Interfacial slip reduces polymer-polymer adhesion during coextrusion

Transcription

1 Interfacial slip reduces polymer-polymer adhesion during coextrusion Jianbin Zhang, Timothy P. Lodge, a) and Christopher W. Macosko b) Department of Chemical Engineering and Materials Science and Department of Chemistry, University of Minnesota, Minneapolis, Minnesota (Received 20 July 2005; final revision received 3 October 2005 Synopsis Slip occurs at the interfaces between immiscible polymer melts at high shear stress. We demonstrate that this reduces adhesion during coextrusion. A 20-layer polystyrene PS / poly methyl methacrylate PMMA alternating layer sample was coextruded and the adhesion at each internal interface was measured with the asymmetric dual cantilever beam crack propagation test. When the shear stress experienced by an interface is low, interfacial slip is negligible and interfacial adhesion is high, comparable to a laminated interface. When the shear stress exceeds a critical value, interfacial slip begins to develop and interfacial adhesion begins to decrease with shear stress. Above another critical stress, full slip has been developed at the interface and adhesion reaches a plateau value, which is about 1/3 of the equilibrium value. The changes in adhesion versus shear stress follow a master curve for different flow rates. This supports the hypothesis that polymer chains at the interface are disentangled by the shear stress during coextrusion. It was also found that annealing restored adhesion on the reptation time scale indicating that entanglements were reestablished at the interface. Creating block copolymer by a coupling reaction at the interface during coextrusion increased adhesion to level even higher than the laminated interface The Society of Rheology. DOI: / I. INTRODUCTION Multilayer technology allows two or more polymers to be combined in a layered structure to give a wide range of desirable properties. Depending on the application, the number of layers can range from two to hundreds. Packaging materials, for example, are typically comprised of 3 7 layers Selke Each layer serves a different function, such as providing mechanical strength, permeation barrier, or surface wettability. For optical applications, on the other hand, the multilayers consist of hundreds of submicron layers. Weber et al reported unique optical properties for multilayers with a layer thickness less than 100 nm. A common problem for all these layered products is adhesion control. The adhesion between polymers has been widely studied over the last two decades. Generally, adhesion is quantified with a destructive test to evaluate the ability of an interface to transfer mechanical stress. Depending on different fracture mechanisms as proposed for glassy polymers by Kramer et al and by Wool 1995, the adhesion a Author to whom correspondence should be addressed; electronic mail: lodge@chem.umn.edu b Electronic mail: macosko@umn.edu 2006 by The Society of Rheology, Inc. J. Rheol. 50 1, January/February /2006/50 1 /41/17/$

2 42 ZHANG, LODGE, AND MACOSKO can fall into three regimes: For highly immiscible polymer pairs, the interface fractures through chain pullout short chains or chain scission long chains. The adhesion in this regime is relatively low, typically in the range of 0 25 J/m 2. When the miscibility is good which results in a thick interface and the molecular weight is high, the interface fractures through crazing, and the fracture energy is correspondingly high on the order of hundreds of J/m 2. In the intermediate regime, adhesion lies in between these limits. Since many useful properties can only be achieved by combining immiscible polymers Paul and Bucknall 2000, focus has been put on the low adhesion regime. The adhesion between many glassy immiscible polymer pairs has been measured by Brown et al. 1993, Washiyama et al. 1993, and Cole et al. 2003, and has been summarized in a review by Creton et al Chain entanglement is believed to be the origin of enhanced adhesion Creton et al Silvestri et al calculated the entanglement density at an interface with a mean-field approach, and predicted the critical fracture toughness G c for immiscible polymers. Agreement was achieved between theoretical prediction and experimental results Brown 2001 and Silvestri et al The agreement was particularly good for the polystyrene PS /poly methyl methacrylate PMMA system. Anastasiadis et al reported the interfacial thickness for PS/PMMA is 5 nm, which is higher than the tube diameter. Thus, breaking of entangled chains at the interface likely controls the fracture toughness. Interfacial slip is responsible for the abnormal viscosity decrease of immiscible blends under high shear stress Utracki 1982 ; This behavior has been studied both theoretically de Gennes 1992 ; Goveas and Fredrickson 1998 ; Narayanan et al and experimentally Migler et al ; Zhao and Macosko 2002 ; Lam et al Interfacial slip is related to disentanglement of polymer chains at interfaces. Zhao and Macosko 2002 systematically investigated interfacial slip with a polystyrene PS /polypropylene PP multilayer system, by measuring the pressure drop through a slit die during coextrusion and the viscosity of the multilayer samples in a shear rheometer. They found that at high shear stress, significant slip occurs at the interfaces between layers. The slip velocities calculated from both slit and shear rheometer measurements matched very well, and were a function of shear stress. Commercial polymer multilayers are usually made by coextrusion, where high shear stress is experienced by the polymer melt. An important question is whether and how the high shear stress experienced by a multilayer melt during coextrusion will affect the already poor adhesion for immiscible polymers. The focus of this paper is to study coextrusion effects on interfacial adhesion between immiscible polymers. A 20-layer PS/PMMA model system was created using coextrusion. The PS/PMMA layers flowing near the die wall experience higher shear stresses than layers near the center line. This enabled us to study the effect of shear stress on polymer-polymer adhesion quantitatively. The effect of an interfacial coupling reaction of functional polymers premixed with the layers was also explored. II. EXPERIMENT A. Materials The polymers used in this work are described in Table I. The functional polymers, amine-terminal PS PS-NH 2 and anhydride-terminal PMMA PMMA-anh-pyr were synthesized by atom transfer radical polymerization ATRP. Detailed procedures for synthesis and characterization of these polymers are described by Moon et al and by Zhang et al They have low molecular weight but relatively narrow distribution and high functionality. The commercial PS and PMMA used here were supplied by

3 INTERFACIAL SLIP REDUCES POLYMER-POLYMER 43 TABLE I. Characteristics of polymers used in this work. Polymer Sources M n kg/mol M w /M n Functionality PS Styron Dow Chemical PMMA Plexiglas V825-NA Arkema PS-NH 2 Synthesized PMMA-anh-pyr Synthesized Dow Chemical and Arkema, respectively. According to the manufacturers, there were no additives in those polymers and they were used as received. The molecular weights and distributions listed in Table I were measured by size exclusion chromatography SEC, Waters 410 based on PS standards. The viscosities of the commercial polymers were measured at 235 C in a rotational shear rheometer ARES, Rheometrics Scientific using 25 mm parallel plates. The frequency sweep data were fit with the Ellis model after applying the Cox-Merz rule Macosko, 1994, = 0 1+ k s 1, where 0 is the zero shear rate viscosity, is the shear stress, and s and k are the Ellis parameters. These data for PS and PMMA are summarized in Table II. B. Multilayer coextrusion The multilayers were made with a coextrusion line at 235 C in our laboratory. Details about this special setup are described by Zhao and Macosko Initially, two polymers are brought together in a feed block which arranges them into 20 alternating layers. The thickness ratio of the layers is determined by the feed rate of each polymer melt, which is controlled by a gear pump Zenith PEPII interfacing between each single-screw extruder and the feed block. The melt flow from the feed block is shaped into a mm square by a die as shown in Fig. 1 a. A fish-tail sheeting die transforms the square flow into a 51 mm-wide by 1.8 mm-thick rectangular shape. It is in this sheeting die that most of the interface between the alternating layers is generated. At the end of the sheeting die is a 28 mm long, mm die land where the layers experience the highest shear stress. At the land exit, the multilayers are picked up by a water-cooled double chill roll and quenched to room temperature. Layer thickness was measured by optical microscopy. A cross section of the multilayer extrudate was microtomed at room temperature with a glass knife to achieve a smooth surface. The surface was then observed with an optical microscope Olympus, BH2-1 TABLE II. Ellis model parameters at 235 C. PS PMMA 0 Pa s s k 10 3 Pa

4 44 ZHANG, LODGE, AND MACOSKO FIG. 1. a Schematic drawing of the coextrusion die. The rectangular flow after the feed block is shaped into a square, which is transformed into a sheet in a fish-tail sheeting die. After the die land, the melt is picked up by a double chill-roll. b Optical micrograph of about half of a 20 layer PS/PMMA extrudate. The scale bar represents 100 m. HLSH in reflection mode. A section of the layer structure is shown in Fig. 1 b. The bright layer is PMMA and the dark layer is PS. The total thickness of the multilayer tape is about 1 mm and the thickness of each layer is 50±2 m. As shown, the interface between layers is flat and the layer thickness distribution is uniform, which is expected for the uniform flow in the coextrusion die. The composition of the two components was controlled to be 50/50 by weight, confirmed by the layer thickness ratio and by proton nuclear magnetic resonance 1 H-NMR spectroscopy on a sample dissolved in deuterated chloroform. C. Adhesion testing Interfacial adhesion was measured using the asymmetric dual cantilever beam crack propagation ADCB test. To prepare samples, a 3 10 cm section was carefully cut from the center of a multilayer tape without delaminating the layers and was then glued onto a glass slide with cyano-acrylate adhesive Quicktite, Loctite. The glass slide was used to create a stiff substrate and keep the sample flat during measurement. One end of the

5 INTERFACIAL SLIP REDUCES POLYMER-POLYMER 45 FIG. 2. Schematic drawing of measurement of interfacial adhesion by the ADCB test: a at even-numbered interface; b at odd-numbered interface the top PMMA layer was peeled away before measurement. a is the crack length. The sample was glued to the glass slide with cyano-acrylate adhesive. multilayer tape was manually separated into 10 pairs of PS/PMMA bilayers. The separation was monitored by measuring the thickness of each bilayer. A rectangular stainless steel blade of thickness 0.5 mm was then driven into the interface between the first PS/PMMA bilayer and the rest of the multilayer tape which is the second interface numbered from the top to generate a crack, as shown in Fig. 2 a. After allowing the crack to equilibrate for half an hour, the crack length, a, was then measured with a micrometer and an optical microscope. The critical strain energy release rate or the critical interfacial fracture toughness G c was quantified using the equation described by Creton et al. 1992, G c = 3 2 E 1 E 2 h 1 3 h 2 3 8a 4 C 1 2 E 2 h C E 1 h 1 C 3 1 E 2 h C 3 2 E 1 h 3 1 2, where C i = h i /a, E i is the modulus of component i, and h i is the thickness of component i. Since the multilayer tape was fixed on a glass slide and the thickness and modulus of the glass are much larger than that of the polymers, Eq. 2 can be simplified to the following: G c = E 1 h 1 8a 4 4 C, 3 1 where the subscript 1 indicates a PS/PMMA bilayer. The thickness of the bilayer was measured with a micrometer and the modulus was calculated as the arithmetic average of the two components. After the first crack, the blade was further inserted into the interface to create a new crack and the second data point was achieved. After repeating five times, G c was obtained by averaging over the five measurements. Then the first PS/PMMA bilayer was peeled away from the rest of the multilayer tape. The blade was inserted to the fourth interface, which is between the revealed top bilayer and the rest of the multilayer tape. By repeating 2

6 46 ZHANG, LODGE, AND MACOSKO FIG. 3. Interfacial adhesion after coextrusion vs interface number. N=1 is the PS/PMMA interface closest to the surface; 10 is at the center. G c for the laminated PS/PMMA interface,, from Brown et al and Cole et al this procedure, the adhesion at the even-numbered interfaces was measured. Since the multilayer is symmetric in the direction perpendicular to the layer, only the adhesion from the second to the tenth interface was measured. To measure the adhesion at the odd-numbered interface, the first layer indicated by the PMMA layer in Fig. 2 b, but it could also be PS was peeled away before measurement. Then the adhesion was measured in a similar way to that at the even-numbered interfaces as shown in Fig. 2 b. For the first interface, a blade was inserted between the top layer and the rest of the layers and G c was calculated using the same E value for the other interfaces, considering that PS and PMMA used here have similar modulus. To increase the reliability of the data, the measurements were repeated on a second sample. Thus the reported G c values are an average of at least 10 tests and the error bars are one standard deviation. III. RESULTS AND DISCUSSION A. Adhesion at different interfaces The critical fracture toughness G c at each even-numbered interface N, N starts from the top is plotted in Fig. 3. As shown, G c is the highest at the center interface. As N decreases, which means that the interfaces are located further away from the center and closer to the surface, the interfacial adhesion decreases significantly. For N 4, the adhesion does not change further. To confirm the adhesion changes vs. interface number and the occurrence of a plateau in adhesion at the interfaces near the surface, G c for the odd-numbered interfaces from the first to the ninth interface were measured by the ADCB test described above, and the results are also plotted in Fig. 3. For a laminated PS/PMMA interface, G c was reported to be 12±2 J/m 2 independently by Brown et al and by Cole et al As shown in Fig. 3, this value agrees with that of the center interface. The adhesion at all the other interfaces is significantly lower than this value. In the plateau region, the adhesion is the lowest and there is about a threefold decrease compared to that of the laminated interface. Clearly, coextrusion has a strong effect on adhesion.

7 INTERFACIAL SLIP REDUCES POLYMER-POLYMER 47 FIG. 4. Schematic drawing of the velocity profile inside and outside of the die. The no-slip boundary condition is assumed between polymer melt and die wall. Slip occurs at the interface between PS and PMMA. Outside of the die, full-slip boundary condition is assumed at the melt/air interface. Thus the layer next to the wall must accelerate dramatically. Similar phenomena were also found by Morris 1996 in coextruded films where the peel strength between HDPE/Adhesive/EVOH decreases with processing time and by Cole 2002, where G c decreases with increasing flow rate for 16 layer PS/PMMA coextrudates. Several potential reasons were proposed by Morris, which might also be responsible for the adhesion decreases here. The first possibility is cooling of the extrudate. Immediately after coextrusion, the multilayer tape was cooled by a double chill roll from 235 C down to room temperature. To check whether sequential quenching of the interfaces is the reason for decreasing adhesion, the temperature change vs time for each interface was calculated with the unsteady state heat conduction model Bird et al. 2002, assuming an isothermal boundary at 20 C. It was found that even for the center of the multilayer tape, the time to reach 100 C below T g for both PS and PMMA is less than 1 s. Clearly, therefore, cooling is rapid. Furthermore, if cooling were responsible for the adhesion decrease, it is hard to account for the existence of the plateau in adhesion near the surface; one would expect a continuous variation. In Fig. 3, the adhesion at interface N=1 which will quench in less than 0.1 s is the same as at interface N=4, which will quench after 0.3 s. The second possible reason for variation of adhesion with layer position is the high extensional stress at the die exit experienced by the polymer melt. Figure 4 shows a schematic diagram of the flow velocity profiles inside and outside of the extruder. As shown, the velocity is discontinuous, and there is a huge acceleration in a narrow transition zone near the die exit as shown by the gray in Fig. 4. The extrudate is then subjected to a sudden extensional stress. This extensional stress is not uniform across the layers and is the highest at the surface. It could possibly result in weakening of the interfaces close to the surface and lead to decreases in adhesion. However, the depth of this transition zone was found to be on the order of tens of microns, as simulated by Venet and Vergnes 2000 and measured by Migler et al With the flow rates used here 30 g/min for this sample, the average linear velocity is on the order of mm/s. The time period for the melt experiencing extensional stress is much less than the longest chain relaxation time, 0.01 s vs 1 s. Thus there is insufficient time for chains to disentangle. Furthermore, the extensional stress is most significant at the first and perhaps second interfacial layers of the multilayer extrudate. Therefore, if this is the cause for

8 48 ZHANG, LODGE, AND MACOSKO adhesion decrease, the adhesion at the interfaces N =3 9 should not be affected. This is not the case. Shear rather than extensional stress at the multilayer interfaces is the most probable cause of the reduction in adhesion as we demonstrate in the next section. B. Interfacial slip Zhao and Macosko 2002 studied slip at the interfaces in a 32-layer of the same PS and a PMMA with very similar rheology Plexiglas VA26-100, Atofina to our PMMA. The multilayer melt from the coextruder was fed into a slit die, and the pressure drop at different flow rates was measured. Figure 5 a replots the pressure drop vs flow rate Zhao and Macosko The data points show the measured pressure drop for the PS and PMMA homopolymers, and a 32-layer PS/PMMA. The solid lines through the points of the homopolymers are the calculated pressure drops using the Ellis parameters for the homopolymers. For the 32-layer PS/PMMA, the pressure drops were also calculated similarly without considering interfacial slip, as indicated by the dashed line in Fig. 5 a. As shown, this line does not match the measured values well, especially at high flow rates. Interfacial slip was assumed to have a four parameter sigmoidal dependence on stress Eqs. 12 and 16 in Zhao and Macosko By adjusting these parameters, the calculated pressure drops for the 32 layer sample could be fit to agree well with the experimental results, as shown by the solid line in Fig. 5 a. As shown in Fig. 5 b, V I strongly depends on the magnitude of the shear stress and three regimes can be identified accordingly. The interface shows no slip or very small slip behavior at low shear stress, which is designated regime I. No-slip behavior persists up to the onset of a rapid increase of V I, which signals the beginning of regime II. The critical shear stress for this transition is represented by 1. V I in this regime increases exponentially with shear stress. Regime III is characterized by a high but almost stress-independent slip velocity. The critical shear stress for the onset of this regime of full slip is designated 2. These three regimes defined for the slip at polymer-polymer interfaces qualitatively agree with the prediction of the scaling theory by Brochard-Wyart and de Gennes The interfaces of the multilayers experienced different levels of shear stress in the coextrusion die. The melt flow in the die is pressure-driven. The shear stress increases linearly from the center to a maximum at the wall. Assuming isothermal and onedimensional creeping flow, the Navier-Stokes equation describing the flow can be simplified, 0= d dy P L, 4 where is the shear stress in the x-y plane the interface plane and P/L is the pressure gradient in the flow direction which is a constant and can be calculated from flow rate Q, Q = WH3 P % L 2+s H P s 1, 5 2k L 0, s and k are the Ellis parameters for the polymers. W and H are the width and the height of the die channel, respectively. Equation 5 neglects the die side walls, a valid assumption for W 10 H Tadmor and Gogos During coextrusion, the smallest gap and thus the highest stress occurs in the die land. This is also the last shear stress the interfaces experience. Thus, the dimensions of the die land W=51 mm and H =1.8 mm are used to calculate the shear stress profile. Here, P/L for the multilayer melt is estimated to be the arithmetic average without slip of two individual pressure

9 INTERFACIAL SLIP REDUCES POLYMER-POLYMER 49 FIG. 5. a Pressure drop for PS, PMMA homopolymers and 32 layers flowing through a slit die. The dashed line is calculated assuming no interfacial slip. The solid lines through the homopolymers and 32 layer data are fitted using Ellis parameters and the slip velocity in b. b The slip velocity of PS/PMMA calculated by assuming a sigmoidal functional and fitting the pressure drop shown in a. The shear stress is divided into three regimes based on V I. replotted from Zhao and Macosko gradients calculated assuming only PS or PMMA flowing through the die. With P/L known, integrating Eq. 4 gives the shear stress distribution in the y direction. Figure 6 left axis plots shear stress vs interface number N for the flow rate of 30 g/min. As shown, the shear stress decreases linearly as N increases from 0 the surface of the multilayer melt, =53 kpa=wall shear stress to 10 the center of the multilayer melt, =0. 1 and 2 for PS/PMMA are indicated by the two arrows. With these two critical shear stresses, the interfaces can be classified into the three regimes defined for V I.As shown in the figure, regime I is a narrow region located near the center of the multilayer

10 50 ZHANG, LODGE, AND MACOSKO FIG. 6. Comparison between interfacial adhesion at different interfaces and shear stress for the 30 g/min multilayer sample. The three regimes are defined by the two critical shear stresses 1 and 2, see Fig. 5 b for the slip at PS/PMMA interface. The stress distribution at flow rate of 10 g/min is also plotted. melt. The only interface that obviously falls in this regime is the tenth interface. The shear stress at this interface is lower than 1, and thus slip should be negligible. Regime II includes the interfaces from the fourth to the ninth. In this regime, the shear stresses experienced by the interfaces range between 1 and 2, and thus slip should be significant. From Fig. 5 b, V I increases quickly as N decreases in this regime. Regime III includes the fourth to the first interface. Shear stresses higher than 2 are experienced by all these interfaces, and thus full slip has developed in this regime. Figure 6 also plots the critical fracture toughness for each interface right axis. As shown, G c is consistent with the three regimes defined for interfacial slip. In regime I, G c is highest. In regime II, the interfacial adhesion decreases quickly with N. Once reaching regime III which starts from the fourth interface, G c shows no significant change with N. Clearly, a close correlation exists between the slip phenomena and the interfacial adhesion. As discussed by Creton et al for immiscible polymers such as PS/PMMA, mechanical stress is transferred across an interface through entangled polymer chains in the interfacial region. The strength of adhesion depends strongly on the density of entanglements. In regime I, when the shear stress is low, polymer chains at the interface are hardly affected by the flow, and thus the entanglement density does not change much. The adhesion in this regime is the highest and is comparable to a laminated interface. In regime II, V I increases quickly with shear stress and thus chain disentanglement is speculated to be expedited accordingly. Therefore, G c in this regime decreases with shear stress increasing or N decreasing. In regime III, full slip is reached, and thus the adhesion reaches a plateau value. But note that it is not necessarily the case that the polymer chains have to be completely disentangled at the interface in the full slip regime. A detectable amount of adhesion still exists, which must come from residual entanglements. It is possible that the maximum extent of chain disentanglement has developed in this regime, and the entanglement density at the interface does not change further with increasing shear stress.

11 INTERFACIAL SLIP REDUCES POLYMER-POLYMER 51 FIG. 7. Comparison of interfacial adhesion for extrudates at different flow rates vs interface number, N. G c for the laminated interface is from Brown et al and Cole et al C. Adhesion at different flow rates The shear stress in the coextrusion die is determined by flow rate. When the flow rate is high, for example 30 g/min, the shear stress experienced by the interfaces can cover all the three regimes discussed above. For a flow rate of 10 g/min, the stress is almost half as shown by the dashed line in Fig. 6. The stress at this flow rate only covers two regimes. From the center of the multilayer tape to the eighth interface, the shear stress is lower than 1, and thus the interfaces in this region fall in the no-slip regime. From the eight interface to the surface, the shear stress is higher than 1 but always below 2. This indicates that interfacial slip can develop at these interfaces, but it will never reach the full-slip regime. G c values for both flow rates are plotted in Fig. 7. As shown, for 10 g/min, adhesion in the no-slip regime seem to be N-independent. As the interface reaches the slip regime, the adhesion begins to decrease with N as expected. But note that there is no low G c plateau for this flow rate. This is consistent with the stress distribution in the die as shown in Fig. 6. The adhesion for these two flow rates are considered vs shear stress in Fig. 8, as well as further data at 20 g/min and 40 g/min. As shown, the G c values converge into a master curve which is only a function of shear stress. This universal behavior further supports the loss of interfacial entanglement as the mechanism for adhesion decrease during coextrusion. D. Restoring adhesion Since vitrification of the disentangled polymer chains at interfaces is proposed to account for the persistent adhesion decrease, the effects of shear stress should be reversible upon annealing of the interfaces, i.e., by allowing the polymer chains at the interfaces to relax at temperature above the glass transition temperature T g should reestablish entanglements. To test this idea, the 20-layer PS/PMMA produced at 30 g/min was annealed, by placing the multilayer tape between two steel plates 3 mm thick, using

12 52 ZHANG, LODGE, AND MACOSKO FIG. 8. Interfacial adhesion vs shear stress for multilayer samples extruded at different flow rates. G c values for all the flow rates converge to a master curve which is only a function of shear stress. shims to maintain the original thickness of the tape and putting the assembly into a hot press preheated at 150 C, a temperature above T g for both polymers. The sample was held between the hot plates for 2 min, followed by quenching with cool water. After annealing, the interfacial adhesion at each interface was measured as described above. The adhesion between the annealed interfaces is plotted in Fig. 9. As shown, G c no FIG. 9. Adhesion vs layer position. quenched after coextrusion at 30 g/min; same sample annealed 2 min; quenched after coextrusion at 30 g/min but with 10 wt. % of the chain functional enabling reactive coupling at the interface.

13 INTERFACIAL SLIP REDUCES POLYMER-POLYMER 53 FIG. 10. Adhesion vs annealing time for the second interface of a 20 layer PS/PMMA at 220 C longer varies with N, and is equal to the adhesion for a laminated PS/PMMA interface Fig. 3. Clearly, annealing reestablished the interfacial entanglements and restored the decreased adhesion back to the equilibrium value. To further establish that chain relaxation at the interface is responsible for the recovering of adhesion, its time dependence was checked. A multilayer tape produced at 30 g/min flow rate was glued onto a glass slide and was annealed on a hot plate pressed by hand at 220 C for different time intervals and the adhesion at the second interface was measured. G c vs annealing time is plotted in Fig. 10. As shown, the adhesion does not change significantly in the first 2 s, but then it increases rapidly to the equilibrium value discussed above. The total annealing time including heat transfer and chain relaxation for adhesion restoration is about 4 5 s. From Prager and Tirrell 1981 and Kim and Wool 1983, the healing time for the homopolymer fracture is dominated by the longest chain relaxation time, which can be estimated from the center of mass diffusion data. According to Green et al. 1988, the diffusion coefficients D for PS and PMMA used here are on the order of and cm 2 /s, respectively, at 220 C. Based on D and the radius of gyration, the longest relaxation times for PS and PMMA are estimated to be around 0.4 and 25 s, respectively. The time range spanned by the longest chain relaxation time for these two polymers is consistent with the adhesion restoring time. Therefore, this observation supports the interpretation that adhesion restoration is dominated by chain relaxation at interfaces. E. Interfacial block copolymer Copolymers can be used to improve the interfacial strength between immiscible polymers, as described in the review of Creton et al Zhao and Macosko 2002 also used block copolymers to suppress slip at nylon/ PP and PS/PP interfaces. We expect that the adhesion decrease in a coextruded multilayer can be prevented by forming block copolymers reactively during coextrusion. To test this hypothesis, 10 wt. % PS-NH 2 and PMMA-anh-pyr see Table I were blended with the corresponding commercial PS and PMMA using a 16 mm corotating twin screw extruder Prism TSE16TC at 200 C,

14 54 ZHANG, LODGE, AND MACOSKO TABLE III. G c values vs layer number at various condition. 10 g/min 25.7 kpa a 20 g/min 41.3 kpa G c J/m 2 at different flow rates 40 g/min 64.0 kpa 30 g/min 53.6 kpa N Quenched Quenched Quenched Quenched Annealed b With BCP c G c STD G c STD G c STD G c STD G c STD G c STD a Wall shear stress. b Annealed at 150 C for 2 min. c Block copolymer interfacial coverage was estimated to be 0.02 chain/nm rpm. These materials were then fed to the coextrusion die to make a reactive multilayer at flow rate 30 g/min. During coextrusion, block copolymer PS-b-PMMA was formed at the interface through the coupling between the amine group on PS and the anhydride group on PMMA Schulze et al. 2000, Jeon et al. 2004, and Zhang et al After coextrusion, the adhesion at each interface was measured. As shown in Fig. 9, the adhesion does not vary with N any more. Moreover, compared to the annealed multilayer, there is a significant increase in adhesion due to the interfacial block copolymer, as summarized in Table III of all the adhesion data for the multilayers experienced various processing condition. However, even though the adhesion is promoted by the coupling reaction of PS-NH 2 /PMMA-anh, the reinforcement is moderate. One possible reason is the low molecular weight on the order of entanglement molecular weight functional polymer used. Washiyama et al and 1994 has reported that to achieve an improvement on adhesion, the molecular weight of the blocks should be above the entanglement molecular weight for the homopolymers. Another possible reason is the low conversion of the coupling reaction as discussed below. For the 20 layer reactive PS/PMMA, the amount of block copolymer formed at the interface can not be measured due to its low concentration. In order to detect block copolymer, its concentration must be increased by increasing the number of layers. A multilayer sample with a much smaller layer thickness on the order of 1 m but the same functional polymers was prepared at the same flow rate, by increasing the layer number to 640 using 5 multiplication dies Zhao and Macosko With this reactive multilayer, the amount of block copolymer formed is sufficient to be characterized by SEC with a fluorescence detector Hitachi F1050 Moon et al The copolymer interfacial coverage, which is defined as the number of block copolymer chains per unit interfacial area, was measured to be about 0.02 chain/nm 2 for the multilayer after coextrusion. It is about 10% of the maximum coverage at a PS/PMMA interface for the block copolymer used here, according to Anastasiadis et al The thickness of the layers

15 INTERFACIAL SLIP REDUCES POLYMER-POLYMER 55 does not affect the amount of copolymers formed at a flat interface, as suggested by many thin film studies Jones et al. 2003, Jeon et al. 2004, Yinet al. 2003, etc.. Thus, the interfacial coverage for the 20-layer PS/PMMA is believed to the same, about 10% of the maximum coverage. With this low coverage, the adhesion increases by about 50%. This is a promising improvement. Clearly, chemical linkages at an interface not only can prevent slip as observed by Zhao and Macosko 2002, they also can greatly improve adhesion. IV. SUMMARY Shear stress can have a strong effect on interfacial adhesion under coextrusion. Three regimes were defined for slip phenomena at polymer-polymer interfaces, which were used to classify the interfaces of a multilayer coextrudate into three regimes. In regime I, the shear stress experienced by interfaces is low, and interface slip is negligible. The adhesion in this regime is high, equal to that of interfaces laminated under equilibrium conditions. In regime II, the interface experiences higher shear stress than the critical slip shear stress 1. The slip velocity increase at each interface further from the center line of the flow and adhesion begins to decrease rapidly. When the interface reaches the location such that the shear stress is above the critical shear stress for full slip 2, adhesion reaches a plateau value, 1/3 of the equilibrium value. The existence of this plateau in G c argues strongly against heat transfer or extensional stresses at the die exit being the source of adhesion decrease. The adhesion variation during coextrusion was found to be only a function of shear stress for different flow rates. This supports the idea that shear stress is the main reason for the adhesion decrease. We propose that polymer chains across the interfaces are disentangled by the high shear stress during coextrusion. The entanglement density is related to the interfacial thickness, which is determined by the miscibility of the two polymers, and the length between entanglements or tube diameter of the polymer chains. It is not clear in detail how stress affects the interfacial chain packing, for example, whether the interfacial width is modified, whether chain segments are oriented, or whether the mean entanglement spacing is altered. Also, it is still not clear yet why the adhesion just drops by a factor of 3 and then stays constant and whether the plateau toughness represents some particular kind of interface, for example an unentangled interface. More work is required to clarify these questions. The adhesion decreases can be restored quickly by annealing following coextrusion; the time required is comparable to the longest relaxation time of the chains. Also, it was found that a small amount of block copolymer not only can prevent adhesion decrease under coextrusion, but also can result in a significant increase in adhesion. ACKNOWLEDGMENTS This research has been supported partially by the MRSEC program of the National Science Foundation under Award No. DMR , and by IPRIME the Industrial Partnership for Research in Interfacial and Materials Engineering at the University of Minnesota. J. Z. thanks Mike Dolgovskij for help with the coextrusion and Umang Nagpal for preparing some samples for the adhesion measurements. We appreciate the discussion with Professor David Morse and Dr. Lifeng Wu of the University of Minnesota and Professor Guo-Hua Hu of CNRS-ENSIC-INPL, Nancy, France.

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