The characterization of microporous carbons by means of the dubinin-radushkevich equation

The Characterization of Microporous Carbons by Means of the Dubinin-Radushkevich Equation H. M A R S H AND B. R A N D 1 Northern Coke Research Laboratories, School of Chemistry, The University of Newcastle upon Tyne, Newcastle upon Tyne, NEt 7RU, England

Received October 24, 1969; accepted December 30, 1969 The Dubinin-Radushkevieh (D-R) equation of adsorption predicts a R~yleigh distribution of adsorption free energy with adsorption (mieropore) volume. Only when this distribution is present in microporous solids will a completely linear D-R plot result. Adsorption data of carbon dioxide at 195°K and nitrogen and argon at 77°K on various microporous polymer carbons are interpreted in terms of the D-R equation and distributions of free energy with pore volume. In no case is the complete Rayleigh distribution found to apply and corresponding deviations from linear D-R plots occur. Highly activated carbons show ~ bimodal distribution of free-energy values to nitrogen and argon at 77°K, but not to CO2 at 195°K. Tentative suggestions for this behavior are presented. INTRODUCTION Recently it has become customary (1, 2) to divide the pore structure of solids into the three approximate classifications, micropores (radii < about 15A), transitional pores (radii > 15o < 200A), and macropores (radii > 200A). The basis of this classification is the behavior of each type of pore in the process of vapor adsorption. However, although meaningful information about the pore-size distribution in the transitional size range can be obtained b y judicious application of the Kelvin equation to the high relative pressure (>0.3-0.4 p/po) part of the adsorption isotherm, and in the macro-range b y use of the technique of mercury porosimetry, there is, as yet, no satisfactory method of estimating the size distribution in the micro-range. Recourse is often made to the technique of molecular sieves (3), in which the ability of a pore to exclude adsorbate molecules greater i Present address: Department of Chemical Engineering, The University of Birmingham, Birmingham, England.

in size than its own orifice is utilized. Information is obtained, therefore, about the size distribution of the orifices, but these may not be characteristic of the interior pore structure. Furthermore, the method is limited because adsorbates of molecular diameter greater than about 8A exist either as solids or as liquids with low vapor pressures. I t has been established (4-9) t h a t micropores tend to fill with adsorbate at low relative pressures (p/po < 0.3)--an effect which is often attributed to enhanced dispersion forces resulting from the proximity of the pore walls. Dubinin et al. (1, 8, 10, 11) have directed attention to this low-pressure region of the isotherm for the investigation of micropore structure and extended the Polanyi potential theory of adsorption to give their "theory of volume filling of micropores." There are two principal assumptions in this theory. 1) The characteristic curves for different adsorbates on the same adsorbent can be superimposed by use of an affinity coefficient Journal of Colloid and Interface ScienCe, Vol. 33, No. 1, M a y 1970

101

102

MARSH AND RAND

, • ,i.e., AG = R T In (p/po) = flf(W).

[1]

Here AG is the differential molar free energy ,change of adsorption (with the bulk liquid adsorbate at the same temperature taken as the standard state) and W is the volume of adsorption space filled with adsorbate. 2) The equation of the characteristic ,curve, for the adsorption of vapors onto microporous carbons, takes the form

free energies with adsorption volume of the form, f(aa)

-

- 2 k a a exp

This is the so-called Rayleigh distribution. Figure 1 shows the shape of this distribution obtained from linear D-R plots (Fig. 2) and the effect of the constant k in governing the "spread" of the distribution (fl = 1). It is clearly seen that the distribution is skewed towards high values of -AG. ( exp - ~ ] , I2] ~w Marsh and Siemieniewska (17) have suggested that linear D-R plots result because the so-called Dubinin-Radushkevich (12) the distribution of adsorption free energy (D-R) equation. In this equation k is a con- with adsorption volume follows the Rayleigh stant and W / W o is the fraction of the total distribution. On the other hand, Gregg and adsorption volume (Wo) filled at any value of Sing (2) and Sutherland (18) consider that AG. the apparent wide applicability of the D-t{ It is the main purpose of this publication equation arises because the log W vs. logs to examine the validity of this second as- (p/po) plot is inherently insensitive and the sumption of the theory, although some dis- distribution of adsorption free energy with cussion of the first assumption is also pre- adsorption volume need not be of the Raysented. The implications of the latter equa- leigh type. This implies that these log vs. tion are first reviewed before testing its logs plots would linearize any curve which validity for certain microporous polymer resembles an isotherm in shape. However, carbons. no attempt appears to have been made to The Dubinin-Radushtcevich Equation. The test this implication, and it can be done by D-R equation (Eq. [2]) can be expressed in calculating the D-R plots resulting from the linear form other distribution functions. Figures 3-5 show the D-R plots resulting log W = log Wo -- D logs (p/po), [3] from arbitrarily constructed Gaussian, Poiswhere D = 2.303 lcR2T2/~ 2. Dubinin et al. son, and log-normal distributions. It is clear (1, 8, 10-13) presented experimental data to that for these distributions linear D-t{ plots show that Eq. [3] adequately describes, over do not result when a range of --AG values a wide pressure range, the adsorption data of covering the whole distribution is considered. many adsorbates onto a wide variety of However, if only high values of --AG are microporous carbons, both activated and considered, the Poisson distribution with unactivated. Also it has been shown (14-16) values of >/3 can be linear in the D-R that many adsorption isotherms of vapors coordinates. Certainly it does not appear to on nonporous solids can be linearized, in the be justifiable to say that the D-R equation submonolayer region, by Eq. [3]. Therefore, is insensitive to the type of distribution. It is now pertinent to ask whether the at first sight, it would appear that the D-t{ equation is of surprisingly wide applicability. linear D-R plots previously reported in the However, deviations from linearity can be literature cover a wide enough pressure observed at low values of log2 (p/po) owing range to describe the whole distribution of to capillary condensation in transitional adsorption free energy with adsorption pores or multilayer formation on the walls of volume. If this is so then a Rayleigh distrimacropores (10, 12) when the plot deviates bution of free energies is available to the adsorbate. If not the linearity is fortuitous, upwards with increased slope. The D-R equation is empirical in origin arising because only a limited part of, for and predicts that there is a distribution of example, a Poisson or some irregular distriJournal of Colloid and Interface Science, VoL 33, N'o. 1, M a y 1970

CHARACTERIZATION

OF M I C R O P O R O U S C A R B O N S

103

0"3

I dW/W o

d(-A [;I cm3(Srel ~1 mote kca( 1

0.2

""~ "'" ~"%.q.,I11: ./

0.1

//-"

.f\f

x

//%/.-\ ,i

, / l" /.. /

...

..:¢...

...............,

,i ..J

. .......

........... ,

\,, .-.

-,

.-., ........... [ "~.~ ,~ "~.,~ -.~.. ""~..,~ .,.~,

7

~

6

-AG kcat mute"1 k values:

I

03

2i 0"1

TiT 6x10 -2

"iV /.xl0 -2

"9" 2x10 -2

Fro. 1. Distributions of W with AG from the Dubinin-Radushkevich plots. o o ~%=:.u-.........

lOgl0W/Wo

I

".

"~0

20

g

30

All 2 [kca[)2 mole"2 k values:

T

0"3

"IT 0"1

]]I 6 x 1O-2

W

t, x 10-2

"9" 2 s 10-2

Fro. 2. Idealized Dubinin-Radushkevich plots. bution has been investigated. For example, if the distribution covers a range of --AG values from 0-4.0 kcal mole -1 the adsorption data must extend down to a relative pressure of 3.6 X i0 -a at 195°K. However, at a temperature of 77°K the data must be extended e v e n further to 6 X 10-12 p/po to cover the whole distribution. Thus, it is not a suffi-

ciently rigorous test of the equation that it can linearize isotherm data over a wide pressure range. The important factor is that this range covers the whole distribution of

free energies. It has been suggested by Marsh (19) and Walker et al. (20) that tile adsorption of carbon dioxide at a temperature of 298°i~ is, Journal of Colloid and Interface Science, VoI. 33, N o . 1, May 1970

104

MARSH AND RAND 0.0

Iogl0W/Wo -1.0

-2.0

,

[

i

i

20

,

'LO

i

,

i

60

\

80

462

FIG. 3. D-R plot of Gaussian distribution of W with AG. 0"0

LOgloW/We -1"0

\ i i

'\, \. ~.

\ \\

-2'0

\

I

,

\\

L

,

1O0

'1

I

2g0

,

f

,

300

A62 ra values:

1" 1

~

3

"m" 5

'IT 10

FIo. 4. D-R plot of Poisson distributions of W with AG. perhaps, the most useful technique for investigating the micropore structure of coals and their carbonized products, especially where these show molecular sieve properties. Carbon dioxide is a small molecule with no permanent dipole moment and at 298°K activated diffusion effects should be minimized. Marsh et al. (21, 22) have shown t h a t D - R plots, resulting from adsorption of carJournal of Colloid and Interface Science, Vol. 33, No. 1, l~Iay 1970

bon dioxide at various temperatures on m a n y mieroporous carbons and coals, are linear over wide pressure intervals. Furthermore, Lamond and Marsh (21) observed t h a t on activated polyfurfuryl alcohol (PFA) carbons and polyvinylidene chloride (PVDC) carbons the adsorption of carbon dioxide at 195°K differed significantly from t h a t of nitrogen at 77°K.

CHARACTERIZATION OF MICROPOROUS CARBONS

105

O'O 0"0

[OOIoW/We -1"0 LOOIoW/W e -0.1

OL2

'0'4,

i 80

,

-2"0

-3'0

,

q 20

B

i t.O

,

i 50

,

A52 FIG. 5. D-R plot of log-normal distribution of W with AG. In view of the usefulness of these two adsorbates in the investigation of the microporosity of carbonaceous materials it was decided to investigate how closely the Rayleigh distribution predicts the distributions of free energy with adsorption volumes, obtained from the adsorption of nitrogen and carbon dioxide on various heat-treated and activated polymer carbons. Activated PFA carbons comparable to those used by Lamond and Marsh (21) have been employed along Mth unaetivated carbons prepared at various heat treatment temperatures. These latter show molecular sieve properties and activated diffusion effects typical of many coals and cokes. Also, activated polydivinyl benzene (PDVB) carbons have been examined. This carbon, before activation, has its microporosity completely inaccessible to the adsorbate (even at 298°K) because of the smallness of pore orifices ( < 5A diameter). EXPERIMENTAL DETAILS Carbons. PFA and PDVB were prepared and carbonized in a nitrogen atmosphere as has been described previously (23). The finely ground carbons (< 60 BS mesh) were then activated in a stream of earbon dioxide at 800°-850°C to various degrees of burnoff at a rate of about 1% weight loss per hour. Adsorption Measurements. All adsorption

measurements were carried out using conventional 1VfcBain, silica spring, balances. The apparatus consisted of two parts, each with two adsorption tubes, a U-tube manometer, McLeod gauges, and a gas inlet system, eommeted to a central pumping system. The four adsorption tubes eould be used together, in units of two, or individually, as desired. The limit to the accuracy of the adsorption measurements was of the order of 0.5 em3 (STP) gm-1 depending upon the exact weight of adsorbent and the gas employed. Adsorption measurements were made in the pressure range 10.3 to 760 torr. Highpurity, cylinder grade carbon dioxide, nitrogen, and argon were used, further purified by passing through liquid nitrogen (nitrogen and argon as adsorbate) and Dry Ice (carbon dioxide as adsorbate) traps. Temperatures of 77°K and 195°K were obtained by use of liquid nitrogen and Dry Ice, respectively. Adsorption equilibrium was attained in all cases even though 24 hours was required per adsorption point in the adsorption of carbon dioxide at 195°K on the unactivated polyfurfuryl alcohol carbons. This was checked by adsorbing carbon dioxide at 273°K (activated diffusion effects minimized) when a temperature-invariant characteristic curve was obtained. Journal of Colloid and Inter/ace Science, Vol. 33, No. 1, May 1971}

106

MARSH AND RAND

The weight changes accompanying adsorption were corrected for buoyancy effects. The method of Bennett and Tompkins (24) was used to correct the pressure readings for thermal transpiration effects at low relative pressures.

RESULTS

Adsorption of Carbon Dioxide at 195°K. Figures 6, 8, and 10 show the D-R plots for carbon dioxide adsorbed at 195°K on the carbons. The D-R plots are in the eoordi-

2"0

t0gl0V 1"5

1-2

8

12

15

i

Log~O( P/Po) 53G°C

~

630"C

~

720°C

FIG. 6. D-R plots of adsorption of carbon dioxide at 195°Kon polyfurfuryl alcohol carbons.

0'8

dW.102 di-AG) cm3g"1

0"6

mole kcaL-1

A

O'~

V

0

0"2

,'.o

21o -AG

530°C

~

630°C

~

3'-0

kcat moLe"1 720°C

FIG. 7. Distributions of W w i t h ~G from adsorption of carbon dioxide at 195°K on polyfurfuryl alcohol

carbons. Journal of Colloid and Interface Science, Vol. 33, :No. 1, m a y 1970

CHARACTERIZATION OF MICROPOROUS CARBONS

107

2-5 Io910V

1"5

J

I.

8

12

16

LOg~oIP/Po) '/, Burn-off

---0---

O-O

~

27'5

~

t,8-O

0

89.0

FzG. 8. D-R plots of adsorption of carbon dioxide at 195°K on activated, 850°C polyfurfuryl alcohol carbons. q

dW.lO 2

10

g

_

d[-AG] cm3g-'i moLe kca1-1

5

1-0

2"0 -AG

"/, Burn-off

~

0"0

~

3"0

keaL mole-1 27-5

~

48"0

0

89.0

FIG. 9. Distributions of W with AG from adsorption of carbon dioxide at 195°K o n activated, 850°C polyfurfuryl alcohol carbons.

na~es, log V = log Vo - D log ~ (p/po),

[5]

where V is the volume (STP) of v a p o r adsorbed per g r a m at equilibrium pressure p. I t has previously been shown (21) t h a t at

195°K carbon dioxide behaves, in the adsorbed phase, like a supercooled liquid and t h a t at this t e m p e r a t u r e po = 1.86 a r m as calculated b y extrapolating the d a t a of Bridgeman (25). This value has been used here. Journal of Colloid and Interface Science, Vol. 33, No. i, 3]lay 1970

108

MARSH AND RAND

24

Log10V 1"6

O'S

B

/*

12

16

log Io(P/Po) "h Born-off

---0---

16.0

~

91.5

l~zo. 10 D-R plots of adsorption of carbon dioxide at 195°K on activated, 900°C polydivinylbenzene carbons.

24

dW.lO 2 3-1 om g

mole kcai-1 1'5

0'9

1'0

2"0 -,',G

"/. Born-off

~

16.0

~

3"0

kcat mote1

91.5

FzG. 11. Distributions of W with AG from adsorption of carbon dioxide at 195°K on activated, 900°C polydivinylbenzene carbons. Figures 7, ~, and 11 show the corresponding distributions of W with - AG. These were constructed as follows. The characteristic curve W = f(--AG) was differentiated by plotting the increase in W over intervals of --AG of 100 cal mole -1 against the mean Journal of Colloid and Interface Science, Vol. 33, No. I, ~[ay 1970

--AG of this interval. The vMue of W was calculated from the formula W

-

VM X 10-3 22,414 p

[6]

where V is the volume (STP) of vapor ad-

CHARACTERIZATION

OF MICROPOROUS

CARBONS

109

3"0 [

1o919 V 2"5

2.2

i

i

,

L

i

,

,'2

,;

Log~0(P/Po I '/, Burn-off

~

27-9

~

/,8"0

O

99"6

FzG. 12. D-R plots of adsorption of nitrogen at 77°14 on activated, 850°C polyfurfuryl alcohol carbons.

sorbed cm ~ gm -I, M is the molecular weight of the vapor, and p is the density of the adsorbed vapor gm cm-3. p was assumed to be invariant with the amount adsorbed and taken as 1.36 gm cm-~, from the data of Dubinin et al. (26). The D-R plots are in no case completely linear over the whole pressure region studied. The unactivated and 27.5% burnoff PFA carbons all show two linear sections of differing slope. The point at which the slope changes is marked on the corresponding distribution curves, which, incidentally, do not show the general shapes predicted by the Rayleigh distribution and tend towards a Gaussian type. These distributions cannot, however, be accurately described by the Gaussian law. The highly activated carbons show no evidence of linearity in their D-R plots and the distributions of W with --AG are markedly skewed towards high values of --AG. The D-R plots are similar in shape to that given by the log-normal distribution and indeed plots of the cumulative distribution on log-probability paper show that these distributions approximate to this law. The 8g0°C PFA carbon (89% burnoff) shows no definite ]node in the distribution of W with --AG. However, the CO2 adsorption

data could be taken only to a relative pressure of 0.4, and it is considered that had the data extended to a higher value such a mode would have been observed, when the micropore structure is filled with adsorbate (cf. adsorption of nitrogen at 77°K). Adsorption of Nitrogen at 77°K. The unactivated carbons showed no adsorption of nitrogen at 77°K owing to the activated diffusion effect (cf. Marsh and Wynne-Jones (23). Figures 12-15 show the adsorption data for the activated carbons. Again, none of the systems exhibit complete linearity in the D-R plots over the whole distribution of W with -AG. The 27.5 % burnoff PFA carbon shows a linear D-R plot over the whole pressure range investigated, but this is seen to represent only half of the total distribution. Very low relative pressures would have to be investigated to study the whole of the distribution for this carbon. The carbons activated to high burnoff all show a bimodal distribution of free-energy values which are a consequence of the nonlinearity of the D-R plots. These deviations correspond approximately to the modes of the distributions or to the troughs between the two modes. The volume of pores in the first distribution (high values of -AG) can be estimated, approximately, by extrapolatJournal of Colloid and Interface Science, Vol. 33, No. I, M a y 1970

110

MARSH AND RAND

dW.lO 2

20

d(-/~G)

crn3g"l mule kca["1

10

0'5

1-0

-hG "/. Bern-off

~

27'5

~

1"0

kca[ mole-1 L~'9

g

89"0

FIG. 13. Distributions of W with AG from adsorption of nitrogen at 77°K on activated, 850°0 polyfurfuryl alcohol carbons.

2.~

|O91o¥

2.o

1-0

i,

8

12

16

109 ~0(PiPe) "/. 9urn-off

- - ~

18"0

+

91"5

FIG. 14. D-l% plots of adsorption of nitrogen at 77°K on activated, 900°C polydivinylbenzene carbons. ing the second linear section to zero log 2 (p/po) (as shown in Figs. 12 and 14). The volume in the second distribution can then be estimated as the difference between this value and the total pore volume calculated b y the Gurvitsch (27) rule. This procedure neglects the fact t h a t the two distributions overlap to some extent. Journal of Colloid and Interface Science, Vol. 33, No. I, May" 1970

I n calculating the micropore volume (W) from the nitrogen adsorption data the density of the adsorbed phase was assumed to be invariant with amount adsorbed and t a k e n as 0.808 gm cm -s, the bulk density of the liquid at 77°K. Adsorption of Argon at 77°K on the 850°C P F A Carbon -- 89% Burnoff. Figures 16

CHARACTERIZATION OF MICROPOROUS CARBONS

dW.lO 2

111

10

d(-AG)

cm3g-1 mole kcat-1 I 5

0"9

1"0 -AG

"/, B0rn-0ff

~

16"0

1"9

kcat m0Le-I

~

91"5

FIG. 15. D i s t r i b u t i o n s of W w i t h AG f r o m adsorption of nitrogen at 77°I~2 on a c t i v a t e d , 900°C po]y-

divinylbenzene carbons. 92

leg 10V

24,

1-6

I,

!

1

16

log Io(P/Po)

FIG. 16. D-R plot of adsorption of argon at 77°K on activated (89% burnoff), 850°C polyfurfuryl alcohol carbon. and 17, respectively, show the D - R plot and the distribution of W with --AG for this system. The value of po for argon at 77°K was t a k e n as 23 torr and the density of the adsorbed phase was assumed to be 1.46 gm cm -s. This latter value was calculated b y extrapolating the data for the t e m p e r a t u r e

variation of the density of the bulk liquid phase. Thus, the adsorbed phase was assumed to possess the properties of a supercooled liquid (28). DISCUSSION

Significance of the Dubinin-Radush/cevich Equation. The results presented here show Journal of Colloid and Interface Science, VoL 33, No. 1, May 1971)

112

MARSH AND RAND 30

dW.102

d{-AGI cm3g-1 mole kcal''1 20

10

o!s

,

,Io

i

,~

-A G kcal mole"1

FIG. 17. Distribution of W with AG from adsorption of argon at 77°K on activated (89% burnoff), 850°C polyfurfuryl alcohol carbon. that adsorption of carbon dioxide at 195°K and nitrogen at 77°K on microporous carbons does not follow the D-I~ equation accurately. Recent observations in these laboratories confirm these results for coals and certain commercially available active carbons. However, if only limited pressure ranges, corresponding to part of the distribution of W with -AG, are investigated, linear plots may be obtained. The fact that deviations from linearity are prevalent renders considerable doubt on the method of extrapolating low-pressure data to zero logs (P/po) to determine Wo, the micropore volume, or to determine the monolayer capacity of a nonporous adsorbent as suggested by Kaganer (16). In order to determine these parameters the data must be extended as near as possible to unit relative pressure. Deviations from linearity of the D-R plot have been observed in a number of other cases, notably carbon dioxide adsorbed on coals (28), nitrogen on nonporous TiO2 and silica gel (29), ammonia on sepiolite (30), and ethyl chloride and butane on activated carbons (31). It may well be that the Rayleigh distribution rarely describes the distribution of W with - A G for adsorbents, and that its apparent success has resulted Journal of Colloid and Interface Science, Vol. 33, lifo. 1, M a y 1970

from application to only a limited part of this distribution. According to Dubinin (1, 8, 10) the constant k in Eq. [2] is a measure of the average micropore size. Dubinin (32) has used this constant to demonstrate changes in micropore structure accompanying activation and heat treatment. In fact k determines the spread of the Rayleigh distribution (Fig. 1) and is a measure of micropore structure only if the distribution of W with - A G is governed entirely by this structure. Also, since k is determined from the slope of the I)-R plot (cf. Eq. [3]) its validity becomes extremely doubtful if a Rayleigh distribution of W with - A G is not present. For example, consider the D-R plots shown in Fig. 6. Here, there are two linear sections of differing slope and hence two values of k can be determined. Physical Significance of Distributions of W with - AG. If the adsorption of any vapor on a microporous solid is governed only by dispersion forces, the characteristic curve, according to the potential theory of adsorption, should be temperature invariant. Under these conditions Dubinin (8, 10) considers that use of the affinity coefficient ~ can cause the characteristic curves for different adsorbates on the same adsorbent to coin-

CHARACTERIZATION OF MICROPOROUS CARBONS

113

cide. If this latter assumption is correct, the characteristic curve, expressed in the form -AG W = f - will be dependent only upon the physical structure of the adsorbent surface. Since --AG is a measure of the affinity of the surface for the adsorbate molecules, the distribution of W with -AG is an approximate measure of the energetic heterogeneity of the surface. It has already been emphasized by Ross and Olivier (33) that --AG is only a crude measure of the affinity of the surface for a particular adsorbate since, it is "an unanalyzable blend of various factors." Nevertheless, the distributions shown here change markedly as the micropore structure is altered and may be useful in characterizing such microporous adsorbents. When a polar adsorbate is adsorbed onto a surface containing polar sites, a temperature-invariant characteristic curve should not result because of the effect of thermal motion on the orientation of the dipole or quadrupole in the adsorbent molecule. Also, the distribution of W with --AG for such a system should not be representative solely of the physical nature of the surface but will also be markedly affected by its chemical nature. Thus, in order to use the distribution of W with --AG to characterize an adsorbent surface, it is necessary to know whether electrostatic interactions play an appreciable role in the adsorption process. In the case of carbons there is adequate evidence (34) available that dispersion forces predominate. Hence, if the carbon is microporous the distribution of W with - A G should be dependent upon the micropore-size distribution. The relationship between these two distributions is, however, not known precisely. In an attempt to resolve this difficulty, Radushkevich (35) assumed that: 1) each micropore can be described by an average value of -AG, 2) each micropore adsorbs independently of the others, and 3) at any one value of --AG all micro-

{a)

{b)

FIG. 18. Adsorption potential energy within narrow (a) and wider (b) micropores. pores of average --AG greater than this are filled with adsorbate whereas those of --£~G lower than this are unoccupied. The first of these assumes that the enhanced dispersion interaction resulting from the proximity of the pore walls can completely mask the heterogeneity of adsorption energy, along the pore walls, which could arise from different interaction energies on edge and basal planes of graphitie structure, aliphatic linkages, surface oxide, and other impurity atoms. This may well be a reasonable approximation for adsorption in micropores in carbons of width less than about two molecular diameters, when the adsorption potential energy is enhanced over that to be expected on an open surface, and may be of the form shown in Fig. 18 (a). However, the situation may be different in the case of adsorption into pores approachiong the upper limit of micropores (~-~30 A for nitrogen at 77°K). In this case, the variation of adsorption potential energy across the pore will be of the form shown in Fig. 18 (b). There will be no enhancement of the adsorption potential energy to mask heterogeneity along the walls. The third assumption is strictly valid only at absolute zero temperature. Nevertheless, in the case of very small micropores an adsorbate molecule within the pore is subject to the force field from the pore walls until such time as it can diffuse into a wider pore where the diffusion process changes from surface diffusion to ]~nudsen diffusion. If the pore contains other adsorhate molecules, the passage of the molecule may be restricted, resulting in a longer residence time within the pore. Therefore, in such Journal of Colloid and Interface Science, Vol. 33, 1~'o. 1, M a y 1970

114

MARSH AND RAND

dW.]O2

20

d(-,~G/~l

/\/I

/'

'"/ ~ /

~

Ar at 77"K

~

,~,t,'X

cm3g-1 rno[e kcal"1

10

0!5

1:o (-/IG/p)

'/.s

kcz~ mote-1

FIG. 19. Comparison of distributions of W with AG/[3from adsorption of nitrogen (77°K), of argon (77°K), and of carbon dioxide (195°K) on activated (89% burnoff) 850°C polyfurfuryl alcohol carbon. small pores the third assumption of Radushkevich may again be reasonable. It would seem that when an adsorbent contains very small micropores the distribution of W with - A G resulting from the adsorption of a nonpolar molecule may be temperature invariant and be a qualitative measure of the micropore size distribution (36). However, when wider micropores, approaching the upper limit, are present the relationship between the distribution of W with --AG and the micropore-size distribution is not clear.

gasification widens the micropores of carbon by eroding the pore walls. The distributions of W with --AG are pushed towards lower values of - A G as activation proceeds suggesting that it is the micropore-size distribution which principally governs the distribution of W with - A G as discussed earlier. For the activated carbons, except the 27.5 % burnoff PFA carbon, the adsorption behavior of nitrogen and carbon dioxide is clearly very different. The nitrogen adsorption results in a bimodal distribution of W Comparison of Adsorption of Carbon with --AG whereas carbon dioxide adsorpDioxide and Nitrogen. Adsorption of carbon tion does not resolve the bimodal distribudioxide at 195°K on the unactivated PFA tion. Argon adsorbed on the 89% burnoff carbons results in pore filling at low relative PFA carbon also gives a bimodal distribupressures. There is no appreciable adsorption tion of W with --AG. Figure 19 compares of nitrogen at 77°K in these carbons, and the distributions of W with --AG for these it is believed (23) that the pores are ac- three gases on this latter carbon. The discessible only through orifices of about 4A in tributions have been corrected by use of the diameter. The unactivated PDVB carbon affinity coefficient ~: (carbonized at 900°C) shows no detectable VAt Vco~ adsorption of carbon dioxide at 195°K, ~Ar = VN--~' ~co~ = V ~ ' suggesting that all the porosity "closed off" from the carbon particle exterior or is accessible only through orifices less than 4A where V denotes the molar volume of the bulk liquid phase at the same temperature. in diameter. After activation, the micropore structure It can be seen that the argon and nitrogen of the carbons becomes accessible to nitro- distributions are almost indistinguishable. That the distributions of W with --AG for gen at 77°K. It is established (37, 38) that Journal of Colloid and Interface Science, Vol. 33, No. 1, May 1970

CHAI:~ACTERIZATION OF M I C R O P O R O U S CARBONS

these two gases coincide is further evidence that the distributions are determined by the mieropore structure of the carbon as suggested above. 5Ioreover, argon has no permanent magnetic moment so the possibility of electrostatic interactions is exeluded. Since nitrogen gives an almost identical distribution of W with --AG it seems reasonable to assume that quadrupole interactions are unimportant in the adsorption of this gas also. The whole of the adsorption volume of the carbons investigated here lies within micropores. This is shown by the adsorption isotherms which show little adsorption above a relative pressure of 0.3-0.4 even after 89 % burnoff. Thus, the second mode of the distributions of W with - A G probably describes adsorption in wider micropores, approaching the upper limit of size. There are two possible reasons why a bimodal distribution of W with --AG may occur. 1) There is a bimodal distribution of micropores developed because of uneven gasification of the carbon particles during the activation process. 2) The micropore size distribution is monomodM, but the adsorption mechanism of nitrogen changes with pore size. This could occur if pores showing an adsorption potential energy of the type depicted in Fig. 18 (a) fill at higher - A G values, whereas the wider pores, in which there is no enhancement of adsorption potential energy (Fig. 18 (b)), fill at lower values of -AG. A very small widening of the mieropore can result in an overlap of the attractive forces from the pore walls and hence a rapid drop in adsorption potential energy. Such a rapid change with a small increase in pore size could explain the bimodal distribution. The adsorption of carbon dioxide at 195°K on activated carbons does not result in a bimodal distribution of W with --AG. Approximately the same pore volume is filled as for nitrogen at high values of --AG ( > 1.0 keal mole-1) (cf. Fig. 19), suggesting that the difference in behavior is due to the adsorption in the wider mieropores forming the second mode in the distributions of W with --AG from nitrogen and argon adsorption.

115

Further experimental work involving precise thermodynamic measurements is required to resolve this discrepancy in adsorption behavior. However, a tentative explanation which may help to direct further work is as follows. In the case of adsorption of nitrogen the second mode of the distribution describes monolayer formation on the walls of micropores showing a double potential energy well (cf. Fig. 18 (b)), followed by filling of the remaining pore space. The larger quadrupole of carbon dioxide may interact strongly either with surface-oxide groupings on the pore walls or with the 7r electron system of the carbonaceous structure, resulting in adsorption at higher values of --AG. If this is so, the effect on the adsorption potential energy of widening the pore walls could be much smaller than with nitrogen or argon, resulting in a lack of resolution of the bimodal distribution of W with -AG. It is certainly relevant that quadrupole interactions have been invoked to explain the adsorptive behavior of carbon dioxide in other carbonaceous and microporous systems (39, 40). The quadrupole moment of nitrogen does not appear to affect its adsorptive behavior when compared to the nonpolar argon; this is in agreement with the findings of Xington (40). It is considered that a detailed analysis of the mieropore structure of microporous solids, in particular carbons, can be made only by investigation of the low relative pressure part of the isotherm when the pores are being filled with adsorbate. The DubininRadushkevieh equation may not apply over the whole distribution of pore space with adsorption free energy, but the form of this distribution can help in elucidating micropore structure since in the case of adsorption of a nonpolar adsorbate it is governed primarily by this structure. Similar arguments should apply to the distribution of "site" energies as determined by the method of Adamson and Ling (41). Further work, however, is necessary to establish these suggestions and to elucidate the detailed mechanisms of adsorption in micropores. ACKNOWLED GMENTS This s t u d y forms p a r t of the f u n d a m e n t a l research programme of the British Coke Research Journal of Colloid and Interface Science,

Vol. 33, No. 5, May 1970

116

MARSH AND RAND

Association, and we are grateful to the Council of the Association for permission to publish this paper, We appreciate the interest and support of Lord Wynne-Jones, Honorary Director of the Northern Coke 1%esearch Laboratories, during the period of the study. One of us (B.1%.) gratefully acknowledges financial support from the British Coke Research Association.

19. MARSh, H., Fuel 44,253 (1965). 20. WAr,KER,P. L., JR., AUSTIN,L. G., ANDI~ANDI, S. P., In P. L. Walker, Jr., ed, "Chemistry and Physics of Carbon," Vol. 2, p 279. Arnold, London, 1966. 21. LAMOND,T. G., ANDMARSII, H., Carbon 1,281, 293 (1964). 22. CrecHE, P., MARSH, H., AND PREGERMAIN, S., Fuel 46,341 (1967). REFERENCES 23. MARSE, H., AND WYNNE-JONES, W. F. K., Carbon 1,269 (1964). 1. DUBININ, M. M., Quart. Rev. (London) 9,101 (1955). 24. BENNETT,M. J., AND TOMPKINS,F. C., Trans. Faraday Soc. 53,185 (1957). 2. GREGG,S. J., ANDSING, K. S. W., "Adsorption, Surface Area and Porosity," p 5. Academic 25. BRIDGEMAN, 0. C., J. Amer. Chem. Soc. 49, 1174 (1927). Press, London, 1967. 3. S~'ENC]~R,D. H. T., in 1%. L. Bond, ed, "Por- 26. DUBININ, M. M., BERING, B. P., SERPINSKII, V. V., ANn VASlr.V.V, B. N., "Surface Pheous Carbon Solids," Chapt 3. Academic Press, nomena in Chemistry and Biology," p 172. London, 1967. Pergamon Press, London, 1958. 4. GI~EGG,S. J., AND STOCK, R., Trans. Faraday 27. GURVlTSC~,L., J. Phys. Chem. Soe. Russ. 47, Soe. 53, 1355 (1957). 805 (1915). 5. KIS~LEv, A. V., "Structure and Properties of 28. GREGG, S. J., AND SING, K. S. W., "AdsorpPorous Materials," p 200. Butterworths, tion, Surface Area and Porosity," p 90. London, 1958. Academic Press, London, 1967. 6. PX~RCE, C., WIImy, J. W., AND SMITH, R. N., 29. RAND, B., Unpublished results. J. Phys. Chem. 53,669 (1949). 30. DANDY,A. J., J. Phys. Chem. 72,334 (1968). 7. PIERCE, C., J. Phys. Chem. 63, 1076 (1959). 8. DVBININ, M. M., J. Colloid Interface Sci. 9.3, 31. LAMOND, W. G,, Ph.D. Thesis, University of Durham, (King's College), 1962. 487 (1967). 9. GREeG, S. J., ANDSING, K. S. W., "Adsorption, 32. DUBININ, M. M., Proe. Conf. Carbon 5th, 1, 81 (1962). Surface Area and Porosity, "Chapt 6. Aca33. Ross, S., AND 0LIVIER, J. P., "On Physical demic Press, London, 1967. Adsorption," p xiii. Interscience, New York, 10. DUBININ, M. M., in P. L. Walker, ed, "Chem1964. istry and Physics of Carbon," Vol 2, p 51. 34. BARREn, R. M., J. Colloid Interface. Sei. 21, Arnold, London, 1966. 415 (1966). 11. By,ruNe, B. P., D~rmNIN, M. M., AND SERPINSKY, V. V., J. Colloid Interface Sci. 9.1, 378 35. 1%ADUSHKEVICtI,L. V., Z h . F i z . Khim. 23, 1410 (1949). (1966). 12. DUBININ, M. M., Z±VERINA, E. D., AND 36. MA~AJAN, O. P., AND WALKER, P. L., JR., J. Colloid Interface Sci. 29,129 (1969). 1%ADUSHK:EVICtI,L. V., Z h . F i z . Khim. gl, 37. CULVER, R. V., AND WATTS, H., Rev. Pure 1351 (1947). Applied. Chem. 10, 95 (1960). 13. DUBININ, M. M., Chem. Rev. 60,235 (1960). 14. HOBSON,J. P., in E. A. Flood, ed, "The Solid- 38. DACEY, J. R., in E. A. Flood, ed, "Solid-Gas Gas Interface," Vol. 1, Chapt 14. Arnold, Interface," Vol 2, Chapt. 34. Arnold, LonLondon, 1967. don, 1967. 15. HOBSON, J. P., AND ARMSTRONG, P. A., J. 39. AMBERe, C. H., EVERETT, D. H., 1%VlTER,L. Phys. Chem. 67, 2000, (1967). H., AND SMITH, F. W., Proc. Intern. Congr. 16. KAeANER, H. G., Russ. J. Phys. Chem. (Eng~urface Activity, 2rid London 9., 3 (1957). lish Trans.) 33,352 (1959). 40. KINGTON,G. L., "Structure and Properties of 17. MARSH, H., AND SIEMIENIEWSKA, T., Fuel 46, Porous Materials," p 59. Butterworths, 44! (1967). London, 1958. 18. SUTHERr.ANDJ. W., in 1%.L. Bond, ed, "Porous Carbon Solids," Chapt. 1. Academic Press, 41. ADAMSON,A. W., AND LINe, I., Advan. Chem. Set. 33, 51 (1961). London, 1967.

Journal of Colloid and Interface Science, ¥ol. 33, No. 1, May 1970