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Fundamental understanding and modeling of diffuse interphase properties and its role in interfacial flow stability of multilayer polymers.


In general, owning the advantage of combining separate features of different individual polymers together in a facile way, technology of coextrusion has been widely used to fabricate multilayered composite sheets or films for various applications ranging from food packaging products to optical reflective films [1]. Its processing technique is realized by a combination of two or three extruders using a multimanifold die or a feedblock within which polymer melts are brought together and a specific multilayer assembling is created. However, in this kind of processing, the contrast in rheological and physico-chemical properties of polymers and the variations of experimental conditions (like coextrusion designs, flow rate, and die geometry, etc.) may cause defects at the interface of neighboring layers, which may bring severe detrimental defects on the optical, barrier and adhesion/mechanical properties of the final extrudate products [2-5]. Two main defects that have been commonly observed are the interfacial instability (wave-type distortion or zig-zag defect) [3, 4, 6] and the encapsulation phenomena that occur due to the tendency of the lower viscous polymer to encapsulate the higher viscous polymer [6, 7].

In the industrial production of multilayered structures, to get rid of bad adhesion between different incompatible polymers, normally a tie layer (usually block polymers) is introduced to link both the outer and inner layer through a physicochemical interaction (interdiffusion and/or reactive couplings) [1], So far, the interface/interphase (a non-zero thickness physicochemical zone) has aroused researchers' great interests regarding its effects on the physics and rheology of the multiphase systems of multilayer and/or blend [1, 8]. Recently the interphase triggered between neighboring layers as a result of the interdifusion and/or reactive compatibilization has been reported to affect the final properties of multilayered films like electrical property [9], transport property [10] and optical property of refractive index [11], etc [1], The performance of the interphase is closely related to the interfacial microstructure, exactly speaking, local entanglements that are gradually established via interchain penetration during the interdiffusion and/or reaction process. Due to its being experimentally unobtainable, detailed picture of such an interfacial structure has yet to be fully understood. Liu et al. [11] made up an interphase material by decreasing the layer thickness of multilayer structure to a comparable size of the interphase through layer multiplying coextrusion, but with only mechanical strength being examined by T-peel test. Studies to understand the microstructure and properties of the interphase are still on the way, being far from enough. It should be of experimental and theoretical value to shed lights on such a physicochemical interaction as well as its role in controlling the interfacial defects of coextrusion.

Regarding the interfacial defects of coextrusion, a large number of literatures have come up reporting on the theoretical and experimental advances and the underlying origins from both mechanical and numerical approaches |1], Yih [12] was the first who conducted a systematic numerical study on the stability of plane Poiseuille flow of two Newtonian fluids considered within a framework of linear stability theory and he pointed out that the viscosity difference can cause instability regardless of the Reynolds number. Li [13] first applied the linear stability theory to a non-Newtonian fluid by introducing an elastic component (relaxation and retardation time) and proposing an Oldroyd model for the How of Oldroyd-B fluids. Su and Khomami [14] performed both asymptotical and numerical calculations for Oldroyd-B fluids and gave the most complete results on the interfacial instability for these fluids with constant and shear rate-dependent viscosities. Following the numerous studies published, a series of crucial parameters determining the interfacial defects have been pointed out and noted: layer depth ratio, viscosity ratio, elasticity ratio, and die geometry, etc. Recently, Wilson and Khomami [6, 15, 16] have published a series of comprehensive works on the interfacial instabilities in multilayer flow of viscoelastic fluids. The authors investigated the linear stability of coextrusion processing from a mechanical viewpoint. Their facilities introduced temporally regular disturbances with controllable amplitudes and frequencies, by which they measured the growth rate of the disturbance amplitude along the downstream die position to examine the interfacial stability. They first investigated flows of immiscible fluids (PP/HDPE incompatible system) and found that theoretically predicted growth rates agreed with their experimental data. Subsequently, they considered a plane Poiseuille flow of a compatible polymer system (LLDPE/HDPE). In comparison to the high growth rate of the disturbance amplitude along the downstream die position in the cases of PP/HDPE incompatible system, the growth rate for the LLDPE/HDPE compatible system is significantly less despite the fact that the viscosity ratio for the LLDPE/HDPE system is higher. They pointed out that the linear stability in the compatible polymer systems was related to the interphase resulted from the diffusive and intermixing in the vicinity of the interface [15].

Despite of the interesting nature of this kind of research, it is of no help in understanding either the connection between the properties of the present interphase and the resulting final properties of multilayer polymers or the generation of interfacial flow instabilities. The direct correlation of interphase to the interfacial defects of coextrusion has not yet been reported. Even though improvement of the interfacial defects have been aware of in the coextrusion of compatible polymer couples [15], no sufficient attention have been paid to the role of the interphase and much less the quantitative characterization of this interphase. Few studies have, with regard to fundamental and experimental aspects, been dedicated to the physical modeling of the present inteiphase and its effect on the flow stability. After presenting an upstream rheological study on the reaction/ diffusion competition at neighboring layers based on a reactive multilayered system (RS) of polyamide (PA6)/polyethylene-grafted with glycidyl methacrylate (PE-GMA) and a non-reactive multilayered system (NRS) of PE/PA6, Lamnawar and Maazouz [17, 18] demonstrated the importance of the generated interphase on alleviating the interfacial instabilities in coextrusion of this kind of reactive multilayered structures. However, the systems they used were very complex with regard to the high polydispersity and reactivity. To have a better understanding, it would be preferable to work firstly with model polymers in order to probe the effects of the diffuse interphase in the Bow stability during coextrusion. The complexities in analyzing the role of interphase in coextrusion of two incompatible, reactive polymers are considerably reduced by using a compatible pair. This is because in the incompatible, reactive polymer system, the amount of the triggered interphase is limited during the short contact time of the two melt streams in the coextrusion while in the compatible ones, the interphase are more considerable as interdiffusion can occur in a more rapid rate [1].

In our previous work [19, 20], rheology has been demonstrated to be a reliable method for monitoring the diffusion process at a polymer/polymer interface based on both symmetrical and asymmetrical bilayer structures consist of PVDF and PMMA model polymers. Modeling has been realized to describe the kinetics of the interdiffusion (self-diffusion, mutual diffusion) and to express the developments (thickness, rheology) of the interphase triggered between the neighboring layers. These upstream studies render us to understand the interphase at polymer/polymer interface generated in compatible and/or reactive systems from a fundamental aspect. But the direct correlations of the understandings on the interphase to the real processing is still lacking, especially the study of the interphase in flow field. The main objective of this article is to probe the interdiffusion as well as the growth and structural evolution of the interphase triggered in the approx real experimental conditions of processing before disclosing its role on weakening the interfacial flow instability of coextrusion. To attain this objective, a brief view of the diffuse interphase at fundamental conditions is given before the interfacial rheology of multilayered structures as well as the microphysics of the interphase at practical condition of coextrusion being investigated and discussed. Then the processing properties, especially the interfacial flow instability and encapsulation, of multilayer compatible systems are focused.



The polymers used in this study were supplied by ARKEMA. Poly (methyl methacrylate)(PMMA)/poly(vinylidcnc fluoride) (PVDF) were used as a compatible system and PMMA/ polyethylene(PE) were also employed as an incompatible system for comparison purpose. Two poly (methyl methacrylate) (PMMA)s of different molar mass, namely PMMA-1, PMMA-2 were included to allow us to vary the viscosity and elasticity ratios. The main characteristics of the materials are listed in Table 1. For clarity purpose and easy reading of this article, more characterization information of the studied polymers which have been provided in Refs. [19-21], are not addressed here.

Rheological Measurements

Rheology of Monolayers. All the polymer granules were dried at 80[degrees]C under vacuum to remove any moisture before use. Samples for the measurements in rotational rheometer were prepared by compression molding at 180[degrees]C with a pressure of 200 bars between two Teflon films to obtain a smooth surface. Then the samples were cut into round disks with a diameter of 25 mm and the disks were annealed at 80[degrees]C under vacuum for at least 24 h before measurements to eliminate the possible effect of surface orientation brought about by the compression molding.

Dynamic rheological measurements of neat polymers were carried out using a strain-controlled rotational rheometer, ARES (Advanced Rheometrics Expansion System) and a stresscontrolled rotational rheometer, DHR-2 (Discovery Hybrid Rheomter, TA instrument) with a parallel-plate geometry ([PHI] = 25 mm) at varying temperatures from 180[degrees]C to 260[degrees]C under nitrogen atmosphere. All dynamic frequency sweep tests were carried out in a linear viscoelastic (LVE) region. Dynamic strain sweep tests were conducted beforehand to determine the linear viscoelastic domain. Steady shear measurements of the neat polymers were carried out in the same rotational rheometer (parallel-plate geometry, [PHI] = 25 mm) for low nominal shear rates. For high shear rates, a pressure-controlled CEAST Capillary rheometer using a die with a 180 degrees entry angle and various L/D ratios for Bagley correction (L/D = 30, 20, 5) was employed.

Rheology of Multilayer Structures. The interdiffusion process and inteiphase development occurred at asymmetric polymer/ polymer interfaces of multilayer assemblies were monitored by small amplitude oscillatory shear (SAOS) measurements (parallel-plate, [PHI] = 25 mm, gap = 1.2 mm). The multilayer assemblies (total thickness = 1.2 mm, same geometry of each layer) were prepared by bringing round disks of PMMA (upper layer) on top of PVDF (lower layer) alternately into intimate contact at room temperature before loading them between the plates and annealing them in the oven at a given temperature. Steady shear measurements were also carried out to investigate whether the interfacial slippage may occur in such compatible multilayered structures. Nitrogen purging was maintained throughout all the measurements to avoid potential degradation and oxidation of the polymers.

Effect of Pre-Shear

To take into account and simulate factors like high steady shear, intermixing, etc. that may be encountered in the practical and complex conditions of coextrusion processing, a pre-shear mode was introduced to the multilayer structures before carrying out the dynamic time sweep test to examine its effect on the interdiffusion kinetics. Meanwhile, cross-section morphology of the specimens which were immediately quenched upon being subjected to the pre-shear were observed under scanning electron microscopy (Enviromental SEM Hitachi S-3500N). Also observed under SEM were those specimens that experienced annealing process for a given time with and without pre-shear.

SEM-EDX Analysis and TEM Observation of the Interphase Generated in Flow Field

For a purpose to characterize the interphase triggered between PMMA and PVDF neighboring layers in flow field during coextrusion process in a quantitative manner, a technique combining SEM and energy dispersive X-ray analyzer (EDX) was employed to determine the concentration profile across the interphase upon the bilayer extrudates. This technique makes use of the characteristic X-ray fluorescence of characteristic atoms present in the sample (that is, fluorine (F) for PVDF and oxygen (O) for PMMA). It has been demonstrated to be more than adequate for measuring the interdiffusion of compatible polymer systems [20, 22]. The quenched coextruded bilayer specimens were microtomed normal to the interfacial plane using an ultramicrotome before being exposed in a Hitachi S800 FEG Scanning electron microscopy (SEM) with an EDX microanalysis system. The EDX analyzer collected the X-ray data across a path (20 analysis points) of a line scan of electron beam that conducted from one bulk (e.g. PVDF) to the other (e.g. PMMA) in a desired field. At each point the number of X-ray events of given energy generated within a fixed time period was recorded as a function of X-ray energy and at the same time the position of the path was photographically recorded. As the number of X-ray counts is directly proportional to the number of atoms (and hence the amount of characteristic element of the polymer) from which they originate, a concentration profile can be developed for the characteristic element, and the involved polymer across the interphase in the annealed specimen. Moreover, the cross section morphology of the quenched coextruded bilayer specimens were examined in a Philips CM 120 transmission electron microscopy (TEM) operating at an accelerating voltage of 80 kV.

Coextrusion Process and Interfacial Stability

Apparatus. In contrast to the work of Lamnawar and Maazouz [21] in which an industrial machine was used, a laboratory instrumental setup of coextruder especially designed in a home mode, which was equipped with a feedblock/ multimanifold hybrid system connecting three extruders and a hanger die, was employed to elaborate the multilayer sheets in this study. The manipulations of the extruders (temperature, rotating rate, pressure drop, ...) were accomplished in an independent automatic operating panel. Details concerning this specific laboratory setup are presented in Table 2. A schematic of the instrumental coextrusion device composed of three extruders is given in Fig. 1. The video camera was used to observe and capture the How stability and possible generated defects of the coextruded melts upon the exit of the die.

Experimental Procedures. In the coextruder setup, extruder A ([PHI]s = 18 mm, L/d = 25) was used for PMMA and extruder C ([PHI]s = 15 mm, L/d = 25) for PVDF in order to elaborate mono and bilayer structures. The temperature profile in the extruder was set to 210, 220, and 220[degrees]C from the feeding to the metering zone, respectively. The polymers were brought together in the multimanifold/feedblock system before going to the hanger die that arranged them into more than two alternating layers. Two typical configurations, CBABC 51ayers and CA bilayers, are shown in Fig. 2a and b. To make easy reading of this article, only the CA bilayer structure results are to be presented and discussed here. The geometry and dimension of the fluid channels in the feedblock, multimanifold and the connecting hanger die are also given in Fig. 2c and d. The thickness ratio of the layers was changed by varying the flow rate of each polymer melt. A calibration curve of flow rate versus screw rate for each polymer was created beforehand by adjusting the screw rate of extruder from 5 to 65 rpm/min. After exiting the die, the bilayer films were passed over a water-cooled double chill roll and quenched to room temperature. Both the extrudates at the die exit and the quenched ones were visualized to examine the interfacial defects (flow stability, encapsulation, etc.) at the fluid interface.

Estimation of the Contact Time in Coextrusion Process. To quantitatively characterize the interdiffusion process and the interphase development during the coextrusion process, mathematical calculations of some parameters like contact time are needed. The contact time is the time that the polymer streams resided in the confluent region in the multimanifold system and the die. That is, the time between the moment that the separate polymer fluent merged into a combine when they How into the die land to the moment that the confluent flows out at the die exit and being quenched. It could be estimated by an expression as follow:

[] = [[V.sub.conf]/[Q.sub.mass]] [rho] (1)

where [V.sub.conf], [rho], [Q.sub.mass] represent the volume of the confluent region in the manifold of feed block and die, the apparent density of the confluent melts and the mass flow rate, respectively. According to the dimensions of the fluid channels and die given in Fig. 2c and d, [V.sub.conf] has been estimated to be 1.7 X [10.sup.-5] [m.sup.3].


Viscoelastic Properties of Neat Polymers

Rheological properties like storage modulus (G'), loss modulus (G'), and dynamic viscosity ([[eta].sup.*]), etc. of the investigated polymers in the molten state have been measured as a function of angular frequency at given temperatures ranging from 180[degrees]C to 260[degrees]C. Master curves of the polymers have been obtained at a reference temperature of 220[degrees]C, from which the activation energies of viscous flow were calculated, as listed in Table 1. More molecular characteristics of the polymers have been given in our earlier publications [19, 20], and those concerning PE involved in this article have been reported in previous series [17, 18]. Here, only typical curves of [[eta].sup.*] versus angular frequency of PMMA-1 and PVDF are shown in Fig. 3a, where one can observe a shear-thinning behavior at higher frequencies and a Newtonian behavior at lower frequencies for the two neat polymers. PVDF exhibited a more moderate shear-thinning behavior than PMMA at any given temperature. Indeed, as the temperature increases, the Newtonian behavior is more pronounced for both polymers. The corresponding viscosity ratios of PMMA to PVDF at different temperatures are plotted versus angular frequency in Fig. 3b. It is worthy of mentioning that PMMA is more viscous than PVDF at the same temperature, but as the temperature is raised, their viscosities approach each other and become nearly equivalent at 260[degrees]C.

Moreover, typical experimental results of PMMA and PVDF obtained in steady shear measurements that conducted by rotational rheometer for low shear rate and by capillary rheometer for high shear rate are given in Fig. 4. As shown in this figure, it is obvious that dynamic shear viscosity and steady shear viscosity well satisfy the Cox-Merz relationship. The dashed lines are fitting lines of power law to the experimental data for the non-Newtonian region, from where the power-law constant n are obtained: 0.39 for PMMA and 0.52 for PVDF, respectively.

Modeling of the Diffuse Interphase Triggered at Fundamental Conditions

In order to understand the diffuse interphase generated at neighboring layers under practical coextrusion condition, it is of necessity to first give a brief view of the interdiffusion kinetics and its interphase development at a fundamental and static condition. For this, comprehensive studies on the interdiffusion occurs at a symmetrical and an asymmetrical polymer/polymer interface have been carried out by annealing bilayer structures in the oven of rotational rheometer [19, 20]. Measurements were performed at a given temperature and a given angular frequency in LVE by online tracking variation of the rheological functions (like complex modulus [G.sup.*]) of the assembly versus annealing time. During the healing process, chains on both sides began to invade the interface, with a motion pattern generally considered to be governed by repation kinetics that put forward by de Gennes [23] and developed by Doi and Edwards [24], As chains on both sides uninterruptedly penetrate into the other side and entanglements in the interfacial region continuously become established, the sharp interface decays as the time elapses. It is replaced by a broadening interphase, which can be considered as a macroscopic blend composed of PMMA and PVDF chains. As more and more chains cross the interface, the entanglement density at the interfacial zone increases, thus the interphase becomes strengthened and more robust. Therefore more torque is required for shear and hence the higher the complex modulus of the system becomes. The increment of the complex modulus is only attributed to the strengthening brought about by the interdiffusion process since no variation of the G* has been found for the neat polymers due to their thermal stability at the experimental conditions. This is the physics of monitoring the interdiffusion kinetics by following the evolution of the viscoelastic properties of bilayer assembly versus healing time.

Indeed, quantification of the diffusion coefficient, especially in polymer melts, is quite a tremendous task since a great number of parameters are needed upon modeling. For the aysmmetrical bilayer system, a rheological model correlating the [D.sub.m] to the measured rheological properties has been developed in our earlier work [20] based on a primitive model of Qiu and Bousmina [25], The new model takes into account rheology of the interphase (complex modulus of interphase [G.sup.*.sub.I](t)) rather than using rhcolgy of the total sandwich structure ([G.sup.*.sub.s,t]) for the [D.sub.m] determination. The model is derived within the framework of reptation theory of Doi-Edwards [24] and fast-mode theory of Kramer et al. [26]. Here, for clarity purpose, only the final mathematical term of the modified model is shown as follow:


with mathematical functions p and q as

p = [8[beta][omega][G.sup.0.sub.N]/[[pi].sup.2]] ([[[phi].sub.A]/[G.sup.*.sub.A,0]] + [[[phi].sub.B]/[G.sup.*.sub.B,0]]) (3)

q = [8[beta][omega][G.sup.0.sub.N]/[[pi].sup.2]] [H/[2t.sup.1/2]] ([1/[G.sup.*.sub.s,t] - [1/[G.sup.*.sub.s,0]]) (4)

where [beta] is a shorten form of


In the equations, [[phi].sub.i], [N.sub.i], denote volume fraction and repeat unit number of composition i,i = A or B and [chi] is the Flory-Huggins interaction parameter; [N.sup.e.sub.b], [N.sub.b], [b.sub.b], [e.sub.b], and [G.sup.0.sub.N] are the average number of repeat units between entanglements, the repeat unit number, the effective bond length, the step length of the virtual tube and the plateau modulus of the inteiphase (or equivalent blend), which is also a function of the composition. [G.sup.*.sub.i,t] represents the complex modulus of layer i at a diffusion time t > 0 with an initial complex modulus of layer i as [G.sup.*.sub.i,0] at t = 0; and H is the total thickness of the sandwich (1.2 mm for the PMMA/PVDF assembly used in this work). Details on the deduction of the model and the information of the modifications are available for readers in Ref. [20], Indeed, the original modification of the model consists on the calculation and modeling of the monomeric friction coefficients of each polymer in the multiphase systems and correlates it to the diffusion quantifications. The rheology method, Lodge-McLeish model, and test of the time-temperature superposition (tTS) principle were employed to probe the thermorheological complexity of this polymer couple. The monomeric friction coefficient of each species in the blend has been examined to vary with composition and temperature and to be close in the present experimental conditions, and the failure of the tTS principle was demonstrated to be subtle.

According to the model of the mutual diffusion coefficient proposed above based on the concept of the interphase (Eq. 2), we can also gain some insights into the feature of the interphase. In particular, thickness of the interphase could be determined from the mutual diffusion coefficient via an equation as follow:

[h'.sub.l] = 2[([D.sub.m], t).sup.1/2] (6)

Figure 5 portrays a typical plot of the evolution of apparent mutual diffusion coefficient ([D.sub.m]) and the corresponding thickness of the generated interphase with time for a PMMA-1/ PVDF asymmetrical bilayer at T = 200[degrees]C, at = 0.1 rad/s. The apparent [D.sub.m] decreases gradually with time before reducing to a constant in the longer time limit. At the first beginning, the dynamics is dominated by short chains or segmental motions in a Rouse behavior with a higher diffusion coefficient. After more and more long chains participate into the diffusion, the [D.sub.m] decreases to a plateau stage, which is a sum of contributions from species of different chain lengths according to Doi and Edwards theory [24]. Likewise, the interphase grows gradually versus time, reaching a thickness of several dozens' microns after diffusion for 45 mins (e.g. ~77 [micro]m at 200[degrees]C), a similar order as that reported by other methods and techniques. Moreover, as the time elapsed, [G.sup.*] of the interphase asymptotically approached the corresponding value of its equivalent blend as shown in our earlier work [20]. This implies that a short-time interdiffusion along with the establishment of entanglements by interchains within the interphase give rise to greatly enhanced properties of the interphase. Anyway, it is clear that the interphase can reach an order of microns in a time scale of several minutes to tens minutes even in a fundamental condition of small-amplitude oscillatory shear measurements. One can imagine that in the practical condition of coextrusion processing, where shear flow is involved, the interdiffusion situation can be more complicated and the kinetics can be more rapid. This is the dedication of following sections to quantify the interphase properties in the practical condition of coextrusion processing.

Rheology at Compatible Alternating Multilayer Structures With Various Number of Layers

Rheological Measurements of PMMA/PVDF Multilayer Structures. With a knowledge that the rheological response of bilayer is sensitive to the interdiffusion process and generation of the interphase occurs at the interface, it is also of great interest to examine the rheology of such miscible multilayer structures by varying layer number. The complex viscosity, [[eta].sup.*] is reported versus the angular frequency ([omega]), for all PMMA-1/ PVDF multilayers of different layer numbers (2, 4, 6, 8) in Fig. 6. For comparison, complex viscosities of the pure polymers as well as blends of identical compositions and the theoretical predictions of log-additivity rule, lg [[eta].sub.mul] = [[phi].sub.A] lg [[eta].sub.N] + [[phi].sub.B] lg [[eta].sub.B] (plotted in broken curve) and reciprocal rule, [[eta].sub.mul] = [[phi].sub.A]/[[eta].sub.A] + [[phi].sub.B]/[[eta].sub.B] (plotted in dotted curve), are also incorporated into the figure. As one can see, the complex viscosities of multilayer structures lie between those of their constitute components, independent of the total number of layers, with values closer to the predictions of reciprocal rule, except for the terminal region (at low angular frequencies) where slight increases are observed and the higher the number of layers, the greater the increase. These increases can be attributed to the pronounced consequences of interdiffusion occurred between neighboring layers at low angular frequencies since longer times were allowed at these regions for diffusion than at high angular frequencies. Moreover, it is noted that PMMA-1/PVDF blend has a similar complex viscosity with multilayer systems as well as that predicted by reciprocal rule through the frequency ranges measured.

It seems that the effect of layer number is not very apparent. Note that in this section the fundamental study was carried out in LVE regime in which the diffusion is decoupled from flow. Now, one more interesting objective of this study is to perform some experiments in which the flow is coupled to the diffusion. Hence, an open question is addressed here, can slip occur at the polymer/polymer interface of a compatible alternating multilayer structure?

Steady Shear Flow of Compatible Alternating Multilayer Structures. Slip that occurs at a polymer-polymer interface was firstly proposed to interpret the macroscopic observations of anomalously low viscosities in blends of immiscible polymers by Lin [27] in a phenomenological model. The mechanism of slip can be attributed, from polymer chain dynamics viewpoint, to the lack of chain entanglements at the interface of immiscible polymers. Typically, formation of chain entanglements in the interfacial region is believed to be the origin of enhanced adhesive strength at the interface. For an immiscible polymer pair, commonly the interfacial width [h.sub.1](~b/[square root of 6[chi]]) is less than the radius of gyration [R.sub.g](~b/[square root of 6/N]), that means the number of chain entanglements in the interfacial region is less than the entanglement density in the bulk phase and the interfacial friction is dominated by Rouse dynamics. Thus with low entanglement density and weak interactions, the interfacial region cannot sustain high stress transferred from one component to the others when they are subjected to shear and hence slip occurs [28].

Zhao and Macosko [28] unambiguously evidenced the interfacial slip with polystyrene (PS)/polypropylene (PP) multilayer system by pressure drop measurements in an in-line slit rheometer and apparent steady shear viscosity measurements in parallel-plate rheometer. They observed that significant slip occurs at high shear stress and slip velocity can be scaled versus shear stress. At the same time, Lam et al. [29, 30] also simplified the morphology of a polymer blend into a multilayer structure, and quantified the interfacial slip based on this structure. They used a confocal microscopy to visualize the interfacial slippage directly and also proposed an energy model to quantify the interfacial slip velocity from dynamic shear measurements of multilayer structures. Later, Zhang et al. [31] demonstrated an idea that the rapid shear flow experienced by a multilayer melt during coextrusion can destroy interfacial entanglements, disentanglements of polymer chains at interfaces induced by high shear stress promote interfacial slip, and further reduce the adhesion of interface.

Now one might have an idea in mind that interfacial slip is dependent upon entanglement density of the interfacial region, hence any factors that affect the entanglement density (like diffusion. disentanglement, etc.) may have an impact on the occurrence of interfacial slip. For immiscible polymers, interfacial slip has been widely accepted to happen under certain conditions due to the fact of low entanglement density at the interface. Nevertheless, for miscible and/or compatibilized immiscible polymers, since the spontaneous interdiffusion and/ or reaction process progressively evokes the establishment of entanglements at the interface, slip phenomenon has not been focused. In fact, at the very short welding time of miscible polymers, the entanglement density at the interface is also very low. So it is of interest to check whether slip can occur in miscible polymer pairs at short welding time, especially under high shear conditions.

Despite the maximum shear stress experienced by the multilayers that is about 3700 to 4000 Pa at 100 rad/s, it is still not high enough to induce a slip in this study, showing no significant deviation from the reciprocal rule (Fig. 6). This accords with the preceding experimental results of Zhao and Macosko [28] and Lam et al. [30] etc. though their polymer systems are immiscible and ours are miscible. According to Zhao and Macosko [28], interfacial slip that unlikely to be observed under small amplitude dynamic shear is due to the fact that the shear stress in linear viscoelastic region where material structure remains undisrupted, is too small to cause interfacial slip. Steady shear measurement in parallel plate rheometer has been demonstrated to be able to detect the slip [28, 30]. For the purpose to probe the possible slip in short diffusion period, we performed steady shear measurements on the PMMA/PVDF multilayer structures at 200[degrees]C. For immiscible polymer pairs like PMMA/PE, we have demonstrated that slippage can appear at a relatively lower shear rate (<1.0 [s.sup.-1]). Likewise, we firstly implemented steady shear tests on PMMA-l/PVDF multilayer structures within lower shear rate (<1.0 [s.sup.-1]). However, the apparent viscosities show no any deviations from reciprocal rule, indicating no slip, as shown in Fig. 7a (open symbols). When steady shear measurements were conducted over higher shear rate which began from 1.0 [s.sup.-1] (filled symbols in Fig. 7a), negative deviations of apparent viscosities from f]mm, ,/,,, of neat PMMA-1 and PVDF appear when [??][greater than or equal to]10 [s.sup.-1]. One may argue that these negative deviations must be due to the effect of edge failure at high shear rate. Indeed, edge failure can be determined by monitoring the first normal stress difference ([[sigma].sub.11]-[[sigma].sub.22]) versus shear rate. Failure to reach steady state and a continuous decrease in the magnitude of ([[sigma].sub.11]-[[sigma].sub.22]) at a given shear rate was used as a sensitive indication of the onset of edge failure [32], In Fig. 7b, it can be seen that edge failure did not appear above [??] = 10 [s.sup.-1] until [??] [greater than or equal to] 15.8 [s.sup.-1]. Therefore the deviations of viscosities over the range 10 [s.sup.-1] [less than or equal to] [??] 15.8 [s.sup.-1] may be attributed to possible slip induced by high shear stress ([tau] ~25 kPa when [??] = 10 [s.sup.-1]). The slip velocity displayed in Fig. 7b was determined from the apparent viscosity of multilayer structure via a relation given by Eq. 7 [28].

[V.sub.slip] = [H[??]/[n - 1]] (1 - [[[eta].sub.n]/[[eta]]]) (7)

in which

[eta]]] = [[[eta].sub.A][[eta].sub.B]/[[[phi].sub.A][[eta].sub.A] + [[phi].sub.B][[eta].sub.B]]] (8)

Here, H is total thickness of multilayer structure and n is layer number; [[eta].sub.n], [[eta].sub.A] and [[eta].sub.B] are apparent visocity of multilayer structure, component A and component B at nominal shear rate [??], respectively. Note that the slip velocities at [??] [greater than or equal to] 15.8 [s.sup.-1] displayed in the figure in fact are questionable due to the significant effect of edge failure in this zone. They are shown here just for guides to eyes.

Despite the experimental data are limited, a clear tendency of slip for miscible multilayer structures at short welding time still can be achieved. At low shear conditions, slip can absolutely be negligible as it is inhibited by the rapid diffusion and low shear stress, while above a high critical shear rate (or shear stress), subtle slip can be detectable before the edge failures of sample happen. That is because the weakly entangled polymer chains at the interface within the short welding time may be disentangled by the high shear stress. Theoretically, after diffusion along one dimension direction for a time scale of reptation time ([[tau].sub.rep]), interfacial thickness reaches a distance of one entanglement mesh size, strong adhesive bond strength at the interface is supposed to achieve. Nevertheless, in practice, chains diffuse towards tri-dimensional space and it takes a longer time than [[tau].sub.rep] for the chains to form entanglements at the interface with a density similar to the bulk. Thus due to lack of entanglement density at the short welding time, the Rouse-like region at the interface is vulnerable to high shear conditions. Indeed, experimental results here are greatly corroborated from those of step strain and startup shear experiments of our work shown elsewhere.

Interdiffusion Quantification in Experimental Conditions of Coextrusion Process

Orientation Effect. In the previous sections, some achievements have been obtained on the interdiffusion process in a fundamental bilayer system by rheology regarding the diffusion coefficient and the interphase thickness. In the practical conditions of a coextrusion system, the situation is more complicated considering that the orientation of polymer chains in shear flow field may pronouncedly influence the rate of interdiffusion [33], According to this work, it is necessary to take into account the effect of the orientation by introducing an orientation factor, [alpha], into the calculation of the diffusion coefficient. Our new contribution in this field is to gain a rheological modeling of the diffusion coefficient as developed in our previous work [19, 20]. It is supposed that when there is no flow, the polymer chains have an average orientation angle of 45 degrees whereas the average orientation angles in the respective phases will be greater than 45 degrees when they are under a shear field, as schemed in Fig. 8. In fact, aside from the chain orientation, there are some intermixing at interface vicinity happening in shear flow field in the practical processing of coextrusion, the effect of which will be discussed in next section. In a shear field, the orientation factor can be described by an expression as follow:

[[alpha].sub.i] = [cos{([pi]/4) + [[tan.sup.-1] (3[[sigma]] [([[bar.M].sub.wi]/[[bar.M]]/[[bar.M]]).sup.3]/[G.sup.0.sub.Ni])]/2}/cos ([pi]/4) (9)

where [[sigma]] is the interfacial stress at the interface. To determine the [[sigma]], firstly we assume that the velocity distribution for the multilayer flow of incompatible non-Newtonian fluids is also valid for the case of PMMA/PVDF in this study.

Thus, [[sigma]] can be calculated by solving the equation of motion in rectangular coordinates (x, y, z):

-[partial derivative]P/[partial derivative]Z + [partial derivative][[sigma].sub.yz]/[partial derivative]y = 0 (10)

for phases A and B, respectively, with boundary conditions being that [([[sigma].sub.yz]).sub.A] = [([[sigma].sub.yz]).sub.B] = [[sigma]] at y = [delta], where [delta] is the position of interface; [([v.sub.z]).sub.A] = 0 at y = 0 and [([v.sub.z]).sub.B] = 0 at y = h. The parameter [[sigma].sub.yz] is the shear stress, and [([v.sub.z]).sub.A], [([v.sub.z]).sub.B] are the velocities for phases A and B, respectively. Moreover, a power law

[([[sigma].sub.yz]).sub.i] = [m.sub.i][[??]] (11)

is used for phase i, where i is A or B and [m.sub.i], [n.sub.i] are the power law constants for phase i. and [??] is the velocity gradient defined as

[??] = [[absolute value of [dv.sub.z,A]/dy].sub.0 x [less than or equal to] x y x [less than or equal to] x [delta]] (12)

for phase A and

[??] = [[absolute value of [dv.sub.z,B]/dy].sub.[delta] x [less than or equal to] x y x [less than or equal to] x h] (13)

for phase B. On the basis of the above equations, the [[sigma]] can be determined as follow:

[[sigma]] = -k([delta] - [mu]) (14)

in which k is the pressure gradient defined by k = -[partial derivative][P.sub.A]/[[partial derivative].sub.z] = -[partial derivative][P.sub.B]/[[partial derivative].sub.z]=const.; [delta] is the position of interface and [mu] is the position at which the maximum in velocity (and hence, the minimum in shear stress) occurs. These two parameters can be determined from the velocity profile based on the following equation group (Eqs. 15 and 16):



where [S.sub.i] = 1/[n.sub.i], [Q.sub.A]/[Q.sub.B] is the volumetric flow ratio.

With the pressure gradient detected by the transducers and the rheological behaviors of polymers being known. [delta] and [mu] are able to be calculated via the above equations for a given volumetric flow ratio in experiments. For example, in the case of PMMA-1/PVDF bilayer coextruded at 200[degrees]C, the interfacial position [delta], the position of maximum velocity [mu], the interfacial stress [[sigma]] and the interfacial shear rates obtained in the runs of different flow rate ratios are listed in Table 3. In fact, for a compatible system, the thin interface can be replaced with a thick interphase after a certain time.

We can note that the How is not symmetrical and the interfacial position [delta]/h decreases when the flow rate is increased. Among the different flow rate ratios ([Q.sub.PVDF]/[Q.sub.PMMA]) ranging from 0.3 to 2.6, one can see that when ([Q.sub.PVDF]/[Q.sub.PMMA] = 0.6, the [delta]/h is closest to the [mu], with the interfacial stress and the interfacial shear rate being the smallest. It should be important to note that the interfacial shear stress (or interfacial shear rate) as shown in Table 3, is too small to generate the interfacial slip-page since the shear stress required for slippage is above 25 kPa, as demonstrated in the above section.

On the basis of these important parameters as shown in Table 3, orientation factor, [alpha], of each polymer chain can be determined. Then the average chain orientation factor, [[alpha].sub.av], as displayed in Fig. 9(a), was determined as arithmetic average of the orientation factor of PMMA chains and that of PVDF chains. According to the orientation factors and the mutual diffusion coefficient [D.sub.m] evolving with time obtained at the fundamental conditions of rheological measurements in LVE, the apparent mutual diffusion coefficient in the shear flow field of coextrusion conditions can be estimated as follow:

[[??].sub.m] = [[alpha].sub.av][D.sub.m] (17)

The results of [[??].sub.m], are given in Fig. 9(b) and the corresponding interphase thickness calculated based on the [[??].sub.m] are also given in the figure. Obviously, the orientation factors are below 1, which results in lower diffusion coefficient during coextrusion process than that in the static condition. This means that the polymer chain orientation in the shear flow field during coextrusion has a decelerating effect on the interdiffusion process between neighboring layers. Moreover, when ([Q.sub.PVDF]/ ([Q.sub.PMMA] = 0.6, where the [delta]/h is closest to the [mu] and the interfacial stress and the interfacial shear rate is the smallest, the orientation factor is close to 1. The larger deviation of the [Q.sub.PVDF]/ [Q.sub.PMMA] from 0.6, the higher the value of the interfacial shear stress and the greater the orientation effect. The variation of ([Q.sub.PVDF]/[Q.sub.PMMA] was realized by fixing [Q.sub.PMMA] = 0.6 kg/h and varying the [Q.sub.PVDF], thus the total flow volume was changed. So as the [Q.sub.PVDF]/[Q.sub.PMMA] increased, the contact time of polymers inside the die was decreased and so as the thickness of the interphase.

Intermixing Induced from Shear Flow: Probed by Performing a Pre-Shear in Rheological Measurement of Multilayer Structures

Although an interesting work has been dedicated to the effect of orientation on the interdiffusion in coextrusion of compatible polymers, a very important point, i.e. intermixing induced from the high shear flow in the processing conditions was neglected in the study of Kim and Han [33], Indeed, effect of the shear flow could be very significant, especially in the early stage of processing. It has been reported that the flow in heterogeneous melt blending can result in a rate constant over 1000 times higher than that in the quiescent bilayer condition for an interfacial reaction between amine and anhydride terminal functions [34]. A shear flow is able to induce a local pressure drop at the interface between two fluids and thus gives rise to undulated structure and hence convective mixing [35].

Due to the high complexity of probing this problem in the real shear flow field of processing conditions in coextrusion, it is of interest to simulate this problem by introducing a certain amount of pre-steady shear before the rheological measurements of interdiffusion process at PMMA/PVDF multilayer structures in linear viscoelastic regime. Implement of a pre-steady shear to the multilayer structures may give us some ideas on the practical mixing process, especially in the early stages of polymer processings. This would be a good option to simulate intermixing in the practical situation of coextrusion and to see its effects on the interdiffusion process in a more closely manner. A given amount of steady shear flow [gamma](t)=[??] * t was introduced to the multilayer assembly, by rotating the plate of the parallel-plate rheometer before beginning a time sweep test in LVE. Figure 10 shows the G*(t) versus healing time for PMMA-1/PVDF-6 alternating layer structures at T = 200 C, [omega] = 0.1 rad/s without and with a given pre-shear [gamma](t) = 4[s.sup.-1] X 60s, respectively. We can see that the effect of pre-shear is pronounced, that is, the G*(t) of multilayer assemblies subjected to pre-shear experiences an increase with a higher slope before reaching a steady stage in comparison to those without pre-shear. The characteristic diffusion time needed to reach the steady stage is significantly reduced and the steady value was lowered down a bit.

Different underlying physics behind the effect of such pre-shear on diffusion process are to be addressed here. On the one hand, as stated in literatures [17, 18, 36], the applied pre-shear to the multilayer assembly may perturb the chains configuration at the interface, extract some chains from the bulk to the interface and consequently influence the segmental motions. This may result in a situation of excess chain ends at the interfacial region, which is in favor of interdiffusion kinetics according to the theory of "Minor chain reptation model" proposed by Wool [37], On the other hand, the steady shear flow imposed to the multilayer assemblies would be presumed to deform or change the interfacial structure. To examine this potential variation of the interfacial structure, once the pre-steady shear was accomplished, we removed the specimens out of the rheometer and quenched them immediately in liquid nitrogen before observing their cross-section morphology under SEM.

Evidenced from Fig. 11, the cross-section morphologies of specimens subjected to pre-shear are significantly distinguished from those without pre-shear. In great contrast to the evident uniform 6-layers assembly structure observed in the specimens without pre-shear (Fig. 11a. 1), fractal undulated structure can be clearly visible in the specimens being subjected to the high amounts of pre-shear (4 [s.sup.-1] X 60 s) as shown in Fig. 1 la.2. This indicates certain amount of steady shear enables structural deformations at the vicinity of the interface at neighboring layers. Furthermore, after the whole healing process for 1.5 h, the multilayer assembly specimens have also been quenched rapidly and observed under SEM. Apparently, different from the visible light boundary of two phases observed in that being subjected to no pre-shear (Fig. 11 -b. 1), the specimens being subjected to pre-shear owns a homogenous morphology without any visible boundaries as shown in Fig. ll-b.2. These experimental observations manifest the acceleration of the interdiffusion and homogenization process caused from certain amount of pre-shear.

An attributable origin to the fractal undulated structure may be related to a local pressure gradient developed at a vicinity of the interface due to the viscosity imbalance between upper and lower polymer layers in the presence of a steady shear flow field. A considerable pressure gradient may result in an invasion of a less viscous fluid to a more viscous one (i.e. more viscous fluid is extended to the less viscous one) and hence leads to the formation of undulated structure (as schemed in Fig. 12). The greater the viscosity ratio, the more serious the evolution of the interface disturbance behaves. The purposed mechanism is in accordance with those of Patlazhan et al. [35]. Indeed, this origin for the interfacial perturbation is to some extent identical with the so-called "viscous encapsulation" that results from the viscosity contrast at the interface. However, such interfacial indulated structures and the viscosity imbalance vanish rapidly in the compatible systems thanks to the fast interdiffusion at micro-level and thereby the intermixing is greatly acclerated.

Recently, basing on incompatible functional polymers. Song et al. [38, 39] demonstrated that the extensional and compressive flow in coextrusion overcomes the diffusion barriers by decreasing the diffusion length scale, thus enhances diffusive flux of local reactive functions and eventually contributes to the accelerated reaction rate during coextrusion. Change of the diffusion lengthscale or diffusion layer after being subjected to the external flow could be appraised from a theoretical viewpoint. In principle, when a steady shear flow [gamma](t) - [??] * t is imposed to the multilayer structure, effect of the appearing fractal undulated structures on the diffusion kinetics can be laterally described by the reduction of the initial striation thickness (i.e. a length-scale for interdiffusion), [r.sub.0], varying with time in a term of [40]:

r(t) = [r.sub.0]/(1 + [??] * t) (18)

Here, the striation thickness, r(t), is defined in as total volume divided by one-half of the total interfacial area. A foremost contribution of the flow in shear field given to a mixture is to initiate the interfacial surface to increase as a result of the continuous deformation or shear strain whereby the components are separated. Thus, the striation thickness is reduced from the total shear strain to a lower level for interdiffusion process in order to arrive at the disappearance of the composition nonuniformity.

Reduction of the corresponding characteristic diffusion time for such striation thickness could be expressed in a term of

[t.sub.D] = [r.sup.2](t)/[D.sub.m] (19)

This theoretical prediction well accords the experimental observations in this study in a qualitative aspect. We can hereby conclude that certain amount of pre-steady shear could promote the kinetics of interdiffusion process, more exactly, homogenizing process, by introducing excess chain ends at the interface and more importantly inducing fractal undulated structures at the vicinity of the interface from flow. The latter strikingly increases the interfacial area and hence reduces the striation thickness whereby shortens the characteristic time for interdiffusion and homogenization process in a pronounced way. These investigations give us a clear idea that even though the orientation/extension of polymer chains in the shear flow field of processing may slow down the [D.sub.m], the intervention of the intermixing arise from the shear flow could shorten the striation thickness to a level that the interdiffusion process can readily occur, thus effectively accelerate the homogenization rate of the liquid-liquid phase. We can take the case of [Q.sub.PVDF]/[Q.sub.PMMA] = 10 at 200[degrees]C given in Table 3 as an example, assuming an interfacial shear rate [[??]] being averaged from [[??].sub.PMMA]/[[??].sub.PVDF] to be 1.97 [s.sup.-1], with a contact time of 65 s, one can obtain r(t) = [r.sub.0]/129 from Eq. 18. Thus even though the diffusion coefficient is 0.72 times lower as a result of chain orientation in this case (i.e., [[??].sub.m] = 0.72 [D.sub.m] as given by Eq. 17), the characteristic diffusion time [t.sub.D] can be a factor of 8.3 X [10.sup.-5] lower than that in static condition according to Eq. 19. Obviously, in the practical condition of coextrusion, the intermixing in the shear flow field acts a more significant role in reducing the diffusion length scale than the deceleration of diffusion coefficient arised from chain orientation. The interfacial stress resulted from the rheological contrast of the two components at the vicinity of the interface gives rise to intermixing (a much greater flow effect). Dominant contribution of such flow effect is augmenting interfacial area through generating undulated structures therefore increasing the diffusive flux between two phases. Thus, the eventual combination effect of orientation and intermixing is to impel the homogenizing process and undoubtedly to favor the broadening of the interfacial zone (development of the interphase). Broadening of such interphase developed during the coextrusion process has been well confirmed by experiments of SEM-EDX analysis and TEM observation on the quenched coextruded bilayer (details shown in next section). As shown in Fig. 9b, under a coextrusion processing condition of 200[degrees]C with [Q.sub.PVDF]/ [Q.sub.PMMA] = 1, the theoretical value of the interphase thickness according to the only effect of chain orientation with the intermixing effect neglected is predicted to be ~ 12.8 [micro]m. Indeed, experimental result of the real interphase thickness from SEM-EDX analysis for the coextruded bilayer at similar condition is shown to be 28 pm (Fig. 13b), implying that the flow effect of intermixing broadens the interfacial zone by at least two folds.

Characterization of the Diffuse Interphase Generated in Coextrusion by SEM-EDX and TEM

As demonstrated before, in the practical processing conditions of coextrusion, the coupling between interdiffusion process and intermixing (i.e., flow effect) resulted from the interfacial stress significantly favors development of the interphase and homogenization process at the interface. We remain that few work has been dedicated to the physicochemical affinity (i.e., interphase) between the neighboring layers of coextruded multilayer structures and its impact on the interfacial defects. In the present work, to quantitatively characterize the interphase generated in coextrusion process, scanning electron microscopy combining with energy dispersive X-ray (SEM-EDX) analysis has been employed to determine the concentration profile of composition and hence the geometrical properties of the interphase on the quenched coextruded PMMA/PVDF bilayer. The physics of this spectroscopic technique on determining the interphase has been detailed in our earlier work [20], which makes use of the X-ray fluorescence of the characteristic fluorine (F) atom in PVDF and the characteristic oxygen (O) atom in PMMA to monitor the composition changes versus the interfacial region. As shown in Fig. 13a is a micrograph superimposed with a trace of the line scan including 20 points collected within a distance of 134.9 pm perpendicular to the interphase in the case of PMMA-1/PVDF bilayer specimen coextruded at 200[degrees]C with [Q.sub.PMMA]/[Q.sub.PVDF] = 1.0. In this case, the interphase is theoretically predicted to be 12.8 pm according to the only effect of chain orientation under shear flow field in the absence of other flow effects (as shown in Fig. 9b). The corresponding experimentally measured concentration profile of F and O element (quantified in portion of peak area, A%) obtained on this bilayer specimen is displayed in Fig. 13b, from which an approximate 28 [micro]m thick interphase could be observed. This implies that under the real practical condition of coextrusion process, the interphase could be exactly greater than that theoretically predicted in conditions of no flow effect. In other words, the intermixing in processing conditions actually expands the amount of the interphase. We have also confirmed that the interphase is asymmetrical rather than absolutely symmetrical. In effect, the intermixing is attenuated when temperature is increased as the interfacial shear stress is reduced when the rheology of the components is approaching each other at higher temperatures. Properties of the interphase are related to a lot of parameters like contact time, processing temperature, interfacial shear stress and compatibility of the polymers, etc.

We had a first mind that the generated interphase should be undoubtedly greater at higher temperatures during the coextrusion process since the [D.sub.m] is higher at higher temperatures [20]. However, beyond our expectation, as displayed in Fig. 13c, at high temperatures the bilayer was coextruded, that is, at 220[degrees]C and 240[degrees]C, the created interphase owns a thickness with only a similar order of magnitude (20-30 [micro]m) as that of low temperatures (i.e. 200[degrees]C). Note that normalized position is made using interface position (1.0 mm, total thickness h = 2 mm, PVDF is upper layer) as reference. As a matter of fact, this is not extraordinary if we take into consideration of the impact of intermixing on the interphase development in coextrusion process. As indicated in our earlier work [20], the effect of temperature on the [D.sub.m] between PMMA and PVDF is not in a very large scale, nevertheless, the intermixing resulted from interfacial stress could reduce the characteristic diffusion time by several orders as explained in the former section of this study. In effect, as temperature increased, the interfacial stress could be significantly decreased and also reduced was the intermixing. As displayed in Table 4, the interfacial stress could be reduced by about 2 orders of magnitude from 200[degrees]C to 240[degrees]C, which greatly explains the existence of weaker intermixing at higher temperatures. Moreover, it can be assumed that the interfacial stress and intermixing is overestimated, especially at high temperatures, as an assumption of sharp interlace is taken for all the calculations but in fact an interphase appears rapidly due to the interdiffusion for the compatible system, so the intermixing can be even weaker than expected. Obviously, attenuation of the intermixing is more predominant than the increase of the [D.sub.m] when the temperature is increased. This explains the result of similar interphase obtained at higher temperatures. Additionally, the reduction of contact time in the die at higher temperatures allows a shorter time for interdiffusion process and interphase development.

Furthermore, TEM was used for morphological observations of the interfacial zone on the PMMA-l/PVDF bilayers after the coextrusion process. As presented in Fig. 14, no matter in the bilayer coextrudcd at 220[degrees]C (Fig. 14a) or at 240[degrees]C (Fig. 14b), crystalline morphology in PVDF-rich side and amorphous morphology in PMMA-rich side are clearly distinguished. It should be noted that besides these two morphologies, it seems that an intermediate morphological region lies between these two phases could be observed in the TEM images. It has been well known that in PMMA/PVDF blends, crystallization can take place when the contents of PVDF are more than 60% by weight [41]. The interfacial zone generated from the interdiffusion process can be assumed to be equivalent blends with varying compositions, where perfect PVDF crystals were well produced at the PVDF-rich side as shown in Fig. 14c. It was argued that the transition from the perfect order in the crystal to the isotropy in the amorphous phase cannot occur abruptly, rather is replaced by a crystal-amorphous interphase [42]. The existence of such crystal-amorphous interphase in polymer blends has been claimed by previous researchers. It was explained based on the theoretical consideration of chain packing at the surface of lamellar crystals and the different morphological components lead to distinct relaxation dynamics. The intermediate morphological region here (Fig. 14d) is characterized with a weaker crystallization and different crystal structures scaling with ~4 [micro]m thickness. We do not extend much on this point as it is not the objective of this study, but it will be an interesting focus in our further work. One another point interests us is that both the TEM images and SEM-EDX analysis indicate that the interfacial zone experiences a smooth and stable transition between neighboring layers even after coextrusion process as like that observed in static conditions, with no any interfacial instability being found. This absolutely proves that creation of the interphase at the interface exactly removes the interfacial defects without causing any waviness or rugged shape.

Highlighting Role of the Diffuse Interphase in the Processing Properties of Coextrusion

After having a basic understanding of the interdiffusion kinetics and the triggered interphase in both fundamental conditions of rheological measurements and practical processing conditions of coextrusion, a set of experiments concerning optimizing the coextrusion process have been carried out by listing some important parameters that govern the interfacial How stability. Bilayer systems composed of PMMA/PVDF was firstly studied as a compatible polymer pair and PMMA/PE was considered as an incompatible one for comparison. In this work, the films were visualized from the flow direction when they were flowing out at the die exit to examine its flow stability. Upon the observations, special attentions were paid to the wavelike shape (highly irregular or sometimes regular waviness) appearing at the How and the encapsulation that emerges with an appearance of a greater thickness at the edge of the bilayer films.

In the experiments, following variables were considered: viscosity ratio of polymer pairs varied by changing the processing temperature; thickness ratio varied by changing the flow rate ratio of the two polymer melt streams; elasticity ratio (average relaxation time ratio or first normal stress difference ratio) by using PMMAs of different molecular weight. It is noted that other factors such as interfacial tension and density difference which had been reported to have minor effects were not considered in this work [1], Indeed, for the compatible systems, the interfacial tension is close to zero. More importantly, greater interests were given to the effect of the presence or absence of the interphase at polymer-polymer interface. Role of the interphase was highlighted by comparing the situations of flow stability of the compatible pair to that of the incompatible ones at similar conditions. The experiments were carried out at different conditions, with temperatures varying from 190[degrees]C to 260[degrees]C, and with flow rate ratio of PVDF or PE versus PMMA varying from 0.3 to 2.6. To observe more clearly the flow instability and the edge caused from encapsulation, traces of colored PVDF pigments were mixed into the PVDF layer with a presumption of no effect on their rheological properties.

Coextrusion of Different Polymer Systems and Investigation of Inteifacial Flow Stability

Indeed, whether or not the compatibility or incompatibility of polymer pair being coextruded plays a role in bringing about the onset of interfacial instability was considered by Han [43], whereas the role of the interphase was not highlighted and no further focus was given in their work. In our recent review article [1], we have focused on the fundamental studies of the interfacial phenomena (i.e., interdiffusion/interfacial slippage/ interfacial reaction) and addressed the importance of the physicochemical affinity (i.e., interphase, a result of the interfacial phenomena) at neighboring layers related to the interfacial defects of the coextrusion process based on the advances reported in the literature. Despite this, the experimental studies dedicated to the role of the interphase in coextrusion are still rare. In this study, with such an aim to disclose the role of the interphase in controlling the flow instability, compatible polymer pairs of PVDF/PMMA1 or PMMA2; symmetrical bilayers of same polymers and incompatible polymer pair composed of PMMA/PE are taken into considerations and their interfacial How situations are compared. Typical samples obtained at an interfacial stability theoretically favorable condition of Q ratio = 1 are illustrated in Fig. 15, where a severe wave-like distortion at the interface with rugged shape can be obviously observed in the case of PMMA/PE incompatible bilayer coextrudates (Fig. 15a). This is in quite a good agreement with those reported in literatures regarding the unstable appearance. Nevertheless, the coextrusion of PMMA/PVDF (Fig. 15b) and PVDF/PVDF (Fig. 15c) compatible bilayers exhibit a stable interfacial How at the exit of the die under this condition, with smooth surface and stable flow observed. Indeed, for the PMMA/PE pair, in addition to the wavelike form at the interface, the solid co-extruded bilayer could be easily delaminated by hand since there is no adhesion between neighboring layers. On the contrary, no sharp interface can be found and good adhesion is formed for the cases of PMMA/PVDF and PVDF/PVDF or PMMA/PMMA pairs.

In the analysis, to compare the interfacial flow stability between different experimental conditions, we construct a stability chart by listing the situation of the flow stability obtained at different conditions in a same figure, as shown in Fig. 16. Here, the x-axis indicates the varying flow rate ratio employed in the experiments from 0.3 to 2.6, the varying flow rate ratio indicates varying thickness ratio. The y-axis indicates the zero-shear viscosity ratio of the investigated polymer pairs at 200[degrees]C. In this stability chart, two types of interfacial defects, flow instability (wavy shape, etc.) and encapsulation, are considered, the empty and wavy small rectangle in the left part of the symbol indicates stable and unstable (or wavy interface) of the bilayer systems, respectively; and the light colored empty and hachured small rectangle in the right part of the symbol represents the state of no encapsulation and that of high encapsulation, respectively.

In particular, the zero shear viscosity ratio and elasticity ratio of PMMA versus PVDF at different temperatures are plotted in Fig. 17. It should be noted that here the elasticity ratio is expressed by the average relaxation time ratio of PMMA versus PVDF. The relaxation times were determined from the Cole-Cole curves ([eta]" vs. [eta]') in their rheological characterizations. In general, the first normal stress difference of polymers, [N.sub.1] = [[sigma].sub.11] - [[sigma].sub.22], is used more often to describe their difference in elasticity [14, 16, 21]. According to the relation [N.sub.1,i] = 2[[eta].sub.0,i][[lambda].sub.i][[??].sup.2] where [[eta].sub.0,i], [[lambda].sub.i] are zero shear viscosity and relaxation time of component i, respectively, the first normal stress difference ratio (indication of elasticity), [N.sub.1,A]/[N.sub.1,B] = ([[eta].sub.o,A]/[[eta].sub.o,B])([[lambda].sub.A]/[[lambda].sub.B], is directly related to the relaxation lime ratio [M.sub.[lambda]] = [[lambda].sub.A]/[L.sub.B] at a given shear rate [??]. When the viscosity ratio is known at certain conditions, their relaxation time ratio, [M.sub[lambda]], can be enough to express the elasticity ratio at a given shear rate [??]. Indeed, the Weissenberg number, [W.sub.i] [equivalent to] [??][lambda] which governs the degree to which the normal stress differences differ from zero, can also be used as an elasticity expression, thus [M.sub.[lambda]] = [[lambda].sub.A]/[[lambda].sub.B] = [??][[lambda].sub.A]/[??] [[lambda].sub.B] = [W.sub.i,A]/[W.sub.i,B] is sufficient to indicate the elasticity ratio.

Hence, based on this analysis guide-line and the experimental results obtained for the various bilayer systems as summarized in this stability chart (Fig. 16), we can see at the first sight that the interfacial flow situation including the instability and encapsulation of the incompatible PMMA/PE bilayer system is pronouncedly distinguished from those of compatible counterparts. Despite of the change of flow rate ratio from 0.3 to 2.6, severe flow instability is always observed for the PMMA/PE bilayer system. Such flow instability is only a bit alleviated at [Q.sub.PE]/ ([Q.sub.PMMA] = 0.3. Contrast to the severe flow instability, only few encapsulation is found in this bilayer system within the range of the measured flow rate ratios. Completely different from the incompatible PMMA/PE bilayer, at the similar conditions the interfacial flow in the compatible PMMA/PVDF bilayer and those symmetrical bilayers of same polymers appear to be stable without apparent interfacial distortion or rugged interface observed. Only some subtle encapsulation (reflected by a thicker edge) could be noted for the PMMA/PVDF bilayers at higher value of [Q.sub.PVDF]/[Q.sub.PMMA]. In fact. from the y-axis it is clearly shown that the PMMA/PVDF pairs have higher viscosity ratios than that of PMMA/PE pair. It has been widely reported that the higher the viscosity stratification is, the more severe the interfacial instability appears given that the thickness ratio deviates from 1 and the less viscous fluid is not the thinner layer [1]. Evidently, it is not the case in this study. Having greater viscosity ratio than PMMA-2/PE pair, the PMMA-1 or PMMA-2/PVDF pairs experience stable interfacial flow rather than the severe flow instability of its counterpart at a given thickness ratio and temperature. This implies that there are some other underlying mechanisms behind here. Exactly speaking, the flow instability in coextrusion encountered by the incompatible polymer systems under certain conditions could be removed in the compatible systems. As demonstrated in the above sections, in the compatible systems like PMMA/PVDF, especially under the practical conditions of coextrusion, certain mount of interphase is able to be generated at polymer-polymer interface from the interdiffusion process and be favored from the intermixing. The presence of mounts of the interphase seems to be the sole reason for the removal of the flow instability in the case of the compatible systems .

Flow Stability of PMMA/PVDF Bilayer Coextruded at Different Temperatures

Different temperatures were used to vary the viscosity ratio of PMMA versus PVDF to examine its effect on the flow stability in such compatible systems. For this, a new stability chart has been established as shown in Fig. 18 by listing together the situation of flow stability obtained at different temperatures varying from 190[degrees]C to 260[degrees]C and different flow rate ratio [Q.sub.PVDF]/[Q.sub.PMMA] ranging from 0.3 to 2.6. In the figure, the y-axis is the zero shear viscosity ratio of PMMA-1 versus PVDF (i.e. [[eta].sub.PMMA]/[[eta].sub.PVDF]). Besides, the elasticity ratio expressed by the average relaxation time ratio [M.sub.[lambda]]=[[lambda].sub.PMMA]/ [[lambda].sub.PVDF] is also listed in the chart. We can see that even at the condition of high viscosity ratio and elasticity ratio at low temperatures, e.g. [[eta].sub.PMMA]/[[eta].sub.PVDF] = 30.8 and [M.sub.[lambda]] = 12.89 at 190[degrees]C, the interfacial flow is still stable, with few interfacial waviness observed during the flow exiting the die. This is quite distinct from the viscous instability reported in the literature for incompatible polymer pair which says that high viscosity ratio of the fluids may destabilize the interface. In fact, this universal tendency of severer interface instability at higher viscosity ratio is also valid in the present system considering that the interfacial How stability situation is worse at lower temperature as shown in Fig. 18. But the extent of the instability is rather limited, which is probably attributed to the appearance of the interphase at the present pair. On the other hand, different from the few interfacial waviness observed at the low temperatures, a great thickness has been found at the edge of the bilayer films, that is so-called encapsulation. Photographs of the experimentally observed encapsulation are shown in Fig. 19. It is noted that colored pigments were used for PVDF layers for clear observations. As pointed out by Wilson and Khomami [6], encapsulation phenomena occur irrespective of the stability/ instability of the interface. In the case of this study, the less viscous polymer, here PVDF, tends to immigrate to the region of high shear rate (i.e. the wall), thereby producing encapsulation, that is, the less viscous fluid encapsulating the more viscous components, and resulting in a great thickness nonuniformity in coextrusion flow which gives rise to a thick edge of the sheet. The encapsulation becomes even more serious as flow rate ratio increases, as shown in Fig. 18.

Furthermore, both Figs. 18 and 19 show that at a given flow rate ratio, as the temperature increases, the interfacial How of the PMMA/PVDF bilayer becomes more stable and the encapsulation is also reduced. In particular, at T = 260[degrees]C, the flow is always stable irrespective of the flow rate ratio (layer thickness ratio) and no encapsulation is found. On the one hand, this could be attributed to the decrement of the rheological difference between PMMA melt and PVDF melt as temperature increase, especially the [[eta].sub.PMMA]/[[eta].sub.PVDF] and [[lambda].sub.PMMA]/[[lambda].sub.PVDF] approach 1.0 when T = 260[degrees]C, as indicated in Fig. 17. On the other hand, as the temperature increases, the interdiffusion process between the melts and the development of the interphase are evidently mounting up, hence the How stability and the encapsulation situation are greatly improved. Apparently, this is in accordance with the results obtained in our earlier studies [44] that the encapsulation appeared to be hindered by the interdiffusion process occurred in the case of compatible pair system and the formation of a certain amount of interphase.

In addition, it has been reported in the literature that for non-Newtonian fluids, the variation of the elasticity ratio could have an independent effect as viscosity ratio on the interfacial flow stability of coextrusion processing [14, 45]. To examine this effect of elasticity ratio, a condition with constant viscosity ratio but different elasticity ratio is necessary to be selected. PMMA1/PVDF and PMMA-2/PVDF pairs satisfy this requirement at 190[degrees]C since they have similar viscosity ratio while PMMA-2/ PVDF has a higher relaxation time ratio than PMMA-1/PVDF in this condition as shown in Fig. 17. Coextrusion experiments performed on PMMA-2/PVDF and PMMA-1/PVDF with same processing conditions were compared at 190[degrees]C. Unexpectedly, no significant difference was observed between these two polymer pairs with regard to their interfacial waviness and encapsulation situation despite of the change of thickness ratio. This implies that the elastic instability is also weakened in such compatible pairs.

With regard to the interfacial How instability of coextrusion, it has been reported that the interfacial flow instability is related to the interfacial shear stress, [[sigma]]. That is, there exists a critical value, [([[sigma]]).sub.crit] for a given polymer system above which the interfacial instability sets in and may appear to be independent of layer thickness ratio [3, 4], Actually, results in this study also give some hints that higher [[sigma]] brings about severer interfacial flow instability. More importantly, as demonstrated in former section, the high [[sigma]] in low temperature, especially at early stage (as the [[sigma]] may diminish when interdiffusion occurs) contributes to bringing about some intermixing that promotes formation of thick interphase, which ultimately guarantees good interfacial flow stability.

Hitherto, a clear idea comes into mind is that for compatible polymer systems like PMMA/PVDF, existence of certain interphase at the interface may greatly alleviate the viscous instability as well as the elastic instability. The plausible mechanisms for such weak sensitivity of compatible polymer systems embodying mounts of interphase to the interfacial disturbance may be two folds. On the one hand, the effective viscosity and elasticity differences between the two components at the vicinity of the interface are greatly reduced by the interdiffusion process since the interphase appears as a continuous transition zone with characteristic gradually varying from one component to the other, which has been well demonstrated by SEM-EDX and TEM tools (see the above section). On the other hand, the interdiffusion process and intermixing consume the great portion of the energy from the shear stress and normal stress imbalance at the interface which at first should allow the interfacial waviness to be produced in the incompatible polymer systems. It is worthy of noting that despite here only a qualitative relation between the interfacial defects of coextrusion and the amount of the generated interphase have been highlighted, it is believed that a sufficient amount of interphase is required for stable flow stability. That is because the interphase alleviates the rheological difference at the vicinity of the interface and has an energy dissipation effect.


This study is dedicated to understandings of the diffuse interphase generated both under the fundamental condition of rheological measurement and under the practical processing condition of coextrusion before highlighting its role in controlling the interfacial flow instability of multilayer coextrusion. For this, a model couple based on a PMMA and PVDF compatible bilayer system is used for the measurements.

Under fundamental conditions, interdiffusion kinetics, rheological and geometrical properties of the generated interphase were estimated via a modified rheological model. Moreover, rheology of PMMA/PVDF laminated multilayer structures was examined by varying the layer number and interfacial slippage was also focused by steady shear measurements. The interfacial slippage can be excluded in such compatible systems since the small shear stress is not enough to fight against the entanglement formation brought about from the interdiffusion, with potential to occur only at short welding time under an extremely high shear stress.

During the coextrusion process, orientation of polymer chains in shear flow field was demonstrated to hinder the diffusion coefficient. Nevertheless, intermixing that occurs at the vicinity of the interface due to the interfacial stress could significantly reduce the characteristic diffusion time and hence favors the development of the interphase. This has been investigated by performing a pre-shear mode on the PMMA/PVDF multilayer structures before tracking the interdiffusion process in LVE. The flow effect contributes to increasing the interfacial area through generating undulated structures as demonstrated by SEM, therefore reducing diffusion lengthscale (striation thickness) thus increasing the diffusive flux between two phases. It may reduce the characteristic diffusion time to several orders of magnitude lower at certain conditions. Effect of intermixing predominates that of chain orientation. The eventual combination effect of orientation and intermixing is to widen the interphase and significantly accelerate the homogenization rate in the interfacial region, thus improve the interfacial flow stability of coextrusion. Indeed, effect of intermixing can be attenuated when temperature is increased since the interfacial shear stress diminishes as the rheological difference is narrowing at higher temperatures. This may also affect the development of the interphase. Geometrical and morphological properties of the interphase generated in the real conditions of coextrusion process have been well determined via SEM-EDX and TEM tools. Within the short time of processing, thickness of the interphase can reach more than 20 pm. Moreover, the measured real interphase supports the favorable effect of the intermixing and its attenuation as temperature increase. TEM morphological observations show that the morphology in the interfacial zone consists of a crystalline PVDF-rich phase, an amorphous PMMA-rich phase and an intermediate morphological region involves crystal-amorphous interphase. More interestingly, TEM observations indicate that after coextrusion processing a stable interfacial zone can be obtained with smooth and continuous transition from one layer to its neighbor without causing any interfacial disturbances.

With respective to the flow stability and encapsulation of multilayer coextrusion, classical parameters such as thickness ratio, viscosity ratio and elasticity ratio, etc. have been evaluated by elaborating stability charts based on PMMA/PVDF asymmetrical and PMMA/ PMMA (or PVDF/PVDF) symmetrical compatible bilayer systems as well as PMMA/PE incompatible bilayer system. Thickness ratio, viscosity ratio and elasticity ratio were changed by varying flow rate ratio, temperature and using different PMMAs (i.e. PMMA-1 and PMMA-2), respectively. Results indicate that differing from the severe flow instability observed in the PMMA/PE incompatible bilayers, coextrusion of the compatible bilayers appear to be smooth and stable with no apparent interfacial defects observed at the similar conditions. Despite of their decisive role in the incompatible system, these key factors seem not that important in a compatible system. The interfacial flow instability of coextrusion is also reduced (or even eliminated), despite of the very high viscosity ratio as well as the high elasticity ratio of PMMA versus PVDF, especially at low temperature. This would be attributed to the appearance of certain amounts of interphase generated from interdiffusion at neighboring layers and favored from intermixing. In other words, presence of the interphase weakens the viscous instability and elastic instability in compatible multilayer systems as it alleviates the rheological difference at the vicinity of the interface and has an energy dissipation effect.

Overall, this study will be of some value on showing guide-lines for stable coextrusion of multilayer polymers since it presents us an idea that it is imperative to enrich the classical mechanical approach by taking into account of the role of the interphase during the optimization of the coextrusion processing conditions.


The authors express their appreciation to the reviewers for their meticulous assessment. They thank ARKEMA for the polymer samples. Mr. Pierre Alcouffe from the "Centre Technologique des Microstructures" of the University Claude Bernard Lyon 1 is acknowledged for his kind assistance with the SEM-EDX and TEM characterizations. Moreover, H. Zhang is grateful to China Scholarship Council (CSC) for the scholarship.


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Huagui Zhang, (1,2) Khalid Lamnawar, (1,3) Abderrahim Maazouz (1,2,4)

(1) Universite de Lyon, F-69361, Lyon, France

(2) CNRS, UMFt 5223, Ingenierie des Materiaux Polymeres, INSA Lyon, F-69621, Villeurbanne, France

(3) CNRS, UMR 5259, INSA-Lyon, LaMCoS, Laboratoire de Mecanique des Contacts et des Structures, Groupe de Recherche Pluridisciplinaire en Plasturgie, F69621, Villeurbanne, France

(4) Hassan II Academy of Science and Technology, Rabat, Morocco

Correspondence to: K. Lamnawar; e-mail: or A. Maazouz; e-mail:

DOI 10.1002/pen.23945

Published online in Wiley Online Library (

TABLE 1. Characteristics of the investigated polymers.

                                  [T.sub.c]          [T.sub.g]
Samples   Trademark/supplier   ([degrees]C) (a)   ([degrees]C) (a)

PVDF      Kynar 720/ARKEMA          136.40              -42
PMMA-1    V825T/ARKEMA                --                112
PMMA-2    V046/ARKEMA                 --                102
PE        Lacqtene/ARKEMA

Samples   [T.sub.m] ([degrees]C) (a)   [M.sub.w] (b) (g/mol)

PVDF                 170                      210,000
PMMA-1                --                      100,000
PMMA-2                --                      137,000
PE                   114                      207,000

Samples   [M.sub.w]/[M.sub.n] (b)   [E.sub.a] (KJ/mol) (c)

PVDF                2.0                       59
PMMA-1              1.9                      160
PMMA-2              2.0                      157
PE                  9.9                       53

(a) Measured in our laboratory by a TA Instruments Q20 DSC at a
heating and cooling rate of 10[degrees]C/min under [N.sub.2].

(b) Determined in our laboratory by size exclusion chromatography
(SEC) with tetrahydrofuran (THF) as the eluent for PMMA, dimethyl
formamide(DMF) for PVDF and trichlorobenzene (TCB) for PE at

(c) Energy of activation of the viscous flow ([E.sub.a]) obtained
from [InEla.sup.0] plotted versus I/T within a temperature range of
180[degrees]C<T< 240[degrees]C.

TABLE 2. Characteristics of extruders.

Extruder/details      A(central)   B(binder)   C(external)

Screw diameter (mm)       18          12           15
L/d                       25          25           25
N max (rpm)              69.9        69.9         69.9
Flow rate (g/min)        0-69        0-69         0-69

TABLE 3. Interfacial shear stress and interfacial shear rate
calculated for the PMMA-l/PVDF bilayer at 200[degrees]C.

      Flow rate(kg/h)
                                                 Pressure gradient
                              []         [kappa]
[Q.sub.PMMA]   [Q.sub.PVDF]         (s)         (X [10.sup.7] Pa/m)

0.6            0.18                 93                 4.86
0.6            0.36                 79                 4.73
0.6            0.6                  65                 5.57
0.6            0.96                 52                 5.83
0.6            1.56                 39                 6.46

      Flow rate(kg/h)
                                                 position Of
                              Interfacial    [[upsilon].sub.max],
[Q.sub.PMMA]   [Q.sub.PVDF]   position (a)           [mu]

0.6            0.18               0.81               0.76
0.6            0.36               0.73               0.78
0.6            0.6                0.66               0.76
0.6            0.96               0.58               0.75
0.6            1.56               0.51               0.72

      Flow rate(kg/h)
                              Interfacial stress
[Q.sub.PMMA]   [Q.sub.PVDF]   (X [10.sup.4] Pa)

0.6            0.18                  0.49
0.6            0.36                  0.47
0.6            0.6                   1.17
0.6            0.96                  1.92
0.6            1.56                  2.65

      Flow rate(kg/h)
[Q.sub.PMMA]   [Q.sub.PVDF]   (X [10.sup.-2] [s.sup.-1])

0.6            0.18                      0.38
0.6            0.36                      0.35
0.6            0.6                       3.58
0.6            0.96                     12.83
0.6            1.56                     29.12

      Flow rate(kg/h)
[Q.sub.PMMA]   [Q.sub.PVDF]        ([s.sup.-1])

0.6            0.18                    1.10
0.6            0.36                    1.04
0.6            0.6                     3.91
0.6            0.96                    8.38
0.6            1.56                    9.30

(a) The interfacial position is expressed as [delta]/h; total
thickness h = 2 mm in the studied die.

TABLE 4. Interfacial shear stress and interfacial shear rate
calculated for the PMMA-1/PVDF bilayer at different temperatures
with [Q.sub.ratio] = 1.0.

Temperature         Pressure gradient
([degrees]C)   [kappa] (X [10.sup.7] Pa/m)   Interfacial position (a)

200                       5.57                         0.66
220                       3.48                         0.60
240                       1.71                         0.58
260                       0.66                         0.55

Temperature           Position of            Interfacial stress
([degrees]C)   [[upsilon].sub.max.] [mu]   [[sigma]] (Pa)

200                      0.76                 1.2 x [10.sup.4]
220                      0.66                 4.2 x [10.sup.3]
240                      0.56                 7.8 x [10.sup.2]
260                      0.50                 7.2 x [10.sup.2]

Temperature    [[??]]   [[??]]
([degrees]C)        ([s.sup.-1])              ([s.sup.-1])

200               3.6 x [10.sup.-2]         3.9
220               2.6 x [10.sup.-3]         0.8
240               3.5 x [10.sup.-5]         3.3 x [10.sup.-2]
260               2.8 x [10.sup.-5]         2.8 x [10.sup.-2]

(a) The interfacial position is expressed as [delta]/h; total
thickness h = 2 mm in the studied die.
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Date:Apr 1, 2015
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