||<p>Pattern formation is a mysterious phenomenon occurring at all scales in nature.
The beauty of the resulting structures and myriad of resulting properties occurring
in naturally forming patterns have attracted great interest from scientists and engineers.
One of the most convenient experimental models for studying pattern formation are
colloidal particle suspensions, which can be used both to explore condensed matter
phenomena and as a powerful fabrication technique for forming advanced materials.
In my thesis, I have focused on the study of colloidal patterns, which can be conveniently
tracked in an optical microscope yet can also be thermally equilibrated on experimentally
relevant time scales, allowing for ground states and transitions between them to be
studied with optical tracking algorithms. </p><p>In particular, I have focused on
systems that spontaneously organize due to particle-surface and particle-particle
interactions, paying close attention to systems that can be dynamically adjusted with
an externally applied magnetic or acoustic field. In the early stages of my doctoral
studies, I developed a magnetic field manipulation technique to quantify the adhesion
force between particles and surfaces. This manipulation technique is based on the
magnetic dipolar interactions between colloidal particles and their "image dipoles"
that appear within planar substrate. Since the particles interact with their own
images, this system enables massively parallel surface force measurements (>100 measurements)
in a single experiment, and allows statistical properties of particle-surface adhesion
energies to be extracted as a function of loading rate. With this approach, I was
able to probe sub-picoNewton surface interactions between colloidal particles and
several substrates at the lowest force loading rates ever achieved. </p><p>In the
later stages of my doctoral studies, I focused on studying patterns formed from particle-particle
interaction, which serve as an experimental model of phase transitions in condensed
matter systems that can be tracked with single particle resolution. Compared with
other research on colloidal crystal formation, my research has focused on multi-component
colloidal systems of magnetic and non-magnetic colloids immersed in a ferrofluid.
Initially, I studied the types of patterns that form as a function of the concentrations
of the different particles and ferrofluid, and I discovered a wide variety of chains,
rings and crystals forming in bi-component and tri-component systems. Based on these
results, I narrowed my focus to one specific crystal structure (checkerboard lattice)
as a model of phase transformations in alloy. Liquid/solid phase transitions were
studied by slowly adjusting the magnetic field strength, which serves to control particle-particle
interactions in a manner similar to controlling the physical temperature of the fluid.
These studies were used to determine the optimal conditions for forming large single
crystal structures, and paved the way for my later work on solid/solid phase transitions
when the angle of the external field was shifted away from the normal direction.
The magnetostriction coefficient of these crystals was measured in low tilt angle
of the applied field. At high tilt angles, I observed a variety of martensitic transformations,
which followed different pathways depending on the crystal direction relative to the
in-plane field. </p><p>In the last part of my doctoral studies, I investigated colloidal
patterns formed in a superimposed acoustic and magnetic field. In this approach, the
magnetic field mimics "temperature", while the acoustic field mimics "pressure". The
ability to simultaneously tune both temperature and pressure allows for more efficient
exploration of phase space. With this technique I demonstrated a large class of particle
structures ranging from discrete molecule-like clusters to well ordered crystal phases.
Additionally, I demonstrated a crosslinking strategy based on photoacids, which stabilized
the structures after the external field was removed. This approach has potential
applications in the fabrication of advanced materials. </p><p> My thesis is arranged
as follows. In Chapter 1, I present a brief background of general pattern formation
and why I chose to investigate patterns formed in colloidal systems. I also provide
a brief review of field-assisted manipulation techniques in order to motivate why
I selected magnetic and acoustic field to study colloidal patterns. In chapter 2,
I present the theoretical background of magnetic manipulation, which is the main technique
used in my research. In this chapter, I will introduce the basic knowledge on magnetic
materials and theories behind magnetic manipulation. The underlining thermodynamic
mechanisms and theoretical/computational approaches in colloidal pattern formation
are also briefly reviewed. In Chapter 3, I focus on using these concepts to study
adhesion forces between particle and surfaces. In Chapter 4, I focus on exploring
the ground states of colloidal patterns formed from the anti-ferromagnetic interactions
of mixtures of particles, as a function of the particle volume fractions. In Chapter
5, I discuss my research on phase transformations of the well-ordered checkerboard
phase formed from the equimolar mixture of magnetic and non-magnetic beads in ferrofluid,
and I focus mainly on phase transformations in a slowly varying magnetic field. In
Chapter 6, I discuss my work on the superimposed magnetic and acoustic field to study
patterns formed from monocomponent colloidal suspensions under vertical confinement.
Finally, I conclude my thesis in Chapter 7 and discuss future directions and open
questions that can be explored in magnetic field directed self-organization in colloidal