Adsorption in pores

These calculations lend theoretical support to the view arrived at earlier on phenomenological grounds, that adsorption in pores of molecular dimensions is sufficiently different from that in coarser pores to justify their assignment to a separate category as micropores. The calculations further indicate that the upper limit of size at which a pore begins to function as a micropore depends on the diameter a of the adsorbate molecule for slit-like pores this limit will lie at a width around I-So, but for pores which approximate to the cylindrical model it lies at a pore diameter around 2 5(t. The exact value of the limit will of course depend on the actual shape of the pore, and may well be raised by cooperative effects. 

Y. K. Tovbin, E. V. Votyakov. Adsorption in pores with heterogeneous surfaces. Langmuir 9 2652-2660, 1993. 

We first note the gradual behaviour of the adsorption isotherms, and this is typical for super-critical fluid adsorption in pores of all sizes. For sub-critical adsorption which we will consider later, there is a possibility of phase transition for certain pore widths. 

Attempts at imderstanding adsorption hysteresis have a long history (Everett, 1967 Steele, 1973 Gregg and Sing, 1982). An important e2U ly contribution was made by Cohan (1938) who applied the Kelvin equation to adsorption in pores. Cohan suggested that the occurrence of hysteresis in a single pore is related to differences in the geometry of the Uquid-vapor meniscus in condensation and evaporation. 

Coasne, B., Pikunic, J.P., PeUenq, R.J.M., and Gubbins, K.E. (2003). Comparison between adsorption in pores of a simple geometry and reahstic models of porous materials. Mater. Res. Soc. Symp. Proc., 790, 53—8. 

Nicholson, D. (1975). Molecular theory of adsorption in pore spaces. Part 1. Isotherms for simple lattice models. J. Chem. Soc. FaradayTrans. I, 71, 238-55. Saam, W.F. and Cole, M.W. (1975). Excitations and thermodynamics for liquid-helium films. Phys. Rev. B, 11, 1086-105. 

The specific surface area of solid materials is usually determined by applying the Brunauer-Emmett-Teller (BET) equation to nitrogen adsorption data between relative pressures (P/Pq) approximately 0.05 and 0.3 [51]. However, there are many shortcomings of the BET model. For example, it does not consider adsorption in pores. It is well known that the BET method seriously overestimates the specific surface area for many porous materials. For carbons, the theoretically highest possible specific surface area is approximately 2630 m /g... 

Recently, Terzyk et al. [35] have proposed a hybrid model that describes adsorption on porous solids and which takes into account the possibility of adsorption in pores and on external surfaces that are characterized by different fractal dimensions. The resulting adsorption isotherm is the sum of two terms, each involving the relevant fractal exponent. The first term describes the pore filling and the second term accounts for the adsorption on external surfaces. Nonetheless, to the best of our knowledge, the hybrid isotherm of Terzyk et al. [35] has not yet been applied to describe experimental data. 

Recently, E)o and co>workers [6-10] have proposed a very simple method but it does reveal the mechanistic pictures of what are occurring in pores of different size. The process of adsorption in pore is viewed as follows. Molecules in pore are constantly in motion but statistically there is a spatial distribution of these molecules due to the interactive forces between them and the surface atoms. We treat this spatial distribution as a stq> function uniformly high density near the surface and uniformly low density in the inner core of the pore. Due to the long range interaction of the surface, the pressure of the fluid in the inner core is not the same as that in the bulk phase. Assuming a Boltzmann distribution, the pressure of the inner core is related to the bulk fluid as... 

We suggest a model of adsorption in pores with amorphous and microporous solid walls, named the quenched solid non-local density functional theory (QSNLDFT) model. We consider a multicomponent non-local density functional theory (NLDFT), in which the solid is treated as a quenched component with a fixed spatially distributed density. Drawing on several prominent examples, we show that QSNLDFT model produces smooth Isotherms of mono- and polymolecular adsorption, which resemble experimental isotherms on amorphous surfaces. The model reproduces typical behaviors of N2 isotherms on micro- mesoporous materials, such as SBA-15. QSNLDFT model offers a systematic approach to the account for the surface roughness/heterogeneity in pore structure characterization methods. 

Binary adsorption in % theory has not been thoroughly tested due to the lack of appropriate experimental data. Here two approximations are presented. First, the approximation for the adsorption on nearly flat surfaces is discussed and, second, adsorption in pores that are filled or nearly filled is presented. For both of these cases there is some information in the literature against which the assumptions could be tested. 

The density functional theory appears to be a powerfid tool for studying adsorption on heterogeneous surfaces. In particular, the valuable results have been obtained for adsorption in pores with chemically stractured walls. The interesting, new phenomena, such as bridging, have been discovered in this way. The phase diagrams characterizing various phase transitions in surface layers can be determined quite quickly from the functional density theory. In this context, we emphasize the economy of the computational efforts required for the application of the fimctional density methods. For this reason, the density theory can be under certain conditions, competitive with computer simulations. However, many applications of the density fimctional theory are based on rather crude, oversimplified assumptions, so the conclusions following firom the calculations should be treated very cautiously. 

It is very difficult to measure the coexistence curves of confined fluid experimentally, as this requires estimation of the densities of the coexisting phases at various temperatures. Therefore, only a few experimental liquid-vapor coexistence curves of fluids in pores were constructed [279, 284,292,294-297]. In some experimental studies, the shift of the liquid-vapor critical temperature was estimated without reconstruction of the coexistence curve [281-283, 289]. The measurement of adsorption in pores is usually accompanied by a pronounced adsorption-desorption hysteresis. The hysteresis loop shrinks with increasing temperature and disappears at the so-called hysteresis critical temperature Teh. Hysteresis indicates nonequilibrium phase behavior due to the occurrence of metastable states, which should disappear in equilibrium state, but the time of equilibration may be very long. The microscopic origin of this phenomenon and its relation to the pore structure is still an area of discussion. In disordered porous systems, hysteresis may be observed even without phase transition up to hysteresis critical temperature Teh > 7c, if the latter exists [299]. In single uniform pores, Teh is expected to be equal to [300] or below [281-283] the critical temperature. Although a number of experimentally determined values of Teh and a few the so-called hysteresis coexistence curves are available in the literature, hysteresis... 

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