Porous solids adsorption description

The rest of the book is dedicated to adsorption kinetics. We start with the detailed description of diffusion and adsorption in porous solids, and this is done in Chapter 7. Various simple devices used to measure diffusivity are presented, and the various modes of transport of molecules in porous media are described. The simplest transport is the Knudsen flow, where the transport is dictated by the collision between molecules and surfaces of the pore wall. Other transports are viscous flow, continuum diffusion and surface diffusion. The combination of these transports is possible for a given system, and this chapter will address this in some detail. 

This description is traditional, and some further comment is in order. The flat region of the type I isotherm has never been observed up to pressures approaching this type typically is observed in chemisorption, at pressures far below P. Types II and III approach the line asymptotically experimentally, such behavior is observed for adsorption on powdered samples, and the approach toward infinite film thickness is actually due to interparticle condensation [36] (see Section X-6B), although such behavior is expected even for adsorption on a flat surface if bulk liquid adsorbate wets the adsorbent. Types FV and V specifically refer to porous solids. There is a need to recognize at least the two additional isotherm types shown in Fig. XVII-8. These are two simple types possible for adsorption on a flat surface for the case where bulk liquid adsorbate rests on the adsorbent with a finite contact angle [37, 38]. 

From this description it becomes obvious that a mechanical tension must develop in the surface film, because the atoms will tend to assume a closer packing. Hence any adsorbed molecule or atom which can improve the screening of the solid will decrease their state of tension and cause the surface film to expand and release some of the pressure which it exerted upon the subjacent layers. Adsorption of screeners, even of inert gas atoms such as argon, causes many porous solids to expand. 

One method for the characterization of porous solids bases on the concept of the adsorption integral equation [1,2]. It requires to access the local isotherms for a wide range of pore widths. Because experiments cannot provide local isotherms of well-defined pores, a big demand results for suitable theoretical descriptions of the physical adsorption. 

Today two models are available for description of combined (diffusion and permeation) transport of multicomponent gas mixtures the Mean Transport-Pore Model (MTPM)[21,22] and the Dusty Gas Model (DGM)[23,24]. Both models enable in future to connect multicomponent process simultaneously with process as catalytic reaction, gas-solid reaction or adsorption to porous medium. These models are based on the modified Stefan-Maxwell description of multicomponent diffusion in pores and on Darcy (DGM) or Weber (MTPM) equation for permeation. For mass transport due to composition differences (i.e. pure diffusion) both models are represented by an identical set of differential equation with two parameters (transport parameters) which characterise the pore structure. Because both models drastically simplify the real pore structure the transport parameters have to be determined experimentally. 

By applying an appropriate perturbation to a relevant parameter of a system under equilibrium, various frequency modulation methods have been used to obtain kinetic parameters of chemical reactions, adsorption-desorption constants on surfaces, effective diffusivities and heat transfer within porous solid materials, etc., in continuous flow or batch systems [1-24]. In principle, it is possible to use the FR technique to discriminate between all of the kinetic mechanisms and to estimate the kinetic parameters of the dynamic processes occurring concurrently in heterogeneous catalytic systems as long as a wide enough frequency range of the perturbation can be accessed experimentally and the theoretical descriptions which properly account for the coupling of all of the dynamic processes can be derived. 

German DIN standards on the characterization of dispersed or porous solids are collected in ref. [6]. The most comprehensive description of the adsorption method is found in an lUPAC recommendation (7). Nowadays national standards are being harmonized either in the framework of the European Communities or at the international level. A list of standardization committees working in this field is appended (Table 4). Different methods of particle counting and characterization are collected in a VDI manual [8j. 

The geometrical structure of pores is of great concern, but the three-dimensional description of pores is not established in less-crystalline porous solids. Only intrinsic crystalline intra-particle pores offer a good description of the structure. The hysteresis analysis of molecular adsorption isotherms and electron microscopic observation estimate the pore geometry such as cylinder (cylinder closed at one end or cylinder open at both ends), cone shape, slit shape, interstice between closed-packing spheres and inkbottle. However, these models concern with only the unit structures. The higher order structure of these unit pores such as the network structure should be taken into accoimt. The simplest classification of the higher order structures is one-, two- and three-dimensional pores. Some zeolites and aluminophosphates have one-dimensional pores and activated carbons have basically two-dimensional slit-shaped pores with complicated network structures [95]. 

We presented a novel quenched solid non-local density functional (QSNLDFT) model, which provides a r istic description of adsorption on amorphous surfaces without resorting to computationally expensive two- or three-dimensional DFT formulations. The main idea is to consider solid as a quenched component of the solid-fluid mixture rather than a source of the external potential. The QSNLDFT extends the quenched-annealed DFT proposed recently by M. Schmidt and cowoikers [23,24] for systems with hard core interactions to porous solids with attractive interactions. We presented several examples of calculated adsorption isotherms on amorphous and microporous solids, which are in qualitative agreement with experimental measurements on typical polymer-templated silica materials like SBA-15, FDU-1 and oftiers. Introduction of the solid density distribution in QSNLDFT eliminates strong layering of the fluid near the walls that was a characteristic feature of NLDFT models with smoodi pore walls. As the result, QSNLDFT predicts smooth isotherms in the region of polymolecular adsorption. The main advantage of the proposed approach is that QSNLDFT retains one-dimensional solid and fluid density distributions, and thus, provides computational efficiency and accuracy similar to conventional NLDFT models. 

In the previous classical modelling, the elements mentioned above were supposed to be independent. At present, it is obvious that this assumption leads to a distortion in description of various processes occurring in porous solids, such as desorption of sorbate, intrusion of mercury, filtration, molecular-sieve adsorption. Por this reason, modelling of the primary elements may be considered as the first step, which is necessary though insufficient. The second step must be the modelling of interconnection between the elements. At present, it is conducted by the network models, and processes in them — by percolation theory (refs.4-7) ... 

Finally, intraparticle diffusion appears to be an important factor in adsorption kinetics for many types of systems. In the past it has been customary to define such mass transfer quantitatively in terms of an effective diffusivity. However, even in gas-solid systems more than one process can be involved for porous particles. Thus, two-dimensional migration on the pore surface, surface diffusion, is a potential contribution. Liquid systems appear to be more complex, and, with electrolytes, it has been shown that the electric potential induced by counter-diffusing ions should be taken into account. A realistic description of intraparticle mass transfer in such cases requires more than a single rate coefficient for a binary system. 

Many catalysts are porous, a feature which greatly increases their surface area [48]. Pores above 50 nm in width are termed macropores, those with widths below 2 nm are called micropores, and those of intermediate size are mesopores. Not only the size but also the shape of pores can vary widely and common descriptions refer to open and closed cylinders, slits, cones, spheroidal cavities, and ink-bottle shapes. The type of pore can frequently be identified from the shape of the hysteresis loop in physical gas adsorption experiments [32, 49], The absence of hysteresis indicates that the pores are closed perfect cylinders, or that the solid is microporous or, indeed, non-... 

The series of 10 chapters that constitute Part 3 of the book deals mainly with the use of adsorption as a means of characterizing carbons. Thus, the first three chapters in this section complement each other in the use of gas-solid or liquid-solid adsorption to characterize the porous texture and/or the surface chemistry of carbons. Porous texture characterization based on gas adsorption is addressed in Chapter 11 in a very comprehensive manner and includes a description of a number of classical and advanced tools (e.g., density functional theory and Monte Carlo simulations) for the characterization of porosity in carbons. Chapter 12 illustrates the use of adsorption at the liquid-solid interface as a means to characterize both pore texture and surface chemistry. The authon propose these methods (calorimetry, adsorption from solution) to characterize carbons for use in such processes as liquid purification or liquid-solid heterogeneous catalysis, for example. Next, the surface chemical characterization of carbons is comprehensively treated in Chapter 13, which discusses topics such as hydrophilicity and functional groups in carbon as well as the amphoteric characteristics and electrokinetic phenomena on carbon surfaces. 

Thus, both NMR cryoporometry and solid-state NMR spectroscopy give useful textural and structural information on mixed porous oxides, and this information can be broadened and deepened with the use of DSC, TG, adsorption, FTIR, Raman, XPS, XRD, and other methods. The authors not always used obtained information for maximum comprehensive description of the materials in terms structure— properties. Frequently, this is due to a small number of used techniques, as well as incomplete analysis of obtained experimental results. 

---