Theory and Experiments Leading to Self-Assembled Magnetic Dispersions of Magnetic Tape

Transcription

1 Theory and Experiments Leading to Self-Assembled Magnetic Dispersions of Magnetic Tape John M. Wiest Department of Chemical Engineering and University of Alabama Tuscaloosa, AL The Flexible Media Team: Anand S. Bhandar, Meihua Piao D. T. Johnson (ChE), A. M. Lane (ChE), G. J. Mankey (Phys)., D. E. Nikles (Chem.), S. C. Street (Chem.), P. B. Visscher (Phys.) Jerry He, Krishnamurthy Vemuru, Ilir Zoto, Lichun Dong, David Chae, Young-Sil Lee, Mike Hawkins, Min Chen

2 Magnetic Tape TEM Cross-sections of DLT IV Tape Made by a double slot-die coating process: Magnetic layer 150 nm Under layer 1.5 µm Base film 6.8 µm Back coat 500 nm The magnetic layer contains iron particles oriented parallel to the length of the tape H c ~1,800 Oe M r δ 7 to 8 memu/cm 2 SQ 0.76 to 0.81 The under layer contains TiO 2 or α-fe 2 O 3 particles The back coat contains carbon black for anti-static

3 INSIC Magnetic Tape Storage Roadmap Track density (tpi) 900 2,700 9,800 Bit density (kbpi) Tape Thickness (µm) Length (m) 600 1,000 1,400 Areal Density (Gb/in 2 ) Volumetric Density (TB/in 3 ) Tape cartridge capacity (TB)

4 Track density and bit density are limited by NOISE. Thinner, Smoother, More Ordered Magnetic Layer

5 Double Slot-Die Coating Process

6 Goal: Predicting structure and rheology of dispersions in flow and magnetic fields. Mean Field Model Examine only one test particle. Assume that all particles are identical. Assume that particles do not cluster.

7 Order Parameter S = uuf (u,t)du 1 3 δ=s nn 1 3 δ where S = 9 3 tr(s S S) 2 n S = 1 : perfect prolate order S = -1/2 : perfect oblate order

8 No Flow or Field N+B ~ (concentration) x (L/d) stable unstable Order Parameter S N + B 6 8

9 Field and Flow S 6λ & γ σ H

10 Field and Flow 1.0 Order Parameter S H = 10 H = H = λ & γ σ

11 Shear Flow v x = γ& ( t) y Steady Inception Oscillatory & γ = constant & γ = & γ H ( t) 0 & γ = & γ cos( ωt) 0 Ψ Ψ 1 2 η = τ = ( τ = ( τ xx yy xy τ τ & γ yy zz ) ) 2 & γ 2 & γ Ψ Ψ η + = ( τ = ( τ = τ xx yy xy τ τ & γ yy zz 0 ) ) 2 0 & γ 2 0 & γ τ xy = η & γ cos( ωt) 0 η & γ sin( ωt) 0

12 Steady Shear Flow: Viscosity (η ηs) σ /nktλ N+B= 3 N+B= 5 N+B= λγ/σ

13 Steady Shear Flow: First Normal Stress Ψ 1 σ 2 / nktλ N+B = 2 N+B = 1 N+B = λγ/σ

14 Inception of Shear Flow

15 10 2 Small Amplitude Oscillatory Shear Flow η '' / ω N+B= 1 N+B= 1.5 N+B= λω η' N+B= 1 N+B= 1.5 N+B= λω

16 Viscosity Data Comparison η [Pa s] λ = 5s, σ = 0.01, L = 90nm γ [s 1 ]

17 First Normal Stress Data Comparison Ψ 1 [ Pa s 2 ] λ = 5s, σ = 0.01, L = 90nm γ [s 1 ]

18 Shear Stress Growth Data Comparison 25 η + (Pa s) Model Parameters λ = 1s σ = 0.5 L = 100nm Experimental Data t (sec)

19 Small Amplitude Oscillatory Shear Data Comparison G' ω[rad/s] 10 1 G'' 10 0 G = ω η G = ω η ω[rad/s]

20 Non-Steady Flow Behavior

21 Small Angle Neutron Scattering in Shear and Magnetic Field Measurements made at the Center for Neutron Research at NIST

22 SANS Data Model Predictions

23 Cryogenic Magnetometry: Angular Dependence of Remanence Remanence (memu) Ms (memu) Mp (memu) Mt (memu) Angle (degrees) Angular dependence of parallel remanence (M p ) and transverse remanence (M t ) Orientation Distribution

24 1.2 Particle Orientation Distribution data fit φ = angle

25 Cryo-VSM Results φ = 3.9% H (Oe) S 6λ & γ H σ

26 To Do Experiments: Rheometry Rheo-SANS flow and transverse field Cryo-VSM Co-axial Shear Magnetometry flow and parallel field Model: Polydispersity Fixed Magnetic Moments Mean Fields Spatial Inhomogeneity Equilibrium Network Structure

27 The Interfacial Tension Of Colloidal Dispersions Duane Johnson MINT Center and Department of Chemical Engineering THE UNIVERSITY OF ALABAMA

28 Motivation As the tape coatings become thinner and thinner the surface to volume ratio increases and the interfacial properties become more important. Interfacial tension plays a very important role in determining the properties and processing of the colloidal suspensions (e.g. magnetic inks). Measurements of the interfacial tension have proven to be difficult and unpredictable. THE UNIVERSITY OF ALABAMA

29 Instabilities in the Double Coater Double layer coaters create a smoother coating for high density magnetic tape. Two fluid layers coated at high speeds have many instabilities that are not present in a single coater. Fluid interface deflections Create non-uniformities in the tape Can lead to mixing of the two layers Disorients the dispersion THE UNIVERSITY OF ALABAMA

30 Current Experiments Qualitative experiments to determine which instabilities are present and which ones are important. Measuring the critical speed at which the interface deflects. Couette cell (picture and top view) THE UNIVERSITY OF ALABAMA

31 Surface Waves Visualization of the interfacial deflections for a SiO 2 dispersion below a layer of silicone oil. Waves at the Interface THE UNIVERSITY OF ALABAMA

32 Interfacial Waves Several predictions for the critical speed versus fluid parameters Critical Reynolds Number Viscosity Ratio (µ + /µ) THE UNIVERSITY OF ALABAMA

33 Design Parameters to Avoid Waves Upper viscosity increases, critical velocity increases Lower viscosity increases, critical velocity decreases Upper density increases, critical velocity increases Lower density increases, critical velocity increases Depth ratio increases, critical velocity increases (thin layer effect) THE UNIVERSITY OF ALABAMA

34 Surface Tension of Titania Dispersion Using Ring Method 72 Surface Tension (dyne/cm ph=10 ph= Weight Percentage of TiO 2 (%) THE UNIVERSITY OF ALABAMA

35 Particles at an Interface The adsorption of a particle onto an interface is typically an energetically favorable process. The total entropy is increased (shadow force). The potential energy is sometimes decreased. F = U TS THE UNIVERSITY OF ALABAMA

36 Capillary Interaction between Particles φ r The capillary interaction energy between two particles, W Analogous to electrostatic interaction W = 2πγ Q K 0 2 ( ql ) q -1 = ( ρg/γ) -1/2 = capillary length Q = r sin(φ) =capillary charge γ = interfacial tension ρ = density L = separation distance THE UNIVERSITY OF ALABAMA

37 The Capillary Interaction Energy Between particles Plot of the interaction energy between two immersed spherical particles of the same radius, r. (γ = 72 dyne/cm, ρ = 1 g cm -3, φ = 60 o ) THE UNIVERSITY OF ALABAMA

38 Physical Explanation At low surface concentrations, the particles act much like surfactant molecules d γ = Γ G RT d ( ln φ ) THE UNIVERSITY OF ALABAMA

39 Physical Explanation At high volume percent, the interface concentration saturates. The capillary interaction forces dominate. γ = W A s T, irr THE UNIVERSITY OF ALABAMA

40 Summary Interfacial tension of a colloidal dispersion can be a strong function of the particle concentration. The adsorption of particles at the interface decreases the surface tension at lower concentrations. The attractive capillary force increases the surface tension at higher concentrations. THE UNIVERSITY OF ALABAMA

41 The Interfacial Tension of Magnetic Dispersions What s different? Particles are not spherical. Orientation of particles at the interface becomes important. Magnetic interactions. Additional work terms involving the magnetic interactions. Shear rate dependence.

42 Order Parameter The orientation of the particles in the magnetic dispersions is important and sensitive to external aligning fields (shear and magnetic). Simulations show that the magnetic dispersion have smectic ordered structure. n THE UNIVERSITY OF ALABAMA

43 Surface Order Parameter of Liquid Crystals The interface can orient the particles in a liquid crystal (LC). The surface tension of the LC is dependent on the surface order orientation. The anisotropy of the surface order parameter can create tangential surface tension gradients that can cause capillary flows. THE UNIVERSITY OF ALABAMA

44 Interfacial Tension of Liquid Crystals The interfacial stress boundary condition at the LC/ isotropic interface is expressed by: k ( τ τ se + τ = f ) = τ, f s is the surface free energy per unit area = γ s I s + τ sd s se, f 2 s ( Q) = fs(0) + β11k Q k + β20q Q + β21k Q Q k + β22( k Q k) 3 1 Q = S nn 1 I, S = n a 2, n = a THE UNIVERSITY OF ALABAMA

45 Mean Field Model for the Stress Tensor of a Magnetic Dispersion A general expression for the stress tensor under external magnetic fields and shear flows τ = η γ& 1 1 3nkT λγ& s : S S + δ A ( N + B 3) S ( N + B) ( )[ J 3( JJ S JJ JJ S) ( J 2JJ : S) δ 5J S] C + JH J H JJJ J 5 [ HJ + JH + + ( H J) ( S HJ + JH S + H JS) 2( S HJ + JH S + HJ : Sδ )]} Bhandar and Wiest, J. of Coll. Int. Sci., 257, , (2003) δ S S S : 1 S S + δ 3 THE UNIVERSITY OF ALABAMA

46 Goal Derive a general model of the anisotropic surface stress tensor for the magnetic dispersion. Study the influence of the external magnetic field and shear stress on the surface properties of the magnetic dispersions. Relate these findings back to the linear instability analysis (wave generation). THE UNIVERSITY OF ALABAMA

47 Improving Magnetic Dispersions by Applying DC Magnetic Fields Meihua Piao, Alan M. Lane, Duane Johnson Department of Chemical Engineering The University of Alabama Acknowledgments: Dr. D. Nikles, MINT Center, NASA EPSCoR, Simmons Endowment Fund THE UNIVERSITY OF ALABAMA

48 Objectives To investigate the behavior of magnetic dispersions before and after applying a DC magnetic field Rheological characteristics Magnetic characteristics Investigate the break-up of doublets THE UNIVERSITY OF ALABAMA

49 Magnetic Susceptometer

50 Magnetic Dispersion: Doublets Two particles aligned antiparallel to each other Doublet

51 Theory of Doublet Break-up Particles bound antiparallel to each other Transverse DC field aligns particles and switches their magnetic moment Particles move apart and surfactant absorbs onto new surface

52 DC On/Off Experiment DC field on Magnetic Susceptibility (a.u) DC field off DC field off 100 G 400 G 800 G 1200 G 1400 G 1800 G 2200 G 2600 G Time (seconds)

53 Percent Increase in Magnetic Susceptibility 30% 25% Percent Increase in χt 20% 15% 10% 5% 0% DC Field (Gauss)

54 Switching Field Distribution dm/dh Applied Field (Oe)

55 Percent Increase in Storage Modulus 25% Percent Increase in Storage Modulus 20% 15% 10% 5% 0% DC Field (Gauss)

56 Magnetic Susceptibility of a Doublet Magnetic field created by one particle interacts with the moment of the other particle. The field pins the moment. Net decrease in magnetic susceptibility.

57 Magnetic Susceptibility of a Doublet Split doublets will increase the magnetic susceptibility

58 Conclusions DC magnetic fields can be used to better disperse magnetic particles. Breaking the doublets increases: Magnetic susceptibility Storage modulus (elasticity) Combine magnetic field with shear to produce novel mixing apparatus