Diffusivity mesopore-controlled process

The measured surface area consists of both external and internal area where internal surface area includes all cracks or connected pores that are deeper than they are wide, varying from subatomic defects to pores of extreme size (Gregg and Sing, 1982). For example, micropores are dehned as pores with radius <2 nm, mesopores as pores with radius from 2 nm to 50 nm, and macropores as those with pores of diameter >50 nm. The main distinction between internal and external surface is that advection can control transport to and away from external surface while diffusion must control transport for internal pore space (Hochella and Banheld, 1995). Porosity may be related to crystallization or replacement processes (Putnis, 2002). 

Understanding the adsorption, diffusivities and transport limitations of hydrocarbons inside zeolites is important for tailoring zeolites for desired applications. Knowledge about diffusion coefficients of hydrocarbons inside the micropores of zeolites is important in discriminating whether the transport process is micropore or macropore controlled. For example, if the diffusion rate is slow inside zeolite micropores, one can modify the post-synthesis treatment of zeolites such as calcination, steaming or acid leaching to create mesopores to enhance intracrystalline diffusion rates [223]. The connectivity of micro- and mesopores then becomes an... 

The narrow molecular weight distributions accomplished by the supported catalysts were attributed to the absence of any organoaluminium co-catalyst dissocia-tion/reassociation processes at the heterogenized active neodymium centers. Furthermore, the order of the grafting sequence seemed to have minor implications for the catalyst performance. Control experiments have been conducted to explain the lower activity [0.9 (47) and 1.1 kg-PBD molNd h (48)] of the supported neodymium catalyst. Accordingly, an increase of the catalyst concentration (48) and use of a nonporous silica support (49) suggested that monomer diffusion and accessibility of the Nd centers are limited by the relatively small mesopores [dp = 2.4 (47) and 2.5 nm (48), after grafting]. 

A number of recent developments in 129Xe NMR spectroscopy are presented with direct applications to the study of mesopore space in solids. This includes the establishment of a relationship between pore size and chemical shifts for a number of controlled pore glasses and the exploration of hyperpolarized (HP) xenon for a number of NMR and microimaging applications to porous solids. With HP xenon, the increase in experimental sensitivity is remarkable. Experiments illustrated include the rapid characterization of the void space in porous solids, including the in-situ study of processes such as diffusion and dehydration, and imaging with chemical shift resolution. 

The majority of the published literature on improved adsorbents for H2 purification by PSA deals with equilibrium adsorption properties (adsorption capacities of the impurities and their selectivities over H2) of the materials. The adsorbents are generally chosen in such a way that the kinetics of adsorption of the impurities into the adsorbents are relatively fast, primarily being controlled by macro- and mesopore diffusion within the adsorbent particles. The kinetics of adsorption may, however, become an issue for the removal of the trace amounts (ppm) of a relatively weakly adsorbed impurity (N2 or CH4) at the product end of an H2 PSA due to the existence of a very low driving force for the adsorption process. It was suggested that a layer... 

The textural properties govern the diffusion process so that a well-defined structure may facilitate diffusion-controlled reactions. For example, the adsorption of heavy-metal ions (Hg + and Cu ) reveals a dramatic discrepancy between ordered and disordered mesoporous silica grafted with the aminopropyl or mercaptopropyl group [55]. The ordered mesostructure with a mean pore size of 6.5 nm brings about complete accessibOity of the functional groups. While... 

This is applicable to various carrier symmetries such as planar, cylindrical and spherical. Here Q is the amount of molecules released per unit exposed area of the carrier, t denotes time and a, b and k are constants. This power-law function is related to the Weibull function that has been suggested as a universal tool for describing release from both Euclidian and fractal systems, and may be considered as a short-time approximation of the latter (Kosmidis et al. 2003). The constant a takes initial delay and burst effects into account, and is a kinetic constant (Jamzad et al. 2005). The power law exponent, k, also called the transport coefficient, characterises the diffusion process and equals 0.5 for ordinary case I (or carrier conttoUed) diffusion in systems for which no swelling of the carrier material occurs, which can be expected for mesoporous material (Ritger and Peppas 1987). Diffusion-controlled release from a planar system, in which the carrier structure is inert, may be described by the Higuchi square-root-of-time law ... 

Generally, however, the aim is to avoid conditions leading to film diffusion control. This means that the focus is shifted towards transport processes that occur at the intermediate level (that is, in the mesopores and macropores within the macroparticle or pellet itself) and those which occur at the smallest dimensional level (viz., in the very micropores of the molecular sieve) [45, 89]. Within the mesopores and macropores between the primary zeolite crystallites transport will be dominated by molecular and ionic intercrystalline diffusion possibly coupled to surface diffusion processes, while, in the zeolite micropores themselves, intracrystalline diffusion occurs, also possibly coupled... 

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