Browsing by Subject "Statistical Mechanics"

Now showing 1 - 3 of 3
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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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    Molecular Simulation of Adsorption in Zeolites
    (2014-08) Bai, Peng
    Zeolites are a class of crystalline nanoporous materials that are widely used as catalysts, sorbents, and ion-exchangers. Zeolites have revolutionized the petroleum industry and have fueled the 20th-century automobile culture, by enabling numerous highly-efficient transformations and separations in oil refineries. They are also posed to play an important role in many processes of biomass conversion. One of the fundamental principles in the field of zeolites involves the understanding and tuning of the selectivity for different guest molecules that results from the wide variety of pore architectures. The primary goal of my dissertation research is to gain such understanding via computer simulations and eventually to reach the level of predictive modeling. The dissertation starts with a brief introduction of the applications of zeolites and computer modeling techniques useful for the study of zeolitic systems. Chapter 2 then describes an effort to improve simulation efficiency, which is essential for many challenging adsorption systems. Chapter 3 studies a model system to demonstrate the applicability and capability of the method used for the majority of this work, configurational-bias Monte Carlo simulations in the Gibbs ensemble (CBMC-GE). After these methodological developments, Chapter 4 and 5 report a systematic parametrization of a new transferable force field for all-silica zeolites, TraPPE-zeo, and a subsequent, relatively ad-hoc extension to cation-exchanged aluminosilicates. The CBMC-GE method and the TraPPE-zeo force field are then combined to investigate some complex adsorption systems, such as linear and branched C6--C9 alkanes in a hierarchical microporous/mesoporous material (Chapter 6), the multi-component adsorption of aqueous alcohol solutions (Chapter 7) and glucose solutions (Chapter 8). Finally, Chapter 9 describes an endeavor to screen a large number of zeolites with the purpose of finding better materials for two energy-related applications, ethanol/water separation and hydrocarbon iso-dewaxing.
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    Statistical Thermodynamic Isotherm-Based Model for Activity Coefficients in Complex Aqueous Solutions with Atmospheric Aerosol Applications
    (2015-05) Ohm, Peter
    Aqueous aerosol particles are nearly ubiquitous in the atmosphere and yet there remain large uncertainties in their formation processes and ambient properties. The uncertainty is in part due to the complex nature of the individual particle microenvironment, which can involve a myriad of chemical components and multiple phases. The calculation of gas-liquid-solid equilibrium partitioning of the water, electrolyte, and soluble organic components is critical to accurate determination of atmospheric chemistry properties and processes such as new particle formation and activation to cloud condensation nuclei. Previously, a transformative model for capturing thermodynamic properties of multicomponent aqueous solutions over the entire concentration range (Dutcher et al. J. Phys. Chem 2011, 2012, 2013) was developed using statistical mechanics and multilayer adsorption isotherms. That model needed only a few adsorption energy values to represent the solution thermodynamics of each solute. In the current work, we posit that the adsorption energies are due to dipole-dipole electrostatic forces in solute-solvent and solvent-solvent interactions. This hypothesis was tested in aqueous solutions on (a) thirty-seven 1:1 electrolytes, over a range of cation sizes, from H+ to tetrabutylammonium, for common anions including Cl-, Br-, I-, NO3-, OH-, ClO4-, and (b) twenty water soluble organic molecules including alcohols and polyols. For both electrolytes and organic solutions, the energies of adsorption can be calculated with the dipole moments of the solvent, molecular size of the solvent and solute, and the solvent-solvent and solvent-solute intermolecular bond lengths. Many of these physical properties are available in the literature, with the exception of the solute-solvent intermolecular bond lengths. For those, predictive correlations developed here enable estimation of solute and solvent solution activities for which there are little or no activity data. The model was successfully validated using thirty-seven 1:1 electrolytes and twenty non-dissociating organic solutions (Ohm et al. J. Phys. Chem. 2015). However, careful attention is needed for weakly dissociating semi-volatile organic acids. Dicarboxylic acids such as malonic and glutaric acid are treated here as a mixture of non-dissociated organic species (HA) and dissociated organic species (H+ + A-). It was found that the apparent dissociation was greater than that predicted by known dissociation constants alone, emphasizing the effect of dissociation on activity coefficient predictions. To avoid additional parameterization from the mixture approach, an expression was used to relate the Debye-H�ckel hard-core collision diameter to the adjustable solute-solvent intermolecular distance. This work results in predictive correlations for estimation of solute and solvent solution activities for which there are little or no activity data.