Comparative study of crystallization rates by d.s.c. and depolarization microscopy

Comparative study of crystallization rates by d.s.c, and depolarization microscopy C. F. Pratt and S. Y. Hobbs General Electric Researchand Development Center, P.O. Box 8, Schenectady, N Y 12301, USA (Received 17 June 1975; revised 20 September 1975) Markedly slower crystallization half times for poly(butylene terephthalate) and poly(ethylene terephthalate) are found by d.s.c, than by depolarization microscopy although similar values are obtained for isotactic polypropylene. In both the microscopic and calorimetric experiments an Avrami analysis of data on each polymer gives n ~ 3 (predetermined nucleation, spherulitic growth), over the range of crystallization temperatures investigated. Possible reasons for the observed discrepancies are discussed.

INTRODUCTION Measurements of isothermal crystallization rates by the depolarization of light in the hot stage microscope have been reported by several authors 1-s. In this method the light transmission through crossed polarizers, is monitored as a function of time with a photocell and chart recorder. Crystallization half-times can be interpolated directly from t h e I v e r s u s t profiles or, as suggested by Magill 1'2, from normalized light transmission/time plots of the form (Ic - l t ) / ( I c - I 0 ) vs. log t where I0 and Ic are initial and final intensities and I t t h e intensity at time t. Rate constants can be calculated from the Avrami equation: 0 = e -kin

(1)

where 0 is the fraction of untransformed material, k is a constant and n an integer depending on the type of nucleation and growth 6-7. With 0 = (lc - I t ) / ( I c - I 0 ) , n can be obtained directly from ln(-ln0) vs. In t plots. In spite of the widespread use of this technique it is not obvious that the depolarized light/time traces should provide a correct measure of polymer crystallization rates or should give the proper Avrami exponent. Binsbergen has shown, for example, that only when it is assumed that the birefringent entities in the crystallizing aggregates increase in number and length with time, (probably a reasonable model for spherulite development), is there a linear relationship between the birefringence and volume of crystalline material s. Other analytical techniques may show a similar sensitivity to the details of the crystallization process. Godovsky has recently indicated that for some polymers calorimetry may give n = 2 while dilatometry gives n = 3 9. In explanation he suggests that the first technique is more sensitive to the development of two-dimensional lamellae while the second reflects the formation of threedimensional spherulites. Gilbert and Hybart have noted a similar but smaller difference in d.t.a, and dilatometric measurements of aliphatic polyester crystallization rates is. In general, however, when different analyses give similar Avrami exponents on a given system other kinetic parameters such as the crystallization half-times are found to be comparable. Some recent studies of the crystallization kinetics of isotactic polypropylene, poly(butylene terephthalate) (PBT), and poly(ethylene terephthalate) (PET) by differen-

12

POLYMER, 1976, Vol 17, January

tial scanning calorimetry (d.s.c.) and depolarization microscopy, have been reported. Our calorimetric data on PBT are in quantitative agreement with those recently presented by Shultz and Stang 1°. The comparative results are noteworthy in that the two polyesters appear to exhibit similar Avrami kinetics but quite different crystallization half-times when examined by the two techniques. In contrast, similar t l / 2 values are obtained for polypropylene by the two methods.

EXPERIMENTAL PBT samples were obtained from the GE Plastics Division (Pittsfield, Mass.) (Valox ® 310 resin, [77] at 25°C in hexafluoroisopropanol (HFIP) = 1.32 dl/g), PET from Cellomer Associates ([r/] 2 ~ = 0.67 dl/g), and polypropylene from the GE Capacitor Department in Hudson Falls (Rexene PP41E3 resin). All calorimetry was carried out in a DSC-2 calorimeter and all microscopy in a Zeiss polarizing microscope equipped with a Mettler FP-2 hot stage. Light transmission between crossed polarizers was monitored as a function of time using a beam splitter and photocell whose output was channeled into a Hewlett-Packard x - y recorder. Both instruments were calibrated over the temperature range 30°-300°C using the following standards: naphthalene, (80.24°C + 0.05°C); adipic acid, (151.46°C -+ 0.05°C); 2-chloroanthraquinone, (208.95°C -+ 0.05°C); anthraquinone, (284.23°C -+ 0.05°C). Equilibrium temperatures were determined by scanning the standards at increasingly slower rates and extrapolating to zero cooling rate. In the hot stage these values were checked using a copper-constantan thermocouple sandwiched between 9 mil glass cover slips. The values agreed within -+0.2°C. All samples were melted for 2 min prior to crystallization; polypropylene at 210°C, PBT at 250°C, and PET at 290°C. No changes in the measured crystallization rates were observed on increasing the melting temperature or time and it is assumed that in all cases crystallization proceeded from the equilibrium melt. In both the calorimeter and the hot stage the samples were first cooled to an intermediate temperature* sufficiently high that no measurable crystallization took place, equilibrated for 1 min, and then dropped * For polypropylene 140°C, PBT 210°C, and PET 240°C.

S t u d y o f c r y s t a l l i z a t i o n b y d.s.c, a n d d e p o l a r i z a t i o n m i c r o s c o p y : C. F. P r a t t a n d S. Y. H o b b s 50

t and ~ c the total measured heat of crystallization. The depolarization data were reduced as described by Magill. In both cases (see Figures 3 and .5) the times in the In(--In0) vs. In t plots include induction times. Slopes were determined graphically over the range 0 = 0.2-0.8 to avoid difficulties associated with unusual birefringence variations during the

40

3O

IO

E

t-

20

/ If ,"/i

IO

c O,

1

I

40

0

61

50 A

1

0

70

80

T(oc)

r c

o.

Figure 1

Time for sample to reach thermal equilibrium as a function of supercooling, A T

IO

i

l/

i

~o

i

O

0"01

i

0-1

I

,

I

I

I

I

i

I

I

i

~ ~

~

J

I

0.1

,

~

L

i

,

,

L

I00 In t Figure 3 Avrami plot of depolarization data for polypropylene. Note shift in exponent from 3 to 2 as spherulite diameters approach film thickness at higher Tc values. O, Tc = 120°C,n = 3.0; X, Tc = 123°C, n = 2.9; A, Tc = 125°C, n = 2.9; [3, Tc = 127°C, n = 2.9; l , Tc = 130°C, n = 3 . 0

/

c c

0"01

Table I

I0

Avrami exponents obtained from d.s.c, and depolarization

data

i

I

I

I

,

i

Avrami exponent n

Polymer

Technique

polypropylene

O..s.c.

110 115 120 125 130

3.0 3.1 2.9 2.9 2.7

depolarized l igh t

120 123 125 127 130

3.0 2.9 2.9 2.9 3.0

D.s.c.

200 205 210

2.7 2.9 2.8

depolarized light

200 203 205 207 210

2.9 3.0 3.0 3.0 3.1

D.s.c.

200 205 210 215 220 225

3.1 3.2 3.0 3.1 3.2 3.1

depolarized light

210 215 220 225

2.9 3.0 3.1 3.5

I

I0

I00 lnt Figure 2 Avrami plot of d,s.c, data for polypropylene. 0 Tc = 110°C, n = 3.0; X, Tc = 115°0, n = 3 . 1 ; ~ , Tc = 120°0, n = 2.9; [], Tc = 125°C, n = 2.9; I , Tc = 130°C, n = 2.7

to the crystallization temperature. This procedure allowed any thermal stresses to be relieved and permitted more rapid equilibration at Tc. Indicator lights on the two pieces of apparatus were found to give an accurate measure of temperature stabilization. Other investigators employing the depolarization technique have used two furnaces, one at Tm and one at Tc and transferred the sample into the low temperature furnace to initiate crystallization. Our experiments with imbedded thermocouples have indicated that a fairly large but variable time may be required to reach thermal equilibrium using this technique (see Figure 1), giving rise to appreciable uncertainty in the determination of t O. By dropping the entire stage temperature with a cool nitrogen jet, t O could be accurately rLxed although the maximum measurable crystallization rate was somewhat reduced. The calorimetric data were reduced by setting 0 = AHtc/ Z ~ c where £d-/tc is the integral heat of crystallization at time

Crystallization temperatu re (°C)

poly(butylene terephthalate)

poly(ethylene terephthalate)

POLYMER,

1 9 7 6 , V o l 17, J a n u a r y

13

Study of crystallization by d.s.c, and depolarization microscopy: C. F. Pratt and S. Y. Hobbs I00

I00

I0

IC

E

/

/

," o~///

t-

(

/

///7"/ /

¢

"ZZ O"

0.I 90 ,Figure 4

,

l

,

,

,

II0 130 Tcmpcrotur~ (°C)

150

Crystallization half times for polypropylene. O, D.s.e.,

O, hot stage

A

I

I

I

I

180

200 220 240 Tcmpcrotur¢ (°G Figure 5 Crystallization half times for poly(ethylene terephthahot stage late). - - - - - , D.s.c.; - - ,

early, non-spherulitic stage of crystallization and truncation effects near the end of crystallization. Independent linear regression analyses of the data gave slopes within +0.05 of the graphical values.

I0

RESULTS Avrami plots obtained by d.s.c, and depolarization microscopy for polypropylene are shown in Figures 2 and 3 and the crystallization temperatures and the corresponding n values for each polymer are listed in Table 1. In the polypropylene samples crystallized in the hot stage above 127°C the diameters of the growing spherulites become comparable to the film thickness and two-dimensional growth ensues. This change is reflected as a shift from 3 to 2 in the slopes of the Avrami plots as shown in Figure 3. In all other cases the slopes of the isotherms remain approximately equal to 3. The crystallization half times for the three polymers are presented in Figures 4-6. In the case of polypropylene the agreement is excellent between the two techniques over the range of crystallization temperatures investigated, whereas there is considerable disparity in the case of PBT and PET. (The log scale on the ordinate minimizes the displacement in the curves which is approximately a factor of 2.) Crystallization half times for PBT samples with different thermal and processing histories as measured by the two techniques are shown in Figure 6. (The key 450•70, etc. indicates the

14

POLYMER, 1976, Vol 17, January

l

lft

,'x ",1I iI

II I ? /

////¢

r-

,' ,,

,,',,,/// x,

OI

i

160 Figure 6

1

,,Iol

I

180

I

200 Temperature PC)

i

220

Crystallization half times for poly(butylene terephthalate). X, Valox 310; O, Valox 310, moulding 450/70; O, Valox 310, moulding 450/250. Note relatively large sample to sample variation in both techniques. --------, D.s.c.; , hot stage

Study of crystallization by d.s.c. and depolarization microscopy: C. F. Pratt and S. Y. Hobbs

c~ 0 _J

-I0

0

510

t

I00

I 150

200

Temperature {oc} Figure 7 C o m p a r i s o n o f Avrami k values obtained by d i f f e r e n t techni.ques on several p o l y p r o p y l e n e s a m p l e s . A Magill=; • Marker 11 . . ' ' eta/. ; O.d.s.c.; X, depolarization

melt and mould temperatures respectively in °F.) Again the tl/2 values obtained from the depolarization experiments are approximately half of those measured by d.s.c. although the data appear to show some convergence at higher crystallization temperatures. In all cases the measured Avrami n values ranged from 2.8-3.0. It is noteworthy that there is a considerable increase in the crystallization rate of PBT resin which has been injection moulded although very little change in the viscosity average molecular weight is observed. Very likely the nucleation density is increased in these samples. A comparison of our data with those obtained by dilatometry on Profax 6513E u polypropylene and by depolarization microscopy on Shell Carbona White polypropylene2 is presented in Figure 7. The respective values for tl/2 are conveniently replaced with the respective values for Avrami's k since n = 3 in all cases. The three sets of data show surprisingly good agreement for independent measurements on three different polymer samples using three analytical techniques.

DISCUSSION At the present time we cannot offer a totally satisfactory explanation for the differences in the tl/2 vs. Tplots obtained for PBT and PET by calorimetric and depolarized light techniques. Repeated measurements showed that the differences are real and reproducible. Although it appears that the curves can be nearly superimposed by a shift along the temperature axis, repeated calibration of both instru-

ments with melting standards indicate that there is less than 0.5°C temperature error in the data points. Similarly there is no evidence that the differences can be attributed to differences in sample configuration or to heterogeneous nucleation on the glass cover slips. The observed spread in tl/2 values was maintained when microtomed films of identical thickness were used in the hot stage and calorimeter. Similar half times were measured for unfilled- and glass-filled polyester resins in the calorimeter and no preferential nucleation could be observed on the glass cover slips in the optical microscope. It has been suggested that the value oflc obtained from the depolarized light intensity curves may be too low because of improper correction for scattering. This agrument finds some support as there are other reports of anomolous maxima in some intensity time traces which may be attributed to competing depolarization and scattering effects. These peaks occur most commonly in samples which are excessively thick or which crystallize extremely rapidly. It is not considered that such effects lead to major errors in the present analyses. Data points were collected only from sigmoidal curves showing no decrease in intensity after reaching maximum height. The half-times normally fell in the steepest section of the traces requiring an unacceptably large 'error' in Ic to displace tl/2 to the values obtained by calorimetry. Furthermore, it is unlikely that such competing effects could combine to give 'correct' integral Avrami exponents. Another common reported problem in these experiments is in the selection of r, the induction time, as the slopes of the ln(-ln0) vs. In t plots are very sensitive to the value of r. However, we would expect such errors to show up as fluctuations in the Avrami n well before deivations in tl/2 are observed. Such variations were not observed. Furthermore inbedded thermocouples indicate that to, the time at which equilibrium temperature is obtained, is accurate 3% or better even in the most rapidly crystallized samples. Stein has found upon annealing quenched samples of PBT that considerable non-birefringent crystallization may occur which is detectable by low angle light scattering and density measurements but which is not detectable in the optical microscope 12. It is possible that the rate of primary spherulitic development is given accurately by the depolarization measurements while the calorimetric data more accurately reflects the overall rate of crystallization. The latter may include contributions from numerous small crystals which mirror the development of more well developed spherulites but do not contribute appreciably to increases in birefringence. In support of this argument we note that significant heat output is observed in the calorimeter, before the first signs of birefringence develop in the hot stage, especially at higher temperatures. It is also likely that secondary growth processes which proceed at a much lower rate than spherulite development make substantial contributions to the heat of crystallization but only small contributions to increased birefringence. This explanation is undoubtedly oversimplified in that several theoretical treatments have indicated that substantial secondary crystallization should introduce a large fractional component to the Avrami exponents la'14. This result is partly attributable to the fact that such growth is proportional to the time a given volume element has resided in a growing spherulite. We hope that more extensive light scattering experiments, in wliich contributions from primary spherulite growth are separated from other types of crystallization, will help to explain the observed discrepancy in half-times.

POLYMER, 1976, Vol 17, January

15

Study of crystallization by d.s.c, and depolarization microscopy: C. F. Pratt and S. Y. Hobbs REFERENCES 1 2 3 4 5 6 7 8

16

Magill, J. H. Polymer 1961, 2,221 MagiU,J. H. Polymer 1962, 3, 35 Hock, C.W. and Arbogast, J . F . Anal. Chem. 1961,33,462 Jackson, J. B. and Longman, G. W. Polymer 1969, 10, 873 Binsbergen, F. L. and deLange, B. G. M. Polymer 1970, 11, 309 Avrami, M. J. J. Chem. Phys. 1939,7,1103 Morgan, L B . J. AppL Chem. 1954,4,160 Binsbergen, F. L. J. Macromol. ScL (B) 1970, 4,837

POLYMER, 1976, Vol 17, January

9 10 11 12 13 14 15

Godovsky, Yu. K. and Slonimsky, G. L. J. Polym. ScL 1974, 12, 1053 Shultz, A. R. and Stang, L. D. GeneralElectric Analyt. Symp., Cleveland, 1974 Marker, L., Hay, P. M., Tilley, G. P., Early, R. M. and Sweeting, O. J. J. Polym. Sci. 1959, 38, 33 Misra, A. and Stein, R. S. Internal Reports to the General Electric Company, December, 1973; May, 1974 Hillier, I . H . J . Polym. ScL (A) 1965, 3, 3067 Price, F. P. J. Polym. Sci. (A) 1965, 3, 3079 Gilbert, M. and Hybart, F. J. Polymer 1974, 15,407