Effect of Activation Energy and Crystallization Kinetics of Polyethylenes on the Stability of Film Casting Processes

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1 Korea-Australia Rheology Journal Vol. 21, No. 2, June 2009 pp Effect of Activation Energy and Crystallization Kinetics of Polyethylenes on the Stability of Film Casting Processes Joo Sung Lee* and Joon Hee Cho LG Chem / Research Park, Daejeon , Korea (Received March 19, 2009; final revision received May 28, 2009) Abstract Effect of activation energy and crystallization kinetics of polyethylenes (PEs) on the dynamics and stability has been investigated by changing rheological properties and crystallization rate in film casting process. The effect of changes of these properties has been shown using a typical example of short-chain branching (SCB) in linear polyethylenes. SCBs in linear polymers generally lead to the increase of the flow activation energy, and to the decrease of the crystallization rate, making polymer viscosity lower in the case of equivalent molecular weight. In general, the increment of the crystallinity of polymers under partially crystallized state helps to enhance the process stability by increasing tension, and lower fluid viscoelasticity possesses the stabilizing effect for linear polymers. It has been found that the fluid viscoelasticity plays a key role in the control of process stability than crystallization kinetics which critically depends on the cooling to stabilize the film casting process of short-chain branched polymers operated under the low aspect ratio condition. Keywords : activation energy, crystallization, film casting, stability 1. Introduction Film casting process is an industrially important polymer extensional deformation process to manufacture many kinds of thin films (Kanai and Campbell, 1999). In this process, polymer melts are extruded from a slit die (or T- die) and simultaneously stretched in the machine direction by the motion of a chill roll, which also provides rapid cooling necessary for solidifying them in the molecular orientation produced during stretching (Fig. 1). This process is mainly governed by planar extension flow, although a portion of uniaxial deformation contributes to edge bead formation. These films, therefore, contain very different tear and tensile properties in the machine and transverse directions, because the molecular structure is highly oriented in the machine direction. The die opening is typically in the order of 1 mm and the final film thickness ranges from 5 to 200 µm. Recently, the rapid growth of IT cutting-edge technologies, e.g., optical films for flat panel displays and separators for Li-ion batteries, has augmented needs for the advanced quality control of film products. Enhancing the process productivity and the uniformity of the film products in this process always entails an in-depth understanding of the dynamics and stability of the system. As in any other industrial processes, however, various kinds of unexpected disturbances inevitably affect the process stability and sensitivity, giving rise to detrimental defects of produced films. There exist of course instabilities and defects in film casting processes, e.g., draw resonance, neck-in of the film width, and edge bead on the final film product (Kanai and Campbell, 1999; Jung and Hyun, 2006). Draw resonance, which is a representative instability in the extensional deformation processes, reveals when the drawdown ratio (the ratio of fluid velocities at take-up roll and T-die) is raised beyond its onset (Kim et al., 2005; Shin et al., 2007; Zavinska et al., 2008). Above the critical point, all state variables including film thickness and film width periodically oscillate along the time like other extensional deformation processes, e.g., fiber spinning and film blowing. Neck-in of film width along the machine direction due to the strong extensional deformation in the drawdown region *Corresponding author: jslee96@grtrkr.korea.ac.kr 2009 by The Korean Society of Rheology Fig. 1. Schematic diagram of film casting process. Korea-Australia Rheology Journal June 2009 Vol. 21, No

2 Joo Sung Lee and Joon Hee Cho from the die to take-up roll and edge bead (or dog-bone) with thicker film thickness at edges than at center are not uncommon in the film casting process. Since the first works laid the foundation for studying the film casting (Yeow, 1974), illuminating the draw resonance instability of this process, there have been many research efforts on the dynamics and stability in this process. Co s group interestingly exploited the stability results with Newtonian and viscoelastic fluids (Anturkar and Co, 1988; Iyengar and Co, 1996) using constant width 1-D models. Agassant s group developed more refined 1-D models (Silagy et al., 1996), which are capable of explaining neckin as well as draw resonance, with the assumption of the constant deformation rate in film width and film thickness directions. Recently, 2-D film casting models for Newtonian fluids (Silagy et al., 1998) and for viscoelastic fluids (Kim et al., 2005; Shin et al., 2007) have been reported to elucidate the edge bead as well as draw resonance and neck-in. The influence of side chain branching on the properties of polyethylenes, e.g., basic rheological and thermal properties, has gained much interest by several researchers (Kim et al., 1996; Vega et al., 1998; Munstedt et al., 1998; Bubeck, 2002; Chiu et al., 2002; Park and Larson, 2005; Stadler et al., 2007; Stadler and Munstedt, 2008). Longchain branching (LCB) in polymer, which has a length scale comparable with the polymer main chain and can be possible to make entanglement, shows drastically stabilizing effect on the extensional deformation processes by changing their melt rheological properties (Wood-Adams and Costeux, 2001; Lee et al., 2003). On the other hands, short-chain branching (SCB) primarily controls the polymer density and only have an influence on the thermodynamic properties. Especially, the increase of short-chain branching in the linear polymers effectively elevates the activation energy with lower crystallization temperature, crystallization rate, and melting temperature. For this reason, the fluid viscoelasticity and the crystallization rate are decreased under the same extrusion temperature condition so that the short-chain branched polymers are suitable to make highly transparent polymer film caused by low crystallinity. In this study, the authors have theoretically elucidated the effect of short-chain branching in polyethylenes on process dynamics and stability due to the change of the material properties (e.g., fluid viscoelasticity, activation energy, and crystallization rate, etc.) by the nonlinear transient response method of film casting process. 2. Time-Dependent Governing Equations: Varying Width 1-D Model The constant film width 1-D model introduced by Co s group (Anturkar and Co, 1988; Iyengar and Co, 1996) is very similar to the governing equations of fiber spinning process in that it can only describe the draw resonance instability. The neck-in and edge bead phenomena, however, have no counterpart in fiber spinning and their characteristics should be considered in the mathematical model. To do that, Agassant s group (Silagy et al., 1998) suggested the improved 1-D model employing the following assumption: the fluid velocity into film width direction is proportional to the distance with respect to the film width. By adopting aforementioned rate of deformation tensor, the dimensionless governing equations are expressed as follows. Equation to describe film width is added in governing equations, derived from edge stress condition on the film free surface (σ n = 0). The Phan-Thien Tanner (PTT) fluids were employed to describe the rheological properties of linear and short-chain branched polymers (Phan-Thien, 1978). Even though the PTT constitutive equation has inevitable stability problem when ξ is not zero (Kwon and Leonov, 1995), this model is not only more robust than other constitutive equations, but also suitable to describe extensional thinning behavior of linear or short-chain branched polyethylenes when ξ is greater than 0.5. The crystallization kinetics considering both thermally-induced and flowenhanced crystallization (Muslet and Kamal, 2004) was adopted to explain the effect of short-chain branching. ( ew) ( ewv Equation of continuity: z ) = 0 (1) t z where e ---- E, w W V, ν z z , z Z t * V = = = = --, t = z0 L L Equation of motion: F = σ zz ew (2) where F FL σ * , σ ij L = ij = η 0 E 0 W 0 V z0 2η 0 V z0 Constitutive equation (Phan-Thien Tanner model): where, = ---- η. (3) D E De = De 0 exp a. RT θ ( α β)x, L = ν ξd Equation of energy: θ v θ +. (4) t z = h -- ( θ θ a ) + H x f v x + z e t z ---- z where E 0 W 0 V z0 Kτ+ De τ ν τ L τ τ L T t K exp 2εDetrτ , exp( βx) η E = = η a 0 exp RT θ αx, G= G 0 exp[ βx] η 0 θ T T ----, θ a = ---- a, h 2h * L H * , H f X = = f = T 0 T 0 ρc P V 0 E 0 C P T Korea-Australia Rheology Journal

3 Effect of Activation Energy and Crystallization Kinetics of Polyethylenes on the Stability of Film Casting Processes Crystallization kinetics: x ν x t z ---- = n 1n z 1 x ( n 1) n ( 1 x)k m exp 41n2 T T max κτDe d 0 where x X K -----, k max L = m = X V z0 Edge stress condition: σ w zz = A 2 z r σ yy L where A r = W 0 Boundary conditions: e=e 0 =1, w=w 0 =1, v=v 0 =1 v=v L =D R v=v L = D R (1+δ ). (5) (6) at z=0 and t=0 (7a) at z=l and t=0 (7b) at z=l and t>0 (7c) where, e denotes the dimensionless film thickness, w the dimensionless film width, v z the dimensionless axial velocity, t the dimensionless time, v the velocity vector, σ the dimensionless total stress tensor τ the dimensionless extra stress tensor, θ the dimensionless temperature, x the dimensionless crystallinity, D the dimensionless strain rate tensor, η 0 the zero shear viscosity, De the Deborah number, h the dimensionless heat transfer coefficient, θ a the dimensionless cooling air temperature, E a the activation energy, ρ the density, C p the heat capacity, H f dimensionless crystallization heat, k m dimensionless maximum crystallization rate, T max the temperature at maximum crystallization rate, d crystallization half width temperature range, D R the drawdown ratio, δ the magnitude of disturbance, ε, ξ PTT model parameters, α, β the model parameters representing the crystallinity dependency of viscosity and modulus, and κ the FIC enhancement factor. The aspect ratio, A r, defined as the flow distance divided by the film width, has been also included. In this 1-D model, the Avrami index, n, is set to unity. Subscripts 0 and L mean die exit and take-up conditions, respectively. The model parameters are summarized in Table 1. Linear high density polyethylene (HDPE) was adopted as a reference for our calculation, and sample #1 and #2 were assumed short-chain branched polymer of equivalent molecular weight. The processing conditions for film casting process were same, but the material properties are slightly different with one another due to the short-chain branching effect. These material properties were obtained from literatures (Vega et al., 1998; Bubeck, 2002; Stadler et al., 2007; Stadler and Munstedt, 2008) in the reasonable range. For example, the activation energy (E a ) of linear PE is found to be around 27~ 28 kj/mol, while slightly higher values of 32 ~ 40 kj/mol are reported for short-chain branched polymers (Stadler et al., 2007) because the addi- Table 1. Model parameters in this study Linear polymer Sample #1 Sample #2 Source T 0 ( o C) ρ(kg/m 3 ) Measured Comonomer - Butene Octadecene - SCB/10 3 C Measured ( 13 C NMR) E a (kj/mol) Stadler et al. (2007) λ 0 (sec) at T Vega et al. (1998) η 0 = λ 0 ) η 0 (Pas) at T Measured K max (sec -1 ) Chin et al. (2002) T max (K) κ Muslet & Kamal (2004) α and β 5.1, , , 3.2 Muslet & Kamal (2004) X (%) Measured ε and ξ 0.015, , , 0.7 Shin et al. (2007) Korea-Australia Rheology Journal June 2009 Vol. 21, No

4 Joo Sung Lee and Joon Hee Cho Fig. 2. Apparent extensional viscosities along the machine direction using upper convected Maxwell (UCM) and Phan- Thien Tanner (PTT) fluids without crystallization at D R =25, A r = 0.4, and De = tion of comonomers is likely to hinder the overall mobility, indicating that a higher thermal activation is necessary for the motion of molecule segments. On the other hands, short-chain branching polymers cannot make significant impact on the rheological properties (e.g., PTT model parameters). Even though the zero shear viscosity is almost same near the melting temperature (Stadler and Munstedt, 2008), there is a wide difference in melt viscosities at typical extrusion temperature due to their different activation energy levels. Also, the decrease of the melt viscosity leads to the decrease of material longest relaxation time (Vega et al., 1998). Moreover, a short-chain branch prevents the formation of crystallinity in its immediate vicinity and increases the probability that the main chain to which it is attached will be incorporated into two different lamellae, and hence establishing that chain as a molecular bridge (i.e. a tie ) molecule (Bubeck, 2002). So that, both the crystallization kinetics and maximum crystallinity is decreased along with the amount and length of short-chain branches and they show strong dependence on the fluid density. 3. Results and Discussion 3.1. Steady state solutions Prior to the analysis, the apparent extensional viscosities along the flow direction (or extension rate) were checked using different constitutive equations and model parameters. As shown in Fig. 2, the general upper convected Max- Fig. 3. Steady state solutions at chill roll position (A r =0.4): (a) dimensionless film width, (b) dimensionless temperature, and (c) dimensionless crystallinity with drawdown ratio for three different polymers. 138 Korea-Australia Rheology Journal

5 Effect of Activation Energy and Crystallization Kinetics of Polyethylenes on the Stability of Film Casting Processes well (UCM) model can only describe the extensional thickening behavior. On the other hands, the Phan-Thien Tanner (PTT) model used in this study can portray the contrasting behavior of the extensional viscosity depending on the value of ξ. The parameter, ξ, thus plays the key role in deciding the dichotomous behavior of extension deformation. In this study, we selected 0.7 for the value of ξ (Shin et al., 2007) to describe the extensional thinning behavior of linear and short-chain branched polymers. As mentioned before, the existence of short-chain branches gives an influence in the activation energy and crystallization rate. From the neck-in point of view (Fig. 3(a)), the short-chain branched polymers are slightly inferior to linear polymer. It is noted that short-chain branched polymer films can easily be shrunk in the transverse direction because of lower axial tension acting in the drawdown region since the crystallinity. Besides, the fluid viscoelasiticy imbedded in Deborah number alleviate the neck-in phenomena in the film casting process (Lee et al., 2003). However, this value for short-chain branched polymers has relatively lower value than linear polymers. The film temperature just before the chill roll position (Fig. 3(b)) shows almost isothermal behavior due to the low aspect ratio (A r = 0.4) of film casting process and crystallization heat during stretching of oriented crystalline polymers. The final film temperature of linear polymer is slightly high due to the higher crystallinity. In all cases, the dimensionless crystallinity can t reach its maximum value and it decreases as the drawdown ratio increases (Fig. 3(c)) due to the reduction of fluid residence time to allow crystallization. For the low speed film casting process, it is important to incorporate thermally-induced crystallization (TIC) rather than flow-induced crystallization (FIC). For this reason, it is effective to change residence time or ambient temperature to control film crystallinity. Moreover, shortchain branches hinder the formation of crystallinity, so that it is favorable to produce highly transparent film by reducing the hazeness triggered by crystallinity Effect of manipulating variables on the process stability The representative manipulating variables of the extensional deformation processes are fluid viscoelasticity, heat transfer coefficient, and crystallization rate. For the high speed spinning case, the secondary forces such as inertia and air-drag are also important. Regarding the fluid viscoelasticity, it is well known to show the dichotomous behavior of polymer melts in the extensional deformation process (Jung et al., 2002; Lee et al., 2003). The extension thickening fluids (i.e., long-chain branched polymers) show drastically stabilizing effect with increasing Deborah number or fluid viscoelasicity, whereas, extension thinning fluids (i.e., linear or short-chain branched polymers) are the opposite. Such a dichotomous Fig. 4. (a) Stability window for extensional thickening and thinning fluids determined by linear stability analysis of isothermal varying width 1-D model by Lee et al. (2003) and (b) transient responses for extensional thinning linear polymer using non-isothermal varying width 1-D model accompanied by crystallization kinetics at D R =27 and A r =0.4. behavior of polymer melts is attributed by the opposite behavior of the extensional viscosity on the molten film, depending on the value of ξ in PTT model. For the isothermal film casting of PTT fluids, ξ value is around 0.5 to demarcate these two different behaviors. Using the linear stability analysis of the isothermal varying width 1-D model, the stability windows well reflects this tendency like Fig. 4(a) (Lee et al., 2003). For the new model employing non-isothermal nature and crystallization kinetics, we have further scrutinized this effect of fluid viscoelasticity using nonlinear stability analysis. As depicted in Fig. 4(b), the destabilizing effect of fluid viscoelasticity has been sub- Korea-Australia Rheology Journal June 2009 Vol. 21, No

6 Joo Sung Lee and Joon Hee Cho Fig. 5. The effect of short-chain branched polymers on the process stability at DR = 27 and Ar = 0.4: Transient responses of (a) dimensionless film thickness, (b) dimensionless film width, (c) dimensionless temperature and (d) dimensionless crystallinity. stantiated by transient responses of the film casting process for linear polymer melts (Deref = and ξ = 0.7). The crystallinity or crystallization kinetics on the extended polymer film can affect the process stability. In the low-speed fiber spinning process which can t reach its maximum crystallinity (Shin et al., 2005), the crystallinity under partially crystallized conditions shows the stabilizing effect on the extensional deformation process, because it makes an increase in spinline tension and a decrease of the spinline tension sensitivity. However, the effect of crystallinity on the stability was insignificant in film casting process, because this process is generally operated under the quasi-isothermal condition so that the final crystallinity in the film is too small to affect on the process stability Effect of short-chain branching on the process stability For the short-chain branched polyethlenes, it is expected that SCB can has both stabilizing effect due to the decrease of the viscoelasticity in extension thinning fluids, and destabilizing effect by the lower crystallinity and higher sensitivity of the system to the temperature. This conflict in the role of SCB on the process stability is associated with 140 the trade-off relationship, so it is hard to strictly define the process stability. However, Fig. 5 only shows the stabilizing effect of the short-chain branched polymers on the film casting dynamics under the general operating conditions, owing to very small aspect ratio (Ar = 0.4) to attenuate the neck-in phenomena. In other words, the effect of fluid viscoelasiticity has dominant on the process stability rather than crystallinity or temperature sensitivity due to the lower cooling rate. It is particularly noted that the nonlinear dynamics of the film width is quite complex and also very sensitive to process parameters like fluid viscoelasticity and the aspect ratio of the casting equipment in the isothermal varying width 1-D model (Lee et al., 2001). This contrasts dramatically with that of the film thickness which shows rather simple dynamic patterns, similar to the cross-sectional area of fiber spinning process, almost insensitive to the changing parameters values. In this improved varying width 1-D model, considering non-isothermal nature and crystallization kinetics, similar complex nonlinear characteristics of the film width in unstable draw resonance region has been found under the same operating conditions of linear polymer shown in Fig. 5. Korea-Australia Rheology Journal

7 Effect of Activation Energy and Crystallization Kinetics of Polyethylenes on the Stability of Film Casting Processes 4. Conclusions By considering the non-isothermal nature and crystallization kinetics in varying width 1-D model of film casting process, we have construct more sophisticated model than our previous studies (Lee et al., 2001; Lee et al., 2003), and it has applied to examine the process dynamics and stability by changing activation energy and crystallization kinetics assumed the case of introducing the short-chain branches in linear polymers. Especially, the conflicting effect of viscoelasticity and crystallinity which are simultaneously changed by the degree of side chain branches in linear polymers, on the process stability has been compared. In other words, side chain branches lead to lower viscoelasticity which is favorable in the film formation of linear polymers, however, they make the crystallinity lower, giving higher sensitivity to the temperature on the system. It turns out that the stabilizing effect of lower viscoelasticity for extensional thinning fluids is more dominant than the destabilizing effect of lower crystallinity in short-chain branching polymer films in case of low aspect ratio condition operated almost isothermal condition. References Anturkar, N. R. and A. Co, 1988, Draw resonance in film casting of viscoelastic fluids: a linear stability analysis, J. Non-Newtonian Fluid Mech. 28, 287. Bubeck, R. A., 2002, Structure-property relationships in metallocene polyethylenes, Mat. Sci. Eng. R, 39, 1. Chiu, F.-C., Y. Peng and Q. Fu, 2002, Bulk crystallization kinetics of metallocene polyethylenes with well-controlled molecular weight and short chain branch content, J. Polym. Res., 9, 175. Iyengar, V. 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