Lattice and Continuum Studies of Fluids and Fluid Mixtures

该基金由DMR的材料理论计划和CHE的理论和计算化学计划共同资助，旨在了解流体及其混合物的微观结构和宏观行为之间的相关性。研究工具是理论上的，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介质模型的结果。近年来，由于研究人员可以获得越来越复杂的测量类型，复杂流体的行为一直受到高度关注。此外，在过去的十年里，模拟稠密流体混合物的能力已经大大扩展。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。这里的研究涉及Born-Green-Yvon(BGY)积分方程法。利用BGY形式，导出了晶格系统和连续系统的描述，并对两者的结果进行了比较。晶格理论给出了感兴趣的热力学量的封闭形式的表达式。格子理论的优势包括它对非理论家的可访问性，以及使用相对复杂的流体和混合物的格子模拟结果来测试它的能力，这些结果比连续介质模拟数据更丰富。连续统理论能够处理更微妙的问题，涉及局部结构和整体性质之间的相互作用。然而，连续体解涉及到数值方法，关于混合物的模拟数据还不够丰富。如上所述，类似晶格和连续统理论的发展产生了确定哪种平衡性质对施加晶格约束敏感的可能性。在目前的赠款中，格子研究将侧重于发展对聚合物溶液和混合物的理解，建立在格子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已证明能力的基础上。这项工作将包括分析数据，包括(这项工作的新工作)小角中子散射结果，以获得特征微观参数。在确定了表征系统所需的最小数据集之后，目标是预测较难获得的特性，例如共存曲线的压力依赖关系。这类信息很重要，例如在决定加工条件时。BGY理论还能够探索结构和能量差异对相容性的影响，以努力在更复杂的水平上理解两者之间的平衡。在连续介质方面，该小组最近的研究表明，BGY理论在描述硬球溶剂中硬球链的链崩溃和收缩等现象方面是有效的。这项研究将集中在稠密流体和通过方势垒相互作用的混合物上。这种势能之所以令人感兴趣，是因为它很简单，但能够捕捉到真实流体的基本物理。这个势已经被用来进行第一次晶格-连续体的比较，发现链尺寸和链长度之间的标度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，以便与BGY晶格研究正构烷烃进行比较。晶格和连续体之间的这种联系将使对正构烷烃的“元”研究成为可能，包括理论以及模拟和实验数据。一个主要的问题是，是否可以使用晶格和连续统BGY理论来获得类似的结果，如果是这样的话，需要什么程度的复杂程度。另一个问题是，是否希望将理论发展留在晶格和连续统的不同阶段，牺牲微妙的易用性，以描述连续统中更复杂的系统的能力。%这项拨款由DMR的材料理论计划和CHE的理论和计算化学计划联合资助，旨在了解流体及其混合物的微观结构和宏观行为之间的相关性。研究工具是理论上的，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.***