This thesis is about "nano-cellular" polymer foams, i.e., to understand nano-bubble nucleation and growth mechanisms, we used Self-Consistent Field Theory(SCFT) for the research.\\ Classical Nucleation Theory (CNT) is often used to calculate nucleation rates, but CNT has assumptions which break down for a nano-sized bubble: it assumes planar sharp interfaces and bulk phases inside bubbles. Therefore, since the size of a nano-sized bubble is comparable to the size of the polymer molecule, we assumed that a bubble surface is a curved surface, and we ivestigated effects of curvature on the nucleation barrier. SCFT results show that sharper curvatures of smaller s cause a higher polymer configurational entropy and lower internal energy, and also the collapse of the bulk phase for smaller bubbles causes low internal energy. Consequently, the homogenous bubble nucleation barrier for curved surfaces is much smaller than flat surface (CNT prediction).\\ We calculated direct predictions for maximum possible cell densities as a function of bubble radius without calculation of nucleation barrier or nucleation rates in CNT. Our results show higher cell densities at higher solvent densities and lower temperatures. Moreover, our cell density prediction reveals that rather than surface tension, the volume free energy, often labelled as a pressure difference in CNT, is the dominant factor for both cell densities and cell sizes. This is not predicted by CNT.\\ We also calculated direct predictions for the maximum possible cell densities as a function of system volume in compressible systems. With an assumption that system pressure has an optimal pressure which gives the maximal density of good quality foams (bulk phase inside bubble), we calculated the inhomogeneous system pressure, the homogeneous system, and cell density as a function of system volume.\\ Maximal cell prediction in compressible system shows the incompressible system prediction is the upperbound maximal cell density, and qualitatively consistent with the compressible system results - higher cell densities at low temperatures and high solvent densities.\\ In addition, our results show a bigger expansion as well as a high cell density at low temperature and high solvent density, but temperature is a more dominant factor than the solvent density. From our results, we assume that a quick pressure dropping is required to get a better quality foam of a higher cell density.

This thesis is about "nano-cellular" polymer foams, i.e., to understand nano-bubble nucleation and growth mechanisms, we used Self-Consistent Field Theory(SCFT) for the research.\\ Classical Nucleation Theory (CNT) is often used to calculate nucleation rates, but CNT has assumptions which break down for a nano-sized bubble: it assumes planar sharp interfaces and bulk phases inside bubbles. Therefore, since the size of a nano-sized bubble is comparable to the size of the polymer molecule, we assumed that a bubble surface is a curved surface, and we ivestigated effects of curvature on the nucleation barrier. SCFT results show that sharper curvatures of smaller s cause a higher polymer configurational entropy and lower internal energy, and also the collapse of the bulk phase for smaller bubbles causes low internal energy. Consequently, the homogenous bubble nucleation barrier for curved surfaces is much smaller than flat surface (CNT prediction).\\ We calculated direct predictions for maximum possible cell densities as a function of bubble radius without calculation of nucleation barrier or nucleation rates in CNT. Our results show higher cell densities at higher solvent densities and lower temperatures. Moreover, our cell density prediction reveals that rather than surface tension, the volume free energy, often labelled as a pressure difference in CNT, is the dominant factor for both cell densities and cell sizes. This is not predicted by CNT.\\ We also calculated direct predictions for the maximum possible cell densities as a function of system volume in compressible systems. With an assumption that system pressure has an optimal pressure which gives the maximal density of good quality foams (bulk phase inside bubble), we calculated the inhomogeneous system pressure, the homogeneous system, and cell density as a function of system volume.\\ Maximal cell prediction in compressible system shows the incompressible system prediction is the upperbound maximal cell density, and qualitatively consistent with the compressible system results - higher cell densities at low temperatures and high solvent densities.\\ In addition, our results show a bigger expansion as well as a high cell density at low temperature and high solvent density, but temperature is a more dominant factor than the solvent density. From our results, we assume that a quick pressure dropping is required to get a better quality foam of a higher cell density.

Size effects in out-of-plane bending stiffness of honeycomb cellular materials were studied using analytical mechanics of solids modeling, fabrication of samples and mechanical testing. Analysis predicts a positive size-effect relative to continuum model predictions in the flexure stiffness of a honeycombed beam loaded in out-of-plane bending. A method of determining the magnitude of that effect for several different methods of constructing or assembling square-celled and hexagonal-celled materials, using both single-walled and doubled-walled construction methods is presented. Hexagonal and square-celled honeycombs, with varying volume fractions were fabricated in Nylon 12 using Selective Laser Sintering. The samples were mechanically tested in three-point and four point-bending to measure flexure stiffness. The results from standard three-point flexure tests, did not agree with predictions based on a mechanics of solids model for either square or hexagonal-celled samples. Results for four-point bending agreed with the mechanics of solids model for the square-celled geometries but not for the hexagonal-celled geometries. A closed form solution of an elasticity model for the response of the four-point bending configuration was developed, which allows interpretation of recorded displacement data at two points and allows separation the elastic bending from the localized, elastic/plastic deformation that occurs between the loading rollers and the specimen’s surface. This localized deformation was significant in the materials tested. With this analysis, the four-point bending data agreed well with the mechanics of solids predictions. / text