Moisture sorption in pet influence on the thermokinetic parameters

Eur. Polym. J. Vol. 30, No. 3, pp. 339 345, 1994 Copyright © 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0014-3057/94 $6.00 + 0.00

Pergamon

MOISTURE SORPTION IN PET INFLUENCE ON THE THERMOKINETIC PARAMETERS D. LANGEVIN, t* J. GRENET 2 and J. M. SAITER2 ~URA CNRS 500 "Polym6res, Biopolym6res, Membranes" and 2Laboratoire d'Etude et de Caract6risation des Compos6s Amorphes et des Polym6res, Facult6 des Sciences et des Techniques de Rouen, 76821 Mont-Saint-Aignan Cedex, France

(Received 21 January 1993; accepted 28 May 1993) Abstract--The objective of this experimental study is to obtain some new information on the plasticization of thermoplastic polymers by water. The effect of moisture on the poly(ethylene terephtalate) (PET) thermal properties has been investigated using differential scanning calorimetry. By heating PET film samples at different rates, thermokinetic parameters such as the apparent activation energy for glass transition, the apparent activation energy, Avrami exponent and heating function for crystallization, have been determined in relation to the polymer water content.

NOMENCLATURE D= E~ = Ea = Ec =

Diffusion coefficient (cm2 sec 1), activation energy of the or-mode transition, activation energy of the fl-mode transition, effective activation energy of the crystallization transition (kJ m o l i ) , E o = effective activation energy of the glass (kJ moVl), f = volume fraction l = sample thickness (cm), n = Avrami's exponent, R = Universal molar gas constant (J K -I mol-I), r = heating rate (K min-I), r.h. = relative humidity (%), S = solubility coefficient [cm3(NPT)cm-3(cmHg)-~], Tc = crystallization temperature (°C), T~ = glass transition temperature (°C), T~ = glass transition temperature of the diluent, t = time (sec), vf = free volume, w = water content (g of water per 100 g of dry polymer), w(eq) = water content at equilibrium, ACp = heat capacity difference, E = thermal expansion coefficient (K ~), X = heating crystallization function, r = dimensionless time (Dr~F). INTRODUCTION Small a m o u n t s of a b s o r b e d water are k n o w n to induce significant changes on the physical properties o f thermoplastic polymers such as poly(ethylene terephtalate) (PET). This can create serious problems in industrial applications, for example by altering the dimensional stability of m a n u f a c t u r e d articles. The reduction of the mechanical properties of moist P E T has been attributed to a plasticizing effect by water molecules. This structural change results in a decrease in T G, the glass transition temperature, a n d in Tc, the crystallization temperature, as *To whom all correspondence should be addressed.

reported by J a b a r i n and Lofgren [l] and H a t a k e y a m a a n d H a t a k e y a m a [2] w h o studied h u m i d P E T by differential scanning calorimetry (DSC). Recently, Bianchi et aL [3] have shown that the effect of water sorption should be qualitatively different for the glass transition a n d the crystallization p h e n o m e n a . In the present work, a m o r p h o u s P E T film samples were prepared at r o o m t e m p e r a t u r e at different relative humidities a n d analysed by DSC at different heating rates from the glassy state. The experimental results have been interpreted in terms of thermokinetic parameters relative to the glass transition and crystallization. The effect of water sorption o n these parameters brings new i n f o r m a t i o n on the plasticizing effect of water on PET.

EXPERIMENTAL PROCEDURES

Experimental measurements were made on l0 and 25 mils PET films (actually 2.87+0.09 and 6.18+0.07 10-2cm thick, respectively) supplied by Kodak Co. The films were amorphous judging from their X-ray diffractometry and were used in this form. For gravimetric study, the original film was cut into circular test samples 6 cm in dia. Discs of dia 0.6 cm were sampled for thermal properties determination. Dry specimens were obtained by drying in a vacuum desiccator in the presence of P2Os until constant weights. Humidity conditioning was achieved by storing samples at room temperature (20 _+ F'C) in desiccators with relative humidities (r.h.) adjusted to 20.5, 41 and 59% by using aqueous sulphuric acid solutions at different concentrations (56, 46 and 37%). These humidity conditions were controlled by a TTH.20 Snelco moisture/temperature sensor and known with an accuracy of about 2%. Some samples were immersed in pure water (r.h. = 100%). In water sorption kinetic experiments, dry samples were introduced in the dessicators or in water then periodically removed and weighted using a model AE 240 Mettler analytical balance with an accuracy of 0.01 mg. The samples were considered as at moisture equilibrium when the moisture regain remained constant. 339

340

1.a~~ I iY

D. LANGEV1Net al.

1

[

0.9 0.8

I

0.7

. . . . . . . . . .

t

i

l

//

0.6

0.4- ~

.

.

.

.

.

.

.

0.3 ....

.....

o

t 0

0.1

0.2

0.3

0.4

0.5

0.6

sqr(tau)

....

0.2

I 0.7 0.8 0.9

y 'J

/,

/

0.4,

.

/

j/'

0.1 1

0

-/-

l.......

........ ! I

10 20 30 40 50 60 70 80 90 100 rh(~)

Fig. 1. Water sorption kinetics. Sorption rate w/w(eq) as a function of the dimensionless parameter (Dt/12)t/2. r.h. = I-q, 20.5%; x, 41%; *, 59%; and +, 100%. The continuous line corresponds to equations (1) and (2) assuming D = 4.5 10 -9 c m 2 sec - I . Thermal properties were determined using a Setaram differential scanning calorimeter (DSC 92) on sample at moisture equilibrium. Scanning rates were 2.5, 4, 5, 7, 10 and 20 K min-m. Glass transition temperatures were taken at the intersection of the extrapolated pretransition base line with the extrapolated straight line portion of the transition region curve. The peak crystallization temperatures were taken as the maximum displacement of the crystallization exotherm. RESULTS AND DISCUSSION

Moisture sorption Moisture sorption experiments have been carried out for the various relative humidity conditions defined above. Measurements of moisture content w (in g of moisture regain per 100 g of dry polymer) of 25 mils thick film samples were made as a function of time t. The kinetics of sorption agrees well with a Fickian diffusion law as shown in Fig. 1 where sorption data have been plotted as w/w(eq) vs the square root of the dimensionless parameter z = ( D t / F ) , with w(eq) being the moisture content at equilibrium, D the water apparent diffusion coefficient and l the film thickness.

Ref. [1] [5] [6] [7] [8] [9] [10] [I 1] This work

Fig. 2. Sorption of water by PET at 20°C. Experimental isotherm. Thickness of the film samples: x, 2.87 l0 -z cm; and rq, 6.18 10-2cm. By adjusting the value of D to 4.5 10-gcmZsec -~ the set of experimental data is fairly described by a single theoretical curve calculated from Crank [4]:

w/w(eq) = 4(z/~)1/2; oo

for z ~< 0.0492

(1)

1

w/w (eq) = 1 - 8/n 2 v~ ~

e x p [ - (2n + 1)2n zz ]; for z > 0.0492.

(2)

The value of D is in good agreement with the results of the literature collected from Table 1 and obtained for different kinds of PET at different temperatures. Water content w(eq) at equilibrium for 10 and 25 mils thick film samples allows one to draw the experimental sorption isotherm represented in Fig. 2. Water sorption in amorphous P E T is generally described by a linear relationship (Henry's law) between water content and relative humidity [1, 5, 6] or by a linear behaviour at low concentration followed by an up-swing effect for high relative humidity [8, 9]. In the latter case, the straight line corresponds to the Henry's law solubility while the convex part is attributed to the clustering of water molecules [12]. The observed sorption isotherm at 20°C in Fig. 2 does not display a clustering effect. It is almost linear

Table 1. Sorption and diffusion coefficientsof water in PET Type of Henry's Type Temperature sorption coefficient of PET (°C) isotherm (cm3NPTcm-3cmHg 1) DuPontamorphous film 23 Linear 6.82 DuPont Mylar A 15-20% cryst. 25 Linear 4.46 idem[5] 30 Linear 3.40 idem[5] 25 S-shaped 5.01 Quenchedfilament 30 Linear + upswing 4.03 Film3.3% cryst. 30 Linear + upswing 3.75 Vivipackmontefibre amophous 25 (Liquid water) 4.84 TeijinC° amorphous 20 (Liquid water) 6.82 Kodakamorphous 20 Linear 8.8

Diffusion coefficient (. 109cm2sec-i) 3.99 5.45 5.6 1.4 3.7 4.5

Moisture sorption in PET

341

.6,

B

Fig. 3. Schematic representation of water absorption in PET and Nylon-6. The position and orientation of the water molecules and of the polymer chains have been energy-minimized using "Sybyl/Unix" software tools. The Van der Waals surface of the water moleculeshas been represented. Water/PET system (A): 2 H20/18 monomers; Water/nylon system (B): 10 H20/18 monomers.

showing however a tendency for an S-shaped curve as previously mentioned by Myers et al. [7] who attributes the initial shape of the curve to hydrogen bonding of water to the end-groups of the polymer. Assuming linearity, a mean solubility coefficient S can be computed [S = 8.8 cm 3 (NTP) cm-3 (cm Hg)-1 or 9.3 10-3% of moisture regain per % of relative humidity] which is in good agreement with previous reported values presented in Table 1. Moisture effect At saturation (r.h. = 100%) PET water content corresponds to about 1 water molecule (Mw~ter = 18) per 10PET monomer units (MpET= 192), this is

schematically represented in Fig. 3(A). This is low compared for example to the situation in the more hydrophilic Nylon-6 [13] [w(eq)~ 10% for r.h. = 100%, MI~YLON= ll3] where this ratio reaches 6 water molecules per l0 monomers [Fig. 3(B)]. But it is apparently enough to affect PET physical properties such as dielectric constant [I l], mechanical and thermal properties [1,2,10] due to plasticizing phenomenon. The effect of absorbed water is appreciable using thermal scanning calorimetry. Figure 4 shows typical DSC curves of PET at various moisture contents for a heating rate r of 5 K/min. On each enthalpic curve we observe an endothermic reaction for T ~<80°C,

342

D. LANGEVlN et al. Table 2. Glass transition apparent activation energy r.h. (%) EG (kJmol i)

0 303

20.5 286.6

41 282.5

59 260.5

100 183.7

a

100%) while extrapolated Tc varies from 127.1 to 117.7°C. In comparison, TG of Nylon-6 is about 100°C for dry material, 71°C for 1% water content (r.h.= 12%) and - 8 ° C for 10% water content (r.h. = 100%) [13].

Glass transition

TEMPERATURE I

I

45

~

I

I

8

I

I

125

I

165

I

olc

I

205

245

Fig. 4. Typical D S C curves obtained on PET with various moisture contents, r.h. = 0% (a), 20.5% (b), 41% (c), 59% (d) and 100% (e). Heating rate r = 5 K/min.

which corresponds to the glass transition phenomenon, followed by an exothermic reaction of crystallization (100°C~< T~< 180°C), and for the highest temperatures, by a second endothermic reaction which is the fusion. It is easy to find that the glass transition (Tc) and the crystallization (Tc) temperatures slightly shift to the low temperatures while no apparent modification in the melting peak occurs when the sample moisture increases. It should be also noted the decrease in intensity of the endothermic peak associated to the glass transition. The decrease in To and Tc with respect to the relative humidity, r.h., are represented respectively in Figs 5 and 6 for the different heating rates. The extrapolated values for T~ and Tc at zero heating rate (dotted lines) give a quasi-linear behaviour in aggreement with Jabarin and Lofgren [1]. The extrapolated TG value decreases from 71.5°C for completely dried material to 56.8°C at 0.93% water content (r.h. =

80

I

I

t

~

i

I

I

I

I

'

Qualitatively the effect of absorbed water on TG in PET (Fig. 5) can be explained as due to problem of contact between the segments of the chains by the plasticizer molecules and a decrease in interchain interactions. The glass transition, which results from a change in the vibrational to the micro-brownian motion mode with increasing temperature, will need less energy and occur at a lower temperature since the chains move more easily. Byershtein et al. [14] assume that the two main modes (ct and /~) of relaxational transitions correspond respectively to the intermolecularly correlated and kinetically independent rotational motion of portions of the chains. These two modes are characterized by their effective activational energies E= and Ea with E = = ( 4 + 1)Ep. From these authors, the presence of plasticizer in the polymer decreasing the interchain interactions must lead to a fall and at the limit to a suppression of the cooperative motion of the segments. Therefore, sorption of plasticizer must be accompanied by a sharp fall in the overall activation energy and by a shift of the TG to lower values. The apparent activational energy of the glass transition in the PET/water system has been determined from the shift in Tc with change in the heating rate according to Salter et al. [15]:

dLn(r )/d( l / To ) =-AE/R

+cACpT~--Eo/R

(3)

170 < <

160 '

..... :: ...... 70 . . . . . .

"

/

~" i i _r- ' I ' . ............................... ' , . _ . _ + _ _ - , .~ j ! i

• .......t

....

i-

-J

'I | r .......... L ...... -~ i

i d

.............................. ~- ~ ~_-_.._L__,,I I "~--,~ |

I ...... l"' ......... t -

50

,

0

10

20

I /

........... "

i

i

i

4 ......

1

I I

30

40

150"

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i

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60

I

~_ ...........

i ....... j

i i ! ...... ' ~ ' i ........... ~ . . . . . . . . t . . . . . .

50 rh~)

j

, i ~- ..... J ;

3 ...............

! ..... ~.

r

r

I t ~ ..... i

i

~

.

J

"',k,

,:--.............

80

90

' .... I"

'

130 |

120

", 70

I

100

Fig. 5. D S C o f humid PET films: Glass transition temperature TG (in °C) vs the relative humidity r.h. (in %). r: n , 2.5; i-q, 5; - , 7; + , 10; and x , 20 K/min. ,, Extrapolated values at zero heating rate.

110

0

10

20

30

40

50 60 rh (%)

70

80

90

100

Fig. 6. D S C of humid P E T films: crystallization temperature Tc (in °C) vs the relative humidity r.h. (in %). r: i , 2.5; IS], 5; - , 7; + , 10; and x , 20 K/min. *, Extrapolated values at zero heating rate.

343

Moisture sorption in PET where c is a constant depending on the material, ACp is the difference between the equilibrium and glass heat capacities (constant), R is the universal molar gas constant, AE is the activation energy and EG the apparent activation energy of the glass transition. According to equation (3), a quasi linear variation of log(r) vs I/TG is observed whatever the moisture content of the samples. The calculated slopes for these data allow one to present in Table 2 the variation of EG with the relative humidity r.h. As predicted, the activational energy decreases appreciably with increasing water content (303 to 184 kJ/mol). Kelley and Bueche [16] propose another approach to the glass transition phenomenon based on the free volume theory and consider the plasticizer as a diluent which dilutes the amorphous phase of the polymer. Assuming that the free volume vf of a polymer can be related to the temperature by: vf = 0.025 + 4.8 10-4(T - TG)

(4)

where 0.025 represents the free volume at the glass temperature, and 4.8 10 4 corresponds to the difference between the thermal expansion coefficient above and below TG, and considering that the free volume contributed by the diluent may be added to that of the polymer, an expression of/)f as a function of the concentration of the plasticizer can be derived: Uf=f[0.025 + 4.8 10 4(T -- TG)] +(1 --f)[0.025 + E ( T - - T~)]

(5)

with f the volume fraction of the polymer, E and T~ the thermal expansion coefficient and the glass temperature of the diluent, respectively. At the glass temperature of the (polymer-diluent) system, vf = 0.025 so that equation (5) leads to: TG(system) = [4.8 10-4f TG + E(1 -f)T'~] /[4.8 10-4f+E(1 - f ) ]

(6)

giving a relationship for the composition dependent TG in polymer-diluent systems. Equation (6) or similar relations have been successfully applied to systems such as PS~liethylbenzene

3.5

2.5 c

./

2

/

// /.

1,5 ~/ 1 0.5 0 120

125

130

135

140

145

150

Temperature (°C)

Fig. 8. Dynamic heating PET crystallization: estimated values of n vs the temperature for r.h.: U], 0; +, 41%; and *, 59%. and PMMA-diethyl phtalate [16] and to some epoxy resin-water systems [17-19] with relatively good results. The depression in TG [ATG = TG(system) -- TG(dry polymer)] with respect to the relative humidity has been computed from equation (6) for the PET/water system assuming the thermal expansion coefficient E to be equal to 5.47 10 -4 K -l [20] and the T~ of water to be equal to 134 K [17]. These values are compared in Table 3 to the ATG corresponding to the extrapolated TG at zero heating rate of Fig. 5. It is easy to see that PET-water system presents a more depressed TG than predicted by theory. The principle of additivity of volumes may not be quite obeyed in this system which contains very low concentration of water. It has been suggested also [21] that in systems where specific interactions such as hydrogen bonds are present, then a greater than normal change in TG could be expected.

Crystallization In non-isothermal crystallization experiments, the nature of crystallization can be deduced from the following relation derived by Ozawa [22]: log{ - Ln[l - X(T)]} = log X(T) - n log r

°4

.............. i.................. t............. :;¢-;" ...........

0.8+

............... 4 ................... I ................ ;~ +4-

_1 °"T- ................. i ....................... t-7--i,~

i

i

I/

/~ 115

120

.

.

4- ...................

................... ;rl ................... T.........................

/

i

o.,~... ....................... ~ ........................ ~,~........... J---i---,-,*-.+

_ _ . o . , . - ...................... _ _

.... i ......................

................. ~':- ..........

"

............................

i

!

........................... 4.......................

............

140

145

Fig. 7. Dynamic heating PET crystallization. Crystallized fraction X(t) vs the temperature (in °C). r = 5 K/min. r.h.: II, 0; +, 41% ; and ,, 59%. EPJ 30i3--E

where X(T) is the fraction of crystallized material at temperature T, ~(T), the heating function, which depends on the growth and nucleation rates, r is the heating rate and n is the Avrami exponent describing the mechanism of crystallization. The fraction X(T) has been computed from our experimental data for different moisture contents and different heating rates. The shift of the curves in the example of Fig. 7 shows the moisture effect on the rate of conversion of

i ...............................

--if I

125 130 135 Temperature (°C)

(7)

Table 3. Glass transition temperature depression A T G = TG(system) -- TG(dry polymer) r.h. (%) A T G (K) experimental A T G (K) computed

0 0

20.5 -2.5

41 -5.4

59 -7.7

100 -14.7

0

-0.73

-1.28

-I.74

-3.0

344

D. LANGEVINet al. Table 4. Crystallization apparent activation energy r.h. (%) E c (kJ mol -l)

0 100.9

20.5 103.1

41 97.8

59 113.1

100 94.4

//

The plot of log(r) vs l/Tc for different PET water content allows one to calculate Ec from equation (8). f j~ The resulting energies are given in Table 4 while Fig. 10 compares the apparent activation energy of ;" : . / / /7" crystallization to the glass transition apparent activation energy Ec (from Table 2). It is concluded that 1 /. / / the apparent activation energy of crystallization does / ./ not change appreciably with the humidity compared to Eo. 13 This may be attributed to the partial vanishing of 120 125 130 135 140 145 150 Temperature (*C) water but is in agreement with previous studies of humid PET crystallization. Fig. 9. Dynamic heating PET crystallization: estimated Jabarin [24] has studied the isothermal crystallizavalues of log[z(T)] vs the temperature for r.h.: I-], 0; +, tion of PET from the glassy state using depolarized 41%; and ,, 59%. light intensity technique. He has shown that the the polymer. For r = 5 K/min at 128°C, crystalliza- reaction rate for the wet samples is several times tion of dry PET is beginning while 41% r.h. PET is greater than the dry samples and that the spherulite half crystallized and 59% r.h. PET is completing its growth rate and the nature of crystallization are not affected by moisture sorption. He concluded that the transformation. The plot of l o g [ - L n ( l - X ) ] vs log(r) at a given increase in the overall rate of crystallization could temperature allows one the estimation of n and result from an increase in the rate of nucleation. Bianchi et al. [3], using DSC, have shown very log[z(T)] from the slope and the intercept of the corresponding mean square lines. The resulting val- different behaviours of TC and Tc for low moisture ues for n and log[z(T)] are represented in vs the contents in PET when heating from the glassy state. They found that very low moisture contents produce temperature in Figs 8 and 9, respectively. Between 120 and 150°C, log(z) increases when the very small decreases in TG but very large decreases in Tc, with respect to the completely dry sample. Theretemperature is increased while n seems to pass through a maximum. Considering, as in Fig. 7, the fore the change in the crystallization reaction should shift in temperature of the curves, the results are quite not be related to the plasticization effect. It could similar whatever the moisture content so that, taking result from an increase in the nucleation rate generinto account the precision of the method, the effect of ated by a different sorption state of water when it is water sorption is not noticeable on the crystallization present in a very low amount. mechanism and on the heating function. The apparent activation energy (Ec) for crystal CONCLUSION growth has been also determined using the known The effect of moisture sorption at room temperaOzawa's equation [23]: ture on the thermal properties of PET films has been log(r) = - 0 . 4 5 6 7 E c / ( R T c ) + constant (8) examined using DSC at different heating rates. The sorption kinetic study (at 20°C) shows that the where Tc is the crystallization peak temperature. water diffusion process agrees well with a Fickian law assuming a constant effective diffusion coefficient of i i ! i .........i.........l.... i i i 4.5 10-9 cm2 s -l. The water sorption isotherm follows a quasi linear ' I relation with respect to the relative humidity corre~+. . . . . . /. . . . . . . . . " " - - - ~ . . . . 24o ........... ~......... ~_ ! .............. I~--..... . ..... sponding to a Henry's coefficient equal to 8.8 cm 3 (NTP) cm 3 cmHg-l (or 9.3 10-3% of water regain per % of relative humidity). The DSC analysis shows a decrease in the glass transition temperature ( A T e - - - - 1 5 ° C ) and in the ~,~o ........ i ......... ~......... I ....... ! ....... i .... ~--i ......... 4 ....... !..... crystallization temperature (ATe "" - 1 0 ° C ) with in80 .............................. :::::.:: :;-::- : -. :--:: ....... creasing relative humidity r.h. (0-100%). The Tc depression is higher than predicted by the • ! + ! ~ i I ~ i + free volume theory while, during the glass transition, ,o.......... f........ ~ ....... i......... i.......... ~ ....... f............. T ........... i....~r-the plasticizing effect of water is accompanied by a o I ! I I i I i ~ ! foreseable decrease of the effective activation energy rh(~) ,/

:./ ,,/ ,/ / / / jl

i/t-7"=

co.

Fig. 10. Glass transition and heating crystallization of humid PET: comparison of the effective activation energies EG (F1) and Ec ( I ) (in kJ/mol) of the glass transition and crystallization respectively vs the relative humidity r.h. (in %).

Concerning the crystallization, while its rate is strongly enhanced by the increase in humidity, water sorption seems to have a weak effect on the apparent activation energy of crystal growth, Avrami's exponent and heating function.

Moisture sorption in PET According to this experimental study, water should have qualitatively different influences on glass transition and crystallization phenomena. This is in agreement with previous works: the depression in Tc and EG (the plasticization), is attributed to the fall of the interchain interactions while the decrease in Tc (increase in the overall rate of crystallization) of wet samples results from an increase in the rate of nucleation induced by the presence of water molecules.

REFERENCES

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9. M. Fukuda, H. Kawai, N. Yagi, O. Kimura and T. Ohta. Polymer 31, 295 (1990). 10. C. Bastiolli, I. GuaneUa and G. Romano. Polym. Composites 11(1), 1 (1990). 11. E. Ito and Y. Kobayashi. J. appl. Polym. Sci. 25, 2145 (1980). 12. Tim deV. Naylor. Permeation properties. In Comprehensive Polymer Science, Vol. 2 (edited by C. Booth and C. Price) 1st edn. Pergamon Press, Oxford (1989). 13. C. Pai, R. Jeng, S. J. Grossman and J. Huang. Adv. Polym. Techn. 9(2), 157 (1989). 14. V. A. Byershtein, L. M. Yegorova, V. M. Yegorov and A. B. Sinani. Polym. Sci. USSR 31(12), 2719 (1989). 15. J. M. Saiter, A. Assou, J. Grenet and C. Vautier. Philosophical Magazine B, 64(1), 33 (1991). 16. F. N. Kelley and F. Bueche. J. Polym. Sci. L, 549 (1961). 17. T. S. Ellis and F. E. Karasz. Polymer 25, 664 (1984). 18. E. L. McKague Jr, J. D. Reynolds and J. E. Halkias. J. appl. Polym. Sci., 22, 1643 (1978). 19. A. T. Rodriguez, J. Sanchez, S. Lascano and A. Sanchez. In Basic Features of the Glassy State (edited by J. Colmenero and A. Agrea). World Scientific, Singapore (1989). 20. Handbook of Chemistry and Physics, 66th edn. CRC Press Inc, New York (1985-86). 21. C. A. Angell, .I.M. Sare and E. J. Sare. J. phys. Chem. 82, 2529 (1978). 22. T. Ozawa. Polymer 12, 150 (1970). 23. T. Ozawa. J. Thermal Analysis 2, 301 (1970). 24. S. A. Jabarin. J. appl. Polym. Sci. 34, 103 (1987).