Surface diffusion separation types

In which b° is the mechanical mobility for a molecule on an otherwise empty lattice, the concentration of available sites, R the universal gas eonstant, T absolute temperature, and 0 <6 < 1 is the average site occupation. Equilibrium between the site occupation and feed eoncentration on both sides of the membrane can be used as the boundary condition to solve the above eqnation. Non-eqnilibrinm correction factor 0 < j < 1 is often very close to nnity bnt can be very small for the molecule of low occupancy (low 0) when the other molecnle occnpies the sites strongly and hinders the movement of the former molecnle. The above generic expression leads to the following two types of microporous and surface diffusion separation ... 

On the basis of the separation mechanism, restricted-access media can be classified into physical or chemical diffusion barrier types. The limited accessibility of the former type is due to the pore structure of the support that represents physical diffusion barriers for macromolecular compounds. The restricted access of the latter type is due to covalently or adsorptively bonded synthetic or natural polymers that cover the support surface, preventing macromolecules from being adsorbed on or denatured by the column packing material. 

The rationale of using hybrid simulation here is that a classic diffusion-adsorption type of model, Eq. (2), can efficiently handle large distances between steps by a finite difference coarse discretization in space. As often happens in hybrid simulations, an explicit, forward discretization in time was employed. On the other hand, KMC can properly handle thermal fluctuations at the steps, i.e., provide suitable boundary conditions to the continuum model. Initial simulations were done in (1 + 1) dimensions [a pseudo-2D KMC and a ID version of Eq. (2)] and subsequently extended to (2 + 1) dimensions [a pseudo-3D KMC and a 2D version of Eq. (2)] (Schulze, 2004 Schulze et al., 2003). Again, the term pseudo is used as above to imply the SOS approximation. Speedup up to a factor of 5 was reported in comparison with KMC (Schulze, 2004), which while important, is not as dramatic, at least for the conditions studied. As pointed out by Schulze, one would expect improved speedup, as the separation between steps increases while the KMC region remains relatively fixed in size. At the same time, implementation is definitely complex because it involves swapping a microscopic KMC cell with continuum model cells as the steps move on the surface of a growing film. 

The rate of contaminant adsorption onto activated carixm particles is controlled by two parallel diffusion mechanisms of pore and surface diffusion, which operate in different manners and extents depending upon adsorption temperature and adsorbate concentration. The present study showed that two mechanisms are separated successfully using a stepwise linearization technique incorporated with adsorption diffusion model. Surface and pore diffiisivities were obtained based on kinetic data in two types of adsorbers and isothermal data attained from batch bottle technique. Furthermore, intraparticle diffiisivities onto activated carbon particles were estimated by traditional breakthrough curve method and final results were compared with those obtained by more rigorous stepwise linearization technique. 

Modification of mesoporous membranes can result in (i) a decreased pore size which increases the contribution of surface diffusion, and (ii) a change in the nature of the pore surface and consequently a change in all types of interaction energies with the gas phase. Both phenomena have an effect on permeation and separation. 

The gas is applied as a mixture to the retentate (high pressure) side of the membrane, the components of the mixture diffuse with different rates through the membrane under the action of a total pressure gradient and are removed at the permeate side by a sweep gas or by vacuum suction. Because the only segregative mechanisms in mesopores are Knudsen diffusion and surface diffusion/capillary condensation (see Table 9.1), viscous flow and continuum (bulk gas) diffusion should be absent in the separation layer. Only the transition state between Knudsen diffusion and continuum diffusion is allowed to some extent, but is not preferred because the selectivity is decreased. Nevertheless, continuum diffusion and viscous flow usually occur in the macroscopic pores of the support of the separation layer in asymmetric systems (see Fig. 9.2) and this can affect the separation factor. Furthermore the experimental set-up as shown in Fig. 9.11 can be used vmder isobaric conditions (only partial pressure differences are present) for the measurement of diffusivities in gas mixtures in so-called Wicke-Callenbach types of measurement. 

Four types of diffusion mechanisms can be utilized to effect separation in porous membranes. In some cases, molecules can move through the membrane by more than one mechanism. These mechanisms are described below. Knudsen diffusion gives relatively low separation selectivities compared to surface diffusion and capillary condensation. Shape selective separation can yield high selectivities. The separation factor for these mechanisms depends strongly on pore-size distribution, temperature, pressure, and interactions between the solute being separated and the membrane surfaces. 

FEM has been widely used for surface diffusion studies, but is somewhat limited in that several effects are superimposed on the measurements, particularly the effects of coverage-dependent diffusion parameters [252, 253] (due to inter-species lateral interactions) and differing types of adsorption sites on the surface. Probe-hole FEM [254] (a method for investigating the emission from individual planes on the tip surface) goes some way towards separating these two effects. 

Surface diffusion Different molecules have different mobility on the surface of the capillary due to their different extent of interaction with the surface. Hence a binary mixture can be separated using this type of flow, like the Knudsen diffusion. 

After 10 h of operation the presenee of Ru islands on Pt inereased the oxidation current density approximately 20-fold in the case of PtRu-53, followed closely by PtRu-35. Combining cyclic voltammetry with surface NMR two COad populations were identified COad close to (or possibly on) Ru sites undergoing fast thermally activated diffusion and COad on Pt characterized by slow diffusion [91]. These two types of COad are responsible for two separate peaks in CO stripping voltammetry, at low ( 0.3 V) and high (above 0.4 V) potentials, respectively. Ru decreases the activation barrier for COad surface diffusion by reducing electron back-donation. 

Surface-selective flow membranes made of nanoporous carbon, which is a variation of molecular sieving membranes, were developed by Rao et al. (1992) and Rao and Sircar (1993). The membrane can be produced by coating poly(vinylidene chloride) on the inside of a macroporous alumina tube followed by carbonization to form a thin membrane layer. The mechanism of separation is by adsorption-surface-diffusion-desorption. Certain gas components in the feed are selectively adsorbed, permeated through the membrane by surface diffusion, and desorbed at the low-pressure side of the membrane. This type of membrane was used to separate H2 from a mixture of H2 and CO2 (Sircar and Rao, 2000), and their main advantage is that the product hydrogen is at the high-pressure side eliminating the need for recompression. The membrane, however, is not industrially viable because of its low overall separation selectivity. In addition, since the separation mechanism involves physical adsorption, operation at low temperatures is required. 

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