Topological Polymer Chemistry: Concepts and Practices

Preface
Contents
1 Introductory Remarks
	References
Part I Theories and Practices of Multicyclic and Topological Polymers
2 Graph Theoretical and Knot Theoretical Analyses of Multi-cyclic Polymers
	2.1 Topology of polymers
	2.2 Graph Theoretical Analyses Of polymers
		2.2.1 Graphs
		2.2.2 Nomenclature
		2.2.3 Folding Construction of Graphs (Polymers)
		2.2.4 Types of Graphs (Polymers)
	2.3 Knot Theoretical Analyses Of polymers
		2.3.1 Knots, Links, And spatial Graphs
		2.3.2 Topological Isomers
		2.3.3 Topological Chirality
		2.3.4 Rigid Vertex Versus Non-rigid Vertex
	2.4 Summary and Perspective
	References
3 Classification, Notation and Isomerism of Topological Polymers
	3.1 Classification of Polymer Substances by Their Topologies
	3.2 Classification of Acyclic and Monocyclic Polymer Topologies
	3.3 Classification of Dicyclic Polymer Topologies
	3.4 Tri-, Tetra- and Pentacyclic Polymer Topologies
	3.5 Topological Insights into Polymeric Constitutional Isomers
	3.6 Topological Insights into Polymeric Stereoisomers
	References
4 Exact Evaluation of the Mean Square Radius of Gyration for Gaussian Topological Polymer Chains
	4.1 Introduction
	4.2 Elements of Graph Theory
		4.2.1 Boundary Matrix
		4.2.2 The Space of Paths
		4.2.3 Singular Value Decomposition of Boundary Matrix B
	4.3 Graph Embeddings
		4.3.1 Direct Sum Decomposition of the Space of Paths
		4.3.2 Centered Conformations
		4.3.3 Diagonalization of the Graph Laplacian in Terms of Eigenmodes
		4.3.4 Mean Square Radius of Gyration
	4.4 Exact Dependence of the Mean Square Radius of Gyration on Polymerization Degree
		4.4.1 Subdivision
		4.4.2 Resistance Distances in Electrical Circuits
		4.4.3 Derivation of an Exact Formula for the n-subdivided Theta Graph
		4.4.4 Exact Expressions of the Mean Square Radius of Gyration for the n-subdivided Complete Graphs
	4.5 Asymptotic Value of the Mean Square Radius of Gyration for an Arbitrary Complete Graph
	4.6 Perspectives on Gaussian Networks
	4.7 Concluding Remarks
	References
5 Fundamentals of the Theory of Chromatography of Topologically Constrained Random Walk Polymers
	5.1 Introduction
	5.2 Basic Model and Equations
	5.3 Unified Approach for Calculating the Partition Coefficient of an Arbitrary TCRW Polymer
		5.3.1 Generalized Model and Common Parameters for a Complex TCRW Polymer Interacting with Walls of a Slit-Like Pore
		5.3.2 Graph Representation of a Complex Macromolecule
		5.3.3 Partition Coefficient
		5.3.4 A Theoretical Chromatograph
	5.4 Theory in Chromatographic Applications
		5.4.1 Chromatographic Separation of Linear and Ring Polymers
		5.4.2 More Complex Topological Polymers
		5.4.3 Simulating Chromatographic Separations of Heterogeneous Topological Polymers and Copolymers
		5.4.4 Comparison of Theory and Experiment
	5.5 Concluding Remarks and Prospects for Further Development of the Theory of Chromatography of Topologically Complex Polymers
	Appendix
	References
6 Construction of Multicyclic Polymer Topologies through Electrostatic Self-assembly and Covalent Fixation (ESA-CF)
	6.1 Introduction
	6.2 Electrostatic Self-assembly and Covalent Fixation by Telechelic Polymers
	6.3 Preparation of kyklo-Telechelics by the ESA-CF Protocol
	6.4 Construction of fused-Multicyclic Polymer Topologies
	6.5 Construction of spiro-, bridged-, and hybrid-Multicyclic Polymer Constructions
	6.6 Future Perspectives on the Construction of Complex Polymer Topologies
	References
Part II Theories and Practices of Polymer Folding Topologies
7 Topological Analysis of Folded Linear Molecular Chains
	7.1 Circuit Topology of Folded Chains
		7.1.1 Principles of Circuit Topology
		7.1.2 Topology Rules and Their Inference
		7.1.3 Coding Circuit Topology
	7.2 Generalized Circuit Topology
		7.2.1 Entanglement Expressed via Soft Contacts
		7.2.2 Beyond Soft Contacts: Completeness of Generalized Circuit Topology
		7.2.3 Circuit Topology and Knot Theory
		7.2.4 Circuit Topology and Network Topology
	References
8 DNA Knots
	8.1 Introduction
	8.2 Spontaneous Knotting of DNA in Solution
		8.2.1 Experimental Results
		8.2.2 Theoretical Modelling and Interpretation
	8.3 Native Knotting of Genomic DNA
		8.3.1 Viral DNA
		8.3.2 Theoretical Modelling and Interpretation
		8.3.3 Bacterial DNA
		8.3.4 Eukaryotic DNA
	8.4 RNA (un)Knotting
	8.5 Conclusions
	References
9 Cyclotides—Cyclic and Disulfide-Knotted Polypeptides
	9.1 Introduction
	9.2 Biosynthesis
	9.3 Cyclotides
	9.4 Topology
	9.5 Concluding Remarks and Outlook
	References
10 Construction of a Macromolecular K3,3 Graph Topology by the ESA-CF Polymer Folding
	10.1 Introduction
	10.2 Preparation of a Dendritic Precursor for the Construction of a K3,3 Graph Topology
	10.3 Constructing a Macromolecular K3,3 Graph by the ESA-CF Protocol
	10.4 Perspectives Toward Elusive Polymer Topologies
	References
11 Programmed Polymer Folding
	11.1 Introduction
	11.2 Topology and Folding Landscape
	11.3 Guided Folding and Folding Catalysts
	11.4 Bond and Backbone Chemistry
		11.4.1 Designing New Proteins
		11.4.2 Designing DNA-Based Folded and Knotted Chains
		11.4.3 Folded Single-Chain Polymers of Non-biological Origin
		11.4.4 Enzyme Inspired Design of Polymeric Catalysts
		11.4.5 Optically Controlled Folding Polymers
	11.5 Purification and Characterization
	11.6 Concluding Remarks and Outlooks
	References
12 Spatially and Chemically Programmed Polymer Folding by the ESA-CF Protocol
	12.1 Programmed Polymer Folding
	12.2 A Pair of Telechelic Precursors for the Programmed Polymer Folding
	12.3 The Programmed Polymer Folding of Telechelic Precursors Having Periodic Nodal Units
	12.4 SEC Deconvolution Analysis of the Polymer Folding Products from the Linear Precursor Having Periodic Nodal Units
	References
13 Macromolecular Rotaxanes, Catenanes and Knots
	13.1 Introduction
	13.2 Polyrotaxanes and Polypseudorotaxanes
		13.2.1 Cyclodextrin-Based Polyrotaxanes and Pseudorotaxanes
		13.2.2 Crown Ether-Based Polyrotaxanes and Polypseudorotaxanes
		13.2.3 Polyrotaxanes and Polypseudorotaxanes Based on Other Macrocycles
	13.3 Polymeric Knots or Knotted Polymers
	13.4 Polycatenanes
	13.5 Summary and Prospectus
	References
Part III Cyclic Polymer Innovations: Syntheses
14 Recent Progress on the Synthesis of Cyclic Polymers
	14.1 Introduction
	14.2 Bimolecular Ring-Closure
	14.3 Unimolecular Ring-Closure
	14.4 Homodifunctional Ring-Closure
	14.5 Heterodifunctional
	14.6 Ring-Expansion Polymerization
	14.7 Ring-Expansion Polymerization of Lactones
	14.8 Ring-Expansion Metathesis Polymerization
	14.9 Zwitterionic Ring-Opening Polymerization
		14.9.1 Nitroxide-Mediated Radical Polymerization
		14.9.2 Thermally Induced Radical Ring-Expansion Polymerization
		14.9.3 Ring-Expansion Polymerization of Thiiranes
		14.9.4 Catenanes and Knotted Polymers via the Ring-Expansion Polymerization of Lactones
		14.9.5 Conclusion
	References
15 Recent Progress on the Synthesis of Cyclic Polymers via Ring-Closure Methods
	15.1 Introduction
	15.2 Unimolecular Ring-Closure Strategy
		15.2.1 Unimolecular Ring-Closure Strategy Based on Non-irradiated Click Chemistry
		15.2.2 Unimolecular Ring-Closure Strategy Based on Photo-Induced Click Chemistry
	15.3 Bimolecular Ring-Closure Strategy Based on Self-accelerating Click Chemistry
	15.4 Conclusions
	References
16 Ring-Expansion Polymerization of Cycloalkenes and Linear Alkynes by Transition Metal Catalysts
	16.1 Introduction
		16.1.1 Background
		16.1.2 Cyclic Polymer Synthesis
		16.1.3 Ring-Expansion Polymerization (REP)
	16.2 Ring-Expansion Metathesis Polymerization (REMP)
		16.2.1 Ruthenium Catalysts for REMP
		16.2.2 Tungsten Catalysts for Ring-Expansion Metathesis Polymerization
	16.3 Conclusion
	References
17 Synthesis of Cyclic Vinyl Polymers via N-Heterocyclic Carbene (NHC)-Initiated Anionic Polymerization and Subsequent Ring-Closure Without Highly Dilute Conditions
	17.1 Research Background in Synthesis of Cyclic Polymers via Chain Polymerization
	17.2 NHC-Initiated Anionic Polymerization of Alkyl Sorbate in the Presence of Bulky Lewis Acid and Subsequent Ring-Closure Without Highly Dilution
	17.3 Expansion of Range of Acceptable Vinyl Monomers
	17.4 Direct Observation of Cyclic Structures
	References
18 Controlled Ring-Expansion Polymerization Based on Acyl-Transfer Polymerization of Thiiranes with Aromatic Heterocycles as Initiators
	18.1 Introduction
	18.2 Ring-Opening Reaction of Thiiranes with Active Ester Groups Catalyzed by Quaternary Onium Halides
	18.3 Acyl-Transfer Polymerization of Thiiranes
	18.4 Ring-Expansion Acyl-Transfer Polymerization of Thiiranes with Cyclic Initiators
		18.4.1 Ring-Expansion Polymerization of Thiiranes with Cyclic Aromatic Thiourethane Initiator: The Polymerization Properties
		18.4.2 Ring-Expansion Polymerization of Thiiranes with Cyclic Aromatic Dithiocarbamate Initiator: Comparison of Acyl-Transfer and Thioacyl-Transfer Polymerization
		18.4.3 Post-polymerization and Block Copolymerization Based on Cyclic Aromatic (Di)thiocarbamates-Initiated Polysulfides as Macro-initiators
		18.4.4 Glass Transition Properties of BT-Initiated Cyclic Polysulfides with Well-Defined Cyclic Topology
	References
19 A Conjunctive RC and RE Polymer Cyclization with Zwitterionic Telechelic Precursors
	19.1 Introduction
	19.2 Telechelic Poly(THF)s Having a Pair of a Cyclic Ammonium and a Carboxylate Groups for Unimolecular ESA-CF Polymer Cyclization
	19.3 Unimolecular Polymer Cyclization with Telechelic Poly(THF)s Having a Pair of a Cyclic Ammonium and a Carboxylate Groups
	19.4 Perspectives of Unimolecular Polymer Cyclization with Zwitterionic Telechelic Precursors
	References
20 Cyclic Polymers Synthesized by Spontaneous Selective Cyclization Approaches
	20.1 General Approaches for Synthesizing Cyclic Polymers
	20.2 Unique Approaches for Synthesizing Cyclic Polymers via Spontaneous Selective Cyclization Approaches
	20.3 Synthesis of Cyclic Polymers via DCC: Using Ring/Chain Equilibria
	20.4 Synthesis of Cyclic Polymers via DCC: Using REP
	20.5 Synthesis of Cyclic Polymers via Rotaxane Chemistry
	20.6 Foresight
	References
21 Unstoichiometric Polycondensation for the Synthesis of Aromatic Cyclic Polymers
	21.1 Introduction
	21.2 Cyclic Polymer from Conventional Polycondensation
	21.3 Cyclic Polymer from Unstoichiometric Polycondensation
		21.3.1 Background and Discovery
		21.3.2 Cyclic Polyphenylenes
		21.3.3 Extensively Conjugated Cyclic Polyarylenes
		21.3.4 Cyclic Polyheteroarylenes
	21.4 Conclusion
	References
Part IV Cyclic Polymer Innovations: Topology Effects
22 Entanglement in Solution of Non-concatenated Rings
	22.1 Introduction
	22.2 Brief Reminder on Ring Conformation
		22.2.1 Size Scaling
		22.2.2 Topological Volume
	22.3 Entanglement
	22.4 Dynamical Entanglement Analysis
		22.4.1 Displacement Correlation
		22.4.2 Vector Field Representation
		22.4.3 Spatial-Temporal Entanglement Structure
		22.4.4 Mean Field Picture
	22.5 Outlooks
	References
23 Dilute Solution Properties of Ring Polymers
	23.1 Gaussian Ring
	23.2 Wormlike Ring
	23.3 Analyses of Experimental Data
	References
24 Cyclic Polymers for Innovative Functional Materials
	24.1 Introduction
	24.2 Amphiphilicity and Self-assembly
	24.3 Reversible Topological Transformations
	24.4 All π-Conjugated Cyclic Polymers
	24.5 Stabilization of Gold Nanoparticles
	24.6 Conclusions
	References
25 Surface Functionalization with Cyclic Polymers
	25.1 Introduction
	25.2 Cyclic Polymers on Macroscopic Surfaces
	25.3 Cyclic Polymer Shells on Nanoparticles
	25.4 Conclusions
	References
26 Morphological Significances of Cyclic Polymers in Solution and Solid State
	26.1 Introduction
	26.2 Morphology of Cyclic Polymers in Solution
	26.3 Morphology of Cyclic Polymers in Bulk State
	26.4 Morphology of Cyclic Polymers in Thin Films
	26.5 Concluding Remarks
	References
27 Transforming Cyclic/Linear Polymer Topologies: Emerging Techniques and Opportunities
	27.1 Introduction
	27.2 Reaction Design for Topological Transformation
		27.2.1 Reversible Cycloaddition Reaction
		27.2.2 Cyclization by Stable Radicals
	27.3 Linear–Cyclic Topological Transformations Based on Cycloaddition Reactions
	27.4 Linear–Cyclic Topological Transformations Based on Radical Reactions
	27.5 Creation of Dynamic Functions Based on Topological Transformations
		27.5.1 Development of Polymers that Control Viscoelasticity with Recombination of Network–Star–8-Shaped Topology
		27.5.2 Development of Silicone Materials with Physical Properties Changed by Recombination of Cyclic–Linear Topology
	References