Isothermal filling

There is a growing interest in the presentation of physisorption isotherms in a generalized integral form. This approach was first applied to physisorption in the submonolayer region (Adamson et al., 1961), but much of the current interest is centred on the analysis of micropore filling isotherms. An apparent advantage is that it provides a means of constructing a series of model isotherms by systematically... 

Fig. 5. Thickness f of the adsorbed nitrogen film as derived from SANS (frill symbols) and from the filling isotherm on the basis of Eq. (7) (open symbols and frill line). The predictions of the Dollimore-Heal (DH) and Harkins-Jura (HJ) models are indicated by dashed lines...

The BET equation filled an annoying gap in the interpretation of adsorption isotherms, and at the time of its appearance in 1938 it was also hailed as a general method for obtaining surface areas from adsorption data. The equation can be put in the form... 

Adsorption isotherms in the micropore region may start off looking like one of the high BET c-value curves of Fig. XVII-10, but will then level off much like a Langmuir isotherm (Fig. XVII-3) as the pores fill and the surface area available for further adsorption greatly diminishes. The BET-type equation for adsorption limited to n layers (Eq. XVII-65) will sometimes fit this type of behavior. Currently, however, more use is made of the Dubinin-Raduschkevich or DR equation. Tliis is Eq. XVII-75, but now put in the form... 

The physical adsorption of gases by non-porous solids, in the vast majority of cases, gives rise to a Type II isotherm. From the Type II isotherm of a given gas on a particular solid it is possible in principle to derive a value of the monolayer capacity of the solid, which in turn can be used to calculate the specific surface of the solid. The monolayer capacity is defined as the amount of adsorbate which can be accommodated in a completely filled, single molecular layer—a monolayer—on the surface of unit mass (1 g) of the solid. It is related to the specific surface area A, the surface area of 1 g of the solid, by the simple equation... 

The model proposed by Zsigmondy—which in broad terms is still accepted to-day—assumed that along the initial part of the isotherm (ABC of Fig. 3.1), adsorption is restricted to a thin layer on the walls, until at D (the inception of the hysteresis loop) capillary condensation commences in the finest pores. As the pressure is progressively increased, wider and wider pores are filled until at the saturation pressure the entire system is full of condensate. 

If the region FGH of the isotherm represents the filling of all the pores with liquid adsorbate, then the amount adsorbed along to plateau FGH, when expressed as a volume of liquid (by use of the normal liquid density) should be the same for all adsorptives on a given porous solid. This prediction is embodied in a generalization put forward many years ago by Gurvitsch and usually known as the Gurvitsch rule. 

This widespread conformity to the Gurvitsch rule constitutes powerful support for the capillary condensation hypothesis in relation to Type IV isotherms. It is perhaps hardly necessary to stress that in order to test data for conformity to the rule it is essential that the stage which corresponds to the complete filling of the pores shall be clearly identifiable—as in the... 

At the point where capillary condensation commences in the finest mesopores, the walls of the whole mesopore system are already coated with an adsorbed film of area A, say. The quantity A comprises the area of the core walls and is less than the specific surface A (unless the pores happen to be parallel-sided slits). When capillary condensation takes place within a pore, the film-gas interface in that pore is destroyed, and when the pore system is completely filled with capillary condensate (e.g. at F in Fig. 3.1) the whole of the film-gas interface will have disappeared. It should therefore be possible to determine the area by suitable treatment of the adsorption data for the region of the isotherm where capillary condensation is occurring. 

If a solid contains micropores—pores which are no more than a few molecular diameters in width—the potential fields from neighbouring walls will overlap and the interaction energy of the solid with a gas molecule will be correspondingly enhanced. This will result in a distortion of the isotherm, especially at low relative pressures, in the direction of increased adsorption there is indeed considerable evidence that the interaction may be strong enough to bring about a complete filling of the pores at a quite low relative pressure. 

These various considerations led Pierce, Wiley and Smith in 1949, and independently, Dubinin, to postulate that in very fine pores the mechanism of adsorption is pore filling rather than surface coverage. Thus the plateau of the Type 1 isotherm represents the filling up of the pores with adsorbate by a process similar to but not identical with capillary condensation, rather than a layer-by-layer building up of a film on the pore walls. 

The values of external specific surface /C(ext) calculated from the slopes of the parallel branches of the o(,-plots are in close agreement (cf. Table 4.8, column 4) and the whole picture is therefore internally consistent the four isotherms represent different degrees of filling of the micropores with nonane, leaving the external surface unaffected. 

I (curve D). Thus the micropores had been able to enhance the adsorbent-adsorbate interaction sufficiently to replace monolayer-multilayer formation by micropore filling and thereby change the isotherm from being convex to being concave to the pressure axis. 

The first stage in the interpretation of a physisorption isotherm is to identify the isotherm type and hence the nature of the adsorption process(es) monolayer-multilayer adsorption, capillary condensation or micropore filling. If the isotherm exhibits low-pressure hysteresis (i.e. at p/p° < 0 4, with nitrogen at 77 K) the technique should be checked to establish the degree of accuracy and reproducibility of the measurements. In certain cases it is possible to relate the hysteresis loop to the morphology of the adsorbent (e.g. a Type B loop can be associated with slit-shaped pores or platey particles). 

If a Type I isotherm exhibits a nearly constant adsorption at high relative pressure, the micropore volume is given by the amount adsorbed (converted to a liquid volume) in the plateau region, since the mesopore volume and the external surface are both relatively small. In the more usual case where the Type I isotherm has a finite slope at high relative pressures, both the external area and the micropore volume can be evaluated by the a,-method provided that a standard isotherm on a suitable non-porous reference solid is available. Alternatively, the nonane pre-adsorption method may be used in appropriate cases to separate the processes of micropore filling and surface coverage. At present, however, there is no reliable procedure for the computation of micropore size distribution from a single isotherm but if the size extends down to micropores of molecular dimensions, adsorptive molecules of selected size can be employed as molecular probes. 

Fig. 8. Adsorption isotherms of H2O, O2, and / -hexane on 2eolite NaX (open symbols) and silicalite (filled symbols). Oxygen is at — 183°C and water and...

Fig. 10. Adsorption ( , O)"desorption (A, A) isotherms of water vapor on poly(vinylidene chloride) (PVDC) carbon before (filled symbols) and after...

During the adsorption or occlusion of various molecules, the micropores fill and empty reversibly. Adsorption in zeoHtes is a matter of pore filling, and the usual surface area concepts are not appHcable. The pore volume of a dehydrated zeoHte and other microporous soHds which have type 1 isotherms may be related by the Gurvitch rule, ie, the quantity of material adsorbed is assumed to fill the micropores as a Hquid having its normal density. The total pore volume D is given by... 

The Snamprogetti process utilizes a tubular isothermal reactor (tubes filled with catalyst) for the first reactor with cooling water on the shell side to control temperature. The Huls process uses either an adiabatic or isothermal reactor for the first reactor. 

The effective therm conductivity values generally obtained in practice are at least a factor of two greater than the one-dimensional thermal conductivity values measured in the laboratoiy with carefully controlled techniques. This degradation in insulation thermal performance is caused by the combined presence of edge exposure to isothermal boundaries, gaps, joints, or penetrations in the insulation blanket required for structure supports, fill and vent hnes, and high lateral thermal conductivity of these insulation systems. 

Flat Surface Isotherm Equations The classification of isotherm equations into two broad categories for flat surfaces and pore filling reflec ts their origin. It does not restrict equations developed for flat surfaces from being apphed successfully to describe data for porous adsorbents. 

Compression of CNG to 20 MPa requires four stage compression. Provision of such facilities is costly, and it is an energy consuming process. There is also a substantial heat of compression which results in a temperature rise of the compressed gas. This means that in practice less than 230 VfV are stored when a CNG vessel is filled to 20 MPa unless the filling process is carried out isothermally. 

Isotherm measurements of methane at 298 K can be made either by a gravimetric method using a high pressure microbalance [31], or by using a volumetric method [32]. Both of these methods require correction for the nonideality of methane, but both methods result in the same isotherm for any specific adsorbent [20]. The volumetric method can also be used for measurement of total storage. Here it is not necessary to differentiate between the adsorbed phase and that remaining in the gas phase in void space and macropore volume, but simply to evaluate the total amount of methane in the adsorbent filled vessel. To obtain the maximum storage capacity for the adsorbent, it would be necessary to optimally pack the vessel. 

Example 5.14 A power law fluid with constants i]q= 1.2 x lO Ns/m and n = 0.35 is injected through a centre gate into a disc cavity which has a depth of 2 mm and a diameter of 200 mm. If the injection rate is constant at 6 X 10 m /s, estimate the time taken to fill the cavity and the minimum injecdon pressure necessary at the gate for (a) Isothermal and (b) Non-isothermal conditions. 

It is convenient to calculate a TNT equivalent of a physical explosion to use the military results of Figures 9.1-4 and 5. Baker et al. (1983) give a recipe for the rupture of a gas filled container assuming expansion occurs isothermally and the perfect gas laws apply (equation 9.1-25), where W is... 

In Fig. 15 we show similar results, but for = 10. Part (a) displays some examples of the adsorption isotherms at three temperatures. The highest temperature, T = 1.27, is the critical temperature for this system. At any T > 0.7 the layering transition is not observed, always the condensation in the pore is via an instantaneous filling of the entire pore. Part (b) shows the density profiles at T = 1. The transition from gas to hquid occurs at p/, = 0.004 15. Before the capillary condensation point, only a thin film adjacent to a pore wall is formed. The capillary condensation is now competing with wetting. 

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