Browsing by Subject "Monte Carlo Simulation"

Now showing 1 - 5 of 5
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    Correlations in polymer blends: simulations, perturbation theory, and coarse-grained theory.
    (2009-09) Chung, Jun Kyung
    A thermodynamic perturbation theory of symmetric polymer blends is developed that properly accounts for the correlation in the spatial arrangement of monomers. By expanding the free energy of mixing in powers of a small parameter α which controls the incompatibility of two monomer species, we show that the perturbation theory has the form of the original Flory-Huggins theory, to first order in α. However, the lattice coordination number in the original theory is replaced by an effective coordination number. A random walk model for the effective coordination number is found to describe Monte Carlo simulation data very well. We also propose a way to estimate Flory-Huggins χ parameter by extrapolating the perturbation theory to the limit of a hypothetical system of infinitely long chains. The first order perturbation theory yields an accurate estimation of χ to first order in α. Going to second order, however, turns out to be more involved and an unambiguous determination of the coefficient of α2 term is not possible at the moment. Lastly, we test the predictions of a renormalized one-loop theory of fluctuations using two coarse-grained models of symmetric polymer blends at the critical composition. It is found that the theory accurately describes the correlation effect for relatively small values of χN. In addition, the universality assumption of coarse-grained models is examined and we find results that are supportive of it.
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    Incorporation of Reliability in Minnesota Mechanistic-Empirical Pavement Design
    (Minnesota Department of Transportation, 1999-07) Timm, David H.; Newcomb, David E.; Birgisson, Bjom; Galambos, Theodore V.
    This report documents the research that incorporated reliability analysis into the existing mechanistic-empirical (M-E) flexible pavement design method for Minnesota. Reliability in pavement design increases the probability that a pavement structure will perform as intended for the duration of its design life. The report includes a comprehensive literature review of the state-of-the-art research. The Minnesota Road Research Project (Mn/ROAD) served as the primary source of data, in addition to the literature review. This research quantified the variability of each pavement design input and developed a rational method of incorporating reliability analysis into the M-E procedure through Monte Carlo simulation. Researchers adapted the existing computer program, ROADENT, to allow the designer to perform reliability analysis for fatigue and rutting. A sensitivity analysis, using ROADENT, identified the input parameters with the greatest influence on design reliability. Comparison designs were performed to check ROADENT against the 1993 AASHTO guide and the existing Minnesota granular equivalency methods. Those comparisons showed that ROADENT produced very similar design values for rutting. However, data suggests that the fatigue performance equation will require further modification to accurately predict fatigue reliability.
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    Large enhancement of capacitance driven by electrostatic image forces.
    (2011-04) Loth, Matthew Scott
    The purpose of this thesis is to examine the role of electrostatic images in determining the capacitance and the structure of the electrostatic double layer (EDL) formed at the interface of a metal electrode and an electrolyte. Current mean field theories, and the majority of simulations, do not account for ions to form image charges in the metal electrodes and claim that the capacitance of the double layer cannot be larger than that of the Helmholtz capacitor, whose width is equal to the radius of an ion. However, in some experiments, and simulations where the images are included, the apparent width of the capacitor is substantially smaller. Monte Carlo simulations are used to examine the interface between a metal electrode and a room temperature ionic liquid (RTIL) modeled by hard spheres (the “restricted primitive model”). Image charges for each ion are included in the simulated electrode. At moderately low temperatures the capacitance of the metal/RTIL interface is so large that the effective thickness of the electrostatic double-layer is up to 3 times smaller than the ion radius. To interpret these results, an approach is used that is based on the interaction between discrete ions and their image charges, which therefore goes beyond the mean-field approximation. When a voltage is applied across the interface, the strong image attraction causes counterions to condense onto the metal surface to form compact ion-image dipoles. These dipoles repel each other to form a correlated liquid. When the surface density of these dipoles is low, the insertion of an additional dipole does not require much energy. This leads to a large capacitance C that decreases monotonically with voltage V , producing a “bell-shaped” C(V ) curve. In the case of a semi-metal electrode, the finite screening radius of the electrode shifts the reflection plane for image charges to the interior of the electrode resulting in a “camel-shaped” C(V ) curve, which is parabolic near V = 0, reaches a maximum and then decreases. These predictions are in qualitative agreement with experiment. A similarly simple model is employed to simulate the EDL of superionic crystals. In this case only small cations are mobile and other ions form an oppositely charged background. Simulations show an effective thickness of the EDL that may be 3 times smaller than the ion radius. The weak repulsion of ion-image dipoles again plays a central role in determining the capacitance in this theory, which is in reasonable agreement with experiment. Finally, the problem of a strongly charged, insulating macroion in a dilute solution of multivalent counterions is considered. While an ideal conductor does not exist in the problem, and no images are explicitly included, simulations demonstrate that adsorbed counterions form a strongly correlated liquid of at the surface of the macroion and acts as an effective metal surface. In fact, the surface screens the electric field of distant ions with a negative screening radius. The simulation results serve to confirm existing non-mean-field theories.
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    Mass, momentum and energy transfer in aggregated particulate media
    (2013-12) Thajudeen, Thaseem
    Synthesis of nanoparticles in gas phase systems often results in the formation of non spherical particles which are commonly found as clusters of spherical particles, termed as aggregates. Prior studies have shown that these aggregates can be accurately modeled using statistical scaling law. While theories are available for determining the transport properties of spherical particles, the effect of the morphology of the particles has not been well studied. This dissertation focuses on studying how exactly the morphology of the aggregates arises in a given synthesis system and calculation of the transport properties of the formed aggregates. Given the particle morphology, this study also investigates the effect the aggregates have on altering the bulk properties of a system into which they are embedded. The study is computational, experimental and analytical in nature with specific emphasis on studying aggregate formation and transport properties of non spherical particles. An overview of the dissertation is given in Chapter 1. In Chapter 2, an expression is proposed for calculating the drag on non spherical particles (that determines their motion in gas phase systems) and is experimentally validated with a study on flame synthesized Titania aggregates. Chapter 3 looks at calculating collision rates between non spherical particles taking into account the morphology of both the colliding entities for all mass transfer regimes and in chapter 4; aerosol filtration process is studied as quintessentially a collision process. The proposed expressions are validated using a numerical study using Brownian Dynamics simulations. In chapter 5, aggregation process is studied in detail, with specific emphasis on aggregate formation and calculation of the transport properties of the formed aggregates, with the aggregation process occurring in different mass and momentum transfer regimes. Given the particle morphology, its effect in altering the bulk properties of the host medium into which they are embedded is dealt with in chapters 6 and 7, specifically looking into their effect on the thermal conductivity and convective heat transfer. The main conclusions from the study and suggestions for possible future studies based on this dissertation are explained in chapter 8.
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    On A General Theory Of Phase Change, Nucleation, And Growth, And The Formation Of Ice In Cryopreserved Systems
    (2023-01) Kangas, Joseph
    In this work we address longstanding gaps in understanding in phase change theories linkingthe nucleation rate, growth rate, growth geometry, and transformed fraction of phase. We take a first principles approach whereby a fundamental understanding of the relationships between these properties can be derived without obfuscation by previous efforts. This is carried out by examining a growing region of space with some prescribed geometry which is transforming from one phase to another, tracking its volume as it grows and intersects with other transforming regions of space. Using this approach, we derive both ordinary and partial differential equations linking the nucleation rate, growth rate, fractal dimension, transformed fraction, phase size distribution, and initial distributions of phase for a system undergoing phase change. We then show that solutions to these equations under special conditions yield methods for extracting nucleation and growth rates for heat release curves, as well as more detailed descriptions of growth geometries. These nucleation and growth rates are important for understanding systems hindered by phase change, including cryobiology, metallurgy, pharmacology, and food science, among others. Extensions to gas phase allow for a deeper understanding of aerosol science and cavitation dynamics as well. Ice crystallization is studied in cryoprotectant agents (CPAs) in low concentrations via direct quenching and laser calorimetry. Critical cooling rates were measured by examining the temperature-time profiles during the direct quenching of droplets of CPA into liquid nitrogen. Critical warming rates were measured by examining ice crystallization in vitrified droplets of CPAs and plasmonic gold nanoparticles during high energy laser irradiation. High-speed imaging allowed for accurate measurements of the temperature rates necessary for avoiding ice formation on rewarming from a vitrified state. A model linking the critical cooling and warming rates in mixtures of CPA was also developed and verified. Additionally, the phase change theory we derived allow for corroboration of the rates necessary for the vitrification of pure water. The laser warming process was also studied numerically via Monte Carlo simulations of light transport in scattering media. The effect of system geometry, absorption coefficient, scattering coefficient, scattering anisotropy, and domain partitioning were studied for a variety of systems including the laser warming of spherical and hemispherical droplets laden with zebrafish embryos and coral nanofragments. Warming uniformity was the main focus of optimization as it is the driving factor in post-warming survival in laser warmed cryopreserved specimens. Laser warming in multi-laser systems is also briefly discussed.