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EXPERIMENTAL AND SIMULATED STUDY OF DIFFUSION LIMITED AGGREGATION OF SUSPENDED MAGNETIC MICROSPHERES . Group members: Rabia Aslam Chaudary (12100011) Aleena Tasneem Khan (12100127) Supervisor: Dr. Fakhar-ul-Inam. OUTLINE. Diffusion Limited Aggregation What is DLA? - PowerPoint PPT Presentation
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EXPERIMENTAL AND SIMULATED STUDY OF DIFFUSION LIMITED AGGREGATION OF SUSPENDED
MAGNETIC MICROSPHERES
Group members: Rabia Aslam Chaudary (12100011) Aleena Tasneem Khan (12100127)
Supervisor: Dr. Fakhar-ul-Inam
OUTLINE• Diffusion Limited Aggregation
– What is DLA?– The DLA Model and it’s applications– Other models– Fractal Dimensions
• Our approach to the study:– Experimental Study– Simulated study
• Past studies done of DLA clusters
DIFFUSION LIMITED AGGREGATION
What is Diffusion Limited Aggregation?
• Diffusion Limited Aggregation (DLA) is an algorithm of simple growth in which a cluster grows when individual particles are added to it through a diffusion-like process.
• Originally proposed by Witten and Sander in 1981, the model is used to study wide variety of systems from electrodeposited growth and dielectric breakdown to formation of snow flakes and lightening paths.
a. Simulated DLA of about 33,000 particles. b. High-voltage dielectric breakdown
c. Copper sulfate in an electro-deposition cell
USING THE DLA MODEL
• An animation of DLA, for the purpose of our project: Chi-Hang Lam, Applied Physics, Hong Kong Polytechnic University
Fractal Dimensions• Fractal dimension is a statistical quantity that
indicates how completely the fractal fills space.• The geometrical pattern of fractals is repeated at
every small scale• Fractals have non-integer dimension D.
• Fractal Dimension =
)ln(
lnNrD
log(no. of self similar pieces)log(magnification factor)
Fractal Dimensions• For clusters in a plane, (in 2D), the fractal dimension
D is bounded by the value D = 1.71• For clusters in space, (in 3D), the fractal dimension D
is bounded by the value D = 2.5• Fractal dimension is sensitive to the lattice structure
of the particle and to the environment of the structure.
Other models:
• The Eden Growth model:Growth of specific type of clusters like bacterial colonies and deposition of metals. Clusters growth by random accumulation of material on their boundary.
• The Ballistic Aggregation Model:If the random walks of the particles are placed by ballistic trajectories, we have the ballistic Aggregation model. It generates non-fractal Clusters characterized by a power law.
RECENT STUDIES OF THE DLA CLUSTERS
• Diffusion-Limited Aggregation, a Kinetic Critical Phenomenon (1981)
(T. A. Witten, Jr. and I. M. Sander)
Witten and Sander proposed the DLA model studying aggregates formed when a metal vapor produced by heating a plated filament was quench condensed.
• Model for the growth of electrodeposited ferromagnetic aggregates under an in-plane magnetic field (2010)
(C. Cronemberger, L. C. Sampaio, A. P. Guimarães, and P. Molho)
Effect of Increasing magnetic moment and external field on the aggregates and fractal dimensions of ferromagnetic particles.
Aggregates by simulations at different values of magnetic moment and applied magnetic field
• Aggregation of Magnetic Microspheres: Experiments and Simulations (1988)
(G. Helgesen, ' A. T. Skjeltorp, P. M. Mors, ' R. Botet, and R. Jullien)
Diffusion Limited cluster aggregation of magnetic microspheres. Complete agreement of experiment and simulation.
Aggregates formed as a result of experiment as magnetic field increases from a to d.
Simulated Results
a. Without dipolar interactions and rotational diffusion
b. Without dipolar interactions but with rotational diffusion
c. With dipolar interactions and rotational diffusion
d. Adding external magnetic field
Our model for non-magnetic and magnetic microspheres
• We are basing our model on original DLA model for both types of particles.
• First particle is placed in the center. Other particles enter from boundary of the cell undergoing a periodic boundary condition and doing Brownian movement and sticks to make aggregate.
• At each step, particles have four possibilities for its next position and they are assigned probabilities accordingly.
• For magnetic particles, the dipole moment is given by:
• Magnetic interactions between two spheres, i and j, separated by the distance ,is given by the following relation,
• We also have two dimensionless parameters, effective strength of dipole-dipole interactions and dipole-field interactions.
)6
(3dM
jiij rrr
23
2 ).)(.(3.
ij
ijjijiji
ijij r
ruruuur
D
TkBK
TkdK
B
extdf
Bdd
3
2
• The total energy of a particle at the position is given by:
• Differently from DLA, the energy difference between the current position and the four possible new positions is used to calculate the probabilities.
• According to this model, the particle moves to the region of lower energy with higher probabilities.
ir
)(.)( iTiimag rBrU
ii
iB
i P
UTkP
)1exp(
EXPERIMENTAL SETUP FOR THE DLA CLUSTER STUDY
o Study of non-magnetic particles: Particles doing Brownian motion observed by microscope and camera. Possibility of cluster aggregation.
o Study of magnetic particles: Sulfonated polystyrene magnetic microspheres with 30% iron oxide dispersed in water confined to a mono-layer.
Experimental Procedure
Experimental setup:
• Setup to vary temperature• Application of External Field
CONTROL PARAMETERS• Seed Size• Doping• Solvent• External Magnetic field• Temperature
To study: The effect on Fractal dimensions and scaling properties of the
aggregated clusters
SIMULATED STUDY OF THE DLA CLUSTER MODEL
Outline of simulationFORMATION OF LATTICE AND INTRODUCTION OF
SEED
INTRODUCTION OF PARTICLE AR A RANDOM LOCATION AND RANDOM WALK
OF THE PARTICLE (BROWNIAN MOTION)
THE PARTICLE ATTACHES TO THE SEED, WITH A PROBABILITY DEPENDENT ON
STICKING COEDDECIENT OF THE SYSTEM
NEW PARTICLE INTRODUCED AND ABOVE
STEPS REPEATED
LOOP OVER THE DESIRED NUMBER OF PARTICLES
UNTIL A CLUSTER IS FORMED
CALCULATE FRACTAL DIMENSION BY CALCULATING THE RATIO OF
NUMBER OF PARTICLES IN A CERTAIN AREA
Brownian Motion of a Particle
Some results from previous simulations
Dendritic Cluster grown in a DLA simulation with 5000 walkers on a 200 X 200 site
Spectral Dimensions for the DLA model of Colloid Growth,Paul Meakin, H. Eugene Stanley
REFERENCES
• Diffusion Limited Aggregation a Kinetic Critical Phenomenon (1981), (T. A. Witten, Jr. and I. M. Sander)
• Model for the growth of electrodeposited ferromagnetic aggregates under an in-plane magnetic field (2010) , (C. Cronemberger, L. C. Sampaio, A. P. Guimarães, and P.Molho)
• Aggregation of Magnetic Microspheres: Experiments and Simulations (1988) ,(G. Helgesen, ' A. T. Skjeltorp, P. M. Mors, ' R. Botet, and R. Jullien)
• Magnetization behavior of small particle aggregates (1998), (K N Trohidou and D Kechrakos)
• Spectral Dimension for Diffusion Limited Aggregate model for colliod growth, 1983 (Paul Meakin andK N Trohidou and H. Eugene Stanley)
• Scaling Structure of the Surface Layer of Diffusion-Limited Aggregates, 1985 (Thomas C. Halsey, Paul Meakin and Itamar Procaecia)
• Pattern Formation in Diffusion-Limited Aggregation, 1984 (Tamas Vicsek)
THANKYOU !
QUESTIONS?