Microporous volume

Type 1 isotherms, as will be demonstrated in Chapter 4, are characteristic of microporous adsorbents. The detailed interpretation of such isotherms is controversial, but the majority of workers would probably agree that the very concept of the surface area of a microporous solid is of doubtful validity, and that whilst it is possible to obtain an estimate of the total micropore volume from a Type I isotherm, only the crudest guesses can be made as to the pore size distribution. 

Fig. 2.28. The high-pressure branch is still linear (provided mesopores are absent), but when extrapolated to the adsorption axis it gives a positive intercept which is equivalent to the micropore volume. The slope of the linear branch is now proportional to the external surface area of the solid. Microporosity is dealt with in detail in Chapter 4.

If the isotherm is of Type I with a sharp knee and a plateau which is horizontal (cf. Fig. 4.10) the uptake n, at a point close to saturation, say p/p = 0-95, is then a measure of the micropore volume when converted to a liquid volume (by use of the density of the liquid adsorptive), it may be taken as actually equal to the micropore volume. 

More often, however, microporosity is associated with an appreciable external surface, or with mesoporosity, or with both. The effect of microporosity on the isotherm will be seen from Fig. 4.11(a) and Fig. 4.12(a). In Fig. 4.11(a) curve (i) refers to a powder made up of nonporous particles and curve (ii) to a solid which is wholly microporous. However, if the particles of the powder are microporous (the total micropore volume being given by the plateau of curve (ii)), the isotherm will assume the form of curve (iii), obtained by summing curves (i) and (ii). Like isotherm (i), the composite isotherm is of Type II, but because of the contribution from the Type 1 isotherm, it has a steep initial portion the relative enhancement of adsorption in the low-pressure region will be reflected in a significantly increased value of the BET c-constant and a shortened linear branch of the BET plot. 

Fig. 4.11 (o) Adsorption isotherm for (i) a powder made up of nonporous particles (ii) a solid which is wholly microporous (iii) a powder with the same external surface as in (i) but made up of microporous particles having a total micropore volume given by the plateau of isotherm (ii). The adsorption is expressed in arbitrary units, (b) t-Plots corresponding to isotherms (i) and (iii). The o,-plots are similar, except for the scale of... 

A high value of the BET constant c is a useful preliminary indication of the presence of microporosity, but it does not enable one to estimate the micropore volume itself, that is in effect to break down the composite isotherm (iii) into its components (i) and (ii). 

The table convincingly demonstrates how the unsuspected presence of micropores can lead to an erroneous value of the specific surface calculated from a Type II isotherm by application of the standard BET procedure. According to the foregoing analysis, the external specific surface of the solid is 114m g" the micropore volume (from the vertical separation of isotherms A and E) is 105 mm g but since the average pore width is not precisely known, the area of the micropore walls cannot be calculated. Thus the BET figure of 360m g calculated from isotherm E represents merely an apparent and not a true surface area. 

The t and a.-methods, the nature of which was explained in Chapter 2, may be used to arrive at a value of the micropore volume. If the surface of the solid has standard properties, the t-plot (or a,-plot) corresponding to the isotherm of the nonporous powder in Fig. 4.11(a) will be a straight line passing through the origin (cf. curve (i) of Fig. 4.11(6)) and having a slope proportional to the specific surface of the powder. For the microporous powder which yields the isotherm (iii).of Fig. 4.11(a), the t-plot (or Oj-plot) will have the form of curve (iii) of Fig. 4.11(6) the linear branch of this curve will be parallel to curve (i), since it corresponds to the area of the outside of the particles which is identical with that of the nonporous parent particles. 

The intercept on the adsorption axis of the extrapolated linear branch gives the micropore contribution, and when converted to a liquid volume may be taken as equal to the micropore volume itself. It is sometimes convenient indeed to convert all the uptakes into liquid volumes (by use of the liquid density) before drawing the t-plots or the a,-plots. If mesopores are present (in addition to micropores) the plots will show an upward deviation at high relative pressures corresponding to the occurrence of capillary condensation (Fig. 4.12(6)). The slope of the linear branch will then be proportional to the area of the mesopore walls together with the... 

Parameter k of Equation (4.10) is an expression of the breadth of the Gaussian distribution of the cumulative micropore volume IF over the normalized work of adsorption sfifi, and is therefore determined by the pore structure. Thus B also (cf. Equation (4.13)) is characteristic of the pore structure of the adsorbent, and has accordingly been termed the structural constant of the adsorbent. ... 

According to Equation (4.14) the DR plot of logio W (i.e. of logio /Pt) against logfo(p7p) should be a straight line having an intercept equal to the total micropore volume W. From its slope the value of B/p (cf. Equation (4.12)), but not of B and p separately, should be obtainable. 

The extrapolated value of micropore volume (cf. dashed lines in Fig. 4.21) would then need to be corrected for mesopore adsorption which would have contributed to the uptake at lower relative pressures. 

A major difficulty in testing the validity of predictions from the DR equation is that independent estimates of the relevant parameters—the total micropore volume and the pore size distribution—are so often lacking. However, Marsh and Rand compared the extrapolated value for from DR plots of CO2 on a series of activated carbons, with the micropore volume estimated by the pre-adsorption of nonane. They found that except in one case, the value from the DR plot was below, often much below, the nonane figure (Table 4.9). 

For a continuous distribution, summation may be replaced by integration and by assuming a Gaussian distribution of size, Stoeckli arrives at a somewhat complicated expression (not given here) which enables the total micropore volume IFo, a structural constant Bq and the spread A of size distribution to be obtained from the isotherm. He suggests that Bq may be related to the radius of gyration of the micropores by the expression... 

These procedures proposed by Dubinin and by Stoeckli arc, as yet, in the pioneer stage. Before they can be regarded as established as a means of evaluating pore size distribution, a wide-ranging study is needed, involving model micropore systems contained in a variety of chemical substances. The relationship between the structural constant B and the actual dimensions of the micropores, together with their distribution, would have to be demonstrated. The micropore volume would need to be evaluated independently from the known structure of the solid, or by the nonane pre-adsorption method, or with the aid of a range of molecular probes. 

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. 

In very small pores the molecules never escape from the force field of the pore wall even at the center of the pore. In this situation the concepts of monolayer and multilayer sorption become blurred and it is more useful to consider adsorption simply as pore filling. The molecular volume in the adsorbed phase is similar to that of the saturated Hquid sorbate, so a rough estimate of the saturation capacity can be obtained simply from the quotient of the specific micropore volume and the molar volume of the saturated Hquid. 

Fig. 2. Pore size distribution of typical samples of activated carbon (small pore gas carbon and large pore decolorizing carbon) and carbon molecular sieve (CMS). A / Arrepresents the increment of specific micropore volume for an increment of pore radius.

Traditional adsorbents such as sihca [7631 -86-9] Si02 activated alumina [1318-23-6] AI2O2 and activated carbon [7440-44-0], C, exhibit large surface areas and micropore volumes. The surface chemical properties of these adsorbents make them potentially useful for separations by molecular class. However, the micropore size distribution is fairly broad for these materials (45). This characteristic makes them unsuitable for use in separations in which steric hindrance can potentially be exploited (see Aluminum compounds, aluminum oxide (ALUMINA) Silicon compounds, synthetic inorganic silicates). 

Since adsorption takes place at the interphase boundaiy, the adsorption surface area becomes an important consideration. Generally, the higher the adsorption surface area, the greater its adsorption capacity. However, the surface area has to be available in a particular pore size within the adsorbent. At low partial pressure (or concentration) a surface area in the smallest pores in which the adsorbate can enter is the most efficient. At higher pressures the larger pores become more important at very high concentrations, capiDaiy condensation will take place within the pores, and the total micropore volume becomes the limiting factor. 

Fig.l3. Variation of DR micropore volume in a large CFCMS monolith with 10 4 wt% bum-off [27],... 

The micropore volume varied from -0.15 to -0.35 cmVg. No clear trend was observed with respect to the spatial variation. Data for the BET surface area are shown in Fig. 14. The surface area varied from -300 to -900 mVg, again with no clear dependence upon spatial location withm the monolith. The surface area and pore volume varied by a factor -3 withm the monolith, which had a volume of -1900 cm. In contrast, the steam activated monolith exhibited similar imcropore structure variability, but in a sample with less than one fiftieth of the volume. Pore size, pore volume and surface area data are given in Table 2 for four large monoliths activated via Oj chemisorption. The data in Table 2 are mean values from samples cored from each end of the monolith. A comparison of the data m Table 1 and 2 indicates that at bum-offs -10% comparable pore volumes and surface areas are developed for both steam activation and Oj chemisorption activation, although the process time is substantially longer in the latter case. 

Monolith ID Bum-off %) BET surface area (mVg) DR micropore volume (cm /g) DA microporc diameter (nm)... 

The high density hybrid monoliths would thus appear to be well suited to storage applications. However, the data presented here are for hybrid monoliths that are far from optimum as storage carbons. A great deal of development work is required to increase the micropore volume and storage capacity of the monoliths. Some of our preliminary work in this context is discussed subsequently. 

Presently, the most successful adsorbents arc microporous carbons, but there is considerable interest in other possible adsorbents, mainly porous polymers, silica based xerogels or zeolite type materials. Regardless of the type of material, the above principles still apply to achieving a satisfactory storage capacity. The limiting storage uptake will be directly proportional to the accessible micropore volume per volume of storage capacity. 

The issue of the theoretical maximum storage capacity has been the subject of much debate. Parkyns and Quinn [20] concluded that for active carbons the maximum uptake at 3.5 MPa and 298 K would be 237 V/V. This was estimated from a large number of experimental methane isotherms measured on different carbons, and the relationship of these isotherms to the micropore volume of the corresponding adsorbent. Based on Lennard-Jones parameters [21], Dignum [5] calculated the maximum methane density in a pore at 298 K to be 270 mg/ml. Thus an adsorbent with 0.50 ml of micropore per ml could potentially adsorb 135 mg methane per ml, equivalent to about 205 V/ V, while a microporc volume of 0.60 mEml might store 243 V/V. Using sophisticated parallel slit... 

Parkyns and Quinn [20] showed a linear relationship between methane uptake at 25 C, 3.4 MPa and the Dubinin-Radushkievich micropore volume from 77 K nitrogen adsorption for porous carbons,... 

Mcntasty el al. [35] and others [13, 36] have measured methane uptakes on zeolites. These materials, such as the 4A, 5A and 13X zeolites, have methane uptakes which are lower than would be predicted using the above relationship. This suggests that either the zeolite cavity is more attractive to 77 K nitrogen than a carbon pore, or methane at 298 K, 3.4 MPa, is attracted more to a carbon pore than a zeolite. The latter proposition is supported by the modeling of Cracknel et al. [37, 38], who show that methane densities in silica cavities will be lower than for the equivalent size parallel slit shaped pore of their model carbon. Results reported by Ventura [39] for silica xerogels lead to a similar conclusion. Thus, porous silica adsorbents with equivalent nitrogen derived micropore volumes to carbons adsorb and deliver less methane. For delivery of 150 V./V a silica based adsorbent would requne a micropore volume in excess of 0.70 ml per ml of packed vessel volume. 

From the above data, it would appear that methane densities in pores with carbon surfaces are higher than those of other materials. In the previous section it was pointed out that to maximize natural gas or methane storage, it is necessary to maximize micropore volume, not per unit mass of adsorbent, but per unit volume of storage vessel. Moreover, a porous carbon filled vessel will store and deliver more methane than a vessel filled wnth a siliea based or polymer adsorbent which has an equivalent micropore volume fraction of the storage vessel. 

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