Search for Controllable Order in Acicular Magnetic Dispersions

Transcription

1 Search for Controllable Order in Acicular Magnetic Dispersions John M. Wiest Department of Chemical Engineering and Center for Materials for Information Technology University of Alabama Tuscaloosa, AL The Flexible Media Team: D. T. Johnson (ChE), A. M. Lane (ChE), G. J. Mankey (Phys)., D. E. Nikles (Chem.) Anand S. Bhandar, Meihua Piao, Jerry He, Krishnamurthy Vemuru, Ilir Zoto, Tyler Holden, Joseph DeCicco, Lichun Dong, David Chae, Young-Sil Lee, Min Chen

2 Why order? Reduced noise requires thinner, smoother, more ordered magnetic layer. Order is achieved in the coating process. t' =t τ = F t' = { γ [0] ( t,t' ), S}

3 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.

4 ASSUME u Mean Field Forces (hydrodynamic, steric, magnetic, and Brownian) Forces act only at interaction sites at ends of a particle Magnetic moment fixed along particle easy axis Continuity equation for orientation distribution f t = u [[] u Ý ]f CONSIDER TEST PARTICLE u is unit vector describing particle orientation f(u,t)du is probability of particle having orientation within u and u+du at time t; assume f is spatially homogeneous [ ] u Ý is the velocity space average of and can be obtained from a force balance on the particle.

5 Numerical Solution of Diffusion Equation f t + u σ 6λ u u M S mag [( κ u κ uuu) f ] f + [ Φ + Φ ] f = 0 1 kt u Representation in terms of spherical harmonic functions: f ( u, t ) = l l= 0 m= l b lm Y l m ( u ) where blm are complex. Use properties of spherical harmonics to get: t b =I(b lm l'm', N, H,κ)

6 Order Parameter: S = uu 1 3 δ s = 3 9 tr(s S S) 2 S = 1 : perfect prolate order S = -1/2 : perfect oblate order

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

8 Field and Flow S 6λ & γ σ H

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

10 Time Dependent (Periodic) Structure Order Parameter Wagging Tumbling J > 0 Kayaking J > 0 Out of plane oscillating Flow aligning Out of plane aligning J > Log-rolling Shear Rate

11 Rheological Properties 10 1 η [Pa s] G'' γ [s 1 ] λ = 5s, σ = 0.01, L = 90nm ω [rad/s] G' ω [rad/s] Experimental Data Ψ 1 [ Pa s 2 ] λ = 5s, σ = 0.01, L = 90nm η + (Pa s) Model Parameters λ = 1s σ = 0.5 L = 100nm γ [s 1 ] t (sec)

12 Cryogenic Magnetometry to Measure Orientation: Angular Dependence of Remanence 0.8 Remanence ! M p = remanence measured parallel to the applied field! M t = remanence measured transverse to the applied field Angle (degrees) Mp (normalized) Mt (normalized)

13 Cryogenic Magnetometry to Measure Orientation: Angular Dependence of Remanence 1.2 Orientation Distribution M ( M t p + ) f ( θ) = θ 2 Calculating orientation distributions in magnetic tapes J. W. Harrell, Y. Yu, Y. Ye, J. P. Parakka, D. E. Nikles, H. G. Zolla J. Appl. Phys. 1997, 81(8) angle (degrees)

14 Orientation vs. Field (no flow) External magnetic field (Oe) MP 3.2 vol% MP 2.7 vol% MP 2.0 vol%

15 Orientation by Flow and Field: Small Angle Neutron Scattering

16 SANS Data Model Predictions

17 Conclusions We have demonstrated orientational ordering in magnetic dispersions: Ordering in the presence of an applied magnetic field via cryo-vsm and SANS Ordering in the presence of shear and field via SANS The observations are in qualitative agreement with the predictions from modeling, but the model needs refinement.

18 Questions? Comments? Concerns?