SLIP AT THE INTERFACE BETWEEN IMMISCIBLE POLYMERMELTS: EFFECT OF VISCOSITY RATIO
S. K. Sukumaran*, R. Komuro, M. Sugimoto, K. Koyama
Graduate School of Science and Engineering, Yamagata University, 4-3-16 Jonan, Yonezawa,
Yamagata, 992-8510 Japan

E-mail of corresponding author: sa.k.sukumaran@gmail.com
ABSTRACT
Slip at the interface between polymer melts remains poorly understood. Studies that use only
rheological data to deduce the slip velocity usually involve applying a shear deformation to a stack ofparallel multilayers. In order to understand slip in the context of polymer extrusion, we have investigatedslip at the interface between two immiscible polymer melts undergoing pressure driven flow through acapillary die. To enable the measurement of slip velocity at a polymer/polymer interface during capillary
flow, we have adapted the Mooney method, a method usually used to study wall slip. Using the method,
one can measure the dependence of the interfacial slip velocity on the interfacial shear stress forcylindrical core-sheath samples of Polypropylene and Polystyrene. We use this method to investigate theeffect of varying the shear-rate dependent viscosity of the two polymers on slip at the polymer/polymer
interface. We vary the viscosity either by varying the molecular weight of the polymer(s) or by varying
the temperature at which the experiment is performed. Our results indicate that polymer/polymer
interfacial slip is not sensitive to variations in the molecular weight of the polymers. Increasing thetemperature led to an increase in the interfacial slip velocity at a given interfacial stress. A possible
reason for this behaviour is discussed.

1. INTRODUCTIONPolymer coextrusion is widely used fordeveloping products for use in a range ofindustries. An important advantage of polymer
coextrusion is that not only the various physicalproperties of the final product but also its cost
can be easily varied to satisfy the needs of thedesired application. The variation in theproperties can be accomplished by varying thepolymers used, the number of layers in the final
product, the thickness of the layers etc.
Parallel multilayered products are typicallymanufactured using either a feedblock, or a
distribution block along with single manifold or
multi-mainfold dies. Owing to the complexity
resulting from both the shape of the extrusion
die and the actual flow behaviour, the principal
technique for investigating multilayer flow inindustry and academia is through viscoelastic
flow simulations. In order to investigate flow
phenomena using computer simulations, it isnecessary to utilize
boundary conditions
appropriate to the particular flow underconsideration. Most simulations of flow
phenomena, including those for non-Newtonian
fluids, assume that the velocity is continuous at
all phase boundaries. Thus, in addition to therelevant constitutive equation, simulations ofmultilayer coextrusion usually use the “no-slip”
boundary condition at a polymer/polymerinterface.
Naturally, polymers used for manufacturingmultilayers are mutually immiscible. Therefore,
one can expect the the density of entanglements
at the interface to be low. If interfacial
entanglements are the main source of adhesion
between the different polymer layers, high shear
stresses cannot be sustained by thepolymer/polymer interface and slip can occur atthe interface. Early experiments [1,2] on
multilayer flow indicated that the pressure
gradient necessary to extrude a multilayer at aparticular flow rate was significantly lower thanthe pressure gradient necessary to extrude asingle layer of either polymer at the same flow
rate. In order to explain this, Han and Chin [3]postulated the existence of slip at the interface
between immiscible polymers.
Several researchers have investigatedpolymer/polymer interfacial slip either using
rheological [4-7] or flow visualization [8-9]techniques. Flow visualization techniques areconceptually straightforward and rely on few
assumptions. However, such experiments needequipment that is transparent to the kind of lightused to probe the suspended particles.
Rheological techniques do not need such special
equipment. Typically, these experiments use thequantitative deviation in the flow properties due
to slip, when compared to the corresponding
values assuming the no-slip boundary condition,
to estimate the slip velocity. Therefore, suchmeasurements critically depend on obtaining
good estimates for the flow properties (such asthe viscosity) under the no-slip condition. This
restriction has limited most of the available
studies to multilayers where parallel layers arestacked on top of each other. In this parallelgeometry, the mixing rule for the viscosity canbe easily derived. Any deviation from thederived value of the viscosity can be used toestimate
theslipvelocity
atthepolymer/polymer interface. If however, theparallel arrangement of the layers were to bemodified by the flow, the mixing rules could
cease to be valid and the accuracy of thedetermined the slip velocity is not guaranteed.
More importantly, obtaining estimates for theflow properties (such as the viscosity) for
multiphase flow in arbitrary geometries is notstraightforward [5,7]. Currently proposed
mixing rules are either empirical or rely on
approximations whose range of validity is notalways clear [5,7]. Due to this limitation of thedeviation from no-slip method, interfacial slip
velocity measurements for other important
flows, such as coextrusion through a capillary
die are few. One way to approach this problem
would be to devise a method that does not relyon the estimates for the flow viscosity of themultiphase sample under the assumption of noslip.
Recently, we proposed a novel approach toestimate the slip velocity at a polymer/polymer
interface undergoing two-phase coaxial flow[10]. The approach uses an adaptation of theMooney method, which is usually used to study
slip of a polymer liquid at a solid wall.
Henceforth, we will refer to this new approachas the “modified Mooney method”. In ourearlier work, we established the validity of themodified Mooney method by comparing theinterfacial slip velocity obtained from thismethod with that obtained using the deviationfrom no-slip [10]. In order to facilitate thedetermination of the slip velocity using thedeviation from no-slip, we chose samples withidentical shear-rate dependent viscosities over arange of shear rates. Therefore, in that work, themodified Mooney method was used only withpolymers with almost identical viscosities [10].
The main advantage of the modified Mooneymethod is that it can be applied to investigate
polymer/polymer interfacial slip even whenpolymers with different viscosities areundergoing capillary flow. Therefore, in thiswork, we use the modified Mooney method to
obtain the dependence of the slip velocity on theinterfacial stress for several pairs of isotactic
polypropylene (PP) and the atactic polystyrene(PS). By choosing PPs of three different
molecular weights, we investigated the effect ofvarying the molecular weight of the inner layeron the slip velocity. In addition, we also
investigated the effect of varying thetemperature for one of the polymer pairs.
2. EXPERIMENTS
Three different PPs (differing by theirmolecular weights and labelled as PP1-3) andone PS (labelled PS3) were chosen. The PPs
were kindly supplied by Sumitomo ChemicalCorporationandJapan
Polypropylene
Corporation. The PS was kindly supplied by PS
Japan Corporation. The molecular weights of thepolymers and the experimental temperature werechosen such that the viscosities of two of thePPs (PP1 and PP2) are larger and that of PP3 isapproximately equal to that of PS3 over a rangeof shear-rates (see Fig. 2(a)). The interfacial slip
velocity was evaluated using capillary dies ofthree different diameters D=1.0, 1.5 and 2.0mm.
Fig. 1(a) shows an illustration of the crosssection of the core-sheath samples used for thecoextrusion through the capillary die. The core
consists of PP with a thin PS sheath surrounding
the PP core. A schematic of the expected flow
velocity distribution during two-phase coaxial
flow is shown in Fig. 1(b). The slip velocity at
the polymer/polymer interface is evaluated usingthe modified Mooney method. For details aboutsample preparation, experimental procedure,
extensive discussions regarding the modified
Mooney method including its limitations, pleaserefer Komuro et al. [10].

Fig. 1 (a) Cross section of the core-sheath sample
with the PP core and PS shell and (b) schematic of
the flow velocity distribution during two-phasecoaxial flow.

3. RESULTS AND DISCUSSION
3.1 Effect of molecular weightFig. 2 (a) |η*| and ηs of PP1-PP3 and PS3 at230oC. and (b) Vs-i as function of σi for PP1PP3/PS3 at 230oC.
Fig. 2(b) shows a log-log plot of Vs-i versus σifor the three polymer pairs investigated, PP1PP3/PS3. In agreement with prior results[5,7,9,10], Vs-i exhibits a power-law dependenceon σi (i.e., Vs-i = Kσim). The power-law
dependence of Vs-i comprises two distinct powerlaw regimes with different power-law
exponents. The transition from the regime withm ≈ 3 to that with m ≈ 2 occurs at a criticalinterfacial shear stress ≈ 2×104 Pa.
Several striking features can be immediately
discerned from Fig. 2(b). This can besummarised by noting that the dependence of
the Vs-i on σi, over the entire range of theinvestigated σi, appears to be almost identical for
all three of the polymer pairs studied. This isirrespective of the molecular weight of the PP(PP1-PP3) and the consequent difference in theviscosity ratio of the polymer pairs. Theseresults suggest that the polymer/polymer
interfacial slip velocity is not sensitively
dependent on the molecular weight of the inner(PP) layer.
In our previous work, we determined thepolymer/polymer interfacial slip velocity at thesame temperature (230oC) for another PP/PS
pair that also possessed almost identicalviscoelastic properties over a range of shear
rates [10]. In that case, the molecular weights ofboth the PP and the PS were larger than that ofPP3 and PS3 such that the zero-shear viscosities
of both of the polymers were approximately 10times that of PP3 and PS3. The data for the slip
velocity for the higher viscosity pair, referred toas PP/PS, is also shown in Fig. 2(b) [10]. From acomparison of the data for these two pairs, it isclear that the slip velocities for both of thepolymer pairs (PP/PS and PP3/PS3) are almost
identical although the shear-rate dependent
viscosities for each of the pairs is rather
different ((ηPP ≈ ηPS) > (ηPP3 ≈ ηPS3)).
As the slip velocities of all four of thepolymer pairs are rather close to each other, wetentatively suggest that the slip velocity isessentially independent of the molecular weightof either of the two polymers. However, it isgermane to note that all of the samples used here
are rather polydisperse. The polydispersity of
the PP samples is about 4 while that of the PS isabout 2. Regrettably, the effect of polydispersity
on interfacial slip, especially the depedence of
Vs-i on σi, has hitherto not been elucidated.
Therefore, the aforementioned lack ofdependence of the slip velocity on the molecularweight is indeed only a tentative suggestion.
3.2 Effect of temperature
Fig. 3 shows Vs-i as a function of σi for thePP1/PS3 polymer pair at three different
temperatures: 230oC, 208oC, and 187oC. At agiven σi, the slip velocity progressively increases
with an increase in the temperature. However,the power-law dependence of Vs-i on σi and thevalue of the power-law exponent, do not appear
to be affected by the change in temperature.
With an increase in temperature, the viscosityof both of the polymers decreases. However, insubsection 3.1, we found that Vs-i was essentiallyindependent of the viscosities of either of thetwo polymers. Therefore, it appears unlikely thatthe increase in Vs-i with temperature is related tothe effect of the temperature on the viscosity.
For wall slip, de Gennes [11] hypothesisedthat the friction at an interface is related to themonomer viscosity. Adapting that hypothesis
and noting that the monomer viscosity decreases
with temperature allows us to suggest that, at agiven σi, the Vs-i increases with temperature tocompensate for monomer viscosity decrease.

Fig.3 Vs-i as function of σi for PP1/PS3 at 230oC,208oC, and 187oC.

4. SUMMARY
Using the recently introduced modified
Mooney method, we have measured the slip

velocity at the interface between immiscible
polymers undergoing capillary flow. The results
suggest that the polymer/polymer interfacial slip
velocity is not sensitively dependent on thevariations in the molecular weight of the twopolymers. In addition, we have found that thethe interfacial slip velocity increases with anincrease in the temperature. Still, thedependence of Vs-i on σi remains a power-law
with almost identical power-law exponents forall of the temperatures investigated. Future work
will involve investigating the reasons for theobserved (in)dependence on molecular weight
and temperature and the light this sheds on themechanism of polymer/polymer interfacial slip.
5. ACKNOWLEDGMENTS
The authors gratefully acknowledge financial
support from the Japan Society for Promotion ofScience (JSPS) through Kakenhi (24350114)
and the Dissemination of Tenure Tracking
System Program of the Ministry of Education,
Culture, Sports, Science and Technology –Japan.
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