Measuring Slip at a Polymer/Polymer Interface during Three-Layer Flow

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1 Rapid Communication Nihon Reoroji Gakkaishi Vol.41, No.4, 235~239 (Journal of the Society of Rheology, Japan) 2013 The Society of Rheology, Japan Measuring Slip at a Polymer/Polymer Interface during Three-Layer Flow Ryohei Komuro, Sathish K. Sukumaran, Masataka Sugimoto, and Kiyohito Koyama Graduate School of Science and Engineering, Yamagata University, Jonan, Yonezawa, Yamagata, , JAPAN (Received : March 6, 2013) Key Words: Interface / Slip / Multilayer / Coextrusion / Polypropylene / Polystyrene 1. INTRODUCTION Multilayer technology is widely used for developing packaging materials for a range of applications in the food, medical, electronics and several other industries. An important advantage of multilayer technology is that not only the barrier, mechanical, optical and other physical properties of the final product but also its cost can be easily varied to satisfy the needs of the desired application. 1-5) The variation in the properties can be accomplished by varying the polymers used, the number of layers in the final product, adjusting the thickness of the layers etc. Multilayered products are typically manufactured using either a feedblock or a distribution block along with single manifold or multi-mainfold dies. Owing to the complexity of both the shape of the extrusion die and the actual flow behaviour, the principal technique for investigating multilayer flow in industry and academia is through computer simulations. 6-8) In order to investigate flow phenomena using computer simulations, it is necessary to utilize boundary conditions appropriate to the conditions of the flow. Most simulations of flow phenomena, including those for non- Newtonian fluids, assume that the velocity is continuous at phase boundaries. Thus, in addition to the relevant consitutive equation, simulations of multilayer coextrusion usually use the no-slip boundary condition at a polymer/polymer interface. 6-8) In the case of multilayers, the polymers consituting the adjacent layers are essentially mutually immiscible. Hence, one can expect low entanglement density at the interface and consequently weak adhesion between the layers. As Corresponding author Tel: , Fax: , sa.k.sukumaran@gmail.com interfacial entanglements are the main source of adhesion between the layers, high shear stresses cannot be sustained by the polymer/polymer interface and slip is likely to occur. Early experiments 9,10) on multilayer flow indicated that the pressure gradient necessary to extrude the multilayer at a particular flow rate was significantly lower than the pressure gradient necessary to extrude a single layer at the same flow rate. This was interpreted by Han and Chin 11) as evidence for the existence of slip at the interface between immiscible polymers. In the past, polymer/polymer interfacial slip has been investigated using rheological 12-15) and flow visualization 16,17) techniques. However, most of these studies are restricted to multilayers where parallel layers are stacked on top of each other. In this geometry, the mixing rule for the viscosity can be easily derived and any deviation from this expected value of the viscosity can be used to estimate the slip velocity at the polymer/polymer interface. If however, the parallel arrangement of the layers were to be modified by the flow, the mixing rules could cease to be valid and the accuracy of the determined the slip velocity would become questionable. In addition, when two or more polymers with different shear-rate dependent viscosities are coextruded, irregularities occur at the polymer/polymer interface ) This irregular interface is particularly troublesome as it can interfere with the determination of the polymer/polymer interfacial slip velocity as a function of the interfacial stress. Using polymers with almost identical shear-rate dependent viscosities this potential difficulty can be managed. Therefore, in this study, we investigate polymer/polymer interfacial slip during three-layer flow using isotactic polypropylene (PP) and atactic polystyrene (PS) with almost identical viscoelastic properties over a range of shear-rates (see Fig. 1). 235

2 Nihon Reoroji Gakkaishi Vol EXPERIMENTS 2.1 Materials The materials chosen for the experimental study were PP (M w = 345,000 g/mol, M w /M n = 5.02), PS (M w = 312,000 g/mol, M w /M n = 2.66). PP was kindly supplied by Japan Polypropylene Corporation and the PS by PS Japan Corporation. 2.2 Rheological Measurements Small amplitude oscillatory shear measurements were performed using a rotational rheometer (ARES, TA instruments,) at o C in a nitrogen atmosphere. The samples were sandwiched between parallel plates of 25 mm diameter and the gap was set at 1 mm. Steady shear viscosity, η s, values above 10 2 s -1 were measured using a capillary rheometer (Capilograph, Toyo Seiki Seisakusho Ltd.). The wall shear stress values were corrected for capillary end effects by applying the Bagley correction to the pressure drop. The true wall shearrate was determined by applying the Rabinowitsch correction to the apparent wall shear-rate. Three different capillary dies, all with diameter, D = 1 mm and lengths, L = 5, 10, 20 mm were used. The polymer/polymer interfacial slip measurements during three-layer flow were performed using a twin-screw extruder (ULT nano, Technovel Co.). One important problem while using such a design is to ensure that the flow in the die can be considered as two-dimensional. Wales 27) showed that the perturbation introduced by the presence of the die walls could be neglected provided the aspect ratio of the die (width over height) was greater than 10. Therefore, we used a slit die with an aspect ratio of 20 (width = 10 mm, height = 0.5 mm). The slit die contains two pressure sensors to measure the pressure gradient, P, across the die. The total volumetric flow rate of the three-layer sample is calculated by using the total gravimetric flow rate of the three-layer extrudate along with the density at 230 o C and the thickness value for each of the Polymers A and B. The y-positions of the interface (see Fig. 2) is determined using the density at 230 o C and the thickness of each of the Polymers A and B. To ensure the validity of the calculation of the y-position, we verified that the two outer layers (Polymer A) were essentially symmetric with respect to the middle layer (Polymer B) in the slit die. 2.3 Experimental Estimation of the Polymer/Polymer Interfacial Slip Velocity in Three-Layer Flow: Fig. 2 shows a schematic of the flow velocity distribution in three-layer flow. For convenience, henceforth we shall refer to the inner layer as Polymer B and the two outer layers as Polymer A. Whenever wall slip is negligible, the polymer/ polymer interfacial slip velocity, V s-i, can be estimated from the deviations in the flow variables when compared to the values estimated assuming no-slip boundary conditions. In Fig. 1. Master curve of (a) the storage modulus G' and the loss modulus G" and (b) the complex viscosity η * of PP and PS at the reference temperature T r = 230 o C. Fig. 2. Schematic of the flow velocity distribution during three-layer flow. 236

3 KOMURO SUKUMARAN SUGIMOTO KOYAMA : Measuring Slip at a Polymer/polymer Interface during Three-layer Flow order to easily determine the flow variables under the no-slip assumption, we used the Carreau-Yasuda (C-Y) equation to fit the shear viscosity, η versus shear-rate, 4 g data. 21) The equation reads: a n 1 a 0 1 (1) where η 0, λ, n and a are the zero shear viscosity, time constant, power-law exponent and a dimensionless parameter, respectively. To extend the shear-rate range of the viscosity data, we combine the viscosity obtained using the oscillatory shear data with that from the capillary rheometry using 4 g = w (Cox-Merz rule). For the combined data on the dependence of viscosity on the shear-rate, the solid lines in Fig. 1(b) are fits to the C-Y equation for PP and PS. For fully developed Poiseuille flow subject to a pressure difference, P, the following equation holds: Py xy y (2) 2 where σ xy (y) is the shear stress at a particular y value. The shear-rate in the slit die is: V H y 0 r (3) y 2 where H is the total thickness of the multilayer sample and V is the velocity field. Then, the flow velocity of the inner layer (V (C-Y) B ) and the outer layers (V (C-Y) A ) can be evaluated using equations (1)-(3). For a three-layer sample consisting of two interfaces, the following equations are applicable: V s Q i Q no-slip AB 2 Q 2 Wh hi 0 no-slip i WyV (CY) B dy 2 H 2 (CY) WyVA hi where Q AB is the total volumetric flow rate of the three-layer sample. The Q no-slip is the volumetric flow rate of three-layer sample under the assumption of no-slip. The W is width of the slit die. The h i is y-position of the interface. Irregular interfaces, such as those mentioned in ref ) were not observed in our samples. Fig. 1 shows the master curve of (a) storage and loss moduli (G' and G") and (b) complex viscosity η* of PP and PS at the reference temperature T r = 230 o C. We found that the steady shear viscosity, η s, obtained using the slit die showed good agreement with that determined from the oscillatory moduli using the Cox-Merz rule. 22) As mentioned earlier and shown in Fig. 1(b), the PP and the PS used in this study have similar shear-rate dependent viscosities at 230 o C. Further, as can be seen from Fig. 1(b), the C-Y equation could dy (4) effectively describe both the PP data (to within 1.7 %) and the PS data (to within 1.5 %). Therefore, the fitted C-Y function can be used to determine the shear-rate dependent viscosity under no-slip. Using this value of viscosity, the interfacial slip velocity V s-i can be determined using equation (4). 3. RESULTS AND DISCUSSIONS Fig. 3 shows the dependence of the pressure gradient P on the total volumetric flow rate Q AB for four different geometries of the three layer samples: PP/PP/PP, PS/PS/PS, PS/PP/PS and PP/PS/PP. The solid line in Fig. 3 indicates the P predicted using the C-Y equation while assuming no-slip boundary conditions during three-layer flow. As seen from Fig. 3, it is clear that the dependence of the pressure gradient on the total volumetric flow rate of PP/PP/PP and PS/PS/PS exhibits good agreement with the C-Y prediction (no-slip). These results imply that the slip at the wall is negligible for both the PS and PP at the conditions investigated. This is consistent with the fact that for both PP and PS melts wall slip is expected to occur only when the wall stress exceeds 10 5 Pa ) Therefore, slip at the wall will be neglected in the analysis to be presented below. On the other hand, the variation of the pressure gradient as a function of the total volumetric flow rate for the PS/PP/PS and PP/PS/PP three-layer samples deviates from that obtained using the C-Y equation assuming no-slip. This suggests the existence of slip during three-layer flow. As the slip at the wall is negligible under these conditions, the likely origin of the observed slip is at the interface between the PP and the PS. Fig. 3. Dependence of the pressure gradient on the total volumetric flow rate for PP/PP/PP, PS/PS/PS, PS/PP/PS and PP/PS/PP samples. 237

4 Nihon Reoroji Gakkaishi Vol Fig. 4 shows the dependence of the interfacial slip velocity, V s-i, on the interfacial shear stress, σ i, for the PS/PP/PS and the PP/PS/PP samples. The figure suggests that the slip at the PP/ PS interface occurs at shear stress values that are significantly lower than the stress at the onset of wall slip ( 10 5 Pa) ) The dependence of V s-i on σ i is a power-law with a power-law exponent of approximately 1.7. Further, Fig. 4 also indicates that the interfacial slip velocities, V s-i of both the PS/PP/PS and the PP/PS/PP samples are rather close. This suggests that the relationship between the interfacial slip velocity and the interfacial shear stress is essentially unchanged when the inner and the outer layers switch locations. The behaviour of slip at the PP/PS interface during multilayer flow is similar to that found by Zhao and Macosko. 15) They investigated polymer/polymer interfacial slip using multilayer samples with 8, 32 and 64 layers and found three power-law regimes with the transitions between the power-laws occurring at approximately Pa and Pa. We have succeeded in determining the V s-i of PS/ PP/PS and PP/PS/PP at 230 o C for σ i > Pa and find that the V s-i values are consistently larger than the results of Zhao and Macosko. 15) One possible origin for the discrepancy is the difference in the temperature at which the slip velocity is measured in the two cases. As the temperature used in our experiments (230 o C) is larger than that used by Zhao and Macosko (200 o C), it is reasonable that the values of the measured V s-i are larger in our case. On the other hand, the V s-i values and the power-law exponent (m 1.7) is similar to that determined for a different polymer pair by Park et al. using rheological measurements 14) and Migler et al. using stroboscopic optical microscopy, 17). Further studies to confirm the proposed origin of the discrepancy in the slip velocity values and to elucidate the nature of slip at a polymer/polymer interface are currently underway. 4. SUMMARY We have investigated slip at a polymer/polymer interface during three-layer flow. To enable straightforward determination of the polymer/polymer interfacial slip velocity, we choose two polymers with similar viscoelastic properties over a wide range of shear-rates. In addition, choosing two polymers with matched viscosities allows us to avoid considering the effects of the difference in the viscosity of the polymers in the different layers on polymer/polymer interfacial slip. Such a judicious choice of polymers and flow conditions also prevents the reduction of accuracy in the determination of the slip velocity due to the irregular interface that can be generated during multilayer flow when the viscosity of the polymers constituting the various layers are unequal. The slip at the polymer/polymer interface occurs at values of shear stress significantly lower than the onset of wall slip ( 10 5 Pa). The slip velocity at a polymer/polymer interface exhibits a power-law dependence on the interfacial shear stress. The slip velocity at a particular interfacial shear stress and consequently the power-law relationship between the slip velocity and the shear stress is essentially unchanged even if the polymer in the inner layer is switched with that in the outer layer. Acknowledgment The authors gratefully acknowledge financial support from the Japan Society for Promotion of Science (JSPS) through Kakenhi ( ) and the Dissemination of Tenure Tracking System Program of the Ministry of Education, Culture, Sports, Science and Technology -- Japan. Fig. 4. Dependence of the interfacial slip velocity on the interfacial shear stress for PS/PP/PS and PP/PS/PP samples. REFERENCES 1) Schrenk WJ, Alfrey T, SPEJ, 29, 38 (1973). 2) Corbett HO, US Patents, 3, 320, 636 (1967); 3, 398, 431 (1968). 3) Squires PH, US Patents, 3, 476, 627 (1969). 4) Wiley DF, US Patents, 3, 769, 380 (1973); 3, 882, 219 (1975); 3, 900, 548 (1975). 5) Nissel FR, US Patents, 3, 919, 865 (1975); 3, 940, 221 (1976); 3, 959, 431 (1976). 6) Mavridis H, Shroff RN, Polym Eng Sci, 34, 559 (1994). 7) Matsunaga K, Funatsu K, Kajiwara T, Polym Eng Sci, 38, 1099 (1998). 238

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