The theoretical and experimental data on the breakup of droplets are reviewed. Several factors influence development of droplets: flow type and its intensity, viscosity ratio, elasticity of polymers, composition, thermodynamic interactions, time, etc. For Newtonian systems undergoing small, linear deformation, both the viscosity ratio and the capillary number control deformability of drops. On the other hand, the breakup process can be described by the dimensionless breakup time and the critical capillary number. Drops are more efficiently broken in elongational flow than in shear, especially when the viscosity ratio A 2 3. The drop deformation and breakup seems to be more difficult in viscoelastic systems than in Newtonian ones. There is no theory able to describe the deformability of viscoelastic droplet suspended in a viscoelastic or even Newtonian medium. The effect of droplets coalescence on the final morphology ought to be considered, even at low concentration of the dispersed phase, (bd 2 0.005. Several drop breakup and coalescence theories were briefly reviewed. However, they are of little direct use for quantitative prediction of the polymer blend morphology during compounding in a twin-screw extruder. Their value is limited to serving as general guides to the process modeling.
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Density Functional Theory Study of Transitional Metal Macrocyclic Complexes' Dioxygen-Binding Abilities and Their Catalytic Activities toward Oxygen Reduction ReactionZheng Shi and Jiujun Zhang* National Research Council Institute for Fuel Cell InnoVation, 4250 Wesbrook Mall, VancouVer, BC, Canada V6T 1W5 ReceiVed: October 31, 2006; In Final Form: March 23, 2007 In this paper, density functional theory method is applied to study the dioxygen-binding abilities of transition metal macrocyclic complexes and their electrocatalytic activities toward oxygen reduction reaction. Both end-on and side-on binding modes are examined. Electronic properties, such as ionization potential and Mulliken charge, are evaluated. The effects of central metal, ligand, and substituents on catalyst's dioxygen-binding ability and catalytic activity are investigated. The binding nature of dioxygen adduct is analyzed based on structure property. The general activity trend observed for phthalocyanines and porphyrins is rationalized with the calculated properties. It is illustrated that the catalyst's oxygen reduction activity is related to its ionization potential and dioxygen-binding ability. Cobalt porphyrin derivatives have high ionization potentials, which make them better catalysts than the corresponding iron derivatives, whereas for phthalocyanine systems, iron derivatives have large ionization potential and better dioxygen-binding ability, which make them good catalysts.
It is shown that the form of the Laplacian of the charge density provides a more complete resolution of the shell structure of atoms than the radial density function. The complete shell structure is resolved for s-block and most p-block atoms, but only the inner shells are resolved in the d-block elements. The shell structures revealed by the Laplacian of the charge density and the radial density function parallel one another where direct comparison is possible.
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