ELASTICITY OF SEMICRYSTALLINE POLYMERS
141
Elasticity of Semicrystalline Polymers’
by D. Puett, K. J. Smith, Jr., and A. Ciferri ChemStTaltd Research Center, Inc., D u r h a m , North Carolina
(Received J u n e 26, 1964)
I n order to investigate how the elastic properties of a rubber change as the degree of crystallinity of the system is increased up to the extreme of a fully crystalline substance, stressstrain-temperature analysis was performed using ethylene-propylene block copolymers of varying degrees of crystallinity, nylon and keratin samples. Stress-strain isotherms of all samples show a peculiar behavior: if a polymer sample is first stretched to an elongation a’ and then released, the subsequent stress-strain isotherm shows an abrupt change of course a t an elongation corresponding to a’. The portion of the isotherm at elongations greater than a’ is unaffected by the mechanical treatment. A similar effect is shown by filled rubber samples, polyurethane elastomers, cellulose filaments, and metals such as aluminum and copper. From a phenomenological viewpoint two conditions were found necessary for the occurrence of the phenomenon, namely, (1) the structure resulting from strain a t a given (Y’ should be permanent and (2) the constraints which hinder deformation above a’ should not be relieved by the previous mechanical treatment. From a structural viewpoint the occurrence of the phenomenon was explained, for substances possessing low degrees of order, in terms of ability of amorphous chains to pull loose from pseudo-crystalline regions and, for crystalline substances, in terms of crystal-crystal transforniations and of crystalline orientation accompanied by plastic flow. This description accounts for the sinal1 set and large softening caused by the mechanical treatment on samples with low degree of order and for the large set and hardening caused, instead, for crystalline substances. The stress-temperature analysis for the block copolymer samples also reveal a peculiar effect. Segative stress-temperature coefficients are exhibitied when data obtained from isothernial stretching are considered. However, positive coefficients are exhibited when isotherms obtained from stress-temperature data a t constant length are considered. The phenomenon is explained on the basis that the nielting distribution of the crystalline coniponent Is, even in absence of strain, within the range where experimental analysis was performed. Recrystallization in state of strain results in a decrease of stress while recrystallization in a state of null strain results in an increase of modulus.
I. Introduction Large, reversible deformations and positive temperature coefficients of the stress are well-known properties of cross-linked, Polymer networks. The success of the rubber elasticity theory in describing the behavior of these networks is well established.2 Elasticity exhibited by macromolecular systems is not, of course, limited to the behavior of amorphous rubbers. Consideration Of the variety of “states” in which a macromolecu~arnetwork may exist clearly suggests a variety of elastic behaviors and elastic mechanisms. A fully crystalline (oriented) fiber may, for instance, ex-
hibit short-range elasticity, common among crystalline substances, or a long-range elasticity if a crystal-crystal transition takes place. Intermediate to the fully crystalline and the amorphous state, there exists a variety of semicrystalline states that are common among ma,cromo~ecu~ar systems. The study of the elastic behavior of semicrystallirle systems is the subject of the present paper. (1) From a thesis submitted by D. Puett to the Graduate School of the University of North Carolina, 1964, in partial fulfillment of the requirements for the degree of Master of Science. (2) A. Clferri, J . p o l y m e r sei., 54, 149 (1961). (3) A. Ciferri and K. J. Smith, Jr., ibid., ~ 2 , 7 3 (1964). 1
Volume 69, Number 1
J a n u a r y 1966
142
I n spite of the great technological interest associated with systems possessing elastic properties ranging between those of rubbers and those of crystalline substances, fundamental studies of the elastic behavior of semicrystalline systems (of varying degree of crystallinity) have been relatively scarce. A reason for this is probably the lack of adequate models and theories for such structurally complex systems. A model which has long been considered is the fringed micelle structure whereby submicroscopic crystallites are imbedded in an amorphous matrix. Since a given chain may traverse one crystallite, pursue an irregular pattern through a n amorphous region, and then re-enter the same or a different crystallite, the chains in the amorphous regions are generally limited in length and constrained in position. For homopolymers, such as nylon under ordinary conditions, these constraints may become so important that it is no surprise that several attempts to describe the elastic properties of such systems primarily in terms of elasticity of amorphous regions (crystallites being regarded as giant cross linkages or as inert fillers having a much larger modulus than the amorphous matrix) have met with very limited success. I n fact, recently, the view that another model may better describe the properties of a polymer such as nylon has gained consideration. According to this model, nyIon, a t least, is regarded as a typical crystalline substance. Dislocatioiis are considered to be the analog of the amorphous regions of the fringed micelle model. Experimental data appear to substantiate the view that deformations take place in the crystal through the motion of the dislocations, rather than in the amorphous regions themselves. There is, however, a class of polymeric systems where the fringed micelle model can be conceptually applied with less reservations than for nylon. This is the class of block copolymers, for instance, one where each macromolecule is constituted by regular sequences of a monomer A alternated with sequences wht.re monomers A and B are randomly distributed. ie., . . . AAAAAAABABBABAAAAAAA , . . The A sections may crystallize while the A B sections have typical rubber behavior. Thus, the amorphous regions are not merely prevented from crystallizing by the restraints exerted by adjacent crystalline regions but are intrinsically uncrystallizable. Clearly, by increasing the amount of crystalline regions, though adequate variations of the A B ratio, a range of polymers having elastic properties intermediate between those of a rubber arid those of a crystalline substance can be obtained. This approach is followed here, using mainly ethylene-propylene block copolymers, in an attempt to cxplore how the saIient features of the eIasThe Journal of Phvsical Chemistry
D. PUETT, K. J. SMITH, JR.,AND A. CIFERRI
tic behavior of rubbers are modified as the crystallinity of the system is increased.
11. Experimental A . Materials. Two unfilled, uncross-linked ethylene-propylene block copolymer films were kindly supplied by Dr. E. G. Kontos of the Naugatuck Chemical Division of the U. S. Rubber Co. Details concerning the preparation and characterization of the polymers have been discussed in the original paper by Kontos, Easterbrook, and Gilbert.s Characteristics of the samples, also supplied by Dr. Kontos, are reported in Table I. The structural scheme is suggested by the polymerization procedure and by additional characteri~ a t i o n . ~It does not imply that minor variations are not present. Sampl? A, having lower modulus and lower crystallinity than sample B, is of the “crystallizable” type,5 i e . , apparently amorphous in the undeformed state (as detected by X-ray analysis) but able to crystallize when stretched to about four to five times the original length giving a polyethylene-type diff raction pattern. Sample B is of the “semicrystalline” type,5 ie., showing a low crystallinity content in the unstretched state. Strips 04 cm. long and = l o X cm.2 in crosssectional area were used for the experiments. Data reported for sample A in Figures 1-4 and also for sample B were obtained with strips annealed to about 85” for 3 hr. (under vacuum) followed by slow cooling. The stress-strain curves for nylon reported in Figure 5 , kindly supplied by Dr. D. A. Zaukelies of this laboratory, were obtained with undrawn samples of nylon 66 (single filaments of cross-sectional area ~ 8 . 7 X 10-5cm.2).
c
“E/
I /
I .o
O f
io
40
80
60
I ao
a Figure 1. Master stress-strain curve for sample A at T including a 15-hr. relaxation period at = 7.0.
=
30”
(Y
(4) D. A. Zaukelies, J . A p p l . Phus.. 33, 2797 (1962).
( 5 ) E. G. Kontos, E. K. Easterbrook, and R. D. Gilbert, J . Polymer Sci., 61, 69 (1962).
ELASTICITY OF SEMICRYSTALLINE POLYMERS
143
Table I: Physical Properties of Stereoblock a-Olefin Copolymers
Class of material Structure according to polymerization procedure Average E / P weight ratio Crystallinity, %, by X-ray; ( a ) unstretched ( b ) stretched 500%', Density, g./ml., at 24"
Sample A
Sample B
Crystallizable
Semicrystalline
(E),, - ( E P ) , - ( E ) z 2 (EP),, - ( E ) v j- (EP),, - ( E ) v 2- (EP),, - ( E ) u 8(EP)z, 52:48
73: 27
0
25 E orientation with additional crystallization 0 905
E crystallization 0.856
i
a=2.0
30.0 O F - - - -
N5 \
0
-L 2 0 . 0 .
b
U 10.0
Figure 2. Two master stress-strain curves for sample A a t T = 30 and 60'. Second, third, and fourth isotherms were performed in the order and a t the temperature indicated using the sample for which the master curve was performed a t 30".
Corriedale wool fibers (unmedulled) of uniform cross-sectional area ( ~ 1 . 7X cm.2 f 5%) were kindly supplied by Dr. M.Feughelman of the Division of Textile Physics of the C.S.I.R.O.,Australia. B. Dynamometry. Most stress-strain and stresstemperature data were obtained according to techniques described elsewhere.6 For sample A the force was recorded a t 10-min. intervals during the standardized stepwise procedure for obtaining the stress-strain isotherm. For the keratin sample, which was analyzed while immersed in water, 3-min. intervals were used. Stress-strain curves for sample B and for the nylon sample were obtained a t 23" and 65y0relative humidity. Data in Figures 1,2, arid 5-9 include the first stress-strain isotherm performed on a sample which had no previous mechanical treatment. This isotherm, referred to as the 'lmaster isotherm," was extended to the maximum elongation for each sample and is represented through-
20
30
40
50
60
70
80
9?
T ('C)
Figure 3. Stress-temperature curves for samples A and B at the indicated elongation (measured at the lowest experimental temperature). Broken lines represent the corresponding variation of birefringence with temperature. Arrows indicate the sequence of heating and cooling.
out with crosses ( X ) to distinguish it clearly from the isotherms, represented with closed circles, referred to as "second isotherms" which were obtained with independent similar strips (or fibers) previously lengthened (according to the standard procedure) to elongations characterized by the value of cy'. I n all cases a cycle was performed, ie., after the elongation a' was attained, the elongation was decreased according to the stepwise procedure outlined above (the recovcry part of the cycle is not always represented in the graphs). In the case of sample A and the keratin fiber (Figures 6, 7 , and 9) a period of 16 (6) K. J. Smith, Jr., A. Greene, and A . Ciferri, KoZloid-Z., 194, 49
(1964).
Volume 69, Sumber 1
Janzcary 1966
D. PUETT, K. J. SMITH,JR.,.4ND A. CIFERRI
144
r_-_:::::: O
20
30
40
T
50
(OC)
Figure 4. Stress-temperature curves for sample A a t the indicated elongations.
a Figure 6. blaster, second, and third stress-strain curves for sample A a t T = 30”: , increasing elongation; - - - -, decreasing elongation.
U
Figure 7. Master and second isotherms a t 2‘ = 30” for sample A performed on independent strips previously elongated to a1 = 2.0, 3.0, and 3.8.
U
Figure 5 . )laster and second isotherms a t T = 23’ for the nylon sample. The second isotherms were performed using a single fiber c.arried through successive a1 values.
hr. was allowed before the performance of the next stress-strain isotherm; for sample B and for the nylon sample 110 time was allowed to elapse between consecutive cycles. S o difference was observed using independent strips which were stretched to different a’ values or using a single strip (or fiber) which was carried through successive a’ values. The Journal of Physical Chemistry
I n all cases, the extension ratio (a)is referred to the original rest length of the sample before any mechanical treatment was performed. The stress (7) is usually referred to the original cross-sectional area of the dry sample. However, in the case of sample B (Figure 8) and the nylon sample, values of the true stress ( u ) are plotted, ie., the force divided by the actual cross-sectional area at the given elongation. The “JIullins effect” is evident irrespective of whether stress or true stress is plotted. For the stress-temperature data, reported in Figures 4 and 10, long times (up to 24 hr.) of relaxation a t the highest temperature were required before the force at-
ELASTICITY OF SEMICRYSTALLINE POLYMERS
145
I .5-
7
P
.I
N^ 1.0-
2
c
b
4.0
6.0
8.0
a Figure 8. Master and second isotherms of T = 23" for sample B. The second isotherms were performed using a single strip carried through successive a1 values.
I
2.0
3.0
4.0
a Figure 10. The energy component E p and the isothermal stress-strain curves a t T = 30 and 50' obtained from the data in Figure 4.
0
d 1.20
1.10
1.30
a Figure 9. Master and second isotherms a t T = 83" in water for Corriedale wool fibers. The second isotherms were performed using a single fiber carried through successive a1 values.
0
10
20
30
40
50
60
70
80
I lhrs.)
tained sensibly constant values. Thereafter, the temperature was lowered a t a rate of ao/!20 min. which appeared satisfactory for obtaining stress-temperature cycles with negligible hysteresis.'j The birefringence (Figure 3 ) was measured simultaneously with the measurement of the stress according to the technique described in detail elsewhere.' Other details of stress-temperature measurements are given in section IIIB.
111. Results and Discussion A . Isothermal Behavior. Relaxation and Conditioning Attempts. Figure 11 shows the large relaxation exhibited by sample A, and Figure 6 shows the large
Figure 11 Stress-relaxation for sample A a t a = 3.8 and T = 30".
hysteresis presented by the master stress-strain isotherm and the large difference between the master and the second isotherm. The set a t the end of the first cycle is not permanent. In the case of Figure 6, it corresponds to an extension ratio of CY = 1.4 a t the end of the cycle which was then reduced to cy = 1.2 after 16-hr. standing (when the second cycle was initiated). The elastic behavior exhibited by the second stressstrain isotherm more closely approaches that of a (7) To be published.
Volume 69.Number 1
January 1965
D. PUETT, K. J. SMITH,JR.,AND A. CIFERRI
146
rubber-like network. The modulus is lower, and, while some hysteresis still persists, the third and the following isotherms are very close to the second one, provided the limiting elongation 01' reached during the first cycle is not exceeded (cases where the elongation 01' is exceeded are reported in Figures 7 and 8). Thus, in spite of the large initial time effects, the system appears to possess an "equilibrium" elastic component which, since the system is not chemically cross-linked, is probably due to pseudo-crystalline aggregates (not revealed by wide angle X-ray measurements) which resist the rearrangement of structure evident during the first stages of relaxation. Figure 1 illustrates a master curve for sample A. At a = 7 a relaxation period of 15 hr. was allowed. It is seen that on increasing the strain after the long relaxation period the stress rises abruptly, and the course of the master curve is resumed (this coincides with an independent master curve for which no long relaxation period was allowed). This fact may be interpreted as indicating that, in spit? of the relaxation which occurred in the course of 15 hr. a t 01 = 7.0, there are restraints to the deformation which remain largely ineffective at (Y = 7.0 but which become effective as soon as the elongation is increased past 01 = 7.0. This interpretation will receive further substantiation and clarification from the data subsequently presented. In an attempt to eliminate the difference between the master and the second isotherm several approaches were used, namely, (1) performing stress-strain isotherms at high temperature (SO'), (2) annealing the sample at 85" for 3 hr. (under vacuum) and then slowly cooling it, and ( 3 ) allowing permeation of a limited amount of xylene which was subsequently pumped off. Invariably, these attempts resulted in a large decrease of the stress (up to 50%) a t all elongations for bot,h the master and the second isotherm. The difference between the two curves remained large, however, and the "Mullins effect" was never eliminated. X-Ray analysis did not reveal significant development of the crystallinity of unstretched samples after the various treatments. A more detailed analysis of the effect of temperature on the sequence of the isotherms is presented in Figure 2. Two indepe~identmaster curves, one a t 30" and the other at GO", reveal the great effect of temperature in reducing the stress. For the sample which was stretched a t 30", a series of consecutive isotherms (16-hr. i~itervnlswere allowed among the various isotherms) are represented. The second isotherm at 30" again reveals the difference exhibited also in Figure 6 ; the third isotherm was performed at 60°, and it is seen to fall below the independent master curve a t GO" (had T h e Journal
Physical Chemistry
the second isotherm at 60" been plotted for the latter, it would have been indistinguishable from the one reported). The fourth isotherm was performed at 30"; although the master isotherm could not be regenerated, a partial reversibility is clearly indicated which could have been improved by allowing longer recovery or using somewhat different conditions. The fact that the isotherm a t 30" lies above the one a t 60" appears to be in contrast to the behavior of rubbers. The origin of this behavior will be discussed in connection with the stress-temperature analysis in section IIIB. In the following part, attention is devoted to the analysis of the difference, so generally exhibited, between the master and the second isot,herm. The dlullins Eflect. I n both Figures 2 and 6 the elongation CYof ' the master isotherni is not exceeded during the subsequent isotherm. The shape of the second isotherm clearly indicates an upturn of the stress which tends to coincide, when CY' is reached, with the value of the master curve. Figures 7 and 8, for samples A and B, respectively, clearly indicate this trend and also the sudden change of course of the second isotherm, past cy', which henceforth coincides with the master curve. The phenomenon is seen to be general for different CY' values and for the two different samples. As has been reported in a preliminary communication,g the phenomenon is seen to be superficially similar to that described by Holt, Xullins, arid Buecheg for "filled" natural rubber vulcanizates (the filler being, for instance, carbon black) and has been often called the "Mullins effect." llIullins has presented a general interpretation of the phenomenon in terms of soft and hard regions connected in series, the hard regions converting to soft as a result of stretching. Bueche has presented a somewhat more elaborate model whereby the filler particles are regarded as giant (secondary) cross linkages undergoing quasi-affine deformations with the result that chains, which at a given CY' value happen to be highly strained, will pull loose from the filler particle, thus, decreasing the stress during the second stress-strain isotherm for elongations which do not exceed CY'. According to Bueche, in an unfilled network a similar softening phenomenon will be comparatively negligible since the nctwork junctions do not undergo an affine deformation in the vicinity of a highly strained chain. As in the case of our samples (cf. Figure G and Table 11),the lower modulus persists in a filled rubber eveii when the material is allowed to (8) D. Puett, K. J. Smith, Jr., A. Ciferri, arid E. G. Kontos, J . Chem. Phys., 40, 253 (1964). (9) W. L. Holt. Rubber Chem. Technol., 5 , 79 (1932); L. Mullins. ibid., 21, 281 (1948); F. Bueche, J . A p p l . Polymer Sci., 4 , 107 (1960).
ELASTICITY OF SEMICRYSTALLINE POLYMERS
147
Table 11: The Dependence of Set and Modulus on d E/P 52/48?
YA. 01
1.0 1.1 1.2 2.0 3.0 3.8 4.0
aga
E/P 73/27-
-3.
Y, kg./cm.z
--Keratin-
Y, kg./om.*
..
7.7
..
.. ..
... ...
..
1.06 1.14 1.23
5.6 4.8 4.7
1.20 1.85
..
...
2.45
3.3
x
102
-
-
Nylon 66----
6 . 8 X 108 2.3 2.0
a8
Y, kg./cm.a
..
1.8
...
...
...
.. .. ..
...
..
, .
...
3.50
2.8 2.5
..
..
Y, kg./om.'
1.02 1.03
, . .
..
a1
2.3
...
..
.. 1.60 2.55
x
104
... ...
1.6 1.3 ...
1.2
' a, is the ratio of the rest length before the performance of the second isotherms to the initial rest length.
relax for many days at room temperature (the rubber recovers its original high modulus if it is allowed to rest at about 100" while our master isotherms could be regenerated after complete melting and reformation of the fibers according to the original procedure). As stated in the introductory section, our samples are expected to conform ideally to the fringed micelle model; the presence of relatively large "regions" where the crystallizable (E)=portion of the macromolecules occurs in more or less perfect crystalline arrangements is expected. A superficial analogy of these "regions" to filler particles is. therefore, suggested. A main difference is, however, the fact that, while, in the case of rubber, the filler particle is of a chemical nature different from the network, in our samples, A and B, selected sections of only one macromolecular species form these regions. It is, consequently, more difficult to specify the nature of the bonds which are broken during the first stretching. A quantitative description of the original structure would be extremely difficult unless drastic simplifications are introduced. Thus, we believe that a qualitative description will have to suffice. The structure prevailing in the original unstretched samples A and B is probably very different from the ideal fringed micelle picture where all crystallites are relatively perfect and well delimited from the adjacent amorphous regions. Rather, we suspect a gigantic chaotic array where strong interactions are more evenly distributed throughout the sample than is expected for the model. The complexity of this structure could, by certain treatment, perhaps, be simplified to the state where each crystalline region is clearly delimited from the matrix (if the chemical structure has the necessary regularity). The preliminary conditioning attempts (to anneal or to allow a diluent to increase the mobility of the macromolecules), as well as the mechanical conditioning achieved by the first stretching, have probably helped the formation of a less disordered structure. The Mullins effect has not, how-
ever, disappeared as a result of these conditioning attempts, which is not surprising since it may be expected that this effect exists also in the ideal fringed micelle structure; ie., amorphous chains, which at a given a' happen to be highly strained, could rupture if the matrix as a whole undergoes affine deformation. While for a typical rubber vulcanizate the elastic properties are determined by a given network structure which is stable at all degrees of deformation, a block copolymer, such as sample A, possesses in the original undeformed state no definite network structure. Rather, the network structure which assures elastic behavior during the second isotherm is formed in the first stretching and depends upon the particular a' a t which the sample is mechanically conditioned. This network structure is then stable for all elongations below the particular a', but it can be modified (in one of lower modulus, cf. Table 11) just by exceeding this given a' value. It is this possibility of establishing a network structure which depends upon the a' value and upon the presence of strong intermolecular interactions, which assures this system of a high modulus and longrange extensibility which may considerably exceed those exhibited by an amorphous vulcanizate where the molecular network is structurally stable. Inspection of Figures 7 and 8 and of the data collected in Table I1 indicates that, the Rlullins effect persists, in spite of great variations of the set arid of the modulus (or the general shape) of the second isotherm (at each a' value), which suggest that these factors are not essential to the occurrence of the effect (negligible set was observed for filled rubber vulcani~ates~).The generality of these conclusions is illustrated by the data in Figures 5 and 9, which show the occurrence of the Nullins effect in the case of an undrawn nylon sample and in the case of a wool fiber. In the case of nylon, the stretching is equivalent to a cold drawing (performed under conditions under which no necking was likely to occur). The structure which is formed by stretching a t Volume 69, S u m b e r I
J a n u a r y 1966
148
a given a' is that of the partially oriented fiber, as is evident from the change in the X-ray diffraction pattern. lo This oriented structure does not spontaneously revert to the original unoriented state. The set is particularly large, as is the modulus of the set sample. This modulus does not increase with increasing set (cf. Table 11) because of the high rate of stretching which was used ; under conditions where longer intervals between consecutive stretchiiigs is allowed, the modulus, as is well known, increases with set. In fact, although the set and the shape of the second isotherm are not essential for the llullins effect, there are evident connections betwccn them. The transition from a rubber to a crystalline substance on increasing the degree of crystallinity is quite evident from the set and the elastic properties of the second isotherm when data in Table I1 for a given a' value for different samples are considered. A smaller set, necessarily associated with a longer range of elastic behavior up to the given a', corresponds to a lower Young's modulus. For sample A the modulus appears, i1 fact, to decrease with a' when also the set/a' ratio decreases. The fact that, on increasing a', a sample with low crystallinity is progressively softened (while a sample with a high degree of crystallinity is progressively hardened) is not unexpected since, for the former sample, the part played by the amorphous network is preponderant, and this, according to Bueche's description, will contain a smaller number of constrained chains the higher a' is (to what extent the elastic behavior of the resulting network is rubber-like mill be discussed in section IIIB) . In the case of the keratin fiber immersed in water, it is well known that a certain value of the stress is required in order to initiate the a @ p transformation." This stress value is usually attained when an elongation of about 5'; is reached. However, a t ordinary temperatures the transformation is quickly reversible and no 1Iulline effect was observed in these conditions. I t is, howeiw, well known that, a t higher temperatures where the transformation is no longer reversible, the fiber can be permanently set in the p-form, probably because of ch(3mical changes (elimination or displacement of some chemical cross linkages'o). Accordingly, stressstrain curv('s pcrformed a t 83" reveal the Mullins effect. The large set is attributed to the permanence of the pstructure ar zero force; the set increases with a' since the amouni of a transformed into 13 depends upon a' (cf. ref. 11). The lower modulus of the second isotherm (with respect t o the one exhibited by the master curve, 6.Table 11) docs not necessarily reflect a difference in the modulus of the a- and @-form but, very likely, a general bi eaking down due to prolonged exposure a t high tempwaturc The .Journal o f Phyezcal Chemtstry
D. PUETT, K. J. SMITH,JR.,AND A. CIFERRI
For other materials the occurrence of a Mullins effect has been reported. Effects similar to those described in Figure 1 have been observed by Hermans12 using cellulose filaments, and the occurrence of stress-strain curves similar to those reported in Figure 7 was reported by TrickI3 using polyurethane elastomers. The occurrence of the Mullins effect is not limited to polymeric materials. Stress-strain curves for metals such as aluminum, copper, etc., also reveal a Mullins effect associated with the occurrence of orientation and large plastic flow.14 When the variety of conditions under which the Mullins effect is observed is considered, some generalizations can be made. Two requirements appear necessary for its occurrence. One requirement is that whatever structure results from strain at a given a' (a network with fewer constrained chains or the pform for a polypeptide chain or a crystalline orientation accompanied by plastic flow) is permanent or, at least, very slowly reverts to the original form. The second requirement is that the constraints which hinder deformation above a' should not be relieved by the previous mechanical history and relaxation of the sample a t elongations less than a'. The preceding examples give a clear illustration of this latter requirement. In the case of sample A, the constraints which limit elongation above a' can be conveniently regarded, extending Bueche's model for filled rubber, as chains which are near full extension. Thus, a relaxation a t a' (cf. Figure 1) cannot contribute appreciably to the relief of these constrained chains; the largest part of the time effects should be ascribed to other viscoelastic processes. In the case of the keratin fiber, if the solid-solid transition theory" is accepted and the strain in the yield region (cf. Figure 9) reflects the a F! p transformation, then it is clear that a critical value of the stress has to be reached in order for additional a Ft 0 transformation to occur. This critical stress value is strictly related to the thermodynamic heat of transformation of the a- into the 0-form. I n the case of metals, the constraints which hinder deformation above a' are essentially related to the interaction of the dislocations with lattice vacancies and other dislocations. While from a phenomenological point of view the Mullins effect has been shown to be a quite common phenomenon among semicrystalline and crystalline (10) R. Jieredith, "The Mechanical Properties of Textile Fibres," North-Holland Publishing Co.. Amsterdam, 1956. (11) A. Ciferri, Trans. Faraday Soc., 5 9 , 562 (1963). (12) J. J. Hermans, Rec. traa. chzm., 65, 624 (1946). (13) G. S. Trick, J . A p p l . Polymer Sci., 3 , 252 (1960).
(14) H. G . Van Bueren, "Imperfections in Crystals." North-Holland Publishing Co., Amsterdam, 1961.
ELASTICITY OF SEMICRYSTALLINE POLYMERS
substances, we have found it expedient to interpret its occurrence and the consequent softening effect for samples having a low degree of crystallinity in terms of restrained chains pulling out from more ordered pseudocrystalline regions. ,4s the degree of crystallinity is increased, deformations within the crystallites become predominant so that ultimately an interpretation in terms of dislocation motions must be offered. The transition from a rubber to a crystalline substance will involve a transition from a case where the former effect prevails to a case where the latter effect is predominant. It should be emphasized that this interpretation represents a preliminary descriptive attempt-more refined descriptions can be expected. B. Stress-Temperature Behavior. Figure 3 illustrates stress-temperature data for samples A and B held at constant length. Sample A was first stretched at 30", and at the end of a 24-hr. relaxation, when the stress attained a sensibly constant value (cf. Figure l l ) , the temperature was raised a t a rate of 5'/20 min. According to this schedule the temperature was raised to 60", lowered, and then raised again. The birefringence was measured following a similar schedule. For sample B a similar approach and a somewhat different temperature range were used. It is seen that the initial decrease of the stress between 30 and 60" is not reversible; when the elongated sample is cooled, a positive stress-temperature coefficient is exhibited. As for rubbers, a cycle of cooling and heating can be performed showing negligible hysteresis. This surprising behavior can be explained on a basis which also accounts for the relative position of the isotherms a t 30 and 60" illustrated in Figure 2. I n fact, though wide angle X-ray analysis gave no evidence of crystallinity for the unstretched sample A, the analysis of the preceding section (cf. the similarity of behavior with sample B which is crystalline in the rest state) indicates the occurrence of pseudo-crystalline aggregates. Viewed under a polarizing microscope, sample A (unstretched) reveals considerable depolarization which is indicative of crystallization. On increasing the temperature up to 60" this depolarization was almost eliminated while it reappeared when the sample was cooled again. Thus, in the case of Figure 2 the modulus a t 60" is lower than the modulus a t 30" essentially because a t the higher temperature less "crystallinity" is present. This reduction of crystallinity overshadows the rubber-like behavior according to which the curve at 60" should exhibit a larger modulus. Further, when a sample examined a t 60" is relaxed and subsequently examined a t 30", the re-increase of modulus testifies to the reversibility of melting. The redevelopment of crystallinity in the relaxed state is, how-
149
ever, to be clearly distinguished from the redevelopment of crystallinity on cooling a sample held stretched a t constant length. I n fact, in the latter instance a preferential orientation in the direction of stretch will be assumed by the growing crystallites, and this, as is well known, will generally decrease the stress6 Thus, the initial decrease of stress on heating a stretched sample (Figure 3 ) is due to the melting of crystallites which were not formed in an oriented state while a subsequent recrystallization in the oriented state will not overshadow, but rather emphasize, the positive stresstemperature coefficient due to the network. Redevelopment of crystallinity on cooling the elongated sample is unmistakably proved by the concomitant increase of birefringence (cf. Figure 3). Thus, in spite of the mechanical conditioning a t a given temperature, the crystallites have not attained the degree of orientation that can be achieved by cooling an oriented specimen. For a typical rubber vulcanizate the decrease of stress with temperature illustrated in Figures 2 and 3 is not observed only because no crystallinity is present (under ordinary conditions) in the unstretched state. I n the preceding section it has been emphasized that the network structure which assures elastic behavior during the second isotherm is formed and depends upon the particular a' value a t which the sample is mechanically conditioned. The results illustrated in this section add a further restriction to the stability of this network structure : the structure stabilized during the mechanical treatment at cy' will be essentially stable only at a given temperature. In Figure 4 several stress-temperature data a t constant length are reported. In obtaining these curves, in accordance with the above observation, the sample was conditioned the sample was with respect to cy' and temperature, w., mechanically conditioned at a' = 4 and allowed to relax at the highest experimental temperature. At the end of a stress-temperature cycle the elongation was decreased so that the original a' value was in no case exceeded. Under these conditions the elastic contribution of the network should be best observed. The curves in Figure 7 are practically linear, and good reversibility is exhibited (cf. also Figure 3 ) . The value of the stress a t 50 and 30" and the corresponding energy component E , (derived from the relation6 T = E , T ( 8 7 / b T ) ~obtained ) from the data i n Figure 4 are reported in Figure 10. The large decrease of E , Ivith a can be associated with crystallization as evidenced by the increase of birefringence (cf. Figure 3). It is remarkable, though riot unjustified, l 5 that the stress-
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temperature curves (Figures 3 and 4) are essentially linear and hysteresis-free, even under these conditions.6 I n contrast to the data in Figure 2, the curve a t 50' lies above the curve a t 30" in Figure 10 which is coherent with the fact that, once the main variation of crystallinity with temperature takes place in the oriented state, the rubber-like network contribution can be observed. The shape of the isotherms is similar to the shape expected for a iiongaussian network. However, we believe that the present results do not offer compelling evidence for concluding that the shape of these curves is exclusively due to nongaussian behavior. The problem of analyzing the shape of stress-strain isotherms in terms of nongaussian behavior and stressinduced crystallization has been dealt with, in much detail, elsewhere.6 The upturn exhibited by the isotherms obtained from stress-temperature data can be safely attributed to nongaussian behavior, only if it is possible to stretch a network a t temperatures where crystallization and large, ticgative energy components are absent. These conditions are clearly not fulfilled by the present system. I n spite of the large difference for the degree of crystallinity of samples A and B, the stress-temperature analysis reported above is characteristic of samples having a melting distribution within the temperature range where the experiments were performed. From the point of view of discussing the behavior of semicrystalline polymers in general, it would be desirable to study cases where the melting range is above the temperature range investigated, this for polymers
The Journal of Physical Chemistry
D. PUETT, K. J. SMITH, JR., AND A. CIFERRI
having different degrees of crystallinity. On the basis of the present results, some predictions about the stresstemperature behavior of these substances can be made. If the degree of crystallinity is low, small energy components and positive stress-temperature coefficients should be observed. If viscoelastic effects are not too severe, the conventional stress-strain isotherms should exhibit increased modulus a t higher temperatures. On increasing the degree of crystallinity, the elongation a t which positive stress-temperature coefficients are observed should increase because of the opposite effect associated with the crystalline component. This has been, in fact, observed in the stress-temperature analysis of nylon samples. 16'l7
Acknowledgment. Pleasure is taken in acknowledging the kindness of Dr. E. G. Kontos for supplying the copolymer samples, for their characterization, and for his interest in this work. AckriowledgmeIlt is also due to Dr. D. A. Zaukelies, who kindly supplied the data on the nylon sample and contributed interesting and clarifying discussions, and to Dr. A I . Feughelman for kindly supplying the wool fibers. The authors are particularly indebted to Professor J. J. Hermans for his great interest and guidance throughout the course of this work. (16) M.L. Williams, Trans. SOC.Rheol.. 4, 297 (1960). (17) NOTEADDEDI N PROOF. After the manuscript was completed, we found that It. S. Stein and A. V. Tobolsky (Textile Res. J . , 18, 201 (1948)) found similar forcetemperature behavior for elastic polyamides.
