ICCAS OpenIR
Graph theory of viscoelastic and configurational properties of Gaussian chains
Yang, YL
1998-09-01
Source PublicationMACROMOLECULAR THEORY AND SIMULATIONS
ISSN1022-1344
Volume7Issue:5Pages:521-549
AbstractThe spring-and-bead model proposed by Rouse and Zimm can theoretically treat the viscoelastic behaviour of polymers. In this paper, we first point out that the Rouse and Zimm matrices in the molecular theory of polymer viscoelasticities are equivalent to the adjacency matrix and admittance (or Kirchhoff) matrix in graph theory, respectively. In order to solve the eigen-value problems of Rouse and Zimm matrices, the matrices are first represented by their corresponding eigen-graphs, which reflect the topological structure of the real chain. Starting from the eigen-graph, instead of tedious mathematics, the eigen-value problems are solved by a series of simple graphic operations, such as cutting-off the bonds, removing the closed pathways, etc. The eigen-polynomial of Rouse and Zimm matrices and the viscoelastic properties of the chain are obtained by using the theorems given in this paper. It is also shown that the eigen-polynomial of the chain can be greatly reduced if the chain graph has elements of symmetry. As the Rouse theory of viscoelasticity is closely related to the conformational statistics of Gaussian chains, it is demonstrated that the graph-theoretic approach developed here can also be applied to solve the configurational properties of Gaussian chains, such as the distribution function of the radius of gyration and its moments, the shape of a Gaussian chain, etc. We have also demonstrated that the graph-theoretic approach developed here is also applicable to copolymeric chains.
Indexed BySCI
Language英语
WOS IDWOS:000075914600008
PublisherWILEY-V C H VERLAG GMBH
Citation statistics
Cited Times:14[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.iccas.ac.cn/handle/121111/74500
Collection中国科学院化学研究所
Corresponding AuthorYang, YL
Affiliation1.Fudan Univ, Dept Macromol Sci, Lab Macromol Engn, SEDC, Shanghai 200433, Peoples R China
2.Acad Sinica, Inst Chem, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Yang, YL. Graph theory of viscoelastic and configurational properties of Gaussian chains[J]. MACROMOLECULAR THEORY AND SIMULATIONS,1998,7(5):521-549.
APA Yang, YL.(1998).Graph theory of viscoelastic and configurational properties of Gaussian chains.MACROMOLECULAR THEORY AND SIMULATIONS,7(5),521-549.
MLA Yang, YL."Graph theory of viscoelastic and configurational properties of Gaussian chains".MACROMOLECULAR THEORY AND SIMULATIONS 7.5(1998):521-549.
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