Integral Equation Theory Study On Polymer Materials

Integral equation theory has an advantage of investigating the microscopic structure and macroscopic thermodynamic properties of materials and it has been one of the hot spots of the theoretical research in the field of chemical engineering and material physics. Based on the statistic mechanics and combining polymer integral equation theory with conformational statistics of polymer chain and the renormalized technique of longe-range electrostatic interaction, the intramolecular and intermolecular correlation interaction of branched chains and other complex polymer systems can be accurately obtained. Furthemore, the present work can be used to investigate the macroscopic thermodynamic properties of the polymers. The present work mainly contains:(1) It contains the entile framework and mathematical construction of the reference interaction site model (PRISM) theory. Different kinds of convenient models for describing the intramolecular correlation functions and the relationdhip between the generator matrix method and the factual chain structure are discussed extensively, together with the general closure approximations used in the PRISM theory. We also have deduced the renormalized technique of the electrostatic interaction of the mixed polymer systems and introduce some numerical methods to solve the PRISM equation including the Fourier transformation technique. Thus, it can establish a theretical basis for further inverstigation of the complex polymer chains.(2) Using PRISM theory, a six-site freely-jointed chain model is proposed to descibe the site interaction of the atactic polystyrene (aPS) chains with complex styrene ring. The method is reasonable to investigate the direct correlation functions and the intermolecular correlation functions of different sites. Furthermore, it can be used to capture the local structure and thermodynamic properties of the polymer systems.(3) Based on the polmer chain configurational theory, a six-site semiflexible chain model which has fully considered the physical characteristics (the diameters, bond lengthes, bond angles, bond energies and so on) of the polymer chains is proposed and applied to describe the structure and properties of aPS melt. The intramolecular correlation functions are obtained analytically by Koyama distribution function and the generator matrix method. The calculated X-ray scattering intensity and total radial distribution function are compared with both simulation and experiment data. The results indicate that the model is an effective way to investigate the microscopic structure of styrene polymers. Otherwise, in the whole construction and calculation of the model, it does not need any experimental parameters and can provide a new useful method to capture the microscopic structure and marcoscopic properties of the complex polymer systems.(4) Applying the above multi-site semiflexible chain model, a new PRISM equation for the gas-polymer system is proposed to investigate the structure distribution of the small molecues in polymers. Combining the particle scaled theory with perturbation theory; the equation of state for the mixed system is derived by using the intermolecular correlation functions. Then, the solubility coefficients of a wide range of gases in aPS are predicted at low pressure. Based on the CO2 sorption isotherms, the swelling of aPS under high pressures can also be investigated. These results demonstrate that the theoretical model is reliable to describe the sorption properties of small molecules in aPS chain. Thus obtained method can provide a substantial foundation for the application of the PRISM theory to factual systems.(5) Combining the recently proposed multi-site semiflexible chain model with Koyama distribution function and generator matrix method, a new renormalized technique of the electrostatic potentials in systems with strong hydrogen-bond interactions is constructed. The present method is applied to investigate the microscopic structure of poly(ethylene glycol) (PEG) aqueous solution. Therefore, the theoretical model can provide a new tool to capture the microscopic structure and properties of other complex systems with strong hydrogen bonding.(6) A new 3D-PRISM theory has been proposed to capture the microscopic structure and properties of the macromolecular liquids and the detailed computational procedure has also been represented. For simplicity, we have studied the three dimensional distribution functions of water without losing the generality of the model to describe the polymers. The calculated results demonstrate that the present method can be used to investigate the orentaional positions and spatial structures of the complex systems.