Alignment of Platelet-Grain Ceramic Particles in Shear and Elongational Fluid Flows

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1 Alignment of Platelet-Grain Ceramic Particles in Shear and Elongational Fluid Flows Andrew Schlup Prof. Rodney Trice and Prof. Jeffrey Youngblood Purdue University, School of Materials Engineering

2 Particle Alignment can Enhance Material Properties Optical Decreased n Mechanical Crack deflection Aligned microstructures of Al 2 O 3 (top) and h-bh (bottom) Property improvements of aligned (left) vs. un-aligned (right) H. Yi, X. Mao, G. Zhou, et al. Ceram. Int. 38 (2012) R. Trice, J. Halloran, J. Am. Ceram. Soc. 82 (1999)

3 There are Several Different Methods to Align Ceramics Electrophoretic deposition Gravitational Sedimentation Magnetic field Shear/Elongational Flow High aspect-ratio particles (rods/platelets) Particles suspended in a flowing medium Shear/elongational flows cause alignment L. Zhang, et. al., J. Eur. Ceram. Soc., 30 (2010) H. Yi, X. Mao, G. Zhou, et al. Ceram. Int. 38 (2012) H. Watanabe, et. al., J. Am. Ceram. Soc. 72 (1989) S. Lienard, D. Kovar, J. Mat. Sci. 35 (2000) μm Bi 4 Ti 3 O 12 platelets h-bn platelets 3

4 Two Main Types of Alignment-Inducing Fluid Flows Shear Flow Elongational Flow Capillary Couette Different types of flow have different velocity profiles Uniaxial Biaxial Planar T. Chou, Y. Ko, M. Yan, J. Am. Ceram. Soc. 70 (1987) A. Singh, A. Rey, Liquid Crystals, 18 (1995)

5 Velocity Profiles Shear Flow 5

6 Velocity Profile of Shear Flow: Capillary Parallel, non-moving plates Pressure-driven Boundary conditions u x,cap = 0 at surface of each plate P max at x = 0 P min at x = L Parabolic gradient P u x,cap = h 0 2 P 2ηL y h 0 (1 y h 0 ) T. Chou, Y. Ko, M. Yan, J. Am. Ceram. Soc. 70 (1987) h 0 : height between plates P: pressure exerted on fluid y: incremental distance between plates η: Fluid viscosity L: length of plates 6

7 Velocity Profile of Shear Flow: Couette Parallel plates One plate moves parallel to the other stationary plate Boundary conditions Fluid velocity = plate velocity u x,cou = U at y = 0 u x,cou = o at y = h 0 ΔP = 0 Linear gradient u x,cou = U(1 y h 0 ) U: velocity of moving plate h 0 : height between plates y: incremental distance between plates T. Chou, Y. Ko, M. Yan, J. Am. Ceram. Soc. 70 (1987)

8 Velocity Profiles Elongational Flow 8

9 Applied Forces and Responses in Elongational Flow Uniaxial Biaxial Planar Applied force: tensile along a single direction Response: shrinking in other directions Applied force: compression along a single direction Response: expands in other directions Applied force: tensile along a single direction Response: shrinking in only one direction Changing cross-sectional areas A. Singh, A. Rey, Liquid Crystals, 18 (1995)

10 Velocity Profile of Uniaxial Elongational Flow dv dz = 1 Fv λ Q dv: change in velocity dz: distance along direction of flow F: force used to draw the polymer melt λ: elongational viscosity Q: volumetric flow rate N. McCrum, et. al., Priciples of Polymer Engineering 2nd Ed. (1997) Change in cross-sectional area along direction of flow + Constant volumetric flow rate = Velocity gradient along direction of flow 10

11 Shear and Elongational Flows Have Velocity Profile Gradients Shear Flow Elongational Flow Velocity changes between the boundary walls Velocity changes along direction of flow Velocity gradients cause high aspectratio ceramic particles to rotate T. Chou, Y. Ko, M. Yan, J. Am. Ceram. Soc. 70 (1987) N. McCrum, et. al., Priciples of Polymer Engineering 2nd Ed. (1997)

12 Orientation Dynamics How does a rotating particle result in alignment? 12

13 Particle Orientation is Defined by Two Angles: φ & Θ y Φ: angle with respect to x (the direction of flow) Short rod Θ: angle with respect to z This is for a rod θ φ x Similar for a platelet z Direction of flow G. Jeffery, The Motion of Ellipsoidal Particles Immersed in a Viscous Fluid, (1922) C. Tucker, et. al., Flow and Rheology in Polymer Composites Manufacturing, (1994)

14 Jeffrey s Equations are Used to Describe the Orientation of Particles in Shear/Elongational Flows Shear Flow Elongational Flow cotφ = r e tan( 2πt T + κ) tanθ = T = 2π G (r e + 1 r e ) Cr e cos 2 φ + r e 2 sin 2 φ r e = a b tanφ = tanφ 0 exp( 3 2 λεt) λ = (a b )2 1 ( a b )2 +1 t: Time T: Period of rotation κ: Phase C: Orbit constant G: Shear rate r e : Equivalent ellipsoidal axis ratio a & b : Length and diameter of particle (respectively) a > b = rod a < b = platelet G. Jeffery, The Motion of Ellipsoidal Particles Immersed in a Viscous Fluid, (1922) C. Tucker, et. al., Flow and Rheology in Polymer Composites Manufacturing, (1994) φ 0 : Initial angle θ: Constant λ: Constant that defines particle shape ε: Elongational strain t: Time a & b : Length and diameter of particle (respectively) a > b = rod a < b = platelet 14

15 Particles Have a Periodic Rotation in Shear/Elongational Flows Shear Flow Elongational Flow G. Jeffery, The Motion of Ellipsoidal Particles Immersed in a Viscous Fluid, (1922) C. Tucker, et. al., Flow and Rheology in Polymer Composites Manufacturing, (1994)

16 Orientation Dynamics Particle rotation in shear flow 16

17 y Periodic Rotation in Shear Flow: φ *Dilute suspension Direction of shear flow φ x t 1 t 2 t 3 t 4 t 5 t 6 t 7 t 8 t 9 t 10 t 11 t 12 t 13 C. Tucker, et. al., Flow and Rheology in Polymer Composites Manufacturing, (1994)

18 Periodic Rotation in Shear Flow: θ θ x *Dilute suspension Direction of shear flow z t 1 t 2 t 3 t 4 t 5 t 6 t 7 t 8 t 9 t 10 C. Tucker, et. al., Flow and Rheology in Polymer Composites Manufacturing, (1994)

19 Majority of Particle Rotation is Oriented Parallel to Direction of Flow Direction of shear flow φ: t 1 t 2 t 3 t 4 t 5 t 6 t 7 t 8 t 9 t 10 t 11 t 12 Θ: Particle alignment C. Tucker, et. al., Flow and Rheology in Polymer Composites Manufacturing, (1994)

20 Concentrated Suspensions Result in Particle-Interaction Previous description is for dilute suspensions For concentrated suspensions: Rotary Diffusion Model Particles rotate until they collide with an adjacent particle Both particles rotations are disrupted Steady-state orientation distribution reached after finite time. Direction of shear flow F. Folgar, C. Tucker, J. Reinforced Plastics & Composites, 3 (1984) C. Tucker, et. al., Flow and Rheology in Polymer Composites Manufacturing, (1994)

21 Orientation Dynamics Particle rotation in elongational flow 21

22 Particle Motion in Elongational Flow: φ y φ x Direction of elongational flow t 1 t 2 t 3 t 4 t 5 t 6 t 7 t 8 φ 0 = 75 C. Tucker, et. al., Flow and Rheology in Polymer Composites Manufacturing, (1994)

23 Particles Rotate Monotonically Toward φ = 0 in Elongational Flow Direction of elongational flow Particle alignment C. Tucker, et. al., Flow and Rheology in Polymer Composites Manufacturing, (1994)

24 Orientation Dynamics Shear Flow Elongational Flow Particles periodically rotate Majority of rotation is parallel to direction of flow Particles monotonically orient parallel to direction of flow High aspect-ratio ceramic particles in shear/elongational flows will orient parallel to direction of flow G. Jeffery, The Motion of Ellipsoidal Particles Immersed in a Viscous Fluid, (1922) C. Tucker, et. al., Flow and Rheology in Polymer Composites Manufacturing, (1994)

25 Platelet Alignment in Ceramic Processing Tape-Casting Co-extrusion Warm-pressing 25

26 Platelet Alignment in Ceramic Processing Tape-Casting 26

27 Tape-Casting Exhibits Couette and Capillary Flows Ceramic suspension Doctor blade Mylar film pull direction Couette Stationary doctor blade = stationary top plate Moving bottom Mylar sheer = moving bottom plate Capillary Height of fluid in reservoir = pressure T. Chou, Y. Ko, M. Yan, J. Am. Ceram. Soc. 70 (1987) H. Kim, et. al., J. Am. Ceram. Soc. 89 (2006)

28 Tape-Casting Exhibits Couette and Capillary Flows Ceramic suspension Doctor Blade Doctor blade Mylar film pull direction Couette Stationary doctor blade = stationary top plate Moving bottom Mylar sheer = moving bottom plate Capillary Height of fluid in reservoir = pressure T. Chou, Y. Ko, M. Yan, J. Am. Ceram. Soc. 70 (1987) H. Kim, et. al., J. Am. Ceram. Soc. 89 (2006)

29 Tape-Casting Effectively Aligns Bi 4 Ti 3 O 12 Platelets Tape-casting direction Bi 4 Ti 3 O 12 platelets 4 μm Bi 4 Ti 3 O 12 platelets aligned via tape-casting H. Watanabe, et. al., J. Am. Ceram. Soc. 72 (1989)

30 Platelet Alignment in Ceramic Processing Co-Extrusion 30

31 Co-Extrusion Exhibits Capillary and Elongational flows Co-extrusion direction Converging heated nozzle P Polymer/ceramic feed-rod Capillary Feed-rod being pushed = pressure Uniaxial elongation Converging nozzle = changing crosssectional area S. Lienard, D. Kovar, J. Mat. Sci. 35 (2000) T. Chou, Y. Ko, M. Yan, J. Am. Ceram. Soc. 70 (1987)

32 Co-Extrusion Effectively Aligns h-bn Platelets h-bn platelets H-BN platelets aligned via co-extrusion S. Lienard, D. Kovar, J. Mat. Sci. 35 (2000)

33 Platelet Alignment in Ceramic Processing Warm-Pressing 33

34 Warm-Pressing Exhibits Capillary and Elongational flows Heated platens Polymer flow Polymer flow Ceramic platelets t 1 Thermoplastic polymer t 2 t 3 Capillary Elongational Heated platen y v 0 v 1 v 2 x Heated platen x 0 x 1 x 2 A. Singh, A. Rey, Liquid Crystals, 18 (1995)

35 Warm-Pressing Exhibits Capillary and Elongational flows Heated platens Polymer flow Polymer flow Ceramic platelets t 1 Thermoplastic polymer t 2 t 3 Capillary Elongational Heated platen y v 0 v 1 v 2 x Heated platen x 0 x 1 x 2 A. Singh, A. Rey, Liquid Crystals, 18 (1995)

36 Warm-Pressing Effectively Aligns h-bn Platelets Pressing direction h-bn platelets h-bn platelets aligned via warm-pressing S. Lienard, D. Kovar, J. Mat. Sci. 35 (2000) R. Trice, J. Halloran, J. Am. Ceram. Soc. 82 (1999)

37 Summary 37

38 Research Topic Forming Transparent Ceramics via Alignment of α-al2o3 Platelets 38

39 Transparency of Alumina is Affected by Surface Roughness, Porosity, and Grain boundaries Applications Ballistic protection, nose cones, radomes Surface Roughness Reflection of entering light Porosity n PCA-pore = 0.76 >0.1% is detrimental Grain Boundaries: α-al 2 O 3 is birefringent Reflection Refraction R. Apetz, P. van Bruggen, J. Am. Ceram. Soc. 86 (2003) CeraNova s polycrystalline alumina CeraLumina HOW DO WE IMPROVE TRANSPARENCY? Polished surfaces High density (ρ>99.9%) Particle Alignment 39

40 Particle Alignment Improves Transparency of Alumina Aligned by slip-casting under a 12T magnetic field Aligned particles = decreased n Increased in-line transmittance (Sapphire) 12T 0T Magnetic alignment not easily scalable HOW DO WE SCALE-UP ALIGNMENT? Shear/Elongational flow H. Yi, X. Mao, G. Zhou, et al. Ceram. Int. 38 (2012)

41 Goal: Use Shear/Elongational Flow to Align Alumina Platelets For Improved Transparency Processing approach: Compound platelet alumina with fugitive polymer Warm press to align platelets Burn-out polymer and hot-press Envisioned result: fully dense transparent alumina with aligned platelet microstructure RonaFlair White Sapphire, Merck KGaA D. Kovar et. al.. J. Am. Ceram. Soc. 80, (1997). R. Trice, J. Halloran, J. Am. Ceram. Soc. 82 (1999)

42 Process Used to Produce Transparent Alumina with Aligned Microstructure Compound 40 vol% platelet alumina + polymer in high-shear mixer Polymer/ceramic removed from highshear mixer Warm-press mixture in hydraulic press with heated platens (alignment step) Warm-pressed sheet Repeat Hot-press to full density Burnout polymer Cut/press into final shape Cut/stack/repeat warm-press 42

43 (104) (113) (024) (116) (018) (214) (300) Intensity Preliminary Results: Alignment and Carbon Diffusion XRD after each pressing step Increasing alignment with each pressing step Hot-pressing non-aligned alumina yields gray samples Carbon diffusion c-plane (006) (1010) XRD being performed on a cut section 7x press 6x press 5x press c-plane (006) (1010) 3x press 1x press Raw platelet powder Angle (2q) 1750 C, 1hr, 25 MPa, ~0.8mm thick, sitting on printer paper 43

44 Future Work Determine optimal sintering window Explore possible sintering aids Effect of particle alignment and particle size on optical properties Transmission Transmittance Transparency Mechanical properties Fracture stress Fracture toughness Hardness 44

45 Acknowledgements Committee Members Prof. Rodney Trice Prof. Jeffrey Youngblood Prof. Elliott Slamovich Prof. Kevin Trumble Lab mates Willy Costakis Erich Weaver Andrew Ianlo Annie Brenner Angel Peña Jorge Ramírez Peers & Friends Mitch Rencheck Allie Burch Paul Mather Matt Korey Caitlyn Clarkson Undergraduates Monica Viers Joseph Trouba Benjamin Stegman Questions? 45