EXTENSIONAL FLOWS IN POLYMER PROCESSING: EFFECTS ON MIXING AND MATERIAL PERFORMANCE SIDNEY OLIVER CARSON

Transcription

1 EXTENSIONAL FLOWS IN POLYMER PROCESSING: EFFECTS ON MIXING AND MATERIAL PERFORMANCE by SIDNEY OLIVER CARSON Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Thesis Adviser: Dr. João Maia Department of Macromolecular Science and Engineering CASE WESTERN RESERVE UNIVERSITY August 2016

2 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis/dissertation of Sidney O. Carson Candidate for the degree of Doctor of Philosophy * Committee Chair Dr. João M. Maia Committee Member Dr. Ica Manas-Zloczower Committee Member Dr. Alexander Jamieson Committee Member Dr. James McGuffin-Cawley Date of Defense May 19 th, 2016 *We also certify that written approval has been obtained for any proprietary material contained therein. 2

3 Dedication To G, G, and G. 3

4 Table of Contents List of Figures and Tables... 8 Acknowledgements Abstract Introduction: Extensional Mixing in Twin-Screw Extrusion Chapter Overview of the Extensional Mixing Element Design Principle Flow Channel Geometry Experimental Processing Equipment Material and Rheological Characterization Simulation Methods Results and Discussion Operational Concept Validation Single Channel Simulations Full Channel Simulations Conclusions

5 1-5. Figures and Tables References Chapter Liquid-liquid Mixing in Twin-screw Extrusion Experimental Processing Equipment Rheological Characterization Morphological Analysis Results and Discussion Determining Effective Viscosity Ratios Pressure Profiles Blend Morphology Conclusions Figures and Tables References Chapter Polymer/Carbon Filler Composites Experimental Composite Fabrication and Sampling Optical Microscopy of Filler Dispersion

6 Composite Characterization Results and Discussion Process Characteristics Optical Microscopy: Micro-level Dispersion Rheological and Electrical Properties: Nano-level Dispersion Importance of Dispersion Length Scale Conclusions Figures and Tables References Chapter Simulation of Twin-screw Extrusion Processes Methods for Simulation of TSE Elements Analysis of Flow and Mixing in Kneading Blocks Comparison of Flow through Extensional Mixing Elements and Kneading Blocks107 Optimization of Next Generation EME Geometry through Simulation Experimental Simulation Methods Rheological Modeling Generation 2 EME Design Flow through EME Channels

7 Comparison of EME and Kneading Blocks Results and Discussion EME vs. Kneading Blocks Optimization of EME Geometry Conclusions Tables and Figures References Appendix A-1. Introduction Injection Molding of Composites Carbon Nanotube Composites Network Formation during Molding A-2. Experimental Composite Production and Fabrication Resistivity Testing A-3. Results and Discussion Resistivity Mapping of Plaques Effects of Extension Rate A-4. Conclusions A-5. Figures and Tables

8 A-6. References Bibliography

9 List of Figures and Tables Figure 1-1 (a) Assembled element package. (b) Disassembled element package, showing internal shafts and construction. (c) EME assembled between kneading blocks on a TSE screw, with flow paths through the element indicated. (d) Full elements after operation. (e) Half hyperbolic channel implemented for flow balance and successive element usage.. 38 Figure 1-2 Hyperbolic contraction geometry design parameters. Lc = length of the contraction, wu = entrance width of the contraction, wc = throat width of the contraction, and wz = width of channel at position z. Dimensions of the actual channels are shown. 39 Figure 1-3 Screw configuration for the TSE24MC. T indicates transport element, KBXX indicates kneading block at a set stagger angle, RT indicates reverse transport, and DC indicates discharge. Transport sections are abbreviated. Measurement locations before and after the EME are indicated Figure 1-4 Geometry and boundary conditions for single channel simulations Figure 1-5 (a) Average and centerline velocity measurements for single contraction with linear fit. Closed symbols represent average measurements, open symbols maximum values. (b) Plane velocity profiles at m increments along flow channel Figure 1-6 Geometry for full channel simulations. (b) Channel labeling convention. (c) Inflow and outflow boundary locations. (d) Boundary conditions for Cartesian inlet condition simulations, where vz is the translational velocity in the flow direction, and ω is the rotational component

10 Figure 1-7 Velocity profiles for first (a) and second (b) contractions with the rotational and translational velocity inflow condition Figure 1-8 Centerline velocity measurements for the channels of the first contraction in the EME Figure 1-9 Centerline velocity predictions for the channels of the second contraction in the EME Figure 1-11 Inlet and outlet pressure predictions for the Cartesian inflow condition simulations Figure 2-1 Critical capillary number necessary to breakup Newtonian droplets in a Newtonian matrix for increasing viscosity ratios. Solid line indicates experimental data for simple shear flows, dashed line indicates elongational flow. Adapted from Manas- Zloczower, et. al. and Grace Figure 2-2 Sensor port arrangement for the barrel of the twin screw extruder used in this study Figure 2-3 Screw configurations for all experimental trials. (a) 90 kneading block configuration ( KB ) and (b) extensional mixing element configuration ( EME ). Relevant measurement and sampling locations are indicated Figure 2-4 (a) The Sample Collector (SC), attached to a P/T port of a TSE. (b) The SC attached with collected sample shown. (c) Final disk with cross sectional face indicated. (d) Cross sectional view of the SC in operation. Material flow is transverse to the extrusion 10

11 direction and is indicated by arrows. Three positions are: closed during normal operation, purge to clear collection channel, and collection for flow into mold Figure 2-5 Complex viscosity measurements at chosen processing temperatures for all blends, with processing shear rates highlighted Figure 2-6 SEM micrographs of blend morphologies for all blends. Left column shows KB results, right column shows EME results Figure 2-7 Size distribution histograms for all measured droplet areas. Values displayed as percentage of total number of droplets measured Figure 2-8 Cumulative area ratio distribution measurements for all blends at all screw configurations. Dashed line at 1 μm2 for the agglomerate area represents the chosen cutoff for dispersion effectiveness Figure 2-9 Aspect ratio histograms for all measured droplet areas. Values displayed as percentage of total number of droplets measured Figure 3-1 Positioning of key mixing sections relative to P/T ports for measurement and sample collection Figure 3-2 Optical micrographs of filler dispersion for all systems. Scale bar represents 200 microns Figure 3-3 Size distribution graphs for measured agglomerate areas, cut off at 300 square microns for clarity Figure 3-4 Cumulative area ratio vs. measured agglomerate area for all compositions

12 Figure 3-5 G' trends for all composites and all screw configurations Figure 3-6 Complex viscosity trends for all composites and all screw configurations Figure 3-7 Volume resistivity values for all samples, with detail cutout of 20% CB Figure 4-1 Frequency and shear rate dependent rheological modeling, encompassing inelastic shear-thinning (Cross), viscoelastic non-strain-hardening, and viscoelastic strainhardening Figure 4-2 Transient extensional viscosities for viscoelastic strain-hardening (top) and nonstrain-hardening (bottom) material models Figure 4-3 Trouton ratio as a function of strain for all extensional rheology tests. Closed symbols represent viscoelastic strain-hardening model, while open symbols represent nonstrain-hardening Figure 4-4 Full 3D representations of all simulated geometries. Left column displays actual element, right column displays flow channels extracted for simulations Figure 4-5 Geometry and boundary conditions for single channel, ¼ symmetry simulations. IF and OF indicate locations of inflow and outflow boundaries Figure 4-6 Geometry and boundary conditions for simulations of left handed rotating kneading blocks with a 60 stagger angle Figure 4-7 Values of the calculated mixing index at each fluid element for all contractions and KB geometries. Values between 0.6 and 1.0 are considered to be extensional flows. Shown for inelastic shear-thinning model

13 Figure 4-8 Distribution charts of mixing index values displayed as percentages of total elements in each simulation. Shown for inelastic shear-thinning model Figure 4-9 Velocity profile cross sections and measured average velocities vs.channel position with best fit lines for each geometry. Shown for inelastic shear-thinning model Figure 4-10 Pressure drops through all contractions as measured by average inflow minus average outflow pressure. Shown for inelastic shear-thinning model Figure A-1 Hyperbolic channel design Figure A-2 Image of as-synthesized CNano Flo-Tube Figure A-3 As-synthesized morphology of CNS. Reproduced from ANS, LLC Figure A-4 Geometries molded for electrical resistivity studies. L to R: plaque, mild, and extreme contractions Figure A-5 Hyperbolic geometry details. Channels were sized according to the position along the flow length (direction of Lc) to create the contracting geometries Figure A-6 Resistivity testing geometries and dimensions Figure A-7 Surface resistivity measurements for 1.5% PC/CNano (top) and PC/CNS (bottom) plaques Figure A-8 Volume resistivity measurements for 1.5% PC/CNano (top) and PC/CNS (bottom) plaques

14 Figure A-9 Surface resistivity measurements for 3% PC/CNano (top) and PC/CNS (bottom) plaques Figure A-10 Volume resistivity measurements for 3% PC/CNano (top) and PC/CNS (bottom) plaques Figure A-11 Resistivity vs. injection velocity for the mild contraction parts at 1.5 and 3% PC/CNano (top) and PC/CNS (bottom) Figure A-12 Resistivity vs. injection velocity for the extreme contraction parts at 1.5 and 3% PC/CNano (top) and PC/CNS (bottom)

15 List of Tables Table 2-1 Temperature rise in mixing sections under operating conditions for both screw configurations. Displayed as averages between entrance and exit temperatures Table 2-3 Pressure profiles for all blends compounded through both screw configurations Table 2-4 Maximum measured area for each viscosity ratio and screw configuration Table 2-5 Percentage of total measured droplets with areas under 1 μm2 as displayed from the cumulative area ratio distribution curves Table 3-1 Pressure drop and motor load measurements for all material compositions Table 3-2 Number of measured agglomerates per measured area for all compositions. 102 Table 4-1 Rheological parameters for all models Table 4-2 Geometrical values controlling extensional profiles of each simulated contraction Table 4-3 Mixing index and stress values for all contractions and KBs Table 4-4 Flow profile statistics for all contractions and material models Table 4-5 Pressure drop values for all contraction geometries and percent increases for all experimental geometries compared to L Table A-1 Processing parameters for compounding

16 Table A-2 Processing parameters for injection molding of plaques Table A-3 Extension rates for contracting bars Table A-4 Processing parameters for contracting bars

17 Acknowledgements The most thanks is due to my research adviser at Case Western, João Maia, for the support, guidance, and challenge as he turned me into a productive and contributing scientist. I m nothing without my parents, Grant and Gina, who have always been my biggest supporters and fans, even when I don t always deserve it. Their dedication to teaching me the importance of being a better human being has enabled me to achieve greater heights than I could have ever imagined. My brothers, one by biology, one by choice: Garrett and Mark. I m humbled every day by the strength of the bond that we ve formed. The 3 Force is unstoppable. My thesis committee, Dr. Ica Manas-Zloczower, Dr. Alexander Jamieson, and Dr. James McGuffin-Cawley, deserves thanks for freely imparting their years of knowledge and experience on me. Thanks to the entirety of the EMAC department at Case Western: the students, faculty, staff, and everyone in between. There was never a dull day in this building. Thanks to the professors and students in the Class of 2011 in the Plastics Engineering Technology department at Penn State Erie. My time there sparked a passion for engineering and problem solving that carried me through some of my hardest days. And to all of the people who have helped me and who I ve helped along the journey, thank you for the lesson that supporting those who have the same goals as I do helps uplift everyone and makes those goals that much closer for everyone. 17

18 Extensional Flows in Polymer Processing: Effects on Mixing and Material Performance Abstract by SIDNEY OLIVER CARSON This dissertation focuses on the study of the presence of extensional flows in common plastics processing operations, mainly in twin-screw extrusion. Twin-screw extruders are one of the most commonly used pieces when a mixing task for polymer processing is presented, and as such there is much interest in the investigation of its overall mixing capabilities. Shear flows have been proven time and again to be inferior in mixing efficiency when compared to extensional flows. Kneading blocks (KB) make up the majority of the mixing profile of a typical twin-screw extruder screw, and while there are extensional flow component present in their mixing operations, the main mixing mechanism in these elements is still shear dominated. Considering this, the Extensional Mixing Elements (EME) for twin-screw extrusion were developed for the purposes of imposing extension dominated flow during twin-screw extrusion and therefore increase the mixing capabilities of current mixing and processing equipment. The EME was designed as a static element that interfaces directly with the screw shaft of a twin-screw extruder, being built in a screw configuration like a standard element. It achieves mixing by forcing flowing material through channels around the diameter of 18

19 each element that are designed as hyperbolic contractions, which impart extension dominated flow along their centerline. Computational investigations of the velocity profiles through each of the contractions at typical operating conditions suggest the presence of these extensional flows with measurable and predictable strain rates. The first experimental validation of the EME was performed by compounding incompatible polypropylene/polystyrene blends (PP/PS) and comparing with the same blends produced through a standard KB configuration. Four viscosity ratios were investigated (0.3, 1, 3, and 10) and the resulting morphologies were characterized using SEM and image analysis. Statistically, the EME proved to be the superior dispersive mixing device when considering the measured droplet sizes over all viscosity ratios. This was extended further to the compounding of polymer-solid filler composites using carbon black, carbon nanotubes, and graphene nanosheets. These composites were characterized using optical microscopy to probe micro-level dispersion followed by rheology and electrical resistivity measures to probe nano-level dispersion. At the micro-level (investigating agglomerate sizes), the EME outperformed the chosen KB configuration by a large margin; however, at the nano-level, there does not seem to be any improvements in property enhancement or individualization of filler particles with the two geometries. More computational investigations of more extreme contraction geometries were undertaken to determine the limits of design flexibility for the EME. The mixing profiles (degree of shear vs. extensional flow, overall stress level) of these geometries were also compared with a KB configuration. All contractions showed more extension dominated flow patterns when compared to the KB, with more extreme contractions also matching the average stress level seen in operation. Increasing the contraction intensity predictably 19

20 increased the extensional profile of the contractions, but balance with the required pressure in operation had to be considered as well. Finally, the presence of extensional flows in injection molding and their influence on final part properties was investigated as an extension of the consideration of flow type in practical processing operations. Polycarbonate/carbon nanotube composites were molded into shear dominated parts (plaques) and two different hyperbolic contractions and their electrical resistivity was measured. Highly extension dominated flow decreased the resistivity of the resulting composites, indicating that part design and flow type in injection molding play a role in the development of important composite properties. 20

21 Introduction: Extensional Mixing in Twin-Screw Extrusion Twin-screw extrusion is one of the most prevalent technologies in the plastics industry for the purposes of plastics compounding. Its usefulness stems from the wide range of thermo-mechanical histories that can be imparted on the melts, its ease of implementation and use, modularity, continuous production capabilities, and variation of workable scales, from the lab bench through to production. For these reasons, twin screw extrusion sees application in the main areas of plastics compounding, including but not limited to: incorporation of solid fillers into a polymer melt, the blending of polymers and polymer modification, often involving chemical reactions simultaneously with flow and heat transfer (denoted as reactive extrusion). The distributive and dispersive mixing capabilities of a TSE can be controlled by the proper choice of the type and geometry of the available screw elements. The majority of the dispersive mixing action in twin screw extrusion takes places during shear dominant flows in elements called kneading blocks (KB). However, the work of Grace [1] on the ability of rotational (shear) and irrotational (elongational) flows to disperse suspended droplets of differing viscosity ratios (defined as the ratio viscosity of the dispersed phase to that of the major phase), showed experimentally that flows with strong elongational components were more efficient at mixing over a wider range of viscosity ratios. While these fundamental studies were conducted with Newtonian-Newtonian blends, much work since has investigated the contributions of non-newtonian mechanics to the same phenomena, which has a much more practical tie to plastics processing. [2-4] While KBs do generate a degree of extensional flows during processing, they are more of a consequence rather than an intent; the geometrical configuration of a KB (such 21

22 as number of lobes, overall size and width, and configuration with the extruder barrel) determine the relative amount of shear vs. extension during mixing. All of these studies have led to a desire to implement plastics processing devices that generate elongational forces in addition to the shear mixing standard. One of the simplest methods of creating elongational forces in a flowing system is to subject the flow to a series of convergences and divergences. [1, 5-7] In a constrained convergence, a flowing system is subjected primarily to shear stresses at the walls of the convergence and primarily extensional stresses along the centerline, caused by the acceleration of the flow at the centerline relative to the wall. [5, 8-13] The following paragraphs discuss some of the processing devices that utilize converging-diverging (C-D) flows in an effort to create extensional stresses for improved dispersive mixing capabilities. Among the attempts at inducing mixing in extrusion via extensional flows is the Elongational Flow Mixer [2, 14-17] (EFM), which operates as an add-on unit to the end of a melt pump, such as a single screw (SSE) or TSE. It provides specific extensional stress to a flowing mixture through a series of concentric C-D channels. It also subjects the flow to periods of quiescence between convergences, where the dispersed component has a chance to break-up and relax before being subjected to another stretching flow. Several material systems have been tested through the EFM and shown improvements over traditional processing equipment, such as the dissolution of ultra-high molecular weight polyethylene in a high-density polyethylene and polymer- clay nanocomposites. The Elongational Flow Reactor and Mixer [18-20] (RMX) is a laboratory-scale mixing device where material is melted and forced back and forth over a mixing element by reciprocating pistons. The standard design is a small cylindrical chamber with a diameter 22

23 smaller than the feeding channels, subjecting the mixture to a freely converging contraction. It is designed to provide an unlimited number of cycles over the converging geometry. The RMX has also shown improvements in mixing over traditional processing equipment in the production of polystyrene/poly(methyl methacrylate) and polypropylene/epdm blends, as well as increased dispersion of graphite nanocomposites in PLA. In contrast to the EFM, the RMX is positioned towards the laboratory scale, giving it the ability to study new or expensive systems without much material input. Finally, extensional dispersion has been achieved using a modified capillary rheometer setup [21-23] that contained a series of stacked rings with equal outer diameters but alternating larger and smaller inner diameters. Material is forced down through the rings by the piston of the capillary rheometer, resulting in elongationally dominated flow allowing for characteristic flow studies. This setup was shown to increase dispersion levels over twin screw extrusion for traditional melt mixing in polymer/vapor grown carbon fiber and polymer/carbon nanotube composites. Efforts have also been made to impart extension-dominated flow within the barrel of a TSE. Blister discs contain a series of circular bores arranged concentrically around their circumference. Material being extruded can only flow through the bores and the gap between the discs and the wall, introducing a large stretching component to the flow, while also creating a flow constriction and increased residence time inside the extruder barrel. [24, 25] However, the small bore size limits the size of solid particles that may flow through the elements [26], and their pumping characteristics are essentially dependent on the gap between the elements and the extruder barrel. [27] 23

24 The goal of this dissertation is to present and describe the Extensional Mixing Element (EME), a new type of mixing element for twin screw extrusion that stays static as the rest of the extruder screw rotates, providing controllable extensional stress on a melt through converging-diverging (C-D) channels around its diameter where the material in the TSE is forced to flow. First, the operational concept of the EME was analyzed through FEA flow simulation and confirmed with experimental studies on a pre-production scale TSE. Experimental studies were performed using immiscible polymer-polymer blends and polymer-solid filler composites of different starting morphologies to describe its effectiveness at dispersive mixing operations of commonly compounded materials. Further computational studies were performed in order to compare the EME s flow channels to the mixing performance of a standard shear kneading block, and these studies were used to guide the design of the next generation of EME. Finally, the influence of extensional flows on final part properties in an injection molding process of polymer-filler composites is described in an effort to extend the investigation of extensional flows in polymer processing. 24

25 [1] H. P. Grace, Chemical Engineering Communications, 14, (1982). [2] D. Bourry, F. Godbille, R. E. Khayat, A. Luciani, J. Picot, and L. A. Utracki, Polymer Engineering and Science, 39, (1999). [3] S. Guido, Current Opinion in Colloid & Interface Science, 16, (2011). [4] W. J. Milliken and L. G. Leal, Journal of Non-Newtonian Fluid Mechanics, 40, (1991). [5] F. N. Cogswell, Journal of Non-Newtonian Fluid Mechanics, 4, (1978). [6] M. Meller, A. Luciani, and J. A. E. Manson, Polymer Engineering and Science, 42, (2002). [7] M. Meller, A. Luciani, A. Sarioglu, and J. A. E. Manson, Polymer Engineering and Science, 42, (2002). [8] D. Binding, Journal of Non-Newtonian Fluid Mechanics, 27, (1988). [9] D. Binding, Journal of non-newtonian fluid mechanics, 41, (1991). [10] D. Binding and D. Jones, Rheologica acta, 28, (1989). [11] J. M. Maia, Journal of Non-Newtonian Fluid Mechanics, 85, (1999). [12] J. M. Maia and D. Binding, Rheologica Acta, 38, (1999). [13] I. Manas-Zloczower, Mixing and compounding of polymers : theory and practice, Hanser (2009). [14] M. Tokihisa, K. Yakemoto, T. Sakai, L. A. Utracki, M. Sepehr, J. Li, et al., Polymer Engineering & Science, 46, (2006). [15] X. Q. Nguyen and L. A. Utracki, United States Patent (1995). [16] A. Luciani and L. A. Utracki, International Polymer Processing, 11, (1996). 25

26 [17] R. E. Khayat, A. Luciani, L. A. Utracki, F. Godbille, and J. Picot, International Journal of Multiphase Flow, 26, (2000). [18] J. Rondin, M. Bouquey, R. Muller, C. A. Serra, G. Martin, and P. Sonntag, Polymer Engineering & Science, 54, (2014). [19] R. Ibarra-Gómez, R. Muller, M. Bouquey, J. Rondin, C. A. Serra, F. Hassouna, et al., Polymer Engineering & Science, 55, (2015). [20] M. Bouquey, C. Loux, R. Muller, and G. Bouchet, Journal of Applied Polymer Science, 119, (2011). [21] P. Cardoso, J. Silva, D. Klosterman, J. A. Covas, F. W. van Hattum, R. Simoes, et al., Nanoscale research letters, 6, 1-5 (2011). [22] R. M. Novais, J. A. Covas, and M. C. Paiva, Composites Part A: Applied Science and Manufacturing, 43, (2012). [23] S. Jamali, M. C. Paiva, and J. A. Covas, Polymer Testing, 32, (2013). [24] S. Jacobsen, H. Fritz, P. Degée, P. Dubois, and R. Jérôme, Polymer, 41, (2000). [25] M. Garcia, G. Van Vliet, S. Jain, B. Schrauwen, A. Sarkissov, W. Van Zyl, et al., Reviews on Advanced Materials Science, 6, (2004). [26] K. Kohlgrüber, Co-rotating twin-screw extruder, Carl Hanser Verlag GmbH Co KG (2012). [27] N. Wang, T. Sakai, and N. Hashimoto, International Polymer Processing, 13, (1998). 26

27 Chapter 1 Theory, Design, and Computational Validation of Flow through Extensional Mixing Elements in a Twin-screw Extruder This chapter is partially based on: S. O. Carson, J. A. Covas, and J. M. Maia, A New Extensional Mixing Element for Improved Dispersive Mixing in Twin-Screw Extrusion, Part 1: Design and Computational Validation, Advances in Polymer Technology, (2015) Overview of the Extensional Mixing Element Design Principle The EME was designed to meet three initial requirements. First, the element was meant to impart extension-dominated flow through C-D channels. Second, the magnitude and relative amount of shear and extension of the element needed to be controllable and quantifiable through the design of the flow geometry. Finally, it is desired that the element interface with a conventional TSE without interrupting its normal function or adding extra equipment systems or controls. The EME discussed in this work is shown in Figure 1-1. Figure 1-1(a) shows the complete assembly of the unit separate from the TSE. Figure 1-1(b) presents a view of the element package disassembled. The construction of the elements contains the main body with the C-D channels through which material flows through in operation. Two sleeve shafts slip over the shaft of the TSE screws to create an 27

28 interface between the elements and the screw shaft; finally, bronze flanged sleeve bearings, which ride against the rest of the TSE screw assembly and the sleeve shafts, prevent wear on the elements themselves. Figure 1-1(c) displays the entire EME assembled with the rest of the TSE screw shaft, with the material flow path in operation indicated with arrows. One EME assembly (in the context of this paper) contains two mixing elements, and the assembly is designed to be expandable to as many elements as desired, with the flow channels being staggered to each other on each element to eliminate dead flow zones. Figure 1-1(d) is a picture of the full screw of the TSE after operation, where the EME channels are full and display a good seal against the barrel wall with no leakage in between the individual channels. This was achieved with constructing a half hyperbole on the top and bottom of the second element of the set, shown in Figure 1-1(e). This half channel was present for the purposes of ensuring that the flow would remain consistent when transferring from element to element, and another full channel in its place would have created a dead flow zone at the entrance to the second element. Each element encompasses both of the extruder screws with a single piece, which is also displayed in Figure 1-1. Flow Channel Geometry Each C-D channel in the EME is designed to be hyperbolic. Hyperbolic contractions were suggested by Cogswell [5] as a means of imposing a uniform extension rate on a fluid for measurement of extensional viscosity. They were also studied in an axisymmetric configuration by Everage and Ballman [28] for the measurement of the extensional viscosity of a molten polymer. These geometries have been adapted into microfluidics as an additional means of studying extensional viscosity of fluids as well. 28

29 [29, 30] The hyperbolic channel geometry was chosen based on its purely extensional flow taking place along the centerline of the channel, with an extension dominated flow towards the channel walls. Given the difficulties in practically obtaining a fully developed purely extensional flow, this geometry was estimated to be efficient enough to achieve the purposes of the EMEs. Each channel of the EME is shaped according to Equation (1), (2), and (3): [30] a = L c w c (w u w c ) (1) C = L c w u w c 2(w u w c ) (2) x = C (a+z) (3) where z = position along the contraction, Lc = length of the contraction, wu = entrance width of the contraction, wc = throat width of the contraction, and x = half-channel width at given position z. These dimensions are graphically represented in Figure 1-2. The elements were designed to fit a 24mm screw diameter TSE, with the total length of a single element matching 1 L/D for the extruder. Since one complete flow channel is both a convergence and divergence, the total length of one element is equal to 2Lc. The total length was chosen so the element could interface effectively with the rest of the traditional screw geometry and avoid inconsistencies in the screw building process. The required pressure through the elements was a major concern, so one element was kept to one contraction, 29

30 since increasing the number of contractions (while also decreasing the contraction length) would increase the total pressure drop across the element. The first prototype of the EME, presented in this work, was designed to represent a conservative, functional proof of concept for experimental and computational validation. The extensional characteristics of the EME were designed to be relatively mild, as defined later. The important extensional characteristics were characterized nominally by the following equations, as outlined by Ober, et al. [29]: ε H = ln w u w c (4) ε = Q L c h ( 1 w c 1 w u ) (5) where Q is the volumetric flow rate through the channel and h is the channel depth for a planar contraction. Equation (4) was used to calculate the Hencky strain through a single contraction, which is a logarithmic measure of the deformation. This is controlled by the contraction ratio and was calculated to be around 1 for the first prototype design. Equation (5) was used to calculate the nominal extension rate through a channel of given dimensions. For an extruder throughput rate of 5.5 kg/hr of a material with a density approximately equal to 1000 kg/m 3, which is indicative of the conservative process of the 24mm extruder being used for the first validation of the EME, the nominal extension rate through one channel was calculated to be around 1.3 s -1. It should be noted that Equation (5) calculates the extension rate as a result of the average velocity through the channel at a given z 30

31 position, and also neglects any influence of shearing effects at the wall of the flow channel. [29] 1-2. Experimental Processing Equipment The TSE that the EME was designed for and validated on was a ThermoScientific TSE24MC 24mm co-rotating twin-screw extruder with a 40:1 L/D ratio. The screw configuration used for all studies is shown in Figure 1-3. This configuration was designed to melt the material at the first restrictive zone, and provide mixing in the zone containing the EME followed by a reverse conveying element. The reverse conveying element downstream was added for three reasons: i) Increase the distributive mixing, which suffers in the EME because of the short residence times and simple flow patterns created; ii) Guarantee the EME channels are completely filled; iii) Guarantee enough pressure at the end of the EME for samples to be collected (see Chapter 2). The TSE24MC extruder was specially constructed to have 14 pressure/temperature (P/T) transducer ports on movable blocks along the length of the barrel that can also be used to collect small amounts of sample, as explained in Part 2. Material was fed into the extruder at a constant rate of 5.5 kg/hr for all validation studies using a Brabender volumetric feeder with a single spiral screw configuration. Pressure measurements were taken before and after the EME (as indicated in Figure 1-3) using Dynisco MDA422 transducers connected to a Dynisco 1390 instrumentation box. Material was extruded through a three-hole strand die with a hole diameter of 3 mm and collected through a ThermoScientific water bath and pelletizer, to simulate operation of the EME in a real compounding process. Screw rotational speed and 31

32 barrel temperature were kept at a constant 500 RPM and 230 C, respectively, for all experiments. Material and Rheological Characterization Poly(methylmethacrylate) (PMMA) produced by Arkema, Inc., tradename Plexiglas PMMA V920 (MFI = 8.0 g/10min at 3.8kg and 230 C), was chosen as a model system for the computational studies. The PMMA was characterized rheologically in both shear and uniaxial extension to obtain inputs for computational flow simulations. All samples were compression molded at 230 C on a compression molder for 4 min under an applied load of 8 metric tons, after drying for 12h at 80 C under vacuum. Shear samples were 25 mm diameter x 1 mm thick disks, while extensional samples were rectangular with dimensions of 17.7 mm L x 12.5 mm w x 0.8 mm h. Shear measurements were performed using a TA Instruments ARES G2 rotational rheometer equipped with a 25mm parallel plate geometry enclosed in an environmental chamber for temperature control. All samples were dried at the previous parameters before testing. Small amplitude oscillatory shear frequency sweeps were conducted using a strain of 1% at angular frequencies ranging from 0.1 to 100 rad/s for each test. Shear properties were tested at a range of 190 to 240 C in 10 C increments. Time-temperature superposition for the shear viscosity was performed using the IRIS Rheo-Hub software. Simulation Methods Flow through the C-D geometry used in the EME as well as the final EME flow channel geometry was conducted using ANSYS POLYFLOW, assuming 32

33 incompressible and isothermal flow. The equations governing the calculations were the momentum equation, given by p + T + f = ρ a (6) and the incompressibility equation, given by v = 0 (7) where p is the pressure, f is the volume force, ρ is the density, a is the acceleration, v is the velocity vector, and T is the total extra-stress tensor as described by the constitutive model for the fluid s rheological behavior. The constitutive model chosen for all simulations was a generalized Newtonian fluid with a shear rate dependency determined by the Cross model. The extra stress tensor for a generalized Newtonian fluid was given by T = 2 η D (8) where the viscosity η depends on the local shear rate, which is defined as γ = 2 tr D 2. (9) The shear-rate-dependent viscosity was described as 33

34 η(γ ) = η 0 1+(λγ ) 1 n (10) where n is the power law index, η0 is the zero shear rate viscosity, and λ is the natural time, defined as the inverse of the shear rate where the fluid begins to shear thin. The Cross model parameters used in the simulations were as follows: n = 7.2x10-1, η0 = 3521 Pa.s, and λ = 1.9x10-2 s Results and Discussion Operational Concept Validation Figure 1-1(d) shows the EME screw filled with material after operation. The flow constriction and lack of conveying capacity inherent to any static channel resulted in fully filled channels upstream of the device. In the C-D channels, the figure shows that there was a good seal of the EME to the barrel wall and no leakage between flow channels, evidenced by no material being present on the spaces between the channels. This shows that the material was forced through the EME channels properly, with all of the material undergoing the desired convergence and divergence. Finally, pressure measurements indicated that approximately 15MPa of pressure are required to force material through the inlet of the EME, and around 8MPa of pressure to push material through the reverse conveying element present at the end of the EME. This results in a total pressure drop across two elements, i.e., in the EME, of approximately 7MPa bar with the PMMA melt used for validation. Overall, the initial trials with the EME validated the functionality of 34

35 the EME design and its operational concept, and confirmed that a static mixing element in the barrel of a TSE is a feasible design. Single Channel Simulations The first computational studies were performed on a single C-D channel modeled in the dimensions of a real EME channel. The geometry, boundary conditions, and relation to the real EME of the flow channel used for these simulations is shown in Figure 1-4. This was done to evaluate the extensional characteristic of the designed flow channel based on the measured velocity profiles.. The volumetric flow rate used was 2.1x10-7 m 3 /s, converted from the 5.5 kg/hr (split among six channels for the real element geometry) throughput rate of the experimental studies, and the all of the walls were assumed to be a no-slip condition. The inflow condition assumed the flow to be fully developed. Figure 1-5(b) shows the velocity profile as it develops along the contraction. There is a clear acceleration as material flows through the converging section of the channel. Figure 1-5(a) shows a plot of the measured velocities as an average and maximum at each cross section vs. its position along the flow channel. This plot shows the velocity as linearly increasing along the channel length. The true extension rate through the hyperbolic contraction has been shown to be the slope of the line in Figure 1-5(a). [29] As previously stated, the nominal extension rate through a single C-D channel of the given geometry and flow rate was calculated using Equation (5) and was determined to be approximately 1.3 s -1, based on the average velocity. According to Figure 1-5(a), the calculated extension rate based on the average velocity in the channel was determined to be approximately 1.2 s -1, closely matching the nominal value. Also in Figure 1-5(a) were the maximum values of the velocities, which when taking 35

36 the slope of the best fit line provides the maximum extension rate in the channel, determined to be approximately 3.0 s -1, or more than half of the average. Overall, the single channel simulations confirmed the effectiveness of the implemented geometry at imparting an extension dominated flow in a controllable manner. Full Channel Simulations The outline of the geometry, boundary conditions, and naming convention for the individual channels for full element simulations is shown in Figure 1-6. The flow geometry was extracted from the solid model of the real EME used in the experimental studies, while only simulating half of the symmetrical element construction. The boundary condition at the outlet of each geometry imposed a uniform 8 MPa pressure to emulate the pressure required to push material through the reverse conveying elements in the experimental studies, and a no-slip condition was assumed for all of the walls. The inlet condition examined imposed a Cartesian velocity with a rotational component. Since the EME is constructed to sit between rotating KB elements (which are generally full) in operation, there is a rotational as well as a translational component to the flow inside the barrel of the extruder. This becomes important when considering the entrance velocity profiles of the EME, since some channels will receive a higher flow rate of material in both directions as the KBs rotate. It was therefore desired to investigate a simplified representation of this inlet condition based on the average velocity at each channel and average rotational velocity across every face of the inlet. Each channel of the EME begins with a vz component with a magnitude of m/s and a rotational velocity with a magnitude of 52.3 rad/s with a rotational axis at the center point between all of the 36

37 channels. The vz component was calculated from the flow rate through the EME in process (calculated from the throughput rate of the extruder in the experimental studies) divided by six channels, and the rotational component was converted from the 500 RPM screw speed used experimentally. Figure 1-7 shows the velocity profiles through both of the contractions using the Cartesian velocity inflow condition. The first contraction presents a transition zone before the flow stabilizes approximately halfway through the flow channel, which is an expected result when considering the strong rotational component in the entrance velocities. The second contraction evidences fully developed velocity profiles, as the flow has fully stabilized. The split entrance to the second contraction also demonstrated how the flow from two separate channels combines into one, which then undergoes the second acceleration. Figure 1-8 and Figure 1-9 depict a more in-depth view of the velocity profiles through all of the EME channels. Each of the charts in these figures presents the velocity measured at the center point of each channel at each plane in Figure 1-6. The velocity profiles exhibit linearly increasing values along the channel length, which confirms the effectiveness of the hyperbolic channel at creating the desired extensional characteristics. The true maximum extension rate through a hyperbolic contraction is given by the slope of the lines on each velocity map. [29] Figure 1-8 represents the profiles through the first contraction, with channel s calculated extension rate close to 2.5 s -1. The velocity predictions near the entrance of the first contraction are not consistent with the linearly increasing profile (with the first two values not falling on the linear fit), but after flow stabilization the desired extensional flow is present. Figure 1-9 represents the same 37

38 information for the second contraction. The half channels showed extension rates that were slightly less than half of the extension rate of the rest of the channels. The latter presented good agreement with the extension rates and entrance velocities found in the first contraction. These results further validate the use of multiple elements in succession without the hyperbolic characteristic of each contraction being compromised. While the overall magnitude of the maximum extension rate through each channel is smaller when compared to the single channels, each contraction still presents the desired extensional characteristic, and the discrepancy can be contributed to the transition zone at the beginning of the first element. Figure 1-10 displays the local shear rates through the first and second contractions of the EME, which revealed localized high shear rates close to the walls of each contraction, as expected, but very low elsewhere. Figure 1-11 displays the pressure requirements as calculated by the simulations with the transition zone. These predictions show localized areas of high and low pressure at the extreme edges of each contraction entrance, due to the rotating velocity condition. The entrance pressure was calculated as an average over the area of the entrances to all of the channels, and closely matches the experimental results. The simulations predicted a 6.5 MPa pressure drop (14.5 MPa entrance pressure) compared to a 7 MPa (15 MPa entrance pressure) pressure drop measured experimentally Conclusions The Extensional Mixing Element was developed as a new type of dispersive mixing element for twin-screw extrusion. The EME was designed to provide mixing through static, hyperbolic converging-diverging flow channels that impart extension-dominated flow on 38

39 a material system being compounded through a TSE. It interfaced directly with the screw of a traditional TSE. The flow channels of the EME were designed to impart a specific extension rate on a material flowing through them. These channels were also designed in a staggered configuration that allowed the use of multiple elements in succession and eliminated dead flow zones during operation. Overall, the mechanical design of the EME proved that a static mixing element inside a TSE was a valid concept for the design of new types of screw elements. Computational studies of the EME using ANSYS POLYFLOW showed that the centerline of each C-D channel in the final EME unit displayed the desired extensional characteristics, showing a linearly increasing velocity. The pressure requirements for the entrance to the EME channels was also computed and compared to experimental observations, showing good agreement with experimental observations. After this validation, future versions of the EME can be developed based on the knowledge of the flow happening inside the channels. For example, an EME can be designed to specifically work with a single type of material, such as low/high viscosity, filler type, and the like. This can be done by changing the geometry of the flow channels to more or less harsh contractions and using simulation to predict the pressure requirements. This design is also adaptable to any scale of TSE, limited only by the amount of pressure able to be generated safely by the equipment. Overall, the EME is a proposed solution to the question of how to easily and effectively impart extension dominated flow on a compounded polymer melt. 39

40 1-5. Figures and Tables Figure 1-1 (a) Assembled element package. (b) Disassembled element package, showing internal shafts and construction. (c) EME assembled between kneading blocks on a TSE screw, with flow paths through the element indicated. (d) Full elements after operation. (e) Half hyperbolic channel implemented for flow balance and successive element usage. 40

41 h = w u = 9 mm 2.3 mm L c = 12 mm w c = 3.5 mm Figure 1-2 Hyperbolic contraction geometry design parameters. Lc = length of the contraction, wu = entrance width of the contraction, wc = throat width of the contraction, and wz = width of channel at position z. Dimensions of the actual channels are shown. 41

42 Outlet/After EME Inlet/Before EME Measurement Locations Figure 1-3 Screw configuration for the TSE24MC. T indicates transport element, KBXX indicates kneading block at a set stagger angle, RT indicates reverse transport, and DC indicates discharge. Transport sections are abbreviated. Measurement locations before and after the EME are indicated. 42

43 Figure 1-4 Geometry and boundary conditions for single channel simulations. 43

44 Figure 1-5 (a) Average and centerline velocity measurements for single contraction with linear fit. Closed symbols represent average measurements, open symbols maximum values. (b) Plane velocity profiles at m increments along flow channel. 44

45 ω v z Figure 1-6 Geometry for full channel simulations. (b) Channel labeling convention. (c) Inflow and outflow boundary locations. (d) Boundary conditions for Cartesian inlet condition simulations, where vz is the translational velocity in the flow direction, and ω is the rotational component. 45

46 Figure 1-7 Velocity profiles for first (a) and second (b) contractions with the rotational and translational velocity inflow condition. 46

47 Figure 1-8 Centerline velocity measurements for the channels of the first contraction in the EME. 47

48 Figure 1-9 Centerline velocity predictions for the channels of the second contraction in the EME. 48

49 Figure 1-10 Shear rate profiles through the first (a) and second (b) contractions of the EME. 49

50 Figure 1-11 Inlet and outlet pressure predictions for the Cartesian inflow condition simulations. 50

51 1-6. References [5] F. N. Cogswell, Journal of Non-Newtonian Fluid Mechanics, 4, (1978). [28] A. E. Everage and R. L. Ballman, Nature, 273, (1978). [29] T. J. Ober, S. J. Haward, C. J. Pipe, J. Soulages, and G. H. McKinley, Rheologica Acta, 52, (2013). [30] M. S. N. Oliveira, M. A. Alves, F. T. Pinho, and G. H. McKinley, Experiments in Fluids, 43, (2007). 51

52 Chapter 2 Experimental Validation of Extensional Mixing Elements in a Polymer Blending Process This chapter is partially based on: S. O. Carson, J. A. Covas, and J. M. Maia, A New Extensional Mixing Element for Improved Dispersive Mixing in Twin-Screw Extrusion, Part 2: Experimental Validation for Immiscible Polymer Blends, Advances in Polymer Technology, (2016) Liquid-liquid Mixing in Twin-screw Extrusion The practical application of extensional flows for dispersive mixing operations have great implications for the capabilities of a given process. One of the main areas of application for twin-screw extrusion is the production of polymer blends, which require one or more component polymers to be broken down into suitable sizes for the blend to achieve the desired properties. Very simply, this is a liquid-liquid mixing operation. Grace [1] showed experimentally that Newtonian-Newtonian emulsions subjected to flows with strong elongational components resulted in finer morphologies and droplet breakup over a wider range of viscosity ratios when compared to shear flows. In fact, when pure shear flows are applied, Grace showed that above a viscosity ratio of approximately 4 it is effectively impossible to continue the droplet break-up process. More practically, the same phenomena has been studied for non-newtonian suspensions and was generally proven to show similar effects. [2-4] What Grace and others have showed is that materials 52

53 that are not able to be dispersed and mixed under one type of flow (i.e. shear flows in TSE) have a much greater potential to be mixed under different flow conditions (i.e. extensional flows). The conditions for deformation and breakup of droplets in Grace s studies were quantified as the ratio of the stress exerted on a droplet from the flow and the interfacial stress between the droplet and matrix. This quantity is known as the capillary number, and is displayed in Equation (1): Ca = τr σ (1) where τ is the shear stress exerted by the fluid, R is the radius of the droplet, and σ is interfacial tension. The most stable droplet form takes the shape of a sphere, where these stresses are balanced and minimize the surface to volume ratio. Above a certain critical capillary number (Cacrit), the flow stress overtakes the internal, interfacial stresses of the droplet, resulting in the drop being extended and broken up into smaller droplets. Below Cacrit, the drop will only deform under flow. The other critical parameter for droplet breakup that was investigated was the viscosity ratio between the major and dispersed phases of the mixture, defined as: η r = η d η m (2) where ηd is the viscosity of the dispersed phase and ηm is the viscosity of the major phase. The summary of Grace s experimental results is shown in Figure 2-1, which plots the critical capillary number for droplet breakup vs. the viscosity ratio for both pure shear and pure extensional flows. Independent of flow type, the minimum Cacrit for droplet breakup is found around a viscosity ratio of 1. However, shear flows were found to be completely 53

54 ineffective above viscosity ratios of 4, where extensional flows were effective over the entire range of viscosity ratios tested. In this chapter, the first studies on the experimental performance of the EME was investigated, where the dispersion states of incompatible, matched and mismatched viscosity polymer blends were studied. Blends were produced using a traditional, highly restrictive KB configuration as well as a configuration implementing the EME in addition to some KBs. Samples were taken directly out of the melt stream of the extruder using online sample collecting technology developed concurrently with the EME. The overall performances of both screw configuration were quantified using image analysis of the resulting blend morphologies Experimental Processing Equipment The TSE used for the experiments was a ThermoScientific TSE24MC 24mm corotating twin-screw extruder with a 40:1 L/D ratio. The TSE24MC extruder was specially constructed to have 14 movable pressure/temperature (P/T) transducer ports along the length of the barrel. The layout of these ports is shown in Figure 2-2. The two screw configurations used for all studies are shown in Figure 2-3. These configurations were designed to be identical other than the single mixing zone. The KB configuration included 3.25 L/D of 90 kneading block elements at this location. This kneading block geometry is neutral from the conveying point-of-view and therefore directly comparable with the EME, which is also non-conveying. The EME configuration included the EME as well as 90 kneading block elements before and after, with the total length of the mixing section equaling 3.25 L/D as well. The KB elements 54

55 before and after the EME were placed there to keep the total length of the mixing sections equal, and also due to the EME being designed to interface with the KB (instead of conveying) elements. Both configurations have a reverse conveying element placed at the exit of the described mixing sections to promote and maintain distributive mixing characteristics after the EME, to guarantee the EME channels are filled, and to guarantee enough pressure is present in the system to collect samples at the outlet (as described later). It was included in the KB geometry to make the mixing section as restrictive as possible. Screw rotation speed was set to a constant 500 RPM for all experiments. Material was fed into the extruder at a constant rate of 5.5 kg/hr for all experiments using a Brabender volumetric feeder with a single spiral screw configuration. Material was extruded through a three-hole strand die with a hole diameter of 3 mm and collected through a ThermoScientific water bath and pelletizer. Pressure measurements were taken before and after the mixing zones (as indicated in Figure 2-3) using Dynisco MDA422 transducers connected to a Dynisco 1390 instrumentation box. Temperature measurements were taken at the same locations using Pyromation JMM-B23U transducers connected a Fluke 52II thermometer. These transducers were flush-mounted to the extruder screws. Temperature readings were taken in process for all of the neat PP resins and the reported values are shown as averages between the inlet and outlet temperatures (again, as indicated in Figure 2-3). These pressure and temperature readings were taken after allowing the process to stabilize for approximately 15 minutes. All process characteristic measurements were taken in triplicate, after stopping the process and allowing it to return to a quiescent state. 55

56 The Sample Collector (SC), shown in Figure 2-4, was developed as part of an effort to characterize material development in-process along the axis of an extruder. Online measurement techniques have been implemented previously to study the evolution of blend morphologies, chemical reactions, and dispersion processes. [31-37] The SC was meant as a more universal device that would interface with any standard P/T port present on a commercial extruder. The SC acts as a three position on/off valve for the collection of material out of a P/T port, with the ability to mold a sample of any geometry (a disk in this case) directly out of the extruder. One limitation of current on-line sampling methods is the necessity of re-forming the sample after quenching into a useful form, and the SC avoids that by directly molding samples. Figure 2-4(d) shows the different operating positions of the SC: i) The closed position, where no material is flowing out, creating a plug inside the device; ii) The purge position, which is used before collecting to clear the plug out of the device, ensuring fresh material is used for the collected sample; iii) The open position, where material flows directly into the mold, or out of the device. Total time taken to collect a sample from the SC is less than one minute, from the start of the purge cycle, where the material is allowed to completely clear out, to the end of the collection cycle, where the mold and sample are removed and allowed to cool. Each sample diverts approximately 15-20g of material, depending on the amount of time the device is allowed to purge, so the main flow in the extruder is not disturbed. Samples were taken during compounding of all blends with both screw configurations at the after position indicated in Figure 2-3. Three samples of each composition and screw configuration combination were taken. 56

57 Rheological Characterization Three PS and three PP materials were thermo-rheologically characterized for this study. These were named PS1-3 and PP1-3 for the purposes of these experiments. Shear measurements were performed using a TA Instruments ARES G2 rotational rheometer equipped with a 25mm parallel plate geometry enclosed in an environmental chamber for temperature control. Small amplitude oscillatory shear frequency sweeps were conducted using a strain of 1% at angular frequencies ranging from 0.1 to 100 rad/s for each test. Shear properties were tested at a range of 200 to 300 C in 10 C increments. The complex viscosity (η*) at a given frequency obtained from these tests was assumed to be equal to the steady shear viscosity (η) at an equivalent shear rate, as stated by the Cox-Merz relation. [38] Each of the polymers tested in this study were homopolymers with simple flow and relaxation behavior, and therefore the principles of Cox-Merz were assumed to hold. Timetemperature superposition (TTS) for the shear viscosity was performed using the IRIS Rheo-Hub software. Material samples for rheological measurements were compression molded at 230 C on a compression molder for 4 min under an applied load of 8 metric tons. Samples for shear were 25 mm diameter x 1 mm thick disks. Each material was modeled as a generalized Newtonian fluid with a shear-rate dependent viscosity governed by the Cross Law, which is defined as η(γ ) = η 0 1+(λγ ) 1 n (3) where n is the power law index, η0 is the zero shear rate viscosity, and λ is the natural time, defined as the inverse of the shear rate where the fluid begins to shear thin. Four different blends were chosen as model systems to investigate, differentiated by their effective viscosity ratios, as explained later. The blends were all of 80/20 PP/PS 57

58 wt.% and were pre-mixed in 2.2kg batches before being introduced to the extruder feeder. In all cases, the dispersed phase represents the PS and the major phase the PP. Morphological Analysis All blends were characterized using scanning electron microscopy on a JEOL JSM- 6510LV SEM using a 30kV beam voltage. Disk samples taken from the SC were cut and prepared as indicated in Figure 2-4(c). The disks were first punched out and cut to a proper size for the SEM stages. The cross sectioned surface of each sample was cryo-microtomed at -30 C using a glass knife on a Leica EM UC6 microtome, using a cutting speed and thickness of 2 mm/s and 1 μm, respectively. Each sample was soaked in THF for 18 hours to extract the PS phase from the blend, in order to observe contrast. The samples were coated with gold at a thickness of 5 nm with an EMS Quorum sputter coater. The size and shape of PS phases were analyzed using ImageJ. While visible inspection was sufficient to observe general patterns, dispersion, and distribution levels, a more quantifiable method was desired to observe the relative performance of the EME and KB screw configurations. However, since the PS domain size distributions seen in all samples are highly non-uniform, with a combination of spherical and non-spherical droplet phases being observed, taking the average size of the PS domains would not yield useful information. Instead, the variation of the cumulative PS domain area ratio distribution was observed with respect to the PS domain area. The cumulative area ratio distribution was calculated by [23] F [i,j] (%) = ( i=j A [i,j] ) (4) i=j A n 58

59 where A[i,j] represents the area of the PS domain that has been ranked from the smallest to the jth domain, and An represents the total PS domain area. These values were then plotted against domain area Ai. In this way, the shape and asymmetrical size distribution of the measure agglomerate is accounted for in the statistical analysis, giving a more direct measure of the dispersive mixing capability of the two mixers. Approximately 1000 PS domains from different locations on the sample were measured for each composition and screw configuration. These measurements combined with the overall size distributions of all of the measured areas were deemed sufficient to accurately represent the state of dispersion in the samples Results and Discussion Determining Effective Viscosity Ratios The goal of this study was to compound simple, incompatible blends of differing viscosity ratios through both the KB and EME screw configurations and compare their resulting morphologies. Four different effective viscosity ratios were chosen for analysis: 0.3, 1, 3, and 10. These ratios correspond to important viscosity ratios in Grace s analysis of droplet breakup, as shown in Figure 2-1.[1] Viscosity ratios of 0.3 and 1 correspond to the region of optimal droplet break-up, (where the magnitude of the Ca necessary to breakup droplets is the lowest). As the viscosity ratio approaches 3, shear becomes progressively more ineffective at breaking up droplets (which becomes an impossibility in shear flows at ηr> 4). At a viscosity ratio of 10, it is theoretically predicted that a simple shear flow will not be able to break-up the disperse phase droplets. Even though flow in the KBs is sheardominated, there is a significant extensional component due to the squeezing motion of the 59

60 elements against the barrel walls, in the intermeshing zone between individual elements, and possibly in the opposing flow created by the reverse conveying element after the mixing section. Therefore, we expect the conventional KB screw configuration to still be able to provide droplet break-up at high viscosity ratios, but also that the EME configuration will be more efficient at doing so. To obtain the effective viscosity ratio of a given blend, consideration was made to both the approximate temperature (which will differ from the extruder set point due to viscous heating) and shear rate (which can be calculated computationally) inside the mixing sections during processing. This guarantees that the viscosity ratios inside the extruder during mixing are the effective ones and not nominal values. Table 2-1 shows the results of the temperature studies, which are displayed as averages between the measured inlet and outlet (indicated in Figure 2-3) temperatures during processing of all of the neat PP resins at increasing barrel temperatures. It was concluded that PP1 showed approximate temperature rises ranging from C, PP C, and PP C, independently of whether KBs or EMEs being used. These values were used as a guideline for choosing the approximate real temperature of mixing according to the set barrel temperature and the base PP resin being used in a given blend. Following this analysis, each material was fit to the Cross Law at each tested temperature and at shear rates between and 1000 s -1. In this way, viscosity data at all processing temperatures over a wide range of shear rates was determined for all potential material pairs. Complex viscosity vs. frequency curves for the chosen blends are shown in Figure 2-5. The areas of the processing window are highlighted between 30 and 200 s -1. These 60

61 shear rates were chosen based on the minimum and maximum shear rates present in the flow channels in the EME. To determine the viscosity ratios, Equation (2) was applied to the viscosity values in the processing window, and these are shown in Table 2-2. All viscosity ratios displayed in Figure 2-5 were calculated for the temperature of the barrel plus the ΔT calculated for the PP resin in Table 2-1. As can be seen the effective viscosity ratios of the selected material pairs are very close to the nominal values at all shear rates. This elaborate procedure to calculate the effective viscosity ratios under the real thermo-mechanical processing conditions was critical because Grace s analysis of droplet breakup was conducted for Newtonian droplets in a Newtonian matrix; therefore, it was important that the effective viscosity ratios were as independent of shear rate as possible. For the ηr =1 blends, PS3 and PP2 were chosen, and the viscosity ratios were equal to 1.0 and almost completely independent of shear rate. For ηr =10, PS3 and PP3 were chosen, and the viscosity ratio dropped as the shear rate increased, but still averaged at 10.6±0.7, which is quite acceptable. Both of these blends were processed at a barrel temperature of 200 C. For both ηr=3 (PS1 and PP3) and ηr =0.3 (PS1 and PP2), the viscosity ratios increased slightly with shear rate, but again averaged to near the desired values at 3.1±0.3 and 0.3±0.1, respectively. These blends were processed at a barrel temperature of 240 C. Pressure Profiles The inlet pressure, outlet pressure, and pressure drop measurements for all blends compounded through both the KB and EME screw configurations are shown in Table 2-3. All EME configuration processes showed much pressure drops of around one order of magnitude more when compared to the same processes using the KB configuration. The 61

62 pressure drop across a mixing zone can provide an indirect measure of the overall stress levels in the system during compounding. Another consequence of the pressure differences between the mixing geometries could be an increased motor load on the extruder: the average load was 0.40kWh for all of the KB blends and 0.43kWh for all of the EME blends. These values are very similar, even given the large pressure profile difference for each screw configuration, because the differences in pressure arise in a small axial length and both of the mixing geometries are conveying-neutral. Therefore, the EME was concluded to not significantly affect the power consumption of the process. Blend Morphology The SEM micrographs of all of the blends at the end of the respective mixing sections for both screw configurations are shown in Figure 2-6. Each image is shown as a representative sample of each composition and screw configuration. The dark droplet areas represent the extracted PS phases. In general, the EME configuration improved the dispersion and distribution of the PS over the KB configuration across all viscosity ratios. The most visible improvement was shown in the blend with ηr =3, which resulted in a very uniform droplet size and shape from the EME, compared to very elongated and uneven phases from the KB. Blends with ηr =0.3 and ηr =1 also showed noticeable improvement, with an overall smaller apparent droplet size and less elongated phases in the EME, even though these blends have the ideal viscosity ratio for droplet break-up in shear. The ηr=10 blend also showed significant improvement, with the EME configuration yielding a mix of highly elongated droplets and small droplets already broken-up and the KB configuration showing almost elongated droplets only, with little or no small droplets. 62

63 The first statistical evaluation of the droplet areas was performed by plotting the size distribution histograms of all of the measured droplets, displayed in Figure 2-7. These figures were calculated as a percentage of the total droplets measured to correct for small differences in the total number of measured areas. As previously discussed, these size distributions are highly non-uniform, with each containing a long tail of a small number of large droplets (not shown in the distribution graphs). The maximum area measured for each data set is shown in Table 2-4, which confirms a clear improvement in the dispersion of the samples produced with the EME. For all viscosity ratios, there is an increased bias towards smaller measured areas when comparing the EME to the KB configuration in the size distributions, as well as a significant decrease in the maximum measured area, indicating an increase in dispersive mixing capabilities of the process. The cumulative area ratio plots are shown in Figure 2-8. For all of these plots, the percentage of PS domains under 1 μm 2 was chosen as the metric to compare the dispersive mixing efficiencies of the screw configurations. The vertical dashed line represents this cutoff, where an increased slope between data sets indicate a better dispersed system (more domains under 1 μm 2 ). The percentage of measured droplets below this cutoff value for all of the blends is outlined in Table 2-5. Clearly, there is a great improvement in dispersion for viscosity ratios of 0.3, 1.0, and 3.0 using this cutoff criteria, with all EME blends showing ~60% of measured droplets as below 1 μm 2. The improvement is present but less so for the viscosity ratio of 10. These numbers confirm the visual inspections of the samples. Finally, the distribution of the measured aspect ratio of every droplet is shown in Figure 2-9. These values are also displayed as a percentage of the total droplets measured, 63

64 similar to the size distribution graphs. The aspect ratio of a droplet was calculated using ImageJ and is shown as the ratio of the length of major and minor axes of an ellipse fit to the droplet s outline. Since a droplet under shear at high enough viscosity ratio will elongate but not break, the aspect ratio is a useful way to compare the presence of elongated vs. spherical droplets in comparative samples. As with the size distribution graphs, there is a clear skew towards lower aspect ratios (spherical particles) when comparing the EME with KB configurations. This and all of the previously discussed image analysis suggest that the EME is a more effective dispersion tool with a wider viscosity ratio of polymer blends Conclusions This chapter compared the effectiveness of a standard TSE screw to an EME configuration in dispersing simple polymer blend systems with increasing viscosity ratios. Incompatible 80/20 wt.% polypropylene/polystyrene (PP/PS) blends of viscosity ratios of 0.3, 1, 3 and 10 at were compounded using a standard kneading block screw configuration and an experimental EME configuration. Samples at the end of the mixing sections of each screw were collected using the Sample Collector (SC), developed as a method for characterizing materials on-line along the axis of the extruder. These samples were immediately molded into a disk geometry without the need for re-melting. The cross section of these disks was then investigated using SEM after extracting the PS phase using THF, and the areas of the extracted domains were measured and ranked against each other using a cumulative area ratio distribution measurement. Visual inspections of the blends showed that the EME samples had a generally better dispersed PS morphology over all the viscosity ratios when compared to the KB 64

65 samples. In previous studies of droplet deformation under flow, it was observed that above a threshold viscosity ratio, droplets under shear will elongate almost indefinitely without breaking. In the analysis of the blend morphology, we observed extremely elongated PS phases to be more prevalent in the KB configuration samples, and greatly reduced in the EME samples that, in turn, showed smaller droplet size and lower aspect ratio. The cumulative area ratio distribution measurements showed significant improvements in the dispersion levels for all viscosity ratios. The important conclusions to be taken out of these results are: 1) the EME was successful in effectively dispersing immiscible polymer blends of varying viscosity ratios under real extrusion conditions, and 2) the comparison of the KB and EME configurations confirmed previous analyses of droplet breakup effectiveness under shear and elongation, only on a larger and more applied scale. 65

66 2-5. Figures and Tables Figure 2-1 Critical capillary number necessary to breakup Newtonian droplets in a Newtonian matrix for increasing viscosity ratios. Solid line indicates experimental data for simple shear flows, dashed line indicates elongational flow. Adapted from Manas- Zloczower, et. al. and Grace. 66

67 Figure 2-2 Sensor port arrangement for the barrel of the twin screw extruder used in this study. 67

68 Outlet/After Inlet/Before Outlet/After Inlet/Before Figure 2-3 Screw configurations for all experimental trials. (a) 90 kneading block configuration ( KB ) and (b) extensional mixing element configuration ( EME ). Relevant measurement and sampling locations are indicated. 68

69 Figure 2-4 (a) The Sample Collector (SC), attached to a P/T port of a TSE. (b) The SC attached with collected sample shown. (c) Final disk with cross sectional face indicated. (d) Cross sectional view of the SC in operation. Material flow is transverse to the extrusion direction and is indicated by arrows. Three positions are: closed during normal operation, purge to clear collection channel, and collection for flow into mold. 69

70 Figure 2-5 Complex viscosity measurements at chosen processing temperatures for all blends, with processing shear rates highlighted. 70

71 Figure 2-6 SEM micrographs of blend morphologies for all blends. Left column shows KB results, right column shows EME results. 71

72 Figure 2-7 Size distribution histograms for all measured droplet areas. Values displayed as percentage of total number of droplets measured. 72

73 Figure 2-8 Cumulative area ratio distribution measurements for all blends at all screw configurations. Dashed line at 1 μm2 for the agglomerate area represents the chosen cutoff for dispersion effectiveness. 73

74 Figure 2-9 Aspect ratio histograms for all measured droplet areas. Values displayed as percentage of total number of droplets measured. 74

75 Table 2-1 Temperature rise in mixing sections under operating conditions for both screw configurations. Displayed as averages between entrance and exit temperatures. ΔT KB +/- ΔT KB +/- ΔT KB +/- PP PP PP ΔT EME +/- ΔT EME +/- ΔT EME +/- PP PP PP Set = 200 Set = 220 Set =

76 Table 2-2 Real viscosity ratios calculated as a function of shear rate for all of the chosen blends. Shear Rate PS1/PP2 PS3/PP2 PS1/PP3 PS3/PP

77 Table 2-3 Pressure profiles for all blends compounded through both screw configurations. Outlet Inlet Outlet Inlet Viscosity Pressure Pressure ΔP Pressure Pressure ΔP Ratio (KB) (KB) (KB) (EME) (EME) (EME) bar 120 bar 20 bar 100 bar 280 bar 180 bar bar 110 bar 10 bar 80 bar 210 bar 130 bar bar 70 bar 10 bar 80 bar 160 bar 80 bar bar 85 bar 5 bar 75 bar 185 bar 110 bar 77

78 Table 2-4 Maximum measured area for each viscosity ratio and screw configuration. Maximum domain area (μm 2 ) ηr 0.3 ηr 1 ηr 3 ηr 10 KB EME

79 Table 2-5 Percentage of total measured droplets with areas under 1 μm2 as displayed from the cumulative area ratio distribution curves. % of domains w/ area < 1 μm 2 ηr 0.3 ηr 1 ηr 3 ηr 10 KB EME

80 2-6. References [1] H. P. Grace, Chemical Engineering Communications, 14, (1982). [2] D. Bourry, F. Godbille, R. E. Khayat, A. Luciani, J. Picot, and L. A. Utracki, Polymer Engineering and Science, 39, (1999). [3] S. Guido, Current Opinion in Colloid & Interface Science, 16, (2011). [4] W. J. Milliken and L. G. Leal, Journal of Non-Newtonian Fluid Mechanics, 40, (1991). [23] S. Jamali, M. C. Paiva, and J. A. Covas, Polymer Testing, 32, (2013). [31] S. Cho, J. S. Hong, S. J. Lee, K. H. Ahn, J. A. Covas, and J. M. Maia, Macromolecular Materials and Engineering, 296, (2011). [32] J. A. Covas, O. S. Carneiro, P. Costa, A. V. Machado, and J. M. Maia, Plastics Rubber and Composites, 33, (2004). [33] J. A. Covas, O. S. Carneiro, J. M. Maia, S. A. Filipe, and A. V. Machado, Canadian Journal of Chemical Engineering, 80, (2002). [34] J. A. Covas, J. M. Maia, A. V. Machado, and P. Costa, Journal of Non-Newtonian Fluid Mechanics, 148, (2008). [35] J. A. Covas, J. M. Nobrega, and J. M. Maia, Polymer Testing, 19, (2000). [36] S. Filipe, M. T. Cidade, M. Wilhelm, and J. M. Maia, Polymer, 45, (2004). [37] A. V. Machado, J. M. Maia, S. V. Canevarolo, and J. A. Covas, Journal of Applied Polymer Science, 91, (2004). [38] W. Cox and E. Merz, Journal of Polymer Science, 28, (1958). 80

81 Chapter 3 Experimental Validation of Extensional Mixing Elements for Polymer/Carbon Filler Composite Compounding This chapter is partially based on: S. O. Carson and J. M. Maia, A New Extensional Mixing Element for Improved Dispersive Mixing in Twin-Screw Extrusion, Part 3: Experimental Validation for Carbon Filler Composites, submitted Polymer/Carbon Filler Composites Since the EME displayed success in improving mixing in polymer-polymer systems, it was desired to expand its validation to studies of polymer-solid filler composites, which make up another major area of specialty polymer materials. Some of the most widely studied composites in current technologies are those that make use of carbon nanofillers, such as nanotubes or graphene nanosheets. Carbon nanotubes (high aspect ratio tubes of pure carbon) and graphene nanosheets (stacked 2D sheets of pure carbon) have both attracted considerable attention due to their potential for adding mechanical strength, electrical, and thermal conductivity among other properties to polymeric materials even at very low loading levels. As with other polymeric composites, the most important factor in determining these properties is a suitable level of dispersion of the nanofiller within the polymer matrix. Numerous methods have been employed to 81

82 achieve these ends, including dissolution of polymer and filler and subsequent removal of solvent, in-situ polymerization directly onto the fillers, and melt mixing of polymer and filler together. Of these methods, melt mixing is the most scalable, industrially viable, and environmentally friendly approach. [23, 39-46] The problems with effective dispersion of these nanofillers lies in their affinity for themselves rather than any polymers they would be mixed with. The desired state of a filler network inside a composite is individualized particles that are distributed well enough in space to create percolation. However, as produced carbon nanotubes take the form of individual tubes bundled and entangled into large agglomerates, while graphene nanosheets are supplied as similar agglomerates of stacked 2D sheets, akin to nanoclays. [43, 44] The hydrodynamic forces applied to these agglomerates during a mixing process (such as TSE) must overtake the strength of the secondary forces holding the agglomerates together to first break down these initial agglomerates, and subsequently separate individual particles from each other. [43] For fillers less complicated in structure (such as carbon black), the mechanisms by which this occurs is well known and studied. Under high stress flow conditions, agglomerates tend to rupture quickly into smaller agglomerates; at low stress, the same agglomerates erode pieces off of their surfaces. [13, 47-49] The phenomena has been observed for carbon nanotubes, but there are many more factors that influence the breakup of agglomerates and individualization of particles, such as their entangled structure, potential imperfections along their length that act as weak points under stress, and the degree of penetration and wetting into the bundles by the polymer. [39, 43] For graphene nanosheets, intercalation of polymer between the individual sheets is the most important factor to consider. [23, 42, 44] The filler network form that has been established 82

83 to be the most effective at percolation and property enhancement is a secondary agglomerate structure, where initial agglomerates are broken down and partially individualized and then re-formed in more favorable arrangements under flow conditions. This has been observed for both carbon nanotubes and graphene. [23, 39, 41, 42] Effectively applying extensional stresses during the melt mixing step of polymer composite manufacturing has to potential to greatly improve the efficiency of these processes, in that it would allow better dispersive mixing combined with the already good distributive mixing capabilities of a process like TSE. For these reasons, Chapter 3 of this dissertation focuses on the dispersion capabilities of the EME when applied to polypropylene (PP)/carbon filler composites. Carbon black (CB), multi-wall carbon nanotubes (MWCNT), and graphene nanosheets (GNS) were compounded using standard a standard KB configuration and a configuration implementing the EME. Samples of material were taken directly after the mixing zones and sections of these were investigated using optical microscopy to determine the microscopic dispersion levels of the fillers. The rheological and electrical resistivity properties of all composites were probed to determine the state of percolation and polymer-filler or filler-filler interaction in the samples Experimental Composite Fabrication and Sampling The matrix material chosen for all composites was a homopolymer polypropylene (PP), trade name Pro-fax HP403G, produced by LyondellBasell Industries (MFI C, 2.16kg). To investigate the effectiveness of the EME for different filler morphologies, three different carbon fillers were used: carbon black (Cabot Corporation 83

84 Vulcan SC-72, average particle diameter = 30nm), multi-wall carbon nanotubes (Nanocyl NC7000, average diameter = 9.5nm, average length = 1.5μm), and graphene nanosheets (XG Sciences Inc. xgnp M-15, average sheet thickness 6-8nm, average particle diameter = 15μm). All composites were compounded at 2 wt.% of filler using a ThermoScientific TSE24MC co-rotating intermeshing twin screw extruder with a 40:1 L/D ratio. Carbon black was also compounded at a level of 20 wt.% to more closely represent the typical usage of carbon black in a polymer composite. Material was pre-mixed before introduction into the extruder using a Brabender volumetric feeder at a constant rate of 4.5 kg/h. Approximately 3kg of each composite was produced for each screw configuration and composite. Material was extruded out of a three hole strand die with a hole diameter of 3mm and collected using a ThermoScientific water bath and pelletizer. Barrel temperature and screw rotational speed were kept constant at 230 C and 500rpm respectively for all compounding experiments. Two screw configurations were used, deemed the KB and EME configurations. The configurations were identical apart from the last mixing section present on the screw. This section in the KB configuration consisted of 3.25 L/D of 60 left handed rotating kneading blocks, to give a highly restrictive KB section. The EME configuration replaced 2 L/D of this section with the extensional mixing elements, which equaled two elements and two contractions. This KB configuration was loosely based on principles of nanocomposite melt blending, which indicated that increasing the residence time and specific mechanical energy of a given twin screw extrusion process improved the state of dispersion of the resulting products. [50, 51] Figure 3-1 is the placement of the mixing 84

85 section in question in relation to the P/T transducer ports along the length of the extruder barrel. These ports were used for pressure measurements before and after the mixing sections. All pressure measurements were conducted at the highlighted locations using a Dynisco MDA422 transducer connected to a Dynisco 1390 instrumentation box. Disks with a diameter of 20mm and a thickness of 1.6mm were sampled directly out of the melt stream of the extruder using the Sample Collector, a device designed as an on/off valve that interfaces directly with standard P/T ports. Its operation and effectiveness has been described previously. [52] These samples were taken from the locations indicated in Figure 3-1 and were intended to enable observation of the filler dispersion states directly after the mixing sections without any further disturbance through the extruder. Approximately 10 samples for each composite as well as neat PP were taken after a 20min stabilization period in the process. Optical Microscopy of Filler Dispersion To observe the microscopic dispersion levels of the composites, transmission light microscope images were taken on thin sections cut from the disks collected from the outlet of the mixing sections. These sections were cut using a Leica EM UC6 microtome operating at -120 C with a glass knife at a cut angle of 45. Observed sections were 5μm in thickness. The images were taken using an AmScope B120C-E1 microscope with a 4x objective. The microscope was equipped with an AmScope MD MP camera connected to the AmScope software for image capture. Each image was taken at 640x480px resolution, which resulted in a measured image area of approximately 1000x750μm. Image analysis was performed using ImageJ where the area of visible 85

86 agglomerates was measured. Approximately agglomerates were measured for each composite produced through each screw configuration. Composite Characterization All composites from both screw configurations were subjected to rheological analysis using a TA Instruments ARES G2 rotational rheometer equipped with a 25mm parallel plate geometry enclosed in an environmental chamber for temperature control. Frequency sweeps were conducted using a strain of 1% (determined to be within the linear viscoelastic range for all materials) at angular frequencies ranging from 0.05 to 350 rad/s for each test. All tests were conducted at a temperature of 200 C. Each sample was subjected to a heat soaking time of approximately two minutes inside the rheometer chamber prior to testing. Material samples for rheological measurements were compression molded at 200 C on a compression molder for 4 min under an applied load of 8 metric tons. Samples for shear were 25 mm diameter x 1 mm thick disks. Electrical resistivity testing was conducted according to ASTM D257 for volume resistivity. Measurements were carried out with a Pro-Stat PRS-812 resistance meter using two needle probes on the disks that were pressed for rheological testing. Samples were prepared by cutting the disks into square samples and applying conductive silver paint to opposite cross sectional faces, in accordance with the testing standard. Measured resistance values were converted to volume resistivity according using the equation pv = (A/t) Rv, where pv is calculated volume resistivity in Ω-cm, A is the area of the testing area in cm, t is the thickness of the sample in cm, and Rv is the measured resistance. 86

87 3-3. Results and Discussion Process Characteristics Table 3-1 compares the pressure drop across the KB and EME mixing sections, calculated as the measured inlet pressure minus the measured outlet pressure (highlighted in Figure 3-1), and the motor load in steady state, for all composite formulations and screw configurations. As we ve previously reported different material systems, pressure drops across the EME were much higher when compared to a highly restrictive kneading block section. The measured motor load on the extruder in process for all of the screw configurations and material systems indicated that the EME configuration increased the power consumption of the process for every material system, due to the increased pressure drop shown previously. However, the increase is modest, and shows that the EME does not require drastically more power to operate compared to a KB section. It is important to acknowledge that the addition of the EME indirectly alters some of the process characteristics, such as the residence time and the fill ratio of the screw. Investigations into these phenomena should be the subject of a full study. However, given the previously reported work on incompatible blends, the authors are confident that the flow type present in the EME is a dominating factor in determining its performance, regardless of the changes it makes to the process itself. Optical Microscopy: Micro-level Dispersion While the state of the individual particles within any produced composite is very important to the determination of its properties, almost equally as important is the initial 87

88 breakdown of the as-provided large agglomerates of the filler. The dispersion mechanisms of large agglomerates has been well studied for all of the filler morphologies in question, as previously discussed. Optical microscopy to observe the size of any remaining initial agglomerates has become an established method of probing dispersion in these types of composites. [23, 39, 42, 45, 50, 51] For the samples in this study, combining these measurements with the rheology and electrical resistivity measurements can provide a complete picture of the state of the filler network within the composites, and give another direct comparison of dispersion performance between the KB and EME configurations. Figure 3-2 demonstrates the qualitative level of dispersion of each one of the filler systems at the 2 wt.% loading level. Samples produced using 20 wt.% carbon black were too dark to transmit light under microscopy, so no images were taken. Visual investigation of the images suggests that there is an overall size reduction in the observed agglomerates when comparing the KB and EME configurations. This is confirmed in Figure 3-3 and Table 3-2 where the size distributions and number of measured agglomerates per unit area (N) are shown. It clear that the size distribution graphs skew towards smaller measured areas for the EME composites. For the carbon black samples, N values are very similar between the KB and EME configurations, but greatly increase for the CNT and GNS samples. Overall, from Figure 3-3 and the N values, there were many more observable areas at this microscopic size scale for the CNT and GNS, and many less for the CB. The best indication of filler dispersion capabilities of the EME versus a standard kneading block are shown in Figure 3-4, which display cumulative area ratio percentage measurements of the agglomerate plotted against the agglomerate area. This quantity has been used for measurement of microscopic dispersion in CNT and GNS, as well as previous 88

89 work conducted with the EME for incompatible blends. [23, 42, 52] The cumulative area ratio distribution is calculated by: F [i,j] (%) = ( i=j A [i,j] ) (1) i=j A n where where A[i,j] represents the area of the PS domain that has been ranked from the smallest to the jth domain, and An represents the total PS domain area. These values were then plotted against domain area Ai. The result of these graphs is the ability to quantify the percentage of measured agglomerates under a given cutoff value, where a higher percentage under this value indicates a more well dispersed system. For these measurements, a cutoff value of 400 μm 2 was chosen. It is clear that for the CB samples, the EME drastically improved the dispersion level of the samples, which the effect was much less pronounced but still significant for the CNT and GNS systems. Rheological and Electrical Properties: Nano-level Dispersion Dispersion on an individual filler particle level is important when considering final part properties and material performance. However, this study is using material properties as a further method of characterizing the morphology of the compounded material; the overall intent is not to optimize performance of the material itself, but to observe how the morphology changes as a function of mixing geometry. Viscoelastic properties have been widely employed as a method of probing the dispersion states of fillers in polymer composites. [44, 53, 54] While there are a host of rheological quantities that can be analyzed, two of most direct are the storage modulus (G ) 89

90 and the complex viscosity (η*). It has been demonstrated that well-dispersed systems of fillers (nano or otherwise) cause an increase in magnitude of viscoelastic properties, as well as a decreased dependency on frequency, resulting from the increased interaction between filler particles and polymer chains. This interaction is enhanced as the available number of well dispersed filler particles increases, making it a suitable indication for relative dispersion levels between samples of the same formulation. Along the same lines, electrical conductivity/resistivity measurements can also be an indication of meaningful filler-filler interaction in a well dispersed sample, as more pathways for conductivity will be created as fillers are dispersed and distributed throughout a polymer matrix. [41, 44, 54, 55] For both rheological and electrical properties, the loading as well as relative degree of dispersion changes with the filler morphology. Spherical carbon black will display much higher percolation thresholds when compared to anisotropic particles such as carbon nanotubes or graphene nanosheets. The 2% loading level was kept consistent for all fillers to compare how effective the EME was at dispersing different initial filler morphologies. As shown in Figure 3-5 and Figure 3-6, the storage modulus and complex viscosity values for all samples increased for all composite formulations, with more pronounced reinforcement at low frequencies. This is consistent with the previously discussed rheological indicators. Overall, all of the samples at the 2% loading level showed relatively similar reinforcement and interaction profiles, regardless of filler type or screw configuration. Similar trends in the electrical resistivity are shown in Figure 3-7, with a very slight decrease in volume resistivity from neat to filled is observed, but the improvement is modest. Significant transitions in insulator-conductor behavior are usually 90

91 indicated by larger disparities in resistivity values, on the level of several orders of magnitude. Based on these observations, none of the samples at the 2 wt.% loading level produced any composites with meaningful nanocomposite properties. This result is seemingly unusual based on both the previously reported and theoretical percolation loading levels for CB, CNT, and GNS. Typical values for this percolation threshold vary greatly between specific systems and are influenced by not only polymer type but also fabrication process. For twin screw extrusion of a thermoplastic/carbon filler composites, loading levels for both rheological and electrical percolation have been reported from <0.1 to >10 wt.%. [44, 56-59] Based on established geometric theory for high aspect ratio particles, a loading level can be calculated for which percolation should be expected to occur (percolation concentration ~ 1/aspect ratio). [43, 44] For the CNT and GNS used in this study, this value calculates to 0.6 and 0.05 vol.% (1.4 and 0.12 wt.%, based on aspect ratios of ~150 and ~1800), respectively. It is clear that both systems should theoretically be showing percolation behavior at the loading levels used. However, statistical percolation theory based on geometry assumes a random spatial distribution for all particles as well a direct contact between them. [43] Given the reality of the process by which these composites were made as well as the complicated interactions that take place between filler particles and filler-polymer matrix, it is not surprising that a truly percolating network is not being formed in these systems. What can be said, however, is that there is some level of rheological percolation based on the low frequency storage modulus and complex viscosity values; it has been reported that the loading level for percolation in rheology and 91

92 electrical resistivity can differ greatly for these types of systems. [44, 46, 55] These modest increases in viscosity at low frequencies are consistent with many studies that have investigated rheological percolation of composites, with dramatic reinforcement most often taking place at levels beyond those contained in the composites for this study. The more likely explanation for the lack of percolation in the samples is that they are simply not dispersed to the level necessary for nanocomposite reinforcement or conductivity. Many studies that cite low percolation thresholds for melt processed polymer nanocomposites do so using masterbatched starting materials, subjecting the material to a multi-step dispersion process. [39, 43] The rest of the screw profile was based off of previous studies that determined increasing the residence time and specific mechanical energy imparted on the compounded material increased the degree of dispersion seen in CNT composites. [50, 51] In this case, it seems that the dominating factor in nanodispersion of the fillers lied in the rest of the screw configuration and the number of passes through the extruder instead of the mixing section in question. The samples produced with carbon black at 2 wt.% have similar property profiles to the CNT and GNS, and while this is low from an industrial standpoint, there have been several reports of percolation with CB well below this. [56, 59] It is understood that high aspect ratio particles have an easier time forming interconnected networks. Knowing this and investigating the higher loading level of carbon black, it was expected and observed that the samples would be well above the percolation threshold for rheological reinforcement and electrical conductivity. The rheological behavior becomes very independent of frequency, suggesting that the material s behavior is almost completely dominated by the interaction of polymer chains with the dispersed filler particles. The 92

93 electrical conductivity also decreases dramatically when compared to the unfilled samples. Most interestingly, both the rheological and electrical enhancement is more pronounced for the samples produced using the EME configuration when compared to the KB. For these samples, on an individual particle level, evidence points towards the EME configuration being a more efficient dispersive mixing element and aid in forming conductive networks within the composites. Importance of Dispersion Length Scale Overall, for microscopic dispersion states of the composites produced through the KB and EME configurations, the EME clearly reduces the size of the initial agglomerates of fillers as they are added into a polymer system. However, it seems that this most obvious advantage of implementing the EME does not have a great effect on the meaningful properties of any produced composites. The EME was designed as a dispersive mixer based on the concept of using the increased stresses gained from employing extensional flows. Knowing the dispersion mechanisms for CNT and GNS, where high stress breaks up large agglomerates quickly and lower stresses erode and individualize the particles themselves, it is clear that the EME is more or less working as intended. However, it is also clear that the EME is not a singular solution, at least at this loading level. Very simply, it appears that breaking up large bundles of nanotubes or sheets of graphene into smaller bundles or sheets does not greatly improve the nanocomposite s properties. More investigation into the synergistic effects of the EME with other screw configurations (such as the location of the EME in respect to other mixing sections) is necessary to glean more information about its usefulness. Obviously, many other factors 93

94 about the process and materials also determine the final properties of any composite. This study was intended as an attempt to isolate the EME and its singular effects on the process and products. More interestingly, the effects on the percolation concentration that implementing the EME could have would be an interesting follow up study, knowing that the EME improved the agglomerate dispersion to a significant level Conclusions The Extensional Mixing Element was implemented in a twin screw extrusion process to compound composites of polypropylene and carbon black, carbon nanotubes, and graphene nanosheets. The EME has previously been validated to improve the dispersive mixing capabilities in a normal twin screw process while preserving the normal advantages of twin screw extrusion equipment. The resulting composite properties were characterized using rheology, electrical resistivity, and optical microscopy techniques. These results were compared with the same properties of the same composites produced using a similar process implementing only shear kneading blocks. The micro-level dispersion was characterized using optical microscopy and it was concluded through particle size analysis that the EME was much more effective at breaking up the initial agglomerates present in the as-produced fillers. This was expected since the dispersion mechanisms for these agglomerates are mainly stress controlled, and the EME produces higher stresses than a kneading block configuration. This is an important conclusion, since there is little chance of dispersing any fillers effectively if the initial agglomerates are still present in the process. It was concluded through the rheological measurements that the samples produced were not forming meaningful percolating 94

95 networks, despite being above the theoretical limit for percolation for the higher aspect ratio fillers. Moderate reinforcement is present in all samples indicating a weakly interacting network of individualized particles and polymer chains. However, there were not significant differences in the composite s rheological properties between those produced with kneading blocks and those produced with the EME, suggesting that nanolevel dispersion was not greatly affected by the different mixing geometries. Well above the percolation threshold for carbon black, a strongly interacting polymer-filler network was formed, shown by the almost completely solid-like behavior of the rheology. The level of reinforcement was improved when comparing the EME to the kneading block composites. The electrical resistivity measurements confirmed that the low loading level samples were well below the percolation threshold for conductivity, as expected. At the high loading level, the electrical resistivity dramatically decreased compared to the neat polymer, and also showed improvements from kneading block to EME. This also raises the point that the EME is not a singular solution, but should be considered to be another part of the processor s toolbox. Its effect on the process itself, such as the residence time or the fill ratio of the screw in operation, combined with the modularity of twin screw extrusion equipment, should be investigated further to truly understand where it sits in relation to the currently available geometries. It is clear that the possibilities of implementing the EME in combination with a smartly designed screw can create a versatile and powerful mixing process for twin screw extrusion. 95

96 3-5. Figures and Tables Figure 3-1 Positioning of key mixing sections relative to P/T ports for measurement and sample collection. 96

97 Figure 3-2 Optical micrographs of filler dispersion for all systems. Scale bar represents 200 microns. 97

98 Figure 3-3 Size distribution graphs for measured agglomerate areas, cut off at 300 square microns for clarity. 98

99 Figure 3-4 Cumulative area ratio vs. measured agglomerate area for all compositions. 99

100 Figure 3-5 G' trends for all composites and all screw configurations. 100

101 Figure 3-6 Complex viscosity trends for all composites and all screw configurations. 101

102 Figure 3-7 Volume resistivity values for all samples, with detail cutout of 20% CB. 102

103 Table 3-1 Pressure drop and motor load measurements for all material compositions. Composition KB ΔP (bar) EME ΔP (bar) KB Motor Load (kwh) EME Motor Load (kwh) Neat % CB % CB % CNT % GNS

104 Table 3-2 Number of measured agglomerates per measured area for all compositions. Composition N (units/mm2) 2% CB % CNT % GNS KB EME 104

105 3-6. References [13] I. Manas-Zloczower, Mixing and compounding of polymers : theory and practice, Hanser (2009). [23] S. Jamali, M. C. Paiva, and J. A. Covas, Polymer Testing, 32, (2013). [39] G. R. Kasaliwal, S. Pegel, A. Goldel, P. Potschke, and G. Heinrich, Polymer, 51, (2010). [40] Z. Spitalsky, D. Tasis, K. Papagelis, and C. Galiotis, Progress in Polymer Science, 35, (2010). [41] I. Alig, T. Skipa, D. Lellinger, and P. Potschke, Polymer, 49, (2008). [42] C. Vilaverde, R. Santos, M. Paiva, and J. Covas, Composites Part A: Applied Science and Manufacturing, 78, (2015). [43] I. Alig, P. Potschke, D. Lellinger, T. Skipa, S. Pegel, G. R. Kasaliwal, et al., Polymer, 53, 4-28 (2012). [44] H. Kim, A. A. Abdala, and C. W. Macosko, Macromolecules, 43, (2010). [45] P. Potschke, A. R. Bhattacharyya, and A. Janke, European Polymer Journal, 40, (2004). [46] M. Moniruzzaman and K. I. Winey, Macromolecules, 39, (2006). [47] S. P. Rwei, I. Manas-Zloczower, and D. L. Feke, Polymer Engineering and Science, 30, (1990). [48] S. P. Rwei, I. Manas-Zloczower, and D. L. Feke, Polymer Engineering and Science, 31, (1991). 105

106 [49] S. P. Rwei, I. Manas-Zloczower, and D. L. Feke, Polymer Engineering and Science, 32, (1992). [50] T. Villmow, P. Potschke, S. Pegel, L. Haussler, and B. Kretzschmar, Polymer, 49, (2008). [51] T. Villmow, B. Kretzschmar, and P. Potschke, Composites Science and Technology, 70, (2010). [52] S. O. Carson, J. A. Covas, and J. M. Maia, Advances in Polymer Technology, (2016). [53] P. Potschke, T. D. Fornes, and D. R. Paul, Polymer, 43, (2002). [54] F. M. Du, R. C. Scogna, W. Zhou, S. Brand, J. E. Fischer, and K. I. Winey, Macromolecules, 37, (2004). [55] P. Potschke, M. Abdel-Goad, I. Alig, S. Dudkin, and D. Lellinger, Polymer, 45, (2004). [56] R. Schueler, J. Petermann, K. Schulte, and H. P. Wentzel, Journal of Applied Polymer Science, 63, (1997). [57] J. Sumfleth, S. T. Buschhorn, and K. Schulte, Journal of Materials Science, 46, (2011). [58] W. Bauhofer and J. Z. Kovacs, Composites Science and Technology, 69, (2009). [59] J. C. Huang, Advances in Polymer Technology, 21, (2002). 106

107 Chapter 4 Comparative Computational Studies Between Kneading Blocks and Extensional Mixing Element Channels of Differing Geometries This chapter is partially based on: S. O. Carson and J. M. Maia, A New Extensional Mixing Element for Improved Dispersive Mixing in Twin-Screw Extrusion, Part 4: Computational Comparisons to Kneading Blocks, submitted Simulation of Twin-screw Extrusion Processes Methods for Simulation of TSE Elements There is much value in the computational investigation of flow phenomena in a twin-screw extruder, and as such great effort has been expended into performing accurate simulations of many aspects of the process. However, the extremely complicated nature of flow inside a TSE process has created difficulty in the ability to depict true flow conditions on a screw element level. The earliest simulations of TSE elements focused on the open channeled conveying elements, with the simplest simulations representing each element as a continuous 1-dimensional channel where the flow is approximated to be drag flow. [60, 61] This concept was expanded on by using more sophisticated 2 and 3-dimensional geometries to study the same elements as well as kneading blocks. [62-70] Another common method of evaluating the flow inside the TSE elements is through particle tracking 107

108 analysis where a number of massless, volumeless particles are displaced through the measured velocity fields in the simulation, and their positions are tracked to indicate the degree of mixing in the process. [63, 66, 70, 71] Overall, the many different methods that have been developed for the purposes of simulating twin-screw extruders vary greatly in approach, complication, and advantages/disadvantages. Analysis of Flow and Mixing in Kneading Blocks The most interesting of these simulations in regards to the study of the Extensional Mixing Elements are the studies pertaining to full 3-dimensional analysis of kneading blocks. Since full 3D analysis is not limited by geometrical factors, it has the potential for the most accurate simulations possible when characterizing the pressure, temperature, residence time, and overall flow field inside a TSE. Since a few pioneering studies of full 3D kneading block geometries, many have expanded upon them to iterate the accuracy and sophistication. Finite element analysis (FEA), a method by which 3D geometries are broken down into elemental segments where flow calculations are performed, has proven to be a valid and simple way to visualize flow in a screw element. The group of Manas- Zloczower studied the mixing efficiency of both conveying and kneading elements using FEA by solving sequential geometries with different angles that represented the full rotation of one element or set of elements. [62-64] By quantifying statistics about the flow fields such as the interfacial area generated, velocity profiles, mixing index (degree of shear vs. extensional flow), shear rate, and shear stress, they were able to provide a comprehensive picture of the mixing profile in conveying and multiple types of kneading blocks. 108

109 Building off of those simulations, FEA techniques were developed that overlayed separate 3D geometries with separate elemental profiles that were very successful in both iso and non-isothermal calculations of TSE elements. [70, 72] This Mesh Superposition Technique (MST) basically operates by overlaying two or more elemental meshes and defining their characteristics separately. In the case of a TSE, a fluid mesh representing the inside of the barrel without the screws is overlayed with meshes for each one of the screws; material properties such as shear rate dependent viscosity are imposed on the fluid while the screws are defined with a rotational velocity around their axes. The simulations calculate the velocity profiles based on the effect that the motion of the screws has on the fluid elements. Using this technique, it is possible to simulate an infinite number of geometrical configurations of an extruder screw while also customizing the material properties of the process under investigation. Comparison of Flow through Extensional Mixing Elements and Kneading Blocks The purpose of this chapter is to provide a comprehensive investigation into the mixing profiles of a typical kneading block configurations using the previously discussed methods when compared to the same profiles through the channels of the extensional mixing elements. The EMEs and KBs operate on fundamentally different mixing and flow principles: the EMEs force material to undergo intense contraction flows while KBs churn and knead material around and between the rotating elements. However, both geometries are able to be simulated using FEA based on real processing parameters that have been previously investigated experimentally. [52, 73] Through these simulations, the relevant 109

110 mixing characteristics can be quantified and compared to determine overall mixing efficiency. Optimization of Next Generation EME Geometry through Simulation The other main goal of this chapter is to present a comparative study of how changing the shape of the contracting channels on the EME affects its mixing performance as well as its processing characteristics. One of the main advantages of implementing the EME is its flexibility in channel design for different material rheology and processing conditions, such as the throughput rate of the extruder or the required torque on the motor. Previously, simulations of the EME channels based on experimentally observed processing parameters have successfully matched the nominally calculated extension rates through each channel and the overall pressure drop across the elements. [73] Using these simulations as guidance, the defining geometries of the EME contractions (such as channel length, entrance and exit width, and number of channels) can be systematically varied in order to observe the relative changes on the measured process characteristics (such as overall strain, residence time, and pressure drop). Different material properties (such as inelastic vs. elastic) will also be studied to glean how the intrinsic properties of the material affect the process as well. These results will then be used to suggest the next generation of general purpose EMEs that will be manufactured, as well as provide insight into the proper method of optimization of the EME for any material and extruder combination. 110

111 4-2. Experimental Simulation Methods ANSYS POLYFLOW was used to conduct all FEA simulations for both the kneading blocks and the contracting channels of the EME, as we have described previously. [73] Flow was assumed to be incompressible and isothermal. Governing the general calculations were the momentum and incompressibility equations, given by Equation 1 and Equation 2, respectively: p + T + f = ρ a (1) v = 0 (2) where p is the pressure, f is the volume force, ρ is the density, a is the acceleration, v is the velocity vector, and T is the total extra-stress tensor as described by the constitutive model for the fluid s rheological behavior. It was desired that three different types of rheological be modeled through the FEA simulations: an inelastic shear-thinning material, a viscoelastic fluid with strain hardening extensional viscosity, and a viscoelastic fluid with no strain dependent viscosity (dubbed strain-hardening and non strain-hardening, respectively). By implementing all three, insight was gained into how the fluid s rheological behavior affected the overall process characteristics. Sophistication was added with each subsequent material model while keeping the same shear rate dependent viscosity. For the inelastic shear-thinning model, a generalized Newtonian fluid model with a shear rate dependent viscosity controlled by the Cross model was implemented. In each 111

112 simulation, POLYFLOW first calculates the extra stress tensor for a generalized Newtonian fluid, given by: T = 2 η D (3) where D is the rate of deformation tensor and the viscosity η depends on the local shear rate, which is defined as γ = 2 tr D 2. (4) The shear-rate-dependent viscosity was described as η(γ ) = η 0 1+(λγ ) 1 n (5) where n is the power law index, η0 is the zero shear rate viscosity, and λ is the natural time, defined as the inverse of the shear rate where the fluid begins to shear thin. For both of the viscoelastic flow models, the multimode Phan-Thien-Tanner (PTT) model was implemented, chosen for its proven capability of controlling the flow behavior under shear and extensional flows separately. A single mode of the PTT model was used for the simulations to enable simplicity and convergence. For the PTT model, POLYFLOW decomposes the total extra stress tensor T into two components for 112

113 assistance in simulation convergence, with T1 representing the viscoelastic stresses and T2 the purely viscous stresses. The model computes T1 as exp [ ελ η 1 tr(t 1 )] T 1 + λ [(1 ξ 2 ) T 1 + ξ 2 Δ T 1 ] = 2 η 1 D (6) where λ is the relaxation time and ξ and ε are fitting parameters that respectively control the shear and extensional behavior. η1 is the viscosity calculated as η 1 = (1 η r )η (7) η = η 1 + η 2 (8) η r = η 2 η 1 + η 2 (9) and the purely viscous component of the stress tensor T2 is computed as T 2 = 2 η 2 D (10) Specific details of the simulations and their boundary conditions will be discussed in their respective sections. 113

114 Rheological Modeling All rheological modeling was based off of the Daploy WB140HMS long chain branched polypropylene (PP) from Borealis (MFI = 2.1 g/10min at 2.16kg and 230 C). Table 4-1 summarizes the relevant rheological parameters for all material models: inelastic shear-thinning, viscoelastic non strain-hardening, and viscoelastic strain-hardening. Shear viscosity measurements were performed using a TA Instruments ARES G2 rotational rheometer equipped with a 25mm parallel plate geometry enclosed in an environmental chamber for temperature control. Small amplitude oscillatory shear measurements at a temperature of 200 C using a strain of 1% and ranging in frequency from 0.1 to 100 rad/s were performed on 25 mm diameter x 1 mm thick disks. Extensional viscosity measurements were performed at 200 C on an Anton Paar Paar Physica MCR 501 rheometer with a Sentmenat Extensional Rheometer (SER) attachment at constant rates of deformation ranging from 0.01 to 10 s -1. The relaxation spectrum shown was calculated using IRIS Rheo-Hub. Rheological behavior for all models is summarized in Figure 4-1, Figure 4-2, and Figure 4-3. The inelastic shear-thinning model was based off of the complex viscosity data obtained from the SAOS tests, and it was assumed according to the Cox-Merz principle that this was representative of the shear viscosity of the system. [38] The viscoelastic models fit both the shear and extensional behavior separately. For the strain-hardening model, the experimental data from the SAOS and extensional testing at every strain rate was fit using the PTT by adjusting the ξ and ε parameters. In the non strain-hardening model, the same parameters were adjusted to obtain a fit with where the extensional behavior closely followed that of 3η +. For both viscoelastic models, it was desired that the 114

115 shear rate dependent viscosity remain similar as well as equal to the dependency in the inelastic model. Generation 2 EME Design In our previous work on the design of the EME, the important geometrical features of the contractions were outlined as a method to control the extensional profile in each channel. Overall, the entrance and exit widths of the channels, the channel length, and the number of channels acting in parallel were determined to be the important considerations in the design phase. The first generation of the EME was designed as a conservative proof of concept with relatively mild contractions, with each element containing six contractions per screw. Knowing the design flexibility of these channels, three test configurations of the next generation of EME were designed and validated computationally alongside the original design. The geometry of the test configuration channels with full 3D representations is shown in Figure 4-4, and the designs are outlined in Table 4-2. The original configuration was dubbed L2 since the contraction was the long length (equal to 0.5 L/D of the extruder it was designed for) and the contraction ratio from entrance to exit was approximately 2:1. Expanding on this design, the L4 and L8 configurations were designed, each employing the same length of contraction but with contraction ratios of 4:1 and 8:1, respectively. Subsequently, the number of channels per element per screw for the L8 configuration needed to be reduced to 3. Finally, the last configuration that was designed was the S4, which contained a shorter contraction (equal to 0.25 L/D and a contraction ratio of approximately 4:1. The main distinguishing feature of the S4 was that it double the number of contractions per L/D of the extruder. 115

116 Flow through EME Channels The first set of simulations performed in this study was a simple investigation of flow through each EME channel design implementing all three rheological models. Boundary conditions and geometries for these simulations is shown in Figure 4-5. Single channel, contraction only, ¼ symmetry simulations were performed to reduce computational costs as well as increase the attainable level of mesh resolution. It was concluded in prior work that flow through the EME in operation is geometrically symmetrical within each individual channel and similar from channel to channel, lending validity to the simplified approach. [73] The inflow condition was imposed as a volumetric flow rate converted from a 0.45 kg/hr throughput. While this is low in regards to the normal throughput rate of the extruder that the EMEs were designed for, it was necessary for simulation convergence in the more sophisticated viscoelastic models, and still provided meaningful results. Process characteristics such as the velocity profiles, residence times, average strains, and pressure drops through each geometry were investigated as a function of rheological model. Comparison of EME and Kneading Blocks The final computational studies performed were a comparison between the mixing profiles of each EME channel with a kneading block section of equal length. The KB geometries implemented are shown in Figure 4-6 and were modeled after the 24mm extruder that the EMEs were designed for use with. The KBs were configured as a highly restrictive left handed section with a 60 stagger angle between elements. The previously 116

117 discussed Mesh Superposition Technique was used in POLYFLOW for modeling of these complex full 3D geometries. The imposed rotational speed of the KBs was 50 RPM; as with the EME channels, this speed is low comparatively to previous experimental investigations, but represented 10% of the actual speeds used, which was the same reduction in flow rate seen for the EME computations. An inflow condition was imposed on the entrance to the fluid domain at the same volumetric flow rate for the 0.45 kg/hr throughput rate. The inelastic shear-thinning model was the only one to reach convergence in simulation of the KBs. Overall, comparing the shear vs. extensional flow fields as well as the magnitude of stress in all of the investigated geometries provided insight into their relative mixing capabilities Results and Discussion EME vs. Kneading Blocks Since the EMEs are posited as a solution to increase the amount of extensional flow imparted on a compounded material, it was important to examine the overall character of the flow in all of the contracting channels as well as the kneading block. To do this, a quantity called the Mixing Index λ was employed, which is a numeric measurement of the influence of rotational components on the flow field. It is calculated as: λ = D D+ ω (11) 117

118 where D is the magnitude of the rate of deformation tensor and ω is the magnitude of the vorticity tensor. [63] Values of the Mixing Index range from 0 to 1.0, with 0 being purely rotational flow, 0.5 being purely shear flow, and 1.0 being purely extensional flow. Figure 4-7 displays the 3D representation of the Mixing Index values of the fluid elements for all of the contractions and the kneading block. More importantly, it also shows the location and quantity of fluid elements with Mixing Index values between 0.6 and 1.0, which are the more extension dominated areas of the flow. For each contraction, there is a clear concentration of these values along the centerline and in the middle of the channels, as expected. In the kneading blocks, these elements are concentrated around the areas of squeezing flow between the individual elements. Figure 4-8 and Table 4-3 quantify these values in distribution charts (displayed in percentage of total measurements) as well as averages and maximums as measured in the fluid elements. Average values were weighted with the volume of each measured fluid element. In the distributions, a majority of the flow is shown to be shear-dominated/extension-biased for all of the channels as well as the KBs. However, in the contracting channels, there is more of a presence of highly extension dominated elements. The average values for all of the geometries is very similar, but the maximum measured value is much higher in all of the contracting channels. More detailed interpretation of these values are examined in Table 4-3, where the percentage of measurements between 0.4 and 0.6 (dubbed shear biased), 0.6 and 0.8 (dubbed extension biased), and 0.8 and 1.0 (dubbed extension dominated) are compared for all geometries. While the KBs seem to display more extension biased flow fields overall, there are almost no extension dominated elements present when compared to any of the contractions. This table also calculates the average value of the magnitude of the 118

119 stress tensor, concluding that the more aggressive contraction configurations come close in stress magnitude to the kneading block. However, it should be noted that there are up to 24 total contractions in each real EME, causing the fluid elements to undergo this stress multiple times in process. Optimization of EME Geometry Since the first experimental configuration of the EME was designed to be mild based on unknowns of how the concept would interact with the extruder, the next computational investigation was geared towards the optimization of the contraction geometry for production of the next elements. Previously, the markers for EME performance in computation were the calculated strain rates through each channel as well as the pressure drop. These were calculated along with the average residence time and average strain, and all values were compared between the previously described rheological models. Figure 4-9 illustrates the velocity profiles as a function of channel length for each contraction. The values on the chart represent the average velocity at each plane cut in the figures. Each demonstrates a linearly increasing velocity along the channel length, with a calculated extension rate being equal to the fit line of these values. [29, 30] The calculated extension rate increases with increasing contraction intensity, as expected. Along with this, Table 4-4 calculates the average strain through each channel, obtained by multiplying the average residence as measured by POLYFLOW by the average strain rate from the velocity profiles. Interestingly, greatly increasing the intensity (such as in the L8 configuration) results in a very similar flow profile as halving the contraction length (as in 119

120 the S4). This is important to note since the S4 configuration contains double the amount of contraction flows per unit length that any of the other configurations do, essentially doubling the amount of extensional flow seen by the material flowing through it. It should also be noted that changing the material model from inelastic to elastic to elastic strainhardening has little effect on the overall flow characteristic. Finally, Figure 4-10 and Table 4-5 show the pressure profiles and calculated pressure drops through each contraction as a function of material model, also calculating the percent change in measured pressure drop from the L2 configuration to give an idea on how drastically the pressure requirements would increase from the current unit for these future experimental geometries. For all configurations, the pressure requirements increase as the material model becomes more sophisticated, with the highest pressure requirements always coming from the strain-hardening model; this indicates that the extensional viscosity plays a large role in the processing profile of the geometries. Pressure requirements between geometries calculate as expected, with increasing intensity requiring more pressure. The L8 greatly increases the pressure requirements, and comparing it to the S4, it is clear that again for the same extensional profile, the S4 provides a more practical solution vs. the L8. The extreme entry angle into the channel of the L8 geometry could cause a slight recirculation zone, which has huge implications for the amount of pressure required for flow as well as material degradation in operation Conclusions The mixing profiles of a standard, highly restrictive kneading block section of a twin-screw extruder were investigated computationally through finite element analysis and 120

121 compared to the contracting channels of the Extensional Mixing Element. Channels of different contraction profiles were also investigated as a means of optimizing the next generation extensional mixing element geometry that would be produced for experimental use. The channels were adjusted according to the contraction ratio, number of channels operating in parallel, and channel length. Single channels were simulated as representations of the full elements. Simulations were also performed using rheological models of increasing sophistication: inelastic shear-thinning, viscoelastic with a strain-hardening extensional viscosity, and viscoelastic without strain-hardening. Investigating the Mixing Index values of all of these geometries, which quantified the degree of shear vs. extensional flow, it was clear that on average, the values were similar for both the kneading blocks and all contractions. However, looking at the distribution graphs, the contracting channels showed a higher percentage of extension dominated flow in operation, concentrated around the flow s centerline. The overall magnitude of the stress tensor in the kneading blocks was higher than any of the contracting channels, but the aggressive contractions approached the same magnitude. It was also noted that in operation, the EME subjects material to at least 12 different contractions, exposing more of the overall quantity of flowing material to high stress regions than the kneading block does. Optimization of the contracting channel geometries quantified the average extension rate, average strain, and pressure drops through each configuration, and all as a function of rheological model. It was observed that increasing the channel intensity increased the measured extension rates, strains, and pressure drops; however, it was mainly noted that the most intense contraction ratio (8:1) did not produce the most efficient 121

122 extensional flows. By keeping a modest contraction ratio (4:1) and shortening the channel, very similar extensional profiles were obtained while almost halving the pressure requirements. This shorter channel also allowed material to undergo essentially double the exposure to the extensional flows since it doubles the number of contractions per unit length. This was significant since in the design phase of new EMEs that consider different types of materials and other requirements, the tendency to increase the intensity of the contraction indefinitely may not be the most prudent solution to making a more effective geometry in practice. 122

123 4-5. Tables and Figures Figure 4-1 Frequency and shear rate dependent rheological modeling, encompassing inelastic shear-thinning (Cross), viscoelastic non-strain-hardening, and viscoelastic strainhardening. 123

124 Figure 4-2 Transient extensional viscosities for viscoelastic strain-hardening (top) and nonstrain-hardening (bottom) material models. 124

125 Figure 4-3 Trouton ratio as a function of strain for all extensional rheology tests. Closed symbols represent viscoelastic strain-hardening model, while open symbols represent nonstrain-hardening. 125

126 Figure 4-4 Full 3D representations of all simulated geometries. Left column displays actual element, right column displays flow channels extracted for simulations. 126

127 Figure 4-5 Geometry and boundary conditions for single channel, ¼ symmetry simulations. IF and OF indicate locations of inflow and outflow boundaries. 127

128 Figure 4-6 Geometry and boundary conditions for simulations of left handed rotating kneading blocks with a 60 stagger angle. 128

129 Figure 4-7 Values of the calculated mixing index at each fluid element for all contractions and KB geometries. Values between 0.6 and 1.0 are considered to be extensional flows. Shown for inelastic shear-thinning model. 129

130 Figure 4-8 Distribution charts of mixing index values displayed as percentages of total elements in each simulation. Shown for inelastic shear-thinning model. 130

131 Figure 4-9 Velocity profile cross sections and measured average velocities vs.channel position with best fit lines for each geometry. Shown for inelastic shear-thinning model. 131

132 Figure 4-10 Pressure drops through all contractions as measured by average inflow minus average outflow pressure. Shown for inelastic shear-thinning model. 132

133 Table 4-1 Rheological parameters for all models. Inelastic Shearthinning (Cross) Power Law Index, n Zero-shear Viscosity, η 0 Natural Time, λ e e01 PTT, strainhardening PTT, non-strainhardening Relaxation Modulus, G Relaxation Time, λ Viscosity, η Viscosity Ratio, η r ξ ε 2.17e e e e e e

134 Table 4-2 Geometrical values controlling extensional profiles of each simulated contraction. Contraction Contraction Contraction Exit Length (cm) Entrance Width (cm) Width (cm) L L L S

135 Table 4-3 Mixing index and stress values for all contractions and KBs. % % % Ave. Stress Ave. λ Max λ 0.4 < λ < < λ < < λ < 1.0 (Pa) L L L S KB

136 Inelastic Shearthinning Viscoelastic nonsrain-hardening Viscoelastic Strainhardening Table 4-4 Flow profile statistics for all contractions and material models. Residence Time (s) Extension Rate (1/s) Average Strain L L L S L L L S L L L S

137 Inelastic Shearthinning Viscoelastic nonsrain-hardening Viscoelastic Strainhardening Table 4-5 Pressure drop values for all contraction geometries and percent increases for all experimental geometries compared to L2. Pressure Drop (Pa) % Change from L2 L2 4.5e3 -- L4 7.8e L8 1.2e S4 9.4e L2 2.5e5 -- L4 4.0e L8 7.2e S4 5.1e L2 3.9e5 -- L4 6.2e L8 1.1e S4 7.5e

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139 [67] T. Ishikawa, T. Amano, S. I. Kihara, and K. Funatsu, Polymer Engineering and Science, 42, (2002). [68] A. S. Fard, M. A. Hulsen, H. E. H. Meijer, N. M. H. Famili, and P. D. Anderson, Macromolecular Theory and Simulations, 21, (2012). [69] A. S. Fard and P. D. Anderson, Computers & Fluids, 87, (2013). [70] T. Avalosse, Y. Rubin, and L. Fondin, Journal of Reinforced Plastics and Composites, 21, (2002). [71] T. Kajiwara, Y. Nagashima, Y. Nakano, and K. Funatsu, Polymer Engineering and Science, 36, (1996). [72] T. Avalosse and Y. Rubin, International Polymer Processing, 15, (2000). [73] S. O. Carson, J. A. Covas, and J. M. Maia, Advances in Polymer Technology, (2015). 139

140 Appendix Shear and Extensional Flow in Injection Molding: Effects on Network Formation and Electrical Properties in Conductive Polymer Composites This appendix is partially based on: S. O. Carson, J. M. Maia, and J. C. Golba, "Effects of Shear and Extensional Flows on the Electrical Properties of Polycarbonate/Carbon Nanotube Composites During Injection Molding," presented at the ANTEC, A-1. Introduction Injection Molding of Composites In its simplest form, injection molding is a method by which bulk plastics are melted and shaped into useful forms. The development of this technology has allowed polymeric materials to go beyond simple shapes and into the territory of specialty, high end products. The nature of the process is what allows this; plastic material is melted using high temperature, force, and pressure and packed into a mold cavity that represents the desired shape, often using long and complex flow patterns for the material to reach its destination. This exchange of thermal and mechanical energy from the machine to the material during the molding process can have profound effects on the final properties of the part being molded. [74] 140

141 This phenomena is more pronounced when investigating highly filled systems, where the interactions between the polymer and filler and the filler with itself add another layer of complexity to the development of properties in the injection molding cycle. Attempts have been made to characterize this development in both normal and nano-size composites. It has been shown that the energy input into a material during the injection molding cycle causes complex structural and ultimate property formation. [75] Since injection molding is such a key weapon in the plastic industry s arsenal, it is clearly important to understand exactly what happens to a material during an injection molding cycle from a thermal, rheological, and mechanical standpoint. Carbon Nanotube Composites Carbon nanotubes (CNTs) have been employed in many systems in an effort to impart mechanical strength, thermal, and electrical conductivity. [40, 46, 76] CNTs effectively impart these properties due to their high aspect ratio and worm-like structure: this gives the nanotubes more opportunities for percolation in composites. [46] Percolation is observed as the critical loading level at which the nanotubes have established enough non-covalent connections between them to create a pathway for stress transfer, or thermal and electrical conductivity. Percolation is important to characterize in nanotube composites because of their potential to percolate at much lower loading levels than traditional fillers. [58] Given the aforementioned effects of the injection molding cycle on structural formation of composites, it is obvious that injection molding of CNT composites would also be subject to the same effects. 141

142 There has a multitude of research on the properties of carbon nanotube filled polymeric composites and almost an equal amount towards understanding percolation behavior of the same composites. [58, 77-80] It has been found that the most effective percolation of CNTs within polymers is when extreme orientation is avoided. However, some orientation is preferred from this perspective, given that the nanotubes are more likely to percolate when they are stretched out as opposed to coiled up. [79]. Another factor in the percolation of CNTs is the interaction between the CNTs and the polymer in the composite; many methods have been investigated such as mechanical mixing, functionalization of CNT or polymer, among others. [46] Network Formation during Molding The area of how flow fields develop during injection molding is extremely well studied, and have been applied successfully to the analysis of polymeric composites. The development of filler networks within composites relies heavily on the influence of shear and extensional forces imposed on the melt during processing. [43, 81, 82] For carbon nanotubes specifically, it has been shown that to successfully form conductive networks, large agglomerates must be disrupted and then given an opportunity to form secondary networks (interconnections) between the tubes or groups of tubes. [43] These connections are influenced by the aforementioned flow fields, as well as nanotube/polymer interaction properties, and thermal changes on the system. [81, 82] An effective way to study the specific effects of complex injection molding flows on CNT composites is employ geometries that impart specific flow characteristics on a melt. Simple geometries such as a flat plaque will show a shear-dominated flow profile 142

143 through its cross section during molding, while contracting flows have been shown to impart extension dominated flow. [29, 30] Since both flow types are relevant to the formation of composite networks, it is interesting to study the properties of materials that are molded through them separately. Hyperbolic contractions are flow channels that impart a purely extensional flow along the centerline of the channel. This is achieved by reducing the width of the channel as a function of channel length, resulting in a flow profile that displays a linearly increasing velocity at the center point. They have been implemented as microfluidic extensional rheometers, with channel designs shown in Figure A-1 and according to Equation 1 [30]: w x = C a+z (1) where wx is the width of the channel at given position z, a = Lcwc/(wu-wc), and C = Lcwuwc /2(wu- wc). The apparent extension rate through the channel can be calculated according to Equation 2 where Q is the flow rate, ignoring any shearing effects at the walls. ε = Q L c h ( 1 w c 1 w u ) (2) The purpose of this appendix is to expand the discussion of extensional flows in processing to injection molding, which shares almost equal importance with extrusion in the plastics processing industry. Injection molding is a difficult process to systematically study due to its inherit complexity and tendency towards applied manufacturing vs. 143

144 laboratory experimentation. Isolating the effects of certain flow types on the real part properties from an industrial scale injection molding process will help further the understanding of how part design, material properties, and flow types are connected on a practical level. A-2. Experimental Composite Production and Fabrication The material system chosen for these studies was a Lexan IR 2240 polycarbonate (PC) from SABIC, Inc. Two types of CNT systems were implemented: FloTube 9000 multiwalled CNTs manufactured by CNano Technology, Ltd.. and Carbon Nanostructure (CNS) Encapsulated Flakes manufactured by Applied Nanostructured Solutions, LLC. These types of CNT systems were chosen to represent two very different initial forms of the CNT. CNano MWCNTs are typical of a normal CNT implemented into a polymer composite, with an average length of 10μm and an average diameter of 11nm, and an image of the as-synthesized morphology of the CNTs is shown in Figure A-2. [83] CNS is distinguished from normal CNT systems by their branched and entangled structure that is a result of the synthesis process, which involves growing the CNTs on a substrate and crosslinking them with themselves. This results in a system with a more dispersed initial morphology than a typical CNT. The as-synthesized morphology of CNS is shown in Figure A-3. [84] CNT was compounded into the PC at 1.5 and 3% wt. loading levels using a Leistrisz ZSE18 HP co-rotating, intermeshing twin screw extruder with an 18mm screw diameter 144

145 and 60 L/D barrel length. Processing parameters for the compounding experiments are shown in Table A-1. Injection molding trials were conducted on a Boy 90E 90 Ton injection molding machine with a screw diameter of 36mm. Samples were molded into three different geometries: a 6.4cm x 6.4cm x 0.32cm plaque using a flood gate configuration, and two hyperbolically contracting bar geometries with a thickness of 0.32cm using a fan gate. The two contracting geometries were categorized as mild and extreme and were sized off of the previously discussed equations. All geometries are seen in Figure A-4, and the hyperbolic geometries are detailed in Figure A-5. The contraction dimensions were determined by sizing the channel according to the flow length, and the geometry was mirrored to provide an even flow characteristic through the mold. Details about the injection molding process for the plaque are seen in Table A-2. Only one injection velocity was used for the plaque studies, though it is known that flow rate through the mold is a key factor in determining properties of these composites. [85, 86] The effects of injection velocity in the shear-dominated parts was not a focus of the current study. Injection molding trials the contraction geometries were conducted specifically to achieve ascending extension rates through the center of the parts, controlled by the injection velocity of the injection molding machine. The calculated extension rates through the contracting bars were calculated based on the previously discussed equations, and are shown for both bars in Table A-3. The maximum injection velocity (which determined the flow rates for the extension rate calculations) for both bars was determined by the injection pressure required and are also shown in Table A-3. Processing parameters common between both bars are shown in Table A

146 Resistivity Testing All electrical resistivity testing was conducted according to ASTM D257 using for surface and volume resistivity. Measurements were carried out with a Pro-Stat PRS-812 resistance meter using two needle probes on the surface and internals of each geometry. A diagram of the testing layout for each part can be seen in Figure A-6. Nine measurement locations were used for each plaque, which were arranged in a grid with rows labeled A, B, and C and columns labeled 1, 2, and 3. For internal testing, parts were scored along the testing outline, frozen in liquid nitrogen for 3 minutes, and broken along the score line. This was done to insure a clean and consistent break and testing surface for all of the parts. Conductive silver paint was applied to the testing areas in accordance with the testing standard. The paint was applied in 1mm thick strips using a fine paint brush. Measured resistance values were converted to surface and volume resistivity according to the following equations: p s = P g R s (3) p v = A t R v (4) In Equation 3, ps is calculated surface resistivity in Ω, P is the perimeter of the testing area in cm, g is the distance between the silver paint electrodes in cm, and Rs is the measured surface resistance. In Equation 4, pv is calculated volume resistivity in Ω-cm, A 146

147 is the area of the testing area in cm, t is the thickness of the sample in cm, and Rv is the measured resistance. Geometric details for these calculations are shown in Figure A-6. A-3. Results and Discussion Resistivity Mapping of Plaques The plaque parts were molded as a representative shear-dominated injection molding process. The following is a discussion of the observed electrical resistivity trends through the parts for both PC/CNT compositions, and how these trends correlate to the state of the CNT network. The grid setup of these graphs correspond with the physical grids that were laid out on the plaques, seen in Figure A-6. Surface resistivity measurements for the 1.5% CNano and CNS composites are shown in Figure A-7. The gate of the parts was on the edge of row 1 in all of these figures, with the arrows indicating the injection direction. Surface measurements show extremely high resistivities for the CNano, which indicates very low amounts of CNT percolation due to high velocities and shear rates during molding. This trend is uniform along the surface of the entire part. This could also be due to a migration effect where the surface of the parts is polymer rich when compared to the internals. For the CNS parts, the surface of the parts shows a much lower resistivity when compared to the CNano. This could indicate that the differing starting morphology for the CNS is mitigating some of the previously discussed flow effects. Volume resistivity measurements for the same composites are shown in Figure A- 8. For the CNano composites, volume measurements show a decreasing trend in resistivity along the length of the part, with the highest resistivity being directly after the gate. Low 147

148 shear rates in the center of the parts lessen the orientation of CNTs, which in turn leads to a higher chance of retention of an entangled and uniform network. The CNS composites again show a much lower resistivity when compared to the CNano, and also show a more uniform distribution of properties. Since the initial morphology of the CNS is more branched and dispersed, the lessened orientational effects at the center of the plaques give the network of CNTs the best chance of forming a favorably conductive network. Figure A-9 and Figure A-10 respectively show surface and volume resistivity measurements for the 3% composites. The 3% measurements display lower resistivity magnitudes and the same general trends as the 1.5%. However, the surface measurements show a slight decreasing trend, indicating that the uniformity between the surface and core is improved with higher loading levels. This also supports the previously discussed CNT migration effect, since the higher loading would allow more CNT to stay near the surface of the parts during molding. Interestingly, the 3% CNS measurement at the surface of the plaques are lower in magnitude than even the internals of the CNano parts. Overall, all of the CNS composites show much lower resistivity magnitudes when compared to all of the CNano composites. This seems to indicate that the CNS is either easier to disperse within the PC during compounding and subsequent molding, or starts in a more advantageous form before any processing takes place. Effects of Extension Rate The two extensional flow geometries were molded to observe the effects of an extremely extension dominated flow ( extreme contraction) and a mixture of shear and extension ( mild contraction). Since the only location in the part that is pure extension is 148

149 the centerline, the smaller contraction cross section of the extreme parts results in a higher percentage of the part undergoing extensional stress. For the same reason, the mild parts should display a balance between shear and extension in the same part. Figure A-11 shows the resistivities for the mild contraction parts at the surface and internal locations for both 1.5 and 3% CNano and CNS composites. As previously discussed, the injection velocity of the machine translated to different flow rates through the contraction, which translated to different extension rates at the centerline of the parts. The mild contraction, which was labeled as mix between shear and extension in the part, showed no discernible trend in resistivity for the CNano parts as the extension rate increases. The surface measurements for both compositions were very high and equal, and the internal measurements were consistent with the expected trend of increasing loading of CNano. For these parts, it is proposed that the process is still mostly shear dominated, even though the center of the parts has a purely extensional flow. Since this is the case, the CNS parts show the same relative trends as the plaque parts, with a decreased overall magnitude. The surface of the parts also shows an increasing trend. The extreme contraction parts, shown in Figure A-12, show the same trends at the surface of the parts, but show a decreasing trend as the extension rate increases for the CNano composites. The nanotube network is most likely being stretched and aligned in the extension direction. Another explanation is the discrepancy between the level of stress in shear and extension: it is generally known that for a given flow length, the magnitude of stress on the system is much greater for extension. This would increase the dispersion character of the system, and that combined with the stretching and alignment would decrease the resistivity in the system. This effect may not be as pronounced or important 149

150 for the dispersion and arrangement of the branched, crosslinked structure of the CNS, which could be why the same effect is not shown in those parts. A-4. Conclusions Two PC/CNT composites with differing initial CNT morpohologies (CNano, entangled single tubes vs. CNS, branched, crosslinked tubes) were molded into three different geometries with each giving a characteristically different flow type under processing. Flat plaque parts gave a shear characteristic, while two different hyperbolically contracting geometries gave varying degrees of shear vs. extension. The surface and internal volume resistivity of these parts were characterized as a metric to probe the state of the CNT network in the parts and how the injection molding process affected that. The plaque parts showed extreme discrepancies between the surface and the internals of the parts, and this can be attributed to the high degree of orientation at the surface vs. the low shear rate and more entangled CNT network at the center of the parts. The CNS parts showed a uniformly lower resistivity for all compositions and parts when compared to the CNano. The mild contraction, which was proposed to be a mix between shear and extension, showed the same characteristics as the plaque parts, indicating that the small area of pure extensional flow in the parts did not have much of an effect on the overall CNT network. The extreme contraction showed a decreasing trend in resistivity as the extension rate increased for the CNano, which was the most interesting observation of this study. This same trend was not present for the CNS composites, possibly indicating that this flow type does not affect the CNS to the same degree. A few important continuations need to be undertaken in order to investigate this further. It is obvious that 150

151 the different flow types observed in all injection molding processes have an effect on the final properties of composites molded through them. What is not known is how these flow types will ultimately affect the tendency of the parts and material to form conductive, desirable configurations of CNTs or any other fillers. More detailed study into the physical state of the CNTs in these parts is necessary to truly discern these phenomena, and that knowledge can ultimately translate into a useful knowledge base for the efficient production of specialty composites in the future. 151

152 A-5. Figures and Tables Figure A-1 Hyperbolic channel design. 152

153 Figure A-2 Image of as-synthesized CNano Flo-Tube

154 Figure A-3 As-synthesized morphology of CNS. Reproduced from ANS, LLC. 154

155 Figure A-4 Geometries molded for electrical resistivity studies. L to R: plaque, mild, and extreme contractions. 155

156 Mild Extreme z (cm) wz (cm) wz (cm) (Lc) Figure A-5 Hyperbolic geometry details. Channels were sized according to the position along the flow length (direction of Lc) to create the contracting geometries. 156

157 Figure A-6 Resistivity testing geometries and dimensions. 157

158 Figure A-7 Surface resistivity measurements for 1.5% PC/CNano (top) and PC/CNS (bottom) plaques. 158