e c h a n i c a l r e l a x a t i o n in P E was s t u d i e d in [4, 51]. According to these, q u e n c h i n g or r a p i d cooling m a y cause t h e f o r m a t i o n of p o i n t defects, raised c o n t r a r y to t h e e q u i l i b r i u m concentraion. E v i d e n t l y to s t u d y this p h e n o n o m e n , it is e x p e d i e n t to v a r y t h e q u e n c h i n g t e m p e r a t u r e . I t is also o f i n t e r e s t to v a r y t h e s u b s e q u e n t t h e r m a l t r e a t m e n t causing a n n e a l i n g of t h e q u e n c h i n g defects.
0.8
q
2 0.6
IO s 8 6
0"#
q 2 108 8 8
0"2
I -60
I 0
I GO
T°
lq'Io. I. Temperature dependence of the ]ogarithnoJe decrement zl (1) and disl)laecment modulus G (2) of an annealed (120 °, l hr) I~DPE sample,
Measurements were made on a reverse torsional balance in the freely oscillating condition at a frequency of ~-0.2 ttz. The maximum deformation at the sample surface (a squar~ sectioned rod, 50× 1.5 × 1.5 m m 8) did not exceed 10 -3 (amplitude-dependent range). The mechanical loss, A = u tan6 (6--loss angle) and the dy~lamic modulus of displacement, G of the sample, were calculated from the formulae given in reference [6], discounting the elastic and deformation properties of the steel torsion wire. The value of A was determined with an error of ~2°/o . The error in determining G was ~8 (absolute value) and ~1~o°/ (relative change). LDPE and H D P E from domestic production were investig~ted and by X-rays, their degrees of crystallinity ~vere respectively ~ 55 and ~ 70%. T h r e e s t r o n g l y o v e r l a p p i n g m a x i m a can be distinguished in t h e t e m p e r a t u r e r e l a t i o n s h i p of t h e l o g a r i t h m i c d e c r e m e n t of a n n e a l e d ttDPE s a m p l e s (Fig. 1), in w h i c h t h e G(T) curves c o r r e s p o n d to t h r e e sections w i t h different r a t e s of declination. As has a l r e a d y b e e n i n d i c a t e d [6], t h e s p e c t r u m of m e c h a n i c a l loss of P E o v e r t h e 65-120 ° t e m p e r a t u r e r a n g e c o n t a i n s fl a n d ~ m a x i m a . I n L D P E , t h e a - p e a k
2130
Y u . V. Z~.L~rEv and L. A. D~.T.'~,uVA
has a duplet structure [7, 8] b u t o'n the contrary, a unimodal ~ maximum is usually observed with H D P E [8, 9]. On the other hand, it was shown [10] b y dynamic birefringence and dynamic X ray diffraction, that two relaxation proceses with different activation energies take place in the temperature range of the ~ peak of H D P E . This leads to the idea of a fine structure in the ~-peak of H D P E , which was expressed in reference [2] although no proof was presented; the suggested high temperature component of the ~ peak of H D P E might n o t have been seen because of the high frequency of the measurements (12.8 kHz). This is w h y we suggested low frequency measurements ( ~ 0.2 Hz) which guarantee a much higher resolution of the spectrum. For determination of the number of spectrum components the damping curve in Fig. 1 was analysed in hyperbolic coordinates according to the method given in reference [11]. The method was essentially as follows. For a simple relaxation process i.e. one with a single relaxation time v, the damping curve is described b y the equation U
where Amax, Tmax and U are respectively height, temperature and activation energy of the peak. Evidently such curves m a y be plotted on a coordinate grid in which the ordinate A/Amax is scaled as a fuhction of the hyperbolic cosine and the abscissa lIT is a function of reciprocal temperature. This is the basis of t h e method described. The intersection of the straight line with the axis of the abscissa gives the value of Tmax, the half width of the maximum in reciprocal temperature units ~(T -1) m a y be found from the slope of the straight line. B y simultaneous plotting on the diagram of the values of the amplitude x=(U/R) (I/T--1/Tmax) for corresponding values of the function A/Am~x=cosh -1 x, the straight line slope gives the value of U. For the majority of relaxation processe s a more or less broad distribution of z is seen instead of a single value. As a result of this, the actual damping maxima are usually broader than a single peak. As experiment shows, in-such cases t h e equation (1) actually [11] is lower than that found below a temperature-frequency shift of the maximum,* if a provisional activation energy is substituted for U. The damping curves formed b y overlapping of several maxima with different activation energies are represented on a hyperbolic grid in the form of a broken line, if the temperature maxima do not tally. In this case, they are easily graphically separated. The separation procedure is shown in Fig. 2. The straight line part of the high temperature branch of the total curve pertains to the ~-peak (334°K); its slope is responsible for the activation energy, equal to 1.46 kcal/mole, * The activation energy, determined by the method of temperature-frequency displacement of the maximum, U=--R{(d In v)/[d(1--T)]} generally (for example, when it depends on temperature) has the sense of a temperature coefficient of the relaxation time.
Mechanical relaxation in polyethylene
2131
which is about half the value we found from the frequency displacement of the maximum (29 kcal/mole). This substantiates the existence of a fairly broad distribution of relaxation times for an a-process. The lower curve in Fig. 2 was obtained b y graphical subtraction of the a-peak from the upper curve (normalized difference at the maximal value). In addition, two more maxima appear: a' (293°K) and fl (250°K). As an estimate shows, the width of the a' and fl peaks are significantly greater than expected for a simple relaxation process. 10080 60
0.1 0.2
1
i
~
-
ZO
0
-20
-qo
1
I
I
i
t
c L c L / I ~
t
3
~/~_ 2 t..E a
-
0
////
I
"~
11
"q 0"8-
o,-/ /..." O.4
-60 "°
II
0.4-
" 0"6 ~ 0"8
qo
I
I
3"0
3.G
-, q'Z
IO~T,K-~
FIG. 2. Separation of the spectroscopic curve represented in lTig-. 1 into separate components. Lower curve obtained by graphical subtraction of the a-peak from the upper curve.
The half-width of a single maximum is determined b y the expression [12]
where R is the universal gas constant. According to reference [8], the activation energy of the fl-peak is 42 keal/mole. Using this values, we calculated the h a l f width of the fl peak from equation (2), on the assumption of a single relaxation time. The value found (0.125 × 10 -~ K -1) was approximately an order lower than the actual one (1.28 × 10 -a K) Taking U~=29 and U s = 4 2 kcal/mole respectively for low and high estimates of the activation energy of the a-peak, we obtain ~ value 3-4 times greater for the half width of the a' peak, than for a single peak with the same U. The relaxation time of the majority of thermally activated processes (of which the a and fl transformations are considered here) is linked to temperature according to the equation U T=~o exp R T ' (3)~
2132
Yu. V. ZEL]~NEV and L. A. DEL'~u vA
where T0 is the frequency factor. As can be seen from expression (3) the spectrum ofv m a y be specified b y the distribution of T0, U or both simultaneously. The choice between the possible variants m a y be made on the basis of data on the frequency dependence of peak width [12]. I f the spectrum of v is determined only b y distribution of frequency factors (U=const.), the peak width does not depend on frequency measurements, since on the hyperbolic grid the corresponding straight line will be displaced with changing frequency, parallel to itself. In two other eases, (spectra of U or U and T0 together), the peak width is a function of frequency, so that with changing frequency the slope of the corresponding lines on the hyperbolic grid will be changed. A
0"9 rl
T o
qO 20 0.I I
-20
1
1
b
o2 0"6-
0
'.= 0.4 ¢D
I
?
8 0.8 b~ 0.8
2
E .q
0.3
-60
-20
r 20 T °
1.o 0"8 0"6
t
t
j-
/,, 3.e
-qo
-60 I
3
2
I
0 =1~ II -1
q.2
lo /T
FzG. 3. Damping curves for I-II)PE samples drawn through a die, for two frequency changes (vJv~= 3- 33) in the usual coordinates (a) and in a hyperbolic grid (b). Having this in mind, we will examine the data represented in Fig. 3 (changes in 2 frequencies). Whilst on normal coordinates (Fig. 3a) spectrum structure is not resolved, on a hyperbolic grid (Fig. 3b) a curve breaks up into 2 rectilinear parts with different angular coefficients. With changing frequency, the high temperature branch of the curve (~-process) is displaced parallel to itself, whilst at the same time a large change of slope is observed with the low temperature part (/~-process). Therefore, in line with the above remarks, a single energy of activation m a y be proposed for an ~-process but a distribution of activation energies for a fl-process. We shall now examine the influence of heat treatment on each of the components of the H D P E spectrum. With an increase of temperature of quenching from 115 to 130 ° (exposure time, 1 hr, cooled in liquid nitrogen) we observed (Fig. 4) a gradual decrease of the ~-peak with a simultaneous increase of the
Mechanical relaxation in polyethylene
2133
losses in the a' and fl regions. At high temperatures of quenching (130 ° and higher) a and a' maxima were displaced towards low temperatures and were superimposed on the fl-peak. As already noted, quenching of P E leads to the formation of a texture. Therefore in the analysis of the results obtained it is necessary to consider the influence of the texture which will evidently be intensified with increase of quenching temperature. On the other hand, since the acquired texture is pre~ r v e d in the subsequent annealing [3], changes of the spectrum caused b y annealing of the quenched sample (Fig. 5)should be attributed to variations of other morphological parameters. All measurements shown in Figs. 4 and 5 were carried out on the same sample and are thus free from the influence of casual factors. A 0.7
!
0"5
03
-60
, 0
80
T°
:FIG. 4. Spectrum of mechanical loss of I-I__DPEsample ax~maled at 120°, (1) before quenching and after quenching from temperatures of 115 (2), 120 (3), 125 (4) and 130° (5). It was shown earlier [4, 5] that in P E samples with a quenched texture, the a-peak was higher, the higher the degree of orientation (torsion axis perpendicular to the orientation axis). Meanwhile in our experiments under the same conditions of test with increasing quenching temperature, the peak was lowered. This indicates that the texturing effect was overlapped in these conditions by another, stronger and acting in the opposite direction. I f it is accepted, following reference [13] that the a-peak in P E is explained b y thermal activation with slipping of helical dislocations, its decrease after quenching m a y be attributed to tightening of the dislocations b y surplus point defects, fixed b y annealing. For example, thermal generation of vacancies [14] and I~eneker [15] defects are possible. It is easy also to understand the growth of the ~ peak with subsequent annealing, in the framework of this model (Fig. 5). With increase of annealing tempera-
Yr. V. Z~T.~WEVand L. A. DEL'TUVA
2134
ture, the mobility of point defects grows and whilst overcoming the attraction from dislocations, t h e y migrate along the chains and merge into the surfaces of the crystal: the dislocations are loosened and the a peak grows. Comparing the behaviour of the a and a'-peaks in Figs. 4 and 5, we see that their reaction to the inuenee of heat is different: as the a-peak is decreased so the a'-peak grows and vice versa. This contradicts the assumption [13] of the identical nature of the mechanisms of the peaks. An argument was introduced in reference [16] in favour of the fact that the low temperature component of the a-peak in L D P E is dependent on reorientation of the folds on the crystal surfaces due to elasto-meehanical twinning inside the crystals. Extending these ideas to the a' peak of H D P E , its growth on quenching and decrease with annealing m a y be explained in the following way. It is known [17] that as a result of quenching the folded surface becomes less regular; the number of free chain ends increases and gives rise to loop-shaped folds, having considerable free mvement. Annealing zl 0"8
0"6
o.q
0"2
\ I -80
0
FIG. 5
80 T °
-
I
I
J
40
0
40
I
80
]
-
To
FIG. 6
:FIG. 5. S p e c t r u m of m e c h a n i c a l loss of H D P E sample q u e n c h e d from 140 ° after a n n e a l i n g a t t e m p e r a t u r e s of 20 (1), 72 (2), 96 (3), 108 (4) a n d 120 ° (5).
Fro. 6. Spectrum of mechanical loss for LDPE, 1--quenching from 148°, 2--before quenching (annealing, 120°, 1 hr). shows the opposite effect. It is also known [18] that elasto-meehanical twinning becomes possible, if the folds are sufficiently mobile. From this it follows that in a quenched material, conditions for twinning are more favourable than in an annealed one. Experimental evidence of twinning in quenched P E was obtained in reference [3]. Two points of view are generally advanced for the interpretation of the fl-max-
Mechanical relaxation in polyethylene
2135
imum [6]: the vitrification of amorphous regions or the mobility of laterai groups. The basis for such a connection is the often-observed positive correlation between intensity of the maximum and the content of specific fractions, It should be noted however that the lateral groups segregate preferably in the amorphous regions [19] so that with an increase in their number, the weight proportion of the amorphous fraction inevitably increases. That is w h y it is no~ still possible to make a definitive choice between the two points of view, on th(, basis of such measurements. On the other hand, experiments with quenching have the advantage of permitting a change in amorphous and crystalline phase contents without changing the content of branches. According to the results of wide angle X ray diffusion, in the quenching of H D P E from 130 ° the degree of crystallinity is decreased from 55 (before quenching) to 45%. The growth of the fl peak (Fig. 4) observed at the same time compels one to choose the hypothesis of vitrification of amorphous regions. The temperature maximum for mechanical losses is independent of its fundemental mechanism, determined b y intermolecular physical or chemical interactions, b u t the height is a quantity of kinetic units, participating in relaxation. As can be seen from Fig. 4, as long as Tq is less than Tin, the temperature of all 3 maxima remains constant, although their intensity changes. From this it follows that in conditions of mild quenching, ordy a concentration change of r~laxors occurs; the amount of the unattached dislocations is decreased and the number of mobile twins and the bulk proportion of the amorphous fraction grow. With much sharper quenching (Tq higher than TE) a displacement of the a- and a'-peaks towards lower temperatures was observed, in line with the progressive change in intensity. This indicates the lowering of energetic barriers, impeding relaxation. For example, as already noted, elastic mechanical twinning is facilitated when the folds become weaker [18]. The stability of Tp is but one argument in favour of a vitrification process. In contrast with H D P E , quenching of L D P E does not lead to an appreciable change of the spectrum (Fig. 6). Evidently the annealing process in linear P E proceeds at such a high rate that even with sharp quenching from the fused state, a non-equilibrated structure with a surplus concentration of defects is not fixed. It is known that thermal treatment influeces many structure-sensitive properties of polymers. Systematic studies in this direction [1] disclosed an impo~'taut rule (the "fork" principle) having great practical value. It was established that for a wide range of polymers, the physical characteristics of the original samples had an intermediate value in comparison with the same characteristic of quenched and annealed samples. Oll the basis of the data obtained, in ~ddition to this, it can be confirmed that the action of quenching on the mecha~ical spectrum of P E is contrary to that of a:~me~ling and vice versa. Translated by C. W. CAeP
M . G . VITOVSKAYAet al.
2136
REFERENCES
1. Yu. V. ZELENEV, Dessertation for degree of Doctor of Physical Materials Science, p. 387, MOPI, 1971 2. A. Z. GOLIK, Yu. F. ZABASHTA, M. A. GENINA and A. N. ALEKSEYEV, Ukr. fizich. zh. 20: 280, 1975 3. R. K. EBY, J. Appl. Phys. $5: 2720, 1964 4, R. K. E B I r a n d J. COLSON, J. Acoust. Soc. Amer. 39: 506, 1966 5. N. G. McCRUM and E. L. MORRIS, Proe. Roy. Soe. Lond. A292: 506, 1966 6. I. I. PEREPECHKO, Akusticheskiye m e t o d y issled, polimerov, p. 55, Khimiya, 1973 7. I. N. BORODIN and Yu. V. ZELENEV, In: Relaksatsionnye y a v l e n i y a v t v e r d y k h telakh, p. 562, Metallurgiya, 1968 8. Z. H. STACHURSKI and I. M. WARD, J. Macromolec. Sci., Phys. Ser. BS: 445, 1969 9. G. M. BARTENEV a n d Yu. V. ZELENEV, Mekhanika polimerov, No. 1, 30, 1969 10. A. TANAKA, E. P. CHANG, B. DELF, J. K I M U R A a n d R. S. STEIN, J. Polymer Sci., Polymer Phys. Ed. 11: 1891, 1973 11. W. J~NrICHE, E. STOLTE and J. BRAUNER, Tech. Mitt. K r u p p 23: 146, 1965 12. D. H. NIBLETT, J. Appl. Phys. $2: 895, 1961 13. W. PECHOLD, J. Polymer Sci. $2: 123, 1971 14. R. K. EBY, J. Appl. Phys. 32: 2235, 1962 15. D. H. RENEKER, J. P o l y m e r Sci. 59: 539, 1962 16. L. A. DEL'TUVA, Coll. Materialovedeniye (fizika i khim. kondentsir, sred.), p. 89, V.P.L, Voronezh, 1977 17. D. W I T E N H A F E R and J. KOENIG, J. Appl. Phys. $9: 4982, 1968 18. F. (L FRANK, V, B. GUPTA a n d I. M. WARD, Phil. Mag. 21: 1127, 1970 19. A. K E L L E R a n d D. PRIEST, J. Macromolec. Sci. 8: 13, 1970
Polymer Science U.S.S.R. Vol. 23, ~o. 9, pp. 2136-2147, 1981
Printed in Poland
THE
0032-3950/81/[email protected]/0 C) 1982 Pergamon Yress Ltd.
HYDRODYNAMIC PROPERTIES AND THE RIGIDITY EQUILIBRIUM IN DMA AND SULPHURIC ACID OF POLYAMIDOBENZIMIDAZOLE MOLECULES*
M. G. VITOVSKAYA(dec.), P. N. I~VRE~KO, O. V. OKATOVA, E. P. AST~ENKO, V. B. •OVAKOVSKII, S. V. BUS/i-IN, S. A . DIDENKO, L . V. AVROROVA,
A. V. TOXXROV, G. I. KUDRYAVTSEVand V. N. TSVETKOV H i g h Polymers Institute, U.S.S.R. A c a d e m y of Sciences
(Received 20 May 1980) The translational diffusion, r a p i d sedimentation and visoeity have been studied on 32 fractions of polyamido benzinlidazole (PA) in DMA and 97.8 ~o HISO~. The tool. wt. were calculated from the diffusion and sedimendation results in DMA. The * Vysokolzml. soyed. A23: No. 9, 1959-1968, 1981.
0032-$950]81/092128-09507.50]0 © 1982 Pergamon Press Ltd.
MECHANICAL RELAXATION IN POLYETHYLENE WITH A DIFFERENT THERMAL PREHISTORY* Yr. V. ZELENEVand L. A. DEL'TUVA •~¢£oscow Textile :Institute Voronezh Technical Institute
(Received 14 May 1980) The influence of quenching and annealing on the mechanical loss spectrum of H D P E and LDPE in the temperature range of a and fl-relaxation has be~zn studied by a low frequency dynamic method. The total damping curve was divided into components and the existence of a duplet structure of the a peak of H D P E was established. I t was shown that the observed spectrum change accords with the morphological features of the sample if the following hypothesis of the relaxation mechanism is accepted: the a-peak (high temperature component) is due to cooperative slip of helical dislocations; the a' peak (the low temperature component) to reorientation of folds on the surface of erystallites as a result of elastic mechanical twinning inside the crystallites; the fl peak to micro-Brownian movement of molecular chains in interlamellar regions. I t was shown the widths of all three maxima are significantly more than expected for a simple relaxation process. The possible sources of the relaxation time spectra is discussed. THE m a j o r i t y of t h e t e c h n i c a l l y i m p o r t a n t p r o p e r t i e s of plastic m a t e r i a l s (strength, w e a r i n g p r o p e r t i e s , resilience) are d e t e r m i n e d b y t h e possible s e g m e n t a l m o v e m e n t s o f t h e m a c r o m o l e c u l e s w i t h large r e l a x a t i o n t i m e s [1]. I n c o n n e c t i o n w i t h these, low f r e q u e n c y m e t h o d s of m e c h a n i c a l s p e c t r o m e t r y h a v e a c q u i r e d a n i m p o r t a n t role. Specific m o l e c u l a r m o v e m e n t is m a n i f e s t e d in t h e f o r m of a m a x i m u m on t h e m e c h a n i c a l loss c u r v e in a definite t e m p e r a t u r e range. F o r p u r p o s e s of identification, t h e b e h a v i o u r of t h e m a x i m u m w a s s t u d i e d in s a m p l e s w i t h r e g u l a r l y c h a n g i n g t e x t u r e . P E a p p e a r s to be t h e classical m a t e r i a l for t h e s t u d y of a r a n g e of similar species. I n spite of i n t e n s i v e studies, t h e i n t e r p r e t a t i o n of t h e r e l a x a t i o n s p e c t r a of P E r e m a i n s l a r g e l y undefined. T h e p r o b l e m is c o n n e c t e d w i t h s u p e r i m p o s i t i o n of c o m p o n e n t s of t h e s p e c t r u m . T h e i m p o s s i b i l i t y of controlling t h e r e a c t i o n of e a c h of t h e c o m p o n e n t s p e c t r a to t h e a c t i o n of different technological p a r a m e t e r s o f t e n causes discrepancies e v e n w h e n t h e question of t h e r e l a t i o n of t h e c o m p o n e n t s to t h e a m o r p h o u s or crystalline p h a s e s [2] is decided, let alone w h e n the d e t a i l e d molecular m e c h a n i s m s a r e considered. * Vysokomol. soyed. A23: No. 9, 1951-1958, 1981. 2128
Mechanical relaxation in polyethylene
2129
T h e r m a l t r e a t m e n t is one o f t h e m e t h o d s for m o d i f y i n g p o l y m e r s t r u c t u r e s . I n this work, we s t u d i e d t h e influence of q u e n c h i n g a n d a n n e a l i n g on t h e m e c h a n ical loss s p e c t r a of h i g h ( H D P E ) a n d low ( L D P E ) d e n s i t y p o l y e t h y l e n e s . Quenching of P E in t h e m o l t e n s t a t e causes p r i n c i p a l l y o r i e n t a t i o n of t h e b-axis parallel to t h e direction of t h e t e m p e r a t u r e g r a d i e n t [3]. T h e influence of the text u r e of quenching on m e c h a n i c a l r e l a x a t i o n in P E was s t u d i e d in [4, 51]. According to these, q u e n c h i n g or r a p i d cooling m a y cause t h e f o r m a t i o n of p o i n t defects, raised c o n t r a r y to t h e e q u i l i b r i u m concentraion. E v i d e n t l y to s t u d y this p h e n o n o m e n , it is e x p e d i e n t to v a r y t h e q u e n c h i n g t e m p e r a t u r e . I t is also o f i n t e r e s t to v a r y t h e s u b s e q u e n t t h e r m a l t r e a t m e n t causing a n n e a l i n g of t h e q u e n c h i n g defects.
0.8
q
2 0.6
IO s 8 6
0"#
q 2 108 8 8
0"2
I -60
I 0
I GO
T°
lq'Io. I. Temperature dependence of the ]ogarithnoJe decrement zl (1) and disl)laecment modulus G (2) of an annealed (120 °, l hr) I~DPE sample,
Measurements were made on a reverse torsional balance in the freely oscillating condition at a frequency of ~-0.2 ttz. The maximum deformation at the sample surface (a squar~ sectioned rod, 50× 1.5 × 1.5 m m 8) did not exceed 10 -3 (amplitude-dependent range). The mechanical loss, A = u tan6 (6--loss angle) and the dy~lamic modulus of displacement, G of the sample, were calculated from the formulae given in reference [6], discounting the elastic and deformation properties of the steel torsion wire. The value of A was determined with an error of ~2°/o . The error in determining G was ~8 (absolute value) and ~1~o°/ (relative change). LDPE and H D P E from domestic production were investig~ted and by X-rays, their degrees of crystallinity ~vere respectively ~ 55 and ~ 70%. T h r e e s t r o n g l y o v e r l a p p i n g m a x i m a can be distinguished in t h e t e m p e r a t u r e r e l a t i o n s h i p of t h e l o g a r i t h m i c d e c r e m e n t of a n n e a l e d ttDPE s a m p l e s (Fig. 1), in w h i c h t h e G(T) curves c o r r e s p o n d to t h r e e sections w i t h different r a t e s of declination. As has a l r e a d y b e e n i n d i c a t e d [6], t h e s p e c t r u m of m e c h a n i c a l loss of P E o v e r t h e 65-120 ° t e m p e r a t u r e r a n g e c o n t a i n s fl a n d ~ m a x i m a . I n L D P E , t h e a - p e a k
2130
Y u . V. Z~.L~rEv and L. A. D~.T.'~,uVA
has a duplet structure [7, 8] b u t o'n the contrary, a unimodal ~ maximum is usually observed with H D P E [8, 9]. On the other hand, it was shown [10] b y dynamic birefringence and dynamic X ray diffraction, that two relaxation proceses with different activation energies take place in the temperature range of the ~ peak of H D P E . This leads to the idea of a fine structure in the ~-peak of H D P E , which was expressed in reference [2] although no proof was presented; the suggested high temperature component of the ~ peak of H D P E might n o t have been seen because of the high frequency of the measurements (12.8 kHz). This is w h y we suggested low frequency measurements ( ~ 0.2 Hz) which guarantee a much higher resolution of the spectrum. For determination of the number of spectrum components the damping curve in Fig. 1 was analysed in hyperbolic coordinates according to the method given in reference [11]. The method was essentially as follows. For a simple relaxation process i.e. one with a single relaxation time v, the damping curve is described b y the equation U
where Amax, Tmax and U are respectively height, temperature and activation energy of the peak. Evidently such curves m a y be plotted on a coordinate grid in which the ordinate A/Amax is scaled as a fuhction of the hyperbolic cosine and the abscissa lIT is a function of reciprocal temperature. This is the basis of t h e method described. The intersection of the straight line with the axis of the abscissa gives the value of Tmax, the half width of the maximum in reciprocal temperature units ~(T -1) m a y be found from the slope of the straight line. B y simultaneous plotting on the diagram of the values of the amplitude x=(U/R) (I/T--1/Tmax) for corresponding values of the function A/Am~x=cosh -1 x, the straight line slope gives the value of U. For the majority of relaxation processe s a more or less broad distribution of z is seen instead of a single value. As a result of this, the actual damping maxima are usually broader than a single peak. As experiment shows, in-such cases t h e equation (1) actually [11] is lower than that found below a temperature-frequency shift of the maximum,* if a provisional activation energy is substituted for U. The damping curves formed b y overlapping of several maxima with different activation energies are represented on a hyperbolic grid in the form of a broken line, if the temperature maxima do not tally. In this case, they are easily graphically separated. The separation procedure is shown in Fig. 2. The straight line part of the high temperature branch of the total curve pertains to the ~-peak (334°K); its slope is responsible for the activation energy, equal to 1.46 kcal/mole, * The activation energy, determined by the method of temperature-frequency displacement of the maximum, U=--R{(d In v)/[d(1--T)]} generally (for example, when it depends on temperature) has the sense of a temperature coefficient of the relaxation time.
Mechanical relaxation in polyethylene
2131
which is about half the value we found from the frequency displacement of the maximum (29 kcal/mole). This substantiates the existence of a fairly broad distribution of relaxation times for an a-process. The lower curve in Fig. 2 was obtained b y graphical subtraction of the a-peak from the upper curve (normalized difference at the maximal value). In addition, two more maxima appear: a' (293°K) and fl (250°K). As an estimate shows, the width of the a' and fl peaks are significantly greater than expected for a simple relaxation process. 10080 60
0.1 0.2
1
i
~
-
ZO
0
-20
-qo
1
I
I
i
t
c L c L / I ~
t
3
~/~_ 2 t..E a
-
0
////
I
"~
11
"q 0"8-
o,-/ /..." O.4
-60 "°
II
0.4-
" 0"6 ~ 0"8
qo
I
I
3"0
3.G
-, q'Z
IO~T,K-~
FIG. 2. Separation of the spectroscopic curve represented in lTig-. 1 into separate components. Lower curve obtained by graphical subtraction of the a-peak from the upper curve.
The half-width of a single maximum is determined b y the expression [12]
where R is the universal gas constant. According to reference [8], the activation energy of the fl-peak is 42 keal/mole. Using this values, we calculated the h a l f width of the fl peak from equation (2), on the assumption of a single relaxation time. The value found (0.125 × 10 -~ K -1) was approximately an order lower than the actual one (1.28 × 10 -a K) Taking U~=29 and U s = 4 2 kcal/mole respectively for low and high estimates of the activation energy of the a-peak, we obtain ~ value 3-4 times greater for the half width of the a' peak, than for a single peak with the same U. The relaxation time of the majority of thermally activated processes (of which the a and fl transformations are considered here) is linked to temperature according to the equation U T=~o exp R T ' (3)~
2132
Yu. V. ZEL]~NEV and L. A. DEL'~u vA
where T0 is the frequency factor. As can be seen from expression (3) the spectrum ofv m a y be specified b y the distribution of T0, U or both simultaneously. The choice between the possible variants m a y be made on the basis of data on the frequency dependence of peak width [12]. I f the spectrum of v is determined only b y distribution of frequency factors (U=const.), the peak width does not depend on frequency measurements, since on the hyperbolic grid the corresponding straight line will be displaced with changing frequency, parallel to itself. In two other eases, (spectra of U or U and T0 together), the peak width is a function of frequency, so that with changing frequency the slope of the corresponding lines on the hyperbolic grid will be changed. A
0"9 rl
T o
qO 20 0.I I
-20
1
1
b
o2 0"6-
0
'.= 0.4 ¢D
I
?
8 0.8 b~ 0.8
2
E .q
0.3
-60
-20
r 20 T °
1.o 0"8 0"6
t
t
j-
/,, 3.e
-qo
-60 I
3
2
I
0 =1~ II -1
q.2
lo /T
FzG. 3. Damping curves for I-II)PE samples drawn through a die, for two frequency changes (vJv~= 3- 33) in the usual coordinates (a) and in a hyperbolic grid (b). Having this in mind, we will examine the data represented in Fig. 3 (changes in 2 frequencies). Whilst on normal coordinates (Fig. 3a) spectrum structure is not resolved, on a hyperbolic grid (Fig. 3b) a curve breaks up into 2 rectilinear parts with different angular coefficients. With changing frequency, the high temperature branch of the curve (~-process) is displaced parallel to itself, whilst at the same time a large change of slope is observed with the low temperature part (/~-process). Therefore, in line with the above remarks, a single energy of activation m a y be proposed for an ~-process but a distribution of activation energies for a fl-process. We shall now examine the influence of heat treatment on each of the components of the H D P E spectrum. With an increase of temperature of quenching from 115 to 130 ° (exposure time, 1 hr, cooled in liquid nitrogen) we observed (Fig. 4) a gradual decrease of the ~-peak with a simultaneous increase of the
Mechanical relaxation in polyethylene
2133
losses in the a' and fl regions. At high temperatures of quenching (130 ° and higher) a and a' maxima were displaced towards low temperatures and were superimposed on the fl-peak. As already noted, quenching of P E leads to the formation of a texture. Therefore in the analysis of the results obtained it is necessary to consider the influence of the texture which will evidently be intensified with increase of quenching temperature. On the other hand, since the acquired texture is pre~ r v e d in the subsequent annealing [3], changes of the spectrum caused b y annealing of the quenched sample (Fig. 5)should be attributed to variations of other morphological parameters. All measurements shown in Figs. 4 and 5 were carried out on the same sample and are thus free from the influence of casual factors. A 0.7
!
0"5
03
-60
, 0
80
T°
:FIG. 4. Spectrum of mechanical loss of I-I__DPEsample ax~maled at 120°, (1) before quenching and after quenching from temperatures of 115 (2), 120 (3), 125 (4) and 130° (5). It was shown earlier [4, 5] that in P E samples with a quenched texture, the a-peak was higher, the higher the degree of orientation (torsion axis perpendicular to the orientation axis). Meanwhile in our experiments under the same conditions of test with increasing quenching temperature, the peak was lowered. This indicates that the texturing effect was overlapped in these conditions by another, stronger and acting in the opposite direction. I f it is accepted, following reference [13] that the a-peak in P E is explained b y thermal activation with slipping of helical dislocations, its decrease after quenching m a y be attributed to tightening of the dislocations b y surplus point defects, fixed b y annealing. For example, thermal generation of vacancies [14] and I~eneker [15] defects are possible. It is easy also to understand the growth of the ~ peak with subsequent annealing, in the framework of this model (Fig. 5). With increase of annealing tempera-
Yr. V. Z~T.~WEVand L. A. DEL'TUVA
2134
ture, the mobility of point defects grows and whilst overcoming the attraction from dislocations, t h e y migrate along the chains and merge into the surfaces of the crystal: the dislocations are loosened and the a peak grows. Comparing the behaviour of the a and a'-peaks in Figs. 4 and 5, we see that their reaction to the inuenee of heat is different: as the a-peak is decreased so the a'-peak grows and vice versa. This contradicts the assumption [13] of the identical nature of the mechanisms of the peaks. An argument was introduced in reference [16] in favour of the fact that the low temperature component of the a-peak in L D P E is dependent on reorientation of the folds on the crystal surfaces due to elasto-meehanical twinning inside the crystals. Extending these ideas to the a' peak of H D P E , its growth on quenching and decrease with annealing m a y be explained in the following way. It is known [17] that as a result of quenching the folded surface becomes less regular; the number of free chain ends increases and gives rise to loop-shaped folds, having considerable free mvement. Annealing zl 0"8
0"6
o.q
0"2
\ I -80
0
FIG. 5
80 T °
-
I
I
J
40
0
40
I
80
]
-
To
FIG. 6
:FIG. 5. S p e c t r u m of m e c h a n i c a l loss of H D P E sample q u e n c h e d from 140 ° after a n n e a l i n g a t t e m p e r a t u r e s of 20 (1), 72 (2), 96 (3), 108 (4) a n d 120 ° (5).
Fro. 6. Spectrum of mechanical loss for LDPE, 1--quenching from 148°, 2--before quenching (annealing, 120°, 1 hr). shows the opposite effect. It is also known [18] that elasto-meehanical twinning becomes possible, if the folds are sufficiently mobile. From this it follows that in a quenched material, conditions for twinning are more favourable than in an annealed one. Experimental evidence of twinning in quenched P E was obtained in reference [3]. Two points of view are generally advanced for the interpretation of the fl-max-
Mechanical relaxation in polyethylene
2135
imum [6]: the vitrification of amorphous regions or the mobility of laterai groups. The basis for such a connection is the often-observed positive correlation between intensity of the maximum and the content of specific fractions, It should be noted however that the lateral groups segregate preferably in the amorphous regions [19] so that with an increase in their number, the weight proportion of the amorphous fraction inevitably increases. That is w h y it is no~ still possible to make a definitive choice between the two points of view, on th(, basis of such measurements. On the other hand, experiments with quenching have the advantage of permitting a change in amorphous and crystalline phase contents without changing the content of branches. According to the results of wide angle X ray diffusion, in the quenching of H D P E from 130 ° the degree of crystallinity is decreased from 55 (before quenching) to 45%. The growth of the fl peak (Fig. 4) observed at the same time compels one to choose the hypothesis of vitrification of amorphous regions. The temperature maximum for mechanical losses is independent of its fundemental mechanism, determined b y intermolecular physical or chemical interactions, b u t the height is a quantity of kinetic units, participating in relaxation. As can be seen from Fig. 4, as long as Tq is less than Tin, the temperature of all 3 maxima remains constant, although their intensity changes. From this it follows that in conditions of mild quenching, ordy a concentration change of r~laxors occurs; the amount of the unattached dislocations is decreased and the number of mobile twins and the bulk proportion of the amorphous fraction grow. With much sharper quenching (Tq higher than TE) a displacement of the a- and a'-peaks towards lower temperatures was observed, in line with the progressive change in intensity. This indicates the lowering of energetic barriers, impeding relaxation. For example, as already noted, elastic mechanical twinning is facilitated when the folds become weaker [18]. The stability of Tp is but one argument in favour of a vitrification process. In contrast with H D P E , quenching of L D P E does not lead to an appreciable change of the spectrum (Fig. 6). Evidently the annealing process in linear P E proceeds at such a high rate that even with sharp quenching from the fused state, a non-equilibrated structure with a surplus concentration of defects is not fixed. It is known that thermal treatment influeces many structure-sensitive properties of polymers. Systematic studies in this direction [1] disclosed an impo~'taut rule (the "fork" principle) having great practical value. It was established that for a wide range of polymers, the physical characteristics of the original samples had an intermediate value in comparison with the same characteristic of quenched and annealed samples. Oll the basis of the data obtained, in ~ddition to this, it can be confirmed that the action of quenching on the mecha~ical spectrum of P E is contrary to that of a:~me~ling and vice versa. Translated by C. W. CAeP
M . G . VITOVSKAYAet al.
2136
REFERENCES
1. Yu. V. ZELENEV, Dessertation for degree of Doctor of Physical Materials Science, p. 387, MOPI, 1971 2. A. Z. GOLIK, Yu. F. ZABASHTA, M. A. GENINA and A. N. ALEKSEYEV, Ukr. fizich. zh. 20: 280, 1975 3. R. K. EBY, J. Appl. Phys. $5: 2720, 1964 4, R. K. E B I r a n d J. COLSON, J. Acoust. Soc. Amer. 39: 506, 1966 5. N. G. McCRUM and E. L. MORRIS, Proe. Roy. Soe. Lond. A292: 506, 1966 6. I. I. PEREPECHKO, Akusticheskiye m e t o d y issled, polimerov, p. 55, Khimiya, 1973 7. I. N. BORODIN and Yu. V. ZELENEV, In: Relaksatsionnye y a v l e n i y a v t v e r d y k h telakh, p. 562, Metallurgiya, 1968 8. Z. H. STACHURSKI and I. M. WARD, J. Macromolec. Sci., Phys. Ser. BS: 445, 1969 9. G. M. BARTENEV a n d Yu. V. ZELENEV, Mekhanika polimerov, No. 1, 30, 1969 10. A. TANAKA, E. P. CHANG, B. DELF, J. K I M U R A a n d R. S. STEIN, J. Polymer Sci., Polymer Phys. Ed. 11: 1891, 1973 11. W. J~NrICHE, E. STOLTE and J. BRAUNER, Tech. Mitt. K r u p p 23: 146, 1965 12. D. H. NIBLETT, J. Appl. Phys. $2: 895, 1961 13. W. PECHOLD, J. Polymer Sci. $2: 123, 1971 14. R. K. EBY, J. Appl. Phys. 32: 2235, 1962 15. D. H. RENEKER, J. P o l y m e r Sci. 59: 539, 1962 16. L. A. DEL'TUVA, Coll. Materialovedeniye (fizika i khim. kondentsir, sred.), p. 89, V.P.L, Voronezh, 1977 17. D. W I T E N H A F E R and J. KOENIG, J. Appl. Phys. $9: 4982, 1968 18. F. (L FRANK, V, B. GUPTA a n d I. M. WARD, Phil. Mag. 21: 1127, 1970 19. A. K E L L E R a n d D. PRIEST, J. Macromolec. Sci. 8: 13, 1970
Polymer Science U.S.S.R. Vol. 23, ~o. 9, pp. 2136-2147, 1981
Printed in Poland
THE
0032-3950/81/[email protected]/0 C) 1982 Pergamon Yress Ltd.
HYDRODYNAMIC PROPERTIES AND THE RIGIDITY EQUILIBRIUM IN DMA AND SULPHURIC ACID OF POLYAMIDOBENZIMIDAZOLE MOLECULES*
M. G. VITOVSKAYA(dec.), P. N. I~VRE~KO, O. V. OKATOVA, E. P. AST~ENKO, V. B. •OVAKOVSKII, S. V. BUS/i-IN, S. A . DIDENKO, L . V. AVROROVA,
A. V. TOXXROV, G. I. KUDRYAVTSEVand V. N. TSVETKOV H i g h Polymers Institute, U.S.S.R. A c a d e m y of Sciences
(Received 20 May 1980) The translational diffusion, r a p i d sedimentation and visoeity have been studied on 32 fractions of polyamido benzinlidazole (PA) in DMA and 97.8 ~o HISO~. The tool. wt. were calculated from the diffusion and sedimendation results in DMA. The * Vysokolzml. soyed. A23: No. 9, 1959-1968, 1981.