Thermodynamic and Structural Phase Behavior of Colloidal and Nanoparticle Systems.

We design and implement a scalable hard particle Monte Carlo simulation toolkit (HPMC), and release it open source. Common thermodynamic ensembles can be run in two dimensional or three dimensional triclinic boxes. We developed an efficient scheme for hard particle pressure measurement based on volume perturbation. We demonstrate the effectiveness of low order virial coefficients in describing the compressibility factor of fluids of hard polyhedra. The second virial coefficient is obtained analytically from particle asphericity and can be used to define an effective sphere with similar low-density behavior. Higher-order virial coefficients --- efficiently calculated with Mayer Sampling Monte Carlo --- are used to define an exponential approximant that exhibits the best known semi-analytic characterization of hard polyhedron fluid state functions. We present a general method for the exact calculation of convex polyhedron diffraction form factors that is more easily applied to common shape data structures than the techniques typically presented in literature. A proof of concept user interface illustrates how a researcher might investigate the role of particle form factor in the diffraction patterns of different particles in known structures. We present a square-triangle dodecagonal quasicrystal (DQC) in a binary mixture of nanocrystals (NCs). We demonstrate how the decoration of the square and triangle tiles naturally gives rise to partial matching rules via symmetry breaking in layers perpendicular to the dodecagonal axis. We analyze the geometry of the experimental tiling and, following the ``cut and project'' theory, lift the square and triangle tiling pattern to four dimensional space to perform phason analysis historically applied only in simulation and atomic systems. Hard particle models are unsuccessful at explaining the stability of the binary nanoparticle super lattice. However, with a simple isotropic soft particle model, we are able to demonstrate seeded growth of the experimental structure in simulation. These simulations indicate that the most important stabilizing properties of the short range structure are the size ratio of the particles and an A--B particle attraction.PhDMaterials Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/120906/1/eirrgang_1.pd

Rigidity Percolation in Disordered Fiber Systems: Theory and Applications

Nanocomposites, particularly carbon nanocomposites, find many applications spanning an impressive variety of industries on account of their impressive properties and versatility. However, the discrepancy between the performance of individual nanoparticles and that of nanocomposites suggests continued technological development and better theoretical understanding will provide much opportunity for further property enhancement. Study of computational renderings of disordered fiber systems has been successful in various nanocomposite modeling applications, particularly toward the characterization of electrical properties. Motivated by these successes, I develop an explanatory model for `mechanical' or `rheological percolation,' terms used by experimentalists to describe a nonlinear increase in elastic modulus/strength that occurs at particle inclusion volume fractions well above the electrical percolation threshold. Specifically, I formalize a hypothesis given by \\citet*{penu}, which states that these dramatic gains result from the formation of a `rigid CNT network.' Idealizing particle interactions as hinges, this amounts to the network property of \\emph{rigidity percolation}---the emergence of a giant component (within the inclusion contact network) that is not only connected, but furthermore the inherent contacts are patterned to constrain all internal degrees of freedom in the component. Rigidity percolation has been studied in various systems (particularly the characterization of glasses and proteins) but has never been applied to disordered systems of three-dimensional rod-like particles. With mathematically principled arguments from \\emph{rigidity matroid theory}, I develop a scalable algorithm (\\emph{Rigid Graph Compression}, or \\emph{RGC}), which can be used to detect rigidity percolation in such systems by iteratively compressing provably rigid subgraphs within the rod contact networks. Prior to approaching the 3D system, I confirm the usefulness of \\emph{RGC} by using it to accurately approximate the rigidity percolation threshold in disordered systems of 2D fibers---achieving $<1\\%$ error relative to a previous exact method. Then, I develop an implementation of \\emph{RGC} in three dimensions and determine an upper bound for the rigidity percolation threshold in disordered 3D fiber systems. More work is required to show that this approximation is sufficiently accurate---however, this work confirms that rigidity in the inclusion network is a viable explanation for the industrially useful mechanical percolation. Furthermore, I use \\emph{RGC} to quantitatively characterize the effects of interphase growth and spatial CNT clustering in a real polymer nanocomposite system of experimental interest.Doctor of Philosoph

Mass & secondary structure propensity of amino acids explain their mutability and evolutionary replacements

Why is an amino acid replacement in a protein accepted during evolution? The answer given by bioinformatics relies on the frequency of change of each amino acid by another one and the propensity of each to remain unchanged. We propose that these replacement rules are recoverable from the secondary structural trends of amino acids. A distance measure between high-resolution Ramachandran distributions reveals that structurally similar residues coincide with those found in substitution matrices such as BLOSUM: Asn Asp, Phe Tyr, Lys Arg, Gln Glu, Ile Val, Met → Leu; with Ala, Cys, His, Gly, Ser, Pro, and Thr, as structurally idiosyncratic residues. We also found a high average correlation (\overline{R} R = 0.85) between thirty amino acid mutability scales and the mutational inertia (I X ), which measures the energetic cost weighted by the number of observations at the most probable amino acid conformation. These results indicate that amino acid substitutions follow two optimally-efficient principles: (a) amino acids interchangeability privileges their secondary structural similarity, and (b) the amino acid mutability depends directly on its biosynthetic energy cost, and inversely with its frequency. These two principles are the underlying rules governing the observed amino acid substitutions. © 2017 The Author(s)