Mesoporous hemispherical

RT ln PJP) ln PJP) for constant, )>=8.8510 J/cm, Fi,=34.71 cm /mol and 7=77.5 K. For a hemispherical miniscus cos0=l, while for a cylindrical cos9=0.5. Values of cos0vapor-liquid interface geometry and y and Vl values that are considered constant and typical of purely mesoporous materials. 

BJH and Dollimore-Heal methods are based on the assumption that the statistical thickness of the adsorbed layer is independent of the surface curvature and assume that the meniscus between vapor and condensed phase is hemispherical. This kind of meniscus is met in the case of a cylindrical pore during desorption. The hypothesis of constant thickness, independently of surface curvature, is justified for large mesopores, but generally leads to underestimation of pore size [7]. 

Yan Z, Meng H, Shi L, Li Z, Shen PK (2010) Synthesis of mesoporous hollow carbon hemispheres as highly efficient Pd electrocatalyst support for ethanol oxidation. Electrochem Commun 12 689-692... 

Figure 11.5 Scanning electron microscop)r (SEM) images of hemispherical mesoporous silicon microparticles containing either large pores (a) or small pores (b). Reproduced from Ref [16], courtesy of Nature Publishing Group.

For very low diffusion coefficients smaller inter-gap spacings are required. Electron and hole hopping diffusion rates in fully shielded mesoporous oxides are low, typically 10 m s V with notable exceptions and therefore sub-micron inter-electrode gaps are necessary for feedback currents to be measurable. A focused ion beam (FIB) machined trench (ca. 400 600 nm wide) in tin-doped indium oxide (ITO) films has been suggested and used for films of mesoporous titania, chromium oxide,and for dye-modified metal-organic framework UMCM-1. The dual-hemisphere... 

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