Capillary condensation, study

In this paper, we present a new vapour desorption set-up based on a microcalorimeter that provides a full control of temperature gradients. We demonstrate that is possible to carry out capillary condensation studies in the nanometer-micrometer range. In a first part the setup and the procedure established to study the desorption of a vapour from a porous solid that is initially immersed in an excess of liquid are described. In the second part a few results are shovra and compared to existent techniques. 

As already indicated in Section 3.1, the study of mesoporous solids is closely bound up with the concept of capillary condensation and its quantitative expression in the Kelvin equation. This equation is, indeed, the basis of virtually all the various procedures for the calculation of pore size... 

Sec. Ill is concerned with the description of models with directional associative forces, introduced by Wertheim. Singlet and pair theories for these models are presented. However, the main part of this section describes the density functional methodology and shows its application in the studies of adsorption of associating fluids on partially permeable walls. In addition, the application of the density functional method in investigations of wettability of associating fluids on solid surfaces and of capillary condensation in slit-like pores is presented. 

The density functional approach has also been used to study capillary condensation in slit-like pores [148,149]. As in the previous section, a simple model of the Lennard-Jones associating fluid with a single associative site is considered. All the parameters of the interparticle potentials are chosen the same as in the previous section. Our attention has been focused on the influence of association on capillary condensation and the evaluation of the phase diagram [42]. 

Adsorption from liquids is less well understood than adsorption from gases. In principle the equations derived for gases ought to be applicable to liquid systems, except when capillary condensation is occurring. In practice, some offer an empirical fit of the equilibrium data. One of the most popular adsorption isotherm equations used for liquids was proposed by Freundlich 21-1 in 1926. Arising from a study of the adsorption of organic compounds from aqueous solutions on to charcoal, it was shown that the data could be correlated by an equation of the form ... 

Only a few studies have been published, showing capillary condensation. Although separation by capillary condensation is not new at all, but has been widely used in separation processes exploiting porous adsorbents, the dynamic behavior of flow of capillary condensate through porous media has received little attention. And it is this dynamic behavior that is important when capillary condensation is used as a separation mechanism. 

Hoinkis E (2004) Small-angle scattering studies of adsorption and of capillary condensation in porous solids. Part Part Syst Charact 21 80-100... 

The same approach is employed to describe shear-induced transport of soot particles. Based on limited amount of experimental information for such phenomena in the literature we have established a flow cell where soot entrainment from the surface of preloaded filters from the engine exhaust can be studied. Preliminary experiments at ambient conditions reveal that no soot entrainment is observed up to relevant shear rates at the entrance of DPFs. We attribute this to the moisture content in ambient conditions of the soot deposits that due to capillary condensation increases adhesive forces between the particles. In the future experiments at high temperatures are planned to evaluate experimentally the shear-entrained fluxes for soot and ash deposits. 

Figure 9.12 contains sketches for several different models of pores that will be useful in our discussion of capillary condensation. Figure 9.12a is the simplest, attributing the entire effect just described to variations in pore radius with the depth of the pore. That is, when liquid first begins to condense in the pore, the larger radius Ra determines the pressure at which the adsorption-condensation occurs. Once the pore has been filled and the desorption-evaporation branch is being studied, the smaller radius Rd determines the equilibrium pressure. Although bottlenecked pores of this sort may exist in some cases, this model seems far too specialized to account for the widespread occurrence of hysteresis. 

For nonane even though a series of trials were further made, the sharp increase due to the capillary condensation is not observed. The material is not a structured compound and no homogeneous pore size distribution is obtained (Figure 7e) Some complementary studies will be done to explain this phenomena. This compound will not be taken into account in following analyses. 

Specific surface areas of the materials under study were calculated using the BET method [22, 23]. Their pore size distributions were evaluated from adsorption branches of nitrogen isotherms using the BJH method [24] with the corrected form of the Kelvin equation for capillary condensation in cylindrical pores [25, 26]. In addition, adsorption energy distributions (AED) were evaluated from submonolayer parts of nitrogen adsorption isotherms using the algorithm reported in Ref. [27],... 

The current study was aimed at generalization of the procedure for the quantitative composition determination for hexagonal/lamellar mixed phases using adsorption isotherms. Recent advances in adsorption on calcined MCM-41 silicas [29-31] made it possible to construct model adsorption isotherms for these materials with arbitrarily chosen pore sizes (or equivalently, capillary condensation pressures). Such model adsorption isotherms can be used instead of experimental adsorption isotherms for pure MCM-41 materials of the required pore size, significantly extending the range of HL materials, for which the phase composition analysis can conveniently be carried out on the basis of gas adsorption data. 

Equation 1 can be used to determine the pore diameter of an MCM-41 sample which exhibits capillary condensation at a certain relative pressure, or to determine the capillary condensation pressure for an MCM-41 sample of a certain pore diameter. To construct model adsorption isotherms for MCM-41, one also needs a description of the monolayer-multilayer formation on the pore walls. This description can be based on the experimental finding that the statistical film thickness in MCM-41 pores of different sizes (especially above 3 nm) is relatively constant for pressures sufficiently lower from those of the capillaiy condensation and can be adequately approximated by the t-curve for a suitable reference silica [29-31], for instance that reported in Ref. 35. In these studies [29-31], the statistical film thickness in MCM-41 pores, tMcM-4i, was calculated according to the following equation [29] ... 

The adsorption of gases and vapors on mesoporous materials is generally characterized by multilayer adsorption followed by a distinct vertical step (capillary condensation) in the isotherm accompanied by a hysteresis loop. Studies of adsorption on MCM-41 have also demonstrated the absence of hysteresis for materials having pore size below a critical value. While this has been reported for silica gel and chromium oxide containing some mesopores, no consistent explanation has been offered [1], However, conventional porous materials, having interconnected pores with a broader size distribution, are generally known to display a hysteresis loop with a point of closure which is characteristic of the adsorptive. These materials have an independent method of estimating the pore size from XRD and TEM, that allows comparison with theoretical results. Consequently, we have chosen these materials to test the proposed model. 

Capillary condensation has been used to evaluate the pore size distribution of mesopores. Various adsorption studies on regular mesoporous silica such as MCM-41 or FSM showed the limitation of the classical capillary condensation theory [1-9]. In the case of the evaluation of the pore size distribution, we assumed that condensates in mesopores are liquid. Recent systematic studies on structures of molecules confined in micropores... 

The adsorption isotherm of N, on FSM-16 at 77 K had an explicit hysteresis. As to the adsorption hysteresis of N-, on regular mesoporous silica, the dependencies of adsorption hysteresis on the pore width and adsorbate were observed the adsorption hysteresis can be observed for pores of w 4.0nm. The reason has been studied by several approaches [5-8]. The adsorption isotherm of acetonitrile on FSM-16 at 303K is shown in Fig. 1. The adsorption isotherm has a clear hysteresis the adsorption and desorption branches close at PIP, = 0.38. The presence of the adsorption hysteresis coincides with the anticipation of the classical capillary condensation theory for the cylindrical pores whose both ends are open. The value of the BET monolayer capacity, nm, for acetonitrile was 3.9 mmol g. By assuming the surface area from the nitrogen isotherm to be available for the adsorption of acetonitrile, the apparent molecular area, am, of adsorbed acetonitrile can be obtained from nm. The value of am for adsorbed acetonitrile (0.35 nnr) was quite different from the value (0.22 nm2) from the liquid density under the assumption of the close packing. Acetonitrile molecules on the mesopore surface are packed more loosely than the close packing. The later IR data will show that acetonitrile molecules are adsorbed on the surface hydroxyls in... 

Capillary condensation has been studied by various methods, and the validity of the previous description has been confirmed for several liquids and radii of curvature down to a few nanometers [18-21],... 

Surface areas and pore size distributions of mesoporous materials are most easily studied by nitrogen adsorption and nitrogen capillary condensation. The most appropriate method for the study of macroporosity is mercury porosimetry [6,7], a technique which will not be treated here. 

In fact, most mesoporous adsorbents possess complex networks of pores of different size. It is therefore unlikely that the condensation-evaporation processes can occur independently in each pore. The complexity of capillary condensation in porous materials is illustrated by the recent Monte Carlo computer simulation studies of Page and Monson (1996) and Gelb and Gubbins (1998). The well-defined hysteresis loops observed in the simulation results of both studies were attributed to the presence of thermodynamically metastable states and not to kinetic effects. However, it appears that the extent of die hysteresis was associated with the overall heterogeneity of the adsorbent structure and not simply due to capillary condensation within individual pores. 

The porosimetry method permits the study of porous structures in a wider pore-size range than does the method of capillary condensation. The two methods do not always agree but porosimetry is better for sizes of 10 nm and higher, whereas the capillary condensation method is more suitable for sizes below 10 nm. A more direct overview of the pore structure of catalysts is obtained by using the stereoscan electron microscope [16]. 

Over the years, vapour adsorption and condensation in porous materials continue to attract a great deal of attention because of (i) the fundamental physics of low-dimension systems due to confinement and (ii) the practical applications in the field of porous solids characterisation. Particularly, the specific surface area, as in the well-known BET model [I], is obtained from an adsorbed amount of fluid that is assumed to cover uniformly the pore wall of the porous material. From a more fundamental viewpoint, the interest in studying the thickness of the adsorbed film as a function of the pressure (i.e. t = f (P/Po) the so-called t-plot) is linked to the effort in describing the capillary condensation phenomenon i.e. the gas-Fadsorbed film to liquid transition of the confined fluid. Indeed, microscopic and mesoscopic approaches underline the importance of the stability of such a film on the thermodynamical equilibrium of the confined fluid [2-3], In simple pore geometry (slit or cylinder), numerous simulation works and theoretical studies (mainly Density Functional Theory) have shown that the (equilibrium) pressure for the gas/liquid phase transition in pores greater than 8 nm is correctly predicted by the Kelvin equation provided the pore radius Ro is replaced by the core radius of the gas phase i.e. (Ro -1) [4]. Thirty year ago, Saam and Cole [5] proposed that the capillary condensation transition is driven by the instability of the adsorbed film at the surface of an infinite... 

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