Density Functional Theory Of Bubble Nucleation During CO₂ Foaming Polymers

Polymer foams have extensive and important values in industrial application. A clear understanding of the bubble nucleation micro-mechanism has a great help for the well controlling of bubble nucleation and growth, which makes it possible to manufacture high performance polymer foams. In this paper, the thermodynamic behaviors during supercritical CO₂ foaming polymer were studied. Based on the interactions between different molecules and sites, the density functional theory was constructed to contain various free energy functional. The CO₂ solubility, polymer swelling, gas-melt interfacial tension between CO₂ and polymer, bubble nucleation energy and critical radius, bubble contact angle on nucleating agent, and nucleation number were studied. The main investigations are listed as follows:?1? The intermolecular correlation functions of polymer topology were determined based on the geometry and chemistry properties of polymer sites. The direct correlation functions between different sites were obtained by the polymer reference interaction site model theory. The corresponding free energy functional was constructed to complete the free energy of polymer conformation in density functional theory. Taken PMMA, PS, PCL and PP as examples, CO₂ solubility and polymer swelling ratio were calculated. The interfacial density profiles and interfacial tension of the dissolved equilibrium polymer/CO₂ mixture systems at high pressure were calculated. Then the effects of temperature, pressure,group in polymer molecular and flexibility of polymer chain on CO₂ solubility, polymer swelling, interfacial structure and energy of gas-melt were analyzed.?2? The homogeneous and heterogeneous bubble nucleation in PMMA/CO₂ and PS/CO₂ systems were studied by one-dimensional density functional theory. The pressure-compositions of polymer/CO₂ mixture after suddenly release of pressure were calculated. The change of local supersaturature and subsaturature after the addition of nanoparticles was corrected by calculating the density profiles of CO₂ and polymer around SiO₂ and fluorinated SiO₂. The bubble nucleation energy barrier, critical radius, and nucleation number for PMMA and PS foaming at different condition were calculated according to density profiles and energy of bubble nucleation in polymer bulk phase or silica nanoparticle surface. The influence of temperature, pressure, polymer structure, and the geometry and chemical properties of nanoparticles on bubble nucleation were analyzed comprehensively. It was found that the nucleation numbers was improved five orders after the addition of nanoparticle for PMMA and PS systems. The predicted values were verified by experimental data. It provided a reasonable explanation for the formation of microcellular bubbles.?3? The foaming behavior of PCL systems was studied based on three-dimensional density functional theory. In this model, PCL chains not only influenced the CO₂ solubility and supersaturation degree, but also played a role as nucleating agent. In other word, it was more reasonable to regard PCL foaming process as a heterogeneous process. After the determination of CO₂ solubility, the effects of CO₂ local supersaturation degree were analyzed by the calculation of CO₂ density profiles around PCL chains. The heterogeneous nucleation mechanisms were illuminated from micro-level by describing the structure density and energy change of bubbles during different nucleation time. The nucleation energy barrier, critical nucleation radius and nucleation number of bubbles under different initial pressure were calculated. The deviation between theoretical values and experimental data was within two orders. Compared with the error of six to ten orders calculated by classical nucleation theory, the results predicted by density functional theory were greatly improved.?4? The foaming process of PP/particle/CO₂ systems was studied by three-dimensional density functional theory. The effects of nanoscale roughness formed by PP and particles in bubble nucleation process were analyzed. Taking fluorinated polyhedral oligomeric silsesquioxane ?F-POSS? as an example, the effects of F-POSS on CO₂ local supersaturation degree were evaluated by CO₂ density around the structure combined by PP and F-POSS. The structure density profiles and energy variation of bubbles in different stage were described. The morphologies of critical bubble nucleated around amorphous or crystalline PP chain with different F-POSS coverage ratio were compared. Furthermore, the values of critical radius, nucleation energy barrier, contact angle, and nucleation number with different F-POSS coverage ratios were calculated. The different effects of amorphous and crystalline PP chain on bubble nucleation were analyzed. The nucleation numbers of PP foaming systems with different F-POSS coverage ratios under different initial pressure were evaluated. The deviation between predicted values and experimental data was within one order. The most favorable bubble nucleation condition for PP/F-POSS was determined, which provided thermodynamic mechanism explanation for microbubble nucleation and improved the comprehensive performances of polymer foams.