Integral Equation Theory Study On The Structure And Property Of Polymer Materials

In fact, all the properties of the polymer materials showed on the macroscopic scale are the reflection of their microscopic structures. With the development of polymer materials in various application fields, understanding the impact mechanism of polymer microstructure on their macroscopic properties is of the most importance to design specific polymer materials with desire properties. The integral equation theory (IET), needs the distribution functions that containing the structure information (the chemical composition and geometric structures) of the macromolecule as input to obtain those distribution functions reflecting macroscopic properties by solving the equations. Thus, using the IET one can understand the relationship between the microstructure and the macroscopic properties of polymer systems from molecular level. The main research contents of this topic include:1. With the solubility of small molecules in homogeneous polymer melts as research object, we studying the impact of the microstructure of the homogeneous polymer melts on their macroscopic properties. The detail work is using the polymer IET (PRISM) to calculate and predict the solubility-temperature curves of Carbon Dioxide (CO2) in different polymer melts containing ether and carbonyl groups. By analyzing and understanding the relationship between the polymer structure and the solubility of the CO2, we predict the solubility trends of CO2in new polymer melts containing ether and carbonyl groups. The chosen polymer for analysis are poly(ethylene oxide)(PEO), poly(propylene oxide)(PPO), poly(vinyl acetate)(PVAc), poly(ethylene carbonate)(PEC) and polypropylene carbonate)(PPC). The packing of PEO, PPO, PVAc, PEC, and PPC are studied by the homogeneous IET. To verify the theory, molecular dynamic simulations are performed. The results show that the theoretically calculated reduced X-ray scattering intensities for these five polymers are in qualitative agreement with the corresponding molecular simulation data. The theory is then employed to investigate the distribution functions between CO2and different sites of the polymers with consideration of different interactions. By analyzing the pair distribution functions of CO2in contact with methylene, ether and carbonyl groups of these five polymers, we find the reason for the CO2-philic properties of polyethers and polyesters. Accordingly, the CO2sorption curves are calculated, by which we analyzed the influence factors for the solubilities of CO2in polymer melts from molecule level. Comparing the theoretically calculated CO2sorption curves with the corresponding experimental data, we find the reliability and the application scope of the present homogeneous IET model for estimating the solubility of CO2in a new polymer.2. The three dimentional IET equation (3D-RISM) is then implied to study the polymer/fluid interfacial systems. For these systems, a density functional based on the fundamental measure theory is constructed to modify the self-consistent of the3D-RISM equations by introducing the energy minimization principle and to form an energy expression for the inhomogeneous system, so as to introduce the inhomogeneous property to the3D-RISM equations. By comparing the theoretically predicted wetting transition behavior of the water on the model polymer surface with that from the molecule simulations, we find that introducing the energy minimization principle to the IET is efficient and reliable. Then the modified3D-RISM equation is applied to the three dimensional real polymer/water interfacial systems. Using the density distributions, free energy distributions and the contact angles of water over four different real polymer surfaces as study object, we analyz the influence of the chemical composition and geometric structures of polymer surfaces on the wetting behavior of water. Further, the approach is used to calculate the water contact angles as a function of temperature, and predict the wetting process of the water on the polymer surfaces. We compare the theoretically predicted contact angles of water on the four real polymer surfaces with the experiment values, the result validate the introduction of energy minimization principle to the IET in three dimensional spaces.3. The improvement of the energy minimization principle to the IET for describing the polymer/fluid interfacial systems has been verified by small molecule fluid, we then apply the IET to describe the structures of polymers in confinement, such as confined by the planar and curved solid surfaces. In the theoretical approach, a bridge function containing polymeric information has been derived from density functional method to modify the inhomogeneous confined polymeric IET equations. By comparing the structures of hard-sphere polymer at planar and curved surfaces with the the available simulation data, we find that the present polymeric IET equations can well reproduce the simulation data. This approach is relatively simple to describe the intra-or intermolecular interactions and geometrical structures of polymer chains, and the various interactions between polymer and solid surface. These are distinct advantages, thus, it could propel us to further study on a number of interesting systems such as confined polymers with more complex chemical structures using the inhomogeneous modified polymeric IET equation.4. Encourage by the success of the modified inhomogeneous polymeric IET equation in describing the structures of confined polymer systems, we use the theory to study the phase transition behavior of the polymer/nanoparticle composite induced by the substrate. In order to investigate the effect of packing and configurational entropies on the phase transitions of polymer/nanoparticle blends near a surface, we consider three parameters of the systems, including particle size, attractive interaction strength between particles and polymer monomers, and the stiffness of polymer chains. And we find that the particle size and particle-monomer interaction have a significant influence on the packing entropy and a moderate increase of polymer stiffness has an obvious impact to the configurational entropy. Validated by the density functional theory as well as molecular simulations, we find the equation is capable of quantitatively predicting the phase transition behavior of the polymer/nanoparticle composite with different conformations. In particular, the PRISM framework ensures the model could be easily extended to real confined systems with complicate polymer architectures, such as star and comb-type branched polymers and copolymers.