Lattice and Continuum Studies of Fluids and Fluid Mixtures

该基金由DMR材料理论项目和CHE理论与计算化学项目共同资助，旨在了解流体及其混合物的微观结构和宏观行为之间的关系。研究工具是理论性的，但研究的主要目的是将小分子和聚合物流体的实验数据联系起来并进行比较。此外，这项工作提供的一个真正的机会是能够使用相同的理论方法比较晶格模型和连续体模型的结果。近年来，由于研究人员可以使用的测量方法越来越复杂，复杂流体的行为引起了人们的高度兴趣。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，出现了更多能够检验统计力学理论的数据，特别是对于复杂的液体混合物。本研究涉及Born-Green-Yvon （BGY）积分方程技术。利用BGY的形式，导出了晶格系统和连续统系统的描述，并对两者的结果进行了比较。晶格理论为感兴趣的热力学量提供了封闭形式的表达式。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，而混合介质的模拟数据尚不丰富。如上所述，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。在目前的资助中，晶格研究将侧重于发展对聚合物溶液和混合物的理解，建立在晶格BGY理论描述简单烷烃流体和混合物以及碳氢化合物聚合物溶液和混合物的演示能力的基础上。这项工作将涉及数据分析，包括小角度中子散射结果（这是这项工作的新内容），以获得特征微观参数。在确定表征系统所需的最小数据集之后，目标是预测不易接近的属性，例如共存曲线的压力依赖性。这些信息很重要，例如在决定加工条件时。BGY理论还能够探测结构和能量差异对混相的影响，从而在更复杂的层面上理解两者之间的平衡。在连续体方面，该小组最近的研究表明，BGY理论在描述链崩溃和硬球链在硬球溶剂中收缩等现象时是有效的。研究将集中在通过方井势相互作用的致密流体和混合物上。这种潜力之所以令人感兴趣，是因为它很简单，但能够捕捉到真实流体的基本物理特性。这一潜力已被用于进行第一次晶格-连续体比较，发现（除其他外）链尺寸和链长度之间的比例关系表现出普遍的行为。未来的工作将测试方井流体作为烷烃模型的能力，允许与正烷烃的BGY晶格研究进行比较。晶格和连续体之间的这种联系将使正构烷烃的“元”研究成为可能，包括理论、模拟和实验数据。一个主要的问题是，是否可以使用晶格和连续体BGY理论获得类似的结果，如果可以，需要什么复杂程度。另一个问题是，是否需要在晶格和连续体的不同阶段离开理论发展，牺牲晶格上的易用性的微妙性，以及在连续体中描述更复杂系统的能力的可访问性。该基金由DMR的材料理论项目和CHE的理论与计算化学项目共同资助，旨在了解流体及其混合物的微观结构和宏观行为之间的关系。研究工具是理论性的，但研究的主要目的是将小分子和聚合物流体的实验数据联系起来并进行比较。此外，这项工作提供的一个真正的机会是能够使用相同的理论方法比较晶格模型和连续体模型的结果

0099541LipsonThis grant, jointly funded by the Materials Theory Program in DMR and the Theoretical and Computational Chemistry Program in CHE, is targeted at understanding the correlation between microscopic structure and macroscopic behavior for fluids and their mixtures. The research tools are theoretical, but a major thrust of the research is to make connections and comparisons with experimental data both for small-molecule and polymeric fluids. In addition, a real opportunity afforded by this work is the ability to compare the results for the lattice and continuum models using the same theoretical approach.The behavior of complex fluids has been of high interest in recent years, stimulated by the increasingly sophisticated kinds of measurements accessible to researchers. In addition, the ability to simulate mixtures of dense fluids has expanded dramatically within the last decade. Thus, more data capable of testing statistical mechanical theories are appearing, particularly for complex liquid mixtures. The research here involves the Born-Green-Yvon (BGY) integral equation technique. Using the BGY formalism, descriptions of lattice and continuum systems have been derived, and comparisons between the results using the two have been initiated. The lattice theory yields 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. As indicated above, the development of analogous lattice and continuum theories yields the possibility of determining what kinds of equilibrium properties are expected to be sensitive to the imposition of a lattice constraint. In the current grant, the lattice studies will focus on developing an understanding of polymer solutions and blends, building on the demonstrated ability of the lattice BGY theory to describe simple alkane fluids and mixtures and hydrocarbon polymer solutions and blends. This work will involve analysis of data, including (new to this effort) 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 to predict less accessible properties, such as the pressure dependence of the coexistence curve. Such information is important, for example in deciding on processing conditions. The BGY theory is also capable of probing the effects of structural and energetic differences on miscibility in an effort to understand at a more sophisticated level the balance between the two.On the continuum side, recent research by this group has shown that the BGY theory is effective in describing such phenomena as chain collapse and the contraction of a hard-sphere chain in a hard-sphere solvent. The research will focus on dense fluids and mixtures which interact via a square-well potential. This potential is of interest because it is simple, yet capable of capturing the essential physics of real fluids. This potential has been used in making the first lattice-continuum comparisons, finding (among other things) that the scaling relationship between chain dimensions and chain length exhibits universal behavior. Future work will test the ability of a square-well fluid to serve as a model for alkanes, allowing a comparison with BGY lattice studies on n-alkanes. This connection between lattice and continuum will enable a 'meta' study on n-alkanes, involving both theories as well as simulation and experimental data. A major question is whether analogous results may be obtained using lattice and continuum BGY theories and, if so, what level of sophistication is required. Another issue is whether it is desirable to leave the theoretical development at different stages in the lattice and continuum, sacrificing subtlety for ease of use on the lattice, and accessibility for the ability to describe more complex systems in the continuum.%%%This grant, jointly funded by the Materials Theory Program in DMR and the Theoretical and Computational Chemistry Program in CHE, is targeted at understanding the correlation between microscopic structure and macroscopic behavior for fluids and their mixtures. The research tools are theoretical, but a major thrust of the research is to make connections and comparisons with experimental data both for small-molecule and polymeric fluids. In addition, a real opportunity afforded by this work is the ability to compare the results for the lattice and continuum models using the same theoretical approach.***