Fractal dimension of zeolite catalysts

Fractal Modelling of Heterogeneous Catalytic Materials and Processes

This review considers the use of fractal concepts to improve the development, fabrication, and characterisation of catalytic materials and supports. First, the theory of fractals is discussed, as well as how it can be used to better describe often highly complex catalytic materials and enhance structural characterisation via a variety of different methods, including gas sorption, mercury porosimetry, NMR, and several imaging modalities. The review then surveys various synthesis and fabrication methods that can be used to create catalytic materials that are fractals or possess fractal character. It then goes on to consider how the fractal properties of catalysts affect their performance, especially their overall activity, selectivity for desired products, and resistance to deactivation. Finally, this review describes how the optimum fractal catalyst material for a given reaction system can be designed on a computer.

Valence Topological Charge-Transfer Indices for Dipole Moments

New valence topological charge-transfer indices are applied to the calculation of dipole moments. The algebraic and vector semisum charge-transfer indices are defined. The combination of the charge-transfer indices allows the estimation of the dipole moments. The model is generalized for molecules with heteroatoms. The ability of the indices for the description of the molecular charge distribution is established by comparing them with the dipole moments of a homologous series of phenyl alcohols. Linear and non-linear correlation models are obtained. The new charge-transfer indices improve the multivariable non-linear regression equations for the dipole moment. When comparing with previous results, the variance decreases 92%. No superposition of the corresponding G_k–J_k and – pairs is observed. This diminishes the risk of co-linearity. Inclusion of the oxygen atom in the π-electron system is beneficial for the description of the dipole moment, owing to either the role of the additional p orbitals provided by the heteroatom or the role of steric factors in the π-electron conjugation. Linear and non-linear correlations between the fractal dimension and various descriptors point not only to a homogeneous molecular structure but also to the ability to predict and tailor drug properties.