Transcript ppt

Pattern formation in dipolar systems.
www.phys.ntnu.no/complex
Håvard Huru Bergene, Kanak Pal Singh Parmar, Jon Otto Fossum, Alex Hansen,
NTNU, Trondheim,
Renaud Toussaint, Eirik G. Flekkøy
University of Oslo,
Geir Helgesen,
Institute for Energy Technology, Kjeller.
Minimum energy configuration:
Dipolar particles tend to form chains
Dipole-dipole interaction energy:
U  s [13cos () ]
Extremum interaction energy

At head to tail contact
2
2
r
3
r
s
U 2
2
dd
Dipolar
moment s
d
d
3
Common competing forces and associated dimensionless numbers
AU /mgh h: system size
dd
Brownian forces from the embedding fluid
 U /kT
dd
Hydrodynamic drag for particles in viscous fluids
BU /3dvh
Gravity – dimensionless number
dd
Pattern forming dipolar systems studied:
Electric Dipoles in the
Metal-Printing-Process
Electrorheological fluids:
Structures Formed by polarizable Nanolayered Particles in electric fields
Anisotropic polarizable clay particles in oil suspension, form
bundles of chains under application of electric field.
A1, From B~1 to B1, 1.
(Dynamic regime) (Equilibrium)
Deposition of dipolar particle layers,
Gravity fall of interacting dipoles.
A
adjustable,
B1, 1.
Examples: Clay gels, about~20% by volume, Electric field ~1 kV/mm, Stabilized structure
after Time ~40 seconds.
Magnetorheological fluids:
Fluctuation dynamics of single chains
of colloidal particles
A1
Chain roughening during field reduction:
transition during melting from U>>kT toU~kT
The Brownian Worm:
Simulations
Experiments
Fe-Fluoro-Hectorite
Na-Fluoro-Hectorite
10m
Goal: pattern conservation during attraction,
brownian dynamics,
Control over pattern formation.
V=V0
 ~ 1.
B ~ 1,
scaling of the lateral fluctuations.
Ni-Fluoro-Hectorite
Natural clay
Simplest model: stokes drag,
uncorrelated random noise on each particle,
harmonic bending restoring energy.
V=0
F
Study of: Polarisibility and orientations of particles, Chain distance, Average width and width
distribution, Yield stress / rupture thresholds.
V=V0
Controlling Parameters: Applied field, Clay composition and granulometry of clay aggregates
(influence of polydispersity and particle anisotropy in these systems).
WAXS PATTERNS FROM BUNDLES OF CHAINS
W
Scaling of
RMS width W:
Inner ring is 1st Bragg peak (001) peak of clay and outer ring is due to silicone oil.
V=0
t
Control parameters:
system height, applied field and induced dipolar moment
F hydrodynamicF random0
magnetic
Left figure-without
applied electric field
and right figure with an
applied electric field
(DC) of 1.0 kV\mm.
p
1/ 2
~t
t
t
for
1/ 4
W ~t
W ~N
for
1/ 2
p
t pt N
2
t
p
for N t pt
2
: pair viscous relax. Time, N: part. number
Theoretical scaling,
together with Experimental and Numerical results:
Tool of study: Numerical simulations, contact dynamics
F FGravityFEfield FDipoleDipoleFContact
Angular plot of 1st Bragg
peak (001).
Fluctuations coupling between neighboring chains rule their
aggregation (bundle formation in electrorheological fluids, left)