Adsorption inside porous networks

In the simple case of a porous network with chemically uniform surfaces, the dependence of the adsorption energy on the pore size can be easily determined. In particular, if the network is composed of sUt-like pores and the interaction of a molecule with a single pore surface is described by Equation (6.34), then the potential energy of a molecule inside the pore can be calculated by summing the potentials from the two surfaces. The minima on the potential curves are identified as the adsorption energies. If the distribution of pore sizes J(R) is fractal, then x(s) depends on the type of distribution, and in turn on the A value. Rudziilski et al. [89, 90] postulated... 

Hg porosimetry and N2 sorption processes have been replicated in simulated 3-D porous networks constructed by Monte Carlo procedures. These two characterization techniques render complementary information about the pore structural parameters of highly-connected porous networks. Through this study, it has been possible to depict a phenomenon labeled as delayed adsorption. This phenomenon consists in that condensation is not taking place inside a cavity unless the pore throats that surround this void have been already filled with liquid. This phenomenon arises when pore necks are comparable in size to the cavities to which they are connected. If condensation occurs this way, the pore-size distributions calculated from N2 adsorption are biased toward overvalued pore sizes. Under this circumstance, Hg porosimetry analysis can still be suitable for realizing and assessing the latter problem since a complementary cavily-size distribution can be calculated from the Hg retraction curve. 

The sources of band broadening of kinetic origin include molecular diffusion, eddy diffusion, mass transfer resistances, and the finite rate of the kinetics of ad-sorption/desorption. In turn, the mass transfer resistances can be sorted out into several different contributions. First, the film mass transfer resistance takes place at the interface separating the stream of mobile phase percolating through the column bed and the mobile phase stagnant inside the pores of the particles. Second, the internal mass transfer resistance controls the rate of mass transfer between this interface and the adsorbent surface. It is composed of two contributions, the pore diffusion, which is molecular diffusion taking place in the tortuous, constricted network of pores, and surface diffusion, which takes place in the electric field at the liquid-solid interface [60]. All these mass transfer resistances, except the kinetics of adsorption-desorption, depend on the molecular diffusivity. Thus, it is important to study diffusion in bulk liquids and in porous media. 

Adsorption of molecules proceeds by successive steps (1) penetration inside a particle (2) diffusion inside the particle (3) adsorption (4) desorption and (5) diffusion out of the particle. In general, the rates of adsorption and desorption in porous adsorbents are controlled by the rate of transport within the pore network rather than by the intrinsic kinetics of sorption at the surface of the adsorbent. Pore diffusion may take place through several different mechanisms that usually coexist. The rates of these mechanisms depend on the pore size, the pore tortuosity and constriction, the cormectivity of the pore network, the solute concentration, and other conditions. Four main, distinct mechanisms have been identified molecular diffusion, Knudsen diffusion, Poiseiulle flow, and surface diffusion. The effective pore diffusivity measured experimentally often includes contributions for more than one mechanism. It is often difficult to predict accurately the effective diffusivity since it depends so strongly on the details of the pore structure. 

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