Fluids and Their Mixtures: Lattice and Continuum Studies and Comparisons

9730976 Lipson这是一项由材料研究部的材料理论项目和化学部的理论与计算化学项目共同资助的续期基金。理论研究的目的是了解流体及其混合物的微观性质如何与其宏观行为相关联。我们感兴趣的系统包括简单分子和复杂分子。此外，这项工作提供了一个独特的机会，即能够使用相同的理论方法将晶格模型的结果与连续体模型的结果进行比较。近年来，复杂流体的行为引起了人们的高度兴趣，这是由于越来越复杂的测量方法变得容易获得而引起的。此外，在过去十年中，模拟致密流体混合物的能力也得到了极大的发展。因此，能够检验统计力学理论的更多数据开始出现，特别是对于复杂的液体混合物。这里进行的研究涉及一种被称为Born-Green-Yvon （BGY）理论的积分方程技术。利用BGY的形式主义，导出了晶格和连续统系统的理论描述，并对两者的结果进行了比较。晶格理论产生了我们感兴趣的热力学量的简单封闭表达式。晶格理论的优点包括它对非理论家的可访问性，以及能够使用相对复杂的流体和混合物的晶格模拟结果来测试它，这比连续体模拟数据更丰富。连续统理论能够解决涉及局部结构和体性质之间相互作用的更微妙的问题。然而，连续介质解涉及数值方法，且混合介质的模拟数据尚不丰富。类似晶格和连续统理论的发展使我们有可能确定哪种平衡性质对晶格约束的施加敏感。这项研究将重点发展对聚合物溶液和混合物的理解，建立在晶格BGY理论描述纯流体、简单烷烃混合物和聚乙烯溶液的证明能力的基础上。这项工作将涉及数据分析，包括状态方程信息和（这些努力的新内容）小角中子散射结果，以获得特征微观参数。确定了表征系统所需的最小数据集之后，接下来的目标是预测不易接近的属性，例如共存曲线的压力依赖性。例如，这些信息对于决定加工条件很重要。BGY理论还能够探测结构差异（例如聚烯烃共混物）和能量差异（例如发生在强相互作用的混合物中）对混相的影响，从而在更复杂的层面上理解这两者之间的平衡。这是由材料研究部门的材料理论项目和化学部门的理论与计算化学项目共同资助的续期基金。理论研究的目的是了解流体及其混合物的微观性质如何与其宏观行为相关联。我们感兴趣的系统包括简单分子和复杂分子。此外，这项工作提供了一个独特的机会，即能够使用相同的理论方法将晶格模型的结果与连续体模型的结果进行比较。研究将集中在聚合物溶液和混合物上。除了提供对这些材料的基本见解外，结果将对这些材料的加工具有重要意义。＊＊＊

9730976 Lipson This is a renewal grant funded jointly by the Materials Theory Program in the Division of Materials Research and the Theoretical and Computational Chemistry Program in the Chemistry Division. The theoretical research is targeted at understanding how the microscopic nature of fluids and their mixtures is correlated with their macroscopic behavior. Systems of interest include both simple and complex molecules. In addition, a unique opportunity afforded by this work is the ability to compare the results for a lattice model with those for a continuum model using the same theoretical approach. The behavior of complex fluids has been of high interest in recent years, and this has been stimulated by the increasingly sophisticated kinds of measurements becoming accessible. In addition, the ability to simulate mixtures of dense fluids has expanded dramatically within the last decade. Thus, more data are beginning to appear whcih are capable of testing statistical mechanical theories, particularly for complex liquid mixtures. The research conducted here involves an integral equation technique known as Born-Green-Yvon (BGY) theory. Using the BGY formalism theoretical descriptions of lattice and continuum systems have been derived, and comparisons between the results using the two have been initiated. The lattice theory has resulted in simple closed-form expressions for thermodynamic quantities of interest. The advantages of lattice theory include its accessibility to non-theorists, and the ability to test it using lattice simulation results on relatively complex fluids and mixtures, which are more plentiful than continuum simulation data. The continuum theory is capable of tackling more subtle issues involving the interplay between local structure and bulk properties. However, continuum solutions involve numerical methods and simulation data on mixtures are not yet plentiful. The development of analogous lattice and continuum theories yields the p ossibility of determining what kinds of equilibrium properties are expected to be sensitive to the imposition of a lattice constraint. This research will focus on developing an understanding of polymer solutions and blends, building on the demonstrated ability of the lattice BGY theory to describe pure fluids, simple alkane mixtures and polyethylene solutions. This work will involve analysis of data, including equation of state information and (new to these efforts) small angle neutron scattering results, in order to obtain the characteristic microscopic parameters. Having determined what minimum data set is required to characterize a system, the goal is then to predict less accessible properties, such as the pressure dependence of the coexistence curve. Such information is important in deciding on processing conditions, for example. The BGY theory is also capable of probing the effects of structural differences (for example polyolefin blends) and energetic differences (such as ocur in strongly interaacting mixtures) on miscibility in an effort to understand at a more sophisticated level the balance between these two. %%% This is a renewal grant funded jointly by the Materials Theory Program in the Division of Materials Research and the Theoretical and Computational Chemistry Program in the Chemistry Division. The theoretical research is targeted at understanding how the microscopic nature of fluids and their mixtures is correlated with their macroscopic behavior. Systems of interest include both simple and complex molecules. In addition, a unique opportunity afforded by this work is the ability to compare the results for a lattice model with those for a continuum model using the same theoretical approach. Research will focus on polymer solutions and blends. Besides providing fundamental insight on these materials, the results will be of importance in the processing of these materials. ***