Film processing

T. Kanai/G.A. Campbell (Editors)

Film Processing With Contributions from M. Cakmak, G.A. Campbell, Ch. Finch, H. Ishihara, T. Kanai, T. Miki, S. Nonomura, J. Perdikoulias, W. Predohl, M. Takashige, N. Takeuchi, K. Tobita, K. Tsunashima, J. Vlachopoulos, JX. White, T. Yamada

Hanser Publishers, Munich Hanser/Gardner Publications, Inc., Cincinnati

The Editors: Toshitaka Kanai, Polymer Research Laboratory, Idemitsu Petrochemical Co, 1-1 Anesaki-kaigan, Ichihara, Chiba 299-01, Japan Gregory A. Campbell, Department of Chemical Engineering, Clarkson University, Potsdam, NY 13676, USA Distributed in the USA and in Canada by Hanser/Gardner Publications, Inc. 6915 Valley Avenue, Cincinnati, Ohio 45244-3029, USA Fax:(513)527-8950 Phone: (513) 527-8977 or 1-800-950-8977 Internet: http://www.hansergardner.com Distributed in all other countries by Carl Hanser Verlag Postfach 86 04 20, 81631 Munchen, Germany Fax: +49(89)98 12 64 The use of general descriptive names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. While the advice and information in this book are believed to be true and accurate at the date of going to press, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.

Library of Congress Cataloging-in-Publication Data Kanai, Toshitaka. Film processing / [Toshitaka] Kanai/[Gregory A.] Campbell. p. cm. - (Progress in polymer processing) Includes index. ISBN 1-56990-252-6 (hardcover) 1. Plastic films. I. Campbell, Gregory A. II. Title. III. Series. TP1183.F5K36 1999 668.4'95—dc21 98-34475 Die Deutsche Bibliothek - CIP-Einheitsaufhahme Kanai, Toshitaka: Film processing / Kanai/Campbell. - Munich : Hanser ; Cincinnati : Hanser/Gardner, 1999 (Progress in polymer processing) ISBN 3-446-17882-1 All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying or by any information storage and retrieval system, without permission in writing from the publisher. © Carl Hanser Verlag, Munich 1999 Typeset in England by Techset Composition Ltd., Salisbury Printed and bound in Germany by Kosel, Kempten

PROGRESS IN POLYMER PROCESSING SERIES

Warren E. Baker, Series Editor

Advisory Board

Prof. Jean-Francois Agassant Ecole Nationale Superieure des Mines de Paris FRANCE Prof. Dr. Ing. Hans-Gerhard Fritz Institut fur Kunststofftechnologie Universitat Stuttgart GERMANY Dr. Lloyd Geottler Monsanto Chemical Co. U.S.A. Prof. Jean-Marc Haudin Ecole Nationale Superieure des Mines de Paris FRANCE Dr. Ed Immergut Brooklyn, NY U.S.A. Prof. Takashi Inoue Tokyo Institute of Technology JAPAN Prof. A. I. Isayev University of Akron U.S.A. Prof. Musa Kamal McGiIl University CANADA

Prof. Takeshi Kikutani Tokyo Institute of Technology JAPAN Prof. S. C. Kim Korea Advanced Institute of Science and Technology KOREA Dr. Hans-Martin Laun BASF GERMANY Prof. Toshiro Masuda Kyoto University JAPAN Prof. Dr. Ing. Walter Michaeli Institut fur KunststoffVerarbeirung Aachen GERMANY Dr. Vikas Nadkarni Vikas Technology INDIA Dr. Tadamoto Sakai Japan Steel Works JAPAN Prof. Zehev Tadmor Technion ISRAEL Dr. Hideroh Takahashi Toyota Central Research and Development Laboratories Inc. JAPAN

Dr. Leszek A. Utracki National Research Council of Canada CANADA Dr. George Vassilatos E. I. Du Pont Co. U.S.A. Prof. John Vlachopoulos McMaster University CANADA

Prof. I. M. Ward The University of Leeds UNITED KINGDOM Prof. James L. White University of Akron U.S.A. Prof. Xi Xu Chengdu University of Science and Technology CHINA

Foreword Since the Second World War, the industry based on polymeric materials has developed rapidly and spread widely. The polymerization of new polymeric species advanced rapidly during the sixties and the seventies, providing a wide range of properties. A plethora of specialty polymers have followed as well, many with particularly unique characteristics. This evolution has been invigorated by the implementation of metallocene catalyst technology. The end-use of these materials has depended on the development of new techniques and methods for forming, depositing, or locating these materials in advantageous ways, which are usually quite different from those used by the metal or glass fabricating industries. The importance of this activity, "Polymer Processing", is frequently underestimated when reflecting on the growth and success of the industry. Polymer processes such as extrusion, injection molding, thermoforming, and casting provide parts and products with specific shapes and sizes. Furthermore, they must control, beneficially, many of the unusual and complex properties of these unique materials. Because of their high molecular weights and, in many cases, tendency to crystallize, polymer processes are called upon to control the nature and extent of orientation and crystallization, which in turn, have a substantial influence on the final performance of the products made. In some cases, these processes involve synthesizing polymers within a classical polymer processing operation, such as reactive extrusion. Pultrusion and reaction injection molding both synthesize the polymer and form a finished product or part all in one step, evidence of the maturing of the industry. For these reasons, successful polymer process researchers and engineers must have a broad knowledge of fundamental principles and engineering solutions. Some polymer processes have flourished in large industrial units, synthetic fiber spinning for example. However the bulk of the processes are rooted in small- and medium sized entrepreneurial enterprises in both developed and new developing countries. Their energy and ingenuity have sustained growth to this point but clearly the future will belong to those who progressively adapt new scientific knowledge and engineering principles, which can be applied to the industry. Mathematical modeling, online process control and product monitoring, and characterization based on the latest scientific techniques will be important tools in keeping these organizations competitive in the future. The Polymer Processing Society was started in Akron, Ohio in 1985 with the aim of providing a focus, on an international scale, for the development, discussion, and dissemination of new and improved polymer processing technology. The Society facilitates this by sponsoring several conferences annually and by publishing the journal International Polymer Processing, and the volume series Progress in Polymer Processing. This series of texts is dedicated to the goal of bringing together the expertise of accomplished academic and industrial professionals. The volumes have a multi-authored format, which provides a broad picture of the volume topic viewed from the perspective of contributors from around the world. To accomplish these goals, we need the thoughtful insight and effort of our authors and volume editors, the critical overview of our Editorial Board, and the efficient production of our Publisher. This volume deals with the manufacturing processes for preparing polymer products, which are very thin. These processes have developed into what is arguably the single largest

outlet for synthetic polymers. They are dependent on the best achievements in polymer design to provide the appropriate shear and extensional viscosity for successful processing. These design achievements have also produced the mechanical and optical properties so important in applications. But most important in this volume are the developments in process hardware and operating techniques that permit increasingly high production rates, optimum property development, unusual degrees of molecular orientation and the co-extrusion of multi-layer, multi-component film and sheet. This volume includes numerous contributions, industrial and academic, from Japan as well as Europe and North America and, as such, forms a very useful contribution to the film and sheet industries. Kingston, Ontario, Canada

Warren E. Baker Series Editor

Contributors Cakmak, Prof. M , Polymer Engineering Center, College of Polymer Eng. & ScL, University of Akron, Akron, OH 44325, USA Campbell, Prof. CA., Department of Chemical Engineering, Clarkson University, Potsdam, New York 13676, USA Finch, Ph.D. C. R., 1280 E. Chippewa River Rd., Midland, Michigan 48640, USA Ishihara, Dr. //., Film Research Laboratory, Toyobo Co., Ltd, 2-1-1 Katata, Otsu, Shiga 520-02, Japan Kanai, Dr. Z, Polymer Research Laboratory, Idemitsu Petrochemical Co. Ltd., 1-1 Anesakikaigan, Ichihara, Chiba, 299-01 Japan MiJd, Mr. T., Nagoya Research Laboratory, Mitsubishi Heavy Industries Ltd., Iwatsuka-cho, Nakamura-ku, Nagoya 453 Japan Nonomura, Mr. S., Katata Research Institute, Toyobo Co., Ltd., 2-1-1 Katata, Ohtsu, Shiga 520-02 Japan Perdikoulias, Dr. = ^ f * * SaJz 2.1.3.3

+

^ Qa

+

*o*

(2.1.41)

Qa

Comparison of One-Dimensional Predicted and Experimental Results

The flow pattern in a T-die is shown in Fig. 2.1.5. Several pigments are used; the upper photograph shows the section cut along the manifold length and the lower photograph shows the section cut perpendicular to the manifold length. The flow pattern represents the velocity pattern of polymer melt in a die. At the center of the die, the maximum flow is located at the center of the manifold, but it is found that the maximum flow is moved to the preland section near the edge of the die. This phenomenon is clearer for the coat hanger die shown in Fig. 2.1.6 than for the T-die and more remarkable for a small manifold radius having large clearance preland than for a large manifold having small clearance. This maximum velocity deviation is caused by the leakage flow of melt from the manifold section to the preland section. The deviation between the position of maximum flow velocity and the center of manifold (r = 0) may cause the difference between theoretically predicted and experimentally obtained results for thickness uniformity and residence time. In general, the die clearance increases with increasing die pressure, namely the die opening. One example is shown in Fig. 2.1.7. Figures 2.1.8 and 2.1.9 present a comparison of calculated pressure with observed pressure for a T-die and a coat hanger die, respectively. The predicted results agree with the experimental ones if the accurate die clearance is input. Figure 2.1.9 shows one example for the residence time distribution of the T-die shown in Fig. 2.1.5. 2.1.3.4

Practical Simple Coat Hanger Die Design from Analytical Equations

The theory based on polymer flow inside a flat die was described in Section 2.1.3. By using the basic theory, a flow analysis of the coat hanger die shown in Fig. 2.1.4 leads to the following useful equations for die design. 2.1.3.4.1 Die Pressure Drop AP

where Qa and L0 are output rate and die width, respectively; T1 and ht are length and gap under choker bar and die land, respectively; n is the power law index; and C is defined as the constant for a specific polymer melt. C = \-TTT\(T-\

2 (n + 2) \2rjJ where rj0 is zero shear viscosity.

(2L43)

Figure 2.1.5

Flow pattern in a T-die

Flow pattern in a coat

Figure 2.1.7 Die lip clearance as a function of pressure for different process conditions (resin, temperature, and output rate) P o b s = Observed pressure resin characteristics at 240 0 C: F700N rj0 = 19,000 poise, « = 1.65; F200s Y]0 = 80,000 poise, n = 2.29

Die Lip Clearance (cm)

Figure 2.1.6 hanger die

!DEMITSU PP P700N IDEMlTSU PP F200S

24Ot

Pobs (kg/cm2)

27CrC

1

24CTC 270C

Pobs (kq/cm 2 )

IDEMITSU PPF700N IDEMITSU PPF200S IDEMITSU PPE100G

Figure 2.1.8 Comparison of calculated pressure (P calc ) with observed pressure (P0^8) for a coat hanger die. Resin characteristics at 240 0 C: F700N rjQ = 19,000 poise, « = 1.65, F200S ^ 0 = 80,000 poise, « = 2.29, ElOOG *70 = 180,000 poise, n = 2.65

Pcaic (kg/cm 2 )

Equation (2.1.42) shows that the die pressure depends on the flow rate, geometry of the die, and viscous properties of the polymer melt. 2.1.3.4.2

Optimum Manifold Design

Optimum manifold design [22], which gives the uniform thickness at the die exit, is given in the following equation:

f =f

(2-1.44)

Equation (2.1.34), with the aid of Eqs. (2.1.35) and equation (2.1.44), gives the next equation: R2(n+3)/n =

^n ^n /l + (dt/dzf\ \ (dt/dzf )

{

where R is the manifold radius, t is the preland length, H is the preland gap, and n is the power law index, (n 4- 3W n+2

«= V / ^

(2 L46)

-

2n(n + 2) Residence Time (sec )

T-Die

Lo= 36.5 cm

Experiment Theory

2

(cm )

Figure 2.1.9 Calculated ( ) and observed ( ) residence times as a function of z for a T-die. Condition: resin PP (F200S), temperature = 230 0 C, output rate = 2kg/h

R/RL

n= 4

Figure 2.1.10 Effect of power law index n on the rate of increase R/RL in a manifold radius

ZIL

In the case of the preland length t as a linear function of z, t is defined as follows: t = t0 +az

(2.1.47)

where a is constant. The manifold radius R is obtained as follows:

R

roi^M^p 27r(»+2)fl11

L

J

The dimension of the radius of the manifold at the entrance RL is:

Another equation derived from Eqs. (2.1.48) and (2.1.49) provides the optimum rate of reduction of the manifold diameter along the width of a coat hanger die as follows: R

/z\1/(w+3)

rrir)

24)/2 - (P17 +P21)/2

(2.1.64)

For the ^-direction:

These pressure differences along with the shear stress values can then be substituted into Eqs. (2.1.55) and (2.1.56) to give; Pu+Pn

P24+P27 2JV + 1 It](I) 2Ax

—2

Pu +P24 Pn +Pn

—2

0 1 ^

J^AW2~^Ql5=

2

2N+\2n(I)2Ay^

JTA^If116

2

(

=0

}

(2AM)

The continuity equation for this control volume 5 takes the form: -Qs-9a+Qis+9u

=0

(2.1.67)

The continuity equation for control volume 2 becomes: -8 cm

H = C1 (kcal/m2h 0C) 2

(3.1.2a) 0

h = C2Zz" (kcal/m h C)

(3.1.2b)

where C1 is 50 for LDPE, 40 for LLDPE, and 35 for HDPE. C2 has values of 1140 for zF of 7 cm, 1020 for zF of 9 cm, and 836 for zF of 12 cm; a is about 1.6. Figure 3.1.16 shows the effect of zF on h for the LLDPE near the die. Values of h up to 70 are found for zF equal to 7 cm. The variation of the frost line height is accomplished through changes in air velocity, blowing along the length of the bubble. Increasing air velocity decreases the frost line height. Measurements of air velocities and their influence on frost line height are indicated in Fig. 3.1.16. This suggests a modified correlation of the form: zK cm where U0 is the initial air velocity.

h = c'UlA (kcal/m2h 0C) a

2 o

h = c2/z (kcci\/m h C)

(3.1.3a) (3.1.3b)

Strain R»U(i« C ")

Bubble Temperature ('C)

Bubble Velocity (cm/tec)

FLH B VL/Vo

Distance from Die (cm)

Figure 3.1.8 Local velocities V1, V2, deformation rates dPU, (Jl11, and temperature T along the length of the bubble for HDPE with vL/v0 = 4, B = 3.5, z F = 12 cm

It would be desirable to express h in a dimensionless form of the type described originally by Nusselt as: hL/kair = C{LUPaiv/n^f(c^r/Kj

(3.1.4a)

or hL/kak = CXLUPaJrjakr

(3.L4b)

where k is thermal conductivity, c heat capacity, and the subscript "air" refers to values for air. Equation (3.1.4b) is a simpler form that may be used. Because air is the only medium involved, the second dimensionless group, the Prandtl number, can be combined with C to give C. Before we consider applying Eq. (3.1.5), we should decide the initial point from which to measure L on the bubble. We chose to define the position of the maximum of the local heat transfer coefficient as L = 0. Those initial points are 6.5 cm for a frost line height zF of 7 cm, 6.5 cm for zF of 9 cm, and 7.0 cm for zF of 12 cm from the die exit. L is the vertical distance from the initial point. The maximum air velocities are chosen to be the value of U.

Strain Rata d,/, duUac'1) Figure 3.1.9(a) Local deformation rates dn, d12 along the length of the bubble for various frost line heights with vL/v0 = 4, B = 3.5; LDPE

Figure 3.1.9(c) Local deformation rates dn, d12 along the length of the bubble for various frost line heights with vL/v0 = 4, B = 3.5; HDPE

FLH FLH

FLH

Strain Rate d-.cMtt

(l+72)(A+B?2)ri0 4~n

(3.2.9)

(3 2 10)

- '

where r and h are the dimensionless bubble radius and thickness, respectively. The prime and double prime represent the first- and the second-order derivative with respect to the distance from the die. The dimensionless inflation pressure, B, and dimensionless axial force, A9 are defined as B=^

(3.2.11)

A^-B(rA2 (3.2.12) Qno VoJ where Q is the polymer volumetric flow rate, r0 is the die radius, and ry is the bubble radius at the freeze line. If we extend the simulations using these generalized Newtonian models above the freeze line, unrealistic bubble radii and velocity profile are predicted above the freeze line as reported by Cao and Campbell [8]. It was found that above the freeze line, the generalized Newtonian models predict a sharp decrease of the bubble radius and rapid increase of the film velocity (Fig. 3.2.4). This is not consistent with reported data on the blown film process. Moreover, Campbell and Cao [9] demonstrated that the predicted force balance at the freeze line:

Fz

(3.2.14)

where X is the relaxation time conventionally defined as a ratio of the viscosity to the modulus, X = rj/G, and D is the deformation rate. The subscript (1) represents the convected derivative, in the notation of Bird et al. [12]:

9T.V

+

9T,V

tik dvi

dv-

^=^ ^wk- trt^

(3 2A5)

-

Restriction to one-dimensional heat transfer analysis at steady state leads to stress independents in the normal direction, the circumferential direction, and time:

O2

0C3

at

Moreover, since xtj = 0 and Dtj = 0 if/ ^j9 in shear-flow, Eq. (3.2.14) then is expanded into Eq. (3.2.17): 4 v ^ - 2 T 1 1 A i ) + T 11 = If]Dn x ( v ^ - 2T22D22^j + T22 = InD22

A

(

V

^"

2 T 3 3 J D 3 3

)

+ T 3 3 = 2

^

(3.2.17)

3 3

This rheological equation can now be related to the force balance developed by Pearson and Petrie [1 to 3]. For a detailed description of the derivation and method used to obtain the results reported here see Cao and Campbell [8, 12]. Numerical results for the Maxwell model in isothermal and nonisothermal conditions were reported previously by Petrie [6], Wagner [13], Luo and Tanner [10], and Cain and Denn [H]. These simulations appear to be fine below the freeze line. However, it has been found that if the Maxwell model is extended beyond the freeze line, similar unrealistic bubble radius and velocity profiles as found for the Newtonian model are predicted [8,12]. The predicted bubble radius rapidly decreases and the velocity appears to be unbounded (Fig. 3.2.5).

3.2.2.3

Maxwell Model above the Freeze Line

The assumption of no deformation above the freeze line leads to incorrect predictions for the Maxwell model. In the case of D = 0, when this model is integrated it leads to: A

+ T =0

(no sum)

(3.2.18)

at

T^T^expf-f

jdA

(no sum)

20

Bubble Radius

Gupta's data of PS, Run Maxwell Model

Distance from Die Figure 3.2.5 Response of Maxwell model when extended above the freeze line

(3.2.19)

By this prediction, the stress components would decay exponentially in the three principle directions. If there is no deformation above the freeze line, both the film thickness and the bubble radius would be constant, leading to a constant cross-sectional area. If the takeup force is a constant, the stress in the machine direction should be a constant. Also, if the internal pressure of the bubble is a constant, the hoop stress should be a constant. These process observations are not consistent with the predicted exponential decay above the freeze line (Eq. 3.2.19). Thus, it appears that the Maxwell model also cannot be extended beyond the freeze line.

3.2.2.4

Other Literature Models

Campbell and Cao [9] have also tested several other models that have been documented in the literature but have not been used in the simulation of the blow film process. Concepts not predicted by the Maxwell model such as anisotropy, nonaffine motion, thermodynamic irreversibility, and reptation are addressed by these models. These models were tested for blown film simulation using Gupta's polystyrene data as a reference amorphous polymer. Giesekus [14] proposed an anisotrophic model from a molecular argument to handle the anistropic property of the polymer melts or concentrated polymer solutions due to the interaction among the oriented polymer chains (dumbbells). AT(1) + T + (XT • T = 2rjD

(3.2.20)

where a is a parameter. The maximum and minimum anisotropy correspond to a = 1 and a = 0. Phan and Tanner [15] developed a network model that incorporates nonaffine motion of the polymer chains. Physically, nonaffine motion means that the relaxation of the polymer chains may be faster than the macroscopic deformation; the polymer chains retract immediately after the entire piece of the polymer is deformed. The PTT model incorporates nonaffine motion by using the Gordon-Schowalter operator. The PTT model leads to the constitutive equation: AT(1)+T + ^(tTT)T = 2l/£>

(3.2.21)

where a is an empirical parameter and G is the modulus. The model reduces to the Maxwell model if a — 0. Mathematically, for thermodynamically reversible models, the convected derivative, which contains the deformation rate tensor, has to approach zero at very rapid deformation rates, because otherwise the change caused from including the deformation rate tensor cannot be balanced by other terms in the constitutive equation. To describe the irreversible motion of the polymers, for example, a double step strain, White and Metzner [16] proposed a modified Maxwell model:

where

(3.2.22)

where the subscript WM represents the White-Metzner model. The relaxation time 1WM is a function of the second invariant of the deformation rate tensor, where a is an empirical parameter. Another thermodynamically irreversible model, which was proposed by Larson [17], was examined. Larson's irreversible model was developed from his reversible model, which was considered to be a differential approximation of the Doi-Edwards reptation model. Instead of using the Gordon-Schowalter expression, a modified Doi-Edwards [18] expression was employed to incorporate nonafflne motion. Larson's irreversible model is expressed as:

^( T ( 1 )

+

^

{ T

+ GS)l(T

+ G3):

Z)]

+)'/+T =

2rfD

(3 2 23)

' -

where oc is an empirical parameter within the range of zero to unity. The term in the brackets, [... ] + , is taken to be the value of the enclosed quantity if it is positive; if the enclosed quantity is negative, the term is set to zero. Recently Alaie and Papanastasiou [19] modeled the nonisothermal blown film process using integral models of the K-BKZ type. In all of these cases, if the models are extended above the freeze line, the radius tends to zero and the viscosity becomes unbounded. It is thus a judgment call as to when to stop the simulation and as to what is solidlike behavior. One way around this problem is to use rheological models that naturally shift from "liquid" like to "solid" like behavior.

3.2.2.5

Aerodynamics

The effect of the air from the air ring was first evaluated by Cao [21] and reported by Campbell et al. [20]. In this evaluation, a momentum balance was undertaken on the wall jet that is emitted from the air ring more or less parallel to the bubble. A simultaneous macroscopic mass and energy balance produced a function that, when the jet entrainment was included, produced very good predictions of the jet velocity as a function of distance from the air ring. An additional AP term, the normal pressure on surface of the bubble, was discovered that should be vectorially added to the bubble pressure:

AP = -£ cos(0) ^Rs dz

(3.2.24)

Here C is related to the initial momentum of the air as it exists the air ring and Rs is the local radius of the bubble. It was found that when this function was included in the force balance that the major effect is to change the shape of the bubble below the frost line. This, of course, changes the strain rate and strain history of the polymer as it is being stretched.

3.2.3

Fluid-Solid Models

3.2.3.1

Viscoplastic Model

The simulations using viscous or viscoelastic models have been found to be lacking when they are extended beyond the freeze line. A very simple viscoplastic model used by Cao [21], the Bingham model [22], introduced the concept of yield stress into blow film analysis. When the imposed stress (or its second invariant) is larger than the yield stress, material will flow, and if the stress is less than the yield stress, fluid will not deform. The concept of yield in polymers is different from that in metal and has been somewhat controversial for the past years. Although most polymers do not display a precise yield point, the yielding beahviour does appear to exist for amorphous polymers, reported by Beatty and Weaver [23] and Chow [24]. It appears that as an "engineering tool," the yield stress may provide a reasonable explanation for the observation that the bubble radius remains constant above the freeze line. The Bingham viscoplastic model is consistent with the assumption of no deformation above the freeze line. Although the Bingham model produced more qualitatively correct simulations, there were some flaws. This might be an expected result, as the Bingham model can be cast as a generalized Newtonian model [21].

3.2.3.2

Visco-Plastic-Elastic Model

Bubble Radius

The lack of success in the simulations using viscous, viscoelastic, and viscoplastic models led to the creation of a new rheological model, a visco-plastic-elastic model. The model is a phenomenological modification of the Maxwell model. The details of its development can be found in Cao and Campbell [8, 12]. Using this model the process is rheologically divided at the plastic-elastic transition (PET). The PET is defined as the position above the die where the deformation changes from a fluid dominated viscoplastic deformation to a solidlike elastic

Current model No yield stress No strain hardening

Distance from Die Figure 3.2.6 Response of visco-plastic-elastic model to parameter changes

deformation. In this model the change in flow mechanism is related to a yield stress criterion. The model can be cast as follows: f 4fft(i) + T = 2riefrD if y n ; > r eff /V3

I

2

T = 2GeffE iff T ^ ; < W V 3 * = 1/1-Z2IT-

^ C 4L^^ X P (-^P)^' >w = n G8S = G(H-O

(3.2.26)

"*= t _ ^/V3 where the subscript (eff) indicates an effective quantity, i/f is a measure of polymer strain hardening, Ix and I2 are the first and second invariants of the finger tensor, and £ is a structure memory function. As with all models to date the modulus had to be adjusted to fit the data. For viscosity, we used the expression given by Gupta. The equilibrium yield stress and its temperature dependence were not reported in Gupta's study. They have been treated as two parameters in the simulation. This of course adds to the adjustable parameters. The yield was defined as: Y= 10" 15 Qxp(AEy/RT)

where the activation energy of yield is assumed to be similar to that of viscosity. It should be pointed out that these parameters were not adjusted for each run number and, in fact, the simulation result is not very sensitive to the value of the equilibrium yield stress. Varying the yield stress over a range of 50% may cause the predicted PET to move up or down with respect to the die without much change in bubble shape if other parameters are slightly adjusted. The hardening constant, Q1, defined in Eq. (3.2.26), is another parameter. We have assigned a value of 0.06 to it in the simulation of Gupta's data, and find that it produces a fit. The hardening constant is also not adjusted with the run number. The parameters that we adjusted in the simulation with the sample number are initial angle of the film contour, initial hoop stress, and a factor to modify modulus, CG. The results of this model are shown in Fig. 3.2.6. We see that by setting the appropriate constants to zero the model reduces to the Maxwell or Newtonian model. For more complete discussions of this model the reader is referred to [8, 9, 12,21].

3.2.3.3

Two-Phase Liquid Models

Modeling the mechanics of film blowing using two phases was introduced by Campbell and Cao [25], who proposed that the film, in the tube-forming area, is composed of two layers.

This work was followed by research of Yoon and Park [26] in which the same technique of Campbell and Cao was extended to Newtonian and Maxwell rheological layers. The surface temperature of the film differs from the bulk average temperature (through thickness) by as much as 15 to 20 0 C in the tube-forming area [27]. This supported the concept that the film has a cooler crystalline layer near the surface and a hotter fluid layer in the interior. Extending the concept of [8,12] yield stress as a criterion for cessation of radial deformation beyond the freeze line leading to plastic-elastic transition (PET), the two-phase analysis of the film blowing process incorporates both viscoelasticity of the melt and yield stress [28] in the solidlike phase as a criterion for the demarcation between predominantly plastic to elastic deformations. This essentially plastic to elastic behavior in the solidlike phase provides a rheological constraint to define the point where the film remains parallel to the tube center line and replaces the traditional kinematically defined freeze line [29].

3.2.3.4

Two-Phase Crystalline Model

Analysis of heat transfer in the film blowing process is essential because the thermal state of the material defines the rheological state of the polymer during the course of the process. Polymer rheological properties are temperature dependent and thus the thermal state of the polymer dictates the polymer's response to an external force. Polymers can be treated Theologically as a combination of a viscous liquids or as elastic solids. All combinations of these effects can be important depending on their temperature. The highly nonisothermal environment in the film blowing process leads to very distinct behavior of the polymer melt at different stages of the process. In film blowing, the heat is transferred from the film to the surroundings predominantly from the outer surface of the bubble by convective and radiative means. In steady-state operations the energy transmission to the trapped air inside the bubble is treated as insignificant. As a result of the temperature gradient across the film, for a bubble of finite thickness, the surface temperature of the bubble reaches the crystalline melting point of the polymer well below the freeze line. Because of the finite thermal conductivity of the polymer melts and limiting heat transfer rates, we cannot assume an instant crystallization of melt throughout the film thickness. So it is believed here that after the inception of the crystallized phase on the film surface, its thickness grows as the film moves toward the nip rolls and more heat is transferred from the film to the surroundings. An idealistic separation of the two phases is shown in Fig. 3.2.7. The rheological behavior of the two phases is believed to be drastically different and hence we use appropriate rheological equations of state for both phases in this investigation. Cessation of the deformation in the radial direction is attributed to the small applied force in that direction instead an infinite viscosity [29]. The Levy-Mises yield criterion is used to define the plastic and elastic deformations of the crystallized phase. This defines the beginning of the reversible stretching on a rheological basis. An upper convected Maxwell viscoelastic equation of state is used to describe the rheology in the liquid region. Before the crystallized phase stops yielding, it is modeled as a perfectly plastic material. For numerical purposes, the modeling area of interest is divided into four distinct regions (Fig. 3.2.7). Region 1 starts at the die and consists only of the liquid phase of the melt. Region 2 begins when the surface temperature of the film reaches the crystallizing temperature of the melt.

This temperature need not necessarily be the crystallization temperature of the polymer under quiescent conditions (supercooling can be taken into consideratioin). It ends when the yield stress of the crystallized phase exceeds the effective applied stress. This plastic to elastic transition replaces the classic freeze line. Deformations in the third and fourth regions are elastic and are negligible owing to the high modulus of the crystallized phase. The third region allows crystallization to continue over the entire thickness of the melt after the transition has been achieved. The kinematic analysis follows Eqs. (3.2.1) to (3.2.7).

3.2.3.5

Constitutive Relationships

In this section we discuss again some of the rheology previously mentioned because it is used in a different context. The total stress tensor components are the sum of the deviatoric stress and a hydrostatic component: °V = -p8v + tv

(3-2.27)

Reg 3 Region 1

Region 4

Region 2

To nip-rolls Solid-like phase

Bubble Radius

Liquid-like phase

Boundaries: 1-2 Crystallization

begins

2-3 Solid phase stops yielding 3-4 Liquid phase disappears

Axial distance Figure 3.2.7 Two-phase concept

The liquid phase is modeled by the Maxwell equation of state given by: y|/r(1) + T = 2rjD

(3.2.28)

where the term T ( 1 ) denotes the upper convective Oldroyd derivative of the stress tensor components, and given by the expression: 3TJ7

3TI7

BK-

+v

T

W-

^=-i ^- 0:

*

(lz£)_ -(1-I)

(3 .4.42a,

which is negative and when a -> TT/2: A A

> +1

(3.4.42b)

tana = «

(3.4.43)

It may be shown that when

the value of (A!IA) goes to zero and the reflected ray is polarized. This is known as Brewster's angle. For glass with n = 3/2, Brewster's angle is 57°.

3.4.3

Measurement Methods

3.4.3.1

Measurement of Crystallinity

Polymers generally possess only limited levels of crystallinity. Unlike low molecular weight materials, they cannot crystallize completely. The reason for this is clearly the inability of polymer chains tofitinto crystallites. Generally crystallinity levels are below 70%. The primary methods of measurement of crystallinity are (1) density (2) heats of crystallization, (3) refractive index and (4) X-ray diffraction. We shall review these concisely. Density-based crystallinity measurements use a two-phase theory of polymers. Essentially it is presumed that all the polymer is either crystalline or amorphous and there are no states of intermediate levels of structure. The exception to this would be when more than one distinctly different crystalline phase is recognized (e.g., by wide angle X-ray diffraction). For a material with amorphous and crystalline regions, the specific volume v may be expressed:

v=Xvc + (\ -X)va

(3.4.44)

where X is the crystalline fraction, vc the specific volume of the crystalline phase, and va the specific volume of the amorphous phase. It may be shown from Eq. (3.4.44) that: X = _Va ~*

(3.4.45a)

In terms of density, this is: 1

1

X = -^—^Pa

(3.4.45b)

Pc

The crystalline and amorphous densities, pc and p a , of important polymers have been tabulated. The value of X is determined from measurement of p alone, together with the values of p a and pc. Usually density is measured using gradient density columns. However, other techniques exist. A second method of measurement of crystallinity involves the determination of heats of crystallization. In these measurements one again presumes a two-phase theory of materials. The specific enthalpy of a material H can be expressed as: H = XH°C + (1 - X)Hl

(3.4.46)

whre Hc is the specific enthalpy of 100% crystalline material and // a is the specific of amorphous polymer. The crystallinity X from Eq. (3.4.46) may be written: ~TT TTO X=_ _" (3.4.47) The value of// — //° is determined from a differential scanning calorimeter. It is necessary to know the value of Hc — Ha the heat of crystallization of a 100% crystalline polymer, to compute the fractional crystallinity in this manner. Crystallinity levels may also be determined from refractive index measurements. From the Lorentz-Lorenz equation [21], the refractive index n depends on the number density of molecules N. Density was first corrected with refractive index measurements by Schael [56, 57] in the mid-1960s. It was subsequently applied by DeVries [58, 59] to both polyolefins and to polyethylene terephthalate (PET). A later article by Cakmak et al. [60] applies this technique to PET. Correlations of this type are sometimes expressed directly in terms of the Lorentz-Lorenz equation as: ^i=Cp

(3.4.48)

where C is an experimentally determined constant. Cakmak et al. [60] cite two expressions for PET films which were obtained by regression analysis: -^-^

= CX+C2X (3.4.49a,b) C1 = n(X = 0)

Refractive index measurements of crystallinity are generally limited to films.

Measurements of the three principal refractive indices are obtained using methods dating to Okajima and Koizumi [6] in 1939. Generally these three refractive indices are different and the values of n used in Eqs. (3.4.48) and (3.4.49) is a mean value determined from: w~ii =

"i+^+"3

(3.4.50)

Okajima and Koizumi [61] proceeded by determining individual refractive indices using the Abbe refractometer [62] which is based on a total reflection technique. This method was subsequently used by Schael [56, 57], DeVries [58, 59], and Cakmak et al. [60]. Wide-angle X-ray diffraction is still another method of measuring crystallinity. It involves measuring the scattering intensity of the amorphous and crystalline regions of a polymer.

3.4.3.2

Measurement of Orientation in Films

Polymer chain orientation on films has primarily been measured by three different wide-angle X-ray diffraction techniques and birefringence, although it is possible to accomplish this by other techniques such as infrared dichroism. Measurements of refractive index and birefringence determine mean levels of orientation in the crystalline and amorphous regions. Generally two-phase models are used for a uniaxially filament. We may write after Stein and Norris [44]: An=XAnc + (\ -X)Ana + Anform

(3.4.51)

where Anc is the birefringence of the crystalline phase and Ana the birefringence of the amorphous phase, A«form is the "form birefringence" which arises whenever two materials of different mean refractive indices exist in an anisotropic configuration. The "form birefringence phenomenon" is discussed by Born and Wolf [23]. The birefringence Anc and A«a may be expressed in terms of the intrinsic birefringence A° and A° of the crystalline and amorphous phases/J and fa through: An0 =/ c A°

An3 =/aAa°

(3.4.52)

so that: An = XfcA° + (1 - X)f:Al

+ Anfom

(3.4.53)

This formulation may be directly generalized to biaxially oriented film. Here there are two birefringences An13 and An23 which may be expressed for an amorphous material as: An 13 =flBA°

An 23 =f2BA°

(3.4.54)

B

where / j and ff are biaxial orientation factors of Eq. (3.4.32). For biaxially oriented crystalline films, we have: An13 = X[J* A°cl +f^Kll

+ (1 - X)f?™A°a + A«form

(3.4.55a)

An23 = X[f»
I.

Problem: Extreme asymmetry causes interfacial instability in FB alone HIPS Tie

Barrier Tie PE II.

FB

MM Die

PP Scrap Barrier Tie

PP

III. Problem: extremely high temperature and/or viscosity of skin layers PC Tie PP Tie Barrier Tie PP Tie PC Figure 5.8 Some uses of one or more feedblocks and a multimanifold die. This combination can make possible the manufacture of structures with extreme asymmetry, high-viscosity skin layers, or high melt temperature skin layers

from Toyo Seikan [2]. Toyo Seikan was one of the pioneers in producing EVOH-containing barrier structures. This report recommends PVDC structures for retorted containers over those with EVOH; for other containers they continue to use EVOH. A single coextrusion line can be designed that is capable of coextruding both of these barrier polymers, plus nylon and others, if it is designed for the most critical material, PVDC. PVDC coextrusion requires the use of corrosion-resistant metals, streamlining the channels, and maintaining low melt temperatures and short residence times. HPM Corp. advertises that the same 20:1 length/ diameter (LID) extruder performs satisfactorily for both EVOH and PVDC polymers; however, it does require a screw change for best performance.

5.6

Coextrusion of Flexible Cast Film

There are both differences and overlaps in the resins used for the semirigid sheet structures discussed so far and the flexible film structures. Semirigid sheet makes most use of resins with high moduli such as HIPS, high-density polyethylene (HDPE), and PP for the bulk layers. Flexible film makes more use of low-moduli bulk layers such as low-density polyethylene (LDPE) and linear low-density polyethylene (LLDPE) and overlaps in using

PP. For barrier layers, EVOH and PVDC are used in both categories. For important reasons, greater use of nylon is made in flexible films. Aside from its gas barrier properties, nylon is valuable for its puncture, tear, and abrasion resistance properties and its thermoformability when required. A few examples of coextruded structures in the thin flexible film application area are given in Fig. 5.9. One example of an important film that is frequently coextruded is that for wiener packages. The compositions of these films do vary considerably. One common package design has a thermoformed half and a printed unformed half. The unformed half is frequently a laminate made using a reverse printed PET plus a sealing layer. The formed half may be coextruded and is commonly 50 to 75 jim (2 to 3 mils) thick. This formed half typically has nylon as an external surface to gain abrasion resistance and for its positive contribution to thermoformability, EVOH as a gas barrier, and ionomer as a heat seal layer. The structure also contains appropriate adhesive layers and LDPE or LLDPE for desirable properties and reduced raw material costs. Thus, there is much similarity between this multilayer structure

Example Coextruded Film Markets versus Typical Structures* Example structure

Application

2

• Trash bags: lawn & g a r d e n , ~_ _ ^1 c i \ 37.5um(1.5mls)

0

% HDTE

• Stretch cling: h a n d - w r a p , w * > ?0iinir0 8

m

20um (

.

U

i

8

l

m

^

i

l

8

0

s

)

L L D P E Green

60% Regrind black20% 5

%

1

0

EVA + 5% PB LLDPE

%

E V A +5 % p B

• Agriculture: g r e e n h o u s e , 3 3 % LLDPE+UV 1 5 0 u m ( 6 m i l s ) 3 4 % LDPE 33% LLDPE+AF (antifog)

• Meat packaging: p r o c e s s e d 1 0 % Nylon meat forming w e b , 1 2 % Tie 1 2 5 M m ( S m I l . ) ™ ™ 56% Ionomer • Cereal liner: barrier film, Z1 n -i \ 6 5 % H D P E An 4 7 . 5 u m ( 1 . 9 m i l s ) i O % T i e 10% Nylon 15% EVA _^m0^^-^m • Laminated

• Snack food: corn c 47.5jim (

1

.

h 9

m

i i

p

s

,

J

J

l

s

)

4

0

J EDPE chocoiatT"I % HDPE white 20% EVA+ionomer |

• Coextruded

* Information from Tom Butler of Dow Chemical, Frecport, TX Figure 5.9 A few examples of the diversity of coextruded flexible films that are less than 250/rni (lOmils) thick. The snack food example is made by a combination of the lamination of a reverse printed film to a three-layer coextruded structure. Most of these films can be made by either the coextruded cast or blown film processes

and those used for sheet. For temperature compatibility in the structure, the nylon used must have a low melting temperature, so nylon-6 or a nylon copolymer is the common choice. Figure 5.1 is a depiction of the layout of a monolayer cast film line. The essential add-ons for coextrusion are the feedblock or multimanifold die plus more extruders. With regard to feedblock or die design, the same principles apply as stated in the previous section on flat-die coextrusion for semirigid structures.

5.7

Coextrusion of Blown Film

A significant trend in the blown film area is the growing manufacturing of complex barrier films utilized in food packaging. Table 5.3 is a list of some of the blown film equipment suppliers. Figure 5.2 depicts the principal components of a monolayer blown film system, and it is also the basic layout for a coextrusion line when supplemented with few equipment adjuncts. The adjuncts are additional extruders and a blown film coextrusion die. Figure 5.10 is a representation of a coextrusion three-layer blown film die. Coextrusion has the ability to produce thinner layers than those available for lamination, which is particularly advantageous if thereby the required amount of an expensive barrier material is reduced. For example, if one-half mil of a barrier polymer is sufficient, coextrusion can produce such a layer, whereas this is too thin for lamination and very often too viscous for coating. Because blown film coextrusion uses annular dies (multimanifold), it can utilize

Die Lips

Extruder A Extruder C

Extruder B

Figure 5.10 Schematic of coextrusion blown film die for three layers. This drawing depicts the three layers being joined sequentially. Other designs have the layers joined together at a common plane. Blown film dies are a member of the multimanifold method of coextrusion. Dies with up to seven layer capability are used commercially

Table 5.3 Some Major Equipment Suppliers of Blown Film Dies Including Coextrusion Types Alpine American Corporation, Natick, MA, USA Battenfeld Gloucester Engineering Co., Gloucester, MA, USA Brampton Engineering Inc., Brampton, Ontario, Canada CA Windmoeller and Hoelscher Co., Lincoln, RI, USA Davis Standard Egan Film Systems, Somerville, NJ, USA Dolci, Milano, Italy Filmaster Inc., Parsippany, NJ, USA Macro Engineering and Technology Inc., Mississauga, Ontario, Canada Paul Kiefel GmbH, Worms am Rhein, Germany Reifenhauser-Van Dorn Co., Lawrence, MA, USA

polymers of widely different viscosities. This is in contrast to feedblock coextrusion, in which viscosities cannot be mismatched as widely. Many of the developments and trends previously covered under the flat sheet or film equipment topics apply equally well to blown film. An arrangement for up to three extruders around a blown film coextrusion die is fairly straightforward. When a fourth or fifth extruder is added the arrangement becomes substantially more cumbersome. Six or seven extruders become nearly impossible, unless extruders are "piggy backed" in compact systems such as the Flat-pak from Davis Standard or similar compact systems from Wilmington Plastics Machinery [3]. As the number of layers increases, the blown film die becomes more complex, bigger, and a challenge to assemble and disassemble for cleaning or maintenance. The number of layers that can be coextruded in blown film systems has more limitations than the number that can be coextruded in cast film coextrusion systems with a feedblock. Coextrusion of three layers is practical and straightforward. More than three layers is more difficult; however, blown film dies with seven-layer capability are commercially used. A complicating factor in blown film systems is that some means must be provided for helically distributing the 5 to 10% thickness variations inherent in the blown film process. Distributing the bands from the die is accomplished by rotating or oscillating the die by itself or with the extruders, or by oscillating the takeoff unit. Rotating the die to eliminate gauge bands for five layers is very difficult, and if done in coextrusion practically eliminates the ability to use internal bubble cooling (IBC). With five-layer coextrusions, some companies prefer to rotate or oscillate the primary nip; this randomizes both die bands and also cooling nonuniformities. Other companies favor mounting the extruders and die on an oscillating platform for these more complex structures. A relatively straightforward way to double the numbers of layers in a film structure is to collapse and seal the bubble, making this double thickness a single film [4]. This is being used to make films with two barrier layers which are claimed to have physical property and fabrication (improved thermoformability) advantages over single barrier layer structures. Tubular coextrusion dies for packaging are typically in the 10 to 150 cm (4 to 60 in) diameter range. The rate for a five-layer line with two 60mm and one 45 mm extruders, making 50 to 100/mi (2 to 4mil) film, with IBC, is about 200kg/h.

Bubble cooling ability normally limits blown film line rates. Cooling rates are being improved in newer systems by a variety of methods. IBC is fairly widely used, but is being applied more vigorously by one company that uses an external pressure equalizing air collar (PEAC) [5]. Another company achieves the same result with their patented method of cooling with a primary air ring, IBC, a secondary dual-lip ring, internal stalk guides, and microprocessor controls that balance these air pressures. With the latter integrated type cooling, production rates 40 to 60% greater than those achievable with single-orifice air rings are achievable. Long-stalk bubbles are achievable by cooling control [6]. This operating method has beneficial effects on the mechanical properties of some polymers, particularly, high molecular weight HDPE. The strong biaxial orientation gained with high molecular weight HDPE increases toughness and modulus properties of the resulting film. These property improvements allow down-gauging of film thickness in some cases. Down-gauging is doubly beneficial in that it reduces raw material costs and is a means of "source reduction" that is environmentally advantageous. Spiral dies are the standard for blown film. A five-layer die typically has five spirals nested on top of one another. The goal of new designs is to decrease polymer residence times, enable operation at lower pressures, minimize shear rates, optimize gauge control, and exhibit less sensitivity to changes in material rheology and rates. These types of improvements increase the versatility of a die with regard to polymers and production rates. They are being achieved by designs with longer spiral wraps, wider flow passages, and lip geometries that decrease shear stresses. They are also being achieved by dies with a more flat plate type design [7] as shown in Fig. 5.11. The most important die design considerations for multilayer blown film systems are pressure drop and residence time in long transfer lines (250 cm long is common). These are of critical importance for the more heat-sensitive polymers such as EVOH and some of the adhesive resins used. So far, PVDC is not being coextruded in blown film dies because of the difficulty of avoiding degradation problems because of long residence times in the blown film system. The transfer lines from the extruder to the die need to be short to achieve short enough residence time for some polymers.

5.8

Coextrusion Equipment Considerations and Auxiliaries

The next few sections contain comments on equipment that can be important to success in manufacturing multilayered films. These are optional equipment items that can prove very important to efficient coextrusion in many cases.

5.8.1

Extruder Screws for Coextrusion

Recycling scrap is important to reduce costs and waste problems for any extrusion operation. To successfully recycle coextruded scrap, adequate dispersion of the dissimilar polymers is most often of paramount importance. Only with adequate dispersion are satisfactory and

Nominal Dia.

•iayer E Layer D

Side fed inlet Layer C Layer B LayerA

Figure 5.11 Flat plate, modularly constructed blown film die. It is called a Slimline Coextrusion Die by Brampton Engineering

uniform physical properties achievable. In some cases, it is necessary to recycle at relatively low polymer melt temperatures. The latter is especially necessary when PVDC is in the scrap, because high temperatures, >210 0 C (415 0 F), will cause rapid degradation. For these reasons the scrap extruder screw design must be carefully selected. Two examples of specially designed screws that are candidates for this type application are the: • Double Wave™ screw offered by HPM Corp. [8] • HG extruder with BLB screw offered by Gloucester Engineering [9].

5.8.2

Mixers for Coextrusion

Stationary mixers are advantageous in coextrusion systems in which there are long transfer lines from the extruder to the feedblock because long transfer lines can introduce melt temperature nonuniformities. These nonuniformities develop from the parabolic velocity profiles in pipes and the mismatches of wall temperatures and melt temperatures that cause variations in incremental polymer residence times, variations in shears experienced, and nonuniform heating or cooling effects. A compensating practice by many OEMs is to put a stationary mixer that is a distributive mixing device at the end of the transfer line, just before

Table 5.4 Motionless Mixer Tradenames and Equipment Suppliers Thermoprofiler™ from Luwa Corp., Charlotte, NC Thermogenizer from Chemineer-Kenics, N. Andover, MA Koch from Koch Engineering Co., New York, NY ISG from Charles Ross & Son Co., Hauppage, NY Komax Equalizer from Komax Systems, Long Beach, CA the melt enters the feedblock, to rehomogenize the melt. Table 5.4 lists some suppliers of stationary mixers that are applicable to polymer blending. A higher shear stress dispersive mixing is frequently essential for the successful recycle of dissimilar polymers. If the polymers are compatible enough, high-shear mixing ensures uniform physical properties in these two or more phase mixtures. This is particularly true when difficult to disperse polymers are in the regrind such as the EVOH polymers. Special mixing screw designs are required with these types of regrinds.

5.8.3

Gear Pumps for Coextrusion

Gear pumps are economically justifiable, most often, as an add-on to the scrap extruder of a coextrusion system. Fifty percent or more total scrap is typical for extrusion forming lines used in making round containers. The bulk density of scrap regrind is relatively low and also varies; this results in more surging with a scrap fed extruder. Welex Inc. says that 100% of the coextrusion lines they supply have gear pumps on the scrap extruders. In contrast, Er-We-Pa GmbH recommends (when needed) a special process that agglomerates and densifies scrap by pressing the ground scrap through a perforated plate with a 3 to 5 LID auger machine [10]. This operation increases the bulk density of the scrap, making it a better and more uniform feed for an extruder. The resulting improved feed density and uniformity can eliminate the need for a gear pump. Extruders processing virgin polymers incorporate gear pumps less often. However, some relatively low melt viscosity polymers, such as PP and PET, extrude with less surging with a gear pump add-on. Gear pumps are not practical on PVDC extruders because of the degradation characteristics of this polymer. Gear pumps are being touted as means of ensuring that a barrier layer, such as EVOH, is present in a structure at the prescribed percentage. In this situation, the gear pump is essentially acting as a positive displacement metering pump. Microprocessor programs are available that allow control of individual layer thicknesses for Harrel, Inc., Welex Inc., and, undoubtedly, other OEMs for coextrusion systems that incorporate gear pumps on each layer. Control is straightforward because a gear pump's output is very close to being linear. Table 5.5 is a list of some of the major gear pump suppliers. Table 5.5

Major Gear Pump Equipment Suppliers

Harrell Inc., E. Norwalk, CT Luwa Corp., Charlotte, NC (agent for Maag Gear Wheel Co., Zurich, Switzerland) Nichols/Zenith, Waltham, MA Normag Corp., Hickory, NC

5.8.4

Gauge Control of Coextruded Sheet and Film

The mass or density of coextruded sheet can vary at a constant thickness if the ratios of different polymers with differing densities vary in the sheet. This means that the rather commonly used beta gauge (which measures mass using a radioactive source) is sometimes not the best choice for a coextruded sheet. In some cases, a preferable choice for total thickness is an air-type caliper. In a coextruded sheet there is, obviously, a real need for online thickness monitoring of individual layers, especially the barrier polymer layers which are critical to the maintenance of specified barrier properties. Infrared is the method being touted by most companies. However, there is a big difference between measuring layers in film of 250/mi (< lOmils), and sheet. Clear film is the easiest to measure and this is being practiced to a limited extent commercially. The general principle of measurement is exposure of the sample to multiple wavelengths, commonly generated by a rotating filter wheel. Measurements of selected absorption bands lead to individual layer thickness values and an online analysis of this information yields the thicknesses of the different layers. Measurement of three to five individual layers is the practical limit, if several corrections are necessary. The types of corrections that are necessary are for materials that affect infrared absorption, such as pigments, foil surfaces, etc. The barrier resin EVOH is rather easily measurable with near-infrared. PVDC is more difficult. For PVDC, some companies recommend a different method that utilizes low-energy X-rays capable of detecting the chlorine atom. Measurements of individual layers in sheet 1000/mi (40 mils) thick or more are not being considered because of the inability of infrared to penetrate such thicknesses. Pigment, when present, limits infrared further. Regrind recycle interferes with barrier layer measurements because the infrared will total-in the barrier polymer contents of the regrind layer. It is a fact that dispersed barrier polymer in regrind layers adds virtually nothing to barrier properties.

5.8.5

Coextrusion Process Control

Total computer integrated manufacturing (CIM) of an extrusion line is not totally achievable on monolayer extrusion lines. It is understandable that it has much further to go on coextrusion lines dedicated to producing complex coextruded structures. Gravimetric hopper weigh feeding systems are a growing method for multilayer control [H]. They are cost effective, in many cases, on the basis of raw material savings. Weigh feeding systems use a load cell on each extruder hopper to determine the feed rate of materials into each hopper. West German manufacturers of extrusion equipment, such as Keifel and Reifenhauser, recommend this approach. This approach controls within 1 to 2% the relative percentages of the different materials in a structure. However, the percentages do not show the uniformity of the layers. In other words, is a barrier layer uniform across the dimensions of the product? Therefore, other methods must be used to determine layer uniformity throughout the product such as microscopic examination of infrared layer measurements. Fortunately, typical operating experience is that once layer uniformity is achieved then the system is stable. Thus, barring any upsets, layer uniformities may be maintained with the gravimetric control system alone. A USA company, Process Control Corp. of Atlanta, says that their gravimetric control

system, called Gravitrol, for extrusion measures feeding weight continuously. This system makes rate calculations to 0.1 to 0.15 kg (0.2 to 0.31bs/h) every 20 s. Some of the European units make batch measurements.

5.9

Coextrusion Coating with Lamination

As previously indicated coextrusion can be used in various ways in combination with other processes. A layout for a process that combines lamination with coextrusion coating is depicted in Fig 5.12. For coextrusion coating, a feedblock designed on the basis of the same principles used for cast film or sheet, as previously described, is most often used. Equipment of the type shown in Fig. 5.12 can be used to manufacture premium cartons for perishable foods.

5.10

Concluding Thought

There are many different reasons why a multilayered product can be advantageous to a given market area, ranging from the need for a easy heat seal layer to needs for gas barrier properties. The structures can vary from two layers for heat seal improvement to five or more layers for gas barrier structures. Coextrusion is certainly the most economic method of making multilayered products when the application volume is large and when the development work to make the structure is complete. This is so true that this author believes that practically all films will be multilayered and made by coextrusion sometime in the future.

Optional

Coating Coextruder Feedblock Paperboard

Coated board

Figure 5.12 A combination process with coextrusion coating of paper board with film lamination. The film could be a reverse printed film

Abbreviations Used EVA EVOH HDPE HIPS LDPE LLDPE OPP PB PC PET PP PVDC

ethylene vinyl acetate ethylene vinyl alcohol, a polymer with high gas barrier properties high-density polyethylene high-impact polystyrene low-density polyethylene linear low-density polyethylene biaxially oriented polypropylene polybutylene polycarbonate polyethylene terephthalate polypropylene polyvinylidene chloride, a polymer with high gas barrier and moisture barrier properties

References 1. Schrenk, WJ., Alfrey, Jr., T. In Polymer Blends. S. Newman, D.R. Paul (Eds.) (1987) Academic Press, Orlando, FL, p. 129ff. 2. Yamada, M. In Proceedings ofEuropak '87: Ryder Conference, Diisseldorf, Germany, p. 127-140 3. Modern Plastics (1986) Dec, p. 58 4. Sorenson, L. "Recent Advances in Multilayered Flexible Films in Vacuum Packaging" In Proceedings of Barrier Pack '88: The Packaging Group, Inc., Chicago, IL 5. Modern Plastics (1987) Feb., p. 12 6. Modern Plastics (1987) March, p. 64 7. Perdikoulias, J. Petric, J., Coextrusion VI. SPE RETEC Proceedings, Chicago (1991), p. 156 8. Calland, W.N. Plastics Eng. (1990) April, p. 31 9. Plastics Technology (1990) May, p. 78 10. Djordjevic, D. In Proceedings of Coextrusion IV: SPE/RETEC, Arlington Heights, IL, p. 81 11. Plastics Technology (1987) Feb., p. 61

6.1

Biaxially Oriented Film K. Tobita, T. Miki, and N. Takeuchi

6.1.1

Introduction

245

6.1.2

Outline of the Tentering System Machine

245

6.1.3

Polymer Handling

249

6.1.4

The Extrusion Process 6.1.4.1 Performance Improvement on the Single-Screw Extruder

249 251

6.1.4.2 Capacity Increase by the Tandem Extruder

252

6.1.5

Filter and Die

256

6.1.6

The Casting Process

258

6.1.7

Stretching and Annealing Processes

265

6.1.8

Takeoff and Winding Processes

273

6.1.9

Process Control 6.1.9.1 Functions 6.1.9.2 Features 6.1.9.3 System Configuration 6.1.9.4 Automatic Film Thickness Profile Control System 6.1.10 Closing Comments

274 274 275 276 276 279

6.1.1

Introduction

In this chapter, the tentering process is described to develop an understanding of how it produces biaxially stretched films. In addition recent trends in biaxial stretching equipment are described. The use of plastic films as packaging and industrial materials keeps increasing at a remarkable rate. Thus it plays a major role in the growing use of thermoplastic polymers and extruders; with this expanding demand comes more complex product needs. Consequently, the function and the performance level required for thermoplastic extruders are becoming more and more stringent; machines having high levels of process control, labor-saving features, energy saving capacity, and preventive maintenance are in great demand. Such being the case, extruder manufacturers are making their utmost efforts to research and develop equipment to meet these demands. Also, in view of the function enhancement, diversity, and requirements of new plastic film products, research and development on various aspects of the essential technology is under way at numerous universities, laboratories, raw material manufacturers, and film manufacturers.

6.1.2

Outline of the Tentering System Machine

Overall there are two processes to produce biaxially oriented film: the tentering process and the double bubble tubular film process. The tentering process is divided further into the stepby-step stretching method (sequential stretching method) and the simultaneous stretching method. These two tentering methods are employed independently in accordance with the characteristics of resins, but production by the step-by-step biaxial stretching method is more common throughout the world. Table 6.1.1 shows that the step-by-step biaxial stretching method is adopted for biaxially oriented polypropylene (OPP), biaxially oriented polyethylene terephthalate (OPET), biaxially oriented polystyrene (OPS), and biaxially oriented polyamide (OPA); the simultaneous biaxial stretching method is used for OPA also. The biaxial stretching process was developed in Germany about 1935, and then put into practical use for the production of OPS film in the second half of the 1940s. But real development of biaxially oriented film began from 1952, when DuPont started to make and sell OPET film [I]. The sequentially biaxial stretching process basically consists of machine direction (MD) stretching and transverse direction (TD) stretching. Generally, OPP film is produced by MD and then TD stretching. For OPET film the following can be used: (1) MD ->TD; single-stretching method (2) MD -^TD -> MD; multistretching method (3) MD -^TD -> MD -> TD; multistretching method The multistretching method, as in (2) and (3), is adapted to the particular stretching machine [I].

Table 6.1.1

Manufacturing Methods of Biaxially Oriented Film and Features Thereof Tentering process

Features

>

I I

&

Tubular film process 1. Produciblefilmthickness range 2. Flexibility on the change of process conditions 3. Total productivity in conjunction with high speed and width broadening 4. Small lot production 5. Thickness accuracy 6. Isotropy in physical properties 7. Range of polymers that can be used

Corresponding film

A (Medium) A

Step by step

Simultaneous

© (Thin-thick) O

A

O (Thin-medium) A O

A

O

A O O

® A O

® ®

PP 5 PE Polyvinyl chloride (PVC) Polystyrene (PS)

PET, PP Polystyrene (PS) Polyvinyl chloride (PVC) Some grades of nylon (PA)

^ Nylon 6 TD process. The typical process of the sequentially biaxial stretching method for PET is shown in Fig. 6.1.1.

6.1.3

Polymer Handling

It is important to reduce water content in the starting raw materials to prevent degradation in the extrusion process of PET. Also, it is necessary to crystallize the pellets partially in the drying stage so that they will not block. Mixing of virgin material and reclaimed material, as well as master batch raw material, is also essential. As for raw material drying equipment, many types are available as shown in Table 6.1.2, and each has its own unique features. A ribbon type dryer in the table has particularly unique features: 1. Crystallization, drying, and mixing are carried out simultaneously. 2. Thermal efficiency is high because the ribbon blade shortens the drying time and less energy is consumed. 3. Processes from crystallization to extruding are treated under a vacuum condition, and thus prevent quality degradation. This drying system is shown in Fig. 6.1.2. Polypropylene (PP) is handled by adding the antistatic agent, the antiblocking agent, and the slip agent to the virgin pellets in master batch form as called for in the end product film. Also reclaimed pellets and trimmed edge films are fed back into the end product film. In addition, the drying process is added for any hygroscopic materials. The flow is shown in Fig. 6.1.3.

6.1.4

The Extrusion Process

Hitherto studies have been carried out to establish the essential conditions to satisfy the following requirements, not only for the biaxial stretching process alone but also for other film and sheet extrusion processes: 1. 2. 3. 4.

Variation in extrusion output shall be minimized. Mixing and melting shall be efficient and yet uniform extrusion shall be obtained. Low-temperature extrusion shall be possible so as not to degrade the resin. Bubbles should not be included. In addition, the extruder must be able to extrude at appropriate, high rates.

Material

Vacuum pump

Steam

Dryer Feed hopper

Steam

Control board Extruder

Figure 6.1.2 Example of PET drying system

1 ~ 5.

Raw material silo

6.

Storage silo and drying process

7.

Hopper

8.

Reclaim line trimmed edges

9.

OPP line

Figure 6.1.3 Example of raw materials flow for OPP

6.1.4.1

Performance Improvement on the Single-Screw Extruder

Inasmuch as there is a limitation resulting from the melting mechanism of the single extruder, major improvements cannot be expected by extending the conventional method. In the single screw, as represented by the Tadmor model [2] shown in Fig. 6.1.4, melting is carried out by shear heating at the thin melt film formed around the wall surface inside the barrel and by the heat transmitted from the barrel. When we designate the molten resin volume as Qm, the area of the melt film portion (the area where the solid contacts the melt film portion) as A, the circumferential speed of the screw as Vp and the density of resin as p, then Qm is expressed approximately by the following equation: Q1n = Q - V p - A . p

(6.1.1)

where Q is a constant dependent on the properties of the resin. Accordingly, it can be presumed that enlarging the melt film area A is necessary to increase the extrusion output rate per screw revolution speed. But it seems that increasing the output rate by enlarging the area A without changing the extruder dimension has already reached its limit. Under these circumstances, the following techniques have been developed recently to break through the obstacles. 1. Supplying as much energy as possible to the resin while it is in the solid state. This can be partially accomplished with a grooved feed barrel (Fig. 6.1.5). It has become known that friction energy between resin particles can be utilized effectively when the properly selected groove shape is provided. The energy thus generated is unexpectedly large compared with melting energy in the melt film. Therefore, the application has great advantages. 2. Feeding raw materials forceably beyond the melting capacity of the screw plasticizing zone. (The grooved feed barrel works effectively in this case also.) The pellets incompletely melted in the plasticizing zone are broken into as many fine particles as Melt film Barrel

Screw Solid bed Direction of screw rotation

Melt film

Figure 6.1.4 Model of melting with the melt surrounding the solid bed

Melt pool

A

A

Cross-sectional view A-A Figure 6.1.5

Grooved feed barrel

Homoge -nizing zone Figure 6.1.6

Metering zone

Mixing zone

Plasticizing zone

Feed zone

Special barrier screw

possible in the following mixing zone, leading to complete melting during flotation in the melt. Based on this concept a special barrier screw was developed as shown in Fig. 6.1.6 [3]. A comparison of performance between this type of screw and the conventional barrier screw is shown in Fig. 6.1.7. Extrusion performance improvement based on such a concept is seen in equipment built by many companies worldwide.

6.1.4.2

Capacity Increase by the Tandem Extruder

Since the first model of the tandem extruder for OPP film production was introduced in 1975 many extrusion systems have been installed around the world. Now there is a tendency to adopt the tandem extruder for high-capacity extrusion lines because it improves their performance. In response to this movement, many producers in the world are moving to make and sell similar model machines, with the following features:

Through - put Q (kg/hr)

Screw speed (rpm) Material used : Unstretched film grade PP (Ml = 9), pellet form Figure 6.1.7 Performance comparison between 90mm diameter special barrier screw and 90mm diameter conventional screw

1. Concept of the tandem extruder. On the conventional single-screw extruders, many functions such as solid conveying of raw materials, melting, mixing, metering, pumping, and the like are carried out by one screw, but on the tandem extruder, these features are divided functionally into two sections. In Fig. 6.1.8, the tandem extruder system is shown.

Primary extruder Heater Secondary extruder Connecting pipe Heater

Screw

Material Reduction gear unit Motor

Screw Pressure control unit Pressure gauge

Die

M oto R

Products Figure 6.1.8

Tandem extruder

Barrel cooling unit

Reduction gear unit

2.

The primary extruder, focused on the melting function, is a high-speed, small extruder with high melting efficiency. The secondary extruder, aimed at homogenizing, maintaining lower melt temperature, and metering, is a low-speed extruder with a larger screw diameter. By controlling the resin pressure at the inlet of the secondary extruder automatically, the machine can be operated as if both extruders were one. Characteristics of the tandem extruder: • High capacity extrusion is possible. • The melt temperature can be lowered.

3.

4.

In Fig. 6.1.9, the throughput and the melt temperature curves of the 200 mm diameter primary extruder are shown. In PP, the melt temperature can be controlled to less than 230 0 C in spite of the melting occurring at the tip of the primary extruder completely. The secondary extruder is a melt extruder and the screw speed is slow, so heat generation caused by shear is less. Thus the outlet melt temperature can be expected to be 20 to 30 0 C lower than that of the single-screw extruder. Quite stable extruding operation. As shown in Fig. 6.1.8, the screw speed of the primary extruder is controlled to keep the resin pressure constant, by measuring it in the connecting pipe between the primary extruder and the secondary one. By doing so, stable operation can be achieved because the inlet resin pressure at the secondary extruder is kept constant, even if raw material conditions such as bulk density etc. are varied. Shorter residence time of the resin in the extruder, which is advantageous for product quality.

Through -put

Melt temperature

melt temp.(°C)

Through - put Q (kg/hr)

PP GPPS

Screw speed (rpm) Figure 6.1.9 Capacity of 200mm diameter primary extruder

Table 6.1.3

Specifications of Tandem Extruder Series

Item

Extruder type

900/1150

1150/1500

1350/1750

Primary extruder

Screw L/D ratio Screw diameter (mm) Designed pressure (kg/cm2) Drive motor capacity (KW) Drive system

17 90 350 200

17 115 350 300

17 135 350 450

4 3

4 3

4 3

Screw L/D ratio Screw diameter (mm) Designed pressure (kg/cm2) Drive motor capacity (KW) Drive system

20 115 500 110

20 150 500 185

20 175 500 250

Temp, control zone Die gate temp, control zone PP (kg/h) PET (kg/h)

4 1 650 to 850 800 to 900

6 1 1100 to 1300 1300 to 1500

6 1 1500 to 1750 1600to 1800

Temp, control zone Connecting pipe control zone Secondary extruder

Out put

1500/2000 17 150 350 550 Direct drive 4 3 20 200 500 300 Direct drive 6 1 1900 to 2200 1900 to 2200

1750/2200

2000/2500

2200/2750

17 175 350 750

17 200 350 950

17 220 350 1200

4 3

4 3

4 3

20 220 500 400

20 250 500 500

20 275 500 600

7 7 1 1 2400 to 2700 2900 to 3300 2400 to 2700 2900 to 3300

7 1 3400 to 3800 3400 to 3800

5.

Because the extruder is compact, operability is excellent and energy saving and space saving advantages can be obtained.

The specifications of a tandem extruder are shown in Table 6.1.3. For OPET, the tandem extruder systems are already in use and this is expected to increase in the future. Not only for PP and PET but also for OPS, the tandem extruder is adopted for its low melt temperature advantage. As for the raw materials for OPP films, there is a trend toward making such films directly from raw material in bead form from the Spheripol process without going through the pelletizing process. Ito reported that a film making test was conducted at a test plant, and he developed a suitable tandem extruder designed for this type of material [3]. Spheripol PP will become an increasingly important starting material for OPP. A new extruder series with 1.5 times the output of the present series has been developed [4]. It has a hexagonal screw, a melt seal for higher pressure, and a special dulmage.

6.1.5

Filter and Die

The molten resin from the extruder is directed to the die through a connecting pipe. A filter is installed between the extruder and the die so as to separate foreign particles from the resin. Before and after the filter unit, pressure gauges are provided to measure the pressure differences caused by contamination of the filter. A wire mesh, sintered wire mesh, sintered metallic powder, and sintered metallic fiber are used for the filter medium. The filter types are classified into cylindrical type filter, candle filter, disc filter, and so forth. Depending on the application such as, for example, PET video tapes, and capacitors that demand high-quality performance, the filter elements range in size from several micrometers to 10 to 3O/mi and disc type filters, using sintered metallic fiber, are extensively used. The filter changes are sometimes regarded as an obstructive factor for the continuous operation of the film plant. Owing to the requirements for high production rates and quality, increased frequency of filter changes causes reduced productivity. Accordingly, a pair of long-life filters with a large filtering area is installed in the line with the aim of prolonging the filter changing intervals and reducing change overs [5]. The die must have an excellent adjusting function for the film thickness and be easy to disassemble, clean, regrind, and reassemble. The typical die construction is shown in Figs. 6.1.10 and 6.1.11. It consists of two bodies and a flexible lip, and the passage is of the coat hanger die type. The parallel plate flow of non-Newtonian fluid is expressed by the following equation:

Q =^ V ^

xW

• (V- x %YnxH^+l^

(6.1.2)

2(2n + 1) \2m dZJ where Q is the volumetric flow rate; His the die gap; W is the slit width; dp/dZ is the pressure gradient; n is the power law index: m = m0 x exp[—a(T — T0)]; melt viscosity m0 is m(T0), where T0 is a reference temperature; a is the temperature dependence coefficient; and T is temperature.

Neglecting the effects of die gap and resin viscosity on pressure gradient, assuming that the slit width is constant, and defining the die gap variation and resin temperature changes as AH and AT respectively, the rate of change of the flow rate is expressed by the following equation:

This equation indicates the effects of the die gap and the resin temperature changes on the film thickness. Let us take PP, PET, and PS, by way of example, to show the changes in flow rate (thickness) against the die gap and resin temperature changes in Fig. 6.1.12. As a result of these potential thickness variations, sheet thickness adjusting methods are used and divided into two different types. One is a die lip gap adjustment and the other is a viscosity adjusting method involving a lip heater [6]. Each method has merits and limits and they are summarized in Table 6.1.4. With regard to PP, there are two systems widely used, one in which the die gap is adjusted by an adjusting bolt rotated by a servomotor, and one in which the die gap is adjusted by the thermal displacement of the adjusting bolt whose temperature is changed by means of a heater. As for PET, it is desirable that the system can be adjusted statically without an external disturbance. As shown in Fig. 6.1.12, the sensitivity of the resin temperature is so high that the resin viscosity adjusting method is employed. Other systems are also being employed. Besides, as shown in Fig. 6.1.12, the flatness and finish of the die lip surface, and the

HEATER

HEAT BOLT Figure 6.1.10

Die for monolayer system (heat bolt type)

LIP HEATER

ADJUSTING BOLT

Figure 6.1.11

Die for three-layer system (robot and lip heater type)

uniformity of temperature in the direction of the die width are important items required for good die performance.

6.1.6

The Casting Process

A molten resin extruded from the die is formed by the casting machine into a base sheet. This process plays a very important role in the overall production process by establishing a base of good or bad quality upon which to build. In the casting process, the molten resin is solidified by quick cooling on the chill roll, ideally with the base sheet being cooled evenly on both sides. To achieve this, various methods have been proposed depending on the type of resin. In the case of PP, the typical casting methods are multirolls of small diameter as shown in Fig. 6.1.13, and a single roll having large diameter (with water bath). Recently, a large roll plus water spray having high cooling efficiency and a compact size has also been developed to cope with the high-speed operation (Fig. 6.1.14). In the case of PET, the casting method is adapted in such a way as to position the die just above the chill roll as is shown in Fig. 6.1.15, because of low viscosity. The important point of the quick quench for solidification is to pin molten resin to the chill roll rapidly. If the pinning is not effective, this not only lowers the cooling efficiency, but also entraps the air between the molten resin and the chill roll. These bubbles can remain on the base sheet and may result in problems called surface roughening or pinner-bubble.

Change in flow rate (thickness) (%)

PP

PET

Change in flow rate (thickness) (%)

Change in die gap

PS

(%)

PET PP

Change in resin temperature Figure 6.1.12

PS

(0C)

Relationship between change in resin temperature, die gap, and change in flow rate

As for the pinning methods that stick a molten resin to the chill roll, there are many, such as the "air knife," "press roll," "liquid application," and "electrostatic" methods. The air knife and the electrostatic methods are generally applied for PP and PET respectively. The air entrapment phenomenon between the chill roll and the molten resin can be modeled as shown in Fig. 6.1.16, and the entrapped air layer thickness (between the molten

Table 6.1.4 Types of Automatic Film Thickness Profile Controllers and Their Advantages Characteristics Classification

Method

Advantages

Disadvantages

Lip gap adjustment

Servo motor

• Wide adjusting range • Quick response time • All bolts act at the same time. • Precise adjustment • All bolts act at the same time. • Precise adjustment • Quick response time

• One by one adjustment • External force acts • Narrow adjusting range

Thermal bolt

Piezo translator

Viscosity adjustment

Heater

• All heaters act at the same time. • Not mechanical (constant lip gap) • Precise adjustment

• Long response time • Heat resistance • Narrow adjusting range

• Confined to specific resin (temperature dependence of viscosity is large) • Narrow adjusting range

resin and the chill roll) can be expressed by the following equation:

where u is (V\ 4- F2)/2; h is the thickness of the entrapped air layer; K is a constant; R is the radius of the roll; fi is the viscosity of air; V\ is the takeup velocity of the molten resin on the

T-Die Air knife

Casting roll

Figure 6.1.13

Typical casting method (three-roll casting machine)

T-Die Air knife

Water bath Chill roll Figure 6.1.14

Water spray

Casting machine (single chill roll with spray cooling system)

chill roll; V2 is the circumferential velocity of the chill roll; P is the pressure of entrapped air; and Fp is the pinning force. In Eq. (6.1.4), [R9P] on the right hand side is balanced with the elongational force [F] of the molten resin film. F = RxP

(6.1.5)

This can be obtained by using the elongational strain rate, which was derived from the elongational flow of the Newtonian flow. The elongational force acting on the molten resin Normal position

Nip roll

Electrostatic pinning wire

Take-off roll

Dancer roll Strip roll

Figure 6.1.15

Casting machine (casting for low-viscosity resin)

Chill roll

PINNING FORCE et. AIR KNIFE PINNING ELECTROSTATIC PINNING

MOLTEN RESIN FILM ELONGATIONAL FORCE

CHILL ROLL ENTRAPPED AIR PRESSURE OF ENTRAPPED AIR Figure 6.1.16

Air entrapping phenomenon between the chill roll and the molten resin film

film is expressed by the following equation: F = Xx — xe

(6.1.6)

where

F is the elongational force of the molten resin film; X is the elongational viscosity; Q is the volumetric flow rate of the molten resin film; F0 is the velocity of the molten resin at the die exit; V\ is the takeup velocity of the molten resin on the chill roll; e is the elongational strain rate; L is the distance between the die exit and the chill roll. UNIT : 70 m/sec 100 m/sec

300 mm Aq (a) VELOCITY DISTRIBUTION Figure 6.1.17

Result of air knife air flow analysis (poor)

- 20 mm Aq

(b) PRESSURE DISTRIBUTION

In the case of PP, as the molten resin can be pinned on the chill roll by the use of air knife in general, this air knife shape and its attaching point are essential for the stable forming of the base sheet. For this reason, the design of the air knife is optimized by the practical application of the computer simulation analysis of the air flow. Figure 6.1.17 shows the distributions of air velocity and pressure in the case where the optimization is not considered. It can be observed that in the air velocity distribution figure, the vortex flow exists in the air current; following this a negative pressure is generated on the upper part of the base sheet shown in the pressure distribution figure. In such a case, the shape and location of the air knife that eliminates the negative pressure can be determined by the use of simulation analysis. The example of optimization is shown in Fig. 6.1.18. The relationship between the pinning force and the thickness of entrapped air at each resin forming speed in the optimized air knife shape can be obtained by using Eq. (6.1.4). An example of the result is shown in Fig. 6.1.19. For a lower viscosity molten film, such as PET, one employs the electrostatic pinning method. In this case the molten resin makes full contact with the chill roll by adding an electrostatic charge to the molten resin. Because such a low-viscosity resin generates vibration in the presence of a slight air current this makes the air knife unusable. The pinning force against the chill roll is determined by factors such as electrode voltages, distance between electrode and chill roll, electrode diameter, and electrical conductivity of the molten resin. The behavior of the electric charge in the case of electrostatic pinning has been considered as shown in Fig. 6.1.20 [7]. With increase of the forming speed, the electric charge density becomes lower and the pinning force decreases, leading to entrapment of air between the molten resin and the chill roll. However, when the electrode voltage is boosted to increase the electric charge density, an arc discharge occurs. The relationship between the line speed and marginal pinning voltage that does not result in entrapment is shown in Fig. 6.1.21 [8]. Various proposals for the improvement of the electrostatic pinning method were reported by Sakamoto et al. [7] and are shown in Fig. 6.1.22. Study and examination have been made of various methods such as modifications on the equipment side and polymer modifications, such as controlling the volume resistivity, etc. Recently, the combination of electrostatic pinning and water coating on the chill roll has been proposed [9]. This method has the following merits. The growth of oligomer on the chill roll greatly decreases, so the cleaning cycle of the roll is more than three times as long as that for the existing method, and frequency of film breaks in the stretching process decreases, leading to improved production efficiency. The molten films pinned to the chill roll are gradually cooled to solidification. The heat balance for the process in which the molten resin films are cooled to soldification can be analyzed by using the equation for non-steady-state heat conduction. However, in the case of a crystalline polymer such as PP, it is necessary to give full consideration to the enthalpy of crystallization. The equation of non-steady-state heat conduction, in which the heat of crystallization is taken into consideration, is expressed as:

pxCx

^

=KW)+^xAH^Xx{-3i)

(6 L7)

-

UNIT : 70m/sec 100m/sec

324 mm Aq

(b) PRESSURE DISTRIBUTION

(a) VELOCITY DISTRIBUTION Figure 6.1.18

Result of air knife air flow analysis (excellent)

Thickness of entrapped air /<m

CHILL ROLL DIA.

:

0.24m

LINE SPEED (m/min)

Pinning force Figure 6.1.19

35 mm Aq

Mpa

Relationship between the pinning force and the thickness of entrapped air

h

I = Ii + I 2

Extruding die

I2 V

I : Total current h : Leakage current I2 : Current provided to web Figure 6.1.20 The stream of charge during electrostatic pinning

where p is density; C is specific heat; T is temperature; t is time; K is heat transfer coefficient; y is thickness direction of the molten resin films; pc is density of a complete crystal; AHC is latent heat of crystallization; X is percent crystallinity.

6.1.7

Stretching and Annealing Processes

Voltage

KV

In the MD stretching process, the mechanical properties in the MD are improved by heating the base sheet and then stretching longitudinally between the rolls with different peripheral speeds, thus giving molecular orientation.

Line speed m/min Figure 6.1.21 Relationship between line speed and voltage

Polymer - p u control Polarity Power supply AC overlapping Material, Shape Improved methods Diameter Electrode

Plural Cover Preventing vibration

Machines Atmosphere

Lower pressure Various kinds of gas Covered with insulator

Casting drum

Rough surface Microcrack

Figure 6.1.22

Improvements of electrostatic pinning method

Consideration for stretching the sheet while suppressing neck-in is necessary to (1) absorb the thermal expansion of the sheet, (2) prevent looseness and slipping in the preheating zone, and (3) maintain widthwise uniformity in the physical properties and thickness in the stretching zone. There are two methods for the roll stretching process: cross-stretching and flat stretching (Fig. 6.1.23) [10, H]. Stretching Point Stretching Point

(a) Cross Figure 6.1.23

Stretching method

(b) Flat

The merit of the cross-stretching method is a smaller stretching gap. This method is used for PP etc., which shows large necking. This method then is preferable as the smaller stretching gap and reduced neck-in lead to more stable stretching and better gauge control. On the other hand, as flat stretching cannot set the stretching gap smaller than the diameter of the stretching roll, the stretching gap is larger than the stretching gap of the cross-stretching. The flat stretching is used for OPS, OPET, and others. Process auxiliary heating by electric heaters at the gap space prevents the film from sticking to the roll. It can increase stretching stability as the gap between the last heater and the high-speed side stretching roll is short. The TD stretching process is composed of the following steps: 1. Preheat the film uniformly by blowing heated air onto both the upper and lower sides while holding the film edges with clips after MD stretching. 2. Stretch widthwise to the required stretching ratio along the clip guide rail set for desired pattern. 3. Cool after annealing. As for the guide mechanism for the tenter clips, two types are available, the sliding type and the roller bearing type. The roller bearing type is preferred for industrial use films that require cleanliness to achieve quality. For the roller bearing type clip, the special roller bearing which is sealed by thermal proof grease is used. This is suitable for high running speeds as there is almost no concern that the film will be contaminated due to scattering of lubrication oil. But in this case, preventive maintenance checks, such as periodic bearing replacements, are necessary. For the heating chamber, the important point is to construct it to ensure uniform heating to the film surface by heated air and to keep different segments of the chamber separate. Thermal control is likewise important because the energy consumption is considerable. 1. Stretching of PET As described previously, generally the step-by-step stretching method is adopted. Stretching in the MD and then TD is carried out in sequence. The MD stretching temperature for PET is 90 to 1100 C, but preferably an infrared heater or nonsticking type roll is used in the stretching zone because there is a tendency to stick on a chromium plated roll in the stretching temperature range. The multistage stretching method also may be used to achieve higher line speeds. The performance requirements for the preheat roll of the MD stretching machine are nonsticking, nonstaining of the roll, durability, stable holding capacity for film, etc. As for the nonsticking property, there are many proposals for roll materials. Using a basic chromiumplated roll, the rolls with a ceramic coating (surface roughness: 1/xm; thickness, 0.1 to 0.5 mm) have been employed for PET at a temperature of 80 to 1250C [12]. Although the satin finish roll has the effect of increasing adhesion temperature, a scratch or abrasion may occur. The Teflon coating has good nonsticking properties; however, it has the problem of durability. Recently, the use of the ceramic roll, despite the high price paid for the nonsticking property, is generally increasing. The method of fixing the stretching point involves the following: • Contacting the film fast to the roll by using static electricity [13] • Concentrating heat energy by using a condensing heater [14]

A

V0

1

V^V1 d A u

V

Drawing rate = V0(A2-1)/2d

B

d

pddds iu 11j

V1

(e-Oix) uv a3ue6uj4ejig

A

Film speed Distance between A and B roll Draw ratio

draw ratio A =3.0 A =4.0 drawing rate u = 1 328% sec

V0 Position

Figure 6.1.24

Experimental behavior in super drawing

Film temperature (0C)

A

B ^B (draw ratio)

^A (draw ratio)

Figure 6.1.25

Schematic representation of apparatus for roll drawing

• Increasing close adhesion to eliminate the air between the film and the roll by installing a nip roll on the stretching roll [10, 11, 14 to 16, 18] • Fixing the separation point by installing a nip roll at the point where the film is separated from the roll [11, 14 to 18]. Super drawing is reported by T. Miki [19]. The experimental behavior of super drawing, which is a relationship between the MD stretching factor and the birefringence An9 is shown

Birefringence An (x10- 3 )

TA=HO0C

Theory

TA= 13O0C

TA : drawing temperature at A

Stretch ratio A( = AAXAB) Figure 6.1.26 Characteristic behavior of super drawing

in Fig. 6.1.24. The birefringence decreases with increasing stretching film temperature, and above 120 0C the drawing rate stops contributing to molecular orientation. In the OPET MD stretching test data, An with a temperature of 1300C at point A is less than An with a temperature of 110 0 C at point A. The MD stretching with a temperature of 130 0 C does not contribute to the molecular orientation at point A and also hardly contributes to the molecular orientation at point B (Fig. 6.1.25 and 6.1.26). This result suggests that the stretching process, which combines the conventional stretching method with the super drawing method, could realize higher stretching and low molecular orientation at the same time. It is thought that each OPET film producer operates with this modification to obtain high MD stretching. 2. Stretching of PP PP is generally heated to a specified stretching temperature (125 to 1400C) by preheating rolls. Because PP suddenly thins down substantially in some regions and stretches endlessly, causing so-called neck stretching, it must be stretched over a small distance between a pair of small diameter rolls. In the case where lower heat seal temperatures skins are involved, the MD stretching equipment and base sheet temperature control program, shown in Fig. 6.1.27, are proposed to protect the surface layer of the base sheet from sticking on the roll surface [20]. The use of Teflon coated rolls for the latter section of the preheating rolls is increasing because the film is apt to stick on the rolls. Recently, for the purpose of improving the physical properties along with the trend toward a high stretching ratio, the adoption of the so-called two-step stretching process, that is, stretching by two stages, is becoming popular. Figure 6.1.28 shows an example of the roll arrangement for a OPP MD stretching machine. In the case of TD stretching of PP for packaging, the sliding clip type is used. Although this technology has generally been limited to slower lines it has recently been applied on highspeed lines of more than 300m/min. The sliding clip type is advantageous from the standpoint of cost and maintenance. The construction of ovens has improved and the heat exchangers and blowers were symmetrically arranged at both sides of each room in the wide zone after the stretching unit. Uniformity of hot air flow was accomplished by constructing the oven in such a way that the air flow is symmetrical around the oven's horizontal center line and vertical center line respectively. For the purpose of realizating energy savings using a smaller oven, it is important to set the position of the air blower holes and their distance to the film so that the heat transfer coefficient to the film is maximized. In addition, as the ratio of exhaust heat to oven heat loss reaches approximately 0.7, an exhaust heat reclaimer contributes effectively to energy saving. 3. Bowing The stretching-annealing processes are most important in influencing the quality of the film products. In particular, the annealing process is conducted with the aim of relaxing the stress from the preceding process so as to improve the dimensional stability. However, in the stretching-annealing processes, a bowing phenomenon often occurs. The manner in which the bowing phenomenon occurs is shown in Fig. 6.1.29 and is indicated by the curvature of the line across the film which was initially perpendicular to the stretching direction.

V1 Furnace

Pre-heat

V2

Stretching gap CHiJI roll

Stretching roll

Stretching roll ©

To Simplified temp, program TK = Seal temp. TKW

Tv

TRW

Surface

Surface

After pre-heat TF : TkW:

Film temp. Chill roll temp.

Figure 6.1.27

TK :

After furnace Seal temp.

TRW :

After chill roll Tv :

Stretching roll temp. TR :

After stretching roll

Theoretical optimized temp, profile after stretching roll (D

Pre-heat temp.

T0 :

Stretching temp.

d :

Longitudinal stretching machine for coextruded multilayer films

Furnace temp, (over heat) Film thickness

Figure 6.1.28 Longitudinal stretching machine for OPP

Annealing zone

Stretching zone

Bowing ratio (%)

Figure 6.1.29 Bowing phenomenon

Preheating zone

Stretching zone

Thermosetting zone

Dimensionless length (—) Figure 6.1.30 Relationship between tenter length and bowing ratio

Cooling zone

Bowing ratio (%) Figure 6.1.31 Relationship between thermosetting temperature and bowing ratio

Thermosetting temperature (0C)

Observation of the bowing behavior shows that the straight line is deformed into a convex line in the initial region of the stretching process and then is returned to the straight line immediately before the end of the stretching process. Then the line is deformed into a concave line at the completion of the stretching process. Furthermore, the concave line reaches the maximum point at the beginning of the annealing process as shown in Fig. 6.1.30 [21]. (In Fig. 6.1.30, the annealing process occurs in the thermosetting zone.) In addition, the relationship between the bowing ratio and the annealing temperature, as illustrated in Fig. 6.1.31 [22], shows that the bowing ratio increases with increasing annealing temperature. In Fig. 6.1.31, the annealing temperature corresponds to the thermosetting temperature. The bowing phenomenon produces defects in the final products. For example, the film that undergoes bowing produces optical anisotropy in the TD owing to molecular orientation, and therefore research and development into its prevention has been conducted especially in the field of OPET films for floppy disk applications. On this basis various methods for optimizing the annealing conditions have been devised and proposed. They involve modifications to the methods of annealing of film: (1) the stretched film is kept first below the glass transition point to recover strength and then the film is subjected to annealing [22], and (2) the rate of heating the film for the annealing after the film has been kept below the glass transition point is controlled [23].

6.1.8

Takeoff and Winding Processes

The film coming out from the annealing process of the transverse stretching machine is taken off, the edges are trimmed, and the film is wound as a mill roll. In the takeoff part, a surface treatment is given to the film so as to activate the film surface with the aim of improving properties such as ink adhesion. The surface treatments are conducted to improve the surface by means of oxidation because of the inertness of the film surfaces. There have been many techniques for

improvement, and a "corona" treatment or a "flame" treatment are used, for the most part in industrial practice. The corona treatment is implemented in such a way that the film is passed through a corona discharge field in which the corona discharge is induced by imposing high voltages across the insulated electrode and the grounded dielectric substance. The main components of the corona treatment machine are discharge electrodes, dielectric coating rolls, and a corona power generator. The shapes of the electrode are based on three types: knifeedge, bar, and shoe, and the multiknife electrode [24] has been developed to obtain soft and uniform discharges. For the dielectric roll, a metallic roll is covered with a dielectric substance to produce the uniform corona discharge. For the dielectric substance, excellent materials are used such as silicone rubber, chlorosulfonated polyethylene, ethylene propylene rubber, etc. with high dielectric constant as well as ozone- and heat-resistant characteristics. Despite the high price, ceramic materials and fiberglass-reinforced plastic (FRP) are sometimes used. The electric power sources are usually solid state. The extent of difficulty of surface treatment varies depending on the chemical structure of the polymer and the kinds of additives used. OPP requires more energy to raise the surface tension to the desired level than OPET. The treatment energy consumed for OPET and OPP are lOWmin/m and 40Wmin/m respectively [24]. The flame treatment is reputed to be a method that does not generate ozone as does corona treatment while operating effectively. However, higher processes are restricted owing to the performances of the burners. Owing to the improvement of the burners and the gas controller, flame treating has improved in recent years. The quality of the winder has become very important with increased winding speed (250 to 350m/min), film width (6 to 8m) [25] and decreased film gauges. As the film speed increases, wrinkles and hence waste increase. To solve these problems, the following items can be adopted. 1. Improvement of wound-up design: The hardness of mill rolls is controlled to the optimum level by programmed control of the winding tension and pressure of the lay-on roll as a function of roll diameter. Wrinkles on winding have been much decreased by the use of spreader rolls. 2. Reduction of winder losses: For roll changes there has been developed a new mechanism that starts the roll by evenly sticking the film over the new core without use of any adhesive tape. Therefore, the folding of the film, wrinkles caused by the adhesive tape, scratches of film by the new core, and other defects have been decreased considerably [3]. Automatic roll unloading and automatic core loading are also gradually being adapted to save labor.

6.1.9

Process Control

6.1.9.1

Functions

With increased production levels and rates, computerized process control systems for the entire film production line are being utilized with the object of upgrading product quality,

increasing productivity, automating production, and saving labor (see Fig. 6.1.32). The functions of the process control system are broadly divided into three categories: 1. automatic setting of the operating conditions 2. centralized supervision and data acquisition 3. automatic film profile control.

6.1.9.2

Features

The technical features of the process control system are: 1. The high quality level of product can be maintained in a stable manner. In particular, product having the guaranteed minimum thickness can be obtained and can result in material saving. 2. The product changeover time can be reduced and can result in material and time savings. 3. The improvements of the production technology lead to reliable accumulation of process information and thereby higher quality levels.

ALARM MEMORY PRN I TER MAIN ALARM COMPUTER

PRN I TER

MOTOR CONTROL

EXTRUDER

FILM THC I KNESS CONTROL

TEMPERATURE CONTROL /S-RAY DIE

0-RAY

CASTN IG LSM TSM

Figure 6.1.32

Computerized process control system

TAKE-OFF

WN I DER

4. Normal operating staff can easily operate the machine. Moreover, the trouble caused by individual differences of operators will be eliminated, and labor savings become possible. Furthermore operators are released from operations such as die bolt adjustment under difficult conditions.

6.1.9.3

System Configuration

Several installations involve distributive type systems in which an overall supervisory system is installed in the center. As a subordinate part of the above system, the control system for line speed, temperature, and film thickness profile is connected with the central system. In addition, these systems are connected with a host computer and this enables total control of the entire film making plant.

6.1.9.4

Automatic Film Thickness Profile Control System

The characteristics of the films produced vary according to the required properties. However, the accuracy of the film thickness profile is common to them all and is very important. Therefore, to improve the film profile accuracy and to shorten the time to attain it, various concepts and devices have been proposed for the die body, the thickness adjustment equipment, and the control system. Thickness variations are classified into three categories: 1. thickness variations with a short period in the MD 2. thickness variations with a long period in the MD 3. thickness variations in the TD. The thickness variations having a short period in the MD are caused mainly by mechanical factors, that is, the extruder performance, variations of circumferential speed of rolls etc., and consistent reduction in these variations becomes impractical in principle, without improvement of the performance of the equipment. The thickness variations having a long period in the MD are caused by contamination of the melt filter, changes in materials or environmental conditions, etc.; adjustment of the average film thickness can be made by using feedback control in such a way that the time average thickness in the MD is measured so as to control the screw speed of the extruder according to the thickness information. The thickness variations in the TD are due to nonuniformity of molten resin, temperature inequality of die, and/or irregularity of die lip gap. To reduce these thickness variations is the main object of an automatic profile control system. An example of an automatic film thickness profile control system is shown in Fig. 6.1.33. To set up such a system, it is necessary to understand the forming process to establish the control method. Knowledge of the following items is essential for the control operation: 1. correspondence of the location in the TD of the measured film thickness profile to the location of the adjusting bolts on the die 2. mutual interference effects of the required die lip gap adjustment on the adjacent bolts

CONTROL DS PANEL IPLAY FL IM THC I KNESS CONTROL PANEL

MAIN CONTROL UNT I SCREW SPEED CONTROL SG I MAL C ( OMPUTER) HEAT CONTROL SG l NAl /?-ray HEAT T H C I K N E S S G A U G E CONTROL UNT I CONTROL PANEL THC I KNESS SG I NAL

/3-ray THC I KNESS GAUGE CONTROL PANEL THC I KNESS SG I NAL

M FILM FLOWDIRECTION TAKE-OFF MACHN IE AND WN I DER

EXTRUDER DE I ADJUSTN I G DEVC IE CASTN I G MACHN IE Figure 6.1.33

3.

/3-ray THC I KNESS GAUGE

LONGT IUDN I AL STRETCHN IG MACHN IE

TRANSVERSE STRETCHN IG MACHN IE

/?-ray THC I KNESS GAUGE

Automatic film thickness profile control system

the amount of the die lip gap adjustment needed to correct the deviation. As to item (1), there are many methods to be considered: • Method 1. After marks are put on the molten resin at the die exit, the positions of the marks are measured on the cast film base sheet, the longitudinally stretched film, and the biaxially stretched film. • Method 2. After the die lip adjusting bolts have been operated in consecutive order at a fixed rate, the profile changes are measured. • Method 3. By carrying out statistical analysis of the control data of the production operation, the appropriate position of the bolt can be determined [26].

As to item (2), the methods are: By using the experimental equation approximating the profile change when one adjusting bolt is operated, the control demand is computed. This is on the assumption that when several adjacent bolts are operated simultaneously, the profiles are regarded as the superposition of individual profile caused by individual bolt operation [27] (Fig. 6.1.33). As to item (3), there are methods that are obtained from Eqs. (6.1.2) and (6.1.3) and from observation of equipment responses. For a newly advanced control system, Mapleston has reported that their "randomization" software program corrects the film thickness having a thick or thin tendency caused by the die, and the thickness accuracy of ± 2 % of set value can be kept on 8 m webs. This stops the buildup of gauge bands or ribs on the mill rolls [28]. Akasaka et al. have reported a fundamental control system designed by using a state predictive servo theory. This fundamental control system controls by predicting the effects of the past control on the present and future output. This system is capable of reducing startup

Thickness set value

Thickness

Integrator State-transition calculation

Regulator gain

Profile process

Dead time

Memory State - prediction calculation

Vector quantity quantity

Thickness gauge Observer Figure 6.1.34

Block diagram of a fundamental control system (block diagram showing control-demand calculation for a fundamental control system) [29]

time and improving thickness accuracy. The average variance at a steady state was 200 (1.4% average thickness error) (Fig. 6.1.34) [29].

6.1.10

Closing Comments

In this chapter, the introduction of the finite tentering process was described at every step from supply of raw materials to winding. The processes are not actually independent but are mutually related, and the process conditions closely relate to the final product and film properties. The biaxially oriented film manufacturing machine must have high speed, wide width, and stable performance. So it is important to carry out fundamental studies on each process and the relationships among the processes.

Abbreviations Used FRP fiberglass reinforced plastic MD machine direction OPP biaxially oriented polypropylene OPET biaxially oriented polyethylene terephthalate OPS biaxially oriented polystyrene OPA biaxially oriented polyamide PP polypropylene PET polyethylene terephthalate PS polystyrene TD transverse direction

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

Murauchi, K., Polymer Digest (1990) 2, p. 42-45 Tadmer, Z., Polymer Eng. ScL (July 1966) 6, p. 187 Ito, T., Japan Plast. Indust. Ann. (1990) 33, p. 80-88 Mod. Plast. Int. (March 1992) p. 67 Hensen, E, Siemetzki, H., Kunststoffe (1980) 11, p. 753-758 Ecchu, M., JP-A-51-109955 (1976) Sakamoto, K., Takizawa, T., Kato, K., Mitsubishi Kasei R&D Rev. (1988) 2, p. 120-125 Tsukamoto, H., Tsutsui, Y., Suzuki, T., Tobita, K., Mitsubishi Heavy Industries Techn. Rev. (1986) 2, p. 186-190 Aoki, S., Tsunashima, K., Ikegami, T, JP-A-3-23913 (1991) Nagasawa, T., Shuto T., JP-A-60-262624 (1985) Kimura, E, JP-A-1-237118 (1989) Sato, K. et al, JP-4844666 (1973) Sugawara, M., Uchida, H., JP-59-8343 (1984) Sudo, K., Shimura, K., Furuya, Y., JP-A-51 130479 (1976) Ichii, T., Matsunaga, S., Nakahira, T., JP-A-63-134222 (1988)

16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.

Tobita, K., Hasegawa, H., Hino M., JP-A-62-147519 (1987) Hagiwara, 0., Sato, K., Okabe, K., JP-A-62-199427 (1987) Sato, K., Okabe, K., Ishitsuka, L, JP-A-62-158026 (1987) Miki, T., Kanesaki, T., Utsumi, S., Mitsubishi Kasei R&D Rev. (1990) 2, p. 109-115 Wellenhofer, P., Plastic Age (June 1980), p. 101-107 Nonomura, C, Yamada, T., Matsuo, T., Seikei Kako (1992) 4, p. 312 Kimura, M., Nanbu, K., Hirotomi, N., JP-A-51-80372 (1976) Shimura, K., Kouno, M., JP-A-61-8324 (1986) Philip, B., In Polymers Laminations and Coating Conference, (1989), p. 169-194 Plastics Age Encyclopedia (1986), p. 113 Iguchi, K., Nitta, S., JP-5-76412 (1993) Ootomi, Y., Kawasaki, K., JP-A-58-39050 (1983) Mapleston, P., Mod. Plast. Int. (June 1990), p. 38-^1 Akasaka,N., Narita, Y., Akiyama, N., Suzuki, T., Tsutsui Y., Mitsubishi Heavy Industries Techn. Rev. (Oct. 1989) 3, p. 1-7

6.2

Influence of Processing Conditions on Structure and Physical Properties of Biaxially Stretched Engineering Thermoplastics M. Cakmak

6.2.1

Chemistry of Polyesters and Its Importance in Processing

282

6.2.2

Solid State Phase Behavior of PET

282

6.2.3

PET Film Technology

284

6.2.4

Stress-Induced Crystallization

285

6.2.5

Development of Structure with Deformation 6.2.5.1 Stretching of PET below Tg 6.2.5.2 Stretching of PET above Tg 6.2.5.3 Deformation Behavior of PET in the Rubbery Region and Its Relationship to Thickness Uniformity 6.2.5.4 Structure and Morphology Developed by Biaxial Stretching of PET 6.2.5.5 Annealing Effects on PET 6.2.5.6 Crystallinity and Thermal Properties 6.2.5.7 Conformational Changes Due to Drawing and Annealing 6.2.5.8 Small-Angle X-Ray Studies (SAXS) on Stretched and Annealed PET

285 286 286 286 288 296 298 299 302

6.2.6

Dynamic and Static Mechanical Properties 6.2.6.1 Dynamic Mechanical Properties 6.2.6.2 Static Mechanical Properties 6.2.6.3 Uniaxial (Constant Width) Stretched Films 6.2.6.4 One-Step (Simultaneous) Biaxially Stretched Film 6.2.6.5 Two-Step Biaxially Stretched Films 6.2.6.6 Long-Term Creep Behavior

303 303 307 308 310 310 312

6.2.7

Other Properties of Interest 6.2.7.1 Gas Permeability Characteristics and Morphology

313 313

6.2.1

Chemistry of Polyesters and Its Importance in Processing

Polyethylene terephthalate (PET) synthesis is generally accomplished by direct esterification of terephthalic acid with ethylene glycol with water as byproduct. This water byproduct in the condensation process is a limiting factor in achieving high molecular weights because its presence in the structure hinders the chain extension reaction. This led to development of other polymerization techniques in which removal of the water molecules was accomplished in the solid state at elevated temperatures. Typical molecular weights as represented by intrinsic viscosity 0.5 to 1.2dl/g are regularly achieved, with the most commonly used range being 0.6 to 0.8 dl/g. Heffelfmger [64] indicates that below a critical degree of polymerization of about 25, PET is friable and brittle and beyond a higher critical value of DP of about 60 further increases in molecular weight are not economically justified and most commercial grades are made slightly above the latter higher critical value. In processing of polyesters, exclusion of moisture is of paramount importance so as not to lose the molecular weight developed during the polymerization process. The presence of moisture in the molten phase causes hydrolysis of ester linkages. Even with the best prevention methods (closed hopper systems, inert gas purging, etc.) this reduction is generally unavoidable and the reduction in molecular weight after a melt processing generally increases with the increase of molecular weight of the initial material.

6.2.2

Solid State Phase Behavior of PET

PET, having relatively rigid chain architecture due to the presence of the para-linked phenyl group, can easily be quenched into the amorphous form from the melt. Single crystals of PET were grown by Yamashita [I]. The polymer chains in parallelogram shaped single crystals are inclined at about 30 0 C to the normal to its basal plane. When crystallized from the melt near its melting temperature this polymer forms double-banded spherulites [2]. It can have positive as well as negative spherulites depending on molecular weight. The crystal structure of this polymer was determined first by Daubeny et al. [3]. The unit cell is triclinic and contains one chemical repeat unit as shown in Fig. 6.2.1. The unit cell parameters are: a = 4.56 A, b = 5.54 A, c= 10.75 A and a = 98.5°, 0=118°, y=112°. The molecules were found to be roughly planar with the aromatic rings nearly parallel to (100) planes. The density of crystals with the above parameters is 1.455g/cm3. For completely amorphous PET, Daubeny et al. [3] reported a density of 1.335 g/cm. More recent studies on PET by Fakirov et al. [4] resulted in the following unit cell parameters: a = 4.48 A, b = 5.85 A, c = 10.75 A and a = 99.5°, 0=118.4°, and y= 111.2°. These parameters give a crystal density of 1.515 g/cm3. There have been other reports on the crystal density of PET, that is, 1.501 g/cm3 by Zahn et al. [5] and 1.495 g/cm3 by Kilian et al. [6]. The glass transition temperature ranges between 67 and 75 °C. When heated, the amorphous PET crystallizes in the range ^ 95 to 145 °C. In general, the higher the chain orientation in the amorphous state, the lower the crystallization temperature is during a

Figure 6.2.1

Unit cell of polyethylene terephthalate

heating experiment. The melting peak of PET occurs at about 250 0 C. When the PET is annealed at temperatures between the melting and cold crystallization temperatures additional endothermic peaks are observed as a result of melting and recrystallization of preexisting imperfect crystals to higher perfection and/or larger sized crystals. This peak typically is observed about 10 to 20 0 C above that of annealing.

6.2.3

PET Film Technology

Various processes have been developed to produce uni- and biaxially stretched PET films [7 to 27]. A typical process involves the following stages: 1. 2. 3. 4.

extrusion of PET through a coat-hanger die; quenching stage; deformation stage(s); post-treatment stage(s).

In early processes the quenching of extruded molten sheets was carried out by immersing the sheet into a water bath. However, the films so produced left surface defects caused by local boiling of water. The water was then replaced by a 80% glycerol and 20% water mixture which resulted in good quality films. Later generation processes used chilled rollers (15 to 180C surface temperature) for quenching. In a process by Chren and Hofrichter [12] an additional localized stream or jet of inert gas is directed on the top surface of molten film at each side edge where the film first contacts the surface of the quenching drum. After the quenching stage, the films with negligible crystallinities are heated above Tg using blower heaters or, in later generations, using quartz heaters. In this stage the thermal operation window is 80 to 1200C and usually the temperature is kept between 80 and 1000C. The sheet that was softened is then stretched uniaxially, sequentially biaxially, or simultaneously biaxially, depending on the end use applications. Knox's [17] design provided simple uniaxial stretching of PET films with various roll systems. The later patent by Alles [8] also describes a uniaxial stretching system with roller assembly that includes slow rollers, idler rollers, and fast rollers. Grabenstein [28] describes a process to produce heat shrinkable PET films. These types of films are extensively used for wrapping articles of various shapes by enclosing an article within a heat shrinkable film, sealing the article, and subjecting the package to elevated temperatures. In the process for producing heat shrinkable sheets, the stretching of the film to 2X at temperatures ranging from 800C to 135°C occurs, permitting the film to cool to room temperature under tension. The film produced this way shrinks ~ 35% in TD and ~ 15% in MD above 80 0 C. Films for magnetic recording are produced by stretching in one direction from about 1.5X to 2X at temperatures of 180 to 200 0 C and heat setting at 190 to 200 0 C under tension such that no shrinkage is permitted [11, 29]. One of the earliest patents that describes sequential stretching is by Alles [7]. The softened sheets are either stretched widthwise and in later stages lengthwise or in the reverse procedure. He suggests that the temperature in the second stage should be at least the same as that used in the first stage or it can be 5 to 30 0 C higher but it should not exceed 1200C, at which thermally activated crystallization becomes appreciable. In a PET film processing for photographic applications [10, 19], first widthwise stretching occurs then lengthwise stretching takes place. After heat setting at about 190 to 200 0 C the film is coated with a colloid solution, that is, vinylidene chloride. The first mention of continuous simultaneously biaxial stretching of PET films was made by Alles [7] and later by Koppehele [18]. The apparatus is a tentering frame and edges of the extruded film were thicker than the rest of the film so that they could be gripped securely by

the tentering frame. Jones [16] described a process for preparing oriented PET film with a deglossed, writable surface. In this process, initially an amorphous film is stretched at 1120C for 4 x 4 . This produces a glossed surface. The same result could be obtained by stretching the film to 2 x 2, cooling it down to room temperature, and reheating and restretching to obtain gloss.

6.2.4

Stress-Induced Crystallization

Crystallization in polymers can take place in various ways. One is thermal induced crystallization in which a polymer is crystallized between the glass transition temperature and melting temperature, either by heating from the initially amorphous state or cooling from the melt. In the second, the polymer chains are subjected to stress fields to produce crystallization at conditions under which the thermal crystallization rate is not appreciable. The term "strain-induced crystallization" is often used in the literature to describe the phenomenon. However, it has been pointed out by Thompson [30] and Spruiell et al. [31] that at low stresses simple flow of structure without appreciable crystallization is observed; however, above a critical stress, crystallization occurs. So the key parameter in the study of flow-induced crystallization in bulk polymers appears to be the magnitude of the effective stresses acting upon the molecules. Therefore, the term "stress-induced crystallization" is more appropriate to represent the phenomenon, particularly in those polymers in which no crosslinks exist. Various theories have been developed to describe the stress-induced crystallization of deformed polymers. A thermodynamic approach was first described by Flory [32] followed by a number of other researchers [33 to 38]. In these studies the observed changes in melting point and crystallization rate were correlated to the orientation functions and applied stress. General conclusions from the studies of the above authors are that stress enhances the rates of crystallization and stress-induced crystallization shows wide deviations from Avrami kinetics [39] which had been successfully applied to many polymer systems that are crystallized under quiescent conditions [40 to 42].

6.2.5

Development of Structure with Deformation

Deformation causes changes throughout the hierarchy of the structure in polymers. The type and extent of changes that occur depends on a variety of properties and process conditions. Some of these are molecular weight, initial state of the polymer, deformation temperature, mode (uniaxial, biaxial, simultaneous, sequential) and rate and extent of deformation. As a result of these changes a variety of properties are influenced, including orientation distribution, crystallinity, thermal properties, optical properties, gas diffusion characteristics, and mechanical properties and their anisotropy. In the following paragraphs, we examine some of these effects.

6.2.5.1

Stretching of PET below Tg

The stretching of initially amorphous PET below its glass transition temperature results in poorly ordered what may be called highly paracrystalline structure [31]. It was postulated both by Heffelfinger and Burton [43] and Spruiell et al. [31] that stretching induces rather imperfect extended chain crystals that can later serve as a site for further thermal crystallization that likely occurs in chain-folded morphology. Under these deformation conditions there have been observations of poorly ordered spherulitelike structure under cross polarizers in films stretched uniaxially at 25 0 C by Desai and Wilkes [44], This was attributed to the local heating effects as a result of plastic deformation in the neck regions. It was experimentally observed that the temperature at the neck regions increases substantially during deformation [45]. This spherulitelike structure was also substantiated by small-angle light scattering which showed a four leaf clover pattern. As has been observed in many other polymers, stretching PET below Tg also gives rise to void formations in the structure [46]. When the extent of these void formations becomes significant and their sizes reach a size range comparable to the wavelength of visible light, the appearance of the PET films turns "pearly" as a result of scattering effects. This is a common observation in the processing of PET, particularly in the stretch blow molded bottles where too low a stretching temperature easily causes such appearance.

6.2.5.2

Stretching of PET above Tg

Above r g , the molecules have higher mobility and if the stretch rates are low, they relax as fast as they are oriented, resulting in little internal stress and thus orientation and crystallization. Above r g and below temperatures at which the thermal crystallization rate is low (i.e., < 1000C), the temperature effect and stretch effect are counter-competing factors at a given temperature [31]. If the rate of stretch is high, molecular orientation and as a result crystallization can take place as compared to low strain rates at which relaxation causes disorientation and inhibits crystallization. Dumbleton [52] studied the stretching of amorphous spun PET fibers. He suggested the following mechanism. As the amorphous fiber is stretched, the orientation of amorphous regions increases to a point at which crystallization starts to occur ( = 2.5X). Thereafter, the orientation of the amorphous regions remains constant because any material that orients past the threshold will crystallize. The orientations of crystalline regions were found to be not much greater than that of the amorphous regions.

6.2.5.3

Deformation Behavior of PET in the Rubbery Region and Its Relationship to Thickness Uniformity

The requirements for surface roughness in manufactured films vary depending on the applications. Films for magnetic recording media or capacitors need to have surface roughness in certain ranges [53 to 58] whereas polymer paper [59] or films for adhesion need to have quite rough surfaces. In the case of dish membrane solar collectors [60 to 63]

STRESS

smooth surfaces and better thickness uniformity are needed to improve the optical performance of the films. As indicated earlier, in the film processing the cast amorphous PET is brought to temperatures between its glass transition (67 to 75 0C) and cold crystallization temperatures (135 to 1450C). This processing temperature is typically in the mid range (85 to 1000C) between the latter two temperatures. In this range, the stress-strain behavior of the PET resembles that of a crosslinked rubber. That is, the stress-strain curve shows a rise in stress and reaches a steady plastic deformation at intermediate deformations. Above a critical value called the onset of stress hardening (sometimes called strain hardening), stress rapidly rises and when a critical stress is passed, fracture occurs [64]. Below the glass transition temperature, the initial deformation is accompanied by a highly localized yielding that manifests as a highly localized neck or a series of necks (see Fig. 6.2.2). The critical strain at the onset of strain hardening depends on several factors. These are molecular weight, processing temperature, and rate of stretching. It decreases with increase of molecular weight, decrease of deformation temperature, and increase of stretching speed. As indicated earlier the stress-strain behavior of amorphous PET resembles that of a crosslinked rubber. There are, however, mechanistic differences. In the case of crosslinked rubber this deformation takes place affinely, that is, the whole body of the part being stretched "feels" the same level of deformation all the way to its smallest molecule, whereas in the case of PET microscopic deformation is slightly different. This is illustrated in Fig. 6.2.3. As demonstrated schematically in Fig. 6.2.3, initial cast films possess certain levels of thickness nonuniformities (Case 1) coming from the casting process. As the stress is applied at the edge(s) of the film for uniaxial and biaxial deformation stress concentrations occur in the thin regions and only those regions experience stress hardening and related crystallization at the intermediate "macro" strain values (Case II). In this condition other regions remain thicker and in fact the thickness uniformity as measured by the standard deviation of thickness profile worsens. Because the thinned and stress crystallized regions (regions A in Case II) can sustain heavier loads, the deformation is transferred to other regions (regions B in Case II) and this continues until the whole film experiences the strain hardening and resulting "self leveling" effect. Once the strain hardening has progressed sufficiently the thickness uniformity begins to improve and eventually surpasses that of the initial film as schematically

T ATD) the density decreases apparently as a result of reduction in packing efficiency of the chains in the crystalline lattice. This disruptive effect is reversed with an increase of ATD until the equal biaxial condition is achieved. When the processing temperature is increased, the latter effect of reduction in crystallinity with the TD stretch lessens and moves to the curves with higher MD stretch ratios. One consequence of these orientation effects can be observed in the thermal behavior of the stretched films (Fig. 6.2.10). As a result of increased crystallinity, the area under the cold crystallization peak in the differential scanning calorimeter decreases and this peak moves to lower temperatures as the oriented chains require less energy to crystallize because of the reduction in their entropy. The phenomena described above give a clear indication of the formation of structure as a result of orientation of chains in preferential directions. The temperatures at which this structural densification (crystallization) occurs are not conducive to the practical thermally activated crystallization. In the 80 to 1000C range, PET exhibits half-times for thermally activated crystallization in hundreds of seconds. So a distinction must be made as to the effects of deformation. These structural changes accompanying orientation are called stressinduced crystallization. Let us examine the particulars of the SIC.

Density (g/cm3)

Crystallinity (%)

Figure 6.2.9(a) Density as a function of biaxial deformation history on simultaneous biaxially stretched PET (processing temperature 8O0C)

6.2.5.7

Conformational Changes Due to Drawing and Annealing

The ethylene glycol linkage in PET chains exists in two rotational isomeric forms: a trans or extended form and a gauche or relaxed form. The trans conformation can be produced by a partial rotation about the carbon-carbon bonds [77]. In unoriented amorphous regions 13% of all ethylene glycol segments were found to be in a trans conformation. The gauche [78] form in the amorphous regions changes into the trans form upon crystallization and the trans form is the only form that exists in crystalline regions. However, the trans form also coexists with the gauche form in the amorphous regions [79]. When the film is stretched at 80 0 C, the trans concentration linearly increased with draw ratio up to 3.5X (which is beyond the onset of strain hardening), and above this value it levels off [80]. Huchinson et al. [81] suggested the following mechanisms. Up to the yield point the elastic strains are concentrated in the glycol linkage, leading to frequency shifts in the bands associated with trans and gauche

Density (g/cm3)

Crystallinity (%)

Figure 6.2.9(b) Density as a function of biaxial deformation history on simultaneous biaxially stretched PET (processing temperature 100 0 C)

conformers and orientation of these parts of the chains. Above the yield point, both stress and this local orientation decrease because the conformational changes can take place to allow the overall network structure to rearrange. After this, networks achieve higher orientation. On stretching the semicrystalline PET, the first region to be stressed is located between the crystalline regions [82]. Then the stresses are transmitted to crystalline regions. Although the conformational changes occur in response to external stresses, the number of taut tie molecules also increases while the amount of folded chains decreases. An increase of deformation temperature causes a slight decrease in the number of these taut tie molecules [83, 84]. Koenig and Cornell [85] studied the effects of drawing and molecular weight on the structure of biaxially stretched films. They also found the stretching causes the same amount of gauche to trans transformation in both low and high molecular weight samples. This

ENDO>

100C, Unannealed Scan rate, 20.00 deg/min

Temperature (K) Figure 6.2.10 DSC scans on PET films stretched at 1000C under a variety of biaxial stretching conditions

indicated that the amorphous regions in low molecular weight samples contain more trans ethylene glycol linkages because crystallinity is higher in high molecular weight samples and all linkages are in trans form in crystalline regions. In sequentially stretched films the amorphous trans content increases as a result of second stretch [50]. This gauche-trans transformation was also observed in the homologues of PET, namely polybutylene terephthalate. Jakeway et al. and Yokouchi et al. found that the conformation of glycol lineage in polybutylene terephthalate chains changes from gauche-trans-gauche sequence in the unstressed state to &\\-trans sequence under stress [86 to 88].

6.2.5.8

Small-Angle X-Ray Studies (SAXS) on Stretched and Annealed PET

SAXS studies have been performed on unoriented, crystallized [89], and uniaxially and biaxially stretched films [90 to 93]. Qualitatively the PET fibers and films show two-point [90] and four-point [90, 91, 94] patterns and equatorial streaks, depending on the deformation levels, annealing conditions, and relative orientation of the incident X-ray beam with respect to the sample. Bonart [94] interpreted the structure of uniaxially drawn and annealed PET as a chessboard array of crystalline/amorphous regions to account for quadrant scattering. Heffelfinger and Lipport's [90] studies indicated the four-point SAXS pattern transforms the two-point pattern with strain relaxation of uniaxially deformed films. Increase of strain was shown to reverse this transformation. Yeh and Geil [95] suggest that the four-point pattern is related to staggered arrangements of spherically shaped paracrystalline domains that were originally present in the unoriented amorphous PET. Statton and Goddard [91] also suggested a model structure for uniaxially deformed PET films. Their model consists of parallel platelets stacked one upon another. They also suggest that within each sheet the individual crystallites are oriented in a chessboard array in an amorphous matrix. Fakirov and Fischer's [4] experiments demonstrated that the appearance of a structure responsible for four-point diagrams is correlated with the macroscopic shape of the sample. They concluded that the four-point pattern is caused by staggering of the molecules along the (100) planes. In a sample with rectangular cross-section, a preferred orientation of these planes parallel to the broader surface takes place during stretching. In samples with circular cross-section (fibers), however, a random orientation about the fiber axis is observed and no largely extended crystalline layer with staggered conformation can be developed. PET films stretched uniaxially or biaxially show center streak scattering when viewed through the transverse direction or through the end (along the machine direction). It was found that this scattering develops at relatively early stages of deformation and is independent of the amount of crystallinity and type of orientation, but dependent on the temperature/tension history of the sample. Statton and Goddard [91] attributed this streak scattering to the presence of microvoids or regions of low electron density in the samples. Heffelfinger and Lippert's results suggest that the shape of center streak scattering is related to differing electron densities of large platelet shaped domains oriented essentially parallel to the surface of the film. This structural interpretation seems to be common among researchers [91, 94, 96]. The platelet formation may be the precursor of the appearance of pearlescence which was observed in low-temperature blown

stretch blow-molded bottles [97]. The low pearlescence in bottles was attributed to void formation. One of the few quantitative SAXS studies performed on PET was carried out on fibers by Fischer and Fakirov [92]. Their results showed that effective densities in amorphous and crystalline regions are no longer material constants but change as a function of thermal and deformation history of the samples. They suggested that the difference between effective density pc and "X-ray density" pc, of the crystalline layers in caused by the lattice vacancies in the boundaries of mosaic blocks. Eisner et al. [93] studied the change of SAXS patterns during the crystallization of preoriented PET fibers using synchrotron radiation with a vidicon camera. Their results indicate a decrease of azimuthal half-width of SAXS peaks and long periods with crystallization time. Fischer and Fakirov [92] and others [95, 98] observed an increase of long spacing of drawn and annealed PET with annealing temperature. It was determined that an increase in regular chain folding as well as decrease in strength occurs when oriented films are annealed. It was then speculated that loss in strength resulted from an increased number of folds [99, 100]. SAXS pole figures on uni- and biaxially stretched and subsequently fixed annealed PET films were done by Cakmak et al. [101], who showed that the shapes of the intensity contours in SAXS patterns taken in identical directions in unannealed and annealed films with the same deformation histories are similar. This suggests that the fixed annealing does not cause a major reorganization of the structure, but it merely perfects the structures developed primarily by stress-induced crystallization. The four-point pattern developed in the SAXS patterns (Fig. 6.2.1 la,b) together with the WAXS analysis suggested that the reason for the formation of the four-point pattern is the formation of staggered crystallite formation in the solid state because the phenyl planes become parallel to the surface of the films with deformation. The angle a remains essentially constant and this is related to the apex angle of the unit cell of the PET as shown in the models in Fig. 6.2.12a-c.

6.2.6

Dynamic and Static Mechanical Properties

The films deformed in two mutually perpendicular directions exhibit orthorhombic symmetry. This implies that the macro properties such as modulus, elongation to break, tensile strength, etc., are expected to show anisotropic behavior in the film plane. Thus, the researchers who study the orientation and mechanical behavior of films generally report these properties obtained in several directions in the film plane. Some of these experiments employed are creep [102], dynamic mechanical (low frequency) [52, 103, 104], ultrasonic (high frequency) [105, 106], and static tensile tests [107 to 115].

6.2.6.1

Dynamic Mechanical Properties

Illers and Breuer [116] studied the dynamic mechanical properties of unoriented PET films of different crystallinities. It was found that the position of the fi relaxation peak that is

MD

TD

,MD 1MD

TD

ND

UNANNEALED

Figure 6.2.1 l(a) SAXS patterns of PET films stretched to various stretch ratios: First column shows pattern taken with the beam along ND; third column shows pattern taken with the beam along TD; fourth column shows the pattern taken with beam along MD

MD

TD

MD ND

TD

ND

ANNEALED

Figure 6.2.11 (b) SAXS patterns of PET films stretched to various stretch ratios and annealed at 15O0C; first column shows pattern taken with the beam along ND; third column shows pattern taken with the beam along TD; fourth column show the pattern taken with beam along MD

UNIAXIAL FREE WIDTH

MD

TD Low Stretch Ratio

MD

TD High Stretch Ratio STRUCTURE Figure 6.2.12(a) samples

SAXS PATTERN

Structural models developed based on the SAXS and WAXS patterns: Uniaxial free width

associated with the glass transition moved to higher temperatures for crystallinities up to 30%; at higher crystallinities the transition moved to lower temperatures. Illers and Breuer attributed this behavior to the effect of crystal size on amorphous regions. At low crystallinities, there would be many small crystallites that would act like crosslinks and inhibit the motion of segments in the amorphous regions whereas at higher crystallinities, the crystallites would be larger and fewer in number and consequently would allow the segments in the amorphous regions more freedom. Dumbleton et al. [52] have shown that drawn crystalline fibers exhibit a shift in the position of transition to lower temperatures. Relaxation moduli of uniaxially [104] and biaxially stretched films [117 to 120] have been measured as a function of stress, time, and temperature. In uniaxially stretched films Murayama et al. [104] found that at constant crystallinity the effect of orientation is to increase the magnitude of modulus without changing its time dependence and to decrease the temperature dependence of the modulus. Fakirov and Stahl [121] reported that the dynamic modulus for drawn PET decreases with increase of annealing temperature. Studies on stress relaxation of biaxially stretched films [117 to 120] suggest that increased uniplanar orientation causes a reduction of both the magnitude and rate of stress relaxation. Time- and temperature-dependent relaxation of

UNIAXIAL CONSTANT WIDTH

MD TD Through Thickness

ND MD Edge View Figure 6.2.12(b) width samples

Structural models developed based on the SAXS and WAXS patterns: Uniaxial constant

ordered noncrystalline regions in PET films has been considered to be the major cause of shrinkage of films [122]. Linear thermal expansion coefficients of biaxially stretched films were also determined by Blumentritt [122]. He found that a minimum coefficient of thermal expansion was observed along the principal orientation direction and a maximum was found perpendicular to the latter direction.

6.2.6.2

Static Mechanical Properties

In undrawn amorphous films, self-oscillation of necking (serration) was observed during testing [121]. This gives rise to serrated stress-strain curves. These serrations occur alternately with opaque bands accompanied by voids and transparent bands in necking during cold drawing. They observed that faster rates resulted in smaller transparent band fractions. This behaviour was attributed to heat dissipation during necking corresponding to local temperature jumps and periodic strong variation of modulus of elasticity due to poor heat conductivity of the polymer. In a recent article, Tant and Wilkes [123] showed that physical aging of PET significantly affects the mechanical behavior of PET. They found that the extent of localized necking and associated strain-induced crystallization was greater for samples aged for longer periods of time. The studies of Biangardi and Zachman [115] showed

MD

TD

MD

ND

Figure 6.2.12(c) samples

Structural models developed based on the SAXS and WAXS patterns: Unequal biaxial

MD

TD

Figure 6.2.12(d) samples

Structural models developed based on the SAXS and WAXS patterns: Equal biaxial

that improvement of mechanical properties with stretching is caused not only by the increasing orientation of molecules but also increasing amount of taut tie molecules.

6.2.6.3

Uniaxial (Constant Width) Stretched Films

The studies of Matsumoto et al. [125] on PET indicate that the anisotropy of mechanical properties of the films uniaxially unconstrained stretched is greater than that of films stretched under constant width at the same stretch ratio in the machine direction. Some for the in-plane anisotropy data on the uniaxially constant width stretched films are shown in Fig. 6.2.13 a,b,c [124].

MODULUS MD GPa Undrawn

80°C

TD

Figure 6.2.13(a)

In-plane modulus anisotropy in uniaxial constant width stretched PET

As expected from the chain orientation behavior, the largest increases of modulus is observed in the machine direction and in the transverse direction it remains roughly the same as that of the original film. Tensile strength data also show similar behavior, although some losses as a result of deformation are observed in the transverse direction. The most interesting behavior is observed in the elongation to break data. With deformation, the largest decrease of this value is observed in the machine direction while in the transverse direction it actually increases to a value larger than that of the original unstretched film. At high deformation ratios is also decreases.

ELONGATION TO BREAK Undrawn MD 800C

TD

Figure 6.2.13(b)

6.2.6.4

In-plane elongation to break anisotropy in uniaxial constant width stretched PET

One-Step (Simultaneous) Biaxially Stretched Film

For PET, it was found [124, 125] that irrespective of stretch ratio, the mechanical properties are equal to both AMD(1) a n d ^MD(2) indicating a planar isotropy in these films. This behavior is shown in Fig. 6.2.14a,b,c [124].

6.2.6.5

Two-Step Biaxially Stretched Films

The extent of the anisotropy of mechanical properties for the sequential biaxial PET [125] films is larger in the first stretching direction than in the second stretching direction before the balanced point (/IMD(1) X >^MD(2)) of mechanical properties is obtained. Then the anisotropy is

TENSILE

STRENGTH MD XIO7Pa

80°C

TD

Figure 6.2.13(c)

In-plane tensile strength anisotropy in uniaxial constant width stretched PET

reversed after the balance point (AMD(I) X ^MD(2))- However, it was observed that the balance points for modulus, tensile strength and elongation to break do not occur at the point where the two stretch ratios in MD(I) first machine direction equal that of the second machine direction , MD(2). This occurs at points where AMD(2) is a little less than AMD(I> Thus, Matsumoto et al. [125] noted that it is hard to obtain films with "all" the mechanical properties in a balanced state by two step biaxial deformation.

MODULUS

SB

Undrawn MD

XiO9Pa

80°C

MD

Figure 6.2.14(a)

6.2.6.6

In-plane modulus anisotropy in equal biaxially stretched PET

Long-Term Creep Behavior

The key structural parameters, crystallinity and the level and type of orientation distribution imposed by the stretching process, have significant influence on the tensile creep behavior and its anisotropy in PET films at temperatures below the glass transition temperature. Increase of crystallinity and increase of chain orientation in a given testing direction invariably cause a rapid reduction in creep strain values. These are demonstrated in Fig. 6.2.15 [126]. The unoriented films with different crystallinities subjected to long-term creep show minimal difference at short testing times and films with higher crystallinity exhibit lower creep strains. The main influence of crystallinity on the creep behavior becomes apparent at high creep times. The samples with higher crystallinities exhibit lower creep strains at all times. The effect of biaxial orientation on the creep strains is demonstrated in Fig. 6.2.16. Biaxial orientation significantly reduces the slope of the long-term creep behavior. This is as a result of a combination of increase of crystallinity which densities the film structure

ELONGATION TO BREAK MD Undrawn

SB

80°C

MD

Figure 6.2.14(b)

In-plane elongation to break anisotropy in equal biaxially stretched PET

and the preferential orientation of the polymer chains, thereby reducing the slower creep process even below the glass transition temperature also.

6.2.7

Other Properties of Interest

6.2.7.1

Gas Permeability Characteristics and Morphology

The preferential orientation of the phenyl planes was found to correlate with the oxygen barrier behavior of biaxially stretched films. Gohil [127] used an orientation index called

MDxIO8Pa

800C

MD

Figure 6.2.14(c)

In-plane tensile strength anisotropy in equal biaxially stretched PET

PROF that was determined from principal refractive indices to describe the orientation behavior of phenyl planes and found a good correlation between this parameter and oxygen permeability as shown in Fig. 6.2.17. In addition he found that in sequential biaxial stretching the oxygen permeability decreases rapidly upon first stretching and on stretching in the second stretching permeability was found to increase slightly, indicating that a structural "opening-up" occurs and with a further increase of stretch ratios, the permeability values decrease (Fig. 6.2.18). Perkins [128] found that annealing decreases the oxygen permeability and annealing the PET films at 1800C produces the least permeability. At this temperature PET shows the fastest crystallization. Annealing above this temperature always causes melting and recrystallization which presumably reduces the orientation gained in stretching. On the other hand, annealing below this temperature causes crystallization which follows a certain amount of orientation relaxation as was found by Venkatesvaran and Cakmak [129] with an online twocolor laser measurement system. At the fastest crystallization temperature, the oriented structure is better preserved, leading to a more tortuous structure in the films which prevents the passage of the small gas molecules.

CREEP STRAIN

CREEP TEST: 5OC, 13.78 MPa UNANNEALED( 7.7%) ANN. 1 MIN.(20%) ANN. 2 MIN.(30%) ANN. 12 HRS.(37%)

TIME(sec) Figure 6.2.15 parentheses)

Long-term creep behavior of unoriented PET samples with varying crystallinities (shown in

CREEP STRAIN

CREEP TEST: 4OC, 13.78 MPa PET 1x1 PET 2X2(STRETCHING: 80 C) PET 3x3

TIME(sec) Figure 6.2.16

Long-term creep behavior of biaxially oriented PET samples (unannealed)

PERMEABILITY(cc-mil/100in2.24h-atm)

UNORIENTED CRYSTALLINE UNIAXIAL SIM. UNANNEALED SEQ. ANNEALED AT 170C SEQ.ANNEALED AT 200C SEQ. UNANNEALED

PROF(%) Figure 6.2.17 Permeability versus PROF(%) parameter on PET films of varying thermal-deformation histories (From ref. [127]) UNANNEALED

PERMEABILITY(cc-mil/100in2.24h-atm)

UNNEALED AT 200C ANNELAED AT 170 C

DRAW RATIO IN TRANSVERSE DIRECTION Figure 6.2.18

Permeability versus transverse stretch ratio in PET films (From ref. [126])

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Kagiyama, T., Oguri, Y., Kunugihara, K., et al., European Patent 0 257 611 A2 (1987) Sakamoto, S., Sato, Y., European Patent 0 229 255 A2 (1986) Fujiyama, M., Kawamura, Y, Wakino, T., Okamoto, T., J. Appl. Polym. ScL (1988) 36, p. 985 Hobbs, S.Y., Pratt, C E , Polym. Eng. ScL (1982) 22, p. 594 Nakatani, M., Kakita, H., Nakatsui, H., Sato, H., Rep. Prog. Polym. Phys. Jpn. (1980) 23, p. 185 Tanaka, A., Nagano, H., Onogi, S., Rep. Prog. Polym. Phys. Jpn. (1982) 25, p. 365 Wilkins, E, Energy (1987) 12, p. 179 Gupta, B.P., Energy (1987) 12, p. 187 Schissel, P., Neidlinger, H.H., Czanderna, A.W., Energy (1987) 12 p. 197 Benson, B.A., Energy (1987) 12, p. 203 Heffelfinger, CJ., Polym. Eng. ScL (1978) 18, p. 1163 Iwakura, K., Wang, YD., Cakmak, M., Int. Polym. Process. (1992) 7, p. 327 Cakmak, M., Simhambhatla, M., Polym. Eng. Sd. (1995) 35, p. 1562 Cakmak, M., Wang, YD., Simhambhatla, M., Polym. Eng. ScL (1990) 30, p. 721 Yoshihara, N., Fukushima, A., Watanabe, Y, Nakai, A., Nomura, S., Kawai, H., Sen-i Gakkaishi (1981) 37, p. 10, T-387 Cakmak, M., White, J.L., Spruiell, J.E., Polym. Eng. ScL (1989) 29, p. 1534 Cakmak, M., White, XL., Spruiell, XE., J Polym. Eng. (1986) 6, p. 291 Gohil, R., J. Appl. Polym. ScL (1993) 48, p. 1649 Venkatesvaran, R.H., unpublished research Cakmak, M., Lee, S.W., Polymer (1995) 36, p. 4039 Cakmak, M., Simhambhatla, M., J. Appl. Polym. ScL (to be submitted) Matsumoto, K., Izumi, U., Imamura, R., Sen-i Gakkaishi (1972) 28, p. 179 Alfonso, G.C., Verndona, M.D., Wasaik, A., Polymer (1978) 19, p. 711 Schmidt, P.G., J. Polym. ScL (1963) 41, p. 1271 Miyake, A., J. Polym. ScL (1959) 38, p. 479 Farrow, G., Mclntosh, X, Ward, I.M., Makromol. Chem. (1960) 38, p. 147 Cunningham, A., Ward, LM., Willis, H.A., Zichy, V, Polymer (1974) 15, p. 749 Hutchinson, LX, Ward, I.M., Willis, H.A., Zichy, V, Polymer (1980) 21, p. 55 Sikka, S.S., Kausch. H.H., Coll. Polym. ScL (1979) 257, p. 1060 Zachman, H.G., Polym. Eng. ScL (1979) 19, p. 966 Prevorsek, D.C., Sibilia, XR, J. Macromol. ScL Phys. (1971) B5, p. 617 Koenig, XL., Cornell, S.W., J Macromol. ScL Phys. (1967) B l , p. 279 Jakeways, R., Ward, I.M., Wilding, M.A., Hall, I.H., Desborough, LX, Pass, M.G., J. Polym. ScL Polym. Phys. (1975) 13, p. 799 Jakeways, R., Smith, T., Ward, I.M., Wilding, M.A., J. Polym. ScL Polym. Lett. (1976) 14, p. 41 Yokouchi, M., Mori, X, Kobayashi, Y, J Appl Polym. ScL (1981) 26, p. 3435 Groeninckx, G., Raynears, H., Bergmans, H., Smets, G., J Polym. ScL Phys. (1980) 18, p. 1311 Heffelfinger, CX, Lippert, E.L., J Appl. Polym. ScL (1971) 15, p. 2655 Statton, WO., Goddard, C , J Appl. Phys. (1957) 28, p. 1111 Fischer, E.W., Fakirov, S., J. Mater. ScL (1976) 11, p. 1041 Eisner, G., Zachman, H.G., Milch, XR., Macromol. Chem. Rapid Commun. (1981) 182, p. 657 Bonart, R., Kolloid Z. Z. Polymer (1964) 199, p. 136 Yeh, G.S.Y, Geil, PH., J. Macromol. ScL Phys. (1967) B l , p. 251 Baker, W P , J. Polym. ScL (1962) 57, p. 993 Miller, B.H., SPEANTEC Tech. Papers (1980) p. 540 Statton, WO., J. Polym. ScL (1972) A2, p. 1587 Koenig, XL., Harmon, M.X, J. Polym. ScL (1969) A2, p. 667 Prevorsek, D.C., Sibilia, XP, J. Macromol. ScL Phys. (1971) B5, p. 617 Cakmak, M., Spruiell, XE., White. XL., Polym. Eng. ScL (1987) 27, p. 893 Buckley, C P , Gray, R.W, McCrum, N.G., J Polym. ScL Polym. Lett. (1970) 8, p. 341 Seferis, XC, McClough, R.L., Samuels, R.X, Polym. Eng. ScL (1976) 16, p. 334 Murayama, T., Dumbleton, XH., Williams, M.L., J. Polym. ScL (1968) A2, p. 787 Price, H.L., SPEJ. (1968) 24, p. 54 Rider, XG., Watkinson, K.M., Polymer (1978) 19, p. 645

107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129.

Marshall, L, Thompson, A.B., Proc. R. Soc. (Lond.) (1954) A211, p. 541 Matsumoto, K., Ishii, K., Kimura, W., Imamura, R., Sen-i Gakkaishi (1971) 27, p. 49 Uejo, H., Hoshino, S., J. Appl. Polym. ScL (1970) 14, p. 317 Matsumoto, K., Sato, K., Ishii, K., Imamura, R., Sen-i Gakkaishi (1970) 26, p. 537 Matsumoto, K., Izumi, Y., Imamura, R., Sen-i Gakkaishi (1972) 28, p. 179 Vadimsky, R.G., Keith, H.P., Padden, Jr., FJ., J. Polym. ScL (1969) A2, p. 1367 Ishai, O., Weller, T., Singer, J., J. Mater. ScL (1968) 3, p. 337 Sacher, E., Mod. Plast. (1976) 53, p. 58 Biangardi, HJ., Zachman, H.G., J. Polym. ScL Polym. Symp. (1977) 58, p. 169 Illers, K.H., Breuer, H., J. Coll. ScL (1963 )18, p. 1 Hawthorne, J.M., J. Appl. Polym. ScL (1981) 26, p. 3317 Ward, I.M., Polymer (1967) 5, p. 59 Pinnock, P.R., Ward, I.M., Polymer (1966) 7, p. 255 Takayanagi, M., Mem. Fac. Eng. (1963) 23, p. 41 Fakirov, S., Stahl, D., Die Ang. Macromol. Chem. (1982) 102, p. 117 Blumentritt, B.F., J. Appl. Polym. ScL (1979) 23, p. 3205 Tant, M.N., Wilkes, G.L., J. Appl. Polym. ScL (1981) 26, p. 2813 Cakmak, M., (unpublished data) Matsumoto, K., Izumi, Y., Imamura, R., Sen-i Gakkaishi (1972) 28, p. 179 Cakmak, M., Wang, YD., J. Appl. Polym. ScL (1990) 41, p. 1867 Gohil, R.M., J. Appl. Polym. ScL (1993) 48, p. 1649 Perkins, W, Polym. Bull. (1988) 19, p. 397 Venkatesvaran, H., Cakmak, M., SPEANTEC Tech. Papers (1993) 39, p. 257

6.3

Stretching Conditions, Orientation, and Physical Properties of Biaxially Oriented Film Kenji Tsunashima, Katsuya Toyoda, and Toshiya Yoshii

6.3.1 Introduction

321

6.3.2 Outline of the Film Making Process

322

6.3.3 Sequential (LD -> TD) Stretching 6.3.3.1 Casting 6.3.3.2 Longitudinal Stretching 6.3.3.3 Transverse Stretching 6.3.3.4 Heat Setting

324 324 324 327 327

6.3.4 General Properties of PET Film 6.3.4.1 Mechanical Properties 6.3.4.2 Thermal Properties 6.3.4.3 Optical Properties 6.3.4.4 Barrier Properties 6.3.4.5 Chemical Resistance 6.3.4.6 Electrical Properties

328 328 330 332 334 334 335

6.3.5 Quality Improvement of PET Films 6.3.5.1 Bowing 6.3.5.1.1 Mechanism of Bowing 6.3.5.1.2 Reduction of Bowing 6.3.5.2 Thermal Stability 6.3.5.3 Gauge Uniformity 6.3.5.4 Tensilized Film 6.3.5.5 To Make the Film Thinner 6.3.5.5.1 History of PET Film Thinning 6.3.5.5.2 Thinning Technology 6.3.5.5.3 Limit of Thinning

339 339 339 340 342 343 344 348 348 349 350

6.3.1

Introduction

Polyethylene terephthalate (PET) is manufactured by the polymerization of terephthalic acid and ethylene glycol, and has the following chemical structure: HO-CH 2 -CH 2 - [ 0 - O C H Q ^ CO-O-CH 2 -CH 2 ]^-OH To obtain good physical properties, PET should have long molecular chains. Molecular chains that are too long, however, are undesirable, because many entanglements of molecular chains disturb the film formability. The number of repeating units, n, is usually about 100 for film grade PET. PET was discovered in 1941 by Winfield and Dickson at ICI, who then promoted the production of PET and established the worldwide patent rights, except in the United States, where DuPont started production by the use of a patent license from ICL PET was first used in the fiber industries. PET fibers went into the market under the brand names Terylene from ICI and Dacron from DuPont. Several years later, PET film was commercialized in the 1950s under the brand name of Mylar of DuPont, followed by Melinex of ICI. DuPont gave the manufacturing license for PET film to Eastman Kodak, and ICI to Kalle (Germany), Le Cellophane (France), Toray (Japan), Teijin (Japan), and other companies. Now, 20 different companies manufacture PET film throughout the world. PET film is characterized by a combination of favorable qualities and fairly low cost. It has good properties such as mechanical strength, optical transparency, electrical insulation, dimensional stability, thermal stability, resistance to chemicals, and hygienic safety. The markets for PET film were electrical insulation, metallized and slit yarns, and stamping foils in the early stage. The market spread to photographic films, capacitors, and tracing papers and further in the 1970s to magnetic tapes such as audio, computer, and video tapes, resulting in a rapid increase in production. In the 1980s, paralleling the development of the electronics and information industries, PET film found increased usage in electronics parts, graphic products, and other new applications for office automation and factory automation. Because of the large growth of the market for PET film, the amount of PET film consumption increased dramatically, and is now around 1.1 million metric tons per year throughout the world. The first step in making PET film is to melt the PET pellets in the extruder, then to form a sheet through a slit type die, and to quench the sheet on the casting drum. The resulting sheet is nonoriented and amorphous, so that the physical properties are not very good. The amorphous sheet is heated and biaxially stretched in both the longitudinal and transverse directions. Biaxial orientation of polymeric molecular chains takes place with this stretching, resulting in the improvement of physical properties. This stretched film, however, has a serious defect, that is, high shrinkage at high temperature. To remove this defect, the stretched film is heat set under tension to promote the crystallization and to remove the stress caused by the stretching. The key characteristic of the PET film manufacturing process is biaxial stretching, which is not usually used in the manufacture of conventional polyethylene and polyvinyl chloride films. Biaxial stretching technology has grown with developments in the PET film industry. Thereafter, this technology has been applied for the manufacture of other films made from polypropylene and polyamide.

The manufacturing method and properties of PET film are explained in detail in the following sections.

6.3.2

Outline of the Film Making Process

Because the cast PET film is brittle, most PET film is biaxially stretched. Biaxial stretching processes are classified as shown below (LD, longitudinal direction; TD, transverse direction): Simultaneous Biaxial Stretching by the Tenter Process Two processes are available: the pantograph process and the pitch screw process. These processes, however, are not very popular for the following reasons: Simultaneous biaxial stretching

Tenter process (A) Tubular process (B)

Biaxial stretching Sequential biaxial stretching

LD —• TD stretching (C) TD - * LD stretching (D)

• • •

complicated structure of tenter, and, therefore, difficult maintenance unsuitable for high-speed processing difficulty in changing the LD stretching ratio.

But recently DuPont has invented the newly simultaneous biaxial stretching technology patented by USP4853602, USP5753172, USP5771547 et al., so-called LISIM (linear motor simultaneous) technology, and Bruckner has commercially developed this process. With this novel LISIM- technology, the advantages of the current simultaneous stretching methods can be maximized and the disadvantages avoided. • •

Good processability (less break, ultra thin possible, high speed, high efficiency, changing of stretching parameters within minutes, low maintenance) simultaneous relaxation (low shrinkage also for tensilized).

Simultaneous Biaxial Stretching by the Tubular Process Tubular cast film, made through circular die, is heated and inflated with the aid of air pressure to form a biaxially oriented film. This process has the following advantages and disadvantages.

Advantages: • •

inexpensive investment cost high production efficiency (as a result of no edge trim, which is necessary in the tenter process). Disadvantages:

• • •

poor gauge uniformity and film flatness, because of instability of the blown film process unsuitable for high-speed processing unsuitable for manufacturing thick film.

The use of the PET film made by this tubular process is limited mainly to shrink film applications such as shrink wrapping of food and electric wires. Sequential Biaxial Stretching (LD —> TD Stretching) As mentioned previously, simultaneous biaxial stretching is less suitable for PET film manufacturing. Most PET film is produced by the sequential biaxial stretching process. Sequential biaxial stretching consists of stretching the cast sheet in one direction; then stretching the uniaxially stretched film in the other direction; and then heat setting the film. Two processes are available for sequential biaxial stretching. One is LD —> TD stretching (the film is stretched first in LD and then in TD), the other TD —> LD stretching (the film is stretched first in TD and then in LD). LD stretching is usually carried out between two pairs of rotating rolls. The stretching ratio is determined by the difference between the rotating speeds of the rolls. TD stretching is done in the clip running tenter. The TD stretching ratio is determined by the ratio of film width of the inlet and outlet of the tenter. Worldwide, LD —> TD stretching is the principal PET film manufacturing process. Sequential Biaxial Stretching (TD -> LD Stretching) This process has some advantages, for example: • • •

easy manufacture of LD-tensilized film low level of "bowing" (mentioned later) easy process for high-speed manufacture (because manufacturing speed is not limited by the tenter speed).

A serious problem with this process, however, is the difficulty in stretching the wide film uniformly in the longitudinal direction, as wide rolls easily bend and wide nip rolls usually give uneven nip pressure. As mentioned previously, the principal process for PET film production throughout the world is the sequential biaxial (LD -> TD) method, which is detailed in the following sections.

6.3.3

Sequential (LD -> TD) Stretching

6.3.3.1

Casting

The role of the casting process is to quench the molten sheet coming from the die slit forming the nonoriented sheet. Because PET has a melting point of about 270 0C and a glass transition temperature of about 70 0 C, the molten sheet, having a temperature higher than 270 0 C, should be quenched down to a temperature lower than 70 0 C. In this process, quick quenching is important. A slow rate of quenching usually causes crystallization in the nonoriented sheet, which has a negative influence on the subsequent stretching. The usual casting method is to use the rotating quenching drum, around which the molten sheet is wound. The molten sheet solidifies to form a nonoriented sheet. This casting method is effective in yielding a sheet with good gauge uniformity, because the drum works as a support for the molten polymer with fairly low viscosity. In the casting process, it is very important to quench the molten sheet as quickly as possible. To attain the quick quenching, two techniques are used. 1. To keep the drum temperature as low as possible. This method, however, is quite limited, because low temperature often causes the formation of dew on the drum surface. To avoid dew trouble, the drum temperature is usually kept at around 20 0 C. 2.

To obtain good contact between drum surface and molten sheet. To improve the contact, several techniques are available:

(a) (b) (c) (d)

pinning by static electricity [1] press roll casting [2] coating the drum surface with some liquid [3] air knife casting

Of these techniques, the electropinning method is usually preferred from the viewpoint of good contact, good gauge uniformity, and defect-free surface.

6.3.3.2

Longitudinal Stretching

This process involves heating and stretching the cast nonoriented sheet in the longitudinal direction, aligning the molecular chains in the stretched direction. Longitudinal stretching is usually carried out in equipment with some preheating rolls and a pair of stretching rolls, each of which is driven at different rotating speeds. The longitudinal stretching ratio is defined as the ratio of speed of these rolls. Figure 6.3.1 [4] shows three basic systems of roll arrangement for longitudinal stretching. Stretching with Long Free Path The sheet is stretched between a pair of nip rolls rotating in the same direction. Radiation energy is supplied to the sheet during stretching. This system usually has a long free path,

Heater

v

x

v.t>vx

v

i

a) Stretching with long free-path Figure 6.3.1

V

x

Vi

vz > Vx

b) Stretching with short free-path

V1

vz>v{

v

x

c) Stretching between densely arranged rolls with small diameter

Roll arrangements of various drawing processes and typical film cross-section

which causes substantial "neck down" (reduction of width during stretching). A large amount of "neck down" is not preferred because of thick edge formation. Stretching with Short Free Path The sheet is stretched between counter-rotating rolls. Because of short free path, this system works well from the viewpoint of avoiding "neck down." This system, however, is vulnerable to the formation of surface defects such as sticking and scratches. Stretching between Multirolls The sheet is gradually stretched between a sequence of many small rolls. This system shows tolerable "neck down." However, sticking and scratches result because of the existence of many rolls. The longitudinal stretching system actually used is the combination of these basic systems. Probably the system differs from company to company. The materials used for the surface of rolls are: • • • •

plated hard chrome sintered ceramics fluorine-containing polymer silicone rubber.

Each material has a different stick-start temperature, above which the nonoriented sheet sticks to the roll surface. Usually, hard chrome is used below 80 0 C, ceramics below 100 0 C, and fluorine and silicone polymer below 120 0 C. Figure 6.3.2 [5] shows differential scanning calorimetry (DSC) chart of amorphous PET. Three peaks are found. The first peak is around 70 0 C because of the change of specific heat, the second endothermic peak around 1400C because of crystallization, and the third exothermic peak around 270 0 C because of melting of crystals. This DSC curve shows the mobility of polymer chains with varying temperature:

EXO ENDO

Annealed at 2000C

Figure 6.3.2 DSC Thermograph of annealed PET

Temperature(°C)

1. At room temperature, polymer chains are frozen, that is, in the glassy state. This condition lasts up to the glass transition temperature (Tg). 2. At temperatures above Tg, the polymer is in a "supercooling" state, which extends to the crystallization temperature (Tc). 3. At the temperature approaching Tc, the polymer molecules begin to crystallize, which is called "heat-induced crystallization." To give the sheet good molecular alignment, stretching should be carried out in the temperature range between Tg and r c , that is, in the supercooled condition. Actually, a suitable temperature range is from 80 0 C to 1200C for the longitudinal stretching. Figure 6.3.3 [6] shows stress-strain curves in the uniaxial stretching of cast PET sheet. Stretching at the temperature below 70 0 C, the curves have clear yield points, which means that the temperature is not sufficient for the good stretching. Such stretching is called "stretching with necking," which does not give the sheet good molecular alignment and usually has poor gauge uniformity. At temperatures above 80 0 C, the stress-strain curves

Stress(Kg/mm2)

Stretching Temp.

Stretching Figure 6.3.3

Stress-strain curve of amorphous PET

Ratio

become smooth, showing that the condition is suitable for stretching. At temperatures above 100 0 C, the stress does not rise much with increasing strain. Such stretching is called "superdraw," which is a "flow" process rather than "stretch." In "super-draw," little molecular alignment takes place with the reduction of thickness and width. By combining this "superdraw" with normal stretching, high stretching ratio is obtained as a result of raising the filmforming speed. This idea originated in PET fiber technology and was later transferred to film. Some patent literature [7 to 9] shows the process of high longitudinal stretching ratios, ranging from 4 to 9 times. In the case of longitudinal stretching, consideration must be given to its influence on successive transverse stretching. Too high a longitudinal stretching ratio causes poor stretchability in the transverse direction, because of excessive strain crystallization taking place. To keep good stretchability in the transverse direction, the longitudinally stretched film should have limited physical properties, for example, density below 1.355 g/cm 3 (density of amorphous PET is 1.335 g/cm3) and the value of birefringence smaller than 0.100. To get such a longitudinally stretched film, the stretching temperature should range from 90 to 1000C and the stretching ratio from 3.5 to 4.0 times its original length.

6.3.3.3

Transverse Stretching

Transverse stretching is generally carried out by the use of tenter, after which a heat set stage follows. Both edges of the longitudinally stretched film are gripped by the tenter clips, which lead the film into the tenter oven, where the film is preheated and transversely stretched to 3.0 to 4.5 times its original width at temperatures ranging from 90 to 120 0 C. In the tenter oven, the film is heated by the hot air blowing from above and below nozzles, and is stretched with diverging clip chains. The important point in the transverse stretching is how to control the "heat-induced crystallization" in the preheating zone. Preheating at high temperature and/or for a long time usually promotes this crystallization, which leads to poor stretchability, for example, and bad gauge uniformity. A good parameter that relates to the level of heat-induced crystallization is the "crystalline initiation temperature." The lower this temperature is, the easier heat-induced crystallization takes place. As a reference, for amorphous cast film this temperature is about 140 0 C, whereas for longitudinally stretched film it is about 110 0 C. To improve the gauge uniformity in the transverse direction, the idea of "stretching during cooling" was proposed [10], the point of which is the combination of high preheating temperature with rather lower stretching temperature.

6.3.3.4

Heat Setting

Biaxially stretched PET film has a lot of built-in stress induced by the stretching, so that the film shrinks when exposed to high temperature and even at room temperature, the film slowly shrinks with time. Hence, the film is usually heat set at the temperature from 180 to 235 0 C. Heat setting increases the crystal size and degrees of crystallization, and permits relaxation in the strained amorphous region which contributes to the improvement of thermal dimensional

Density (g/cc)

Biaxally (3.0x3.5) stretching PET film

Annealing temperature (0C) Figure 6.3.4

Change of film density by annealing for 100 s under fixed lengths

stability. Heat set temperature below 1800C contributes little to the improvement of thermostability, whereas temperatures above 235 0 C degrade the crystal structure induced by the stretching, with serious deterioration of mechanical properties. Figure 6.3.4 [11] shows the relationship between heat set temperature and degree of crystallinity (density). This relationship is useful for estimating the heat set temperature of the sample film by the measurement of the density. Figure 6.3.5 [11] shows the relationship between heat set time and heat shrinkage of the film. Several seconds are required to finish the heat set. Figure 6.3.6 [11] shows the relationship between relaxation rate and heat shrinkage. Relaxation during heat set is effective to improve the thermal stability. However, a large ratio of relaxation usually causes a poor flatness of the film, so that the preferable relaxation rate is below 10% as the original width.

6.3.4

General Properties of PET Film

Some properties of the PET film obtained by the process mentioned previously are discussed below.

6.3.4.1

Mechanical Properties

Tensile Properties Figure 6.3.7 [12] shows the stress-strain curves of stretched PET film. From these stressstrain curves, tensile strength, elongation, elastic modulus, and F-5 value (stress at 5% strain)

Heat shrinkage (%) Figure 6.3.5 Annealing time versus heat shrinkage. (Heat shrinkage was measured at 150 0 C, lmin)

Heat shrinkage (%)

Annealing time (sec)

Figure 6.3.6 Heat shrinkage versus transverse relaxation of annealing zone. (LD, longitudinal direction; TD, transverse direction)

Relaxation ratio (%)

Transverse Direction

1. Uniaxially stretched under free width( 4x1') 2. tMaxially stretched under constant width( 4x1) 3.4.5. Two-way successively biaxially stretched and heat-set (4x3, 4x3.5, 4x4; respectively) 6. Simultaneously biaxially stretched and heat-set ( 4x4)

Stess(Kg/mm2)

Machine Direction

Stain(%) Figure 6.3.7

Strain(%)

Typical stress-strain curves for stretched PET films

are obtained, which are tabulated in Table 6.3.1 [12]. As shown in this figure and table, tensile properties of PET film vary considerably with different preparation conditions. Common biaxially stretched PET film in the market has tensile strength approx. 25 kg/mm 2 , tensile elongation approx. 120%, elastic modulus approx. 400 kg/mm 2 , and F-5 value approx. 11 kg/mm 2 . Viscoelastic Properties Figure 6.3.8 [13] shows the viscoelastic properties of the biaxially stretched PET film. Two peaks exist in the tan 3 curve, one at approx. — 50 0 C and the other approx. 120 0 C. The — 50 0 C peak is called a "/^-transition" caused by the movement of side chains of the molecules. The 1200C peak is called "a-transition" caused by the movement of main chains, which corresponds to glass transition temperature (Tg). Tg of biaxially stretched PET film is much higher than that of amorphous PET (approx. 70 0 C), as a result of the orientation of molecules. Propagating Tear Strength Propagating tear strength of various films is shown in Table 6.3.2 [14]. This strength decreases with biaxial stretching. Impact Strength Table 6.3.2 [14] shows impact strength of various films. Biaxial stretching usually raises the impact strength.

6.3.4.2

Thermal Properties

Reversible Deformation When the PET film is heated and cooled at low temperatures, deformation with heat returns it to the original dimension. This deformation is called reversible deformation. The rate of this

Table 6.3.1

Mechanical Properties of Stretched Polyethylene Terephthalate Films

Methods of stretching

Ratio of stretching

Tensile strength (kg/cm2)

(LD x TD)i

LD

TD

Elongation at break (%)

Young's modulus (kg/mm2)

F 5 value (kg/mm2)

LD

TD

LD

TD

LD

TD

Unstretched, no heat set

1.0 x 1.0

5.8

6.7

410

435

200

235

3.7

3.9

Unstretched, heat set

1.0 x 1.0

6.0

5.0

640

580

180

170

3.8

3.7

Uniaxially stretched under free width, no heat set

1.5 x Y 2.0 x Y 2.5 x Y 3.0x1' 3.5x1' 4.0x1'

7.2 11.9 19.3 23.5 24.6 27.5

3.4 3.5 4.2 4.5 3.1 3.0

380 350 270 140 71 62

430 480 450 600 830 910

150 160 300 320 470 490

150 150 160 170 150 100

4.7 5.2 8.7 9.1 11.3 15.6

3.7 3.6 3.0 2.8 3.3 3.0

6.0 11.1 20.0 22.2 24.5 25.6

5.8 4.8 5.6 5.8 5.9 5.7

530 370 140 96 73 50

610 480 480 490 470 500

180 180 410 480 600 660

160 160 170 190 210 240

3.9 4.5 8.9 12.0 14.2 16.9

3.6 3.5 4.0 4.2 4.3 6.9

4.0x2.5 4.0x3.0 4.0x3.5 4.0 x 4.0

24.7 23.0 22.0 20.5 19.6 16.5

8.1 11.6 15.8 18.3 19.2 18.4

46 43 34 44 47 39

380 130 140 88 62 32

700 600 520 490 430 360

230 310 300 380 410 470

21.3 16.8 15.0 13.2 13.3 12.2

8.1 10.3 10.5 12.3 12.5 16.0

1.5x1.5 2.0 x 2.0 2.5x2.5 3.0x3.0 3.5x3.5 4.0 x 4.0

5.2 10.5 18.4 18.7 22.2 24.0

5.0 10.8 18.2 20.3 22.0 24.1

420 330 110 66 61 41

410 340 100 70 62 36

190 220 360 380 400 390

180 230 330 380 390 400

3.7 6.4 10.5 11.8 13.0 13.6

3.7 6.3 10.4 11.8 12.0 12.9

Uniaxially stretched under 1.5x1.0 constant width, no heat set 2.Ox 1.0

2.5x1.0 3.0x1.0 3.5x1.0 4.Ox 1.0 4.Ox 1.5 Two-way successively biaxially stretched, heat set 4.0 x 2.0

Simultaneously biaxially stretched, heat set

Material, polyethylene terephthalate films prepared by the T-die process; medium of stretching and heat setting, hot dry air.

heat deformation is called "heat expansion coefficient," usually measured between 20 and 40 0 C in the 65% RH (relative humidity). Table 6.3.3 [15] shows the heat expansion coefficients of various PET films. The value of the heat expansion coefficient is closely related to molecular orientation and thermal movement of molecular chains. Usually, the value of the heat expansion coefficient decreases with increasing molecular orientation.

tan 8

Dynamic modulus (dyn/cm2)

LD TD

tana

Teraperature(°C) Figure 6.3.8

Temperature dependence of dynamic modulus of balanced PET film

Irreversible Deformation When the film is heated to high temperature, heat shrinkage takes place, and the film does not return to the original dimension. This is called irreversible deformation. The value of heat shrinkage is controlled by heat set temperature and ratio of relaxation. Figure 6.3.9 [15] shows the relationship between temperature and heat shrinkage for two kinds of PET films. Generally, the higher the molecular orientation is, the higher is the heat shrinkage.

6.3.4.3

Optical Properties

Figure 6.3.10 [16] indicates the variation of three direction refractive indices when the PET film is uniaxially stretched. The value of refractive index increases in the stretched direction and decreases in the thickness direction with increasing stretching ratio, whereas the value in the direction perpendicular to the stretched direction decreases at initial stage and thereafter increases with increasing stretching ratio. This variation is due to the degrees of planar orientation. Figure 6.3.11 [16] shows the variation of refractive indices with elongation of biaxially stretched PET film.

Table 6.3.2

Properties of Nonaxial and Biaxially Oriented Plastics Films

Properties

Units

Branched polyethylene

Polypropylene

NO

BO

NO

1 to 3 50

8 to 10 3 to 5 50 60 to 90 10 to 15 50to 500 1 to 2 18

Tensile strength Tensile modulus

kg/mm2 kg/mm2

Propagating tear strength Impact strength

g/mil

100 to 350 kg • cm/mil 2

Haze

%/mil

6 to 10 1 to 3

Heat shrinkage % 20 to 60 1000C, min Service temperature 0 C -50to -50to range 80 110 g • 0.1 mm Water vapor day • m2 permeability 4.4 0 40 C, 90% RH cc.0.1 mm Oxygen 750 0 day • m2 permeability 25 C, 1300 1 atm

Unplasticized polyvinyl chloride BO

Polyethylene terephthalate

Nylon-6

NO

BO

NO

Vinylon*

BO

NO

13 to 30 200to 300 4 to 15

5 to 8 10 to 15 140to 300to 200 240 350 10 to 100 3 to 10

16 to 25 400to 500 10 to 20

6 to 10 20 to 25 45 to 140to 60 220 50 20 to 28

17

2

15

25

35

25

2 to 4 1 to 2

2 to 3

1

4 to 7

2

0

Oto 8

0

30 to 50

0 to 120

-50to 130

70

-60 to 70

80

6

17

3 to 4 1.5

0

0

-70to 150

130

5.5 10

600

O t o 1 1 to 5

240

* Data of vinyl on BO are those of Emblar, OV coated with PVDC on both sides. NO, nonoriented; BO, biaxially oriented

8 19

90

15

BO

NO

BO

5 to 6 25 70to 480 80 12 1

2 0.5

-60to 130 40

^100

6

^0.5

^0.3

Table 6.3.3

Thermal Expansion Coefficients of PET Film Thermal expansion coefficient, at (/ 0 C)

Film type

70 x22~ 6

Nonoriented film Balanced film

(LD) (TD) (LD) Tensilized film (TD) Uniaxially oriented film ( x 4.8) (LD) (TD)

6.3.4.4

16.5 x 15.9 x 4.5 x 22.0 x 18.7 x 124 x

1(T 6 1(T 6 1(T 6 1(T 6 10~ 6 10~ 6

Barrier Properties

Table 6.3.4 [17] shows the barrier properties of various films against some gases and liquids. Figure 6.3.12 [18] shows the variation of gas permeability with increasing temperature. Generally, gas barrier properties decrease with increasing temperature. Figure 6.3.13 [18] shows the water vapor permeability of biaxially stretched PET film.

6.3.4.5

Chemical Resistance

Heat shrinkage (%)

Table 6.3.5 [19] shows the resistance of PET film against chemicals. PET film is slightly weak against alkalis but strong against acids. PET film is insoluble in the general organization solvents.

Tensilized film

Normal film

Temperature ( 0 C) Figure 6.3.9

Temperature dependence of heat shrinkage

Refractive index n

Draw direction

Perpendicular diijection

Thickness direction

Draw ratio Figure 6.3.10

6.3.4.6

Refractive index versus draw ratio of longitudinal direction

Electrical Properties

Refractive index n

Dielectric properties of PET film are shown Table 6.3.6 [20] compared with those of other films.

LD stretching ratio

TD stretching ratio

Figure 6.3.11

Refractive index of biaxially oriented PET film caused by TD stretching ratio

Table 6.3.4

Permeability of Polymers

Polymer

Gas permeability at 25 0 C, 50%RH / cc • /mi \ 4 2 V10 cm • day • arm/

Liquid permeability at 25 0 C

O2

H2O

SO2

14

0.6

15

0.8

50 24 120 80 140 520

2.0 4.0 6.0 4.6 10.0 28.2

6.0

h-> - - •' /9 s n o w the/values in the nine-point differencing mesh shown in Fig. 6.4.3. By use of the relationships in Eq. (6.4.53), the expanded governing equations (6.4.52) and

(V)

i

(U)

Figure 6.4.3 Nine-point differencing mesh for numerical simulation of flat film stretching

v

u

Figure 6.4.4 Rubber string network as a model of a flat rubber film initially uniform in thickness

(6.4.52') can be transformed into two algebraic equations in the unknown/and g values at the (i, 7) mesh point and its eight neighboring mesh points shown in Fig. 6.4.3. To easily solve the governing equations (6.4.52) and (6.4.52'), an attempt was made to approximate the rubber film extension to the stretching of the "rubber string mesh" shown in Fig. 6.4.4. An individual string mesh consists of square and diagonal rubber strings initially unstressed and welded together at each mesh point denoted by the black dots in Fig. 6.4.4. The rubber strings were assumed to obey the two alternative elasticities shown by Eqs. (6.4.54) and (6.4.55): For the Hookean solid, Vi = T-I

(6.4.54)

For the rubberlike elastic body,

n=^P

(6A55)

where rj is the tensile force acting on an individual string and T is the elongational deformation defined as the present extended string length over the initial unstressed length. In the string mesh model shown in Fig. 6.4.4 the counterparts of the governing equations (6.4.52) and (6.4.52') are two equations stating the balance of x and y component forces, respectively, exerted by rubber strings to each welded mesh point.

Considering the mesh point (i, j) in Fig. 6.4.4 as point 1 and eight points from 2 to 9 neighboring point 1, the strain for the string connecting points 1 and k after stretching is given by

*

VOl-^H-te-^ AorV2A

where the denominator of Eq. (6.4.56) is the initial length between point 1 and point k before stretching; its value is A or -JlA depending on whether k is an even or an odd number. The sum (FF)11 of tensile forces in the u direction acting on point 1 is given by:

(FF\ = !>*(/* -/i)/|"\/(A-/i) 2 +fe-^) 2 1 fc=2 L -I

( 6A57 )

Similarly, the sum (FF)v of the tensile force in the v direction acting on point 1 is given by: (FF)V = J2ik(gk -gi)/\y/(fk -fif + (gk-gif 1 (6A58) where r\k can be obtained by substitution of the Tk in Eq. (6.4.56) into Eq. (6.4.54) or Eq. (6.4.55). The results of equations governing the extension of the string mesh shown in Fig. 6.4.7 are obtained by setting (FF)n = (FF)v = 0 in Eqs. (6.4.50) and (6.4.51). Equations (6.4.52) through (6.4.58) were solved numerically for three different film extension problems. In the first problem a rectangle-shaped rubber film, initially uniform in thickness having unity side lengths as shown in Fig. 6.4.5, is extended in such a manner as to form a trapezoidal outer boundary. As the film is extended point A remains stationary while point B moves to B! by a distance of C and in the direction of 45 ° northeast. Because of symmetry only the upper half of the film plus one extra row of mesh points below the center line are shown in Figs. 6.4.5 and 6.4.6. Each side of the initial square is divided into m (m = 16 as shown) equal differencing increments to form the square mesh as shown.

B'

Figure 6.4.5 Extension of initially square and even film into a trapezoidal shape. Square differencing mesh is Lagrangian (u, v) coordinates

A

B

D E

C F

C F1

B'

A

C

D E

F'

Figure 6.4.6 The (u, v) mesh after the extension described in Fig. 6.4.5. The three different curves of constant u are from left to right (1) solution of Eq. (6.4.52) and (6.4.52'); (2) string mesh approximation; rubberlike elasticity and (3) string mesh approximation, Hookean elasticity

Values of/(/, j) and g (/, j ) on the outer boundary E-A-B / -F / are known because they are forced to be uniformly extended to form the trapezoid. Moreover, owing to the center line symmetry the values of g(i, 2) on the center line are equal to zero and the/(z, 1) and g(i, 1) on they = 1 row are the mirror images of those in they = 3 row: /(i, 1) = / ( / , 3),

g(i, 1) = -g(i, 3),

g(/, 2) = 0

(6.4.59)

This leaves altogether: N = 2(m- l)(m/2 - 1) + (m - 1) = (m - I)2

(6.4.60)

Unknown values of/and g in the field of computation are shown in Fig. 6.4.5. On the other hand, governing equations (6.4.52) and (6.4.52') or (6.4.57) and (6.4.58) must hold at every inside mesh point. Accordingly, the number of equations required to be satisfied is N = (m — I) 2 , matching the number N of unknown variables given in Eq. (6.4.60). The value m = 16 (i.e., Af= 225) was used in the present problem as shown in Figs. 6.4.5 and 6.4.6. As Fig. 6.4.6 shows the above three different numerical solutions are discernible only in the curves of constant u; the rightmost u curves are due to the string mesh approximation with the Hookean elasticity in Eq. (6.4.54), the middle u curves are due to the string mesh approximation with the rubberlike elasticity in Eq. (6.4.55), and the leftmost u curves are the solution for the correct governing equations such as Eq. (6.4.52). The second example is that of a rectangle-shaped rubber film initially uniform in thickness and 1 x 3 in size, as shown in Fig. 6.4.7, extended in such a manner as to form the ABCDE shape outer boundary. The extension along the boundary ABCDE is assumed uniform. As in Fig. 6.4.6 the above three different numerical solutions are discernible only in the curves of constant u in Fig. 6.4.7; the rightmost u curves are due to the string mesh approximation with the Hookean elasticity in Eq. (6.4.54), the middle u curves are due to the string mesh approximation with the rubberlike elasticity in Eq. (6.4.55), and the leftmost u curves are the solution of the correct governing equations (6.4.52) and (6.4.52;).

C

A

D

B

Figure 6.4.7 The (u, v) mesh before and after stretching. The three different u curves are the same as in Fig. 6.4.6

E

The third example, shown in Fig. 6.4.8, is similar to the second problem shown in Fig. 6.4.7 except that the right film end is free. The numerical solution shown in Fig. 6.4.8 is for the string mesh approximation with Hookean and rubberlike elasticities. The solution of the correct governing equations (6.4.52) and (6.4.520 did not converge. In Fig. 6.4.8 the right u curves are due to the Hookean elasticity and the left ones are due to the rubberlike elasticity. It

C

A

B

Figure 6.4.8 The (u, v) mesh before and after stretching. The two different u curves are the (2) and (3) in Fig. 6.4.6

Figure 6.4.9

D

Experimental observation of rubber mesh stretching

E

is confirmed that these numerical predictions are similar to the experimental results shown in Fig. 6.4.9 [5]. When the rubber film is initially uniform in thickness, the string mesh approximation shown in Fig. 6.4.4 may be preferable to the rigorous numerical solution of the correct governing equations (6.4.52) and (6.4.52'). Because the former method produces solutions close enough to the rigorous solution, it is considerably easier for obtaining the convergence of numerical processes and is convenient in handling the unconstrained free edges of the film whenever they are present.

6A3

Numerical Analysis of Film Extension by the Finite Element Method (FEM)

6.4.3.1

Analytical Method for Two-Dimensional Plane Stress or Strain Problem

In the previous section theoretical analysis by the finite difference method (FDM) was introduced for rubber film extension, which is characterized by the finite difference approximation of the physically exact governing equations. In this section, examples of numerical analysis by the finite element method (FEM) are introduced for polymer film extension, which is characterized by replacement of approximate simultaneous linear equations by conceptual finite elements to the governing equation. The theory of a FEM about the plane problem is briefly outlined below. Please refer to a reference text on FEM such as [6] if further information is required. The general analytical procedure of the FEM is conceptually described as follows. 1. The continuum is separated by imaginary lines or surfaces into a number of "finite elements." 2. The elements are assumed to be interconnected at a discrete number of nodal points situated on their boundaries. The displacements of these nodal points are the basic unknown parameters of the problem. 3. A set of functions is chosen to define uniquely the state of displacement within each "finite element" in terms of its nodal displacements. 4. The displacement functions now define uniquely the state of strain within an element in terms of the nodal displacements. These strains, together with any initial strains and the constitutive properties of the material, define the state of stress throughout the element and, hence, also on its boundaries. 5. A system of forces concentrated at the nodes and equilibrating the boundary stresses and any distributed loads is determined, resulting in a stiffness relationship. Using the FEM mentioned previously, we can obtain approximate solutions to practical problems that are difficult to solve by other methods such as FDM, although the computation by FEM requires much computer time and its accuracy is often inferior to that obtained by a special analytical method suited for the particular problem. The above advantage of FEM can

y

m V 1 (V 1 )

Xj

i

U 1 (U 1 )

Yi

j

Figure 6.4.10 An element of two-dimensional continuum

x

be utilized to find a solution to the extremely difficult problems of tentering in film processing. Discussed below is the FEM for plane deformation. Now, we consider a typical triangular element as shown in Fig. 6.4.10, which is defined by nodes i,j, m numbered in a counterclockwise order with straight line boundaries. We first explain the displacement function. The corresponding displacement at of node /, having two components, is given by:

a, = { JJ }

(6.4.61)

All components (six components) for the three nodes of the elements are grouped in a vector ae h i a e =\aj [

(6.4.62)

where the superscript e denotes element. The displacements within an element are uniquely defined by these six values. The simplest expression is clearly given by two linear polynomials: u = (X1 + (X2X + (x3y;

v = a 4 + a 5 x + oc6y

(6.4.63)

The six constants a can readily be evaluated by solving the two sets of three simultaneous equations by substituting the nodal coordinates for (x, y). For example, three simultaneous equations for the u component of the nodal displacements are denoted by: U1 = Oc1 + (X2X1 + cc3y(;

uj = Oc1 + Oc2-Xy = a^-;

um = U1 + a2xm + cc3ym

(6,4.64)

We can easily solve Eq. (6.4.64) for oci, a2, and a3 in terms of the nodal displacements U1, Uj, um. Substituting the results obtained above into Eq. (6.4.63), we finally obtain the horizontal displacement u as follows: w = — {{at + bfc + c-yX + (a,- + bjX + Cjy)uj + (am + bmx + Cn^uJ

(6.4.65)

where «i = ^ym ~ xmyp

bt = yj -ym=

yjm;

ct =xm-

Xj = xmj

(6.4.66)

Similarly, other coefficients at ay, bj, Cj, . . . , cm can be obtained by a cyclic permutation of subscripts in the order i,j, m. Then, the A in Eq. (6.4.65) is given by: 2 A = det 1 Xj yj = 2 x (area of triangle ijm) 1 *m ym

(6.4.67)

The equation for the vertical displacement v is similarly V =

2A {(fl/

+ bfC + coi)Vi +

^

+

^

+ Cjy)Vj + ( m +

"

^*

+ Cmy)Vm]

(6.4.68)

From this point one can represent the above relationships, Eqs. (6.4.65) and (6.4.68), in the following standard form for horizontal and vertical movements of a point within the element:

u = { " } = Na* = [IN,, IN7, I N J . '

(6.4.69)

where the functions N will be called "shape functions," I is a two by two identity matrix, and N k = (ak + b k x + C ky)/ 2 A for k = i, j , m. The chosen displacement function [Eq. (6.4.63)] automatically guarantees continuity of displacements with adjacent elements because the displacements expressed by Eq. (6.4.63) vary linearly along any side of the triangle and, with identical displacement imposed at the nodes, the same displacement will clearly exist all along an interface. Second, we will explain the strain (total strain). With displacements known at all points within the element the strain at any point can be determined. The total strain at any point within the element written in matrix notation, s, can be defined by its three components which contribute to internal work as shown below:

I

ex 1 Vd/dx, sy 1 = O,

yxy\

L9/^'

O "I f , d/dy \ U I = Lu

(6.4.70)

9/9xJ m

where L is a suitable linear operator. Substituting Eq. (6.4.69) into Eq. (6.4.70), we have: h i E = Ba 6 ^[B 1 , Bj, BJJa 7 -

(6.4.71)

where a typical matrix Bt is given by B1=LINj=

"ajVf/ax, 0, \_3NJdy,

o I Vb1, o " dNt/dy = (1/2A) • 0, C1 BNf/dx] \_cf, bt _

(6.4.72)

It should be noted that in this case the B matrix is independent of the position within the element, and hence the strains are constant throughout the element. Third, we will explain the stresses. In general, the material within the element is subjected to initial strains owing to temperature change, shrinkage, crystal growth, and so on. If such initial strains are denoted by £ 0 , then the stresses will be caused by the difference between the present and initial strains. Although this initial strain vector, e0, defined by Eq. (6.4.73), in general, depends on the position within the element, it is usually represented by

average, constant values. This is consistent with the constant strain conditions imposed by the prescribed displacement function.

B0=I

h° 1 6 X)

(6A73)

Anisotropic materials present special problems, because the coefficients of thermal expansion may vary with direction. Letx' a n d / show the principal directions of the material. The initial strain due to thermal expansion becomes, with reference to these coordinates for plane stress:

Ko ) \«xee) «o = { Vo [ = { « / e

I V*/o J

(6-4-74)

l0J

where ocx and a are the expansion coefficients referred to the x' a n d / axes respectively, and 6e is the temperature rise. To obtain the strain components in the x, y system it is necessary to use an appropriate strain transformation matrix T giving 4 = TT£0

(6.4.75)

where superscript T means the transposed matrix. With /?, which is the angle of the x'—y7 coordinate system inclined against the x-y coordinate system, it is easily verified that: cos2 P sin2 P - 2 sin p cos ft 2 T = sin p COs2P 2 sin £ cosjS _ sin P cos P —sin P cos p cos2 P — sin2 P _

(6.4.76)

Thus, £0 can be simply evaluated. It will be noted that the shear component of strain is no longer equal to zero in the x-y coordinates. In addition it is convenient to assume that at the outset of this analysis the body is subjected to an initial residual stress cx0 that may be measured but the prediction of which, without the full knowledge of the material's history, is impossible. These stresses can simply be added onto the general definition. Thus, assuming general linear elastic behavior, the relationship between stresses and strains will be linear and of the form: h i a = I Gy \ = D(e - E0) + a0

(6.4.77)

where D is the elasticity matrix containing the appropriate material properties and s is given by s= \sy

I

Next, a 0 in Eq. (6.4.77) is excluded which is simply additive.

(6.4.78)

For plane stress in an isotropic material we have, by definition: Sx = (Tx/'E - vGy/E + ex0

(6.4.79)

sy = -VOx/E + Gy/E + Sy0

(6.4.80)

yxy

(6.4.81)

= 2(\ + v)TXy/E + yxyQ

where E is the elastic (Young's) modulus and v is the Poisson ratio. Solving the above for the stresses, we obtain the matrix D as

fl

F

v 0

D = —-^- v 1 0 {l v; |_0 0 (l-v)/2_

(6.4.82)

For plane strain in an isotropic material a normal stress oz exists in addition to the three other stress components. For the special case of isotropic thermal expansion we have: sx = Gx/E - VGy/E - VGJE + a6e

(6.4.83) e

Sy = -VGx/E + Gy/E - VGJE + oc6

(6.4.84)

yxy = 2(1 + v)xxy/E

(6.4.85)

but in addition sz = 0 = -VGx/E - VGy/E + GJE + a6e

(6.4.86)

On eliminating GZ and solving for the three remaining stresses and by comparison with Eq. (6.4.74) where G0 is excluded, the matrix D is

E(l-v)

^~v) °

P

D = , 1 ± \ n \ , v/(l-v) 1 (l + v)(l-2v) |^ 0 Q

0 (l-2v)/2(l-v)J

(6.4.87)

where 6e is the temperature rise and a is the coefficient of thermal expansion. For a completely anisotropic material, 21 independent elastic constants are necessary to define completely the three-dimensional stress-strain relationship. If two-dimensional analysis is to be applicable a symmetry of properties must exist, implying, at most, six independent constants in the D matrix. To describe the most general two-dimensional behavior, it can be given by: d

ll

D=

d

12

d22 (sym.)

d

13

Cl23 d33_

(6.4.88)

where the necessary symmetry of the D matrix follows from the general equivalent of the Maxwell-Berti reciprocal theorem and is a consequence of invariant energy irrespective of the path taken to reach a given strain state.

For instance, the D matrix for plane stress of a x-y anisotropic thin film (isotropic in the thickness direction) in two dimensions is given by: D=-

^ -

ri nv

d-nv? y )[ 0

nvxy 0 n 0 Q

(6.4.89)

m( i_nv2 y) J

where n = Ey/Ex, m = Gxy/Ex, Ex and Ey are the Young moduli in the x and y directions, respectively; G^ is the shear modulus; and vxy is the Poisson ratio, and then vyx can be obtained by vyx = nv^ from the relationship vyx/vxy = Ey/Ex = n from the Maxwell-Betti reciprocal theorem. When the direction of the anisotropic principal axis is inclined to the x axis considered now, to obtain the D matrix in the universal coordinates, a transformation is necessary. Taking D' as relating the stresses and strains in the inclined coordinate system (x1', / ) , the D matrix can be easily obtained as follows: D = TD'TT

(6.4.90)

where T is as given in Eq. (6.4.76). Then, the stiffness matrix Ky of the element ijm as shown in Fig. 6.4.10 is defined from the general relationship by coefficient Kg = BjDB^tdxdy

(6.4.91)

where t is the thickness of the element and the integration is taken over the area of the triangle. If the thickness of the element is assumed to be constant, a good assumption as size of elements decreases, then as neither of the matrices contains x or y we have, simply Kfj = BjDBj^A

(6.4.92)

where A is the area of the triangle defined by Eq. (6.4.67). This form is now sufficiently explicit for computation, with the actual matrix operations being left to the computer. Further expressions can be obtained in [7].

6.4.3.2

Observation of Deformation Behavior in a Tenter

Figure 6.4.11 shows a typical tenter process for successive biaxial stretching of PET films. In Fig. 6.4.11, the extruder (EXT) melts and extrudes the polymer. The extruded film is cast (CA) on a chill roll to form an amorphous sheet. The PET sheet subsequently is stretched in EXT TDJS MD

TM FW

CA Figure 6.4.11

Schematic of representative film production process

the machine direction (MD) to become the uniaxially oriented film. The film is then stretched in the transverse direction (TD) and thermoset (TS) to become the biaxially oriented film and finally trimmed (TM) and taken up on the film winder (FW). In the TD and TS sections of the tenter process films often develop the so-called "bowing" phenomenon. Bowing is a kind of uneven stretching in which a straight line drawn transversely on the film entering the tenter bends in a bow shape as the film goes through the TD and TS sections. As shown in Fig. 6.4.12 the distortion of bowing is expressed as the bow height b as percentage of film width W. When the film center lags behind the film edges the bow height b is considered positive. The bowing distortion b/ Wmeasured at different positions within the TD, TS sections consists of four zones: preheating, TD stretching, thermosetting, and cooling as indicated in Fig. 6.4.12. Shown in Fig. 6.4.13 are the changes in the distortion b/ Wof experimentally observed bowing as the film goes through the TD, TS sections. In Fig. 6.4.13 the position in the tenter is expressed as the dimensionless length L/ W which is the distance from the entrance of the Bowing line

W

Bowing line

Film Pre-heating zone

Stretching zone

Thermo-setting zone

Cooling zone TD

b

MD Four zones of tenter

Bowing distortion (%)

Figure 6.4.12

Pre-heating zone

Stretching zone

Thermo-setting zone

Cooling zone

Dimensionless length (-) Figure 6.4.13 Experimentally observed deformation behavior in tenter expressed in bowing distortion versus dimensionless length

Bowing distortion (%) Figure 6.4.14 Bowing distortion at tenter exit versus thermosetting temperature

Bowing distortion (%)

Thermo-setting temperature (°C)

Figure 6.4.15 Bowing distortion at tenter exit versus cooling temperature

Cooling temperature (0C)

tenter L divided by the film length W. We note in Fig. 6.4.13 that bowing remains insignificant in the preheating zone. As the film enters the transverse stretching zone, the film develops a negative bowing followed by a quick change into positive bowing. Bowing takes its maximum positive value in the first half of the thermosetting zone. Thereafter the bowing maintains a high positive level. The above results are somewhat different from the assumptions for the theory in the previous articles by Sakamoto [9, 10]. Figure 6.4.14 shows that higher thermosetting temperatures tend to increase the distortion of bowing, while changing the temperature of cooling does not affect bowing as Fig. 6.4.15 shows. It was found that allowing the film to shrink transversely in the thermosetting zone, that is, relaxing, tends to increase bowing as shown in Fig. 6.4.16. Negative relaxing, that is, restretching, in the thermosetting zone tends to suppress bowing.

6.4.3.3

Simulation of the Bowing Phenomenon in the Tenter Process

A FEM simulation of the phenomenon of bowing occurring in the (TD, TS) sections of the tenter process was carried out assuming the film to be a thin elastic body [H].

Bowing distortion (%)

Relaxation ratio in TD (%)

Figure 6.4.16 Bowing distortion at tenter exit versus relaxation ratio in TD within thermosetting zone

After stretching

After stretching

Figure 6.4.17

Two kinds of initial mesh

As shown in Table 6.4.1, four different materials were considered: homogeneous isotropic, homogeneous anisotropic, heterogeneous isotropic, and heterogeneous anisotropic. The shape of the film before stretching was assumed to be a rectangle (initial shape a) or a rectangle-plus-ramp shape (initial shape b) shown in Fig. 6A.17. The width of the initial rectangle was considered equal to the width of the film entering the TD section of the tenter. Initial division of the film shape into triangular elements is shown in Fig. 6.4.17. The film shapes in Fig. 6.4.17 are intended to cover the region extending from the entrance of the tenter to the point of maximum temperature located in the thermosetting zone. This choice was made because throughout the region between the maximum temperature point and the tenter exit the extent of bowing was known experimentally to remain unchanged. Figures 6.4.18 to 6.4.22 compare experimental observations of b/ W values with the results of the FEM simulation. Bowing is considered positive when the bow shape is concave toward the tenter exit, that is, when the film center lags behind film edges. Figure 6.4.18 compares experimental results with the FEM simulation assuming the film to be homogeneous isotropic and having initial shape a (rectangle). The simulation is not satisfactory. Figure 6.4.19 is the same as Fig. 6.4.18 except that in the FEM simulation the film material was assumed to be homogeneous anisotropic with four independent elastic constants: Ex, Ey, Gxy, and vxy.

Table 6.4.1

Simulation Conditions Material constants Pre-heating zone Start

Stretching zone End

Start

Case Mesh EL no. type (GPa)

ET (GPa)

(")

EL Ex (GPa) (GPa)

(")

1 2 3 4 5

4.000 1.000 4.500 1.125 1.125

0.36 0.36 0.36 0.34 0.34

4.000 4.000 4.500 4.500 4.500

0.36 4.000 0.36 4.000 0.34 4.000 0.34 4.000 0.34 4.000

a a a a b

4.000 4.000 4.500 4.500 4.500

4.000 1.000 4.500 1.125 1.125

EL Ex (GPa) (GPa) 4.000 1.000 4.000 1.000 1.000

Thermosetting zone Start

End

End

EL (GPa)

ET (GPa)

(")

EL (GPa)

Ex (GPa)

(")

EL (GPa)

(GPa)

0.36 4.000 0.36 4.000 0.36 4.000 0.36 4.000 0.36 4.000

4.000 1.000 4.000 4.000 4.000

0.36 4.000 0.36 4.000 0.36 0.500 0.36 0.500 0.36 4.000

4.000 1.000 0.500 0.500 4.000

0.36 4.000 0.36 4.000 0.42 0.500 0.42 0.500 0.36 0.500

4.000 1.000 0.500 0.500 0.500

^LT (")

0.36 0.36 0.42 0.42 0.42

Bowing distortion (%)

Casei Pre-heating zone

Stretching zone

Thermo-setting zone

Cooling

zone

Dimensionless length (-) Figure 6.4.18 Bowing, experiment and FEM simulation, Case 1 in Table 6.4.1. •, experimental; • , calculated

Bowing distortion (%)

Case 2 Thermo-setting zone

Stretching zone

Pre-heating zone

Cooling zone

Dimensionless length (-) Figure 6.4.19 Bowing, experiment and FEM simulation, Case 2 in Table 6.4.1. •, experimental; • , calculated

Figure 6.4.19 shows a comparison of the experimental results with the calculated results under the assumption that the film is a homogeneous anisotropic material with the initial film shape of a rectangle as shown in Fig. 6.4.17(a). With these constants G^ is given by the following equation:

G

xy

E

A5

\Ex

E

y

E

x J

where Ex and Ey are the Young moduli, G^ is the shear modulus (rigidity), v^ is the Poisson ratio, and E45 is the Young modulus in the direction at an angle of 45 ° to the machine (longitudinal) direction which is given by the average of Ex and Ey\ E45 = (Ex + Ey)/2. The subscripts x and y stand for longitudinal (machine) direction and transverse direction, respectively. In addition to the above the reciprocal theorem states that Vyx/v^ = Ey/Ex.

Bowing distortion (%)

Case 3

Pre-heating zone

Stretching zone

Thermo-setting zone

Cooling zone

Dimensioniess length (-) Figure 6.4.20 Bowing, experiment and FEM simulation, Case 3 in Table 6.4.1. •, experimental; • , calculated

Bowing distortion (%)

Case 4

Pre-heating zone

Stretching zone

Thermo-setting zone

Cooling zone

Dimensioniess length (-) Figure 6.4.21 Bowing, experiment and FEM simulation, Case 4 in Table 6.4.1. •, experimental; • , calculated

In the FEM computations fixed values were given to the above elastic constants at the entrance and exit of each zone and the values within the zone were assumed to be linear interpolations of values at the entrance and exit. Isotropic materials were assumed to have two independent elastic constants E and v, meaning that E = Ex = Ey — E45 and v — v^ = vyx. Evidently the simulation shown in Fig. 6.4.19 is not good enough. Figure 6.4.20 shows the comparison for the case of heterogeneous isotropic film with initial shape a (rectangle). Again the simulation is not entirely satisfactory. Figure 6.4.21 is for the case of the heterogeneous anisotropic film with initial shape a (rectangle). The FEM simulation in this case is worse than the one in Fig. 6.4.20.

Bowing distortion (%)

Case 5 Pre-heating zone

Stretching zone

Thermo-setting zone

Cooling zone

Dimensionless length (-) Figure 6.4.22 Bowing, experiment and FEM simulation, Case 5 in Table 6.4.1. •, experimental; • , calculated

Figure 6.4.22 is for the case of the heterogeneous anisotropic film b [rectangle-plusramp; see Fig. 6.4.17(b)]. This particular initial film shape b was conceived to take into consideration the 20% or more shrinkage of the bioriented film entering the thermosetting zone at 105 0 C near the transverse stretching temperature. In other words the ramp part of the initial film shape was intended to include in advance the plastic deformation measured as the shrinkage of the film just after the TD extension. The simulation shown in Fig. 6.4.22 is more satisfactory than any of the ones shown in Figs. 6.4.18 to 6.4.21. Agreement with experimental values is particularly good at and after the point where the bowing turns from negative to positive values.

6.4.3.4

FEM Simulation of Tensile Testing

Tokuda [12] carried out a series of FEM simulations for the tensile testing of polyethylene terephthalate (PET) films, assuming the film to be a two-dimensional elastic-plastic body. The simulation covered several different aspects of the tensile extension of PET films. First was the simulation of the large two-dimensional deformation of PET film specimens in tensile testing. The second was the numerical prediction of the effects of initial transverse thickness nonuniformity. The third simulation concerned the tensile testing of PET film specimens containing fine spherical particles. Local deformation in the vicinity of the particle was simulated with respect to the formation of a protrusion on the film surface and the formation of a void around the particle. For the FEM simulation the rheology of the PET film in the thermoplastic region was assumed to be represented by the dynamic model shown in Fig. 6.4.24 which in turn simulates the rheology of the amorphous (A) and crystalline (C) model structure shown in Fig. 6.4.23. The dynamic model expressed in the form of constitutive equations is: a = ox + (T2

(6.4.94)

dox/dt = -(Jx/T + G' dl/dt (72 = rj- dl/dt

(6.4.95) (6.4.96)

T = rj/G

(6.4.97)

where a, Oe1, and a2 are stresses applied to the film as shown in Fig. 6 A.24; t is time; G is shear modulus (rigidity); X is elongational deformation or stretch ratio; rj is coefficient of viscosity, and T is relaxation time. The C in Fig. 6.4.24 is the nonlinear elastic element and its shear modulus G (rigidity) is given by the formula: G = C1(T)(X"1 - rn) +

C2(X/K)P{T)

(6.4.98)

where Tis absolute temperature: Cx(T), C2, m, n, K, and P(T) are characteristic parameters of a polymer having constant values at a given temperature. The A in Fig. 6.4.24 is the nonlinear viscous element having a coefficient rj of viscosity given by: n =/(A) • n°° • (TT/2) ( "- 1)/2 • exp[t/(l/r - l/T0)/R\

(6.4.99) o

Force

tfi

G2

c A

I

C

A

Figure 6.4.23 Orientation structure model for PET film

A

Figure 6.4.24 Dynamic rheology model equivalent to the model shown in Fig. 6.4.23

where/(i,) is a characteristic parameter of the polymer and is a function only of elongational deformation, rf° is the coefficient of viscosity at infinite time, (/is apparent activation energy in the Andrade expression, R is the gas constant, n is a characteristic parameter, and T0 is the reference temperature. To test the adequacy of the above constitutive equations, three different tensile tests were carried out on PET film specimens. The results shown in Fig. 6.4.25 are (a) tensile testing of as-cast amorphous film, (b) continuous roller drawing of as-cast amorphous film, and (c) transverse stretching of uniaxially oriented film, all over a range of temperatures. Shown in Fig. 6.4.26 are stress (7-elongation curves X due to FEM simulation assuming PET and an elongational strain rate of 50%/s. The simulated curves in Fig. 6.4.26 are in qualitative agreement with the experimental curves in Fig. 6.4.25.

a (MPa) a (MPa)

X (-)

a (MPa)

A(-)

Figure 6.4.25 Experimental stress cr-elongation X curves of PET film. (a) Tensile testing of as-cast amorphous film; (b) continuous roller drawing of as-cast amorphous film; (c) transverse stretching of drawn oriented film on testing machine

a (MPa) Figure 6.4.26 Simulated stress cr-elongation X curves for PET film

A (-)

A

Figure 6.4.27 Experimentally observed deformation of PET film in tensile testing

I

Figure 6.4.28 FEM simulation of the tensile testing shown in Fig. 6.4.27

Pre-heating zone Figure 6.4.29 Transverse unevenness. The shaded part of the film is initially 2% thicker than the rest of the film

Stretching zone

Temperature (0C)

Q T s : Set temperature T: Film temperature Q : Unevenness of thickness T5 T

Unevenness of thickness (-)

Stretching zone

Pre-heating zone

Distance from Inlet of tenter (m)

Stretching zone

Temperature (»r