Adsorption of nitrogen by porous and non-porous carbons

Curhon Prmted

Vol 25, No 1. pp. 59-6X. I” Great Bntam

WXk-6223/X7 E 1987 Pergamon

1987

$3 00 + IX) Journals Ltd.

ADSORPTION OF NITROGEN BY POROUS AND NON-POROUS CARBONS P. J. M. CARROT-T, R. A. ROBERTS and K. S. W. SING Department of Chemistry, Brunei University, Uxbridge, Middlesex, UB8 3PH. United Kingdom (Received 27 March 1986) Abstract-Nitrogen isotherms have been determined at 77 K on a number of carbon blacks and microporous carbons. Application of the Dubinin-Radushkevich (DR) method has shown that linear plots are given by both nonporous and microporous samples. The range of linearity is considerably reduced by increasing the micropore size, while graphitisation of nonporous carbon leads to the formation of two distinct linear regions. Application of the a, method provides strong evidence for two stages of micropore filling: (a) a primary process involving enhanced adsorbate-adsorbent interactions and (b) a secondary process which is the result of cooperative effects associated with the filling of wider micropores. Key Words-Nitrogen

adsorption, carbon black, microporous carbon, ~1,method, DR equation.

the affinity adsorption),

1. INTRODUCTION The mechanisms involved in the filling of micropores are still far from clear. It is known that the enhancement of adsorption energy in very fine pores leads to the filling of the pore volume at low relative pressures, but the upper limit of this micropore filling effect is uncertain[ 11. According to the IUPAC classification of pore size[2], micropores are defined as pores with widths not exceeding 2 nm. Theoretical calculations[3] and recent experimental measurements of adsorption energies[4] have revealed, however, that the enhancement in the gas-solid interaction energy becomes quite small as the pore width is increased to more than a few molecular diameters (i.e. 0.7-0.8 nm for nitrogen adsorption). These findings indicate that pore filling of the larger micropores (termed “supermicropores” by Dubinin[5,6]) must take place at higher relative pressures by a different adsorption mechanism. The limited amount of evidence available indicates that this is a cooperative process involving the interaction between adsorbate molecules[7]. In view of the complexity of physisorption in micropores, it is not surprising that there is no current theory which can provide a general mathematical description of the pore filling processes. An approach pioneered by Dubinin and his co-workers[5,6,8,9] was to combine the Polyani concept of the characteristic curve with the theory of volume filling of micropores. For the simplest case of a microporous carbon containing a fairly narrow distribution of pore size. it was proposed[8] that the characteristic curve could be expressed in the form: V/V,

= exp[-(A/E)2],

r,:i-E

the differential

A = RT ln(p”/p),

free energy

of

(2)

and E is the characteristic free energy of adsorption for the given system. A more general expression was put forward by Dubinin and Astakhov[lO]: V/V,

= exp[ -(A/E)“],

(3)

which contains the additional parameter IZand is applicable to a wide range of microporous carbons and zeolites. Recently, Stoeckli and his co-workers[ll] have developed an alternative generalized treatment for the volume filling of a heterogeneous collection of micropores which is based on the summation of the contributions from individual pore groups, each group giving rise to its own characteristic curve in the form of eqn (1). Although eqns (1) and (3) have been found applicable on an empirical basis to certain systems over a wide range of temperature and pressure[l2], it should be noted that the parameters E and II are not amenable to independent calculations or experimental verification. Furthermore, values of VPas assessed by the application of eqn (1) are often found to be of doubtful validity[l,13]. Another serious limitation of Dubinin’s approach to micropore filling is that the characteristic curve concept does not readily allow for differences in the nature of the gas-solid interactions which may affect the course of the isotherm at low surface coverage (or pore filling)[l4]. It is evident that more work is required to establish the degree of usefulness of eqns (1) and (3). An alternative approach for the study of micropore filling is provided by the application of the a,

(1)

where V is the volume of gas adsorbed at pip” and V,, the volume required to fill the micropores. A is

.A”

(-AC, i.e.

59

P. J. M. CARROTT et al.

60

method[l5]. This is an unashamedly empirical method of adsorption isotherm analysis. To apply the method it is necessary to select an appropriate standard isotherm obtained on a nonporous reference adsorbent having a similar surface structure to the microporous solid under investigation. With carbonaceous materials this requirement presents a problem because in general their surface chemical structures are not as well defined as in the case of oxides[l6]. Four different microporous carbons were chosen for the present investigation. The main objective of the work was to extend and confirm the previous preliminary study[l3] of the two stages of micropore filling and, in particular, explore the usefulness of the DR and a, methods of isotherm analysis. It was also considered appropriate to undertake measurements, especially at low pressures, on various graphitised and ungraphitised carbon blacks. In addition, the a, method has been applied to nitrogen isotherms determined on a mixed microporousmesoporous carbon both before and after the preadsorption of n-nonane. In this manner it was hoped to obtain new information on the scope and limitations of the two methods of isotherm analysis as applied to nitrogen adsorption on carbonaceous adsorbents.

2.EXPERIMENTAL

Four microporous carbons were selected as representative examples of carbon adsorbents with different pore structures. Carbosieve is a polymerbased molecular sieve carbon manufactured by Supelco and suppiied by Bioscan, Canvey Island. AX21 is a petroleum pitch-based active carbon of very high adsorption capacity manufactured and supplied by the Anderson Development Co., Michigan. Two samples of charcoal cloth were specially prepared from viscose rayon cloth by carbonisation in Nz at 850°C followed by activation in COZ at the same temperature[ 171. JFOOSis a low burn-off cloth known to possess only pores of molecular dimensions, while the conditions under which JF517 was prepared were designed to produce a charcoal cloth with a much wider range of pore sizes. In addition a sample of charcoal cloth, XR602, which contains both micropores and mesopores was prepared[l8]. Three ungraphitised carbon blacks, Spheron6, Vulcan3 and Elftexf20 were supplied by Cabot Carbon Ltd, Ellesmere Port. Three graphitised carbon blacks were also studied. Graphon was supplied by CabotC%rbon Ltd., while Vulcan3G and Sterling FI were obtained from the National Physical Laboratory, Teddington. For the purposes of comparison the data of Pierce for Sterling S (ungraphitised)[l9] and Sterling MT (graphitised)]20] have been included in the study. Sooty Silica is a well-characterised nonporous adsorbent made by depositing a carbon layer on the

surface of silica[21]. It was supplied by ICI plc, Runcorn. Nitrogen isotherms at 77 K were determined using a Carlo-Erba Series 1800 Sorptomatic. For certain samples (notably Sooty Silica) the isotherms were repeated using a manual volumetric apparatus of the type designed by Harris and Sing[22]. For the measurement of pressures below 40 mm Hg a Datametrics type 565-91 Barocel transducer was employed. Samples were outgassed at 250°C (140°C for Sooty Silica) for 16 h to a residual pressure <10e5 mm Hg.

3.RESULTS AND DISCUSSION

3.1 Adsorption botherms Representative nitrogen isotherms obtained with the microporous carbons are shown in Fig. 1. The predominant character of all these isotherms is type I, but it is evident that their precise shape varies significantly from one adsorbent to another. In a few cases (notably Carbosieve and charcoal cloth JFO05) there is a steep uptake of gas at very low pIp”, while with other samples (e.g. AX21 and charcoal cloth JF517) there is a more gradual approach to a rather ill-de~ned plateau located at higher pip”. In the case of JF517 the appearance of the small hysteresis loop is indicative of the existence of some mesoporosity. The isotherms in Fig. 2 are representative of those obtained with the various graphitised and ungraphitised carbon blacks. The type-II character of these isotherms indicates that the degree of microporosity and mesoporosity was relatively low. Graphitisation of Vulcan3 has resulted in a slight change in shape of the isotherm with a sharpening of the first knee and the development of a step at p/pa - 0.2. A similar change has been found with Graphon and Sterling FT. 3.2 Dubinin-Ra~ushkevich p&s By combining eqns (1) and (2) we obtain the Dubinin-Radushkevich (DR) equation[8]: V/V,

= exp[ - B( Tlp)Zlog2(polp)],

(4)

where B is the so-called structural constant and 8 is a scaling factor (or “similarity coefficient”). Rearrangement of eqn (4) leads to the DR equation in its linear form, 1ogv = logVp - D log’(p”/p),

(5)

where D = B(T/@)*. The DR plots in Figs. 3 and 4 were constructed in the usual way, i.e. as 1ogV against log2(polp), from the isotherms in Figs, 1 and 2, respectively. It is apparent that the DR plots on the microporous carbons (Fig. 3) are all linear at low p/p’. The range of linearity is most extensive with Carbosieve and charcoal cloth JFOOS, but even in these cases it does not extend above pip’ - 0.05. The other DR plots in Fig. 3 are linear only up to p/p’ - 0.005.

Adsorption of nitrogen According to eqn (S), the intercept of the linear DR plot should equal logV,, where VPis the volume of gas required to fill the micropores. The values of VP so obtained by back extrapolation of the linear sections of the DR plots have been converted into micropore volumes (v,” in Table 1) by assuming that the pores have been filled with liquid nitrogen (taking its density as 0.808 g cm-j). We shall return later to the question of the validity of the values of v,“. It has been noted previously[l] that some nonporous solids give linear DR plots and it is therefore of interest to establish whether this is the case with the carbon blacks studied in the present work. Inspection of Fig. 4 reveals that whereas Spheron6, Sooty Silica and Elftex120 all give nearly linear DR plots over a wide range of low p/p”, Graphon and Sterling FI give DR plots of quite different character, having two separate linear branches at low pIp”. These dif-

61

ferences evidently reflect the marked change in isotherm shape produced by graphitisation. Dubinin and Stoeckli[l2] have pointed out that eqn (1) can be applied to the majority of microporous carbons which possess a fairly narrow distribution of pores of molecular dimensions. Our work confirms that the simple DR equation is indeed applicable to such systems-at least up to p/p” - 0.05. On the other hand, it is evident that linearity of the DR plots provides only the first step in any attempt to establish the validity of the Dubinin theory of micropore filling. 3.3 a, plots Recent work[21] has shown that certain samples of carbon coated silica (Sooty Silica) give reduced nitrogen isotherms which are almost identical in shape to the standard isotherms determined previ-

800

k 600 !c 73 u \ >

LOO CARBOSIEVE rl----c]

”

o-2

v

Y

”

Y

”

Y

V

JFOOS

0.C

O-6

O-8

P/P0 Fig. 1. Adsorption isotherms on microporous carbons. Open symbols, adsorption: closed symbols, desorption.

62

P. J. M. CARROTIet al. I

100 -

80 -

20

I I

I

0.2

I

1

I

0-L

I

0.6

I

I

I

0.8

P/P" Fig. 2. Adsorption isotherms on carbon blacks. Open symbols, adsorption: closed symbols, desorption

ously[23] on TK800 and other nonporous silicas. In view of these findings it was decided to construct the cc,plots in Figs. 5 and 6 with the Sooty Silica adsorption data taken as the standard. As in previous work[l5], the amount of gas adsorbed is plotted against a,, the reduced standard adsorption at the corresponding p/p” (with as = 1 at p/p0 = 0.4). The a, plots for the carbon blacks in Fig. 5 exhibit several interesting features. All the ungraphitised blacks give nearly linear a, plots, which (apart from that for Spheron6) can be back extrapolated to the origin. Although the a, plots for the graphitised blacks undergo pronounced deviation from linearity at low a$ (i.e.
nitrogen multilayer is to a great extent independent of the nature of the adsorbent surface. Values of surface area of the carbon blacks are given in Table 2. The BET area, ABET,was calculated in the usual manner[l] with the molecular area of nitrogen taken as 0.162 nm2. A, was calculated from the slope of the linear part of each a, plot by using the equation A, = 2.861//a,,

(6)

where the factor 2.86 has been obtained by calibration against the BET area of Sooty Silica and various nonporous silicas[21,23,25]. The ungraphitised blacks Vulcan3, Elftex120 and Sterling S give excellent agreement between the corresponding values of ABETand A,, whereas the gra-

63

Adsorption of nitrogen

0.1

P/P" 0.001

0.01

I

I

1

5

0*0001

I

1

I

log2

I

15

10 (p”/p)

Fig. 3. DR plots for microporous carbons. phitised blacks give consistently higher values of A,. These findings are in accord with the work of Pierce[l9,20], who first drew attention to a significant difference between the apparent BET areas of graphitised carbon blacks and the corresponding areas computed from the multilayer section of the nitrogen isotherms. Pierce and Ewing[l9] postulated that on the graphitic basal plane nitrogen molecules do not occupy the normal area of 0.162 nmz molecule but instead have an effective cross-sectional area of

approximately

0.20 nm2. If we accept the values of

A, in Table 2 as being the true surface areas, the

average corrected value of the molecular area, a, (N,), is 0.195 nm*, which is remarkably close to that obtained by Pierce[20]. In the case of Spheron6, the discrepancy between A BETand A, arises in a different way. The form of the (Y,plot indicates that this sample was to some Table 2. Surface areas of carbon blacks

Table 1. Surface areas and pore volumes of microporous carbons. graphitised

AX21 JF517 CARBOSIEVE JF005

6

“,”

m* g-’

4 m2 g-i

cm’ g-’

cm) g-’

3393 1657 1179 882

233 218 41 19

1.52 0.76 0.43 0.33

1.00 0.47 0.45 0.35

A BET

graphitised

VULCAN3 ELFIEX120 STERLING S SPHERON6 VULCAN3G STERLING F-I STERLING MT GRAPHON

84.5 37.4 25.0 123.2 69.8 10.3 7.7 91.4

84.2 37.5 25.4 103.9 85.6 12.4 9.4 103.3

64

P. J. M. CARROT-~et al. 0.1

P/P” 0.001

no1

o.mO1

0.1

p/P’ 0.001

0.01

O.OWl

4.50ii

> z g

t_LING

FT

0.25

y-._

A

-0.25 I 10

\

--Y

0.00

5

/

-

7

15

10 iog+pYp)

5

iog2(p”/pl

\

15

(W

(4

Fig. 4. DR plots for (a) Sooty Silica and ungraphitised carbon blacks and (b) graphitised carbon blacks.

extent microporous and from the slope and intercept we conclude that the external surface area was 104 m2 g-l and the micropore volume was 0.013 cm3 g-l. Analysis of the ctSplots in Fig. 6 has provided the values of external area, A, (from the multilayer slope) and micropore volume, v; (from the intercept of the extrapolated multilayer region). The lack of

agreement between A, and ABETis due to the highly microporous nature of these adsorbents and confirms the unreliability of the BET area. It is of particular interest that the corresponding values of v; and vp” are in fairly good agreement only for the two samples (Carbosieve and JFOOS) possessing relatively small external areas. Preadsorption of n-nonane vapour has been o.ol

,.’

4

d

P/P”

0.1

0.8

Q85

.d

Jl

8Or’

’ ”

7

“‘“;/.*,,,,,,/”

-6o-

E m

%

_ ./XI-CAN ,

3G

,,J’

I

m

,

/I: c

I:0

as

(4

1.k

2:o

‘:

‘,

‘I

I

’ ,’ I’ I

1‘# ‘/

I 0.5

, 1.5

t 1.0 as

@I

Fig. 5. 4 plots for (a) ungraphitised carbon blacks and (b) graphitised carbon blacks.

I 2.0

-I

Adsorption of nitrogen

65

vapour having been followed by overnight outgassing at ambient temperature. It is evident that there is an overall downward displacement of the nitrogen isotherm but no significant change in the hysteresis loop-indicating that the mesopore structure has remained entirely open. This interpretation is confirmed by the change in the nature of the uS plots in Fig. 7. The removal of the positive intercept is the result of blockage of the micropore volume (see Table 3). The close agreement between ABETand A, after nonane preadsorption is also consistent with this explanation.

P/P”

P 800

i

4. CONCLUSIONS

I

0.5

I

1.0

I

I

1.5

2.0

The results reported here confirm and extend our previous findings[l3] that microporous carbons may be broadly divided into two groups: (a) those having pores of molecular dimensions (i.e. of width not exceeding -0.7-0.8 nm) into which adsorptive molecules are physisorbed atpip* < 0.01; (b) those having a range of wider pores (of width up to -2 nm) which are filled at higher pip” (up to pip0 - 0.2-0.3). The high adsorption affinity exhibited by the first group is due to enhancement of the gas-solid interactions and this process of primary micropore filling is associated with a marked distortion of the isotherm shape-as revealed by the form of the a, plots. The wider micropores are believed to fill by a cooperative mechanism which involves little, if any, enhancement of the adsorption energy. In this case there is much less distortion of the isotherm shape over the range of pore filling. It is noteworthy that in all cases so far studied the stage of primary micropore filling is associated with a linear DR plot and the onset of the second, or cooperative, stage by an upward deviation from linearity. However, considerable caution must be exercised in the interpretation of these features since

as Fig. 6. a, plots for microporous carbons.

used1 1,261 as an effective way of filling the micropores while leaving the external surface available for nitrogen adsorption. This method has not so far been applied to many systems containing a range of pore size and it was therefore decided to study a sample of charcoal cloth, XR602, which was known to contain both micropores and mesopores. The nitrogen isotherms obtained before and after nonane preadsorption are shown in Fig. 7, exposure to nonane

600

L E

500-

F;;

A

2'400P

/ 300-

0.5

1.0

P/P” (a)

Fig. 7. (a) Adsorption isotherms on XR602 before and after n-nonane preadsorption. adsorption: closed symbols, desorption: (b) corresponding a, plots.

1.5

Qs (b) Open symbols,

2.0

66

P. J. M. CARROTTet al.

Table 3. Influence of n-nonane preadsorption area and pore volume of XR602.

on surface

ABET before pre-adsorption after pre-adsorption

A,

%

m2 g-’

m* g-l

cm3 g-l

695 315

319 319

0.16 0

linearity of the DR plot does not by itself confirm the occurrence of micropore filling. In our view little is to be gained by the application of the DubininStoeckli generalised treatment unless the mechanism of adsorption can first be established. For this purpose, the cl, method offers a simple and effective procedure provided that due allowance is made for changes in the shape of the standard isotherm, e.g. as a result of graphitisation.

Acknowledgements-We

are grateful to Mr. J. J. Freeman for preparing the samples of charcoal cloth and the following for providing other samples: ICI plc, Cabot Carbon Ltd, Anderson Development Co.. Bioscan, and the National Physical Laboratory.

REFERENCES 1. S. J. Gregg and K. S. W. Sing, Adsorption, Surface Area and Porosity, 2nd edn. Academic, London (1982).

2. IUPAC Manual of Symbols and Terminology, Appendix 2, Part 1, Colloid and Surface Chemistry, Pure Appl. Chem. 54,220l (1982). 3. D. H. Everett and J. C. Powl, J. Chem. Sot., Faraday Trans. Z72, 619 (1976).

4. D. M. Atkinson. P. J. M. Carrott. Y. Grillet. J. Rouquerol and K. S.’ W. Sing, unpublished results. 5. M. M. Dubinin, in Progress in Surface and Membrane Science (Edited by D. A. Cadenhead), Vol. 9, pp. l70. Academic, New York (1975). __ 6. M. M. Dubinin. in Characterisation of Porous Solids (Edited by S. J. Gregg, K. S. W. Sing and H. F. Stoeckli), pp. l-11. Society of Chemical Industry, London (1979).

I. K. S. W. Sing, in Principles and Applications of Pore Structural Characterisation (Edited by J. M. Haynes and P. Rossi-Doria), pp. l-11. Arrowsmith, Bristol (1985). 8. M. M. Dubinin, Chem. Rev. 60,235 (1960). 9. M. M. Dubinin, J. Colloid Interface Sci. 23,487 (1967). 10. M. M. Dubinin and V. A. Astakhov, Adv. Chem. Ser., No. 102, pp. 69-85 (1971). 11. H. F. Stoeckli, J.Ph. Houriet, A. Perret and U. Huber, in Characterisation of Porous Solids (Edited by S. J. Gregg, K. S. W. Sing and H. E Stoeckli), pp. 31-39. Society of Chemical Industry, London (1979). 12. M. M. Dubinin and H. F. Stoeckli, J. Colloid Interface Sci 75,34

(1980).

13. D. M. Atkinson, A. I. McLeod and K. S. W. Sing, J. Chim. Phys. 81,791 (1984). 14. D. Nicholson and K. S. W. Sing, in Colloid Science (Edited by D. H. Everett), Vol. 3, pp. l-62. Chemical Society, London (1979). 15. K. S. W. Sing, in Surface Area Determination (Edited by D. H. Everett and R. H. Ottewill), pp. 25-42. Butterworths, London (1970). 16. N. D. Parkyns and K. S. W. Sing, in Colloid Science (Edited by D. H. Everett), Vol. 2, pp. 1-51. Chemical Society, London (1975). 17. A. Capon, J. J. Freeman, A. I. McLeod and K. S. W. Sing, Extended Abstracts, 6th London International Carbon and Graphite Conference, pp. 154-156. Society of Chemical Industry, London (1982). 18. J. J. Freeman. F. G. R. Gimblett. R. A. Roberts and K. S. W. Sing,‘Extended Abstracts, 17th Biennial Conference on Carbon, Kentucky, pp. 245-246. American Carbon Society (1985). 19. C. Pierce and B. Ewing, J. Phys. Chem. 68, 2562 (1964).

20. C. Pierce, J. Phys. Chem. 72,3673 (1968). 21. P. J. M. Carrott, J. H. Raistrick and K. S. W. Sing, to be published in Colloids and Surfaces. 22. M. R. Harris and K. S. W. Sing, J. Appl. Chem. 5,223 (1955).

23. M. R: Bhambhani, P. A. Cutting, K. S. W. Sing and D. H. Turk. J. Colloid Interface Sci. 38. 109 (1972). 24. P. J. M. Carrott, A. I. McLoud and K.‘S. W: Sing, in Adsorption at the Gas-Solid and Liquid-Solid Interface

(Edited by J. Rouquerol and K. S. W. Sing), pp. 403410. Elsevier, Amsterdam (1982). 25. P. J. M. Carrott and K. S. W. Sing, Adsorption Sci. Technol. 1,31 (1984). 26. S. J. Gregg and J. F. Langford, Trans. Faraday Sot. 65, 1394 (1969).

DISCUSSION Question by H. Marsh It is generally accepted that most active carbons are microporous. You have suggested that some carbon blacks, e.g. Spheron 6, are also to some extent microporous. It is not possible that high energy sites on the carbon surface behave as micropores in distorting the shape of the a,-plot? Reply by K. S. W. Sing The presence of high energy sites would indeed change the shape of the adsorption isotherm range, but would not be expected to give an a,-plot of the shape obtained for Spheron case multilayer adsorption has taken place on the external surface, which is significantly BET area (see Table 2). It is noteworthy that the change of surface structure produced has had a quite different effect on the form of a$-plots in Fig. 5.

in the monolayer 6 (Fig. 5). In this smaller than the by graphitisation

Adsorption of nitrogen

67

Question by A. Groszek Could the difference in the nature of adsorption of NZ on Spheron 6 and Graphon be caused, at least in part, by the removal of polar surface sites during graphitization? Such polar sites may be as strong as they are in zeolites and thus affect the adsorption process. Reply by K. S. W. Sing I think that the surface properties of carbon blacks are modified in three different ways as a result of graphitization: (1) the overall surface becomes more uniform, (2) polar groups are removed and (3) any microporosity is removed, or at least reduced in scale. Some blacks appear to be essentially non-porous and in those cases the specific and non-specific interactions involved in nitrogen adsorption appear to be remarkably similar to those given by the hydroxylated silicas. The changes in the character of the isotherms and ol,-plots in Figs 2 and 5 illustrate the effect of graphitization on the adsorptive properties: development of the graphitic basal planes leads to enhanced dispersion interactions and hence a sharpening of the nitrogen isotherm in the monolayer region. Removal of the surface polar groups leads to a considerable decrease in the specific interactions and this reduction in energetic heterogeneity brings about a change in the shape of the nitrogen isotherm at very low surface coverage. It is fortunate that in spite of the complexities of these changes in the monolayer region, the character of the nitrogen mut~ilayer is not altered to any significant extent. Thus, the ‘universal’ nature of the nitrogen multilayer allows us to apply the @,-method for the assessment of microporosity in a wide range of carbonaceous and other adsorbents. Question by I. Ismail Is there one standard nitrogen isotherm for graphitic materials and another for non-graphitized

carbons?

Reply by K. S. W. Sing Yes, for the reasons given earlier. The shape of the two isotherms in the monolayer region is quite different, but in the multilayer range (i.e. at p/p0 > 0.4) they are remarkably similar. Question by I. Ismail I believe that you were lucky in your application of the nonane pre-adsorption technique. Do you always find that nonane effectively blocks the micropores whilst leaving the mesopores available for nitrogen adsorption? Reply by K. S. W. Sing It is true that nonane pre-adsorption is not always effective in blocking off the micropores. In our experience this depends on the connectivity of the porous network. We have reason to believe that the particular charcoal cloth (XR 602) studied in our paper had two independent pore structures (i.e. in the micropore and mesopore ranges, respectively). Comment by M. Manes You have stated that the DR equation does not conform to Henry’s law as p + 0. In fact the original Polanyi model when accurately applied does meet this requirement. Answer by K. S. W. Sing This is an interesting observation. Of course, I referred only to the DR plot and not the generalized Dubinin treatment of the characteristic curve. Unfo~unately, this refinement of the DR theory would not by itself ensure the validity of the extrapolated value of the micropore volume. Question by V. Deitz McBain demonstrated that the knee of the isotherm became considerably sharper after repeated isotherm measurements. How can this effect be explained in terms of pore structure? Reply by K. S. W. Sing It has been found that repeated flushing some microporous solids (especially those having narrow pore entrances) with adsorptive leads to an increase in the amount adsorbed. In this manner the micropore structure is made more readily accessible. Such an effect is likely to increase the affinity of adsorption, i.e. sharpen the knee. since it is associated with increased adsorption in pores of molecular dimensions, i.e. in the primary micropore filling range.

68

P J. M. CARROTT~~U~. CODER

From Brian McEnaney. When it was originally proposed the Dubinin-Radushkevich (DR) equation was essentially empirical. However, a justification for the equation can be found by considering the Generalised Adsorption Isotherm (GAI). Microporous carbons are energetically heterogeneous so that adsorption may be modelled using the GAI:

where G{P) is the overall, experimental isotherm @‘(P, 4) is the local isotherm equation, and f(g) is the site energy dist~bution function. The GA1 has been the subject of extensive study]l], and there is a number of approaches to a solution for the GAL For example, Sircar[2] proposed a gamma function for f(q) and the Langmuir equation for @‘(P, q) and solved the GA1 a~alyt~~lly. An alternative approachf3] is the Condensation Approximation which assumes that 8’(F, q) is a step function. Assuming that 9 = A = RTln PO/P, and applying the Condensation Approximation to the Dubinin-Astakhov (DA) equation, Stoeckli[4] showed that: f(4)

= n[A - A(o)~-~/[~~E,J” exp - {[A - A(o)flfM$$‘,

(2)

where A(o) is the lower bound of the range of adsorption energies. When n = 2, equation (2) is f(q) for the DR equation. Thus the DR and DA equations can be seen as solutions of the GA1 which follow if the Condensation Approximation applies and the site energy dist~bution fun~ion is given by equation (2). As Cerofohni (3) has noted, the DR equation applies to adsorption on many nonmi~roporous,

heterogeneous adsorbents, such as gtasses and stainless steels. Thus a linear DR isotherm indicates an absorbent which is heterogeneous, but not necessarily microporous. However, due to the enhanced adsorption potential in micropores, the DR isotherm for a microporous adsorbent is characterised by a higher & value than that for a similar, non-microporous adsorbent. For example, Masters and McEnaney[S] have shown that heattreatment of a microporous cellulose carbon from 1270 to 1670 K closed the majority of micropores to COz at 29X and the value of f3Eo from the DR isotherm for CQ fell from about 8 to about 6 kJ/mol.

1.M. Jaroniec, A. Patrykiejew, and M. Borowko, in “Progress in Surface and Membrane Science.“, Vol. 14. (Edited by D. A. Cadenhead and J. F. Daniellif, Academic press, New York, pp. l-68 (1981). 2. S. Sircar, J. Colfoid Interface Sci., 101,452(1984); idem, J. Chem. Sac. Faraday Trans. I. (u1,lfOl (1984). 3, G. F. Cerofoiini, Surface Science, 24,2393 (1971). 4, H. E Stoeckli, Carbon, 19,325 (1981); H. E Stoeckli, A. Lavanchy, and F. Kraeb~~buehl, in “Adsorption at the GasSolid and Liquid-Solid Interface.” (Edited by J. Rouquerol and K. S. W. Sing) Elsevier, Amsterdam, pp. 201-209 (1982). 5. K. J. Masters and B. McEnaney, Carbon, 22,595 (1984).