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
(2007) In Chemistry: A European Journal 13(34). p.9617-9636- 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 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,,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 above-mentioned 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
- Wiley-Blackwell
- external identifiers
-
- wos:000251391000020
- scopus:36649022632
- ISSN
- 1521-3765
- 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
- 148993de-5c2d-428c-9d90-7783aea261a5 (old id 968692)
- date added to LUP
- 2016-04-01 16:58:34
- date last changed
- 2022-02-20 17:43:29
@article{148993de-5c2d-428c-9d90-7783aea261a5,
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 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,,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 above-mentioned parameters.}},
author = {{Odille, Fabrice and Jonsson, Stefan and Stjernqvist, Susann and Rydén, Tobias and Wärnmark, Kenneth}},
issn = {{1521-3765}},
keywords = {{supramolecular chemistry; polymers; NMR spectroscopy; analytical methods; mathematical chemistry}},
language = {{eng}},
number = {{34}},
pages = {{9617--9636}},
publisher = {{Wiley-Blackwell}},
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 two-component hydrogen-bonding system}},
url = {{http://dx.doi.org/10.1002/chem.200700032}},
doi = {{10.1002/chem.200700032}},
volume = {{13}},
year = {{2007}},
}