Indian Journal of Fibre & Textile Research Vol. 16, March 199 L pp. 39-45

Some studies on melt flow behaviour of poly( ethylene terephthalate)

Rajkumar Verma, Y C Bhuvanesh & V B Gupta

Department of Textile Technology, Indian Institute of Technology, New Delhi 11001 6. India

and

T Manabe & Rajesh Jalan

Modipon Ltd, Modinagar 201 204, India

Received 20 December 1990

The flow behaviour of poly(ethylene terephthalate) melt has been studied on a capillary rheome­ter in the temperature range 275-295°C. The intrinsic viscosities of the extrudates were also deter­mined, The melt flow data was corrected for the molecular weight reduction that occurs in the rhe­ometer during the measurement with the help of the intrinsic viscosity data. An empirical equation relating the zero shear melt viscosity to the intrinsic viscosity of the polymer has been derived and it is shown to predict the measured melt viscosity quite accurately. The activation energy for flow has been estimated to be 16.5 kcallmol. The viscosity profiles along the capillary radius have been gra­phically illustrated. The present analysis shows that PET melt flowing through a capillary is Newto­nian close to the capillary axis and pseudo-plastic close to the wall of the capillary.

Keywords: Capillary rheometer, Intrinsic viscosity, Newtonian fluid , Poly(ethylene terephthalate), Rabinowitsch fluid , Zero shear melt viscosity

1 Introduction One of the most critical parameters in melt spinn­

ing is the melt viscosity of the polymer which shows a strong dependence on the molecular weight and its distribution. In industry, the . molecular weight is most conveniently and quickly assessed by measur­ing the limiting solution viscosity of the polymer in a suitable solvent But it is the melt viscosity of the po­lymer which determines its flow behaviour and is of greater practical importance. However, for the mea­surement of melt viscosity, a rheometer is required, In addition to molecular weight, the melt viscosity is also dependent on the shear rate. Therefore, the need has been felt to relate the solution viscosity (in­trinsic viscosity ) of the polymer to its melt viscosity. A number of empirical relationships have been pro­posed \ ·4 which can all be generalized by the follow­ing type of relationship :

rJo= 1<vr( . .. (1)

where rJo is the melt viscosity at zero shear rate; 1<

and P, the constants; and../r, the intrinsic viscosity of the polymer. Some researchers have proposed such relationships for poly(ethylene terephthalate) (PET ) also. These relationships are generally empir­ical in nature and are based on the intrinsic viscosity

data of PET chips, It is worth pointing out that PET can degrade in the molten state and this may result in a reduction in the molecular weight of the polym­er during the transport of the melt. Hence, no inves­tigation or correlation can be taken as completely dependable unless the effect of degradation is ac­counted for. This is important since comparisons can be made only between the data obtained for po­lymers of identical characteristics, Any difference in the intrinsic viscosity values of the polymer due to degradation would only weaken the validity of such correlations .

The present work endeavours to relate melt vis­cosity to the molecular weight of the extrudate and not to the molecular weight of the chips. An empiri­cal rheological equation of state of the Arrhenius type has been developed for molten PET which al­lows direct calculation of the zero shear melt viscos­ity using the intrinsic viscosity of the extrudate, This information has further been used to describe the flow of the polymer melt and its response within a capillary by taking into account its non-Newtonian behaviour. This information could be valuable in optimizing extrusion parameters and also for de­signing melt-spinning equipment the present work aims at achieving a clear insight into some of these

39

INDI AN J. FIBRE TEXT. RES. , MARCH 199 1

factors and their effect on the flow behaviour of PET melt.

The rehological studies have been carried out on a 'Rheograph 2001 ' which is of the capillary extru­sion type. Steady-state conditions of flow are not readily obtainable with this type of viscometer, but they simulate actual conditions of extrusion and are hence useful and popular for carrying out rheologi­cal studies.

2 Non-Newtonian Behaviour of Polymer Melts Polymer melts in general are non-Newtonian, or

more specifically pseudo-plastic (shear thinning), and do not follow Newton's law of viscous flow which states that

r = rrf . . . (2)

where r is the shear stress; 1], the viscosity of the fluid ; and y, the shear rate.

The non-Newtonian nature of polymer melts is principally due to the conformational changes of the macromolecules and to a breakdown of the network structure upon deformation. Consequently, the vis­cosity of the polymer shows a dependence on the rate of deformation. The most generalized and widely used model to represent non-Newtonian flow is the Rabinowitsch model. A convenient sim­plification of the model leads to the Power-law or Ostwald de-Waele equation :

r= KY' ... (3)

where K is the consistency parameter; and n, the flow index.

This model represents the data adequately over a limited range of shear rates . But for very high and very low shear rates, the model fails since the fluid response may be Newtonian in these regions. The typical behaviour of a polymer melt is shown in Fig. 1. It indicates that in the initial region, the melt flow behaviour is Newtonian and then gradually di­gresses from Newtonian response and is better ap­proximated by an ideal Rabinowitsch fluid. The vis­cosities for an ideal Newtonian and an ideal Rabino­witsch fluid are also shown in the figure for compar­ison. The actual behaviour of the polymer can be considered to be Newtonian at low shear rates fol­lowed by non-Newtonian like that of a Rabino­witsch fluid at high shear rates. In the modified fluid 5, the transition occurs at a shear rate of y(trans­ition ) (Fig. 1) and at shear rates above this value, the fluid response is that of a Rabinowitsch fluid and is characterized by the flow index n. Because of the shear rate dependence of viscosity, the viscosity ac­ross the capillary during extrusion may not be con­stant. During actual extrusion conditions, the re-

40

>-III 0 u til

:> 0'1 ~

, , : .y( transi lion )

log she-or ratl!'

b

Fig. 1 - Comparison of actual polymer behaviour with some idealized fluid responses [(a) actual polymer behaviour, (b ) ideal Newtonian fluid, (c) ideal Rabinowitsch fluid, and (d ) modified

fluid]

sponse of the fluid near the core would be Newtoni­an due to the low shear rates prevailing in that re­gion, while towards the capillary walls, the flow pat­tern could be non-Newtonian. If the throughput rate Q is estimated on the assumption of pure Newtoni­an or pure non-Newtonian (Rabinowitsch) flow be­haviour, it would not be representative of actual throughput rate. These idealized flow behaviours are represented by Eqs (4 ) and (5).

Q= CO(!1P)1/1l . . . (4 )

and Q = CI (!1P)l ln .. . (5)

where !1P is the pressure drop; and Co and C I , the constants.

The modified fluid more closely approximates the throughput, which shows the following type of de­pendence on the pressure drop5:

where C2 and C3 are constants.

3 Materials and Methods 3. 1 Sample Specifications

.. . (6)

Poly( ethylene terephthalate) chips supplied by Modipon (India ) Ltd, Modinagar, having the follow­ing specifications were used :

Bright cylindrical shape Length, 4-5 mm Diameter, 3-5 mm Intrinsic viscosity, 0 .63 dVg Diethylene glycol content} 0.725 wt %

3.2 Measurement of Melt Viscosity

The polymer chips were dried at 130aC in a vacu­um oven for 24 h to avoid hydrolytic degradation

VERMA et al.: MELT FLOW BEHAVIOUR OF PET

during testing. Extrusion measurements were carri­ed out in 'Rheograph 2001' of Mis Gottfert which gives data on the piston speed, test pressure, melt temperature, apparent shear rate, apparent shear stress, apparent viscosity, etc. This equipment is microprocessor-controlled and allows the measure­ments to be made at different rates of throughput in a single run. But in the present investigation, the measurements were made at only one extrusion rate in a single run. This was done to enable the polymer to reach a steady state. The time for melting of PET chips allowed in each test was 3 min. Thermo-oxid­ative degradation was minimized by carrying out the test in a medium of nitrogen. The capillary of the Rheograph has a radius of 0.05 cm and is 3 cm long.

The shear rate ( y) range used in the present inves­tigation was 100-3227 s - '. In keeping with the standard practice adopted by various previous workers who have used this type of equipment, we have also assumed that the polymer melt tempera­ture is the same as is indicated by the temperature indicator of the Rheograph 2001. This assumption may not always be true as the polymer melt temper­ature may be different than the set temperature. In this study, the set temperature is reported as the po­lymer melt temperature.

3.3 Measurement ofintrinsic Viscosity

The PET extrudates obtained as a result of each extrusion run were collected. Their intrinsic visco­sities were measured using an Ubbelohde viscome­ter. The solvent system used was a mixture of phe­nol and 1,1 ,2,2-tetrachloroethane in the ratio of 60:40 (wt %) and the measurements were made at 30 ± 0.01 0c. AR grade chemicals were used. They were further purified by distillation; phenol at 180°C and tetrachloroethane at 14S-146°C.

3.4 Determination of DEC Content

The DEG content in PET was determined using the procedure3 adopted by Goodyear, USA.

4 Results and Discussion The values of shear rate, shear viscosity, shear

stress, etc. as given by the Rheograph are the appar­ent values. Moreover, they do not take into account the true nature of their variation within the capillary. Hence, the information cannot be used to character­ize the rheological beh~viour of molten PET. The only true values areQ ~nd !:1P and ,these are showIl in Table 1. Fig. 2 is a log-:Jog plot of I~P vs. Q ob-tained for various temperatpres of extrusion. .

, The plots clearly inqica'te 't:wo linear regions with certain degree of scatter. In' the first' 'region, at low

Table 1 - Data on throughput rate, pressure and intrinsic viscosity

Q- Qnorrn .f1';amplc !l. P* Temp. °C (10 - 2 cm3/s) (1O - 2 cm3/s) dl/g (107 dynes/ cm2)

275

275 275

275

275

275 275

280

280 280

280

280

280

280

28 5 285

285

285

285

285

285

290

290 290

290 290

290 290

295 295

295 295

295

295 295

1.13 1.12 4.52 4.28 9.05

13.57

18.09 17.95 22.62 22.62

27.14

1.13

4.52

9.05

13.57

18.09 22.61

27.14

1.14 4.52

9.05 13.37

18.09

22.62

27.14

1.13

4.52

9.05

13.57 18.09

22.62 27.13

1.13 4.52

9.05

13.57

18.09 22.62

27. 14

31.9

1.09 4.02

20.22

24.78

32.22

1.1

4.28

20.82

30.42

32.25

1.17

4.68

16.22

20.07 22.62

1.14

4.52

9.03 14.35

22.06 23.34

0.559 2.18

0.554 8.41 15 .16

20.88

0.559 27.62

0.56 30.77 0.578

0.556

0.547

0.572 0.57

0.579

0.557 0.554

0.556

0.576

0.593

0.564

0.564

0.58 0.571

0.582

0.56

0.559

0.559

0.566

0.582

0.563

34.05

1.98

6.30 14.34

20.23

24.83

30.48

33.45

1.58 6.53

13.26

18.99 22.95

29.66

32.56

1.48

6.33

11.27 18.01 21.37

24.63

27'.6

, 1.38 '

5.44

10.69

15.23

19.79 21.87

25 .23 -Both Q and !l.P are as observed in the experiment.

rates of throughput, the behaviour is Newtonian with unit slope (n = 1) while m the second region, the average slope is given by n= 0.613; where' the behaviour is non-Newtonictn {pseudo-plastic).

• '\ " 0.. '. j_ '.' • .

4: 1 Analysis' of Extrud~te "

The extrudate obtained from each run Was c61~ lected and its intrinsic Yiscosity ' measlired .· The re-

41

INDIAN J. FIBRE TEXT. RES., MARCH 1991

N

E ~

(1) 275 't (2) 280 "c (3) 285°C

8'4 (4) 290 0(; (5) 295 °c

8-2

&0

I I

I I

I

I I

/

/

" /

~ 78 I: ,..

"0

a. <1

g' 7·6

7· 0''----==:-------:-'=::--~:____::_!_:_-~~-;:_Z;:;__' -2·00 -1 ·75 -1 ·50 -1 ,25 -100 - 075 -0-50

log Q uncorr~l~d(cn,3Is)

Fig. 2-Dependence of pressure drop on uncorrected throughput rate

sults are given in Table 1. In the absence of oxidative and hydrolytic degradation (section 3.2), the only other possible mechanisms could be thermal and mechanical. Mechanical degradation is possible at very high shear rates, leading to cleavage of molecu­lar chains. But the data in Table 1 precludes its pres­ence in the range of throughput rates used in the present investigation as at higher extrusion rates; the degradation shown is less. This further confirms that there is no mechanical degradation. This would suggest that the degradation is mainly due to ther­mal and hydrolytic effects. At higher extrusion rates, the residence time of the polymer in the molten state is less and the resulting degradation is also less.

The scatter of data points in Fig. 2 could be ex­plained as follows. The intrinsic viscosities of the ex­trudates obtained at various temperatures of extru­sion and at different eXtrusion rates are not the same as shown in Table 1 '-'1'" II8IIlpIe)' This implies that the molecular weights of the samples are not the same. The scatter in the data is apparently because the da-

42

N

E ~ III .. I: >-

"0

a. <1 CI ~

8·2

&0

7'8

7·6

(1) 275 't (2) 280 "c (3) 285°C (4) 290 "c (5) 295°C

~~~~OO~--~1'7~S---1~~~O:------·1~·~r-~-~~-~-0~·7;5---no~·~ jog Qnormfanlts)

Fig. 3 - Dependence of pressure drop on corrected throughput rate

ta points relate to materials differing in molecular weights. The throughput rate values were therefore normalized to a reference intrinsiC viscosity. This was achieved by using the following empirical rela­tionshipS:

f' 61'", )] [r. ]5.145 _ """' 0 sample _ J' sample Qnorm - QsamPle , 11'", ) - Qsample -L1':

L """' O~ - ~

. .. (7)

where Qnorm is the normalized or corrected through­put rate with respect to the reference intrinsic vis­cosity Jr.ef (0.56 dVg) for an extrudate sample whose intrinsic viscosity is J1'" sample and which has a throughput rate of Qsamr\e, and ~1'"O)ref and "'1'"o)samPIe, the Newtonian melt viscosities of the re­spective samples. The data on corrected throughput Qnorm are also given in Table 1. The values of Qnorm

are plotted against ll.P in Fig. 3 and it is interesting to see that the scatter of the data points is now

VERMA el a/.: MELT FLOW BEHAVIOUR OF PET

reduced. The Newtonian region again yields a flow index n= 1 for the slope and the non-Newtonian region gives an average value of n= 0.635. These values are more dependable since they do not carry the error introduced by the comparison of polymer extrudates with dissimilar molecular weights.

4.2 Activation Energy

To account for the effect of temperature on the melt viscosity, an Arrhenius type of dependence has been assumed, viz.

. .. (8 )

where Ylo is the zero shear rate viscosity; A, a con­stant; E, the activation energy; R, the universal gas constant; and T, the absolute temperature in K.

An accurate determination of the activation ener­gy is very important. The value of activation energy changes with temperature and hence some precau­tions are necessary in its evaluation6. Melt viscosity measurements have been made at five different tem­peratures. Zero shear rate viscosity or the limiting viscosity has been obtained in the region where Q is proportional to !1P The logarithm of limiting vis­cosity is plotted against WOOl T (Fig. 4) and the va­lue of activation energy obtained from the slope of the plot which is equal to EI R. If the non-limiting viscosity values are used for obtaining activation en­ergy, the activation energy so obtained will be er­roneous. The activation energy with respect to limit­ing shear rate is the only absolute value. Fig. 4 gives a value of 16.5 kcall mol for the activation energy which compares well with the activation energy for dried PET obtained by most of other workers (Table 2).

4.3 Kbeological Equations

The melt viscosity of a polymer depends on its molecular weight, temperature and shear rate. An Arrhenius type of relationship can be assumed since the mobility at high temperatures is closely approxi­mated by an activated rate process. A number of workers have proposed empirical relationships for the melt viscosity of PET, most prominent among them being Gregory 1 and Manaresi 2• For the present analysis, the starting point has been Gregory 's equa­tion [Eq. (9 )] and Gregory's equation as modified by Manabe5 to include the effect of diethylene glycol on the viscosity [Eq. (10 )].

7~r-----------------------------~~

.. "' o Q.

7·5

o 7·1 c'

'" o 71)

o

1·77 1- 78 1·79 1·80 1· 81 1·82 1-83

1 OOOIT (K -1)

Fig. 4 - Logarithm of zero shear rate viscosity vs. WOOl T

Table 2 - Activation energy data

Author(s) E (kcaI/ mol )

Gregory9 13.5 Du Pont 10 13.8 Yasuda et a/." 15.0 This study 16.5 Manaresi et aU 17.0 Goodyear] 17.7 Petukhov7 30.0 Marshall and Todd8 40.0

Yl o ='/1'5145oeXp ( 6802 - 2.1157 - 0.159 (DEG)) t+273

... (10)

where I is . the temperature of the melt in °C and DEG is the wt % of diethylene glycol in PET.

In the present tnvestigation,./1' has been mea­sured using a mixture of phenol and 1,1,2,2-tetra­chloroethane in the ratio of 60:4Q (wt %) at 30°C. Manaresi el aU measured./1' using ortho-chloro­phenol solution at 25°C. The ,/1' value obtained from the latter method is higher than that obtained in the present investigation by 0.010. Taking this in­to account, the equation of Manaresi et al. can, therefore, be written, for purpose of comparison, with the present results as

';0 (8565.6 ) Ylo=V1'+O.OW )-" oexp -5.5182 ... (11 ) 1+273

.,Ai 145 (6802.1 ) Ylo =,/,, ' . exp - 2.321 t+273

... (9 ) The present investigation yields the following equation:

43

INDIAN J. FIBRE TEXT. RES., MARCH 1991

Table 3 - Measured Newtonian melt viscosity of the extrudates and the values predicted by different equations given in the text

Chip intrinsic viscosity, 0.63 dVg Chip DEG content, 0.725 wt% fr, Intrinsic viscosity measured in phenoV 1,1 ,2,2-tetrachloroethane at 30·C DEG, Diethylene glycol unit content in polymer chips (wt %)

Parameter Temp., ·C

275 280 285 290 295

frof extrudate, dl/ g 0.557 0.547 0.556 0.569 0.56

DEG, wt% 0.725 0.725 0.725 0.725 0.725

J{ru, poise

Experimental 1527 1241 1153 1067 981

Eq. (9) 1180 965 936 950 785

Eq. ( lO ) 1295 1059 1027 1043 861

Eq. (11 ) 1438 1147 1077 1058 853

Eq.( 12) 1550 1238 1182 1162 938

., <II -0 a.

?: -iii 0 u <II

>

'" 5:

3·6

3-4

3-2 1285 C

3-0

H

2'6 1 0-8 0 -6 0-4 0 -2 0 0 -2 04 (}6 0-8

rf R

Fig. 5 - Viscosity distnoution along the capillary radius assuming ideal Newtonian fluid response

"',:; 145 ( 8286 ) '70=./1' - °exp ---4.6434-0.159(DEG) t+273

. -. (12)

Eq. (12) approximates the melt viscosity more closely than its previous versions. The intrinsic vis­cosity of the extrudate rather than that of the chips has been used in the present investigation. The melt viscosity values computed using some of the other relationships along with the melt viscosity values predicted by the equation proposed in this paper are given in Table 3.

4.4 Viscosity Distribution within the Capillary

During flow in a capillary, the shear stress is not constant along its radius. PET shows shear rate de­pendent viscosity and there exists a distribution of viscosity within the capillary. For a Newtonian fluid, the response of the sample is independent of the shear rate. But for a non-Newtonian fluid,the re­sponse is more complex. Fig. 5 shows the calculated

44

3·2 ., "5 3-0 a.

Q (cm3fs) t (OC)

(a) 0 ·226194 275 (b) 0 -319038 275

2'2 (e) 0-304210 285 (d) 0-32246 285

2-0 1 0 -6 0 -2 0 0 -2 0-6

r fR

Fig. 6 - Viscosity distribution along the capillary radius assuming ideal Rabinowitsch fluid response

viscosity profiles assuming Newtonian response for PET, which indicates only temperature dependence. Fig. 6 shows the viscosity of PET along the capillary radius if a Rabinowitsch type of response is as­sumed with a flow index of 0.635. ror a modified fluid, the definition of n as referred to in Eq. (3) changes as follows.

y [ l" - I

... (13)

or

[ r/j.pl '7= Tl o 2Lrl .. . (14)

where TI is the melt viscosity at shear rates more than Ylransi lion (poise ); ?Iransition' the critical shear rate (s -1)

VERMA et al.: MELT FLOW BEHAVIOUR OF PET

" <II '0 a.

~ 'iii 0 u III

>

'" ~

~r--------------------------------'

b

2·8

2·6 Q (cm3/s) I (·e )

2-1. (0) 0·23 275 (b) 0·32 275

2·2 (e) 0'30 285 (d) 0'32 285

2·0 1 0·6 0'2 0 0-2 0·6

r / R

Fig. 7 - Viscosity distribution along the capillary radius assuming modified fluid response

where deviation from Newtonian flow starts; and £1'

the critical shear stress (dynes cm -2) where devia­tion from Newtonian flow starts.

£ I = 1]0 Ytransition _ .. (15)

For the traditional Rabinowitsch fluid, It IS as­sumed thatYtransition = 1 s - I. Since the deviation oc­curs at much higher shear rates, the modified fluid model is more appropriate. Fig. 7 shows the viscos­ity response for the modified fluid, which represents more realistically the behaviour of actual polymer melts.

5 Conclusions 5.1 The flow behaviour of PET melt has been

characterized using only raw data (throughput rate and pressure drop). The average value of viscosity index obtained was 0.635.

5.2 Mechanical degradation has been found to be absent in the range of shear rates used in this investi­gation (100-3227 s - .1).

5.3 The activation energy has been obtained with respect to the zero shear rate viscosity of the polym­er and comes out to be 16.5 kcallmol.

5.4 The empirical rheological equation incorpo­rating the intrinsic viscosity of the chips does not re­sult in good agreement between the experimental and predicted viscosity values.

5.5 The empirical rheological equation incorpo­rating the intrinsic viscosity of the extrudate and the activation energy with respect to limiting shear vis­cosity values yields the following relationship for the melt viscosity and gtves good fit with the experimen­tal data.

1]0 =,fr I4 5• exp ( 8286 - 4.6434 - 0.159 (DEG))

1+273

5.6 Pseudo-pl<;istic behaviour of polymer melts is more closely approximated by the modified fluid model. Its use in approximating the flow behaviour of PET is found to yield more realistic flow profiles.

References 1 Gregory D R, J Appl Polym Sci, 16 (1972) 1479. 2 Manaresi P, Giacheti E & Fornasari E De, J Polym Sci, C, 16

(1968 ) 3133. 3 Polyester R&D Division, Goodyear, (unpublished data ). 4 Gregory D R, Trans Soc Rhe04 17 (1973 ) 191 . 5 T Manabe (unpublished work). 6 Gupta V B, Drzal L T, Lee C Y-C & Rich M J, J Macromol

Sci, [B] Phys, 23 (1985 ) 435. 7 Petukhov B V, The technology of polyester fibers (Macmillan,

New York) 1963, 34. 8 Marshall I & Todd A, Trans Faraday Soc, 49 (1953) 67. 9 Gregory D R & Watson M T, J Polym Sci, C, 30 (1970) 399.

10 Nadkarni V M, Computer simulation of melt spinning, in Man-made fibres, Vol 1, edited by V B Gupta and V K

Kothari (lIT, Delhi ) 1988. 11 Yasuda H, Sugiyama H & Yanagawa H, Sen'i Gakkaishi, 35

(9)( 1979)T370.

45