Craig Maloney

Normal modes and density of states of disordered colloidal solids.

Measuring Motion Within a solid, atoms vibrate about their mean position in a series of frequencies known as the normal modes, which relate to the thermal and mechanical transport properties of the material. D. Kaya et al. (p. 656) used video microscopy to observe the motion of colloidal crystals made from microgel particles. The colloidal particles varied slightly in their properties, allowing the behavior of disordered materials to be probed. Long-wavelength plane-wave modes were observed, characteristic of perfect crystals, and a conventional elastic behavior, modified by short-wavelength features, was also observed, in spite of the disorder of the colloidal crystals. The analysis method will allow studies on the effects of different types of disorder on the structure of the normal modes and the elasticity in a range of material systems. The motion of colloidal gel particles is used to determine the mechanical and thermal properties of a disordered system. The normal modes and the density of states (DOS) of any material provide a basis for understanding its thermal and mechanical transport properties. In perfect crystals, normal modes are plane waves, but they can be complex in disordered systems. We have experimentally measured normal modes and the DOS in a disordered colloidal crystal. The DOS shows Debye-like behavior at low energies and an excess of modes, or Boson peak, at higher energies. The normal modes take the form of plane waves hybridized with localized short wavelength features in the Debye regime but lose both longitudinal and transverse plane-wave character at a common energy near the Boson peak.

Avalanches in strained amorphous solids: does inertia destroy critical behavior?

Simulations are used to determine the effect of inertia on athermal shear of amorphous two-dimensional solids. In the quasistatic limit, shear occurs through a series of rapid avalanches. The distribution of avalanches is analyzed using finite-size scaling with thousands to millions of disks. Inertia takes the system to a new underdamped universality class rather than driving the system away from criticality as previously thought. Scaling exponents are determined for the underdamped and overdamped limits and a critical damping that separates the two regimes. Systems are in the overdamped universality class even when most vibrational modes are underdamped.

Evolution of displacements and strains in sheared amorphous solids

The local deformation of two-dimensional Lennard-Jones glasses under imposed shear strain is studied via computer simulations. Both the mean squared displacement and mean squared strain rise linearly with the length of the strain interval Δγ over which they are measured. However, the increase in displacement does not represent single-particle diffusion. There are long-range spatial correlations in displacement associated with slip lines with an amplitude of order the particle size. Strong dependence on system size is also observed. The probability distributions of displacement and strain are very different. For small Δγ the distribution of displacement has a plateau followed by an exponential tail. The distribution becomes Gaussian as Δγ increases to about 0.03. The strain distributions consist of sharp central peaks associated with elastic regions, and long exponential tails associated with plastic regions. The latter persist to the largest Δγ studied.

Toward Accumulation of Magnetic Nanoparticles into Tissues of Small Porosity

Magnetic concentration of drug-laden magnetic nanoparticles has been proven to increase the delivery efficiency of treatment by 2-fold. In these techniques, particles are concentrated by the presence of a magnetic source that delivers a very high magnetic field and a strong magnetic field gradient. We have found that such magnetic conditions cause even 150 nm particles to aggregate significantly into assemblies that exceed several micrometers in length within minutes. Such assembly sizes exceed the effective intercellular pore size of tumor tissues preventing these drug-laden magnetic nanoparticles from reaching their target sites. We demonstrate that by using dynamic magnetic fields instead, we can break up these magnetic nanoparticles while simultaneously concentrating them at target sites. The dynamic fields we investigate involve precessing the field direction while maintaining a field gradient. Manipulating the field direction drives the particles into attractive and repulsive configurations that can be tuned to assemble or disassemble these particle clusters. Here, we develop a simple analytic model to describe the kinetic thresholds of disassembly and we compare both experimental and numerical results of magnetic particle suspensions subjected to dynamic fields. Finally we apply these methods to demonstrate penetration in a porous scaffold with a similar pore size to that expected of a tumor tissue.

Anomalous stress fluctuations in athermal two-dimensional amorphous solids

We numerically study the local stress distribution within athermal, isotropically stressed, mechanically stable, packings of bidisperse frictionless disks above the jamming transition in two dimensions. Considering the Fourier transform of the local stress, we find evidence for algebraically increasing fluctuations in both isotropic and anisotropic components of the stress tensor at small wave numbers, contrary to recent theoretical predictions. Such increasing fluctuations imply a lack of self-averaging of the stress on large length scales. The crossover to these increasing fluctuations defines a length scale ℓ_{0}, however, it appears that ℓ_{0} does not vary much with packing fraction ϕ, nor does ℓ_{0} seem to be diverging as ϕ approaches the jamming ϕ_{J}. We also find similar large length scale fluctuations of stress in the inherent states of a quenched Lennard-Jones liquid, leading us to speculate that such fluctuations may be a general property of amorphous solids in two dimensions.

Mechanical Instabilities in Perfect Crystals: From Dislocation Nucleation to Bucklinglike Modes

We perform atomistic simulations of nanoindentation on Lennard–Jones 2D hexagonal crystals. In this work, we find a new spatially extended buckling-like mode of instability, which competes with the previously known instability governed by dislocation-dipole nucleation. The geometrical parameters governing these instabilities are the lattice constant, a, the radius of curvature of the indenter, R, and the thickness of the indenter layer, Ly. Whereas dislocation nucleation is a saddle-node bifurcation governed by R/a, the buckling-like instability is a pitchfork bifurcation (like classical Euler buckling) governed by R=Ly. The two modes of instability exhibit strikingly different behaviors after the onset of instability. The dislocation nucleation mode results in a stable final configuration containing a surface step and a stable dislocation at some depth beneath the surface, while the buckling modes are always followed immediately by subsequent nucleation of many dislocation dipoles. We show that this subsequent dislocation nucleation is also observed immediately after buckling in free standing rods, but only for rods which are of sufficiently wide aspect ratio, while thinner rods exhibit stable buckling followed only later by dislocation nucleation in the buckled state. Finally, we study the utility of several recently proposed local and quasi-local stability criteria in detecting the buckling mode. We find that the so-called K criterion, based on the stability of a representative homogeneously deformed lattice, is surprisingly useful in detecting the transition from dislocation-type instability to buckling-type instability. [DOI: 10.1115/1.4034564]

Assembling particle clusters with incoherent 3D magnetic fields

Directed assembly of particle suspensions in massively parallel formats, such as with magnetic fields, has application in rheological control, smart drug delivery, and active colloidal devices from optical materials to microfluidics. At the heart of these applications lies a control optimization problem for driving the assembly and dissolution of highly monodisperse particle clusters. For magnetic field control, most attention to-date has been centered around in-phase coherent magnetic fields. Instead, we investigate a family of incoherent 3D magnetic fields that are capable of creating controlled and tunable particle assemblies such as dimers, trimers, and quadramers. These field functions can be tuned to assemble monodisperse clusters with long term stability and can quickly switch the clusters between different states. This subset of three-dimensional field functions that we have studied demonstrates the rich phase space available to tune colloidal suspensions with magnetic fields.