【作者】 刘杰；

【导师】 顾芳；

【作者基本信息】 河北大学 ， 高分子化学与物理， 2022， 硕士

【摘要】 Kirkwood-Buff(KB)理论对于研究复杂流体的局部聚集态与宏观热力学量有重要意义,文中采用KB理论和密度泛函理论对两组分流体进行了相关研究。在溶液理论与密度泛函理论的基础上,引入KB积分与径向分布函数,进一步介绍了KB积分的物理意义与应用。在具体研究中,本文先以两组分硬球流体为研究的对象,根据统计力学原理,构建两组分硬球体系的巨势泛函,并依据最小化原理,对不同条件下两组分硬球体系的平衡密度分布与径向分布函数进行计算,进而得到体系的KB积分。进一步分析密积分数、尺寸比例和摩尔分数等因素对两组分硬球流体KB积分的影响。作为应用,讨论了上述因素对体系局部聚集态结构和等温压缩系数的影响;接下来,选取硬球-氢键流体作为研究的主体,根据相同的原理获取硬球-氢键体系的平衡密度分布与径向分布函数,在此基础上阐明了氢键作用(氢键强度与氢键官能度)和尺寸比例等因素对硬球-氢键两组分流体局部聚集态结构和等温压缩系数的影响。全文内容如下:第一章:绪论。介绍了多组分流体的研究背景、现状及意义,其中主要包括溶液理论的理论研究、分子间作用势和统计热力学原理。与此同时,介绍了KB积分的发展、物理意义与应用。紧接着,我们对经典密度泛函理论的发展过程与研究现状进行了简要概述。最后,对文章研究的主要内容加以概述。第二章:两组分硬球流体的密度泛函理论及KB积分。本章在构建两组分硬球流体巨势泛函的基础上,依据最小化原理获得了两组分硬球体系的平衡密度分布,进一步求取径向分布函数以及该体系的KB积分。在获取流体KB积分的基础上,深入分析了密积分数、尺寸比例以及摩尔分数等因素对两组分硬球流体的局部聚集态结构及等温压缩系数的影响。第三章:硬球-氢键流体的密度泛函理论及KB积分。本章给出硬球-氢键流体的自由能表达式,由此计算了硬球-氢键流体的KB积分与等温压缩系数。进一步探究了氢键作用(氢键强度与氢键官能度)和尺寸比例对该体系KB积分的影响,亦对等温压缩系数受上述因素的影响予以分析。第四章:结论与展望。归纳了双组分流体KB理论的研究工作与结果,指出本文存在的一些不足并对相关发展的前景予以简述。更多还原

【Abstract】 Kirkwood-Buff(KB)theory plays an important role in the study on both the structure of complex fluids and the macroscopic thermodynamic quantities.In this dissertation,the KB solution theory and the classical density functional theory(c-DFT)are used to present the relevant investigations for two-component fluids.Firstly,based on the basic principles of statistical mechanics,the grand potential of two-component hard sphere fluid is expressed as a functional of the particle number density,then the equilibrium density distribution and radial distribution function of fluids can be obtained by minimizing the grand potential functional.As an application,the KB integrals and the isothermal compressibility of the system are also calculated.Consequently,the effects of the packing fraction,the size ratio of two species,and molar fraction of on the KB integral of the two-component hard sphere fluids are discussed.Furthermore,the effects of the above factors on the local aggregation structure and the isothermal compressibility are discussed.Secondly,the system consisting of hard sphere fluid and hydrogen bonding(HB)fluid is further investigated.Accordingly,the equilibrium density distribution and radial distribution function of the hard sphere and HB fluid are obtained according to the same procedure.Furthermore,the effects of HB strength,functionality,and the size ratio of two species on the local aggregation structure and the isothermal compressibility of the mixture are also presented.The present dissertation is divided into the following four parts:Chapter 1: Introduction.the foundation on the multi-component fluids are introduced,which mainly includes the important theoretical studies of solution theory,typical intermolecular interaction potential,and some significant methods based on the principle of statistical thermodynamics.Of the particular interest in this part is focused on the KB integral,which is a fundamental tool to the study on solutions.Meanwhile,we outlined the development process and the status of c-DFT on the relevant systems.Chapter 2: Classical DFT and KB integral for two-component hard sphere fluids.In this chapter,based on the grand potential functional of the two-component hard sphere fluids,the equilibrium density distribution and radial distribution function of the two-component hard sphere system are obtained by the principle of minimization of the grand potential functional.As a result,the KB integral of the system is calculated,and by which the effects of the packing fraction,the size ratio,and molar fraction on the local structure of fluid are analyzed.Furthermore,as a consequence of the correlation between the local structure and global quantities,the isothermal compressibility of the system is carried out.Chapter 3: The classical DFT and KB integral a dilute solution consisting of hard sphere particles immersing a HB fluid.In this chapter,the free energy functional of the system are given,from which the KB integrals and isothermal compression coefficients of hard sphere and HB fluids are calculated.The effects of HB strength,HB functionality,and size ratio on the KB integral of this system are further discussed.As an application,the effects of the these factors on the isothermal compressibility are also discussed.Chapter 4: Conclusions.Some conclusions of the KB theory of two-component fluids are summarized,and also,some drawbacks in the present dissertation and some possible extensions are given.更多还原