On the characterization of dynamic supramolecular systems: A general mathematical association model for linear supramolecular copolymers and application on a complex twocomponent hydrogenbonding system
(2007) In Chemistry: A European Journal 13(34). p.96179636 Abstract
 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... (More)
 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((R)), and a detailed algorithm for the optimization of the different parameters has been developed. The methodology is applied to a case study, a hydrogenbonded supramolecular system, salen 4+porphyrin 5. The system is formally a twocomponent system but in reality a threecomponent 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,,5,, 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 Delta H degrees and Delta S degrees values producing the best global fit. From the derived general mathematical expressions, system 4+5 could be characterized with respect to abovementioned parameters. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/968692
 author
 Odille, Fabrice ^{LU} ; Jonsson, Stefan ^{LU} ; Stjernqvist, Susann ^{LU} ; Rydén, Tobias ^{LU} and Wärnmark, Kenneth ^{LU}
 organization
 publishing date
 2007
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 supramolecular chemistry, polymers, NMR spectroscopy, analytical methods, mathematical chemistry
 in
 Chemistry: A European Journal
 volume
 13
 issue
 34
 pages
 9617  9636
 publisher
 WileyVCH Verlag
 external identifiers

 wos:000251391000020
 scopus:36649022632
 ISSN
 15213765
 DOI
 10.1002/chem.200700032
 language
 English
 LU publication?
 yes
 additional info
 The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Mathematical Statistics (011015003), Organic chemistry (S/LTH) (011001240)
 id
 148993de5c2d428c9d907783aea261a5 (old id 968692)
 date added to LUP
 20160401 16:58:34
 date last changed
 20200819 06:13:09
@article{148993de5c2d428c9d907783aea261a5, abstract = {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((R)), and a detailed algorithm for the optimization of the different parameters has been developed. The methodology is applied to a case study, a hydrogenbonded supramolecular system, salen 4+porphyrin 5. The system is formally a twocomponent system but in reality a threecomponent 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,,5,, 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 Delta H degrees and Delta S degrees values producing the best global fit. From the derived general mathematical expressions, system 4+5 could be characterized with respect to abovementioned parameters.}, author = {Odille, Fabrice and Jonsson, Stefan and Stjernqvist, Susann and Rydén, Tobias and Wärnmark, Kenneth}, issn = {15213765}, language = {eng}, number = {34}, pages = {96179636}, publisher = {WileyVCH Verlag}, series = {Chemistry: A European Journal}, title = {On the characterization of dynamic supramolecular systems: A general mathematical association model for linear supramolecular copolymers and application on a complex twocomponent hydrogenbonding system}, url = {http://dx.doi.org/10.1002/chem.200700032}, doi = {10.1002/chem.200700032}, volume = {13}, year = {2007}, }