Dynamical Density Functioanal Theory For Diffusion Behavior Of Polymer Nanocomposite

Polymer nanocomposites have been widely used in automobile,aviation,aerospace and other fields.In the process of fabricating and using nanocomposites,the movement of nanoparticle and polymer chain plays an important role in the macroscopic properties of the material.Under the microscopic condition,it is difficult to observe the dynamic behavior by the traditional experimental method.Fortunately,the theoretical calculation provides a powerful tool to study the microscopic motion.In this paper,the dynamic density functional theory is used to describe the microscopic motion of nanoparticle and polymer chain in the nanocomposite system based on a combination of mode coupling theory,integral equation theory,and molecular simulation method.The dynamic behaviors in different nanocomposite systems have been extensively studied.The results are as follows:(1)A three-dimensional dynamic density functional approach is used to study polymer chain diffusion in a good solvent under the confinement of nanoparticles,including angle energy of polymer chain and hydrodynamic tensor.The diffusion behavior of polymer chain in nano-confined space and the influence of nanoparticles on chain motion behavior have been quantitatively studied.The scale law of mean square displacement of the polymer chain changes from 0.63 to 0.47,after the chain touches the particles.For each chain segments,the head,side,and middle segments display different scaling laws.The scale law of head segment reduces to 0.33,which means the motion of head segments transforms from Zimm to reputation type.The scale law of side segment also reduces to 0.44,whereas the middle segments almost keep the Zimm motion.Furthermore,as the spacing crack between two posts of particles narrows down,a climbing effect along the posts can be clearly observed in polymer motion.(2)The diffusion of nanoparticles in polymer solutions is studied by consideration of the synergic movement and the asymmetric interaction of particles and polymer chains,in which different diffusion models have been identified by exploiting the density and free energy evolutions.Under the condition of low polymer concentration,the diffusion dynamics is controlled by particle free motion with a normal Gaussian type.As the concentration increases,if the particle size is comparable to the correlation length of polymer chain,the non-Gaussian behavior appears.Particles need to penetrate through a cage and overcome an entropic barrier,where the hopping and the model-coupling diffusion coexist.Further increase of polymer concentration can result in complete restriction of the particles by surrounding polymer segments.In this case,the non-Gaussian process fades away,and particle diffusion is controlled by Rouse dynamics of polymer chains with the generalized Gaussian characteristics.The diffusion mechanism of particles in polymer is illuminated at the molecular level.(3)By integrating the shear field into the dynamic density functional model,the influence of the shear field on nanoparticle distribution and polymer matrix structure has been studied.The effects of particle size,polymer concentration,and particle-polymer interaction on particle diffusion rate,structural damage,and ordered structure are investigated.With the increase of the polymer concentration above 0.8,the relative flow type of the polymer around the particles changes from uniform flow to Stokes flow.Under suitable shear conditions,when the particle size is small,the microphase separation between the particle and the polymer can be observed and cause a large change of the structure of matrix.When the particle size is moderate,an ordered structure is formed in the polymer.If the particle size is too large,the system will form microphase separation or ordered structure depending on the particle-polymer interaction.(4)Based on dynamic density functional theory and mode coupling theory,a statistical dynamic theory method is established to study the glass transition behavior.The glassy transition temperatures of the polymer at different densities are studied by tangential sphere model of free-chain,and the influence of the stiffness of the polymer chain on the glassy transition point is studied by semi-flexible chain model.The glass transition phase diagram of the polymer model system is given.These results show that the glassy transition process is dominated by the thermodynamic second-order transition,but the kinetic method can easily and accurately determine whether the system is in the glass state.At the glassy transition point,the correlation length of the system shows the critical characteristics,and the scale law is about 0.57 and does not change with the systems.The glass transition point of the tangential sphere model is mainly controlled by the density of the system.The stiffness has little direct influence on the glass transition.However,the stiffness has a significant effect on the polymer density,so the effect on the glass transition is indirect.This work provides a feasible method to study the glass transition of the polymer system.