Informational thermodynamic model for nanostructures

Kaatz, Forrest H.; Bultheel, Adhemar

doi:10.1007/s10910-014-0336-y

Cited by 8 publications

(5 citation statements)

References 50 publications

(62 reference statements)

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“…Magic formulas Dimension Our work adds to this analysis by adding more topological indices and more lattice dimensions when considering the graph energy. Also, when using a Hamiltonian in the statistical mechanics approach, we have demonstrated large N logarithmic behavior for the thermodynamic properties of 3D nanoclusters [11]. This work extends that analysis as the dimensionality changes and we find the large N logarithmic behavior still applies.…”

Section: Methodssupporting

confidence: 75%

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Dimensionality of hypercube clusters

Kaatz

Bultheel

2015

J Math Chem

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We investigate clusters of hypercubes in d-dimensional space as a function of the number of vertices, N , and number of cluster shells, L. The number of links, vertices, and exterior vertices exhibit 'magic number' characteristics versus L, as the dimension of the space changes. Starting with only the spatial coordinates, we create an adjacency and distance matrix that facilitates the calculation of topological indices, including the Wiener, hyper-Wiener, reverse Wiener, Szeged, Balaban, and Kirchhoff indices. Some known topological formulas for hypercubes when L = 1 are experimentally verified. The asymptotic limits with N of the topological indices are shown to exhibit power law behavior whose exponent changes with d and type of topological index. The asymptotic graph energy is linear with N , whose slope changes with d, and in 2D agrees numerically with previous calculations. Also, the thermodynamic properties such as entropy, free energy, and enthalpy of these lattices show logarithmic behavior with increasing N. The hypercubic clusters are projected onto 3D space when the dimensionality d > 3.

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Section: Methodssupporting

confidence: 75%

“…It is worthwhile to note that the C++ program only works for fullerenes, while our program only requires the coordinates. In a different type of analysis, we have modeled both fullerenes and nanoclusters [11,12].…”

Section: Introductionmentioning

confidence: 99%

Dimensionality of hypercube clusters

Kaatz

Bultheel

2015

J Math Chem

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“…It is worthy of note that the lattice constant within a nanoparticle might be size dependent. They might be expected to decrease as −(1 + K • D max ) −1 where D max is the diameter, and K shows a dependence on the shear modulus, the surface energy and the shape factor (Kaatz and Bultheel 2014). Among BCC, FCC, and HCP clusters, the last ones are the most likely to show deformation twins under strain, as the number of slip systems for a structural transition is eventually not sufficient.…”

Section: Taxonomy Of Metallic Clusters: Classification and Characteri...mentioning

confidence: 99%

Structural properties of sub-nanometer metallic clusters

Baletto

2019

J. Phys.: Condens. Matter

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At the nanoscale, the investigation of structural features becomes fundamental as we can establish relationships between cluster geometries and their physicochemical properties. The peculiarity lies in the variety of shapes often unusual and far from any geometrical and crystallographic intuition clusters can assume. In this respect, we should treat and consider nanoparticles as a new form of matter. Nanoparticle structures depend on their size, chemical composition, ordering, as well as external conditions e.g. synthesis method, pressure, temperature, support. On top of that, at finite temperatures nanoparticles can fluctuate among different structures, opening new and exciting horizons for the design of optimal nanoparticles for advanced applications. This article aims to overview geometrical features of transition metal clusters and of their various rearrangements.

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“…As molecules in some approaches are approximated as graphs, it was not surprising that the information theory then has come into chemistry. For example, it is used in the original and modified forms to describe structural diversity of organic compounds, − chemical reactions, ,− and physicochemical processes in open systems. − Shannon’s approach is an efficient auxiliary tool when diverse nanosystems − and processes in them are studied (e.g., association of fullerenes or nanotubes).…”

Section: Introductionmentioning

confidence: 99%

Information Entropy of Fullerenes

Sabirov

Ōsawa

2015

J. Chem. Inf. Model.

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The reasons for the formation of the highly symmetric C60 molecule under nonequilibrium conditions are widely discussed as it dominates over numerous similar fullerene structures. In such conditions, evolution of structure rather than energy defines the processes. We have first studied the diversity of fullerenes in terms of information entropy. Sorting 2079 structures from An Atlas of Fullerenes [ Fowler , P. W. ; Manolopoulos , D. E. An Atlas of Fullerenes ; Oxford : Clarendon , 1995 . ], we have found that the information entropies of only 14 fullerenes (<1% of the studied structures) lie between the values of C60 and C70, the two most abundant fullerenes. Interestingly, buckminsterfullerene is the only fullerene with zero information entropy, i.e., an exclusive compound among the other members of the fullerene family. Such an efficient sorting demonstrates possible relevance of information entropy to chemical processes. For this reason, we have introduced an algorithm for calculating changes in information entropy at chemical transformations. The preliminary calculations of changes in information entropy at the selected fullerene reactions show good agreement with thermochemical data.

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Informational thermodynamic model for nanostructures

Cited by 8 publications

References 50 publications

Dimensionality of hypercube clusters

Dimensionality of hypercube clusters

Structural properties of sub-nanometer metallic clusters

Information Entropy of Fullerenes

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