Heat dissipation from carbon nano-electronics

The incorporation of graphitic compounds such as carbon nanotubes (CNTs) and graphene into nano-electronic device packaging holds much promise for waste heat management given their high thermal conductivities. However, as these graphitic materials must be used in together with other semiconductor/insulator materials, it is not known how thermal transport is affected by the interaction. Using different simulation techniques, in this thesis, we evaluate the thermal transport properties - thermal boundary conductance (TBC) and thermal conductivity - of CNTs and single-layer graphene in contact with an amorphous SiO2 (a-SiO2) substrate. First, the theoretical methodologies and concepts used in our simulations are presented. In particular, two concepts are described in detail as they are necessary for the understanding of the subsequent chapters. The first is the linear response Green-Kubo (GK) theory of thermal boundary conductance (TBC), which we develop in this thesis, and the second is the spectral energy density method, which we use to directly compute the phonon lifetimes and thermal transport coefficients. After we set the conceptual foundations, the TBC of the CNT-SiO2 interface is computed using non- equilibrium molecular dynamics (MD) simulations and the new Green-Kubo method that we have developed. Its dependence on temperature, the strength of the interaction with the substrate, and tube diameter are evaluated. To gain further insight into the phonon dynamics in supported CNTs, the scattering rates are computed using the spectral energy density (SED) method. With this method, we are able to distinguish the different scattering mechanisms (boundary and CNT-substrate phonon-phonon) and rates. The phonon lifetimes in supported CNTs are found to be reduced by contact with the substrate and we use that lifetime reduction to determine the change in CNT thermal conductivity. Next, we examine thermal transport in graphene supported on SiO2. The phonon contribution to the TBC of the graphene-SiO2 interface is computed from MD simulations and found to agree well with experimentally measured values. We derive the theory of remote phonon scattering of graphene electrons and compute the heat transfer coefficient dependence on doping level and temperature. The thermal boundary conductance from remote phonon scattering is found to be an order of magnitude smaller than that of the phonon contribution. The in-plane thermal conductivity of supported graphene is calculated from MD simulations. The experimentally measured order of magnitude reduction in thermal conductivity is reproduced in our simulations. We show that this reduction is due to the damping of the flexural (ZA) modes. By varying the interaction between graphene and the substrate, the ZA modes hybridize with the substrate Rayleigh modes and the dispersion of the hybridized modes is found to linearize in the strong coupling limit, leading to an increased thermal conductance in the composite structure.

Shape and chemically anisotropic colloidal particles: A theoretical study of their structure, phase behavior, and slow dynamics

A detailed non-equilibrium state diagram of shape-anisotropic particle fluids is constructed. The effects of particle shape are explored using Naive Mode Coupling Theory (NMCT), and a single particle Non-linear Langevin Equation (NLE) theory. The dynamical behavior of non-ergodic fluids are discussed. We employ a rotationally frozen approach to NMCT in order to determine a transition to center of mass (translational) localization. Both ideal and kinetic glass transitions are found to be highly shape dependent, and uniformly increase with particle dimensionality. The glass transition volume fraction of quasi 1- and 2- dimensional particles fall monotonically with the number of sites (aspect ratio), while 3-dimensional particles display a non-monotonic dependence of glassy vitrification on the number of sites. Introducing interparticle attractions results in a far more complex state diagram. The ideal non-ergodic boundary shows a glass-fluid-gel re-entrance previously predicted for spherical particle fluids. The non-ergodic region of the state diagram presents qualitatively different dynamics in different regimes. They are qualified by the different behaviors of the NLE dynamic free energy. The caging dominated, repulsive glass regime is characterized by long localization lengths and barrier locations, dictated by repulsive hard core interactions, while the bonding dominated gel region has short localization lengths (commensurate with the attraction range), and barrier locations. There exists a small region of the state diagram which is qualified by both glassy and gel localization lengths in the dynamic free energy. A much larger (high volume fraction, and high attraction strength) region of phase space is characterized by short gel-like localization lengths, and long barrier locations. The region is called the attractive glass and represents a 2-step relaxation process whereby a particle first breaks attractive physical bonds, and then escapes its topological cage. The dynamic fragility of fluids are highly particle shape dependent. It increases with particle dimensionality and falls with aspect ratio for quasi 1- and 2- dimentional particles. An ultralocal limit analysis of the NLE theory predicts universalities in the behavior of relaxation times, and elastic moduli. The equlibrium phase diagram of chemically anisotropic Janus spheres and Janus rods are calculated employing a mean field Random Phase Approximation. The calculations for Janus rods are corroborated by the full liquid state Reference Interaction Site Model theory. The Janus particles consist of attractive and repulsive regions. Both rods and spheres display rich phase behavior. The phase diagrams of these systems display fluid, macrophase separated, attraction driven microphase separated, repulsion driven microphase separated and crystalline regimes. Macrophase separation is predicted in highly attractive low volume fraction systems. Attraction driven microphase separation is charaterized by long length scale divergences, where the ordering length scale determines the microphase ordered structures. The ordering length scale of repulsion driven microphase separation is determined by the repulsive range. At the high volume fractions, particles forgo the enthalpic considerations of attractions and repulsions to satisfy hard core constraints and maximize vibrational entropy. This results in site length scale ordering in rods, and the sphere length scale ordering in Janus spheres, i.e., crystallization. A change in the Janus balance of both rods and spheres results in quantitative changes in spinodal temperatures and the position of phase boundaries. However, a change in the block sequence of Janus rods causes qualitative changes in the type of microphase ordered state, and induces prominent features (such as the Lifshitz point) in the phase diagrams of these systems. A detailed study of the number of nearest neighbors in Janus rod systems reflect a deep connection between this local measure of structure, and the structure factor which represents the most global measure of order.

Analysis of Molecular Dynamics Simulations of Protein Folding

Microsecond long Molecular Dynamics (MD) trajectories of biomolecular processes are now possible due to advances in computer technology. Soon, trajectories long enough to probe dynamics over many milliseconds will become available. Since these timescales match the physiological timescales over which many small proteins fold, all atom MD simulations of protein folding are now becoming popular. To distill features of such large folding trajectories, we must develop methods that can both compress trajectory data to enable visualization, and that can yield themselves to further analysis, such as the finding of collective coordinates and reduction of the dynamics. Conventionally, clustering has been the most popular MD trajectory analysis technique, followed by principal component analysis (PCA). Simple clustering used in MD trajectory analysis suffers from various serious drawbacks, namely, (i) it is not data driven, (ii) it is unstable to noise and change in cutoff parameters, and (iii) since it does not take into account interrelationships amongst data points, the separation of data into clusters can often be artificial. Usually, partitions generated by clustering techniques are validated visually, but such validation is not possible for MD trajectories of protein folding, as the underlying structural transitions are not well understood. Rigorous cluster validation techniques may be adapted, but it is more crucial to reduce the dimensions in which MD trajectories reside, while still preserving their salient features. PCA has often been used for dimension reduction and while it is computationally inexpensive, being a linear method, it does not achieve good data compression. In this thesis, I propose a different method, a nonmetric multidimensional scaling (nMDS) technique, which achieves superior data compression by virtue of being nonlinear, and also provides a clear insight into the structural processes underlying MD trajectories. I illustrate the capabilities of nMDS by analyzing three complete villin headpiece folding and six norleucine mutant (NLE) folding trajectories simulated by Freddolino and Schulten [1]. Using these trajectories, I make comparisons between nMDS, PCA and clustering to demonstrate the superiority of nMDS. The three villin headpiece trajectories showed great structural heterogeneity. Apart from a few trivial features like early formation of secondary structure, no commonalities between trajectories were found. There were no units of residues or atoms found moving in concert across the trajectories. A flipping transition, corresponding to the flipping of helix 1 relative to the plane formed by helices 2 and 3 was observed towards the end of the folding process in all trajectories, when nearly all native contacts had been formed. However, the transition occurred through a different series of steps in all trajectories, indicating that it may not be a common transition in villin folding. The trajectories showed competition between local structure formation/hydrophobic collapse and global structure formation in all trajectories. Our analysis on the NLE trajectories confirms the notion that a tight hydrophobic core inhibits correct 3-D rearrangement. Only one of the six NLE trajectories folded, and it showed no flipping transition. All the other trajectories get trapped in hydrophobically collapsed states. The NLE residues were found to be buried deeply into the core, compared to the corresponding lysines in the villin headpiece, thereby making the core tighter and harder to undo for 3-D rearrangement. Our results suggest that the NLE may not be a fast folder as experiments suggest. The tightness of the hydrophobic core may be a very important factor in the folding of larger proteins. It is likely that chaperones like GroEL act to undo the tight hydrophobic core of proteins, after most secondary structure elements have been formed, so that global rearrangement is easier. I conclude by presenting facts about chaperone-protein complexes and propose further directions for the study of protein folding.

Effect of boiling on deposition of metallic colloids

In this study the relationship between heterogeneous nucleate boiling surfaces and deposition of suspended metallic colloidal particles, popularly known as crud or corrosion products in process industries, on those heterogeneous sites is investigated. Various researchers have reported that hematite is a major constituent of crud which makes it the primary material of interest; however the models developed in this work are irrespective of material choice. Qualitative hypotheses on the deposition process under boiling as proposed by previous researchers have been tested, which fail to provide explanations for several physical mechanisms observed and analyzed. In this study a quantitative model of deposition rate has been developed on the basis of bubble dynamics and colloid-surface interaction potential. Boiling from a heating surface aids in aggregation of the metallic particulates viz. nano-particles, crud particulate, etc. suspended in a liquid, which helps in transporting them to heating surfaces. Consequently, clusters of particles deposit onto the heating surfaces due to various interactive forces, resulting in formation of porous or impervious layers. The deposit layer grows or recedes depending upon variations in interparticle and surface forces, fluid shear, fluid chemistry, etc. This deposit layer in turn affects the rate of bubble generation, formation of porous chimneys, critical heat flux (CHF) of surfaces, activation and deactivation of nucleation sites on the heating surfaces. Several problems are posed due to the effect of boiling on colloidal deposition, which range from research initiatives involving nano-fluids as a heat transfer medium to industrial applications such as light water nuclear reactors. In this study, it is attempted to integrate colloid and surface science with vapor bubble dynamics, boiling heat transfer and evaporation rate. Pool boiling experiments with dilute metallic colloids have been conducted to investigate several parameters impacting the system. The experimental data available in the literature is obtained by flow experiments, which do not help in correlating boiling mechanism with the deposition amount or structure. With the help of experimental evidences and analysis, previously proposed hypothesis for particle transport to the contact line due to hydrophobicity has been challenged. The experimental observations suggest that deposition occurs around the bubble surface contact line and extends underneath area of the bubble microlayer as well. During the evaporation the concentration gradient of a non-volatile species is created, which induces osmotic pressure. The osmotic pressure developed inside the microlayer draws more particles inside the microlayer region or towards contact line. The colloidal escape time is slower than the evaporation time, which leads to the aggregation of particles in the evaporating micro-layer. These aggregated particles deposit onto or are removed from the heating surface, depending upon their total interaction potential. Interaction potential has been computed with the help of surface charge and van der Waals potential for the materials in aqueous solutions. Based upon the interaction-force boundary layer thickness, which is governed by debye radius (or ionic concentration and pH), a simplified quantitative model for the attachment kinetics is proposed. This attachment kinetics model gives reasonable results in predicting attachment rate against data reported by previous researchers. The attachment kinetics study has been done for different pH levels and particle sizes for hematite particles. Quantification of colloidal transport under boiling scenarios is done with the help of overall average evaporation rates because generally waiting times for bubbles at the same position is much larger than growth times. In other words, from a larger measurable scale perspective, frequency of bubbles dictates the rate of collection of particles rather than evaporation rate during micro-layer evaporation of one bubble. The combination of attachment kinetics and colloidal transport kinetics has been used to make a consolidated model for prediction of the amount of deposition and is validated with the help of high fidelity experimental data. In an attempt to understand and explain boiling characteristics, high speed visualization of bubble dynamics from a single artificial large cavity and multiple naturally occurring cavities is conducted. A bubble growth and departure dynamics model is developed for artificial active sites and is validated with the experimental data. The variation of bubble departure diameter with wall temperature is analyzed with experimental results and shows coherence with earlier studies. However, deposit traces after boiling experiments show that bubble contact diameter is essential to predict bubble departure dynamics, which has been ignored previously by various researchers. The relationship between porosity of colloid deposits and bubbles under the influence of Jakob number, sub-cooling and particle size has been developed. This also can be further utilized in variational wettability of the surface. Designing porous surfaces can having vast range of applications varying from high wettability, such as high critical heat flux boilers, to low wettability, such as efficient condensers.

In situ characterization of sediment oxygen demand across the spectrum of non-resuspension to full resuspension with varying bed shear stress

Sediment oxygen demand (SOD) can be a significant oxygen sink in various types of water bodies, particularly slow-moving waters with substantial organic sediment accumulation. In most settings where SOD is a concern, the prevailing hydraulic conditions are such that the impact of sediment resuspension on SOD is not considered. However, in the case of Bubbly Creek in Chicago, Illinois, the prevailing slack water conditions are interrupted by infrequent intervals of very high flow rates associated with pumped combined sewer overflow (CSO) during intense hydrologic events. These events can cause resuspension of the highly organic, nutrient-rich bottom sediments, resulting in precipitous drawdown of dissolved oxygen (DO) in the water column. While many past studies have addressed the dependence of SOD on near-bed velocity and bed shear stress prior to the point of sediment resuspension, there has been limited research that has attempted to characterize the complex and dynamic phenomenon of resuspended-sediment oxygen demand. To address this issue, a new in situ experimental apparatus referred to as the U of I Hydrodynamic SOD Sampler was designed to achieve a broad range of velocities and associated bed shear stresses. This allowed SOD to be analyzed across the spectrum of no sediment resuspension associated with low velocity/ bed shear stress through full sediment resuspension associated with high velocity / bed shear stress. The current study split SOD into two separate components: (1) SODNR is the sediment oxygen demand associated with non-resuspension conditions and is a surface sink calculated using traditional methods to yield a value with units (g/m2/day); and (2) SODR is the oxygen demand associated with resuspension conditions, which is a volumetric sink most accurately characterized using non-traditional methods and units that reflect suspension in the water column (mg/L/day). In the case of resuspension, the suspended sediment concentration was analyzed as a function of bed shear stress, and a formulation was developed to characterize SODR as a function of suspended sediment concentration in a form similar to first-order biochemical oxygen demand (BOD) kinetics with Monod DO term. The results obtained are intended to be implemented into a numerical model containing hydrodynamic, sediment transport, and water quality components to yield oxygen demand varying in both space and time for specific flow events. Such implementation will allow evaluation of proposed Bubbly Creek water quality improvement alternatives which take into account the impact of SOD under various flow conditions. Although the findings were based on experiments specific to the conditions in Bubbly Creek, the techniques and formulations developed in this study should be applicable to similar sites.