Extensional Flow Resistance of 3D Fiber Networks in Plasticized

4 hours ago - In the capillary rheometer experiments, the samples are extruded through a 1 mm diameter, zero length capillary die and a 1 mm diameter,...
1 downloads 0 Views 1019KB Size
Download PDF
Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

pubs.acs.org/Macromolecules

Extensional Flow Resistance of 3D Fiber Networks in Plasticized Nanocomposites Ali Rizvi, Seong S. Bae, Nik M.A. Mohamed, Jung H. Lee, and Chul B. Park* Microcellular Plastics Manufacturing Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, Ontario M5S 3G8, Canada

Downloaded via RICE UNIV on August 25, 2019 at 13:15:32 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

S Supporting Information *

ABSTRACT: The presence of a three-dimensional network of high-aspect-ratio CO2-philic fibers increases the extensional viscosity of melts but decreases the shear viscosity under a CO2 atmosphere. The generation of such a rheological response is rare in literature because the addition of solid-state fibers typically increases both extensional and shear viscosities. These results are supported by the high-pressure rheological characterization of polypropylene (PP) containing various loadings of polytetrafluoroethylene (PTFE) fibers. While the shear viscosity decreases with an increase in fiber loading due to the higher uptake of CO2 from the CO2-philicity of PTFE, a strikingly different behavior is seen in extensional flows: below the fiber percolation threshold, the extensional viscosity decreases; however, above the percolation threshold, the extensional viscosity jumps by an order of magnitude. The enhancement in extensional viscosity is attributed to the large resistance offered by the network against extensional deformations. These results have important consequences in CO2-based polymer processes.

■

scission.17 However, these examples are far from being ubiquitous and generally rare to find in the literature. We present a PP nanocomposite that simultaneously achieves an increase in the extensional viscosity and a reduction in the shear viscosity under a CO2 atmosphere. The nanocomposite contains in situ generated high-aspectratio polytetrafluoroethylene (PTFE) fibers which remain in solid-state during the investigation and exhibit a strong thermodynamic affinity for CO2.18−20 Consequently, at a distinct pressure of CO2, a larger amount of CO2 dissolves in the nanocomposite than in the neat matrix, increasing free volume and accelerating relaxation time, ultimately causing the shear viscosity to decrease. On the other hand, the high-aspectratio of the fibers allows the fibers to bend substantially in response to interfiber interactions under conventional industrial processing conditions. At ϕ > ϕj, the fibers form a disordered network which exhibits pronounced resistance against extensional flows, increasing the extensional viscosity despite the shortening of the relaxation times from the enhanced CO2-induced plasticization. The consequences of the reduction in shear viscosity accompanied by an increase in extensional viscosity for CO2-based industrial processes are enormous. In industrial processes, the complex flow is dominated by shear, and a reduction in shear viscosity allows the use of lower processing pressures which translates into

INTRODUCTION

In composites, increasing the fiber content ϕ increases the viscosity until at some critical ϕj, a disordered threedimensional network-like structure of substantial mechanical integrity forms and causes the viscosity to diverge.1−3 If the fibers that make up the network exhibit flexibility, the network can retain the topological entanglements between fibers even when subjected to a flow field, thereby preserving the superstructure.4,5 The stable network exhibits markedly larger resistance against extensional flows because of additional stress generated from the stretching of the network.6,7 This, in turn, increases the extensional viscosity above the linear viscoelastic (LVE) prediction, often termed strain-hardening, and has important consequences in industrial processes as it enables the homogeneous extensional deformation of the composites.8−10 However, such modifications result in a concurrent increase in the shear viscosity,11−16 which is undesirable from a practical stand point because equipment operations become more energy-intensive, and processing rates decline. If higher processing temperatures are used to reduce the viscosity, the degradation kinetics of polymers become a concern. Consequently, achieving a decrease in the shear viscosity while simultaneously enhancing the extensional viscosity can have important and advantageous technological consequences in polymer processing. Electron beam irradiation of polypropylene (PP) is a canonical example where such a rheological response is created through the simultaneous induction of long-chain branching, and backbone chain © XXXX American Chemical Society

Received: April 29, 2019 Revised: July 16, 2019

A

DOI: 10.1021/acs.macromol.9b00885 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

Figure 1. Effect of ϕ on shear viscosity, η, and extensional viscosity, ηe, at PCO2 = 30 MPa, and T = 125 °C; (a) master curves of η as a function of the shear rate. Increasing ϕ results in a monotonic decrease in η due to the CO2-philic nature of the fibers; (b) solubility, S, of CO2 in the nanocomposites. The CO2 uptake from the CO2-philic fibers is shown in red; (c) ηe as a function of extension rate. ηe at ϕ = 2 wt % is below that of the neat matrix, but ηe at ϕ ≥ 3 wt % is higher than the neat matrix, despite acceleration of relaxation times; (d) variation in η and ηe as a function of ϕ. matrix (see Supporting Information S1 for the mechanism of fibrillation of PTFE).24,25 Characterization. Steady shear viscosity is measured at T = 171 °C under a nitrogen purge using the following: (1) an ARES rheometer (TA Instruments) with 25 mm parallel plate disks and 1 mm sample thickness for shear rates 50 s−1. In the capillary rheometer experiments, the samples are extruded through a 1 mm diameter, zero length capillary die and a 1 mm diameter, 20 mm length capillary die simultaneously. The shear viscosity is calculated from the pressure difference between the zero length die and the 20 mm length die after applying the Bagley and Rabinowitch corrections. The uniaxial extensional viscosity is measured using the ARES rheometer equipped with an Extensional Viscosity Fixture. Samples of dimensions 18 mm × 10 mm × 1 mm are subjected to constant extensional strain rates of 0.01, 0.1, 1, and 3 s−1 at T = 171 °C. Strain rates above 3 s−1 are experimentally inaccessible because the sample slips and homogeneous extension is not achieved. Higher temperatures are also inaccessible because the sample sags. The LVE prediction of the extensional viscosity is determined in the start-up of steady shear at a shear rate of 0.01 s−1 and T = 171 °C using an ARES rheometer equipped with a cone-andplate fixture (25 mm diameter, 0.1 rad cone angle). The measured shear viscosity is multiplied by three based on Trouton’s ratio26 to predict the LVE limit under uniaxial extensional flow. Measurements of shear and planar extensional viscosities under CO2 loading are made using a previously established method.27 Briefly, a specially built die (see Supporting Information S2) is mounted on a conventional foam extruder (see Supporting Information S3). The die consists of a rectangular channel with a high-aspect-ratio straight section and a convergent section with hyperbolic geometry. Pressure loss in the straight section is used to calculate the shear viscosity (see Supporting Information S4). Pressure loss in the convergent section cannot be

large energy cost savings, and the enhancement in extensional viscosity allows the materials to withstand a higher degree of stretching without undergoing run-away thinning or “necking” during intense nonlinear extensional deformations which arise in the final shaping phase of many polymer processes including fiber spinning, blow molding, and polymer foaming.

■

EXPERIMENTAL SECTION

Materials. PP is supplied by Sabic (PP, 670 K) with a melt flow rate of 10 g/10 min (at 230 °C/2.16 kg load), density of 0.9 g/cm3, and Tm of 149 °C. The PTFE is supplied by Mitsubishi Chemical Co. (Metablen A-3000) and is a proprietary material which exhibits the following properties: (1) The PTFE is acrylic-modified by the manufacturer to improve dispersion in polyolefins,7 (2) the PTFE readily deforms into high-aspect-ratio fibers when blended with a polymer melt,7,21 (3) the acrylic-modified PTFE exhibits a strong thermodynamic affinity for CO2,21,22 (4) above a threshold concentration, the PTFE fibers form topological entanglements which result in strain-hardening in uniaxial extensional flows,7,21 and (5) the PTFE fibers show mesopores with a pore size distribution ranging from 5 to 30 nm.23 CO2 and N2 gas are purchased from Linde Gas with purities in excess of 99%. All materials are used as received. Preparation of Nanocomposites. The nanocomposites are prepared in a co-rotating twin screw extruder (Toshiba Machine Co. TEM-26SS) with a screw diameter of 26 mm and an aspect ratio of 40. The barrel and die temperatures are maintained at 200 °C, but the hopper zone is cooled with a cold-water sleeve. A screw rotation speed of 200 rpm is maintained. Different contents of PTFE are added to PP through the hopper, and the extrudate is shaped in a cylindrical strand, cooled in a water bath, and pelletized. The resultant in situ nanocomposite shows well-dispersed PTFE fibers in the PP B

DOI: 10.1021/acs.macromol.9b00885 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

Figure 2. LVE properties of the nanocomposites; (a) multifrequency plot of tan δ at different fiber loadings. The ϕj corresponds to the fiber content when an incipient network of entangled fibers first forms; (b) tan δ(ω) for different ϕ; (c) G′(ω) and G′′(ω) for different ϕ. Graphs have been shifted by the factors shown to prevent overlap; SEM micrographs depicting the morphology of the percolated network (d) after permanganate etching and (e) after selective removal of PP.

and temperature T = 125 °C in Figure 1a. Under these conditions, the fibers remain in solid-state but may undergo swelling.29 The figure reveals that η decreases with an increase in ϕ , and the decline is more pronounced at low shear rates. Because the decrease in η through plasticization depends on the amount of CO2 molecules dissolved in the polymer,30 the observed suppression in η is attributed to the increased uptake of CO2 as ϕ is increased due to the CO2-philicity of PTFE. This behavior is in clear contrast with most melts containing solid-state fibers which generally exhibit an increase in η with a higher fiber loading due to prolonged relaxation times31 and the filling effect of solid-state particles.32 For instance, an increase in solid-state fiber content results in a concomitant increase in η for rigid glass fiber-reinforced polystyrene (PS) and polyethylene (PE),11 long glass fiber-reinforced PP,14 carbon nanofiber (CNF)-reinforced PS,12 and CNF-reinforced polyether ether ketone (PEEK).13 A decrease in η is observed in situ acrylate polymer fiber-reinforced PP,33 but the decrease is subtle and the acrylate polymer is not in the solid-state. We verify the higher uptake of CO2 as ϕ increases by measuring the solubility of CO2, S, as a function of ϕ (see Supporting Information S8 for the method), and the results are included in Figure 1b. Neat PP (ϕ = 0 wt %) shows S = 0.22 g g−1, but at ϕ = 3 wt %, the S increases to 0.47 g g−1 and at ϕ = 5 wt %, the S increases further to 0.64 g g−1. The enhancement of CO2 solubility in the nanocomposite through controlling ϕ provides an effective means to tune the degree of plasticization and hence shear viscosity. The affinity of PTFE for CO2 is well established,18−20,34,35 and the mechanism is attributed to strong interactions that occur between CO2 and fluoroalkyl groups of PTFE (see Supporting Information S9 for a detailed mechanism).34,36−39

directly used to calculate the planar extensional viscosity because convergent flows generate a combination of shear and extensional stresses. Consequently, a mathematical approach is used to decompose the complex flow into its shear and extensional components, and the pressure loss due to extension is used to calculate the planar extensional viscosity (see Supporting Information S5). The method is carefully validated by comparing the determined viscosities in the absence of CO2 with those measured using commercial rheometers (see Supporting Information S6 and S7). Once validated, the specially built die is used to determine the shear and planar extensional viscosities of the samples under CO2 loadings of (1) PCO2 = 25 MPa and (2) PCO2 = 30 MPa, at flow rates typically observed in conventional polymer processing, conditions inaccessible in commercial rheometers. Oscillatory shear experiments in the LVE region are performed using the ARES rheometer equipped with the cone-and-plate fixture. The shear moduli, G′(ω) and G″(ω), are evaluated at T = 171 °C under a nitrogen purge. Frequency sweeps from 0.1 to 100 rad/s are conducted at strains within the LVE range. Repeated sweeps with increasing and decreasing frequencies show that the material is stable under the measurement conditions. Prolonged heating of the samples at 171 °C in the rheometer results in no change in the viscoelastic data. The morphology of the nanocomposite is studied using scanning electron microscopy (SEM, JEOL 6060). Dispersion of PTFE fibers in PP is observed by subjecting the nanocomposite to permanganate etching28 for 24 h at room temperature, which etches PP and exposes the PTFE fibers. The exposed surface is sputter-coated with a thin layer of platinum prior to observation. Additionally, the PTFE fibers are examined after removing PP by placing the nanocomposite in boiling xylene for 1 h. PP is soluble in xylene, but PTFE is not. The undissolved residue is dried and sputter-coated with platinum prior to observation.

■

RESULTS AND DISCUSSION

First, we examine the shear viscosity, η, of PP with different fiber loadings, ϕ, at a CO2 injection pressure PCO2 = 30 MPa C

DOI: 10.1021/acs.macromol.9b00885 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

nearly over the entire ω range, for these nanocomposites, tan δ tends to converge at higher frequencies (Figure 2b) due to the response of the matrix becoming dominant rendering the contribution of the fibers difficult to decipher. Thus, the criteria of tan δ being frequency-independent when an incipient network first forms is only seen at ω < 1 rad/s. Similar observations of narrow frequency-independence of tan δ have been reported for crystallization of PP seen as a network formation process.47,48 Rheological signatures of percolation can also be seen in Figure 2c when ϕ = 5 wt %, where G′(ω) exceeds G″(ω) in the terminal zone, suggesting that the nanocomposite behaves as a viscoelastic solid. In contrast, for ϕ = 1 wt %, the rheological response is similar to that of the matrix where G″(ω) exceeds G′(ω) and both moduli scale with frequency as G′ ≈ ω2 and G″ ≈ ω in the terminal zone, characteristics of viscoelastic liquids. The divergence in response at ϕ = 5 wt % from the behavior of the matrix indicates the presence of a stable network of substantial mechanical integrity which has some capacity to store energy. We take additional steps to characterize the network structure of the fibers by conducting electron microscopy of the nanocomposites to complement the dynamic mechanical results. Morphological characteristics of the fiber network are depicted in Figure 2d,e and reveal that the fibers are welldispersed in the matrix, with an average diameter, D, of 310 nm and an average length, L, of 30 μm. Physical networks of highaspect-ratio fibers may impart strain-hardening in extensional flows and create an apparent yield stress at low shear rates under ambient conditions. Indeed, when ϕ = 3 wt % the network imparts strain-hardening in extensional flows (see Figure S5a), but it is not sufficiently developed to show an apparent yield stress (see Figure S6). However, when the fiber content is increased to ϕ = 5 wt %, an apparent yield stress is observed (see Figure S6). It is not uncommon for polymers containing a percolated network of fibers to exhibit a lack of yielding response, for instance, glass fiber-filled polymers exhibit a Newtonian plateau even when the fiber content is 40 wt %.11 Furthermore, CNF-filled PS composites do not show a yield stress at low shear rates even when the CNF content is 10 wt %.49 The highly entangled conformation of the fibers shown in Figure 2d,e is consistent with their low effective stiffness, Seff given by50

The extensional response of the nanocomposites which contain an interconnected network of fibers is strikingly different from those where the network is not developed. To characterize this difference, we plot in Figure 1c the planar extensional viscosity, ηe, of the nanocomposites with different ϕ at PCO2 = 30 MPa and T = 125 °C. Even at ϕ = 2 wt %, the nanocomposite exhibits ηe below that of the neat matrix due to the larger CO2 uptake from the CO2-philicity of the fibers. On the other hand, at ϕ = 3 wt %, ηe unexpectedly exceeds that of the matrix by almost an order of magnitude, despite the CO2induced plasticization which accelerates relaxation times. The decrease in η and ηe with increasing γ̇ and ε̇, respectively (Figure 1a,c), reflects changes in the fiber orientation, which evidently becomes less effective at transmitting shear and extensional stress under flow conditions. Clearly, if the fibers start to orient in the flow field, the viscosity should reduce because the number of fiber−fiber contacts decreases, thus contributing a smaller disturbance to flow. Consequently, the observed decline in ηe and η with increasing deformation rates originates primarily from the increasing orientation of fibers in the flow direction which acts to reduce the flow resistance. Additionally, the distortion of the “entangled” macromolecules of the matrix to an “oriented” state under flow has also been linked to a precipitous drop in the ability of the matrix to sustain stress on large length scales and, consequently, to a drop in viscosity with increasing deformation rates. This effect is observed at much lower deformation rates for fiber-filled polymers than in neat polymers and is interpreted to arise from the additional shear stress exerted on the matrix in the vicinity of the fibers.5,11,40 A comparison of the effect of ϕ on ηe and η is summarized in Figure 1d. ηe is taken at an extension rate ε̇ = 1 s−1 and the η is taken at a shear rate γ̇ = 2 s−1 using the equivalency relationship γ̇ = 2ε̇ for planar extensional flows.41 The figure reveals the contrasting behavior between the two types of flows with an increase in ϕ, where ηe increases rapidly beyond a threshold fiber content but η continues to decrease monotonically. This diverging response in η and ηe is in clear contrast with most fiber-filled composites where the two viscosities generally increase with solid-state fiber loading.11−16 The results in Figure 1c,d rule out the reinforcement effect of the high-aspect-ratio fibers as primary drivers for this increase in ηe above PP because ϕ = 2 wt % shows an extensional response lower than the matrix. This “apparent” independence from the reinforcement effect of the fibers drives us to examine more closely the role of the fiber network on the rheological response. In order to establish that a 3D fiber network has indeed developed in the range 2 wt % < ϕj < 3 wt %, the frequency dependence of the shear elastic stiffness, G′(ω), and the shear viscous dissipation, G′′(ω), is studied in the LVE region for the nanocomposites with varying ϕ. The independence of the loss tangent, tan δ, (tan δ = G′′/G′) from frequency, ω, provides a reliable means of precisely identifying ϕj when the fiber network percolates.42,43 This criterion has been effectively used in identifying the percolation threshold in various filled polymer composites.9,10,44−46 Consequently, tan δ is plotted against ϕ for different ω in Figure 2a and ϕj is identified to be 2.7 wt % taken as the instance where the different frequency curves converge. Only ω < 1 rad/s are used in Figure 2a because contrary to the classical definition of a percolated network where tan δ is independent of frequency

S eff =

E Y π D4 64ηmγL̇ 4

(1)

where EY is the Young’s modulus, L and D are the fiber length and diameter, respectively, ηm is the viscosity of the matrix, and γ̇ is the shear rate. For Seff ≪ 1, the fibers are flexible, whereas for large values of Seff, fibers are considered rigid. Given that EY is ∼108 Pa for the PTFE fibers, and γ̇ ranges from ∼10 to 50 s−1, our Seff is small (∼10−8 to 10−9). Thus, we may infer from this parameter value that the fibers are highly flexible. The large flexibility of fibers leads to an increased number of contacts between fibers which generate a more developed network.51 The number of interfiber contacts for each fiber, nc, can be estimated using52 N= D

4πnc 3 3(nc − 1)

(2) DOI: 10.1021/acs.macromol.9b00885 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

Figure 3. Effect of CO2 pressure on (a) extensional viscosity at ϕ = 3 wt %; (b) shear viscosity at ϕ = 3 wt %. Two pressure conditions are studied at T = 125 °C: (i) PCO2 = 25 MPa, and (ii) PCO2 = 30 MPa. For comparison, the extensional and shear viscosities of the neat matrix are also included in the figures.

where N is the crowding factor, given by N = 2/3 Cv(L/D)2, and Cv is the volumetric concentration of fibers. At a critical nc ≥ 3, each fiber is in contact with at least three other fibers on average, which causes the fibers to be effectively locked into a network in a bent configuration, and through frictional forces between the fibers generate mechanical strength in the network.52 At lower values of nc, fibers occasionally collide and may remain in contact temporarily but do not form a 3D physical network spanning continuously throughout the sample volume.53 Using eq 2, nc is calculated to be above three contacts per fiber at the experimentally determined ϕj, suggesting that the fibers are in the continuous contact regime.53 In comparison, at ϕ = 2 wt %, nc is less than three contacts per fiber confirming the absence of such continuous interfiber contact. From these results, a picture emerges in which network development from topological entanglements of the highaspect-ratio flexible fibers at sufficiently high loadings can elicit a noticeable increase in extensional viscosity under a CO2 atmosphere. In contrast, under shear, the effect of the network does not manifest as evidenced by the absence of any increase in shear viscosity in the vicinity of percolation (Figure 1d). The discrepancy in the rheological response of the network under extensional and shear flows is attributed to the different expressions of the stress tensor in the two types of flows: in extensional flow, the tensile stress reflects the total stress tensor and the principal axes of the stress and strain rate tensors are parallel, but in shear flow, the shear stress does not represent the total stress tensor and the principal axes of the stress and strain rate tensors are different.54 Consequently, in extensional flow, the network is subjected to a larger degree of stretching which promotes the build-up of stress due to the relative difficulty associated with moving entanglement junctions.55 Deformation of the network in extensional flow enhances the penetration of the fibers into a stress-detecting plane and results in an increase in extensional viscosity, despite acceleration of relaxation from the CO2-induced plasticization. On the other hand, in shear flow, the network is subjected to relatively reduced stretching and orientation56 such that the effect of plasticization dominates and produces an overall reduction in the shear viscosity. These results strongly suggest that the enhancement of the extensional viscosity originates primarily from fiber−fiber interactions within the network rather than from fiber−matrix interactions because resistance to stretching is observed even

when the viscosity of the matrix is reduced through CO2assisted plasticization induced by the increase in the content of CO2-philic fibers (Figure 1d). In contrast, extensional flow resistance in composites containing rigid fibers originates predominantly from matrix−fiber interactions where excess localized shear deformation of the matrix occurs between neighboring fibers and generates additional stresses.3,57 Thus, in nanocomposites containing flexible fiber networks, frictional forces between fibers and the resistance force to bending deformation are expected to be the source of elasticity.33,58 We further investigate the origin of elasticity in the nanocomposite by changing the CO2 injection pressure which alters the degree of plasticization and, hence, changes the matrix viscosity. In the case where the elasticity originates primarily from fiber−fiber interactions, altering the matrix viscosity should not significantly influence the elasticity in extension. Thus, in Figure 3a, ηe for the nanocomposite is characterized at two different CO2 injection pressures, PCO2 = 25 MPa and PCO2 = 30 MPa, and is compared with that of the neat matrix. Indeed, the sensitivity of ηe to pressure is significantly less for the nanocomposite than the matrix: the nanocomposite undergoes a viscosity reduction of 23% when the CO2 injection pressure is increased from 25 to 30 MPa, but the neat matrix undergoes a significantly higher viscosity reduction of 42% emphasizing the substantial contribution of the fiber network toward the elasticity of the nanocomposite. However, the fact that a 23% viscosity reduction is observed in the nanocomposite indicates that the contribution of the viscoelasticity of the matrix toward ηe is non-negligible. The contribution of matrix−fiber interactions toward the elasticity of the nanocomposite may originate from the entanglementcoupling between the matrix chains which get entrapped in the PTFE phase during compounding due to the low interfacial tension between PP and PTFE59,60 which leads to a large interfacial thickness.61 In contrast, the effect of increasing PCO2 on the shear viscosity appears to be more pronounced in the nanocomposite compared to the neat matrix (Figure 3b), which is in agreement with the behavior expected from the higher degree of CO2-induced plasticization in the nanocomposite. E

DOI: 10.1021/acs.macromol.9b00885 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

■

ORCID

CONCLUSIONS Processing the nanocomposites under pressurized CO2 reveals two consequences of the PTFE fibers: first, the high-aspectratio of the fibers imparts flexibility to these fibers which allows them to form a physical network of entanglements when the fiber loading exceeds the percolation threshold, and second, the CO2-philicity of PTFE allows the sorption of a larger amount of CO2 in the nanocomposite. Under pressurized CO2, the shear viscosity of the nanocomposite is lower than the matrix and can be formally related to the enhanced plasticization effect from the localization of a larger amount of CO2 in the nanocomposite. Under pressurized CO2, the strong elastic effects of the 3D fiber network in the nanocomposites become evident from the enhancement of the extensional viscosity, despite the acceleration of the relaxation time from the dissolution of a higher amount of CO2 in the nanocomposite due to the CO2philicity of the fibers. On the other hand, when the fiber concentration is insufficient to form a network, the extensional viscosity for the nanocomposite is lower than neat PP as expected due to a higher degree of CO2-assisted plasticization. This result suggests that a strong relationship exists between the extensional flow resistance of the nanocomposite and the presence of a network. This is concluded based on the findings from the dynamic shear moduli experiments which reveal that rheological percolation of the fibers occurs at 2.7 wt %. Given that the polydispersity of the matrix remains nearly unaltered, and the fibers do not react with the matrix chemically, the rapid increase in extensional flow may be used as a cursory indicator for the formation of a rheologically percolated network in the matrix. Furthermore, the sensitivity of the extensional viscosity to the CO2 injection pressure is less than that of the shear viscosity for the nanocomposites containing a percolated network of fibers emphasizing the strong elastic effects of the network. Thus, there is substantial evidence that in CO2-based processes, the formation of a network superstructure through physical entanglements of flexible PTFE fibers increases the extensional viscosity of neat PP while simultaneously reducing the shear viscosity. These results provide valuable insights for developing tailor-made materials for CO2-based industrial processes.

■

Chul B. Park: 0000-0002-1702-1268 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors would like to thank the members of the Consortium of Cellular and Microcellular Plastics (CCMCP) for their financial support of this project. A.R. thanks NSERC (Canada) for providing a CGS-D2 scholarship.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.9b00885.

■

REFERENCES

(1) Metzner, A. B. Rheology of Suspensions in Polymeric Liquids. J. Rheol. 1985, 29, 739−775. (2) Song, Y. H.; Zheng, Q. Concepts and Conflicts in Nanoparticles Reinforcement to Polymers Beyond Hydrodynamics. Prog. Mater. Sci. 2016, 84, 1−58. (3) Batchelor, G. K. The Stress Generated in a Non-Dilute Suspension of Elongated Particles by Pure Straining Motion. J. Fluid Mech. 1971, 46, 813−829. (4) Mewis, J.; Metzner, A. B. The Rheological Properties of Suspensions of Fibres in Newtonian Fluids Subjected to Extensional Deformations. J. Fluid Mech. 1974, 62, 593−600. (5) Yokohara, T.; Nobukawa, S.; Yamaguchi, M. Rheological Properties of Polymer Composites with Flexible Fine Fibers. J. Rheol. 2011, 55, 1205−1218. (6) Yamaguchi, M.; Fukuda, K.; Yokohara, T.; Ali, M. A. B.; Nobukawa, S. Modification of Rheological Properties under Elongational Flow by Addition of Polymeric Fine Fibers. Macromol. Mater. Eng. 2012, 297, 654−658. (7) Ali, M. A. B. M.; Okamoto, K.; Yamaguchi, M.; Kasai, T.; Koshirai, A. Rheological Properties for Polypropylene Modified by Polytetrafluoroethylene. J. Polym. Sci., Part B: Polym. Phys. 2009, 47, 2008−2014. (8) Rizvi, A.; Andalib, Z. K. M.; Park, C. B. Fiber-Spun Polypropylene/Polyethylene Terephthalate Microfibrillar Composites with Enhanced Tensile and Rheological Properties and Foaming Ability. Polymer 2017, 110, 139−148. (9) Rizvi, A.; Park, C. B. Dispersed Polypropylene Fibrils Improve the Foaming Ability of a Polyethylene Matrix. Polymer 2014, 55, 4199−4205. (10) Rizvi, A.; Park, C. B.; Favis, B. D. Tuning Viscoelastic and Crystallization Properties of Polypropylene Containing in-Situ Generated High Aspect Ratio Polyethylene Terephthalate Fibrils. Polymer 2015, 68, 83−91. (11) Chan, Y.; White, J. L.; Oyanagi, Y. A Fundamental Study of the Rheological Properties of Glass-Fiber-Reinforced Polyethylene and Polystyrene Melts. J. Rheol. 1978, 22, 507−524. (12) Kagarise, C.; Miyazono, K.; Mahboob, M.; Koelling, K. W.; Bechtel, S. E. A Constitutive Model for Characterization of Shear and Extensional Rheology and Flow Induced Orientation of Carbon Nanofiber/Polystyrene Melt Composites. J. Rheol. 2011, 55, 781− 807. (13) Werner, P.; Verdejo, R.; Wöllecke, F.; Altstädt, V.; Sandler, J. K. W.; Shaffer, M. S. P. Carbon Nanofibers Allow Foaming of Semicrystalline Poly(Ether Ether Ketone). Adv. Mater. 2005, 17, 2864−2869. (14) Thomasset, J.; Carreau, P. J.; Sanschagrin, B.; Ausias, G. Rheological Properties of Long Glass Fiber Filled Polypropylene. J. Non-Newtonian Fluid Mech. 2005, 125, 25−34. (15) Rajabian, M.; Dubois, C.; Grmela, M.; Carreau, P. J. Effects of Polymer−Fiber Interactions on Rheology and Flow Behavior of Suspensions of Semi-Flexible Fibers in Polymeric Liquids. Rheol. Acta 2008, 47, 701−707. (16) Ramazani, A.; Ait-Kadi, A.; Grmela, M. Rheology of Fiber Suspensions in Viscoelastic Media: Experiments and Model Predictions. J. Rheol. 2001, 45, 945−962.

Mechanism of in situ fibrillation of PTFE; geometry of the specially-built die; tandem extruder setup; shear viscosity determination; extensional viscosity determination; power law parameter; shear viscositymethod validation; planar extensional viscositymethod validation; effect of ϕ on the appearance of a yield stress at low shear rate; evaluation of the shift factors; determination of CO2 solubility; and mechanism of CO2-philicity in PTFE (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. F

DOI: 10.1021/acs.macromol.9b00885 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules (17) Auhl, D.; Stange, J.; Münstedt, H.; Krause, B.; Voigt, D.; Lederer, A.; Lappan, U.; Lunkwitz, K. Long-Chain Branched Polypropylenes by Electron Beam Irradiation and Their Rheological Properties. Macromolecules 2004, 37, 9465−9472. (18) Desimone, J. M.; Guan, Z.; Elsbernd, C. S. Synthesis of Fluoropolymers in Supercritical Carbon Dioxide. Science 1992, 257, 945−947. (19) Zhang, Z. Y.; Handa, Y. P. Co2-Assisted Melting of Semicrystalline Polymers. Macromolecules 1997, 30, 8505−8507. (20) Tomasko, D. L.; Li, H. B.; Liu, D. H.; Han, X. M.; Wingert, M. J.; Lee, L. J.; Koelling, K. W. A Review of Co2 Applications in the Processing of Polymers. Ind. Eng. Chem. Res. 2003, 42, 6431−6456. (21) Rizvi, A.; Tabatabaei, A.; Barzegari, R.; Mahmood, H.; Park, C. B. In-Situ Fibrillation of Co2-Philc Polymers: Sustainable Route to Polymeric Foams in a Continuous Process. Polymer 2013, 54, 4645− 4652. (22) Kazarian, S. G.; Vincent, M. F.; Bright, F. V.; Liotta, C. L.; Eckert, C. A. Specific Intermolecular Interaction of Carbon Dioxide with Polymers. J. Am. Chem. Soc. 1996, 118, 1729−1736. (23) Rizvi, A.; Chu, R. K.; Lee, J. H.; Park, C. B. Superhydrophobic and Oleophilic Open-Cell Foams from Fibrillar Blends of Polypropylene and Polytetrafluoroethylene. ACS Appl Mater Interfaces 2014, 6, 21131−21140. (24) Ali, M. A. B. M.; Nobukawa, S.; Yamaguchi, M. Morphology Development of Polytetrafluoroethylene in a Polypropylene Melt (Iupac Technical Report). Pure Appl. Chem. 2011, 83, 1819−1830. (25) Jurczuk, K.; Galeski, A.; Piorkowska, E. Strain Hardening of Molten Thermoplastic Polymers Reinforced with Poly(Tetrafluoroethylene) Nanofibers. J. Rheol. 2014, 58, 589−605. (26) Trouton, F. T. On the Coefficient of Viscous Traction and Its Relation to That of Viscosity. Proc. R. Soc. London, Ser. A 1906, 77, 426−440. (27) Wang, J.; James, D. F.; Park, C. B. Planar Extensional Flow Resistance of a Foaming Plastic. J. Rheol. 2010, 54, 95−116. (28) Olley, R. H.; Bassett, D. C. An Improved Permanganic Etchant for Polyolefines. Polymer 1982, 23, 1707−1710. (29) Bonavoglia, B.; Storti, G.; Morbidelli, M.; Rajendran, A.; Mazzotti, M. Sorption and Swelling of Semicrystalline Polymers in Supercritical Co2. J. Polym. Sci., Part B: Polym. Phys. 2006, 44, 1531− 1546. (30) Park, H. E.; Dealy, J. M. Effects of Pressure and Supercritical Fluids on the Viscosity of Polyethylene. Macromolecules 2006, 39, 5438−5452. (31) Larson, R. G. The Structure and Rheology of Complex Fluids; Oxford University Press: New York, 1999. (32) Kerner, E. H. The Elastic and Thermo-Elastic Properties of Composite Media. Proc. Phys. Soc. Sect. B 1956, 69, 808−813. (33) Seemork, J.; Sako, T.; Ali, M. A. B.; Yamaguchi, M. Rheological Response under Nonisothermal Stretching for Immiscible Blends of Isotactic Polypropylene and Acrylate Polymer. J. Rheol. 2017, 61, 1− 11. (34) Tuminello, W. H.; Dee, G. T.; Mchugh, M. A. Dissolving Perfluoropolymers in Supercritical Carbon-Dioxide. Macromolecules 1995, 28, 1506−1510. (35) Rindfleisch, F.; DiNoia, T. P.; McHugh, M. A. Solubility of Polymers and Copolymers in Supercritical Co2. J. Phys. Chem. 1996, 100, 15581−15587. (36) Fried, J. R.; Hu, N. The Molecular Basis of Co2 Interaction with Polymers Containing Fluorinated Groups: Computational Chemistry of Model Compounds and Molecular Simulation of Poly [Bis(2,2,2-Trifluoroethoxy)Phosphazene]. Polymer 2003, 44, 4363− 4372. (37) Rindfleisch, F.; DiNoia, T. P.; McHugh, M. A. Solubility of Polymers and Copolymers in Supercritical Co2. J. Phys. Chem. 1996, 100, 15581−15587. (38) Kirby, C. F.; McHugh, M. A. Phase Behavior of Polymers in Supercritical Fluid Solvents. Chem. Rev. 1999, 99, 565−602. (39) Yee, G. G.; Fulton, J. L.; Smith, R. D. Fourier-Transform Infrared-Spectroscopy of Molecular-Interactions of Heptafluoro-1-

Butanol or 1-Butanol in Supercritical Carbon-Dioxide and Supercritical Ethane. J. Phys. Chem. 1992, 96, 6172−6181. (40) Goddard, J. D. The Stress Field of Slender Particles Oriented by a Non-Newtonian Extensional Flow. J. Fluid Mech. 1976, 78, 177− 206. (41) Jones, D. M.; Walters, K.; Williams, P. R. On the Extensional Viscosity of Mobile Polymer-Solutions. Rheol. Acta 1987, 26, 20−30. (42) Chambon, F.; Winter, H. H. Linear Viscoelasticity at the Gel Point of a Crosslinking Pdms with Imbalanced Stoichiometry. J. Rheol. 1987, 31, 683−697. (43) Holly, E. E.; Venkataraman, S. K.; Chambon, F.; Winter, H. H. Fourier-Transform Mechanical Spectroscopy of Viscoelastic Materials with Transient Structure. J. Non-Newtonian Fluid Mech. 1988, 27, 17− 26. (44) Meng, J. R.; Hu, X.; Boey, F. Y. C.; Li, L. Effect of Layered Nano-Organosilicate on the Gel Point Rheology of Bismaleimide/ Diallylbisphenol a Resin. Polymer 2005, 46, 2766−2776. (45) Kakroodi, AR; Kazemi, Y.; Ding, W.; Ameli, A.; Park, CB Poly(Lactic Acid)-Based in Situ Microfibrillar Composites with Enhanced Crystallization Kinetics, Mechanical Properties, Rheological Behavior, and Foaming Ability. Biomacromolecules 2015, 16, 3925−35. (46) Liu, C. Y.; Zhang, J.; He, J. S.; Hu, G. H. Gelation in Carbon Nanotube/Polymer Composites. Polymer 2003, 44, 7529−7532. (47) Schwittay, C.; Mours, M.; Winter, H. H. Rheological Expression of Physical Gelation in Polymers. Faraday Discuss. 1995, 101, 93−104. (48) Pogodina, N. V.; Winter, H. H. Polypropylene Crystallization as a Physical Gelation Process. Macromolecules 1998, 31, 8164−8172. (49) Wang, Y. R.; Xu, J. H.; Bechtel, S. E.; Koelling, K. W. Melt Shear Rheology of Carbon Nanofiber/Polystyrene Composites. Rheol. Acta 2006, 45, 919−941. (50) Switzer, L. H.; Klingenberg, D. J. Rheology of Sheared Flexible Fiber Suspensions Via Fiber-Level Simulations. J. Rheol. 2003, 47, 759−778. (51) Keshtkar, M.; Heuzey, M. C.; Carreau, P. J. Rheological Behavior of Fiber-Filled Model Suspensions: Effect of Fiber Flexibility. J. Rheol. 2009, 53, 631−650. (52) Wahren, D.; Meyer, R. On the Elastic Properties of ThreeDimensional Fibre Networks. Sven. Papperstidning 1964, 67, 432− 436. (53) Kerekes, R. J.; Schell, C. J. Characterization of Fiber Flocculation Regimes by a Crowding Factor. J. Pulp Pap. Sci. 1992, 18, J32−J38. (54) Zülle, B.; Linster, J. J.; Meissner, J.; Hürlimann, H. P. Deformation Hardening and Thinning in Both Elongation and Shear of a Low Density Polyethylene Melt. J. Rheol. 1987, 31, 583−598. (55) Chellamuthu, M.; Rothstein, J. P. Distinguishing between Linear and Branched Wormlike Micelle Solutions Using Extensional Rheology Measurements. J. Rheol. 2008, 52, 865−884. (56) Costanzo, S.; Huang, Q.; Ianniruberto, G.; Marrucci, G.; Hassager, O.; Vlassopoulos, D. Shear and Extensional Rheology of Polystyrene Melts and Solutions with the Same Number of Entanglements. Macromolecules 2016, 49, 3925−3935. (57) Laun, H. M. Orientation Effects and Rheology of Short Glass Fiber-Reinforced Thermoplastics. Colloid Polym. Sci. 1984, 262, 257− 269. (58) Fujii, Y.; Nishikawa, R.; Phulkerd, P.; Yamaguchi, M. Modifying the Rheological Properties of Polypropylene under Elongational Flow by Adding Polyethylene. J. Rheol. 2019, 63, 11−18. (59) Wang, C.; Liu, C.-R. Transcrystallization of Polypropylene Composites: Nucleating Ability of Fibres. Polymer 1999, 40, 289− 298. (60) Rizvi, A.; Tabatabaei, A.; Vahedi, P.; Mahmood, S. H.; Park, C. B. Non-Crosslinked Thermoplastic Reticulated Polymer Foams from Crystallization-Induced Structural Heterogeneities. Polymer 2018, 135, 185−192. (61) Helfand, E.; Tagami, Y. Theory of the Interface between Immiscible Polymers Ii. J. Chem. Phys. 1972, 62, 3592−3601.

G

DOI: 10.1021/acs.macromol.9b00885 Macromolecules XXXX, XXX, XXX−XXX