Topology of C20 Based Spongy Nanostructures
Diudea Mircea V. 1, Szefler Beata 2*
1 Department of Chemistry, Faculty of Chemistry and Chemical Engineering
Babes-Bolyai University, 400028 Cluj,Romania2 Department of Physical Chemistry,Collegium Medicum
Nicolaus Copernicus University,Kurpinskiego 5, 85-096,Bydgoszcz,Poland
∗E-mail: beatas@cm.umk.pl
Received:
Received: 15 April 2015; accepted: 23 April 2015; published online: 06 June 2015
DOI: 10.12921/cmst.2015.21.02.002
Abstract:
Spongy materials are encountered in nature in zeolites used as molecular sieves. There are also synthetic compounds like spongy carbon, metal-organic frameworks MOFs, etc, with a hollow structure. The design and topological study of some hypothetical spongy nanostructures is presented in terms of map operations and genus calculation on their associated graphs. The design of nanostructures was performed by original software packages.
Key words:
References:
[1] M. V. Diudea, ed., Nanostructures: Novel Architecture,
NOVA, New York, 2005.
[2] M. V. Diudea and C. L. Nagy, Periodic Nanostructures,
Springer,Dordrecht,2007.
[3] M. V.Diudea, Nanomoleculesand Nanostructures: Polyno-
mialsand Indices,Univ. Kragujevac, Serbia, 2010.
[4] M. V. Diudea and C.L. Nagy, eds., Diamond and Related
Nanostructures,Springer, Dordrecht, Heidelberg,New York,
London, 2013.
[5] H. Terrones,A. L.Mackay,Triply periodic minimalsurfaces
decoratedwith curvedgraphite, Chem.Phys. Lett.207, 45-
50 (1993).
[6] H. Terrones,M.Terrones,Curvednanostructured materials,
NewJ.Phys5,1261-12637 (2003).
[7] H. Terrones, A.L. Mackay, FromC60to negativelycurved
graphite,Prog.CrystalGrowth Charact.34, 25-36(1997).
[8] S.J. Townsend, T.J. Lenosky, D.A. Muller,C.S. Nichols,
V.Elser, Negativelycurved graphitesheet model ofamor-
phous carbon, Phys.Rev. Lett.69, 921-924 (1992).
[9] H. A. Schwarz, Über Minimalflächen, Monatsber. Berlin
Akad.,Berlin, 1865.
[10] H. A.Schwarz,Gesammelte MatematischeAbhandlungen,
Springer,Berlin, 1890.
[11] F. Harary, Graph Theory, Addison-Wesley, Reading, MA,
1969.
[12] L.Euler, Elementa doctrinae solidorum,Novi. Comm. Acad.
Scient.Imp.Petrop. 4,109-160 (1758).
[13] O. Bonnet,Notesur la therorie generale des surfaces,CR.
Acad. Sci.Paris37, 529-532 (1853).
[14] M.V. Diudea,P.E.John, A.Graovac, M. Primorac, T.Pisan-
ski, Leapfrogandrelated operations on toroidalfullerenes,
Croat. Chem.Acta 76,153-159(2003).
[15] M.V. Diudea, Covering forms in nanostructures, Forma
(Tokyo)19, 131-163(2004).
[16] M.V. Diudea,M.Stefu,
̧
P.E.John,A.Graovac, Generalized
operations onmaps,Croat. Chem.Acta,79, 355-362 (2006).
[17] M. Stefu, M.V. Diudea,P.E.John,Compositeoperationson
maps, Studia Univ.“Babes-Bolyai”,50, 165-174 (2005).
[18] M.V. Diudea,Nanoporous carbon allotropesbyseptupling
mapoperations, J.Chem. Inf.Model.45, 1002-1009 (2005).
[19] T.PisanskiandM.Randi ́c, Bridgesbetweengeometryand
graph theory,Geometry at Work. MAA Notes, 53,174-194
(2000).
[20] M.V. Diudeaand B.Szefler, Nanotubejunctions and the
genusofmulti-tori, Phys. Chem.Chem.Phys., 14,8111-8115
(2012).
[21] CoxeterHSM(1973) Regular polytopes.3rd edn. Dover Pub-
lications,New York
[22] B.Grünbaum(1967) Convex polytopes. Wiley, New York
[23] WellsAF (1977) Three-dimensional nets andpolyhedral. Wi-
ley,NewYork
[24] Ziegler GM (1995)Lectures onpolytopes.Springer-Verlag,
NewYork.
[25] Stefu M, Diudea MV,CVNET software„ Babes-BolyaiUniv,
Cluj, 2005.
[26] Cs.L.Nagyand M.V.Diudea, Nano-Studiosoftware, “Babes-
Bolyai”Univ.,Cluj, 2009.
Spongy materials are encountered in nature in zeolites used as molecular sieves. There are also synthetic compounds like spongy carbon, metal-organic frameworks MOFs, etc, with a hollow structure. The design and topological study of some hypothetical spongy nanostructures is presented in terms of map operations and genus calculation on their associated graphs. The design of nanostructures was performed by original software packages.
Key words:
References:
[1] M. V. Diudea, ed., Nanostructures: Novel Architecture,
NOVA, New York, 2005.
[2] M. V. Diudea and C. L. Nagy, Periodic Nanostructures,
Springer,Dordrecht,2007.
[3] M. V.Diudea, Nanomoleculesand Nanostructures: Polyno-
mialsand Indices,Univ. Kragujevac, Serbia, 2010.
[4] M. V. Diudea and C.L. Nagy, eds., Diamond and Related
Nanostructures,Springer, Dordrecht, Heidelberg,New York,
London, 2013.
[5] H. Terrones,A. L.Mackay,Triply periodic minimalsurfaces
decoratedwith curvedgraphite, Chem.Phys. Lett.207, 45-
50 (1993).
[6] H. Terrones,M.Terrones,Curvednanostructured materials,
NewJ.Phys5,1261-12637 (2003).
[7] H. Terrones, A.L. Mackay, FromC60to negativelycurved
graphite,Prog.CrystalGrowth Charact.34, 25-36(1997).
[8] S.J. Townsend, T.J. Lenosky, D.A. Muller,C.S. Nichols,
V.Elser, Negativelycurved graphitesheet model ofamor-
phous carbon, Phys.Rev. Lett.69, 921-924 (1992).
[9] H. A. Schwarz, Über Minimalflächen, Monatsber. Berlin
Akad.,Berlin, 1865.
[10] H. A.Schwarz,Gesammelte MatematischeAbhandlungen,
Springer,Berlin, 1890.
[11] F. Harary, Graph Theory, Addison-Wesley, Reading, MA,
1969.
[12] L.Euler, Elementa doctrinae solidorum,Novi. Comm. Acad.
Scient.Imp.Petrop. 4,109-160 (1758).
[13] O. Bonnet,Notesur la therorie generale des surfaces,CR.
Acad. Sci.Paris37, 529-532 (1853).
[14] M.V. Diudea,P.E.John, A.Graovac, M. Primorac, T.Pisan-
ski, Leapfrogandrelated operations on toroidalfullerenes,
Croat. Chem.Acta 76,153-159(2003).
[15] M.V. Diudea, Covering forms in nanostructures, Forma
(Tokyo)19, 131-163(2004).
[16] M.V. Diudea,M.Stefu,
̧
P.E.John,A.Graovac, Generalized
operations onmaps,Croat. Chem.Acta,79, 355-362 (2006).
[17] M. Stefu, M.V. Diudea,P.E.John,Compositeoperationson
maps, Studia Univ.“Babes-Bolyai”,50, 165-174 (2005).
[18] M.V. Diudea,Nanoporous carbon allotropesbyseptupling
mapoperations, J.Chem. Inf.Model.45, 1002-1009 (2005).
[19] T.PisanskiandM.Randi ́c, Bridgesbetweengeometryand
graph theory,Geometry at Work. MAA Notes, 53,174-194
(2000).
[20] M.V. Diudeaand B.Szefler, Nanotubejunctions and the
genusofmulti-tori, Phys. Chem.Chem.Phys., 14,8111-8115
(2012).
[21] CoxeterHSM(1973) Regular polytopes.3rd edn. Dover Pub-
lications,New York
[22] B.Grünbaum(1967) Convex polytopes. Wiley, New York
[23] WellsAF (1977) Three-dimensional nets andpolyhedral. Wi-
ley,NewYork
[24] Ziegler GM (1995)Lectures onpolytopes.Springer-Verlag,
NewYork.
[25] Stefu M, Diudea MV,CVNET software„ Babes-BolyaiUniv,
Cluj, 2005.
[26] Cs.L.Nagyand M.V.Diudea, Nano-Studiosoftware, “Babes-
Bolyai”Univ.,Cluj, 2009.
