Ind. Eng. Chem. Res. 2006, 45, 719-723
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Analysis of Film Casting Process: Effect of Cooling during the Path in Air Gaetano Lamberti* and Giuseppe Titomanlio Department of Chemical and Food Engineering, UniVersity of Salerno, Via Ponte don Melillo, 84084 Fisciano (SA), Italy
In this work, polymer film casting experiments have been performed using commercial isotactic poly(propylene) (iPP), under operating conditions such that the solidification takes place during the path in air. The experiments were carried out with and without the presence of two jets of cooling air impinging on both the sides of the film. The effects of the cooling air jets on the experimental profiles of the film width, axial velocity, and temperature are reported and briefly discussed. Introduction The polymer film casting process is shown schematically in Figure 1. Polymer melt is extruded through a slit die, and the film is drawn in air by chill rolls. If the temperature decreases enough, the melt solidifies during the path in air. This needs either a long path in air or a high cooling rate. Because of its industrial importance, the film casting process has been the subject of several studies, experimental as well as theoretical. Modeling of isothermal film casting for a viscous polymer has been proposed following a one-dimensional approach by Agassant et al.,1 a two-dimensional approach by d’Halewyn et al.,2 and a three-dimensional approach by Sakaki et al.3 Two- and three-dimensional modeling approaches describe a number of process features that cannot be predicted on the basis of one-dimensional modeling. Among these features, probably the most important is the shape of the film cross section, hypothesized to be rectangular in the onedimensional modeling, but actually shaped as a dog bone (i.e., the film thickness is practically constant in the film center and it increases in correspondence to the width boundary), a shape correctly predicted by the two- and three-dimensional modeling. The nonisothermal aspects have been analyzed by several authors.4-8 However, in all of these studies, polymer solidification is not explicitly considered; indeed, under industrial process conditions, solidification takes place after the contact between the film and cold rolls. Lamberti, Titomanlio, and co-workers9-11 developed a nonisothermal viscous model accounting for the crystallization in air of isotactic poly(propylene) (iPP) and for the effect of crystallinity on rheology. Because of the facts that (i) the flow is mainly elongational, (ii) the film casting process is stationary, and (iii) on-line measurements are sufficiently easy to perform, we selected the film casting process as a model experiment to study the effect of flow, and in particular of elongational flow, on the crystallization kinetics of polymers.12,13 Indeed, during drawing in air, the flow orients the macromolecules, and if the temperature is low enough, the molecules crystallize with a kinetics faster than that of a sample that undergoes the same thermal history but under quiescent conditions. It was thus of particular interest to obtain polymer solidification during the path in air, because the drawing can be assumed to take place in the melt zone prior to solidification, so the closer to the die the solidification occurs, the higher the deformation rate achieved in the film (and consequently the higher the flow effect on the crystallization kinetics). As noted above, there are two methods for producing solidification in air: to have long path in air and to achieve high * To whom correspondence should be addressed. Tel.: +39 089964077. Fax: +39 089964057. E-mail:
[email protected].
Figure 1. Schematic of the film casting process.
cooling rates. The path in air is limited by apparatus characteristics and by the process itself, because the process becomes unstable if the distance between the die and the rolls is increased too much. On the other hand, the cooling rate can be easily increased by the use of jets of a cooling medium, such as cool air. Furthermore, increasing the cooling rate by external cooling allows an increase in the take-up velocity, and thus the intensity of the deformation rate, still observing the solidification in air. The aim of this work was to investigate the effect of cooling air on the film casting process, in terms of its impact on the evolution of process variables. Experimental Section The resin adopted for the experiments considered in this work is a commercial iPP supplied by Montell (T30G, Mw ) 481000 g/mol, Mn ) 75000 g/mol, tacticity ) 87.6% mmmm). Cast film extrusion was performed with a laboratory-scale extruder equipped with a take-up unit and with a number of sensors for on-line measurements of width, axial velocity, temperature, crystallinity, and orientation, previously developed in our laboratory.12 We recently improved the apparatus by adding a device able to blow quenching air on both sides of the film, so as to increase the cooling rate and thus attain crystallization in air with a higher take-up velocity. The cooling device consists of a couple of linear nozzles. They were built of two PVC pipes, filled with a sponge to distribute the pressure loss, and with a slot along a cylinder generator that acts as the nozzle. The compressed air was fed to the tube from the side opposite the slot. The scheme of the device is recognizable in Figure 1 (both in the front view as in the lateral view), and the tubes are also evident in the snapshots of Figure 5 below. Two experiments were performed in the frame of this work, coded Z1 and Z2. The only differences between these two runs is the presence of cooling air in Z2, whereas Z1 was performed under the same operating conditions but without the presence of
10.1021/ie050899z CCC: $33.50 © 2006 American Chemical Society Published on Web 12/07/2005
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Figure 2. Film casting runs Z1 (cooling air off) and Z2 (cooling air on). Take-up velocity, 0.15 m/s; draw ratio, 32: (a) temperature, (b) axial velocity, and (c) width vs distance from die.
cooling air. Both tests were performed using a rectangular die (having width L0 ) 0.2 m and thickness S0 ) 500 µm), the distance X between the extrusion head and take-up rolls was X ) 0.4 m, and the extrusion temperature was T0 ) 220 °C. The angular velocity of the extrusion screw was set to Ω ) 60 rpm. The mass flow rate m˘ was measured by weighing the extrudate, and it was found equal to 3.47 × 10-4 kg/s. The extrusion velocity Vx(x)0) was calculated as 4.7 × 10-3 m/s from the mass flow rate and melt density, evaluated at the die temperature [F(220 °C) ) 743 kg/m3]. The take-up velocity Vx(x)X) was evaluated as 150 × 10-3 m/s simply by measuring the length of the film collected during a given time interval. Finally, the draw ratio, DR, was obtained from the ratio of these two velocity values as about 32. The experiments were accurately characterized; specifically, width, axial velocity, and temperature profiles along the draw direction were measured for both tests by means of image analysis (width and velocity) and infrared pyrometry (temperature). Other details on the apparatus and methods can be found elsewhere.12 Results and Discussions The experimental distributions of the temperature, axial velocity, and width are reported in Figure 2 for the two runs (Z1 and Z2). The two runs were carried out using the same values for all processing parameters, with the only difference being the presence of cooling air in run Z2 and its absence in run Z1. During test Z1, the temperature starts at 220 °C (extrusion temperature) and gradually decreases; however, the temperature does not decrease sufficiently to give rise to crystallization
within the first 0.2 m, where the temperature is still higher than 125 °C. The axial velocity starts at the extrusion velocity (about 4 × 10-3 m/s) and gradually increases to the take-up velocity (about 0.15 m/s). In parallel, the film width decreases from its initial value of 0.2 m to about 0.05 m. The frozen-line position is defined as the position along the draw direction downstream of which no further change in width and velocity takes place because of film solidification (the solidified film is no longer deformable). In run Z1, the frozen-line position can be identified around xFL ) 0.30 ÷ 0.35 m. During test Z2, the temperature, starting at the same extrusion value of 220 °C, decreases much more rapidly than during test Z1; because of the presence of cooling air, it reaches values comparable to ambient temperature after a distance from the die of less than 0.2 m. The lower temperature causes the material to crystallize closer to the die in test Z2 than in test Z1. The axial velocity ranges between the same extreme values during tests Z1 and Z2. It increases from the extrusion value to the take-up value within a shorter distance and does so more rapidly for test Z2. In this case, the film width decreases from its initial value of 0.20 m to a final value of about 0.10 m. The frozenline position can be identified around xFL ) 0.10 m. The film casting process is usually modeled under the hypothesis that the film cross section (the section orthogonal to the draw direction, x) maintains a rectangular shape during the stretching process. Of course, the stretching affects both the transverse directions (y and z, see Figure 3a). In Figure 3, the (deviatoric) stress components are reported, using the symbol τ. In the following model analysis, we also use the (total) stress
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Figure 3. Schematic of (a) the shape hypothesis for the film casting process, (b) the uniaxial extensional flow field, and (c) the planar extensional flow field.
components, noted by the symbol σ. The real situation is somewhere between uniaxial extensional flow, depicted in Figure 3b (this type of extension is equivalent to the stretching of a cube of material along one direction, x, with corresponding simultaneous contractions along its thickness, z, and along its width, y; τzz ) τyy, the ratio between the stress components along the thickness and the width directions being R ) τzz/τyy ) 1) and planar extensional flow, depicted in Figure 3c (this type of extension is equivalent to the stretching of a thin flat sheet of material along one direction, x, with a contraction only along its thickness, z, while the width of sheet, along the y direction, remains unchanged; τyy ) 0, R ) τzz/τyy f ∞). In the film casting of a viscous fluid, the stress along the thickness direction, τzz, is higher than the stress along the width direction, τyy, approximating the limit of planar extensional flow, i.e., R . 1. Under the further hypothesis that axial velocity is a function only of the distance from the die, Vx ) Vx(x), the ratio between these two stress components can be expressed as (see ref 9 for the derivation of the full velocity field)
Vx dS τzz 2µ S dx SR ) R) ) Vx dL LR τyy 2µ L dx
components, R(x), once the evolutions of the width and thickness are known. In the following discussion, we show that the knowledge of the evolution of the axial velocity is enough to calculate the evolutions of the width and thickness. The width distribution can be obtained by integration of the differential equation that is the definition of LR
1 dL ) LR, with L(0) ) L0 L dx
(2)
This equation can be solved numerically once the LR value is known locally. The latter can be obtained using only the velocity distribution. Let us consider the one-dimensional model proposed by Lamberti et al.,9 that allows the xx and the yy total stress components, σxx and σyy, to be estimated
dVx 1 1 dL 2 + 2µ σxx ) σxx 1 + 3 4 dx dx
[
σxx
( )] 1 1 dL 1 dL 1 dL ) σ ( ) ) σ [1 + ( ) ] + 2µV 4 dx 3 4 dx L dx 2
2
xx
xx
x
(3) (4)
(1)
where Vx is the axial velocity; µ is the polymer viscosity; L and S are the film width and the film thickness, respectively; and LR and SR are the local percentage derivatives (the subscript R is to recall that the width and thickness are reduced along draw direction) of the width and thickness, respectively. It is worth noticing that, on the RHS of eq 1, the viscosity disappears, i.e., there is no need for the knowledge of local material rheology to calculate the evolution of the ratio between the stress
Dividing the first by the second, after some simplifications, one obtains
1 dVx
(dLdx) ) V dx ) V dL 1 dL L - 4 + 2( ) dx L dx 8-
2
x
2
I
(5)
R
where VI is the percentage derivative of the axial velocity (the subscript I is to recall that the axial velocity increases along
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Figure 4. (a) Width distributions for the two runs (symbols, experimental results; lines, eq 2). (b) Thickness distributions for the two runs (eq 7). (c) Ratio between the stress components (eq 1).
the draw direction). Equation 5 can be rearranged [using the fact that (dL/dx)2 ) L2LR2] to give
L2LR3 + 2VIL2LR2 - 8LR - 4VI ) 0
(6)
The value of LR can be calculated by solving the cubic eq 6, because the axial velocity increase is known and the width has been calculated at the previous integrating step. Thus, the width distribution can be obtained by inserting the value of LR in eq 2. Once the width distribution has been calculated, under the further hypothesis of constant material density, the thickness, in turn, can be calculated as
S)
(WxLS)|x)0 m˘ ) FWxL WxL
(7)
where m˘ is the polymer flow rate and F is the polymer density. Summarizing, using only a knowledge of the axial velocity distribution, one can obtain the width, L, by eq 2 (using LR given by eq 6), and the thickness, S, by eq 7. Then, the ratio of the stress components, R, can be calculated by eq 1. Figure 4a shows the width distributions for the two runs, Z1 and Z2, both experimental (symbols) and calculated by eq 2. The model slightly overestimates the final width in both tests. This is probably due to the density increase, a consequence of the film cooling. The thickness distributions, calculated by eq 7, are reported in Figure 4b. The ratio between the stress components along the thickness and the width directions, R ) τzz/ τyy, calculated by eq 1, is reported in Figure 4c. It is evident that the stress in the thickness direction is much larger than the
stress in the width direction, approximating planar extension. In the above reasoning, it has been shown that this ratio is fully determined by the development of the axial velocity. Because the increase in axial velocity is steeper in the presence of cooling air, the value of R is higher than it is in the absence of cooling air (for a given value of L in eq 1, inserting the width percentage derivatives, LR, calculated from eq 6, one can observe that the larger the axial percentage derivatives, VI, the larger the value of the ratio between the stress components, R). This causes a larger decrease in thickness than occurs in the absence of cooling air (as shown in Figure 4b). These considerations were further substantiated by a separate experiment. A blend of iPP and carbon black was processed in the same film casting apparatus, with the aim of producing films more evident in subsequent image analysis, in the presence and absence of cooling air. Two snapshots of the experiments are presented in Figure 5. The two photographs shown in Figure 5 refer to experiments (a) without cooling air and (b) with cooling air. The presence of cooling air causes the film to become thinner (the film in photograph b is brighter than the film in photograph a, because of the lower thickness) and wider (the film in photograph b experiences a lower reduction in width), compared to the film in the absence of cooling air. Conclusions Experiments on film casting were carried out with commercial iPP in a laboratory-scale extruder, with on-line measurements of all relevant variables (film width, axial velocity, temperature), in the presence and in the absence of jets of cooling air on both
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Figure 5. Snapshots of film casting experiments carried out with a carbon black filled iPP: (a) in the absence of cooling air, (b) in the presence of cooling air.
sides of the film. The effects of the presence of cooling air were faster cooling and axial velocity development and lower width reduction, with respect to a test carried out in the absence of cooling air. Because the presence of cooling air allows higher velocity gradients to be produced in the polymer melt, with solidification taking place during the path of the film in air, studies of the effect of flow on crystallization kinetics are facilitated by the use of the cooling air option. Literature Cited (1) Agassant, J. F.; Avenas, P.; Sergent, J. P.; Carreau, P. J. Polymer Processing. Principles and Modelling; Hanser Publishing: Munich, Germany, 1977.
(2) d’Halewyn, S.; Agassant, J. F.; Demay, Y. Numerical Simulation of the Cast Film Process. Polym. Eng. Sci. 1990, 30, 335-345. (3) Sakaki, K.; Katsumoto, R.; Kajiwara, T.; Funatsu, K. ThreeDimensional Flow Simulation of a Film Casting Process. Polym. Eng. Sci. 1996, 36, 1821-1831. (4) Barq, P.; Haudin, J. M.; Agassant, J. F. Isothermal and Anisothermal Models for Cast Film Extrusion. Int. Polym. Process 1992, VII, 334-349. (5) Beaulne, M., Mitsoulis, E. Numerical Simulation of the Film Casting Process. Int. Polym. Process 1999, XIV, 261-275. (6) Acierno, D.; Di Maio, L.; Ammirati, C. C. Film Casting of PolyEthylene-Therephthalate: Experiments and Model Comparisons. Polym. Eng. Sci. 2000, 40, 108-117. (7) Smith, S.; Stolle, D. Nonisothermal two-dimensional film casting of a viscous polymer. Polym. Eng. Sci. 2000, 40, 1870-1877. (8) Satoh, N.; Tomiyama, H.; Kajiwara, T. Viscoelastic Simulation of Film Casting Process for a Polymer Melt. Polym. Eng. Sci. 2001, 41, 15641579. (9) Lamberti, G.; Titomanlio, G.; Brucato, V. Measurement and modelling of the film casting process. 1. Width distribution along draw direction. Chem. Eng. Sci. 2001, 56, 5749-5761. (10) Lamberti, G.; Titomanlio, G.; Brucato, V. Measurement and modelling of the film casting process. 2. Temperature distribution along draw direction. Chem. Eng. Sci. 2002, 57, 1993-1996. (11) Lamberti, G.; Titomanlio, G. Analysis of film casting process: The heat transfer phenomena. Chem Eng. Process. 2005, 44, 1117-1122. (12) Lamberti, G.; Titomanlio, G. Evidences of Flow Induced Crystallization During Characterized Film Casting Experiments. Macromol. Symp. 2002, 185, 167-180. (13) Titomanlio, G.; Lamberti, G. Modeling flow induced crystallization in film casting of polypropylene. Rheol. Acta 2004, 43, 146-158.
ReceiVed for reView August 2, 2005 ReVised manuscript receiVed October 20, 2005 Accepted November 7, 2005 IE050899Z
