Odille Fabrice G J, Jónsson Stefán, Stjernqvist Susann, Rydén Tobias, Wärnmark Kenneth
Organic Chemistry, Department of Chemistry, Lund University, P.O. Box 124, 221 00 Lund, Sweden.
Chemistry. 2007;13(34):9617-36. doi: 10.1002/chem.200700032.
A general mathematical model for the characterization of the dynamic (kinetically labile) association of supramolecular assemblies in solution is presented. It is an extension of the equal K (EK) model by the stringent use of linear algebra to allow for the simultaneous presence of an unlimited number of different units in the resulting assemblies. It allows for the analysis of highly complex dynamic equilibrium systems in solution, including both supramolecular homo- and copolymers without the recourse to extensive approximations, in a field in which other analytical methods are difficult. The derived mathematical methodology makes it possible to analyze dynamic systems such as supramolecular copolymers regarding for instance the degree of polymerization, the distribution of a given monomer in different copolymers as well as its position in an aggregate. It is to date the only general means to characterize weak supramolecular systems. The model was fitted to NMR dilution titration data by using the program Matlab, and a detailed algorithm for the optimization of the different parameters has been developed. The methodology is applied to a case study, a hydrogen-bonded supramolecular system, salen 4+porphyrin 5. The system is formally a two-component system but in reality a three-component system. This results in a complex dynamic system in which all monomers are associated to each other by hydrogen bonding with different association constants, resulting in homo- and copolymers 4n5m as well as cyclic structures 6 and 7, in addition to free 4 and 5. The system was analyzed by extensive NMR dilution titrations at variable temperatures. All chemical shifts observed at different temperatures were used in the fitting to obtain the DeltaH degrees and DeltaS degrees values producing the best global fit. From the derived general mathematical expressions, system 4+5 could be characterized with respect to above-mentioned parameters.
本文提出了一种用于描述溶液中超分子组装体动态（动力学不稳定）缔合的通用数学模型。它是对等量K（EK）模型的扩展，通过严格运用线性代数，使得所得组装体中能够同时存在无限数量的不同单元。该模型能够分析溶液中高度复杂的动态平衡系统，包括超分子均聚物和共聚物，而无需借助大量近似方法，在该领域中其他分析方法存在困难。所推导的数学方法使得分析诸如超分子共聚物等动态系统成为可能，例如可以分析聚合度、给定单体在不同共聚物中的分布及其在聚集体中的位置。这是迄今为止表征弱超分子系统的唯一通用方法。通过使用Matlab程序将该模型拟合到核磁共振稀释滴定数据，并开发了用于优化不同参数的详细算法。该方法应用于一个案例研究，即一个氢键超分子体系，salen 4 + 卟啉5。该体系形式上是二元体系，但实际上是三元体系。这导致了一个复杂的动态系统，其中所有单体通过具有不同缔合常数的氢键相互缔合，除了游离的4和5之外，还产生了均聚物和共聚物4n5m以及环状结构6和7。通过在可变温度下进行广泛的核磁共振稀释滴定对该体系进行了分析。在拟合过程中使用了在不同温度下观察到的所有化学位移，以获得产生最佳全局拟合的ΔH°和ΔS°值。根据推导的通用数学表达式，可以对体系4 + 5的上述参数进行表征。
