Single pore model sorption

A characteristic feature associated with pore condensation is the occurrence of sorption hysteresis, i.e pore evaporation occurs usually at a lower p/po compared to the condensation process. The details of this hysteresis loop depend on the thermodynamic state of the pore fluid and on the texture of adsorbents, i.e. the presence of a pore network. An empirical classification of common types of sorption hysteresis, which reflects a widely accepted correlation between the shape of the hysteresis loop and the geometry and texture of the mesoporous adsorbent was published by lUPAC [10]. However, detailed effects of these various factors on the hysteresis loop are not fully understood. In the literature mainly two models are discussed, which both contribute to the understanding of sorption hysteresis [8] (i) single pore model. hysteresis is considered as an intrinsic property of the phase transition in a single pore, reflecting the existence of metastable gas-states, (ii) neiM ork model hysteresis is explained as a consequence of the interconnectivity of a real porous network with a wide distribution of pore sizes. 

Macroscale models of PEM operation that do not include the proper pressure-controlled equilibrium conditions at the single pore level fail in predicting correctly the responses of membrane water sorption, transport properties, and fuel cell operation to changes in external conditions. Single pore models, on the other hand, that do not account for statistical spatial fluctuations in microscopic membrane properties must fail because they cannot predict the dispersion in pore sizes and the evolution of the pore size distribution upon water uptake. 

A three dimensional capillary network model has been developed, aiming to the simulation of sorption by several model mesoporous adsorbents, such as the one mentioned in the previous section. The model offers realistic simulation conditions and is able to provide satisfactory prediction of adsorption-desorption isotherms of CCI4 and C5H1 for different porosities, temperatures and adsorbates. The expected desorption branch hysteresis is estimated as a two component summation of the thermodynamic (single pore) and the network hysteresis. Similarly, the overall sorbed volume is the two component summation of the volume due to multilayer adsorption and to the volume due to capillary condensation. 

Another pair of isotherms [90] are shown in Fig. 15. Here a Lennard-Jones model of methane has been used in a simulation of sorption in a graphitic slit pore. The two sets of curves in the figure are for a single pore width but for two... 

The basic mathematical model for a calculation of concentration vs. time dependences in sorbent beds accounts for non-isothermal sorption in biporous sorbent particles. It considers mass and energy balances in the interparticle void space of the bed and in the macro- and micropores of sorbent particles. Thus, it comprises three spatial coordinates, besides time, (0 < t < co) (i) the height z along the bed, (0 < z < L) (ii) the radial direction r in macropores of particles, (0 < r < Rp) and (hi) the radial direction p in their micropores, (0 < p < Rzi). Different geometries may exist in each single direction but in each of those geometries the transport equations are one-dimensional. For zeolite-based biporous particles, sorption in the macropores is negligible. These pores serve as transport pores, only. Sorption takes place, exclusively, in micropores. 

Depending on the distribution chosen, as few as three fitting parameters may be required to define a distribution of diffusion rates. In some cases, a single distribution was used to describe both fast and slow rates of sorption and desorption, and in other cases fast and slow mass transfer were captured with separate distributions of diffusion rates. For example, Werth et al. [42] used the pore diffusion model with nonlinear sorption to predict fast desorption, and a gamma distribution of diffusion rate constants to describe slow desorption. 

Carbonization seems to be an effective method to adjust the pore size of PAF-1 to increase the gas selectivity. PAF-1-450 (PAF-1 carbonized at 450 °C), with a narrow micropore distribution of 0.8 nm, shows obvious increased CO2 sorption. Besides, on the basis of single component isotherm data, the dual-site Langmuir-Freundlich adsorption model-based lAST prediction indicates that the CO2/N2 adsorption selectivity may be as high as 209 at a 15 85 CO2 N2 ratio. Also, the CO2/CH4 adsorption selectivity should be in the range of 7.8-9.8 at a 15 85 C02 CH4 ratio at 0adsorption selectivity could be about 392 at 273 K and 1 bar for the 20 80 CO2 H2 mixture (Figure 10.2). ... 

While several simplifying assumptions needed to be made so as to derive an analytical model, the model captures all relevant physical processes. Specifically, it employed thermodynamic equilibrium conditions for temperature, pressure, and chemical potential to derive the equation of state for water sorption by a single cylindrical PEM pore. This equation of state yields the pore radius or a volumetric pore swelling parameter as a function of environmental conditions. Constitutive relations for elastic modulus, dielectric constant, and wall charge density must be specified for the considered microscopic domain. In order to treat ensemble effects in equilibrium water sorption, dispersion in the aforementioned materials properties is accounted for. 

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