Theoretical Study Of Statistical Properties Of Non-gaussian Chain Polymer Systems With Special Intra-chain Degrees Of Freedom

Soft matter generally refers to the complex condensed matter between ideal fluid and solid,which is widely existed in nature,human daily and production life,with many degrees of freedom,complex structure,easy deformation,and other characteristics.Polymer system is the most typical soft matter systems.Studying the relationship between the properties and structures of polymer systems can not only provide a theoretical framework for bottom-up molecular design but also provide a new idea for top-down development of functional polymer materials,which is of great scientific significance and engineering application value for the development of soft matter science.The Gaussian chain model is a polymer chain model based on the statistical properties of polymer mesoscopic,and it is also the most thoroughly studied and widely used polymer chain model.Applying intra-chain constraints on polymer chains(such as changing the topology,increasing the mode of motion,inserting azo-benzene groups with photoisomerism,etc.)will introduce special intra-chain degrees of freedom for polymer systems.The new degrees of freedom can contribute new entropic contributions to the polymer system,which can potentially lead to new structural and responsive properties of the polymer at the mesoscopic scale.Since the intra-chain confinement changes the conformational statistical properties of the polymer and exhibits non-Gaussian statistical behavior,it is difficult to solve by classical self-consistent field theory,which is a classical difficulty in the soft condensed matter physics.This thesis presents an advanced study of the theoretical approach,structure,statistical properties,and response behavior of non-Gaussian chain polymer systems with new intra-chain degrees of freedom by using computer simulations.In terms of theoretical approach,this thesis establishes the single-chain mean-field theory based on the idea of path integration in the worm-chain model applicable to polymer systems with multiple degrees of freedom and multiple constraints,and gives an efficient and accurate numerical solution scheme for this theory,which systematically solves the problem of theoretical description of non-Gaussian chain polymer systems.The new degrees of freedom of the polymer system can be obtained by adding constraints on the conformation within the polymer chain,however,the theoretical description of the constraints requires the introduction of δ functions into the diffusion equations satisfied by the propagators of the polymer,which increase the difficulty of solving them substantially.It is found that the single-chain mean-field theory cleverly transforms the differential problem into an integral issue,so that the introduction of δ function not only does not increase the computational complexity but also reduces the dimensionality of the sampling space and improves the computational speed and stability,thus proving that the method is highly suitable for the study of statistical properties of semi-rigid polymers near surfaces.In terms of practical applications,three model systems are designed to study the subject of introducing new degrees of freedom of intra-chain,and the main research contents and innovations are as follows.(1)A model of Lasso polymer chains with sliding degrees of freedom was constructed by introducing topological constraints in the polymer chains.The structural properties and statistical properties of Lasso polymer chains during the Coil-Globule transition are investigated intensively using Monte Carlo simulations.It is shown that the Lasso polymer has a ζ-like structure in the Coil state,a σ-like structure in the Globule state,and a δ-like structure in the intermediate state.The structural changes of Lasso polymers in different states demonstrate the adaptive structural transition of Lasso polymers and reveal the role of the sliding entropy in the conformational statistics of Lasso polymers.(2)An adsorption system model of polymer brush with sliding degrees of freedom and anisotropic nanoparticle is constructed by introducing a new mode of motion in polymer chains.The response properties of the system are also investigated in depth by using the single chain mean-field theory.It is found that this system exhibits a novel bistable adsorption behavior,revealing the key mechanisms of sliding entropy and orientation entropy of anisotropic nanoparticle in the formation of entropy-dominated adsorption states.(3)A polymer brush-nanoparticle adsorption model with light-switching property is constructed by introducing an azo-benzene group with photoisomeric property into the polymer chain.The photoisomerization of the azo-benzene group introduces new degrees of freedom and new scales to the system.The nature of the response of this system model to UV light and the effect of structural parameters of polymer brush on the photoswitching performance are investigated by using the single chain mean-field theory to reveal the competing matching mechanisms of three scales: the length of the ligand polymer,the position of the azo bond,and the length of the homopolymer polymer.