Diudea Multi-shell Polyhedral Clusters

1. Auflage 2017
ISBN: 978-3-319-64123-2
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 10, 451 Seiten

Reihe: Carbon Materials: Chemistry and Physics

This volume presents new methodologies and rationalizes existing methods that are used in the design of multi-shell polyhedral clusters. The author describes how the methods used are extended from 2D-operations on maps to 3D (and higher dimensional) Euclidean space. A variety of structures is designed and described in detail and classified giving rise to an atlas of multi-shell nanostructures. The book therefore sheds a new light on the field of crystal and quasicrystal structures, an important part of nanoscience and nanotechnology. The author goes on to show how the recently established methods are used for building complex multi-shell nanostructures and how this completes the existing information in the field. The atlas of such structures is completed with atomic coordinates (included as supplementary material). The content of this book gives a useful insight into structure elucidation and suggests new material synthesis.

Prof. Dr. Mircea Vasile Diudea is a  Professor of Mathematical Chemistry and Nanoscience at Babes-Bolyai University, Faculty of Chemistry and Chemical Engineering, Cluj, Romania. 
Prof. Diudea has edited/authored 11 books:   1. A. R. Ashrafi and M. V. Diudea (Eds), Distance, Symmetry, and Topology in Carbon Nanomaterials, Springer Intl. Pub. Switzerland 2016. 2. M. V. Diudea and C. L. Nagy (Eds), Carbon Materials: Chemistry and Physics. Vol. 6, Diamond and Related Nanostructures. Springer, Dordrecht, 2013. 3. M. V. Diudea (Ed), Nanostructures, Novel Architecture, Nova, New York, 2005. 4. M. V. Diudea, (Ed), QSPR/QSAR Studies by Molecular Descriptors, Nova, New York, 2001. 5. M. V. Diudea, Nanomolecules and Nanostructures - Polynomials and Indices, MCM, No. 10, Univ. Kragujevac, Serbia, 2010. 6. M. V. Diudea and Cs. L. Nagy, Periodic Nanostructures, Springer, 2007. 7. M. V. Diudea, M. S. Florescu, and P. V. Khadikar, Molecular Topology and Its Applications, Eficon, Bucharest, 2006. 8. M.V. Diudea, I. Gutman and L. Jäntschi, Molecular Topology, Nova, New York, 2002. 9. M.V. Diudea and O. Ivanciuc, Molecular Topology, COMPREX, Cluj, 1995 (in Romanian). 10.   M. V. Diudea ; M. Pitea; M. Butan, Fenothiazines and structurally related drugs. DACIA, Cluj, 1992 (in Romanian)., 278p. 11.   M. V. Diudea, S. Todor and A. Igna, Aquatic Toxicology. DACIA, Cluj, 1986 (in Romanian).

Autoren/Hrsg.

Diudea, Mircea Vasile

Inhaltsverzeichnis

1;Preface;6
2;Acknowledgements;9
3;Contents;10
4;List of Abbreviations;13
5;Chapter 1: Basic Chemical Graph Theory;14
5.1;1.1 Basic Definitions in Graphs;14
5.2;1.2 Topological Matrices and Indices;18
5.2.1;1.2.1 Adjacency Matrix;18
5.2.2;1.2.2 Distance Matrix;19
5.2.3;1.2.3 Detour Matrix;20
5.2.4;1.2.4 Combinatorial Matrices;21
5.2.5;1.2.5 Wiener Matrices;21
5.2.6;1.2.6 Cluj Matrices;22
5.2.7;1.2.7 Distance-Extended Matrices;24
5.2.8;1.2.8 Walk Matrices;25
5.2.9;1.2.9 Reciprocal Matrices;27
5.2.10;1.2.10 Layer and Shell Matrices;27
5.2.10.1;1.2.10.1 Layer Matrices;27
5.2.10.2;1.2.10.2 Shell Matrices;28
5.2.10.3;1.2.10.3 Centrality Index;30
5.3;1.3 Topological Symmetry;31
5.4;References;32
6;Chapter 2: Operations on Maps;35
6.1;2.1 Dual d;35
6.2;2.2 Medial m;37
6.3;2.3 Truncation t;38
6.4;2.4 Polygonal Mapping pn;38
6.5;2.5 Snub s;39
6.6;2.6 Leapfrog l;39
6.7;2.7 Quadrupling q;40
6.8;2.8 Septupling sn;41
6.9;Chapter 2 Atlas: Single Shell Clusters;43
6.10;References;46
7;Chapter 3: Definitions in Polytopes;48
7.1;3.1 Polyhedra;48
7.2;3.2 n-Dimensional Structures;51
7.3;3.3 Abstract Structures;54
7.3.1;3.3.1 Posets;55
7.3.2;3.3.2 Vertex Figure;56
7.3.3;3.3.3 Abstract Polytope;57
7.4;3.4 Polytope Realization;58
7.4.1;3.4.1 P-Centered Clusters;58
7.4.2;3.4.2 Cell-in-Cell Clusters;60
7.4.3;3.4.3 24-Cell and Its Derivatives;62
7.5;References;64
8;Chapter 4: Symmetry and Complexity;66
8.1;4.1 Euler Characteristic;67
8.2;4.2 Topological Symmetry;68
8.3;4.3 Centrality Index;69
8.4;4.4 Ring Signature Index;70
8.4.1;4.4.1 Ring Signature in a Translational Network;72
8.4.2;4.4.2 Ring Signature in Spongy Structures of Higher Rank;74
8.4.3;4.4.3 Ring Signature in Spongy Hypercubes;77
8.4.4;4.4.4 Truncation Operation;77
8.5;4.5 Pairs of Map Operation;80
8.6;References;85
9;Chapter 5: Small Icosahedral Clusters;87
9.1;5.1 Small Cages: Source of Complex Clusters;87
9.2;5.2 Truncated MP Icosahedral Clusters;88
9.3;5.3 Clusters by Medial Operation;89
9.4;5.4 Clusters of Higher Rank;90
9.5;Chapter 5 Atlas: Small Icosahedral Clusters;96
9.6;References;134
10;Chapter 6: Large Icosahedral Clusters;135
10.1;6.1 Small Complex Clusters;135
10.2;6.2 Icosahedral Clusters Derived from the C45 Seed;137
10.3;6.3 Clusters of Dodecahedral Topology;142
10.4;6.4 Clusters of Icosahedral Topology;143
10.5;6.5 Rhomb Decorated Clusters;145
10.6;Chapter 6 Atlas: Large Icosahedral Clusters;147
10.7;References;195
11;Chapter 7: Clusters of Octahedral Symmetry;197
11.1;7.1 Small Clusters as Seeds for Complex Structures;197
11.2;7.2 Clusters Decorated by Octahedra;198
11.3;7.3 Clusters Decorated by Dodecahedra;199
11.4;7.4 Rhomb Decorated Octahedral Clusters;200
11.5;7.5 Cubic Net Transforming;203
11.6;Chapter 7 Atlas: Octahedral Clusters;205
11.7;References;255
12;Chapter 8: Tetrahedral Clusters;256
12.1;8.1 Small Tetrahedral Clusters;256
12.2;8.2 Tetrahedral Clusters of Higher Rank;257
12.3;8.3 Tetrahedral Clusters Derived From Ada20;257
12.4;8.4 Tetrahedral Hyper-structures Decorated with Only Dodecahedra;260
12.5;Chapter 8 Atlas: Tetrahedral Clusters;262
12.6;References;288
13;Chapter 9: C60 Related Clusters;290
13.1;9.1 Structures Derived from the Cluster P32@dC60.33;290
13.2;9.2 Stellated Clusters;291
13.3;9.3 C750 Related Structures;293
13.3.1;9.3.1 Duals of C750 and Related Structures;296
13.3.2;9.3.2 Medials of C750 and Related Clusters;296
13.3.3;9.3.3 Truncated C750 and Related Clusters;299
13.4;Chapter 9 Atlas: C60 Related Structures;300
13.5;References;343
14;Chapter 10: Chiral Multi-tori;344
14.1;10.1 Design of Chiral Multi-tori;344
14.2;10.2 Dodecahedron Related Structures;347
14.3;10.3 Cube Related Structures;349
14.4;10.4 Tetrahedron Related Structures;350
14.5;10.5 C60 Related Structures;351
14.6;Chapter 10 Atlas: Chiral Multi-tori;356
14.6.1;Dodecahedron Related Structures;356
14.7;References;371
15;Chapter 11: Spongy Hypercubes;372
15.1;11.1 Simple Toroidal Hypercubes;372
15.2;11.2 Complex Toroidal Hypercubes;374
15.3;11.3 Tubular Hypercubes;375
15.4;11.4 Spongy Hypercubes;376
15.5;11.5 Truncation of Hypercube;379
15.6;11.6 Counting Polynomials in Hypercubes;381
15.6.1;11.6.1 Omega Polynomial;381
15.6.1.1;11.6.1.1 Omega Polynomial in Hypercubes;382
15.6.1.2;11.6.1.2 Omega Polynomial in Tubular Hypercubes;382
15.6.1.3;11.6.1.3 Omega Polynomial in Spongy Hypercubes;384
15.6.2;11.6.2 Cluj Polynomials;386
15.6.2.1;11.6.2.1 Cluj Polynomials in Hypercubes;387
15.6.2.2;11.6.2.2 Cluj Polynomials in Toroidal Hypercubes;387
15.6.2.3;11.6.2.3 Cluj Polynomials in SpongyHypercubes;388
15.7;References;392
16;Chapter 12: Energetics of Multi-shell Clusters;394
16.1;12.1 Introduction;394
16.2;12.2 C20 Aggregation;395
16.3;12.3 Hyper-graphenes by D5 Substructures;398
16.4;12.4 Hyper-graphenes by C60 Units;398
16.5;12.5 C60 Aggregates with Tetrahedral and Icosahedral Symmetry;402
16.6;12.6 C60 Network by [2+2] Cycloaddition;405
16.7;12.7 Computational Methods;409
16.8;Chapter 12 Atlas: Energetics of Multi-shell Clusters;410
16.9;References;445
17;Index;448