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On the Characterization of Dynamic Supramolecular Systems: A General Mathematical Association Model for Linear Supramolecular Copolymers and Application on a Complex Two‐Component Hydrogen‐Bonding System
Author(s) -
Odille Fabrice G. J.,
Jónsson Stefán,
Stjernqvist Susann,
Rydén Tobias,
Wärnmark Kenneth
Publication year - 2007
Publication title -
chemistry – a european journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.687
H-Index - 242
eISSN - 1521-3765
pISSN - 0947-6539
DOI - 10.1002/chem.200700032
Subject(s) - supramolecular chemistry , copolymer , supramolecular polymers , component (thermodynamics) , hydrogen bond , monomer , characterization (materials science) , materials science , thermodynamics , computer science , chemistry , nanotechnology , molecule , physics , polymer , organic chemistry
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 4 n 5 m 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 Δ H ° and Δ S ° values producing the best global fit. From the derived general mathematical expressions, system 4 + 5 could be characterized with respect to above‐mentioned parameters.