THERMAL PROPERTIES OF ATACTIC AND ISOTACTIC POLYSTYRENE
that the amino acids are zwitterions and that glycine6 has an entropy of ionization of -8.9 e.u., but these acids must have much smaller dipole moments owing to smaller charge separations than the above classes
2657
of acids. Thus, it appears probable that the pyridinecarboxylic acids exist in solutions principally in nonzwitterionic form, contrary to the conclusion of Millero, etal.
Thermal Properties of Atactic and Isotactic Polystyrene
by F. E. Karasz, H. E. Bair, and J. M. O’Reilly G m r d Eledrk Research Laboratory, Schenedady, New York (Received February 23,1966)
The heat capacities of atactic polystyrene and of amorphous and partially crystalline isotactic polystyrene have been measured from 300 to 520’K. and, in the case of the atactic sample, in the low-temperature region also. The results show that molecular configuration in itself has only a minor effect on bulk thermodynamic properties, and that the partially crystalline material obeys a two-phase additive model reasonably well. Residual entropies and enthalpies for the amorphous polymer were calculated as a function of temperature and related to current theories of glass formation.
I. Introduction A fundamental approach to the understanding of the solid state of polymers is through measurements of their heat capacity. Polymers present unusual opportunities in this respect, because in many cases they can be prepared with widely differing degrees of crystallinity, ranging from an amorphous to a highly ordered state. Many of the types of information that can thus be obtained from heat capacity measurements over a wide temperature range have been discussed by Dole. Polystyrene is one of the oldest and most important synthetic polymers. Until recently it was invariably produced in the atactic form, but currently crystallizable isotactic material has been synthesized, and thus the effect of changes in both molecular configuration and crystallinity on thermal properties may be investigated. Such comparative studies, still relatively ra,re, have usually revealed that the former factor can have an appreciable effect upon these properties. One of the continuing problems of all types of 33
precision polymer measurements is the uncertainty of comparisons in which polymer samples are not completely characterized. Therefore, the fact that atactic polystyrene may now be obtained as a standard sample with known properties from the National Bureau of Standards has added impetus to our study. A further point has been a desire to resolve some discrepancies which are apparent in previous work, particularly in regard to secondary transitions, that is those other than the glass and melting transitions. Finally, by making measurements of heat capacities over a range which extends from close to absolute zero into the liquid state, it becomes possible to calculate accurately the thermodynamic quantities, entropy and enthalpy, necessary to describe the polymerization equilibria. (1) M. Dole, Fortschr. Hochpolyner. Forsch., 2 , 221 (1960). (2) G. Natta, P. Conadini, and I. W. Bassi, Numo Cimento, Sup& 1 , 15, 68 (1960). (3) J. M. O’Reilly, F. E. Karasz, and H. E. Bair, BuW. Am. Phys. SOC.,9,285 (1964). (4) E. Passaglia and H. I(.Kevorkian, J . Appl. Phys., 34,90 (1963).
Volume 69,Number 8 August 1966
2658
Although no single precision measurement has been reported which encompasses both the low-temperature and the liquid-state regions, several authors have determined heat capacities of atactic polystyrene in some part of this range.516 Unfortunately, other properties of the sample were generally not reported. In addition, Ueberreiter and Otto-Laupenmiihlen’ have investigated the effect of molecular weight upon the thermal properties. Their fractions extended only up to a molecular weight of 3650, and it is clear from the data that this is not yet in the region where the properties become independent of this parameter. More recently, Dainton, et ~ 1 . have ) ~ made precision low-temperature determinations using a crystalline isotactic polystyrene sample; their investigation did not include the glass or melting transition regions. Finally, after the experimental part of this work had been completed, we learned that Dole and Abu-Isa had made measurements using both atactic and isotactic polystyrene samples between 230 and 550°K.g The relation of these results to our measurements is discussed below.
II. Experimental A . Samples. (21 Atactic. The standard N.B.S. broad molecular weight distribution polystyrene sample (N.B.S. No. 706) was used in the atactic series measurement. This has Bw = 2.58 X lo5 (from light scattering) and ifZn = 1.36 X lo6 (osmotic pressure). The material was purchased in the form of pellets about 3 mm. in diameter and apart from a vacuum drying treatment (80’ for 24 hr.) was used as received. Negligible weight loss was observed during the drying. (iz] Isotactic. An isotactic polystyrene sample was obtained through the courtesy of the Monsanto Co. (sample designation no. 6811). This was stated to be highly tactic with less than 2% solubility in boiling methyl ethyl ketone. The material was received as a crystalline white powder and was not further extracted. As one of the objects of our experiments was to determine the properties of amorphous isotactic polystyrene, a quantity of the powder was molded into sheets about 1.5 mm. thick and quenched from the melt in ice water. (It has previously been determined that the known cooling rates attainable in situ in the calorimeter sample container could not produce a totally amorphous sample.) The quenched optically clear sheets were then dried at 70’ in vacuo, and were broken into small irregularly shaped pieces about 0.5 cm. across for use in the measurements. Viscosity determinations in o-dichlorobenzene, using the data of Krigbaum, Carpenter, and Newman,’O showed that the molecular weight after this treatment T b J o u r d of Physical Chmietry
F. E. k s z , H. E. BAIR,AND J. M. O’REILLY
had fallen from 2.2 X lo6 to 4.2 X lo6. The fact that this specimen was completely amorphous was established by X-ray and differential scanning calorimeter (Perkin-Elmer DSC-1) measurements, and was verified a posteriori from the heat capacity determinations (see below). For both samples there was some concern regarding the possibility of degradation during measurements, as a result of relatively long residence times at high temperatures. A small quantity of each was therefore heated prior to use in a sealed tube (under helium) and the rate of gas evolution as a function of temperature was determined. From these data, we were able to estimate maximum temperature and residence time combinations which could be employed. The viscosity of both samples after the calorimetric runs was also measured, and confirmed the absence of any further degradation. B. Calorimetric. The calorimetric apparatus was a wide temperature range modification of conventional adiabatic design and will be described elsewhere.l1 A modification to the external refrigerant bath since our earlier work12permitted the use of liquid hydrogen, and thus extended the useful temperature range down to about 17’K. The samples, sealed under a few centimeters pressure of helium, were typically heated at between 1 and 15 deg. hr.-l. An intermittent heating technique was used, with intervals ranging from 2 to about 10’. Equilibration times were normally about 20 min., but increased sharply in the vicinity of transitions. The weights of the atactic and isotactic polystyrene samples used were 30.613 and 38.507 g., respectively. The precision of the apparatus had previously been assessed by a determination of the heat capacity of a standard sample of alumina.I1 For the present measurements, we estimate our errors in the heat capacity to average h0.274 up to about 400°K., with a possible rise to *0.4% at the highest temperatures used. ~
~~
(5) F.G. Brickwedde, referred to in “Styrene,” R. H. Boundy and R. F. Boyer, Ed., Reinhold Publishing Corp., New York, N. Y., 1952. (6) I. V. Sochava, Vestn. Leningr. Univ., Ser. Fiz. i Khim., 16, No. 10,70 (1961). (7) K.Ueberreiter and E. Otto-Laupenmllhlen, 2. Naturforsch., 8a, 664 (1953). (8) F. S. Dainton, D. M. Evans, F. E. Hoare, and T. P. Melia, Polyner, 3, 286 (1962). (9) I. Abu-Is& and M. Dole, J. Phys. Chem., 69, 2668 (1965); we thank Prof. Dole for his courtesy in sending us his data prior to publication. (10) W. R. Erigbaum, D. E. Carpenter, and S. Newman, ibid., 62, 1586 (1958). (11) F.E.Earasz and J. M. O’Reilly, to be published. (12) J. M. O’Reilly, F. E. Karasz, and H. E. Bair, J . Polymer Sci., C6, 109 (1964).
THERMAL PROPERTIES OF ATACTIC AND ISOTACTIC POLYSTYRENE
C . Other Properties. The X-ray diffraction patterns and the densities of several samples with varying thermal histories were also determined. Diffractions were obtained, in reflection, with a General Electric XRD-5 diffractometer using Ni filter radiation, from molded samples, 0.75-1.5 mm. thick. Air scattering was measured and used to correct the observed traces. In the notation of Hermans and Weidinger,13 the value of Oa*/ha* was found to be 7.2 (1 cm. = 2'; hzo* = 3.5 em.). Densities were determined by hydrostatic weighing in water and silicone oil at 25'. In addition, the heats of fusion, AQ,, of the crystalline samples were measured with the Perkin-Elmer differential scanning calorimeter, Model DSC-1, using a heating rate of 40 deg. min. -l. 111. Results
A . Atactic Polystyrene. Two series of measurements were made. In the first, the heat capacities of the dried pelIets were determined from about 85 to 480'K. The sample was then cooled to 290OK. at about 10 deg. hr.-l and the measurements were repeated, up to 380OK. The heat capacities for the two series are recorded in Table I, and the over-all results are shown in Figure 1. Specific features are discussed below. (i) Glass Temperatures. Both series of measurements extended through the glass transition region. In the first, the most conspicuous feature is the sharp peak at 367OK. Such a peak is a consequence of previous thermal treatment; it can be generated if the heating rate through the T , region is greater than the cooling rate.14 This implies that in practice such peaks will be observed more frequently in d.t.a. or similar rapid heating type of measurements; however, we have on previous occasions also observed maxima of this type in calorimetric determinations with heating rates of only 4-10 deg. hr.-1.3 I n this instance it is clear that the drying treatment at 80°, because of its proximity to the glass temperature, created the conditions necessary for the observation of this peak. Thus the second series of measurements through the T , region using the same sample, but with a different thermal history, delineates more customary behavior, with the glass transition indicated by a straightforward discontinuity in heat capacity (AC,, = 0.296 joule deg.-l g. -1). It should be pointed out that these variations are due to the fact that the different effective cooling rates through the transition region permitted the glass to attain correspondingly different residual enthalpies. l5 Under these conditions, the observed heat
2659
Table I: Atactic Polystyrene -As
reoeived-
-Annealed
C,, joules Tav
89.431 97,553 104.342 111.921 121.294 131.902 144.529 156.823 167.492 176.628 186.059 198.687 210.230 220.300 230.404 240.177 250.509 259.927 268.960 279.356 289.625 299.674 309,857 320.054 327.798 336.490 344.794 350.812 355.664 360.705 364.753 367,500 370.207 372.729 376.041 381.041 386.673 393.649 402.984 413,432 422.085 430.911 444.340 459,136 474.137
C,,
0.424 0.450 0.469 0.497 0.527 0.567 0.604 0.651 0.691 0.721 0.760 0.807 0.853 0.895 0.942 0.984 1.017 1.056 1,096 1 .'140 1.185 1.233 1.291 1.321 1.356 1.397 1.433 1.463 1.528 1.673 1.852 1.988 1,869 1.819 1.836 1.842 1.836 1.898 1.931 1.961 1.990 2.035 2.072 2.114 2.158
joules
OK.-1 g.-1
OK.-'g.-1
293.004 298.087 303.804 309.324 314.698 330.050 346.754 354.178 360.133 364.592 367.985 371.148 374.612 378.610
1.185 1,219 1.244 1,268 1.292 1.369 1.429 1.471 1.520 1.629 1.821 1.849 1.843 1.859
capacities, when the samples were subsequently heated, were characteristic of the precise heating regime used, and the relaxation time spectrum associated with this (13) G.Challa, P.H. Hermans,and A. Weidinger, hfakrcrmol.Chem., 56, 169 (1962). (14) Y. A. Sharonov and M. V. Volkenstein, Fiz. Tverd. Tela, 5, 590 (1963). (15) A. J. Kovacs, Fortschr. Hochpolymm. Forsch., 3, 394 (1963).
Volume 69,Number 8 Avgu8t 1966
2660
F. E. KARASZ, H. E. BAIR,AND J. M. O'RE~LLY
appear in the observed slopes, dC,(liquid)/dT. These regime. In the intermittent heating type of experiment (as used here), the situation is further com3.4 X 4.7 X are, respectively, 2.5 X plicated by the fact that though the heating rates in and 3.2 X low3,joule deg.+ g.-I for Dole's, Ueberreiter's, Brickwedde's, and the present measurements. the two series of measurements were nominally the same, the effective heating rate largely depended on It seems improbable, however, that sample differences the precise temperature at which each run was tercould account for such a large disagreement and the reason for the divergence remains uncertain. We minated and the residence time at that temperature. feel that some indirect support for our value lies in The glass transition temperature in this work is dethe fact that a linear extrapolation performed on this fined as the temperature corresponding to the midbasis gives excellent agreement with the heat capacity point of the discontinuity in C,. Alternatively, one of liquid isotactic polystyrene above 510'K. may construct enthalpy-temperature curves represent(iii) 60' Transition. A number of mechanical, ing the glass and liquid states and determine the intern.m.r., and other measurements show evidence for a section of the extrapolated curves. In the case of a second transition in atactic polystyrene below T,, symmetrical C, vs. T curve, as was that observed for centered around 50°.20 This has been interpreted as the annealed sample, these definitions are equivalent. being due to a freezing-in of the torsional vibrations of The latter procedure is of course thermodynamically the phenyl substituents. Secondary transitions have analogous to the method often adopted in dilatometric been observed in a large number of polymers but have measurements for finding glass temperatures. not usually been detected by heat capacity measureWe find T , for the annealed sample to be 362 f ments. However, Wunderlich and Bodily have re1'K. This value is somewhat lower than might be cently observed such a transition in atactic polystyrene expected from earlier reported dilatometric measureusing high speed d.t.a. measurements (-360 deg. ments. However, there is clearly some dispersion in hr.-1),20 and Martin and MtillerZ1similarly have rereported values. Fox and Flory,16 using polystyrene ported a broader, less pronounced maximum in runs fractions, report an extrapolated value for T gof 373'K. made at somewhat slower heating rates, 18-36 deg. for an infinite molecular weight sample which would be hr.-I. It was of considerable interest, therefore, to equivalent to a T, of 372OK. for a sample with our see whether this transition could be detected in the Beeversl' found 368.4'K. using a sample with calorimetric studies. ATn = 7 X lo4 and Zw/Zn = 3.0, while K o v a c ~ ~present ~ ~ ~equilibrium ~ Two runs between 295 and 365'K. were made using has reported values ranging from 360 to 36S°K., the atactic samples with the thermal histories dedepending again on the sample. From Dole's data9 we calculate a value of 365'K. if T, is defined in the scribed above. I n neither case did we observe any irregularity around 320'K. which could be definitely manner described above. associated with the reported transition. In the first It is probable also that the glass transition temperature of our sample is depressed by a few degrees by the run one experimental point at 309'K. lay approxi0.8% volatile material stated by the National Bureau mately 0.8% above a line joining the remainder (whose of Standards to be present (and apparently not reaverage deviation from this line was less than O.l%), but the second series of measurements failed to conmoved by the drying procedure), and differences in heating rates can account for a further variation of 2 firm this behavior, with all the points falling within about 0.1% of a linear plot. or 3'. (ii) Liquid. The heat capacity of thc atactic polyIt is felt, therefore, that as in other systems, equilibstyrene above the glass temperature increased linearly rium measurements carried out at relatively low heatwith temperature as has been observed with all other ing rates do not reveal the existence of any dispersion which might be attributable to changes in internal polymers.' Our values can again be compared with those of Brickwedde5 (though these extend only motion. (iv) Low Temperature Measurements. The heat to 4OO0K.), and Ueberreiter.' The latter values have to be extrapolated to essentially infinite molecular weight and this inevitably creates some un(16) T. G Fox and P. J. Flory, J. Appl. Phys., 21, 581 (1950); J. Polyner Sci., 14, 315 (1954). certainties, but even after taking this point into ac(17) R.B.Beevers, Truns. Faraday SOC.,58, 1465 (1962). count there are considerable differences between the (18) A. J. Kovacs, J. Polyner Sci., 30, 131 (1958). various measurements. Slightly above T,, at 380'K., (19) G.Braun and A. J. Kovacs, Phys. Chem. Glasses, 4, 152 (1963). our results and those of Brickwedde and Ueberreiter (20) B. Wunderlich and D. M. Bodily, J . Appl. Phys., 35, 103 agree to within about 0.3%, while Dole's values fall (1964). some 2% lower. However, much greater discrepancies (21) H.Martin and F. H. Muller, Makroml. Chem., 75, 75 (1964).
an;
The Journal of Physical Chemistry
THERMAL PROPERTIES OF ATACIC AND ISOTACTIC POLYSTYRENE
capacity of the annealed atactic polystyrene was also measured in the range 17 to 80'K. These results will be reported elsewhere. B. Isotactic Polystyrene. Two series of measurements using the isotactic sample with differing thermal histories were carried out. In the first, the heat capacity of a quenched sample, prepared in the manner previously described, was determined in the range 299 to 524'K. In the second series, C, of the same sample,
2661
3.or
2.6
-
lol
-
ATACTIC, AS RECEIVED ATACTIC, A M E W 0 ISOTACTIC, AYQIPHOUS 'ISOTACTIC, T
msTuiNE
2.2-
Y
Table 11: Isotactic Polystyrene
& Annealed-
Amorphous TS"
C,, joules OK. -1 g. -1
301.911 307.190 312.832 319.651 325.728 332.672 339.272 344.961 350.557 356.318 360.781 364.172 367.677 373.930 383.089 392.887 403.883 414.826 425.205 436.993 449.635 463.059 475,005 482.335 490.236 497.072 500.268 503.498 507,818 512.903 516.947 521.352
1.241 1.265 1.291 1.318 1.346 1.384 1.415 1.444 1.493 1.575 1.696 1.807 1,835 1.851 I . 883 1.888 1.882 1.796 1.755 1.546 1.563 1.965 1.981 2.076 2.559 3.254 3.988 5.032 4.604 2.290 2.305 2.323
TW
Cp, joules 'K.-1 g.-1
304.961 319.047 323.538 330,794 339.396 346.868 352.763 358.168 362,824 367.430 371.820 376.006 381.256 387.749 396.215 403.618 411.150 418.873 426.799 434.166 441.578 450.918 461.135 471.530 478.503 484.224 490.279 495.270 499,273 502,337 505.082 508.383 512,194 517.829 525.850
1.251 1.314 1,327 1.369 1.407 1.448 1.487 1.606 1.662 1.702 1.722 1.742 1.762 1.790 1.826 1.842 1.890 1.920 1.967 1.993 2.056 2.081 2.181 2.184 2.162 2.231 2.487 3.066 3.547 4.848 3.962 3.129 2.291 2.300 2.335
this time slowly cooled (-15 deg. hr.-I) from the melt to 450'K. and annealed for 24 hr. before further cooling to room temperature, was measured. In the lower part of this temperature range the results were found to be in agreement to better than 0.2% with the values obtained by Dainton* and hence no low temperature determinations were made. The calculated
i
5 1.8-
1.4-
-
450 550 'K Figure 1. Heat capacity of atactic and isotactic polystyrene. I
heat capacities are recorded in Table I1 and are also plotted as a function of temperature in Figure 1. (i) Amorphow,s Isotactic Polystyrene. The heat capacity of this material below the glass temperature was some 0.006 joule deg.-' g.-l (-0.5%) greater than the heat capacity of the annealed atactic sample. At about 335'K. this difference started to increase (Figure 2), but still remained somewhat less than 3% up to 355'K. The center of the glass transition occurs at 360 i 2'K., while ACp is 0.304 joule deg.-l g.-I. These values are practically identical with those found for the annealed atactic polystyrene. At temperatures above T,, starting at about 380'K., the quenched sample began to crystallize. This was detected by an upward temperature drift in the calorimeter during equilibration periods, and by a depression in the calculated values of Cp in this temperature region. The numerical values, therefore, between 390 and 480'K. are arbitrary in the sense that they depend on the particular time scale in which the data were obtained. Over a period of 24 hr., extensive crystallization occurred, and it is estimated that about 33 joules g. was subsequently needed to melt this sample. The maximum melting point of the material produced in the calorimeter by this heat treatment is 510 Volume 69, Number 8 August 1966
F. E. KARASZ, H. E. BAIR,AND J. M. O'REILLY
2662
1.6
-
1.5
-
1.4
-
b Y
2
latter's heat capacities are consistently lower than ours This difference amounts to 7% at 52OOK. The area of the melting peak, corresponding to the experimental heat of fusion, A&, is 31.4 1.3 joules g.-l. To calculate this quantity it is necessary first to establish the base line which represents the real heat capacity of the quasi-equilibrium mixture of amorphous and crystalline polymer in the melting region. I n the present case the following procedure was adopted. It was first assumed that the observed heat capacity curve linearly extrapolated from below T , to T , represented the heat capacity of the (hypothetical) totally crystalline polystyrene between these temperatures (see Figure 3). The resultant crystal-
*
-0
n
P
.a_ 4 3 -
1.2
280
300
-
320 T, *K
340
I
360
Figure 2. Heat capacity of atactic and isotactic polystyrene below TB. For key to symbols, see Figure 1.
1OK. From Figure 1 we note that the heat capacity of this sample, just before crystallization started, is in good agreement with the heat capacity of the atactic material at the same temperature. Furthermore, C, in this temperature region lies on the line produced by a linear downward extrapolation of C, of the liquid isotactic polystyrene. These points confirm the initial absence of crystallinity in this sample. (ii) Annealed Isotactic Polystyrene. The molten isotactic sample was cooled as described resulting in the development of considerable crystallinity, and the heat capacity was again determined. It was found that below the glass transition temperature C , was only marginally lower than that of the amorphous sample. The average difference was about 0.004 joule deg.-l g.-'or 0.3%. The shape of the heat capacity curve in the T , region was also very similar to that observed previously, except that AC, was substantially lower, as is to be expected of a partially crystalline polymer, amounting to 0.168 joule deg.-l g.-'. Thus the glass temperature, if it is defined in the manner described in section III.A.(i), is 355 f 2'K., slightly below that of the amorphous sample. No irregularities in the thermal behavior were encountered above T,. The heat capacity curve started to turn upward a t about 400OK. and a typical polymer melting peak was observed. The maximum melting point was again 510'K. This value is in good agreement wjth dilatometric data10~22~E3 and with that observed by Dole,g though it may be noted that, as in the atactic samples, the f
The Journal of Physical Chemistry
T, #K
Figure 3. Schematic diagram illustrating the method of obtaining the base line for AQ calculation. Continuous lines represent experimental results for amorphous and partially crystalline samples. Heavy dashed line indicates final base line used. For other dashed lines, see text.
liquid discontinuity in C, at T , was then divided in the same ratio as was that experimentally observed for the partially crystalline material at Tg. The straight line joining this point of division asymptotically to the semicrystalline curve just above T, would then constitute the base line if it were assumed that the degree of crystallinity, 2, remained constant up to T,. This, of course, is not the case, and one may make a further minor correction to obtain the true base line by a series of successive approximations, using the fact that (22) G . Natta, F. Danusso, and G . Moraglio, Mukroml. Chem., 28, 166 (1958). (23) R. Dedeurwaerder and J. F. M. Oth, J . chim. phys., 56, 940 (1959).
THERMAL PROPERTIES OF ATACTIC AND ISOTACTIC POLYSTYRENE
x --t 0 at T,. I n practice, it is necessary to go through an iteration process only once to define adequately the corrected line, denoted as x = f(T) in Figure 3. The heat of fusion, AQf, was then found by summing AC,.AT increments up to T,. The quantity aC, is the observed excess heat capacity referred to the base line at the average temperature of the measurement interval AT. This procedure is equivalent to assuming ideal ( i e . , additive) two-phase behavior for the amorphous and crystalline components in the sample. As is shown below, for polystyrene this appears to be justifiable. It will also be observed that the shape of the heat capacity curve is such that the first noticeable departure from the base line is about 120' below the maximum melting temperature. Given the assumptions indicated, this point is unambiguously defined. The heat of fusion of completely crystalline polystyrene, AH*,has been found by Dedeurwaerder and Oth23to be 80.3 joules g.-l, in reasonable agreement with a value of 86.3 joules g.-l reported by Danusso and M ~ r a g l i o . ~Using ~ the former result we calculate z to be 0.39 for the annealed sample. This is of the same order of magnitude as has been quoted as a representative degree of crystallinity for isotactic polystyrene in other s t ~ d i e s , though ~ ~ ~ 5 of course such values depend not only on the thermal history of the material but also on the nature of its synthesis and the method by which the crystallinity had been determined. A more significant comparison is one in which the internal consistency of this result is checked. As has been pointed out elsewhere,26in principle, x can be determined not only from AQf but also from any other thermal property which is significantly crystallinity dependent. We have been particularly interested in comparing AC, (at T,) for a number of polymers, of varying crystallinities, with the values predicted on the basis of a linearly additive two-phase model. If this model were to be applicable, then
where ACpobsdrefers to the observed quantity for a given crystalline sample with a heat of fusion, AQf, and AC," that of a wholly amorphous sample. In this work, we find 1 - [ACpobsd/ACpa] to be 0.45. While this is somewhat greater than x obtained from the heat of fusion, it should be emphasized that in this respect isotactic polystyrene is a system which adheres much more closely to the two-phase model than any other polymer that has been observed to date.26
2663
C. Other Results. It is informative to compare crystallinities of isotactic polystyrene calculated from different types of physical measurements. Although it was not possible to make these measurements on the crystalline sample discussed above, because the latter was formed in the calorimeter, an approximately equivalent sample (A in Table 111) was produced by annealing specimens, molded from the original powder, to develop maximum crystallinity. A sample (B) of intermediate crystallinity was also produced, and in addition the quenched material was available. These samples, as well as the atactic material, were then studied by differential scanning calorimetry, X-ray diffraction, and density measurements. Table I11 -Density
Isotactic Amorphous A
B Atactic Amorphous
at 25'-
X-Ray z
g . mL-1
z
0 0.26
1.053 1.080
0 0.37
0.21
1.072
0
1.047
-CalorimetryAQt,
PI
oal.
g.-1
2:
0
0.26
0 8.7 5.5
0
0
0
0.45
0.29
Calorimetric fractional crystallinity was calculated from the ratio AQf/AHf (using, as before, Dedeurwaerder and Oth's value of 86.3 joules g.-l for AHf), while the volumetric crystallinity was calculated from
The measured amorphous specific volume, VA, of 0.950 ml. g.-l is in agreement with Newman's result25 but is somewhat lower than that of Kenyon, Gross, and Wur~tner.~'The crystal specific volume, Vc, was taken as 0.885 ml. g.-l from the work of Natta, et aL2 All specific volume data were obtained at 25'. Crystallinities were calculated from X-ray diffraction traces using the procedure of Challa, Hermans, and Weidinger.l2 Results of these measurements for the various samples (24) F. Danusso and G. Moraglio, Rend. Accad. Naz. Lincei, 27, 381 (1968). (26) 8. Newman and W. P. Cox, J . Polymer Sci., 46, 29 (1960). (26) J. M. O'ReUy and F. E. Karasz, presented at 148th National Meeting of the American Chemical Society, Chicago, Ill., Aug. 1964; Polymer Preprints, 5, 351 (1964). (27) A. S.Kenyon, R. C. Gross, and A. L. Wurstner, J . Polymer Sci., 40, 169 (1969).
Volume 69,Number 8 August 1966
F. E. KARASZ, H. E. BAIR,AND J. M. O'REILLY
2664
are summarized in Table 111. The density and calorjmetric methods agree to within the experimental errors if one considers that a limitation in the former is an uncertainty of 1% in VCwhich contributes about 10% uncertainty to x. In the calorimetric method we have to rely on values of A H r and these may also be accurate to +lo%. We find that the X-ray crystallinities are lower than those obtained by the other techniques. This in part is due to the fact that these values are based on the Hermans and Weidinger procedure in which the integrated crystalline scattering coefficient is greater than the amorphous scattering coefficient by a factor of 2.16. Thus crystallinity is calculated from
x=
oc
Oc
+ 2.160~
(3)
where OC and OA are the crystalline and amorphous scatterings integrated in the interval 12' 5 28 5 30'. If we were to force agreement between the X-ray crystallinities and those obtained by the other techniques, the factor would be reduced to 1.3. The above results serve once again to illustrate the complexities of comparing crystallinities of a given polymer sample obtained by different techniques.
IV. Discussion
(i) Comparison of Isotactic and Atactic Polystyrene. Some individual points regarding a comparison of the thermal properties have already been brought out above. The most general conclusion that can be drawn is, in fact, that the isomers are markedly similar. The one exception is, of course, the ability of the isotactic form to develop a considerable degree of crystallinity within the experimental time scale of a few hours, Our results show that when this factor is eliminated and attention is confined to the wholly amorphous isomers, the values of the T , and ACp at T,, and C, in the liquid state are very nearly within experimental error. It has already been known from a comparison of earlier data6,*that the heat capacities below T , are also very similar. The fact that there is very little difference between the stereoregular and the atactic forms in their thermodynamic properties at T , is in agreement with other studies, for example Newman'sZ5 observations using mechanical measurements. An analogous conclusion regarding the volumetric properties may also be reached by considering the data obtained in the present and earlier investigations. 2 2 These show, for example, that the densities of amorphous isotactic and atactic The Journal of Physical Chemistry
polystyrene both a t room temperature and in the melt differ by less than 1%. A pertinent question which thus arises concerns the possibility that the stereoisomeric distinction between the two forms is not as complete as is currently believed. For example, it could be postulated that conventional atactic polystyrene might consist largely of isotactic sequences interrupted by relatively small numbers of random placements. The latter might effectively hinder the process of crystallization, while having a negligible effect on bulk thermodynamic properties. Such a question, although we believe worth considering, does not appear to be conclusively answerable at present. Evidence from solution measurements hardly supports the hypothesis. The differences between the average unperturbed coil dimensions for the atactic and isotactic polystyrenes'o are of the same order of magnitude as those displayed, for example, by the corresponding polymethyl methacrylatesz8in which considerable differences in the bulk properties are known to occur. It is interesting to consider further the behavior of polystyrene, particularly with respect to the glass temperature, relative to that of polymethyl methacrylate (PMMA). As is well known, in the latter system stereoregularity has a very large effect on T,. It may be observed that this difference seems to be closely linked to steric factors and, presumably, to the possibility of rotation about the carbon-carbon bonds in the main chain. Thus we may compare polystyrene and polymethyl acrylate (PMA), on the one hand, with poly-a-methyl styrene (PaMS) and PMMA, on the other. I n the latter pair, there is of course a methyl group substituent on the a-carbon in the chain. The glass temperature of the atactic and isotactic forms of each of these four polymers has been measured, and is shown in Table IV.29-31First, it may be seen that, as with polystyrene, stereoregularity has little effect in PMA. However, an atactic methyl group substitution raises T , in both polymers (i.e., PaMS and PMMA) by a substantial margin, 80 to 90'. Finally, it is seen that isotacticity both in PaMS and PMMA lowers T,, again by roughly the same amount. The symmetry of these relationships is striking, and leads to the prediction that an asymmetric substitution on the a-carbon atom in the main chain will decrease chain flexibility, thereby raising T , rela(28) I. Sahrada, A. Nakajima, 0. Yoshizaki, and K. Nakamae, K ~ l l ~ i d - Z186, . , 41 (1962). (29) R. F. Boyer, Rubber Chem. Technol., 36, 1303 (1963). (30) Y. Sakurada, K.Imai, and M. Matsumoto, Kobunshi Kagaku, 20, 429 (1963). (31) J. A. Shetter, J. Polymer Sci., B1, 209 (1963).
THERMAL PROPERTIES OF ATACTIC AND ISOTACTIC POLYSTYRENE
tive to that of the (atactic) reference polymer. Further, the isotactic stereoisomer of the disubstituted polymer will have a lower T g than that of the atactic form. We would expect these generalizations to become less applicable as the bulk of the substituents increases and the interactions of the latter become dominant.
2665
ment of TVAa/AC, with dT,/bP is satisfying and the comparison is limited by the error in bT$dP (mi10%) and the uncertainty introduced in ACp, Aa, T , V, due to different investigators using different samples. In the absence of measurements of dT,/dP, TVAaIAC, can be used as upper limit to bTg/bP. Table V
Table IV
ACp,
V,,
T,, IsoAtactic tactic
PaMS Polystyrene
170" 117b 89*
87d
OK.
IsoAtactic
A
53 PMMA 2 PMA
tactie
A
103c
8(synd.)" 42c lo8
362
" ~
-2 61
To conclude this section, we consider the contention that crystallinity can rather strongly d e c t internal motion in polystyrene, specifically the torsional vibration of the phenyl substituent (see also section 111. A. (iii)), and that this is revealed by a comparison of the appropriate heat capacities below Tg.20 We b e lieve that while the suggestion may well be valid, thermal data cannot be used as evidence in its support, for a comparison based on results obtained in the present work shows that the difference C , (crystal) - Cp (amorphous) is constant and of the order of 0.6 joule deg.-l mole-' from about 250 to 350'K. and then rises smoothly at T,. We see no evidence for a difference of 3 or 4 joules deg.-l mole-l, for example at 310'K.. as is suggested in Figure 1 of ref. 20. (ii) Pressure Coe-@cient of T,. If the glass tempera ture were a reversible thermodynamic transition of second order, uncomplicated by relaxational effects, then bTg/bP, TVAaIAC,, and Ap/Aa would be identically equal. I n these relations, Aa, A@, and AC, are the changes in expansivity, compressibility, and specific heat at T,, respectively. Using our present result for AC, of amorphous, atactic PS and data for the other qua~itities~3~ the three ratios are shown in Table V. It will be seen that, as has been recently discussed by O ' R e i l l ~ ~ ~ TVAa AD E "
