Crystallization of Copolymers of Ethylene Glycol and Diethylene Glycol Terephthalate

JOURNAL OF POLYMER SCIENCE

\*OT,. S t , PAGES 277-285 (19611

Crystallization of Copolymers of Ethylene Glycol and Diethylene Glycol Terephthalate R. C. GOLIKE and W. H. COBBS, JR., Yerkes Research Laboratory, E. I . d u Pod de Nemours & Company, Inc., Buflalo, New York

INTRODUCTION The crystallization rate of polyethylene terephthalate was, initially, determined by Kolb and Izard,l who used density measurements. Their data are on bulk polymer in the temperature range of 100 to 140°C.; a t higher temperatures the rate becomes too rapid to be measured by this technique. Cobbs and Burton2extended the study to the entire temperature range over which crystallization takes place; by using thin films they were able to follow the rapid crystallization by watching the accompanying change in intensity of an infrared absorption band. A series of papers by Morgan and co-workers3--5 reports a detailed study of the crystallization processes, of the kinetics of crystallization, and of the factors which affect the course of the crystallization. One factor which, they note, may have a profound effect is the presence of copolymers; in particular they cite the presence of diethylene glycol. Additional data on the crystallization rate of polyethylene terephthalate have been obtained by the method of Cobbs and Burton.2 This study has involved : (1) a mathematical analysis and more rigorous interpretation of data in terms of the theoretical equations of polymer crystallization, and ( 2 ) a study of polymers to which diethylene glycol was added for the purpose of determining more accurately what effect the presence of this material has on the crystallization rate.

EXPERIMENTAL DETAILS AND RESULTS Polymers containing 5 and 10 mole-% (based on total moles of glycol) of diethylene glycol were prepared by exchanging the glycol mixture with dimethyl terephthalate and then polymerizing under reduced pressure a t about 280°C. The polymers were extruded from the melt a t this temperature and quenched into amorphous film. A control sample containing pure ethylene glycol was prepared. As noted by Keiler et 2 ~ l .this , ~ sample may have contained a small number of ether linkages; however, the amount was felt to be less than 2%. Films used in this study had intrinsic viscosities of 0.50 f 0.02;2 density measurements showed them to contain initially practically no crystallinity. The experimental apparatus and 277

R. C. GOLIKE AND W. H. COBBS, JR.

278

TABLE I Crystallization Rate (times in minutes)

5% DEG

Control

10% DEG

Temp., "C.

tv,

tind,

ti/,

tin&.

t v 2

tind.

110 120 130 140 150 160 170 180 190 200 210 220 230 240

29.5 6.55 2.33 1.06 0.61 0.38 0.27 0.20 0.18 0.16 0.17 0.21 0.28 0.51

9.8 2.40 1.03 0.35 0.23 0.15 0.13

23.0 4.85 1.98 0.90 0.65 0.41 0.28 0.22 0.23 0.23 0.26 0.32 0.51 -

8.52 1.79 0.82 0.41 0.23 0.17 0.13 -

16.6 4.39 2.01 1.03 0.70 0.48 0.42 0.34 0.32 0.34 0.42 0.55 1.18

5.4 1.92 1.01 0.52 0.33 0.21 -

-

-

-

-

-

-

-

-

-

-

procedure were essentially identical with those described in detail by Cobbs and Burton.2 Half times (a half time is the total time between introduction of the sample into the oven and the halfway point of the crystallization; it includes the induction time, if any) and induction times of crystallization were determined in the manner described by Cobbs and Burton;2 Table I summarixcs values of both these quantities. Three individual runs were made a t each condition, and the results were averaged to obtain the data presented here. Values of the limiting density of the crystallized samples as a function of crystallization temperature were close to those reported.

DISCUSSION Quantitative analysis of the crystallization rate data may be made in terms of the equation?

where Woisthe total mass of polymer, W ,is the mass of crystalline polymer a t time t, X , is the mass fraction of crystalline polymer a t the completion of the process, k is the rate constant, and n is an integer varying between 1 and 4 and depending upon the crystallization process. Ideally, values of li and n should bc determined by fitting degree of crystallinity versus time data to eq. (1). I n order to do this, i t is necessary either to fit data to families of curves or make a plot of In (In { Wo/[W, ( W , / X , ) ] ] )versus In t and determine the slope and intercept. Both

CRYSTALLIZATION OF COPOLYMERS

279

these methods lack sensitivity, and small changes in rate tend to be overlooked ; therefore the most accurate interpretation of our experimental data appears to be one made in terms of the crystallization half times. For the time of one-half crystallization eq. (1) becomes: In 2

=

k -

X,

tl/,n

The rate constant k is defined by the following equations:

k

G

=

n- Pc

= -

3

-AG"

(3)

Pl

Goexp

{- g}

where pc and pI are the densities of the crystalline and liquid phases, A is the nucleation rate, G is the growth rate, m is a n integer dependent upon the type of growth, E D is the activation energy of diffusion, AF* is the free energy of formation of crystal nuclei: and A0 and Go are constants. The free energy of nuclei formation AF* will depend upon the shape of the crystal nuclei; however, the temperature dependence of AF* is independent of the type of nuclei. Here, AF* may be expressed as:6

where C is a constant, u is the interfacial free energy per mole, A H , is the heat of fusion per mole of repeat unit, and T , is the crystalline melting point. Through a combination of eqs. (2) through (6), the taking of logarithms, and rearranging, a n equation expressing the temperature dependence of t,he half time of crystallizat,ion is obtained:

-

Ca3

This equation has the form:

At higher temperatures, near the melting point, the third term of this equation will change so rapidly with temperature that i t will, essentially, determine the temperature dependence of log l/tI/%.However, at lower

R. C . GOLIKE AND W. 13. COBBS, JR.

280

I

-I 0

02

04

06

08

10

L ( L J

T TwT

control, T, Fig. 1. Graph of log 1 / t 1 / ~VB.l/TIT,I(T, - T)I2. (0) 576, T , = 260'C.; and (A) lo%, T , = 255°C.

=

285°C.; (0)

temperatures it tends to become small and constant and the second term will then dominate the equation. As a check on this behavior, Figure 1 shows values of log l / t l / 2 vs. l/T,[T,/(T, - T)12for higher temperatures; as predicted, the relationship is linear. Values of T , for the copoIymers were calculated with FIory's equation for melting point depression of copolymers;7 a value of 5.4 kcal./mole for the heat of fusion was used.s If the temperature dependence of log l/tl/2 at lower temperatures is as described above, a graph of log l/t1l2vs. l / T should be linear. Figure 2 shows such a plot for data on the control sample; the dependence is definitely not linear. Williams e t al.9 have shown that the relaxation mechanism in amorphous polymers is dependent on T - T,, where T, is a function of the polymer system. It was found that log l/t1l2is a linear function of 1/(T - T,), where T , is the glass transition temperature (70°C.) ; Figure 2 shows this plot also. Such a dependence indicates that the crystallization rate a t low temperatures is limited by a relaxation mechanism, probably segment,al motion, rat,her than simple viscous flow.

CRYSTALLIZATION OF COPOLYMERS

15

10

2 0

22

1000 T-T,

25

20

IOOO/T'K~ 4

281

2 6

Fig. 2. Graphs of log l/ti/z vs. 1000/T and 1000/( T - T o ) . (0)log 1 / t 1 / ~vs. IOOO/T. (0) log l/tl/, vs. 1000/( T - T2).

The induction time for the onset of crystallization was found to have a similar temperature dependence; that is, log l / t i n d . is a linear function of l / ( T - To). Values of the constants, calculated by least squares, for plots of log l/t1l2vs. l / ( T - T,)and l/T[T,/(T, - T ) ]and for log l / t i n d . vs. 1/T - T, are summarized in Table 11. It should be noted that the TABLE I1 Summary of Constants

Function 1 Log l/t1/9 vs. ___ T - 2',

1 (A)2 T,-T

Log l/tl/z vs. T h g

l / t i n d . Vs.

1 __ 1' - T ,

Quantity

'Control

Intercept Slope

1.92 -136

Intercept Slope

0.886 -0.670

Intercept Slope

2.19 - 128

5% DEG

DEG

1.79 -125

1.50 -108

10%

0.763 0.608 -0.746 -0.764 2.12 121

1.62 -94

R. C . GOLIKE AND W. H. COBBS, JR.

282 1.c

0.5

C

2

<

-

cl

A 0

-0.:

-I.(

-I.!

0

120

140

160

180

200

220

240

260

TOG

Fig. 3. Comparison of experimental and calculated values of log experimental data and (-) theoretical curve.

t/lj2

vs. t"C. ( 0 )

slopes of the log l/tl,z and the log l / f i n d . . vs. l / ( T - T O )are in fairly good agreement, indicating the two processes are controlled by the same mechanism; all these constants appear to vary with copolymer content. I n view of the temperature dependences of log l/tlI2 discussed above, eq. (Sa) should be modified by replacing T with ( T - T,) in the second term to give :

Since the previous equations represent approximations, using of the constants from Table I1 will not yield the most accurate relation for log l/tl/,. The best values of these constants were obtained directly from eq. (8b) by the least squares method. Values of these three constants and the 95% confidence limits of each are given in Table 111. Figure 3 shows a comparison between experimental values of log l/tl,2 and the curve calculated using these constants for the control sample; similar plots were obtained for the copolymers. I t caii be seen that the agreement is quite good. Values of bo arid bl agree well with the corresponding intercepts and

CRYSTALLIZATION OF COPOLYMERS

283

TABLE I11 Constants of Equation (8b) ~~

Quantity

Control

57, DEG

957, confidence limit of b, confidence limit of 61 9577, confidence limit of 6,

1.97 137 1 .03 f0.08 f6 +0.13

1.86 126 1.32 f 0 . 10

bu bi bz

f 6

f0.20

10% IIEG 1.54 108 1.11 f0.08 k5 f 0 . 13

slopes of the log 1/tLl2vs. 1/(T - To)plots given in Table 11. However, values of bz are considerably higher than those of the corresponding plots of log l/t1l2vs. l/T[T,/(T,- T ) I 2 . The difference probably arises from the fact the second term in eq. (8b) makes too large a contribution to be neglected at higher temperatures. Values of the constants bo and b2 are seen to be accurate (95% confidence limit) to within about 5%, whereas values of b2 are accurate to 13% or less. If it is assumed that, as the above data indicate, eq. (8b) is a valid representation of the crystallization processes of this polymer, then additional deductions may be made and exact expressions for the constants can be given. Several assumptions are implicit in the derivation of eq. (7). All quantities making up the constant terms in this equation were assumed to be insensitive to temperature over the range of our data. This is a severe requirement since the range is 130°C.; however, it appears valid in view of the results discussed above. This implies that n, the exponent in eq. (I), is independent of temperature; such behavior means that the growth process is the same over the entire range studied. Although our analysis did not determine n, a treatment of data, in the manner described previously, indicated its value is about 4; this is consistent with earlier work. A value of n = 4 means the crystallization process is one of spherical growth from randomly formed nuclei. When this assumption is made, m in eq. (3) equals 3 and C in eq. (6) equals 167r/4. Under these conditions the detailed expressions for the constants in eq. (8b) are : 1

7r

l? - - l o g - - '- 4 X, b,

=

-

pf

ln2

ED' ~

R 47r

b

pC AoGo3

a3

3R (AH,)*

The dependence of cv-ystallization rate on the presence of copolymers may be seen from an examination of either the basic data in Table I or the constants of ey. (8b) summarized in Table 111. Consider first the data of Table I; above about 140°C. increasing the diethylene glycol content decreases the rate of crystallization. This is the expected effect since the

284

R. C. GOLIKE AND W. H. COBBS, JR.

inclusion of a different repeat unit makes crystallization more difficult. However, below about 140°C. the rate increases as diethylene glycol content increases. This behavior results from the fact that a t higher temperatures the rate is determined primarily by the degree of supercooling or the change in free energy upon change in state, whereas a t lower temperatures the viscosity or resistance to segmental motion of the polymer chains becomes large and limits the crystallization rate.6 Substitution of the more flexible diethylene glycol link for the ethylene glycol group reduces the viscosity or rigidity of the polymer chains. Examination of Table I11 shows that both bo and bl decrease upon the addition of this copolymer. However, the dependence of bo upon composition does not appear to be a simple one, and from our limited data its nature cannot be determined. The dependence of bl on temperature must be that of E D f ;it was found that bl is approximately proportional to e X a , where X , is the mole fraction of copolymer added. (The values of ED’are equal to 2.303 x 1.98 x b l; this value should not be compared to an activation energy of diffusion, which would be of the order of 20 kcal.) Values of bz do not, within the limits of experimental error, depend upon composition; in theory, none of the quantities making up bz should depend upon the presence of small amounts of a copolymer. The average value of bz is 1.15; for this, crS/(AHJ2equals 0.545 cal./mole; when AHu = 5.4 kcal./mole, the value of u is calculated to be 250 cal./mole. The value of u / A H , equals 0.05; this is low, but not unreasonable in view of data on other polymers.2

SUMMARY It has been shown that, with slight modification, the Avrami type of equations define the crystallization of polyethylene terephthalate over the entire temperature range of crystallization. Modification of these equations was carried out to account for the fact that crystallization a t lower temperatures is limited by a relaxation mechanism rather than by simple viscous flow. Data obtained on copolymers of ethylene glycol and diethylene glycol terephthalate have shown that the introduction of the more flexible aliphatic chain increases the crystallization rate a t temperatures where molecular motion is rate determining. At higher temperatures where the degree of supercooling is rate determining, addition of the copolymer decreases the crystallization rate. References 1. Kolb, H. J., and E. F. Izard, J . A p p l . Phgs., 20, 571 (1949). 2. Cobbs, W. H., Jr., and R. L. Burton, J . Polymer Sci., 10, 275 (1953). 3. Keller, A,, G. R. Lester, and L. B. Morgan, Phil. Trans. Roy. Sor. London, A247, 1 (1954). 4. Morgan, 1,. B., Phd. Trans. Roy. SOC.London, A247, 13 (1954). 5. Hartley, F. D., F. W.Lord, and L. B. Morgan, Phil. Trans. Roy. SOC.London, A247, 23 (1954). 6. Mandlekern, L.,F. A. Quinn, Jr., and P. J, Flory, J . Appl. Phys., 25, 830 (1954).

CRYSTALLIZATION OF COPOLYMEKY

285

7. Flory, P. J., Principles of Polymer Chemistry, Cornell Univ. Press, Ithaca, N. Y., 195, ch. 13. 8. Baker, W. P., Jr., private communication ( t o be published). 9. Williams, M. L., R. F. Landel, and J. L). Ferry, J . Am. Chem. Soc., 77,3701 (1955).

Synopsis Rates of crystallization of polyethylene terephthalate and copolymers of ethylene glycol and diethylene glycol terephthalate were measured in the temperature range of 110 t o 240°C.; this is the region of temperature in which the crystallization takes place at a measurable rate. It was found that the rate is defined by a modified Avrami type of equation over the entire temperature range of crystallization. Molecular motion, which limits crystallization a t lower temperatures, was found to be a relaxation mechanism rather than simple viscous flow; to account for this, a modification of the Avrami type of equation was made. Data on copolymers of ethylene glycol and diethylene glycol terephthalate have shown that introduction of the longer chain yields a more flexible structure; hence a t lower temperatures, where molecular motion is rate-determining, the rate is increased. At higher temperatures introduction of the copolymer decreases the crystallization rate in the manner one T o d d expect from the depression of the crystalline melting point.

R6sum6 Les vitesses de cristallisation du t6rCphthalate de polydthylkne et des copolymhres d’kthylhe-glycol e t de t6rCphtalate de dikthylhe-glycol, ont 6t6 mesurdes b des temp&-atures allant de 110°C B 240°C. Celle-ci est la region de t e m p h t u r e B laquelle la cristallisation a lieu b une vitesse mesurable. On a trouvd qiie la vitesse est d6finie par 1’6quation du type Avrami modifi6e pour toute la rdgion de tempdrature de cristallisation. La mobilit6 mol6culaire qui limite la cristallisation b des tempGratures plus basses s’explique plutBt par le m6canisme de r6laxation que par simple dcoulement visqueux. La modification B l’dquation du type Avrami pour expliquer le mkcanisme cidessus, a 6t6 Btablie. Les donnees sur les copolymkres d’6thylkne glycol ct de t6r6phtalate de diethylbe glycol ont montr6 que l’introduction d’une chaine plus longue donne une structure plus flexible; d’ob b des temp6ratures plus basses o h la mobilite mol6culaire est determinante de la vitesse, la vitesse augmente. A des temperatures plus Blevees l’introduction du copolymhre diminue la vitesse de cristallisation de la manihre dont on pourrait s’attendre en se basant sur la diminution du point de fusion cristallin.

Zusammenfassung Die Kristallisationsgeschwindigkeit von Polyathylenterephthalat und von Copolymeren von Athylenglykol- und Uiathylenglykolterephthalat wurde im Temperaturbereich von 110”bis 240°C gemessen; in diesem Temperaturbereich fintlet die Kristallisation mit messbarer Geschwindigkeit statt. Es wurde gefunden, dass die Geschwindigkeit im ganzen Temperaturbereich der Hristallisation durch eine Gleichung vom modifizierten Avrami-Typ dargestellt werden kann. Die Molckulbem-egung, melche bei niedrigerer Temperatur eine Grenze fur die Kristallisation bildet, entsprach mehr einem Relaxationsmechanismus, als einem einfachen viskosen Flicssen ; eine Modifizierung der Gleichung vom Avrami-Typ zur Erfassung dieses Effekts wurde durchgefiihrt. Die Ergebnisse an Copolymeren von Athylenglykol- und Uillthylenglykolterephthalat zeigten, dass die Einfuhrung langerer Ketten eine flexiblere Struktur liefert; daher wird bei niedrigeren Temperaturen, wo die Molekulbewegung geschwindigkeitsbestimmend ist, die Geschwindigkeit erhiiht. Bei hiiheren Temperaturen setzt die Einfuhrung des Copolymeren die Geschwindigkeit., \vie man narh der 1)eprcssion des Kristallschmelzpunkts erwarten sollte, herab.

Received December 30,1960