拓扑结构高分子在体积排除色谱中的分离：理论模型的建立及淋出曲线的预测

Size exclusion chromatography (SEC), also known as gel permeation chromatography, has evolved into one of the most prevalent characterization techniques for polymers in general, and this is also true for topological polymers, i.e., polymers of non-linear topologies comprising branched or cyclic segments. Topology plays a key role in the chain dynamics and thus in application properties such as mechanical and adhesive properties of topological polymers. It is thus vital to be able to precisely characterize topological variables such as the degree of branching, the branching topology, the distributions of molecular weights of the branches and of the polymer chains. The presence of such multi-dimensional variables is why SEC, even with multiple detectors, yields the molecular weights of topological polymers with varying accuracy: typically low for statistically branched polymers. Since SEC separates polymers based on their size, chains with different molecular weights can co-elute due to differences in their branching structures. Under such circumstances, the molecular weights determined at each elution volume are only local averages. In this project, we seek to develop an improved understanding of SEC elugrams of topological polymers by computer simulations. The proposal is based on several state-of-the-art developments in understanding mechanisms of SEC separation and structure-property relations of topological polymers including the applicant's own work on the separation principle in SEC. The proposed work consists of the following. For a given SEC experiment, we first characterize the SEC column using well-defined linear polymers by the inverse SEC technique to get pore size distributions of the column. We then construct a mode polymer chain either based on structural estimates from the synthesis or from the SEC results, and sample its equilibrium conformations in free solution by Monte Carlo simulations; those conformations are then used to calculate the equilibrium partition coefficients of the polymer in the pore sizes determined for the column. This information allows us to predict the elution volume of the model polymer. To validate the method, we start by considering polymer samples of well-defined architectures, such as cyclic and comb polymers. An important feature differentiating this work from those in the literature is the adoption of more realistic polymer models that have excluded volume interactions. While simulations of excluded volume polymers are common, their use in predictions of SEC elution behavior has been hindered in practice by the computation cost associated with the calculation of equilibrium partition coefficients in pores. This work attempts to overcome this hindrance by the confinement analysis from bulk structures method developed previously by the applicant. We expect the inclusion of excluded volume interactions will provide a better agreement with experiments than those based on ideal Gaussian chain statistics.

体积排除色谱被广泛用来表征拓扑结构高分子的分子量分布以及支化参数，但通常认为其表征结果只能用作定性分析。这一局限虽然可以通过比如联用激光小角散射光度计的方法得以突破，但按照其体积排除分离机理，当试样中存在拓扑结构不同但尺寸相当的高分子时，色谱峰会发生重叠，即便采用多检测器联用技术也只能获得平均信息。本项目基于申请人现有的研究结果，结合或可代表现阶段最新发展水平的对体积排除色谱分离的计算/模拟方法，拟通过理论计算/模拟来预测在表征拓扑结构高分子时色谱峰发生重叠的情况，并探索计算/模拟在描述以致预测拓扑结构高分子的淋出曲线方面的应用。本项目以研究环形和梳形拓扑结构为主，采用更接近实验条件的高分子真实链模型，重点考察体积排除效应对预测结果准确性的提高。鉴于体积排除色谱在表征拓扑结构高分子中所扮演的重要角色，该工作不但具有重要的基础研究价值，而且在对拓扑结构的更精确表征方面有潜在的应用价值。

本项目的核心是探索理论计算与模拟方法在辅助分析高分子在体积排除色谱表征中的淋出信号中的应用，主要针对具有复杂拓扑结构的高分子试样。通过对体积排除色谱分离机理的探索，搭建能够预测高分子淋出曲线的理论框架，并通过开发高分子构象模拟方法，计算高分子在自由溶液中的各种尺寸性质和在微孔中的平衡分配系数，并在此基础上，预测已知分子量和拓扑结构的模型高分子链的淋出曲线，诊断体积排除色谱在表征复杂高分子试样时可能产生的色谱峰重叠的情况，为更准确的把握体积排除色谱的表征结果提供理论指导。.. 经过三年的研究，基本完成了上述研究内容，得到了一些重要的结果，但总体来说，离预期的目标还有一定距离。一方面需要完成对梳状聚合物的研究和对光散射及黏度检测器的检测信号的模拟，另一方面有必要开发便于使用的体积排除色谱信号模拟软件，并积极与实验研究开展合作，以检验本项目理论研究在实际应用中的合理性。.. 截至目前，本项目取得的研究成果如下。首先，在平衡排除理论的基础上，构建起描述和预测高分子在体积排除色谱分析中的淋出曲线的完整理论框架，并将理论应用到（1）基于体积排除色谱机理的DNA分离微流体芯片的设计，和（2）反向体积排除色谱技术对色谱柱内结构信息的表征中，在这两部分工作中通过理论与实验结果的对比检验了我们所构建的理论框架。在此基础上，我们对一系列具有复杂拓扑结构的高分子链的GPC分子量与真实分子量之间的比值（即M[GPC]/M[True]）进行了预测，选择计算M(GPC)/M(True)的原因是实验人员在对复杂拓扑结构高分子的表征中通常报道这一数值，我们先后在高斯“理想”链的模型框架下、“真实链”的标度理论的框架下和“真实链”的计算机模拟的基础上对M(GPC)/M(True)进行了预测，重点考察了链单元之间的排除体积效应和链的刚/柔性对高分子的构象性质及其在微孔中的平衡分配系数的影响。

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