Fluids and Their Mixtures: Lattice and Continuum Studies and Comparisons

9730976利普森这是一个更新补助金共同资助的材料理论计划在材料研究部门和理论和计算化学计划在化学部门。 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它们的宏观行为相关。 感兴趣的系统包括简单和复杂的分子。 此外，这项工作提供的一个独特的机会是能够比较结果的晶格模型与连续模型使用相同的理论方法。 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变得容易。 此外，在过去的十年中，模拟稠密流体混合物的能力已经急剧扩展。 因此，越来越多的数据开始出现whcih能够测试统计力学理论，特别是复杂的液体混合物。 在这里进行的研究涉及一个积分方程技术被称为Born-Green-Yvon（BGY）理论。 使用BGY形式主义的理论描述的晶格和连续系统已导出，并使用两者的结果之间的比较已经启动。 格点理论已经为我们感兴趣的热力学量给出了简单的封闭形式的表达式。 格点理论的优点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点模拟结果来测试它的能力，这些结果比连续模拟数据更丰富。 连续介质理论能够处理更微妙的问题，包括局部结构和整体性质之间的相互作用。 然而，连续介质的解决方案涉及数值方法和模拟数据的混合物还不丰富。 类似的晶格和连续介质理论的发展产生了确定哪种平衡性质对晶格约束的施加敏感的可能性。 这项研究将侧重于发展聚合物溶液和共混物的理解，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能力。 这项工作将涉及数据分析，包括状态方程信息和（新的这些努力）小角度中子散射结果，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，目标是预测不易获得的属性，例如共存曲线的压力依赖性。 例如，这种信息在决定加工条件时是重要的。 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（例如强相互作用混合物中的ocur）对相容性的影响，以便在更复杂的水平上理解这两者之间的平衡。 这是由材料研究部的材料理论计划和化学部的理论和计算化学计划共同资助的更新补助金。 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它们的宏观行为相关。 感兴趣的系统包括简单和复杂的分子。 此外，这项工作提供的一个独特的机会是能够比较结果的晶格模型与连续模型使用相同的理论方法。 研究将集中在聚合物溶液和混合物。 除了提供对这些材料的基本认识外，这些结果在这些材料的加工中也很重要。 ***

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. ***