Studies on birefringence as a function of strain in crosslinked polymers under creep conditions

Polymer Scie~aceU.S.S.R.Vol. 28, No. 10, pp. 2472-2479, 1986 ]Printed in Poland

0032-3950]86 $10.00+.00 © 1987 Pergamon Journals Ltd.

STUDIES ON BIREFRINGENCE AS A FUNCTION OF STRAIN IN CROSSLINKED POLYMERS UNDER CREEP CONDITIONS* B. M. ZUYEV,YE. V. CHISTYAKOV,A. P. FILIPPOVA

and O. S. ARKHIREYEV A. Ye. Arbuzow Institute of Organic and Physical Chemistry, Kazansk Branch U.S.S.R., Academy of Sciences (Received 14 March 1985)

It is shown that the intereonnection between the strain and birefringence for certain crosslinked polymers under creep conditions is described by a linear equation. In the case of the polymers studied, the change in optical sensitivity to the stress differs as between the time and temperature.

IT HAS already been noted by Koker et al. [1] that the birefringence and strain in polymers under creep conditions change synchronously. However, so far this relation has been proved only for a limited number of specimens [2-4] and the amount of data accumulated is insufficient to provide an understanding of how these factors indicate the special features of the chemical and topological structure of the polymer. In this work these problems are discussed on the basis of the results obtained in studying specimens of epoxide oligomer ED-20 (GOST standard 10587-76), cured with 40 wt. ~o phthalic anhydride (polymer I), and oligoester based on 1,3-propylene glycol (1 mole), phthalic anhydride (0"4 mole), and male ic anhydride (0-6 mole), crosslinked with styrene (100 wt. % to the weight of oligoestcr) in the presence of 1 wt. Yo benzoyl peroxide (polymer II), and polydiallyl orthophthalate, polymerized in the presence of 2 wt. Yo t-butyl peroxide (polymer HI). The materials were cured in bulk) in silanized glass ampoules in an argon atmosphere. The curing conditions and the main characteristics of the compounds are given in Table. The test specimens were cut from the blocks in the form of discs of diameter d=18_0.1 and thickness b--2_0-02 mm. After heat treatment, as recommended by Frokht [5], the initial path difference of the specimens did not exceed 1/60 2s,~. The photosensitivity and the creep were studied with the setup described by Zuev et al. [6] over the temperature range 290-480 K under isothermal conditions (AT_0"I°C) under a load applied in the direction of the vertical range of the disc. The scalc divisions of thc tail spindles fixing the movement of the horizontal diameter Ad were 200 nm each division, and each scale division of the path optical difference compensator was 1 nm. The changes in 6 and Ad with time were observed as far as the provisional equilibrium state of the specimen, when the change in path difference and strain over 30 min did not exceed 0.5 % of the maximum values. The initial calculation of the photo-creep was made after 5 sec, and of creep, 1 rain after loading the specimen. The tests on each specimen were repeated 2-3 times and the measurement results were averaged.

* Vysokomol. soyed. A2& No. 10, 2223-2229, 1986. 2472

2473

Birefringence as function of strain in crosslinked polymers CERTAIN CHARACTERISTICS OF THE COMPOUNDS STUDIED

Polymer

Curing time (days) at temperature

Ti*

80 I 90 111011201140 I

II* IIIt

-I-[2 23 2 2 2 21222

-

i

Elasticity modulus (GPa) at 20°C

High elastic modulus at T= + 50°C

3.6 1-95 3-83

0.0431 0"0318 0"0563

137 68 152

MM

o f inter-

point chain M= (N/mole) 3.36 2"56 3'73

branch

!

* Acid number of oligoester 30. t Bromine number of monomer 130. t Determined from thermodynamic measurements (P=(~3 MPa).

Treatment of the experimental data started with combined consideration o f the experimental functions e = Ad/d=f(t) and 3 = 9 (t), obtained at a load P and temperature T. The interconnection between e and & is given by the straight line

(1)

~-----¢5o+ C2 ~b

where J is the observed relative path difference; Jo is the quantity intercepted on the ordinate axis by continuation of straight line (1); e is the total relative strain of the specimen; Cz is the coefficient o f optical sensitivity to high elastic deformation; b is the specimens thickness. It is evident that eqn. (1) is the result of a process based on strong interaction and thermal activation. It was thus necessary to show the effect on the terms of eqn. (1) firstly of varying the stress under isothermal conditions, and secondly of changC~ TPa -1

1120

Cz,IO2

\

--

5GO

-- l~

~.._

/2' ¢]r / / I 2 ,

~

70

;

', - ' ~ 170

I

150

i

I

190

FIO. 1. Optical sensitivities to stress and strain as a function of temperature for polymer I. Here and in Fig. 2: /-provisional elastic character of C~;/'-elastic character of Ca; 2 and 2'-change in elastic and total C,; 3 - thermooptical curve of total Ca; 3'-total C, lof specimen cooled in strained state; 4-thermooptical curve of Co elastic character; 4'-change in high elastic C, during freezing of strained specimen.

2474

B.M. Zu~v et al.

ing the temperature at the same stress. Furthermore, it is interesting to confirm that eqn. (1) applies also to reverse creep when the force field is removed. The tests made in accordance with this programme established that for each material studied ~o is a function of the load and the temperature, but C2 only of the temperature. On varying the stress under isothermal conditions it was found that

~o = K P ,

(2)

where K is a constant. As regards the change in the path difference with the reverse creep time, this is proportional to the strain, i.e. = C2 ~b,

(3)

while the provisional coefficient of this equation is the same as in eqn. (1). In this connection it should also be noted that the isochronic relations e ~ P and ~,-~P at the selected loads (from 0"5 to 200 N) remain linear over the whole range of temperature and time. This, and also the form of eqns. (2) and (3) permitted a comparative analysis of the birefringence of the specimesn in a more general form, using for this purpose the value of the optical sensitivity of the material to the stress C,, which for disc type specimen was calculated from the equation [5]

C~=~zdb/8P The effect of the temperature on the first term and the coefficient (:'2 of eqn. (1) was more complex. Accrdingly, in order to obtain greater accuracy in discussion of the results, the data applying to polymer I were considered first, and these data were then generalized by means of information obtained from the other materials. The first term in eqn. (1) does not contain clear information on the photoelastic properties of the polymer. However, investigation of the elastic properties as a function of temperature is extremely useful since this relation is similar in form to the elastic component of the path difference as a function of temperature, and differs from it by only 10-15 ~o in the high elastic state. Figure 1 shows an example of this, where the temperature change of ~o, expressed through C~, and of provisional elastic nature, is given by curve 1, curve 1' giving the inherent elastic nature. The curves are drawn in the coordinates C~~ T. As can be seen (Fig. l, curve 1) the optical sensitivity to the provisional elastic stresses increases steadily and has an S-shaped profile with a rapid rise at the temperature range where rapid breaking of the intermolecular bonds occurs. This process results in a redistribution of the stresses in the specimen cross-section with respect to the remaining bonds, and the inter-branch point chains, because of their greater rigidity, receive a large proportion of the forces, so that the elastic strain of the specimen is increased. This in its turn results in additional polarization of the bonds and an increase of the path difference in the system. Since the rigidity of the valence angles of the interbranch point chains is significantly lower than that of the chemical bonds, the elastic birefringence in the specimen arises mainly because of their distortion. The size of the contribution from the distorted valence angles is directly related to the temperature since

Birefringencoas function of strain in erosslinkod polymers

2475

the inflow of thermal energy decreases its rigidity. This fact is demonstrated by the steady increase of optical sensitivity of the polymer over the temperature range of the high elastic state. In contrast to the provisionally elastic component, the value of Cz decreases steadily with rise in temperature (Fig. 1, curve 2) and in the region of high elasticity finishes on a plateau.* If tangents are drawn to the mildly sloping and ascending parts of curve 2, then the point of intersection of these tangents determines the temperature region of the development of polymer vitrification processes. As follows from condition (3), C2 characterizes the change in path difference per unit of specimen strain and can be represented in the form C2 =AC*/I~., where I,~ois th~ high elastic compliance, C* is the high elastic component of C,. Both values depend on the temperature; with rise in temperature the change in compliance takes place mainly because of the breaking of physical bonds. However, the change in C* is determined by two processes, i.e. the decrease in the number intermolecular bonds and an increase in the anisotropy of the polarizability of the inter-branch chain. Since side groups and defective elements in the form of cantilever attached small chains take part in intermolecular interaction, the passage of these framework elements into the passive state introduces a negative contribution into the C, of the system and therefore in the region of transition the compliance of a specimen changes more rapidly than its (7# and the C2 curve falls steadily. Over the temperature range of the high elastic state the inter-branch point chains of the polymer are bonded by hardly any physical branch points, but the number of chemical branch points remains constant. The change in (72 in this region is thus slight. However, evidently this change also can be explained by the effect of temperature on the conformation of the lateral spans of the active chains of the network. In the remainder of this article it is expedient, by analysis of the optico-meehanical properties of the polymers, to consider the above results in connection with the isochronic thermooptical curves (Figs. 1-3) for the total C, constructed by treatment of a family of creep curves in the region of times of existence of a provisionally equilibrium state and additional branch 3' reflecting the change in the total C, in the specimen during cooling. Apart from generally known information which follows from these curves [8], they are also useful for plotting the elastic character of the stress C, against the temperature. To do this it is sufficient to subtract from the ordinates of these curves the values of the ordinates of curve 1 corresponding to the given temperature. The results of this calculation are shown in Fig. 1, curve 4, and its S-shaped reflection 4'. After separating the total Ca into its instantaneous and high elastic parts it becomes clear that the elastic component of the birefringence and in the high elastic state, of the polymer, is fairly significant. Accordingly, in evaluating the anisotropy of the polarizability of the between-branch point polymer chain, curve 4 should be used, since the generally accepted method of * The course of curve 2 in this region can be corrected with respect to the size of the ratio of the total path differenceto the total relative strain of the specimen. This data is used to draw a separate curve 2' (total combined C2), which is then displaced downwards until it coincides with curve 2 where it emerges on a plateau.

2476

B.M. Zu'~v et al.

calculating this characteristic from curve 3 give results which are significantly too high [9]. Attention must then be given to the fact that the change in curve 4 in the region o f the plateau is more strongly suported by the proposed theory (broken line on the Figure). Evidently the observed deviations can be explained by the fact that the f r a m e w o r k elements of the macromolecules, which have a specific free rotation, change their conforzfiation on heating irrespective of the inter-branch point chain and thus produce a change in C,, which is not taken into account by the theory. A more complex picture of the change in elastic C, is observed on freezing a strained

-C°'TPe-~

C qO z

3OO 4"8

/ 2

,0o

'

I I

I

I

50

I

1.8

I

80

I

1,70

I

170

I T°

I

FIG. 2. Values of C, and C2 for polymer II as a function of temperature.

ooF

C ,~I/3 : 21

C~, .TPa-I

12

8OO

lOO

8 ,

5~

t_

90

L

I

180

t

_

. I

l

__.._...3 T ~

~7O

FiG. 3. Values of C, and C to the stress as a function of temperature for polymer III: Y'-change m total, and 4" change in high elastic component of C, during freezing of a partially structured specimen. The remaining notation of the curves is the same as in Fig. 1.

Birefringence as function of strain in crosslinkod polymers

2477

specimen (curve 4'). Already at the initial stage of cooling this curve d o e s not repeat the linear section of curve 4, and passes beyond it. Evidently this is because the interbranch point chains of the polymer udergoing cooling are previously strained, and the redistribution of the conformations of the passive framework elements of these chains takes place in an already oriented system. These conformations therefore differ in form from those which arise under creep conditions at a given temperature. On further lowering of the temperature, rapid restoration of the physical bonds between the passive framework elements occurs in the polymer. These elements, which are connected by physical branch points become active and begin to provide an additional contribution to C~. On the other hand, the formation of new bonds entails redistribution of the stresses in the framework of the network. As a result, the load is relieved on those part of the chains which receives the stresses in the high elastic state, and the elastic modulus of the specimen increased. This results in a situation where in the region of vitrification temperatures a C~ of orientational character is rapidly increased (curve 4') and an elastic Co falls rapidly (curve 1). Similar results and similar plots were obtained with polymer I1 (Fig. 2). The difference appeared only in the sign of the function, which can be explained by the negative anisotropy of the polarizability of the inter-branch point chains of the styrene fragment. The similarity of form of the curves reflects, evidently, the generality of the processes taking place in the polymer under the given experimental conditions. However, specific phenomena also appear in these specimens. In the first place, attention is drawn to the effect of the change in sign of the function C~ (curve 1). The reason for this is that in the polystyrene fragments of the network in the glass-like state 16-20 ~ of the benzene rings are bonded by dispersion interaction and 80-84 ~ remain free. During the process of elastic strain of the specimen, the bonded benzene rings, being active, introduce an additional contribution into the birefringence of the system. However, the passive parts of these rings on strain of the valence angles and polystyrene bonds will introduce a negative contribution because of the inductive effect. With rise in temperature the number of bonded benzene rings decreases and the number of free rings increases. Depending on the ratio of the bonded and free aromatic radicals, in the region of the glass-like state the positive curve of the elastic Co decreases, intersects the abscissa axis, and then acquires negative values. These data justify the conclusion that the polystyrene chain, which is not bonded intermolecularly, exhibits negative anisotropy of the polarizability on instantaneous strain. An interesting feature of the properties of polymer II appeared in calculating the high elastic Co : in the high elasticity temperature range curve 4 of this polymer is inclined from the theoretical curve to a greater extent than was observed with polymer I. However, this "anomalous" birefringenee of polymer II can be explained besides by the presence in the system of a significant number of benzene rings. The size of the contribution of such a radical to the high elastic Co depends on the angle between the normal to the plane of the ring and the axis of the inter-branch point polymer network. Evidently this angle is directly related to the temperature and with rise in temperature the contribution of the ring to the C~ of the system is decreased.

2478

B . M . ZUYEV et al.

Results worthy of attention were obtained in investigating polymer III (Fig. 3). Since this specimen was polymerized with final holding of the blocks at 120°C, the process of forming its network was not completed. This was reflected in the values of C~ and (22 as a function of temperature for the system. On heating such a system to 120°C in the creep tests the temperature was insufficient for further crosslinking of the polymer at an appreciable rate, and in the bulk of the polymer all that occurred was breaking of the physical bonds and an increase in flexibility of the between-branch point chains. As can be seen from consideration of curves 1-3, this mechanism produces a steadily change in the optical properties of the polymer. At higher temperatures the crosslinking process was activated, so that the quantity of fixed monomer residues and the mean length of the inter-branch point network chains were decreased. Furthermore, although each small side chain entering into crosslinking reaction was active, its positive contribution to the C~ of the polymer did not compensate for the decrease in anisotropy of the polarizability of the system, resulting from the shortening of the length of the inter-branch point chain (dip in curves 1 and 3). On the other hand, an increase in density of the network has a more marked effect on the value of C2 than the decrease in anisotropy of the polarizability ("hump" on curve 2). Network formation evidently finishes above 140°C, and the curves change to a form which is typical for thermooptical curves of a stable framework.

C~,T,MPa-'

0." 0"2

3

340

t z/~

I T,K

FIG. 4. Change in anisotropy of the polarizability of specimens during cooling from the heated state in the case of 1 -polymer 1, 2 - polymer II, and (3) polymer III on (3) complete and (3') incomplete curing.

In cases where it is necessary to compare the optical properties of different materials, it appears to be more appropriate to use values of their polarizability anisotropy, C,,T =A(~I -~2), and not C~ [10]. Such a comparative analysis is of interest when the optical properties of the specimens change under load. Figure 4 shows plots of C~Tagainst the temperature, obtained after appropriate treatment of curves 4, Figs. 1-3. It follows from an analysis of the carves in this Figure that during the freezing of strained specimens the anisotropy of the polarizability of polymers I-III is changed by 34, 32, 30, and 18 ~o

Birefringence as function of strain in crosslinkod polymers

2479

respectively. The latter two values apply to p o l y m : r . I H on incomplete and complete curing respectively. It is easy to see that the anisotropy of the polarizability in the case o f polymer I I I changes to a greater extent when curing is inzomplzte than when it is complete. This difference is associated mainly with the decrease in the n u m b : r o f fixed cantilever small chains in the bulk of the system. On considering the results from this point o f view, it is reasonable to assume that the character of the change in the curves TCo,,~ T provides a means of judging the degree of imperfection of the network in the form of side branches, which do not take part in elastic reaction of the framework. According to published information [11] the Williams-Landel-Ferry method has often b~en used for predicting optical creep in constructing a generalized C~ curve. However, The experimental data here obtained show that over the glass formation temperature range and over the range of the viscoelastic state the value of (72 for the polymers is not constant (curves 2). Accordingly, the construction of generalized Co curves on the principle of temperature-time superposition cannot give sufficiently reliable results since the change in the Co values of the polymers as a function of temperature and time are not equivalent. Moreover, the complexity of the mechanism of change of the conformations of the small passive chains excludes the possibility of introducing corrections into this procedure, as is done, for example, in constructing generalized compliance curves [12].

Translated by N. STANDEN REFERENCES

1. E. KOKER and L. FAILON, Opticheskii method issledovaniya napryazhenii (Optical Methods of Investigating Stresses), p. 234, ONTI, Moscow-Leningrad, 1936 2. B. I. TARATORIN, Mekhanika Polimerov, 4, 739, 1970 3. A. V. TURAZYAN and A. L. RABINOVICH, Fizikokhimiya i mekhanika orientirovannykh .,~, stekoplastikov (Physical Chemistry and Mechanics of Oriented Glass-Plastics). p. 168, Nauka, Moscow, 1967 4. A. V. TURAZYAN, V. P. NETREBKO and A. L. RABINOVICH, Mekhanika Polimerov, 5, 923, 1975 5. M. M. FROKHT, Fotouprugost (Photoelasticity). pp. 159, 351, OGIZ 1: 159, 351, MoscowLeningrad, 1948 6. B. M. ZUYEV, S. G. STEPANOV and A. A. KORGOV, Issledovanie po teorii plastin i obolochek (Investigations on the Theory of Plates and Shells). pub. Kazan Univ., 4, 550, Kazan, 1966 7. B. M. ZUYEV, E. F. GUBANOV, S. V. SFIULyNDIN, E. P. DIKOLENKO, V. G. ROMANOV and B. Ye. IVANOV, Vysokomol. soyed. A24: 2609, 1982 (Translated in Polymer Sci. U.S.S.R. 24: 12, 3000, 1982) 8. B. M. ZUYEV, Vysokomol. soyed. AI2: 730, 1970 (Translated in Polymer U.S.S.R. 12: 4, 822, 1970) 9. L. TRELOAR, Fizika uprugosti kauchka (Physics of Rubber Elasticity). Inostr. lit., 134, Moscow, 1953 10. M. F. MILAGIN and N. I. SHISHKIN, Fiz. tverd, tela 4: 2682, 1962 1I. S. L. GABRIELYAN, Tr. VIII Vsesoyuz, konf. po metody fotouprugosti (Prec. Eighth ALLUnion Conf, on photoelasti¢ity methods (Ed. I. S. Tallin), Acad. Nauk ESSR 1: 154, 1979 12. D. FERRY, Vyazkouprugie svoistva polimerov (Voscoelastic Properties of Polymers), Inostr. lit., p. 274, Moscow, 1963