Theory and Experiments Leading to Self-Assembled …...φ= 0.039 Center for Materials for Information Technology A NSF Materials Research Science and Engineering Center Cryo-VSM Results

Center for Materials for Information Technology

A NSF Materials Research Science and Engineering Center

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

John M. WiestDepartment of Chemical Engineering and

Center for Materials for Information TechnologyUniversity 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



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

Hc ~1,800 Oe

Mrδ 7 to 8 memu/cm2

SQ 0.76 to 0.81

The under layer contains TiO2 or α-Fe2O3 particles

The back coat contains carbon black for anti-static



INSIC Magnetic Tape Storage Roadmap

2001 2006 2011

Track density (tpi) 900 2,700 9,800

Bit density (kbpi) 125 250 500

Tape Thickness (µm) 8.8 5.3 3.8

Length (m) 600 1,000 1,400

Areal Density (Gb/in2) 0.11 0.68 4.9

Volumetric Density (TB/in3) 0.03 0.3 3

Tape cartridge capacity (TB) 0.10 1 10



Track density and bit density are limited by NOISE.

Thinner, Smoother, More Ordered Magnetic Layer



Double Slot-Die Coating Process



Goal: Predicting structure and rheology of dispersions in flow and magnetic fields.

Mean Field Model

• Examine only one ‘test’ particle.

• Assume that allparticles are identical.

• Assume that particlesdo not cluster.



S = 1 : perfect prolate order S = -1/2 : perfect oblate order

Order Parameter

S = uuf (u, t)du∫ − 13 δ = S nn− 13 δ where S = 92 tr(S ⋅S ⋅S)3

n



No Flow or Field

2 4 6 8-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Ord

er P

aram

eter

SN + B

N+B ~ (concentration)x (L/d)

stableunstable



S

σγλ &6 H

Field and Flow



Field and Flow

10 -3 10 -1 10 1 10 3 10 5

0.0

0.2

0.4

0.6

0.8

1.0

H = 10

H = 0.01

H = 1Ord

er P

aram

eter

S

σγλ &6



ytvx )(γ&=

Shear Flow

Steady Inception Oscillatory

22

21

)(

)(

constant

γττ

γττ

γτη

γ

&

&

&

&

zzyy

yyxx

xy

−−=Ψ

−−=Ψ

−=

=

202

201

0

0

)(

)(

)(

γττ

γττ

γτη

γγ

&

&

&

&&

zzyy

yyxx

xy

tH

−−=Ψ

−−=Ψ

−=

=

+

+

+

)sin(

)cos(

)cos(

0

0

0

t

t

t

xyωγη

ωγητ

ωγγ

&

&

&&

′′−

′−=

=



10-3 10-2 10-1 100 101 102 103 10410-3

10-2

10-1

100σ

( η−η

s)/n

kTλ

N+B= 5

.

N+B= 3N+B= 1

λγ/σ

Steady Shear Flow: Viscosity



10-3 10-2 10-1 100 101 102 103 104

10-4

10-2

100

102Ψ 1

σ2 /

nkT λ

2

.

N+B = 3

N+B = 2

N+B = 1

λγ/σ

Steady Shear Flow: First Normal Stress



Inception of Shear Flow



10-2 10-1 100 101 10210-8

10-6

10-4

10-2

100

102

N+B= 1N+B= 1.5N+B= 2

η''

/ω

λω

10-2 10-1 100 101 10210-6

10-4

10-2

100

N+B= 1N+B= 1.5N+B= 2

η'

λω

Small AmplitudeOscillatory Shear Flow



Viscosity Data Comparison

10-5 10-3 10-1 101 10310-1

100

101

102

103

104

λ = 5s, σ = 0.01, L = 90nm

.

η[P

a s ]

γ [s−1]



First Normal Stress Data Comparison

10-5 10-3 10-1 101 10310-4

10-2

100

102

104

106

108

λ = 5s, σ = 0.01, L = 90nm

.

Ψ 1[

Pa s2

]

γ [s−1]



0 5 10 15 200

5

10

15

20

25

Experimental Data

Model Parametersλ = 1sσ = 0.5L = 100nm

η+(P

a s )

t (sec)

Shear Stress Growth Data Comparison



10-3 10-1 101 103

101

102

G'

ω [rad/s]

10-3 10-1 101 103

100

101

G''

ω [rad/s]

′ G = ω ′ ′ η

′ ′ G = ω ′ η

Small AmplitudeOscillatory Shear Data Comparison



Non-Steady Flow Behavior



Small Angle Neutron Scattering in Shear and Magnetic Field

Measurements made at the Center for Neutron Research at NIST



SANS Data Model Predictions



Cryogenic Magnetometry:Angular Dependence of Remanence

Orientation Distribution

-1

-0.5

0

0.5

1

1.5

2

0 40 80 120 160

Ms (memu)Mp (memu)Mt (memu)

Rem

anen

ce (m

emu)

Angle (degrees)

Angular dependence of parallel remanence (Mp) and transverse remanence (Mt)



Particle Orientation Distribution

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 30 60 90 120 150 180angle

datafit

φ = 0.039



Cryo-VSM Results

S

σγλ &6 H

φ = 3.9%

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 100 200 300 400 500

H (Oe)



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



The Interfacial Tension Of Colloidal Dispersions

Duane Johnson

MINT Center and Department of Chemical Engineering

THE UNIVERSITY OF ALABAMA



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.




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




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)




Surface Waves

• Visualization of the interfacial deflections for a SiO2 dispersion below a layer of silicone oil.

Waves at the Interface




Interfacial Waves

500

1000

1500

2000

2500

3000

3500

0 5 10 15 20 25 30 35 40 45 50 55

Viscosity Ratio (µ+/µ)

Cri

tical

Rey

nold

s N

umbe

r


• Several predictions for the critical speed versus fluid parameters.



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)




Surface Tension of Titania Dispersion Using Ring Method

60

62

64

66

68

70

72

0 5 10 15 20Weight Percentage of TiO2(%)

Surf

ace

Tens

ion

(dyn

e/cm

pH=10pH=11




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.TS UF −=




Capillary Interaction between Particles

φ r

• The capillary interaction energy between two particles, ∆W

• Analogous to electrostatic interaction

( )qLKQW 02πγ2=∆q-1 = (∆ρg/γ)-1/2 = capillary lengthQ = r sin(φ) =capillary chargeγ = interfacial tensionρ = densityL = separation distance




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 = 60o)




Physical Explanation

• At low surface concentrations, the particles act much like surfactant molecules

( )φγ lndRTΓd G=




Physical Explanation

• At high volume percent, the interface concentration saturates.

• The capillary interaction forces dominate.

irrT

s

AW

,

∂

∂=γ




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 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.



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




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.




Interfacial Tension of Liquid Crystals

• The interfacial stress boundary condition at the LC/ isotropic interface is expressed by:

• fs is the surface free energy per unit area = γ

,

,)(

s

ssd

sse

se

τIτ

τττk

+=

⋅∇=−⋅− −+

f

222212011ss )( (0) )( kQkkQQkQQkQkQ ⋅⋅+⋅⋅⋅+⋅+⋅⋅+= ββββff

ananInnQ =

−⋅=

−= ,

31

23,

31 2SS




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

( ) ( )

( ) ( ) ( )[ ]( )[

( ) ( )]}δ

δ

δ

δδλη

S:HJSJHHJSJSHSJHHJS

JHJHHJJJJHJH

SS:JJSJJJJSJJ

SS:SSSSSS:γγτ

+⋅+⋅−⋅+⋅+⋅+

⋅++

−−⋅

−+

−−−⋅−⋅−−+

+−⋅++

−++

+−−=

25

511

3

5231

313

31

313

2251

JJ

C

JJJA

BNBNnkTs &&

Bhandar and Wiest, J. of Coll. Int. Sci., 257, 371-382, (2003)




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).




Improving Magnetic Dispersions by Applying DC Magnetic Fields

Meihua Piao, Alan M. Lane, Duane JohnsonDepartment of Chemical Engineering

The University of Alabama

Acknowledgments: Dr. D. Nikles, MINT Center, NASA EPSCoR, Simmons

Endowment Fund




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”




Magnetic Susceptometer



Magnetic Dispersion: Doublets

Doublet• Two particles aligned antiparallel to each other



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



DC On/Off Experiment

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 10 20 30 40 50 60 70

Time (seconds)

Mag

netic

Sus

cept

ibili

ty (a

.u).

100 G 400 G

800 G 1200 G

1400 G 1800 G

2200 G 2600 G

DC field off

DC field on

DC field off



Percent Increase in Magnetic Susceptibility

0%

5%

10%

15%

20%

25%

30%

0 500 1000 1500 2000 2500

DC Field (Gauss)

Perc

ent I

ncre

ase

in χ

t



Switching Field Distribution

0.0

0.2

0.4

0.6

0.8

1.0

-4000 -3000 -2000 -1000 0 1000 2000 3000 4000Applied Field (Oe)

dM/d

H



Percent Increase in Storage Modulus

0%

5%

10%

15%

20%

25%

0 500 1000 1500 2000 2500DC Field (Gauss)

Perc

ent I

ncre

ase

in S

tora

ge M

odul

us



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.



Magnetic Susceptibility of a Doublet

• Split doublets will increase the magnetic susceptibility



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

The Interfacial Tension Of Colloidal DispersionsMotivationInstabilities in the Double CoaterCurrent ExperimentsSurface WavesInterfacial WavesDesign Parameters to Avoid WavesSurface Tension of Titania Dispersion Using Ring MethodParticles at an InterfaceCapillary Interaction between ParticlesThe Capillary Interaction Energy Between particlesPhysical ExplanationPhysical ExplanationSummaryThe Interfacial Tension of Magnetic DispersionsOrder ParameterSurface Order Parameter of Liquid CrystalsInterfacial Tension of Liquid CrystalsMean Field Model for the Stress Tensor of a Magnetic DispersionGoalImproving Magnetic Dispersions by Applying DC Magnetic FieldsObjectivesMagnetic SusceptometerMagnetic Dispersion: DoubletsTheory of Doublet Break-upDC On/Off ExperimentPercent Increase in Magnetic SusceptibilitySwitching Field DistributionPercent Increase in Storage ModulusMagnetic Susceptibility of a DoubletMagnetic Susceptibility of a DoubletConclusions

Documents

Theory and Experiments Leading to Self-Assembled …...φ= 0.039 Center for Materials for Information Technology A NSF Materials Research Science and Engineering Center Cryo-VSM Results