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Title	Rouse Dynamics of Topological Polymers through Gaussian Random Embeddings and Comparison with Experiments
Creator	Tetsuo Deguchi
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2019-03-28T10:32
Description	Recently, polymers of complex chemical connectivity expressed with graphs have been synthesized in experiments [1-3]. It is indeed marvelous that even such polymers expressed with K3,3 bipartite graph have been produced [2]. We call polymers with nontrivial structures in chemical connectivity topological polymers. We also call polymers with nontrivial topology of spatial graphs as embeddings in three dimensions topological polymers [4]. The Rouse dynamics of a polymer plays an important role in the dynamical aspects of the polymer in dilute solution, and also in melts if the molecular weight is small [5]. In this talk, we formulate the Rouse dynamics of the topological polymer with a given graph. We derive several physical consequences of the model. In particular, we compare the experimental data of Size Exclusion Chromatography (SEC) of some topological polymers with their theoretical estimates of the mean-square radius of gyration obtained by the Gaussian method [6]. We argue physical backgrounds of SEC data and discuss how they are consistent. After reviewing the method for constructing Gaussian random configurations of a topological polymer, i.e. Gaussian random graph embeddings [6], we derive the normal coordinates and modes for the topological polymer. Here we remark that while the Moore-Penrose generalized inverse matrix has been addressed for general Gaussian molecules about three decades ago [7], it seems that important consequences were found later independently [8]. Moreover, it has not been known until quite recently how to generate Gaussian random configurations of a given topological polymer [6]. In fact, we can calculate any physical quantity at least numerically by taking the ensemble averages over generated configurations. It is quite nontrivial to generate such random walks that satisfy the constraints of all independent loops in the graph. The results of this talk are obtained in collaboration with Jason Cantarella, Clayton Shonkwiler, and Erica Uehara. 1)    Topological Polymer Chemistry: Progress of cyclic polymers in synthesis, properties and  functions, Y. Tezuka ed., World Scientific, Singapore, 2013.     2)    T. Suzuki, T. Yamamoto and Y. Tezuka. J. Am. Chem. Soc., 2014, 136, 10148–10155. 3)    Y. Tezuka. Acc. Chem. Res., 2017, 50, 2661–2672. 4)    E. Uehara and T. Deguchi, J. Chem. Phys. 2016, 145, 164905. 5)    M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, Oxford University Press, Oxford, 1986.  6)    J. Cantarella, T. Deguchi, C. Shonkwiler and E. Uehara, in preparation. 7)    B. E. Eichinger, Macromolecules, 1980, 13, 1-11. 8)  E. Estrada and N. Hatano, Chem. Phys. Let. 2010, 486, 166–170.
Extent	28.0 minutes
Subject	Mathematics Biology and other natural sciences Manifolds and cell complexes Mathematical biology
Geographic Location	Banff (Alta.)
Type	Moving Image
FileFormat	video/mp4
Language	eng
Notes	Author affiliation: Ochanomizu University
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2019-09-25
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0380996
URI	http://hdl.handle.net/2429/71769
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
AggregatedSourceRepository	DSpace

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