Shape effects

In classical catalysis by bulk soHd phases, high catalytic activity is often associated with specific surface ensembles defined by the Miller indices [218] of exposed facets that possess favorable geometries, bond distances, and coordination numbers, or with the presence of surface defects containing coordinatively highly unsaturated metal atoms [219-222]. Similar considerations can apply to model catalysts based on nanoparticles atomic ensembles defined by the exposed planar surfaces (facets), defects, and coordinatively unsaturated atoms located at the particle periphery (corners, edges, etc.) play crucial roles in defining shape effects in the catalytic activity of those particles [223-225]. 

Since a milestone paper in Science in 1996, the group of El-Sayed [238-240] has led the field of synthesis and applications of shape-specific nanoparticles. A classical example of the detailed study of metal-particle shape effects in catalysis was reported by Narayanan and El-Sayed using unsupported polyvinylpyrollidone (PVP) polymer-capped Pt shape-specific colloids (cubes, spheres, and tetrahedra) in a model electron transfer reaction between hexacyanoferrate(III) and thiosulfate 

The observed changes in the percentage of particles having a specific shape were most pronounced for tetrahedral nanoparticles, with cubic particles also undergoing significant changes while near-spherical particles proved to be rather 

Formation of hexane was catalyzed by Pt (110) octahedra at temperatures below 240 °C [251]. Catalysts containing Pt-truncated octahedra defined by (100) and (111) surfaces, and Pt spheres containing high-index surfaces produced 2-methylpentane. Finally, Pt (100) cubes led to the formation of cracking products (i.e., Cj-C ) under the same conditions. Interestingly, Pt spheres and truncated octahedra exhibited higher TOFs compared to octahedral (8 times at 240 °C) and cubic (50 times at 240 °C) nanoparticles. 

Finally, Lee et al. [232] have recently reported selective and shape-specific catalytic trans-to-CTsisomerizationofolefinsusingPttetrahedraterminatedwith(l 11) facets. This discovery can help to minimize the formation of unhealthy trans-fats during the partial hydrogenation of edible oils. Upon calcination at 575 K, supported tetrahedra lost their shape, forming round particles, which was reflected in loss of their catalytic activity for trans-to-ds conversion. 

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Tolbert S H et al 1996 Pressure-induced structural transformation in Si nanocrystais surface and shape effects Phys. Rev. Lett. 76 4384... 

UNIQUAC is significant because it provides a means to estimate multicomponent interactions using no more than binary interaction experimental data, bond angles, and bond distances. There is an implicit assumption that the combinatorial portion of the model, ie, the size and shape effects, can be averaged over a molecule and that these can be directly related to molecular surface area and volume. This assumption can be found in many QSAR methods and probably makes a significant contribution to the generally low accuracy of many QSAR prediction techniques. 

These provide a tie between theory and experimentally observed solute shape effects, and lead to a better understanding of SEC calibration practices. 

A Heyd, D Dhabhar. Particle shape effect on caking of coarse granulated antacid suspensions. Drug Cosmet Ind 125 42-45. 1979. 

The slip correction factors are important for particles smaller than 1 pm in diameter, which is rarely the case for pharmaceutical aerosols. Slip correction is required for the Stokes equation to remain predictive of particle behavior for these small particles. Therefore, assuming the absence of shape effects for particles in the Stokes regime of flow, Eq. (1) collapses into the following expression ... 

Microscopy with image analysis Light SEM 1-300 0.2-300 Sampling shape effects 49... 

The validation of CFD codes using pressure drop is most reliable when actual experimental data are taken in equipment identical to the situation that is being simulated. Existing literature correlations such as the Ergun equation are known to have shortcomings with respect to wall effects, particle shape effects, application to ordered beds and validity at high Re. The applicability of literature correlations to typical CFD simulation geometries needs to be examined critically before fruitful comparisons can be made. 

Geng Y, Dalhaimer P, Cai SS, Tsai R, Tewari M, Minko T, Discher DE (2007) Shape effects of filaments versus spherical particles in flow and drug delivery. Nat Nanotechnol 2 249-255. 

Bigeleisen, J. Nuclear size and shape effects in chemical reactions. Isotope chemistry of the heavy elements, J. Am. Chem. Soc., 118, 3676 (1996). 

As discussed above, accurate estimation of molecular weights may not be achieved under native conditions due to molecular shape effects. Performing... 

It was not until recently that Chen and Goodman probed the influence of the oxide support material on the intrinsic properties at the metal surface. By covering a titania support with one or two flat atomic layers of gold they eliminated, direct adsorbate-support interactions as well as particle size and shape effects. Their results definitively showed that the electronic properties at the metal surface changed due to charge transfer between the support and the metal. Furthermore, their comparison of one- and two-layer films highlighted the dependence of these effects on the thickness of the metal slab. 

Figure 5.9 Two examples of dynamic induced band-shape effects, (a) Weak coupling an absorption single line of the Yb + ion in LiNbOs (denoted by an arrow) is accompanied by the appearance of phonon side bands (reproduced with permission from Montoya et al., 2001) (b) Strong coupling the broadband luminescence of the Cr + ion in LiNbOs (reproduced with permission from Camarillo et al., 1992).

Tijssen, R., Schoenmakers, R.J., Bohmer, M.R., Koopal, L.K., and Billiet, H.A.H., Lattice models for the description of partitioning adsorption and retention in reversed-phase liquid-chromatography, including surface and shape effects, J. Chromatogr. A, 656, 135, 1993. 

Selected entries from Methods in Enzymology [vol, page(s)] Acquisition of frequency-discriminated spectrum, 239, 162-166, 170 sensitivity, 239, 169-173 constant-time, 239, 23-26 doublequantum filtered, 239, 236 gradient pulse experiments, 239, 185-189 protein structural information, 239, 377-379 pulse sequence and coherence transfer pathway, 239, 148-149 paramagnetic metalloprotein, 239, 494-497 data recording, SWAT method, 239, 166-169, 172 line shapes, effects of gradient pulses, 239, 162-166 identification of protein amino acid resonances, 232, 100 cyclosporin A, 239, 240-241. 

Molecular contact area, 148, 132, 133, 193 Molecular shape, effect on contact area upon bimUng, 218 MolecuW size of the eluite, 217 Molecular surftce area, in adsorption and partition, 226... 

Interestingly, a logarithmic transformation of the concentration axis will produce an S-shaped effect curve that is perfectly symmetrical around the point (In Cso%, Emsix /2). 

Absorption dominates over scattering for sufficiently small absorbing particles. Volumetric extinction by such particles is independent of their size but not of their shape we shall discuss shape effects further in the following chapter. 

Notable progress in analyzing nonspherical particles has been made by Fuchs (1975), who calculated absorption by cubes in the electrostatics approximation and applied the results to experimental data for MgO and NaCl. We shall discuss Fuchs s results at the end of Section 12.3. Langbein (1976) also did calculations for rectangular parallelepipeds, including cubes, which give valuable insights into nonspherical shape effects. Because the cube is a common shape of microcrystals, such as MgO and the alkali halides, these theoretical predictions have been used several times to interpret experimental data. We shall do the same for MgO. Our theoretical treatment of nonsphericity, however, is based on ellipsoids. Despite its simplicity, this method predicts correctly many of the nonspherical effects. 

More insight into shape effects in absorption spectra of small particles can be acquired from contour plots in the complex c plane lines of constant dimensionless cross section 3(Cabs)/kt> are shown in Fig. 12.9a, b, c. Note that the curves are symmetric about the lines c = — 2, c = - 1, and e = 0 for the sphere, needle, and disk, respectively. Three points representing certain solids... 

At this point the reader who has studied the preceding sections may well wonder why we are so interested in, if not obsessed with, ellipsoidal particles most real particles are no more ellipsoidal than they are spherical. One reason for devoting so much space to ellipsoids is that they are a means for dispelling widespread misconceptions about the nonexistence of shape effects in small-particle absorption spectra. For if there are strong shape effects in spectra of ellipsoidal particles, then there are certainly such effects in the spectra of other, less well-defined nonspherical particles. But there is at least one other reason, which may prove to be of greater practical utility the hope that spectra of ii regular particles can be approximated somehow by suitably averaging over all... 

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