Phase Interfaces, Critical Nuclei, Micelles And Vesicles

In condensed matter physics, the self-consistent mean field theory (SCMFT) is one of the most accurate and most systematic theories on the mean-field level. Free of any additional theoretical assumption besides saddle point approximation, SCMFT can conveniently take the architectures of macromolecular chains into account and provide the information about the macromolecular conformations. In principle, SCMFT can be used to tackle various thermodynamic problems in multi-component polymeric systems irrespective of the strength of segregation. So far, the representative numerical methods for SCMFT, such as real-space algorithm and spectrum technique, have been well-developed and applied extensively to investigate various thermodynamic behaviors in multi-component polymeric systems. In this thesis, we would like to develop some new SCMFT methods and apply them to solve the thermodynamic problems encountered in multi-component polymeric systems and the related aspects.The main contributions and the organization of this thesis can be briefly summarized asfollows.The essence and the basic formulations of SCMFT are introduced briefly in Chapter One. The review emphasis is put on the comparison with the other approximate theories and the numerical algorithms for SCMFT as well as their related dynamic extensions. In the following chapters, we will develop some new SCMFT methods and apply them to some practical thermodynamics problems.In the first part of our study, SCMFT is extended to study the self-organized structures formed by local density fluctuations, including micelles, micro-emulsions, vesicles and the critical nuclei for resulting these self-organized structures. Although the real-space algorithm and spectrum technique for studying the periodically ordered structures are well- developed, neither of them is suitable for studying the local self-organized structures. In order to solve this problem, a new numerical method has been proposed by Z.-G, Wang and was applied to solve the problem of nucleation in binary polymer blends. In this part, we have extended this method to investigate the various effects, such as adding block copolymers(Chapter Two), polydispersity (Chapter Three) and the mesoscopic spherical impurities effect (Chapter Four), on the nucleation in binary polymer blends. In fact, our work fills the gap of thermodynamics study on nucleation for liquid-liquid phase separation in polymer blends and provides the basis for the dynamics of nucleation-growth phase separation in polymer blends.Multi-component block copolymer and homopolymer blends are of wide industrial applications and theoretical interests. Although AB diblock copolymer was used in nucleation experiment of A/B blends, the nucleation mechanism and the role of diblock copolymer in this model blends of A/B/AB have not been uncovered theoretically. Therefore, in Chapter Two, we have examined the effects of adding AB diblock copolyrners to A/B blends on the structure and thermodynamicsAbstractof critical nuclei using SCMFT. At a fixed ratio of two homopolymers, depending on the degree of polymerization and composition of the AB diblock copolymer, the added AB diblock coplolymer can either increase or decrease the nucleation free energy barrier relative to the pure A/B blends. The qualitative trend can be deduced from the shifts of the coexistence and spinodal boundaries resulted from adding AB diblock copolymer. The distribution of copolymer blocks in the critical nuclei depends on the composition of the diblocks and the quench depth. Basically, near the coexistence boundary, symmetric diblocks behaves like surfactant that is highly enriched on the interface of the critical nuclei while near the spinodal, it acts more like co-solvent with a relatively uniform distribution.Polymers in practical applications are inevitably polydisperse. However, its effects on the nucleation are not clear yet. In Chapter Three, we have investigated the polydispersity effects of components on nucleation using a simple three-component model in the frame...