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Adsorption and structure in microporous carbons
Carbon Vol 26, No. 3. pp. 261-274. 1988
Printed mGreatBritain.
REVIEW
ARTICLE
ADSORPTION AND STRUCTURE MICROPOROUS CARBONS * School
of Materials
BRIAN MCENANEY Science, University of Bath, (Received
IN
Bath BA2 7AY, U.K
19 Oclober 1987)
Abstract-The microporous structure of carbons consists of a tangled network of defective carbon layer planes in which micropores are the spaces between the layer planes. Adsorption of gases in micropores is characterized by (1) strong adsorption at low pressure due to overlap of force fields from opposite pore walls, (2) activated diffusion effects caused by constrictions in the microporous network. and (3) molecular size and shape selectivity (molecular sieving). The surface fractal dimension of activated carbons decreases from three to two with increasing activation, indicating that activation smoothens pore surfaces. Calculated adsorption potentials for slit-shaped model micropores show that adsorption potentials are enhanced by a factor of up to 2 and enable critical dimensions for diffusion of gases through micropores to be estimated. The Brunauer-Emmett-Teller equation is unsuitable for analyzing adsorption with a significant microporous contribution but may be used to estimate the nonmicroporous surface area, provided that the microporous contribution can be removed. The Dubinin-Radushkevich and Dubinin-Astakhov equations have been more successful when applied to microporous carbon5 because they reflect the influence of adsorbent heterogeneity. as they result from an approximation to the generalized adsorption isotherm (GAI). More exact solutions of the GA1 enable adsorption energy distribution functions to be obtained. The possibility of extracting micropore size distributions from adsorption measurements is briefly considered. Key Words-Adsorption,
microporous
carbons,
activated
microstructure
micropores. Definitions of pore sizes follow recommendations of the International Union of Pure & Applied Chemistry (IUPAC): micropores-width less than 2 nm; mesopores-width 2 to 50 nm: macropores-width greater than 50 nm[3]. The major sources of industrial, microporous active carbons are coals (lignites, bituminous coals, and anthracites), peat, wood, and a wide range of organic by-products of industry and agriculture. About 90% of active carbons are produced in granular or powder form, with most of the remainder in pelleted form[4]. In addition to these conventional sources. an increasingly wide range of specialized industrial microporous adsorbents has been produced (e.g., active carbon textiles[5,6], and molecular sieve carbons[7,8]). During carbonization the organic precursor is thermally degraded to form products that undergo either condensation or volatilization reactions, the competition between these processes determining the carbon yield. The carbon residue is formed by condensation of polynuclear aromatic compounds and expulsion of side chain groups. However, industrial carbons retain a :,ignificant concentration of heteroelements. especially 0 and H, and many contain mineral matter. The adsorptive capacity of the carbonized materials is usually too low for practical applications, so porosity in the carbon is developed by activation (i.e., by reaction of the carbon with oxidizing gases (e.g., Hz0 or COz) or by incorporation of inorganic additives (e.g., ZnCL) prior to carbonization. For coal-based
1. INTRODUCTION
The literature on adsorption in porous carbons ranges widely from theoretical studies of adsorption from the vapor and liquid phases to technical studies of the many applications of carbon adsorbents. This article is not a comprehensive review of the subject, nor is it a complete survey of the many isotherm equations that have been proposed to analyze adsorption in microporous carbons. Instead, it is confined to consideration of the effects of the microporous structure of carbons on adsorption of gases. Although most nongraphitizing (“hard”) carbons contain numerous micropores, not all are practical adsorbents, since the micropores in them may not be accessible to gases to a useful degree. However. much valuable structural information, relevant to microporous carbon adsorbents, has been obtained from the study of materials such as poly(acrylonitrile)-based (PAN-based) carbon fibers[l] and glasslike (“vitreous”) carbons[2]. Many industrial porous carbons (e.g., coal-based active carbons) in addition to micropores contain macropores and mesopores that may be important in adsorption. However, the role of these larger pores is not considered in this article, since the effectiveness of most active carbons used for gas adsorption depends primarily on the nature and extent of the accessible
*Based on a plenary review lecture given ‘86,” 30 June 1986, Baden-Baden, FRG.
carbons,
at “Carbon
267
268
B. MCENANEY
active carbons, Table 1 illustrates how the proportion of the different pore types varies with the nature of the precursor[4]. By judicious choice of the precursors and careful control of carbonization and activation, it is possible to tailor active carbons to suit particular applications. 2.
THE STRUCTURE
OF MICROPOROUS
CARBONS
Microporous carbons have a very disordered structure as revealed by high resolution electron microscopy and various model structures have been proposed based on studies of polymer carbons[2,9], carbon fibers[l], carbonized coals and kerogens[lO,ll], and active carbons[l2,13]. Although the models differ in detail, the essential feature of all of them is a twisted network of defective carbon layer planes, cross-linked by aliphatic bridging groups. The width of layer planes varies, but typically is about 5 nm[12]. Simple functional groups (e.g., C-OH, C===O)and heteroelements are incorporated into the network and are bound to the periphery of the carbon layer planes. Functional groups can have an important influence on adsorption[l4], but detailed consideration of their effects is outside the scope of this review. In microporous carbons the layer planes occur singly or in small stacks of two, three, or four with variable interlayer spacings in the range 0.34 to 0.8 nm[ll]; Fryer[l2] found an average layer plane separation of 0.7 nm for a steam-activated anthracite carbon, and separations in the range 0.6 to 0.8 nm for Carbosieve. There is considerable microporosity in the form of an interconnected network of slit-shaped pores formed by the spaces between the carbon layer planes and the gaps between the stacks. Thus the widths of pores formed by interlayer spacings (typically from about 0.34-0.8 nm) are significantly less than 2 nm, the arbitrarily defined[3] upper limit for micropore widths. Constrictions in the microporous network are particular features of the structure that control access to much of the pore space. Constrictions may also occur due to the presence of functional groups attached to the edges of layer planes[l5,16] and by carbon deposits formed by thermal cracking of volatiles. 3. ADSORPTION
IN MICROPOROUS
CARBONS
The complex and disorganized structure of microporous carbons, in which the dimensions of the pore space are commensurate with the dimensions of adsorbate molecules, makes interpretation of adsorpTable 1. Pore volumes (ml/g) for coal-based active carbons[4] Coal Precursor Anthracite Bituminous Lignite Blended
Micropores
Mesopores
Macropores
0.51 0.43 0.22 0.42
0.07 0.17 0.58 0.11
0.11 0.26 0.32 0.33
tion in these materials very difficult. First, gases are strongly adsorbed at low pressures in micropores, because there is enhancement of adsorption potential due to overlap of the force fields of opposite pore walls (see below). Second, constrictions in the microporous network cause activated diffusion effects at low adsorption temperatures when the adsorptive has insufficient kinetic energy to penetrate fully the micropore space; this poses problems when using N, at 77 K as the adsorbate[l7]. Third, microporous carbons can exhibit molecular sieve action (i.e., the selective adsorption of small molecules in narrow micropores[7]). Carbons also exhibit molecular-shape selectivity by preferential adsorption of flat molecules, as expected from the slit shape of the micropores[l8,19]. Molecular sieve action can be exploited to effect separation of gas mixtures by microporous carbons (e.g., oxygen and nitrogen separation from air using the pressure swing method[7,20,21]). 4. FRACTAL
ANALYSIS OF MICROPOROUS
CARBONS
Fractal geometry has been applied to many branches of science in recent years, including the properties of porous solids[22]. The surface of a solid may be characterized by a surface fractal dimension, Ds, which is a measure of surface irregularity or roughness. For a smooth surface the value of Ds approaches 2, the dimension of a Euclidean surface. For a very irregular surface, the value of Ds approaches 3, the dimension of a Euclidean volume; thus 2 5 Ds s 3. The value of Ds for a fractal object may be estimated by measuring its surface area with different “yardsticks.” In the case of adsorbent surfaces, the “yardsticks” are usually adsorptive molecules of different size, the value of Ds being found from the increase in surface area of the object with decreasing molecular size. Using this approach, Avnir et al. [23] have shown that for a graphitized carbon black the value of Ds is close to 2, as expected for a smooth, nonporous surface. For a series of activated charcoals, the value of D, decreased from about 3 to about 2 with increasing activation. They concluded that, in addition to increasing pore widths and adsorptive capacity, the process of activation also smoothens pore surfaces. The surface fractal dimension of a porous solid can also be estimated by measuring its surface area as a function of particle size. Using this method, Fairbridge et af.[24] obtained a value of Ds = 2.48 for a Syncrude coke from N2 and CO, surface areas. The concept of fractal dimension provides an interesting new perspective on the properties of porous solids, which is being actively developed at present. 5.
CALCULATIONS
OF ADSORPTION
POTENTIALS
There have been several theoretical studies of adsorption potentials in model micropores[25-271. Adsorption potentials were calculated by Everett and
Adsorption and structure in microporous carbons
269
Table 2. Calculated critical micropore dimensions for diffusion of gases Adsorptive Slit width (nm)
co 0.541
co2 0.542
Pow1[27] for cylindrical pores and aiso for slit-shaped pores formed between semiinfinite slabs (9:3 potentials) and between single layer planes (10:4 potentials). The 10:4 potential function appears to be the more appropriate model, considering the structure of microporous carbons, in which dit-shaped pores are separated by one to four layer planes[ll]. Potentials have a single minimum for narrow pores and two minima in wide pores. Figure 1 shows the minimum 10:4 potential in the model pore, Q *, relative to that on the plane surface, Q, plotted against the pore half-width, d, relative to the collision radius of the adsorptive molecule, r,. For 10:4 potentials the two minima occur when d/r, _Z 1.140. Q*/Q is a maximum of 2.00 at d/r, = 1.00, and Q* JQ decreases to about 1.1 at d/r, = 1.50. At d/r, less than 1.00 (i.e., between a and b, Fig. l), the enhancement of adsorption potential decreases rapidly due to the short range repulsive terms in the 10:4 potential function. Recent measurements~2gl of heats of adsorption at low surface coverage of a range of hydrocarbons on microporous carbons and on carbon blacks confirm that enhancement of adsorption energy in micropores is by a factor of about 2. Pores with enhanced adsorption potential have been termed ultramicro~res and wider pores, up to 2 nm wide, have been termed supermicropores[29]. The definition of the size range of ultramicropores is not precise and depends on the size of the adsorptive molecule, but, for the purposes of illustration, may be taken as the range corresponding to ac in Fig. 1. For Ar (r. = 0.340 nm) and Xe (r. = 0.375 nm), ultramicroporous slit widths, W, = 2d, are 0.58 to 1.02 nm and 0.64 to 1.13 nm, respectively. W, is the internuclear distance between C atoms in opposite walls of the model pore. If slit widths are
2.0
1.a
02 0.544
022
corrected for the finite radius of the C atoms to give W,, in the notation of Everett and Powl[27]. then for Ar and Xet W, = 0.24 to 0.68 nm and 0.30 to 0.79 nm respectively. A further approximate correction can be made for the compressibility of the adsorptive in the force field of the micropore[27], to give the available ultramicroporous pore width, W,; for Ar and Xe, W, = 0.34 to 0.78 nm and 0.40 to 0.89 nm, respectively; these values of pore width are within the range of interlayer spacings measured by high resolution electron microscopy[ 11,12], Calculated adsorption potentials in model micropores have been used to estimate critical dimensions for diffusion of gases. For the Everett-Pow1 10:4 potentials, this dimension corresponds to dir,, at point a in Fig. 1. For pore dimensions less than this value, diffusion of gases becomes activated. The value of this dimension is critical for the ability of molecular sieve carbons to separate gases of different moiecutar size. The results of recent calculations[30,31] for diffusion of several monatomic and polyatomic molecules through slit-shaped model micropores are in Table 2. The value of the critical pore dimension for Ar is in very good agreement with that obtained from the Everett-Pow1 10:4 potentials and the values for Nz and OZ are consistent with experiments on the separation of these gases from air[20]. These results also appear to resolve an anomaly resulting from estimations of critical molecular dimensions using gas phase data. These yield a smaller dimension for NZ than for CO?; this is contrary to experiment, since CO, is known to diffuse more rapidly through carbon molecular sieves than NJ171. As useful as model pore calculations are in elucidating the nature of adsorptive-adsorbent interactions in micropores, they are highly idealized when applied to microporous carbons. For example, the models ignore factors such as (1) the highly defective nature of the carbon layer planes, (2) edge effects resulting from their finite size, and (3) the role of heteroelements and polar surface groups (e.g., C%O) in the adsorption process. The calculations also relate to the interaction of an isolated adsorptive molecule with the pore wall and so cooperative effects during micropore filling are not considered. 6.
THE BRUNAUER-EMMETT-TELLER (BET) EQUATION
Fig. 1. Adsorption potentials Q * in model slit-shaped micropores, relative to the adsorption potential Q on a free surface, as a function of pore half-width, d, relative to the collision radius of the adsorptive, r,; calculated using 10:4 potential functionsf271.
The equation most widely used to analyse adsorption isotherms to obtain surface areas, the BET equation[e.g., 321, is subject to severe limitations when applied to microporous carbons. Values of surface areas, up to about 4000 m2/g for some highly activated carbons[33] are unrealistically high, since
B. MCENANEY
270 800
800
8 9
480
3
I
-8 -
I
200
0
0
I0
I
I
I
0.5
I.0
I.5
alpha
layer
plane,
I
1
1
40
60
80
InaPolP
surface area for an extended graphite counting both sides, is about 2800
m2/g. Adsorption in micropores does not take place by successive buildup of molecular layers, as supposed by the BET theory. Instead, the enhanced adsorption potential in micropores induces an adsorption process described as primary or micropore filling[29]. Because of its widespread use for other adsorbents, the BET surface area will continue to be used for microporous carbons, but its notional character should be recognized. The BET equation can be applied with more confidence to adsorption of gases on the nonmicroporous surface of carbons (i.e., on mesopores, macropores, and the external surface), provided that the microporous contribution to adsorption can be effectively removed. Three types of method have been proposed to isolate microporous adsorption: (1) comparative methods, (2) preadsorption techniques, and (3) isotherm subtraction. In comparative methods, adsorption on a microporous adsorbent is compared to adsorption on a nonporous reference adsorbent of well-defined surface area. The most widely used comparative methods are the t plot[34] and the a plot[35]; these methods have been discussed in detail by Gregg and Sing[32]. The statistical thickness of the adsorbed layer, t, is defined as t = VPIS, where VP is the volume of adsorptive adsorbed at pressure P and S is the total BET surface area of the reference adsorbent. Sing[35] proposed an alternative parameter a = V/ (V at Pl PO = 0.4). Both
t and a are essentially normalizing parameters for producing a reduced isotherm. The choice of a suitable reference material has provoked debate. Lecloux and Pirard[36] proposed that the choice should be dictated by the value of the BET C constant, but Gregg and Sing[32] argue persuasively that the reference material should be selected on the basis of chemical similarity to the test material. Graphitized carbon blacks were originally used [34,37] as reference materials for carbons, but, it has been recently suggested that nongraphitic carbon substrates (a heat-treated carbon[38] and “sooty” silica[39]) are superior reference materials for microporous carbons. For microporous carbons, t plots and a plots are of similar form. Figure 2 shows a plots for adsorption of Ar at 77 K on four coal-based activated carbons[40]. The steep rises at low a values are attributed to micropore filling and the linear regions at high a values to adsorption on the nonmicroporous surface. The micropore volume, V,, is estimated by extrapolation of the linear region to a = 0 and the nonmicroporous surface area, S’, can be estimated from the slope of the linear portion of the a plot; the ratio S’/S provides a useful index of the relative contributions of microporous and nonmicroporous adsorption. Values of these parameters are in Table 3, which shows that these carbons are dominantly microporous. In preadsorption methods[38-411, micropores are filled at room temperature with a strongly adsorbed vapor, usually n-nonane, which is retained in micropores on subsequent outgassing. The nonmicroporous surface area is then measured by adsorption of
Table 3. Parameters obtained from u-plots (Fig. 2) for adsorption of Ar at 77 K on coal-based activated carbons[40] Carbon ABl AB2 AB3 AB4
I
Fig. 3. Adsorption of CO, at 195 K on an activated cellulose triacetate carbon heat-treated to 1600°C plotted in DR coordinates to illustrate the principle of isotherm subtraction[Q].
Fig. 2. Alpha plots for adsorption of Ar at 77 K on four .. coat-based active carbons, ABl-AB4, plotted using a graphitized carbon black, Vulcan-3G, as reference adsorbent[40].
the calculated
I
20
S(m2/g)
S’(m*/g)
V&nl/g)
S’IS
595 773 877 1006
47 80 61 74
0.24 0.31 0.37 0.41
0.08 0.10 0.07 0.07
Adsorption and structure in microporous carbons N, at 77 K, while the micropore volume can be obtained by comparison of N, adsorption before and after adsorption of n-nonane. Isotherm subtraction[43] or decomposition[44] is a simple method for estimating S’ from a single isotherm. The principle of the method is illustrated in Fig. 3 in which the isotherm is plotted in Dubinin-Radushkevich coordinates (see Section 7). The low pressure part of the isotherm, ab, which is dominated by micropore filling, is extrapolated to high pressures, bd, using the DR equation, and subtracted from the total high pressure isotherm, bc, to give a residual, nonmicroporous isotherm, which can be analysed by the BET equation to give S’. Martin-Martinez and co-workers[45] have carried out an extensive comparison of the n-nonane preadsorption and isotherm subtraction methods. They conclude that for carbons with narrow micropores the two methods give very similar results; when the distribution of micropore sizes is wider, the preadsorption technique fails because nnonane is not retained in some wide micropores on outgassing. For superactivated carbons with a very wide range of pore sizes, neither technique was able to separate microporous and nonmicroporous adsorption.
7. THE
DUBININ-RADUSHKEVICH
(DR)
EQUATION
Because adsorption in microporous carbons occurs by primary or micropore filling, Dubinin and his group originally modeled microporous adsorption using the Polanyi potential theory. Dubinin found empirically that the characteristic curves for adsorption on many microporous carbons could be linearized using the DR equation[46]:
271
P/P,,, V,, is the micropore volume, A = RT ln(P,l P) is the adsorption potential, where R is the gas constant and T the absolute temperature, and E is an energy constant. Dubinin showed that the energy constant E could be factorized into a characteristic energy, E,, which relates to the adsorbent, and an affinity coefficient, B, which is a constant for a given adsorptive. Essentially, B is a shifting factor that allows the characteristic curves (linearized by the DR equation) for different adsorptives on the same adsorbent to be superimposed. For some carbons the DR equation is linear over many orders of magnitude of pressure. For others, however, deviations from the DR equation are found[47]. In such cases the Dubinin-Astakhov (DA) equation has been proposed[46], in which the exponent two in the DR equation is replaced by a third adjustable constant n. Figure 4 shows the effect of n on the shape of the DA isotherm when plotted in DR co-ordinates. For n < 2, the isotherm is convex to the abscissa; such deviations from the DR equation are found for wellactivated carbons with a wide range of micropore sizes[48]. For IZ > 2, the isotherm is concave to the abscissa and such deviations from the DR equation are found for unactivated, or slightly activated carbons with a narrow range of micropore sizes. Caution is needed in interpreting deviations from the DR equation because some are due to activated diffusion. These deviations are characterized by a downward deflection in the DR plot at low PIP,,, Fig. 5.
8. THE
GENERALIZED ISOTHERM
V = V,, exp - [A/E]*,
(1)
where V is the amount adsorbed at relative pressure
0
I
I
I
I
20
40
60
80
ln2P,/
ADSORPTION (GAI)
Because of its empirical origins and the numerous types of deviation from it, the DR equation has not met with general acceptance. However. a justifica-
-1.4 -_I
0
5
IO In2 P,I P
15
P
Fig. 4. The influence of the parameter n in the DA equation on the shape of the isotherm plotted in DR co-ordinates; E = 10 kJ/mol, T = 77 K.
Fig. 5. Adsorption of Ar at 77 K on activated carbons from: Saran, n ; almond shells, 0; olive stones, A. The downward deflections at low Pi PO(high In* PO/P) are due . ..^_. P.,. .^7 to activated dittuslon(4U,4X].
B. MCENANEY
272
tion for the DR and DA equations can be found by considering the generalized adsorption isotherm (GAI). The structures of microporous carbons are highly disordered and their surfaces are energetically heterogeneous so that adsorption on them may be modeled by the GAI[49], in which it is assumed that adsorption on sites having energy, q, can be represented by a local isotherm G’(P, q); the overall isotherm, 0(P), is given by G(P)
= lu@YP, q)f(q)
&,
P E 4
(2)
where f is the site energy distribution function defined on a domain fl and 4 is the domain of P; this integral equation is the GAI. Solving the GA1 for f, given 0 and G’, is ill-posed, that is, small perturbations in 8 (e.g., experimental errors) can result in widely different solutions for f. The general approach to solving the GA1 is to restrict the class of possible solutions by imposing constraints on f that correspond to assumptions about or prior knowledge of the system. The solution is then considered to be the f in this restricted class that gives the best fit to the experimentally determined total isotherm (e.g., by least squares). One approach is to constrain f to be a smooth, analytic function which, with a suitable equation for G’, allows the GA1 to be integrated to give an analytic function for 8. A recent example of this approach was presented by Sircar[SO], who chose the Langmuir equation for the local isotherm and a gamma-type function for f. A solution to the GA1 can also be obtained by a numerical method called regularization[5 1,521. A third method used to solve the GA1 is the condensation approximation (CA)[53] in which the local isotherm is approximated by a step function. Applying the CA to the Langmuir local isotherm results in the relationship A = q - go, where go is a constant, minimum ad-
sorption energy. distribution
f(4) =
If
f is assumed to be a Weibull
n(q - So)”- ’ E”
exp -
[VI”,
(3)
then integration of the GA1 gives the DA equation, or the DR equation if n = 2[54]. Thus, go and the DA parameters n and E represent, in an approximate way, the influence of adsorbent heterogeneity on the adsorption process. The ability of the DA and DR equations to reflect adsorption heterogeneity may explain their success in describing adsorption on a wide variety of porous and nonporous solids[53]. Examples of the Weibull functions calculated from eqn (3) are in Fig. 6, where distributions of the dimensionless parameter (q - q,,)lE are plotted for different values of n. For constant q,, and E, the mode increases as n increases from 1.5 to 3. This is as expected in the context of microporous carbons, since a high value of n is found for carbons with narrow micropores. It is also consistent with a recent example[55] of more exact solutions of the GA1 obtained by application of the method of regularization to adsorption of Ar at 77 K on two activated carbons. The energy distributions from regularization, Fig. 7, show that the PVDC-based carbon, which has narrow micropores, has a higher modal value of q than that for anthracite-based AB carbon, which has a wider range of pore sizes, extending to mesopores. 9. ESTIMATIONS
OF MICROPORE
SIZES
A useful objective for adsorption studies is the estimation of micropore sizes. In the case of carbons exhibiting molecular sieve action, the most obvious, if laborious, method to obtain a micropore size dis-
0.6 f(q) 0.4
0
O-5
l-0
(q- q&E Fig. 6. The influence of the DA parameter n on the shape of the Weibull distribution function f(q) of eqn (3).
Fig. 7. Distribution functions obtained by the method of regularization for adsorption of Ar at 77 K on a PVDCbased carbon and an antracite-based (AB) active carbon[52].
Adsorption and structure in microporous carbons tribution is to measure adsorption isotherms of gases of different molecular size; a recent example of this method was presented by Carrott and Sing[56]. Alternatively, a single parameter estimate of micropore sizes can be obtained from the characteristic energy, E,, of the DR and DA equations. From a comparison of En with the average Guinier gyration radius, Rg, obtained from small angle X-ray scattering (SAXS)[57], Dubinin and Stoeckli[58] have proposed a direct inverse relationship E,Rg = 14.8 2 0.6 (nm . kJ/mol)
(4)
A similar relationship was proposed between E and the width of micropores accessible to molecular probes, W,,,, W,,,E, = K (nm . kJ/mol),
(5)
where Kl E. is a weak function of Eo. McEnaney[59] has shown recently that the SAXS and molecular probe data may be correlated equally well with E. using a two-constant, semilogarithmic equation: W, = 4.691 exp( - O.O666E,) (nm).
(6)
Considering the limited nature of the experimental data, these estimates of micropore size must be regarded as approximate, as is emphasized by their authors. The distribution function f, eqn (3) contains information that relates to the disordered structure of microporous carbons, but extracting useful information from it is not easy. Contributions to f from microporous carbons include (1) structural heterogeneity arising from the enhancement of adsorption potentials in micropores and (2) surface heterogeneity arising from the presence of imperfections and heteroatoms on the carbon surface. If the component of f due to structural heterogeneity could be isolated, then a micropore size distribution can be obtained by relating adsorption energy to micropore size. In recent examples of this approach[60,61], eqn (4) was used to relate pore size to E,, and the condensation approximation was used to obtain f. The development of such ideas is a subject of active study at present and may lead to better descriptions of relationships between adsorption and structure in microporous carbons than exist at present. 10.
SUMMARY
The microporous structure of carbons consists of a tangled network of defective carbon layer planes. Micropores are the spaces between the layer planes with dimensions estimated by high resolution electron microscopy to be about 0.34 to 0.8 nm. Adsorption of gases in microporous carbons is characterized by (1) strong adsorption at low pressure due to enhanced adsorption potentials caused by overlap of the force fields from opposite pore
213
walls, (2) activated diffusion effects caused by constrictions in the microporous network, and (3) molecular size and shape selectivity, with preferential adsorption of flat molecules. These properties have enabled molecular sieve carbons to be developed for the separation of gases. Fractal analysis of adsorption in microporous carbons suggests that the surface fractal dimension D, decreases from about 3 to about 2 with increasing activation, indicating that activation smoothens pore surfaces. Adsorption potentials may be calculated for slitshaped model micropores formed between singlelayer planes. These calculations show that adsorption potentials in micropores are enhanced by a factor of up to 2 compared to the free surface and lead to critical dimensions for diffusion of gases through micropores. The nature of the adsorption process in micropores renders the Brunauer-Emmett-Teller (BET) equation unsuitable for analyzing adsorption isotherms with a significant microporous contribution. The BET equation can be used to estimate the nonmicroporous surface area, provided that the microporous contribution to adsorption can be removed. Various techniques have been developed to do this such as t plots, LYplots, n-nonane preadsorption, and isotherm subtraction. The Dubinin-Radushkevich (DR) and DubininAstakhov (DA) equations have been more successful when applied to adsorption on microporous carbons, because they reflect the influence of adsorbent heterogeneity on the adsorption process. The DR and DA equations result from an approximation to the generalized adsorption isotherm (GAI); more exact solutions of the GA1 enable site-energy distribution functions for microporous carbons to be obtained. Micropore size distributions for molecular sieve carbons can be obtained from measurements of adsorption of molecules of different size. Single parameter estimates of pore sizes can be obtained from the DR constant E,,. In principle, micropore size distribution functions can also be obtained from the energy distribution function f of the GAI. Acknowledgments-Thanks go to T. J. Mays for valuable discussions, to S. Ah for the use of unpublished data. and to J. Wang for help in the production of the figures. REFERENCES
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9. L. L. Ban, D. Crawford, and H. Marsh, J. Appl. Cryst. 8, 415 (1975). 10. G. R. Millward and D. A. Jefferson. In Chemistry and Physics of Carbon (Edited by P. L. Walker, Jr. and P. A. Thrower), Vol. 14, pp. l-82. Marcel Dekker, New York (1978). 11. A. Oberlin, M. Villey and A. Combaz, Carbon 18, 347 (1980). 12. J. R. Fryer, Carbon 19, 431 (1981). 13. H. Marsh, D. Crawford, T. M. O’Grady, and A. Wennerberg, Carbon 20, 419 (1982). 14. B. R. Puti, In Chemistry and Physics of Carbon (Edited bv P. L. Walker. Jr.) Vol. 6. DD. 191-282. Marcel Dekker, New York; (1970). ” ’ 15. H. P. Boehm and M. Voll, Carbon 7,227 (1970); idem., Carbon, 8, 481 (1971).
16. H. P. Boehm, A. Vass, and R. Kollmar, Extended Abstracts, 18th American Carbon Conference, Worcester Polytechnic Institute, Worcester, MA, USA pp. 86-87 (1987). 17. P. L. Walker, Jr. and M. Shelef, Carbon 5, 7 (1967).
18. J. R. Dacey and M. J. B. Evans, Carbon 9,579 (1971). 19. S. S. Barton, M. J. B. Evans and B. H. Harrison, J. Colloid Interface Sci. 49, 462 (1974).
20. H. Juntgen, K. Knoblauch, and K. Harder, Fuel 60, 817 (1981). 21. J. Koresch and A. Soffer. J. Chem. Sot. Faradav Trans. Z 76, 2472 (1980).
’
22. D. Avnir, D. Farin, and P. Pfeifer, Nature 308, 261 (1984).
23. D. Avnir, D. Farin, and P. Pfeifer, J. Chem. Phys. 79, 3566 (1983). 24. C. Fairbridge, S. H. Ng, and A. D. Palmer, Fuel 65, 1759 (1986). 25. N. S. Gurfein, D. P. Dobychin, and L. S. Koplienko, Russ. J. Phys. Chem. 44, 411 (1970). 26. H. F. Stoeckli, Helv. Chim. Acta 57, 2195 (1974). 27. D. H. Everett and J. C. Powl, J. Chem. Sot., Faraday Trans. I 619, (1976).
28. P. J. M. Carrott and K. S. W. Sing, Chem. Ind. 360 (1986). 29. M. M. Dubinin, J. Colloid Interface Sci. 46,351(1974). 30. M. B. Rao, R. G. Jenkins, and W. A. Steele, Langmuir 1, 137 (1985). M. B. Rao and R. G. Jenkins, Carbon 25,445 (1987). ;:: S. J. Gregg and K. S. W. Sing, In Adsorption, Surface Area and Porosity, 2nd Edition, Academic Press, London (1982). 33. H. Marsh and T. G. Lamond, Carbon 1, 293 (1963). 34. J. H. de Boer, B. G. Linsen, Th. Van der Plas, and G. J. Zondervan, J. Catal., 4, 649 (1965). 35. K. S. W. Sing, Chem. Ind. 1528 (1968). 36. A. Lecloux and J. P. Pirard, J. Colloid Interface Sci. 70, 265 (1979).
37. M. M. Dubinin, Carbon 23, 373 (1985). J. M. Martin-Martinez, C. 38. F. Rodriguez-Reinoso, Prado-Burguete, and B. McEnaney, J. Phys. Chem. 91, 515 (1987). 39. P. J. M. Carrott, K. S. W. Sing, and J. H. Raistrick, Colloids and Surfaces 21, 9 (1986).
40. S. A.-R. M. Ali, A study of microporous and nonmicroporous adsorption in activated carbons, MSc., Thesis, University of Bath, UK (1984). 41. S. J. Gregg and J. F. Langford, Trans. Faraday Sot. 65, 1394 (1969).
42. A. Linares-Solano, J. D. Lopez-Gonzales, J. M. Martin-Martinez, and F. Rodriguez-Reinoso, Ads. Sci. Tech. 1, 123 (1984). 43. S. Ali and B. McEnanev. J. Colloid Interface Sci. 107. 355 (1985). 44. H. F. Stoeckli and F. Krahenbuehl, Carbon 22, 297 2
I
(1984).
F. Rodriguez-Reinoso, M. 45. J. M. Martin-Martinez, Molina-Sabio, and B. McEnaney, Carbon 24, 255 (1986).
46. M. M. Dubinin, In Progress in Surface and Membrane Science. Vol. 9 (Edited bv D. A. Cadenhead) Academic Press, New York, pp. l-70 (1975). ’ 47. H. Marsh and B. Rand, J. Colloid Interface Sci. 33, 101 (1970). 48. K. J. Masters and B. McEnaney, J. Colloid Interface Sci. 95, 340 (1983).
49. M. Jaroniec,
A. Patrykiejew
and M. Borowko, In Vol. 14 (Edited by D. A. Cadenhead and J. F. Danielli), Academic Press, New York, pp. l-68 (1981). 50. S. Sircar, J. Colloid Znterfnce Sci. 101, 452 (1984); idem.. J. Chem. Sot.. Faradav Trans. I. 80. 1101 (1984). 51. J. A. Britten, B. J. Travis, and L. F. Brown, A.1.Ch.E. Progress in Membrane
and Surface Science,
Symposium Series No. 230, 79, 7 (1983).
52. T. J. Mays, B. McEnaney, and P. D. Causton, Langmuir 3, 695 (1987).
53. G. F. Cerofolini, Surface Sci. 24, 2391 (1971); idem., Thin Solid Films 23, 129 (1974).
54. H. F. Stoeckli, Carbon 19, 325 (1981). 55. T. J. Mays and B. McEnaney, In Characterisation of Porous Solids. Elsevier, Amsterdam, in press. 56. P. J. M. Carrott. R. A. Roberts. and K. S. W. Sina. In Characterisatton of Porous Solids, Elsevier, Amsterdam, in press. 57. M. M. Dubinin and G. M. Plavnik, Carbon 2, 261 (1968).
58. M. M. Dubinin and H. F. Stoeckli, J. Colloid Interface Sci. 75, 34 (1980). 59. B. McEnanev. Carbon 25. 69 (1987). 60. M. Jaroniec and R. Made;, Carbon 25, 579 (1987). 61. M. Jaroniec, R. Madey, J. Choma, B. McEnaney, and T. J. Mays, submitted to Carbon.
Printed mGreatBritain.
REVIEW
ARTICLE
ADSORPTION AND STRUCTURE MICROPOROUS CARBONS * School
of Materials
BRIAN MCENANEY Science, University of Bath, (Received
IN
Bath BA2 7AY, U.K
19 Oclober 1987)
Abstract-The microporous structure of carbons consists of a tangled network of defective carbon layer planes in which micropores are the spaces between the layer planes. Adsorption of gases in micropores is characterized by (1) strong adsorption at low pressure due to overlap of force fields from opposite pore walls, (2) activated diffusion effects caused by constrictions in the microporous network. and (3) molecular size and shape selectivity (molecular sieving). The surface fractal dimension of activated carbons decreases from three to two with increasing activation, indicating that activation smoothens pore surfaces. Calculated adsorption potentials for slit-shaped model micropores show that adsorption potentials are enhanced by a factor of up to 2 and enable critical dimensions for diffusion of gases through micropores to be estimated. The Brunauer-Emmett-Teller equation is unsuitable for analyzing adsorption with a significant microporous contribution but may be used to estimate the nonmicroporous surface area, provided that the microporous contribution can be removed. The Dubinin-Radushkevich and Dubinin-Astakhov equations have been more successful when applied to microporous carbon5 because they reflect the influence of adsorbent heterogeneity. as they result from an approximation to the generalized adsorption isotherm (GAI). More exact solutions of the GA1 enable adsorption energy distribution functions to be obtained. The possibility of extracting micropore size distributions from adsorption measurements is briefly considered. Key Words-Adsorption,
microporous
carbons,
activated
microstructure
micropores. Definitions of pore sizes follow recommendations of the International Union of Pure & Applied Chemistry (IUPAC): micropores-width less than 2 nm; mesopores-width 2 to 50 nm: macropores-width greater than 50 nm[3]. The major sources of industrial, microporous active carbons are coals (lignites, bituminous coals, and anthracites), peat, wood, and a wide range of organic by-products of industry and agriculture. About 90% of active carbons are produced in granular or powder form, with most of the remainder in pelleted form[4]. In addition to these conventional sources. an increasingly wide range of specialized industrial microporous adsorbents has been produced (e.g., active carbon textiles[5,6], and molecular sieve carbons[7,8]). During carbonization the organic precursor is thermally degraded to form products that undergo either condensation or volatilization reactions, the competition between these processes determining the carbon yield. The carbon residue is formed by condensation of polynuclear aromatic compounds and expulsion of side chain groups. However, industrial carbons retain a :,ignificant concentration of heteroelements. especially 0 and H, and many contain mineral matter. The adsorptive capacity of the carbonized materials is usually too low for practical applications, so porosity in the carbon is developed by activation (i.e., by reaction of the carbon with oxidizing gases (e.g., Hz0 or COz) or by incorporation of inorganic additives (e.g., ZnCL) prior to carbonization. For coal-based
1. INTRODUCTION
The literature on adsorption in porous carbons ranges widely from theoretical studies of adsorption from the vapor and liquid phases to technical studies of the many applications of carbon adsorbents. This article is not a comprehensive review of the subject, nor is it a complete survey of the many isotherm equations that have been proposed to analyze adsorption in microporous carbons. Instead, it is confined to consideration of the effects of the microporous structure of carbons on adsorption of gases. Although most nongraphitizing (“hard”) carbons contain numerous micropores, not all are practical adsorbents, since the micropores in them may not be accessible to gases to a useful degree. However. much valuable structural information, relevant to microporous carbon adsorbents, has been obtained from the study of materials such as poly(acrylonitrile)-based (PAN-based) carbon fibers[l] and glasslike (“vitreous”) carbons[2]. Many industrial porous carbons (e.g., coal-based active carbons) in addition to micropores contain macropores and mesopores that may be important in adsorption. However, the role of these larger pores is not considered in this article, since the effectiveness of most active carbons used for gas adsorption depends primarily on the nature and extent of the accessible
*Based on a plenary review lecture given ‘86,” 30 June 1986, Baden-Baden, FRG.
carbons,
at “Carbon
267
268
B. MCENANEY
active carbons, Table 1 illustrates how the proportion of the different pore types varies with the nature of the precursor[4]. By judicious choice of the precursors and careful control of carbonization and activation, it is possible to tailor active carbons to suit particular applications. 2.
THE STRUCTURE
OF MICROPOROUS
CARBONS
Microporous carbons have a very disordered structure as revealed by high resolution electron microscopy and various model structures have been proposed based on studies of polymer carbons[2,9], carbon fibers[l], carbonized coals and kerogens[lO,ll], and active carbons[l2,13]. Although the models differ in detail, the essential feature of all of them is a twisted network of defective carbon layer planes, cross-linked by aliphatic bridging groups. The width of layer planes varies, but typically is about 5 nm[12]. Simple functional groups (e.g., C-OH, C===O)and heteroelements are incorporated into the network and are bound to the periphery of the carbon layer planes. Functional groups can have an important influence on adsorption[l4], but detailed consideration of their effects is outside the scope of this review. In microporous carbons the layer planes occur singly or in small stacks of two, three, or four with variable interlayer spacings in the range 0.34 to 0.8 nm[ll]; Fryer[l2] found an average layer plane separation of 0.7 nm for a steam-activated anthracite carbon, and separations in the range 0.6 to 0.8 nm for Carbosieve. There is considerable microporosity in the form of an interconnected network of slit-shaped pores formed by the spaces between the carbon layer planes and the gaps between the stacks. Thus the widths of pores formed by interlayer spacings (typically from about 0.34-0.8 nm) are significantly less than 2 nm, the arbitrarily defined[3] upper limit for micropore widths. Constrictions in the microporous network are particular features of the structure that control access to much of the pore space. Constrictions may also occur due to the presence of functional groups attached to the edges of layer planes[l5,16] and by carbon deposits formed by thermal cracking of volatiles. 3. ADSORPTION
IN MICROPOROUS
CARBONS
The complex and disorganized structure of microporous carbons, in which the dimensions of the pore space are commensurate with the dimensions of adsorbate molecules, makes interpretation of adsorpTable 1. Pore volumes (ml/g) for coal-based active carbons[4] Coal Precursor Anthracite Bituminous Lignite Blended
Micropores
Mesopores
Macropores
0.51 0.43 0.22 0.42
0.07 0.17 0.58 0.11
0.11 0.26 0.32 0.33
tion in these materials very difficult. First, gases are strongly adsorbed at low pressures in micropores, because there is enhancement of adsorption potential due to overlap of the force fields of opposite pore walls (see below). Second, constrictions in the microporous network cause activated diffusion effects at low adsorption temperatures when the adsorptive has insufficient kinetic energy to penetrate fully the micropore space; this poses problems when using N, at 77 K as the adsorbate[l7]. Third, microporous carbons can exhibit molecular sieve action (i.e., the selective adsorption of small molecules in narrow micropores[7]). Carbons also exhibit molecular-shape selectivity by preferential adsorption of flat molecules, as expected from the slit shape of the micropores[l8,19]. Molecular sieve action can be exploited to effect separation of gas mixtures by microporous carbons (e.g., oxygen and nitrogen separation from air using the pressure swing method[7,20,21]). 4. FRACTAL
ANALYSIS OF MICROPOROUS
CARBONS
Fractal geometry has been applied to many branches of science in recent years, including the properties of porous solids[22]. The surface of a solid may be characterized by a surface fractal dimension, Ds, which is a measure of surface irregularity or roughness. For a smooth surface the value of Ds approaches 2, the dimension of a Euclidean surface. For a very irregular surface, the value of Ds approaches 3, the dimension of a Euclidean volume; thus 2 5 Ds s 3. The value of Ds for a fractal object may be estimated by measuring its surface area with different “yardsticks.” In the case of adsorbent surfaces, the “yardsticks” are usually adsorptive molecules of different size, the value of Ds being found from the increase in surface area of the object with decreasing molecular size. Using this approach, Avnir et al. [23] have shown that for a graphitized carbon black the value of Ds is close to 2, as expected for a smooth, nonporous surface. For a series of activated charcoals, the value of D, decreased from about 3 to about 2 with increasing activation. They concluded that, in addition to increasing pore widths and adsorptive capacity, the process of activation also smoothens pore surfaces. The surface fractal dimension of a porous solid can also be estimated by measuring its surface area as a function of particle size. Using this method, Fairbridge et af.[24] obtained a value of Ds = 2.48 for a Syncrude coke from N2 and CO, surface areas. The concept of fractal dimension provides an interesting new perspective on the properties of porous solids, which is being actively developed at present. 5.
CALCULATIONS
OF ADSORPTION
POTENTIALS
There have been several theoretical studies of adsorption potentials in model micropores[25-271. Adsorption potentials were calculated by Everett and
Adsorption and structure in microporous carbons
269
Table 2. Calculated critical micropore dimensions for diffusion of gases Adsorptive Slit width (nm)
co 0.541
co2 0.542
Pow1[27] for cylindrical pores and aiso for slit-shaped pores formed between semiinfinite slabs (9:3 potentials) and between single layer planes (10:4 potentials). The 10:4 potential function appears to be the more appropriate model, considering the structure of microporous carbons, in which dit-shaped pores are separated by one to four layer planes[ll]. Potentials have a single minimum for narrow pores and two minima in wide pores. Figure 1 shows the minimum 10:4 potential in the model pore, Q *, relative to that on the plane surface, Q, plotted against the pore half-width, d, relative to the collision radius of the adsorptive molecule, r,. For 10:4 potentials the two minima occur when d/r, _Z 1.140. Q*/Q is a maximum of 2.00 at d/r, = 1.00, and Q* JQ decreases to about 1.1 at d/r, = 1.50. At d/r, less than 1.00 (i.e., between a and b, Fig. l), the enhancement of adsorption potential decreases rapidly due to the short range repulsive terms in the 10:4 potential function. Recent measurements~2gl of heats of adsorption at low surface coverage of a range of hydrocarbons on microporous carbons and on carbon blacks confirm that enhancement of adsorption energy in micropores is by a factor of about 2. Pores with enhanced adsorption potential have been termed ultramicro~res and wider pores, up to 2 nm wide, have been termed supermicropores[29]. The definition of the size range of ultramicropores is not precise and depends on the size of the adsorptive molecule, but, for the purposes of illustration, may be taken as the range corresponding to ac in Fig. 1. For Ar (r. = 0.340 nm) and Xe (r. = 0.375 nm), ultramicroporous slit widths, W, = 2d, are 0.58 to 1.02 nm and 0.64 to 1.13 nm, respectively. W, is the internuclear distance between C atoms in opposite walls of the model pore. If slit widths are
2.0
1.a
02 0.544
022
corrected for the finite radius of the C atoms to give W,, in the notation of Everett and Powl[27]. then for Ar and Xet W, = 0.24 to 0.68 nm and 0.30 to 0.79 nm respectively. A further approximate correction can be made for the compressibility of the adsorptive in the force field of the micropore[27], to give the available ultramicroporous pore width, W,; for Ar and Xe, W, = 0.34 to 0.78 nm and 0.40 to 0.89 nm, respectively; these values of pore width are within the range of interlayer spacings measured by high resolution electron microscopy[ 11,12], Calculated adsorption potentials in model micropores have been used to estimate critical dimensions for diffusion of gases. For the Everett-Pow1 10:4 potentials, this dimension corresponds to dir,, at point a in Fig. 1. For pore dimensions less than this value, diffusion of gases becomes activated. The value of this dimension is critical for the ability of molecular sieve carbons to separate gases of different moiecutar size. The results of recent calculations[30,31] for diffusion of several monatomic and polyatomic molecules through slit-shaped model micropores are in Table 2. The value of the critical pore dimension for Ar is in very good agreement with that obtained from the Everett-Pow1 10:4 potentials and the values for Nz and OZ are consistent with experiments on the separation of these gases from air[20]. These results also appear to resolve an anomaly resulting from estimations of critical molecular dimensions using gas phase data. These yield a smaller dimension for NZ than for CO?; this is contrary to experiment, since CO, is known to diffuse more rapidly through carbon molecular sieves than NJ171. As useful as model pore calculations are in elucidating the nature of adsorptive-adsorbent interactions in micropores, they are highly idealized when applied to microporous carbons. For example, the models ignore factors such as (1) the highly defective nature of the carbon layer planes, (2) edge effects resulting from their finite size, and (3) the role of heteroelements and polar surface groups (e.g., C%O) in the adsorption process. The calculations also relate to the interaction of an isolated adsorptive molecule with the pore wall and so cooperative effects during micropore filling are not considered. 6.
THE BRUNAUER-EMMETT-TELLER (BET) EQUATION
Fig. 1. Adsorption potentials Q * in model slit-shaped micropores, relative to the adsorption potential Q on a free surface, as a function of pore half-width, d, relative to the collision radius of the adsorptive, r,; calculated using 10:4 potential functionsf271.
The equation most widely used to analyse adsorption isotherms to obtain surface areas, the BET equation[e.g., 321, is subject to severe limitations when applied to microporous carbons. Values of surface areas, up to about 4000 m2/g for some highly activated carbons[33] are unrealistically high, since
B. MCENANEY
270 800
800
8 9
480
3
I
-8 -
I
200
0
0
I0
I
I
I
0.5
I.0
I.5
alpha
layer
plane,
I
1
1
40
60
80
InaPolP
surface area for an extended graphite counting both sides, is about 2800
m2/g. Adsorption in micropores does not take place by successive buildup of molecular layers, as supposed by the BET theory. Instead, the enhanced adsorption potential in micropores induces an adsorption process described as primary or micropore filling[29]. Because of its widespread use for other adsorbents, the BET surface area will continue to be used for microporous carbons, but its notional character should be recognized. The BET equation can be applied with more confidence to adsorption of gases on the nonmicroporous surface of carbons (i.e., on mesopores, macropores, and the external surface), provided that the microporous contribution to adsorption can be effectively removed. Three types of method have been proposed to isolate microporous adsorption: (1) comparative methods, (2) preadsorption techniques, and (3) isotherm subtraction. In comparative methods, adsorption on a microporous adsorbent is compared to adsorption on a nonporous reference adsorbent of well-defined surface area. The most widely used comparative methods are the t plot[34] and the a plot[35]; these methods have been discussed in detail by Gregg and Sing[32]. The statistical thickness of the adsorbed layer, t, is defined as t = VPIS, where VP is the volume of adsorptive adsorbed at pressure P and S is the total BET surface area of the reference adsorbent. Sing[35] proposed an alternative parameter a = V/ (V at Pl PO = 0.4). Both
t and a are essentially normalizing parameters for producing a reduced isotherm. The choice of a suitable reference material has provoked debate. Lecloux and Pirard[36] proposed that the choice should be dictated by the value of the BET C constant, but Gregg and Sing[32] argue persuasively that the reference material should be selected on the basis of chemical similarity to the test material. Graphitized carbon blacks were originally used [34,37] as reference materials for carbons, but, it has been recently suggested that nongraphitic carbon substrates (a heat-treated carbon[38] and “sooty” silica[39]) are superior reference materials for microporous carbons. For microporous carbons, t plots and a plots are of similar form. Figure 2 shows a plots for adsorption of Ar at 77 K on four coal-based activated carbons[40]. The steep rises at low a values are attributed to micropore filling and the linear regions at high a values to adsorption on the nonmicroporous surface. The micropore volume, V,, is estimated by extrapolation of the linear region to a = 0 and the nonmicroporous surface area, S’, can be estimated from the slope of the linear portion of the a plot; the ratio S’/S provides a useful index of the relative contributions of microporous and nonmicroporous adsorption. Values of these parameters are in Table 3, which shows that these carbons are dominantly microporous. In preadsorption methods[38-411, micropores are filled at room temperature with a strongly adsorbed vapor, usually n-nonane, which is retained in micropores on subsequent outgassing. The nonmicroporous surface area is then measured by adsorption of
Table 3. Parameters obtained from u-plots (Fig. 2) for adsorption of Ar at 77 K on coal-based activated carbons[40] Carbon ABl AB2 AB3 AB4
I
Fig. 3. Adsorption of CO, at 195 K on an activated cellulose triacetate carbon heat-treated to 1600°C plotted in DR coordinates to illustrate the principle of isotherm subtraction[Q].
Fig. 2. Alpha plots for adsorption of Ar at 77 K on four .. coat-based active carbons, ABl-AB4, plotted using a graphitized carbon black, Vulcan-3G, as reference adsorbent[40].
the calculated
I
20
S(m2/g)
S’(m*/g)
V&nl/g)
S’IS
595 773 877 1006
47 80 61 74
0.24 0.31 0.37 0.41
0.08 0.10 0.07 0.07
Adsorption and structure in microporous carbons N, at 77 K, while the micropore volume can be obtained by comparison of N, adsorption before and after adsorption of n-nonane. Isotherm subtraction[43] or decomposition[44] is a simple method for estimating S’ from a single isotherm. The principle of the method is illustrated in Fig. 3 in which the isotherm is plotted in Dubinin-Radushkevich coordinates (see Section 7). The low pressure part of the isotherm, ab, which is dominated by micropore filling, is extrapolated to high pressures, bd, using the DR equation, and subtracted from the total high pressure isotherm, bc, to give a residual, nonmicroporous isotherm, which can be analysed by the BET equation to give S’. Martin-Martinez and co-workers[45] have carried out an extensive comparison of the n-nonane preadsorption and isotherm subtraction methods. They conclude that for carbons with narrow micropores the two methods give very similar results; when the distribution of micropore sizes is wider, the preadsorption technique fails because nnonane is not retained in some wide micropores on outgassing. For superactivated carbons with a very wide range of pore sizes, neither technique was able to separate microporous and nonmicroporous adsorption.
7. THE
DUBININ-RADUSHKEVICH
(DR)
EQUATION
Because adsorption in microporous carbons occurs by primary or micropore filling, Dubinin and his group originally modeled microporous adsorption using the Polanyi potential theory. Dubinin found empirically that the characteristic curves for adsorption on many microporous carbons could be linearized using the DR equation[46]:
271
P/P,,, V,, is the micropore volume, A = RT ln(P,l P) is the adsorption potential, where R is the gas constant and T the absolute temperature, and E is an energy constant. Dubinin showed that the energy constant E could be factorized into a characteristic energy, E,, which relates to the adsorbent, and an affinity coefficient, B, which is a constant for a given adsorptive. Essentially, B is a shifting factor that allows the characteristic curves (linearized by the DR equation) for different adsorptives on the same adsorbent to be superimposed. For some carbons the DR equation is linear over many orders of magnitude of pressure. For others, however, deviations from the DR equation are found[47]. In such cases the Dubinin-Astakhov (DA) equation has been proposed[46], in which the exponent two in the DR equation is replaced by a third adjustable constant n. Figure 4 shows the effect of n on the shape of the DA isotherm when plotted in DR co-ordinates. For n < 2, the isotherm is convex to the abscissa; such deviations from the DR equation are found for wellactivated carbons with a wide range of micropore sizes[48]. For IZ > 2, the isotherm is concave to the abscissa and such deviations from the DR equation are found for unactivated, or slightly activated carbons with a narrow range of micropore sizes. Caution is needed in interpreting deviations from the DR equation because some are due to activated diffusion. These deviations are characterized by a downward deflection in the DR plot at low PIP,,, Fig. 5.
8. THE
GENERALIZED ISOTHERM
V = V,, exp - [A/E]*,
(1)
where V is the amount adsorbed at relative pressure
0
I
I
I
I
20
40
60
80
ln2P,/
ADSORPTION (GAI)
Because of its empirical origins and the numerous types of deviation from it, the DR equation has not met with general acceptance. However. a justifica-
-1.4 -_I
0
5
IO In2 P,I P
15
P
Fig. 4. The influence of the parameter n in the DA equation on the shape of the isotherm plotted in DR co-ordinates; E = 10 kJ/mol, T = 77 K.
Fig. 5. Adsorption of Ar at 77 K on activated carbons from: Saran, n ; almond shells, 0; olive stones, A. The downward deflections at low Pi PO(high In* PO/P) are due . ..^_. P.,. .^7 to activated dittuslon(4U,4X].
B. MCENANEY
272
tion for the DR and DA equations can be found by considering the generalized adsorption isotherm (GAI). The structures of microporous carbons are highly disordered and their surfaces are energetically heterogeneous so that adsorption on them may be modeled by the GAI[49], in which it is assumed that adsorption on sites having energy, q, can be represented by a local isotherm G’(P, q); the overall isotherm, 0(P), is given by G(P)
= lu@YP, q)f(q)
&,
P E 4
(2)
where f is the site energy distribution function defined on a domain fl and 4 is the domain of P; this integral equation is the GAI. Solving the GA1 for f, given 0 and G’, is ill-posed, that is, small perturbations in 8 (e.g., experimental errors) can result in widely different solutions for f. The general approach to solving the GA1 is to restrict the class of possible solutions by imposing constraints on f that correspond to assumptions about or prior knowledge of the system. The solution is then considered to be the f in this restricted class that gives the best fit to the experimentally determined total isotherm (e.g., by least squares). One approach is to constrain f to be a smooth, analytic function which, with a suitable equation for G’, allows the GA1 to be integrated to give an analytic function for 8. A recent example of this approach was presented by Sircar[SO], who chose the Langmuir equation for the local isotherm and a gamma-type function for f. A solution to the GA1 can also be obtained by a numerical method called regularization[5 1,521. A third method used to solve the GA1 is the condensation approximation (CA)[53] in which the local isotherm is approximated by a step function. Applying the CA to the Langmuir local isotherm results in the relationship A = q - go, where go is a constant, minimum ad-
sorption energy. distribution
f(4) =
If
f is assumed to be a Weibull
n(q - So)”- ’ E”
exp -
[VI”,
(3)
then integration of the GA1 gives the DA equation, or the DR equation if n = 2[54]. Thus, go and the DA parameters n and E represent, in an approximate way, the influence of adsorbent heterogeneity on the adsorption process. The ability of the DA and DR equations to reflect adsorption heterogeneity may explain their success in describing adsorption on a wide variety of porous and nonporous solids[53]. Examples of the Weibull functions calculated from eqn (3) are in Fig. 6, where distributions of the dimensionless parameter (q - q,,)lE are plotted for different values of n. For constant q,, and E, the mode increases as n increases from 1.5 to 3. This is as expected in the context of microporous carbons, since a high value of n is found for carbons with narrow micropores. It is also consistent with a recent example[55] of more exact solutions of the GA1 obtained by application of the method of regularization to adsorption of Ar at 77 K on two activated carbons. The energy distributions from regularization, Fig. 7, show that the PVDC-based carbon, which has narrow micropores, has a higher modal value of q than that for anthracite-based AB carbon, which has a wider range of pore sizes, extending to mesopores. 9. ESTIMATIONS
OF MICROPORE
SIZES
A useful objective for adsorption studies is the estimation of micropore sizes. In the case of carbons exhibiting molecular sieve action, the most obvious, if laborious, method to obtain a micropore size dis-
0.6 f(q) 0.4
0
O-5
l-0
(q- q&E Fig. 6. The influence of the DA parameter n on the shape of the Weibull distribution function f(q) of eqn (3).
Fig. 7. Distribution functions obtained by the method of regularization for adsorption of Ar at 77 K on a PVDCbased carbon and an antracite-based (AB) active carbon[52].
Adsorption and structure in microporous carbons tribution is to measure adsorption isotherms of gases of different molecular size; a recent example of this method was presented by Carrott and Sing[56]. Alternatively, a single parameter estimate of micropore sizes can be obtained from the characteristic energy, E,, of the DR and DA equations. From a comparison of En with the average Guinier gyration radius, Rg, obtained from small angle X-ray scattering (SAXS)[57], Dubinin and Stoeckli[58] have proposed a direct inverse relationship E,Rg = 14.8 2 0.6 (nm . kJ/mol)
(4)
A similar relationship was proposed between E and the width of micropores accessible to molecular probes, W,,,, W,,,E, = K (nm . kJ/mol),
(5)
where Kl E. is a weak function of Eo. McEnaney[59] has shown recently that the SAXS and molecular probe data may be correlated equally well with E. using a two-constant, semilogarithmic equation: W, = 4.691 exp( - O.O666E,) (nm).
(6)
Considering the limited nature of the experimental data, these estimates of micropore size must be regarded as approximate, as is emphasized by their authors. The distribution function f, eqn (3) contains information that relates to the disordered structure of microporous carbons, but extracting useful information from it is not easy. Contributions to f from microporous carbons include (1) structural heterogeneity arising from the enhancement of adsorption potentials in micropores and (2) surface heterogeneity arising from the presence of imperfections and heteroatoms on the carbon surface. If the component of f due to structural heterogeneity could be isolated, then a micropore size distribution can be obtained by relating adsorption energy to micropore size. In recent examples of this approach[60,61], eqn (4) was used to relate pore size to E,, and the condensation approximation was used to obtain f. The development of such ideas is a subject of active study at present and may lead to better descriptions of relationships between adsorption and structure in microporous carbons than exist at present. 10.
SUMMARY
The microporous structure of carbons consists of a tangled network of defective carbon layer planes. Micropores are the spaces between the layer planes with dimensions estimated by high resolution electron microscopy to be about 0.34 to 0.8 nm. Adsorption of gases in microporous carbons is characterized by (1) strong adsorption at low pressure due to enhanced adsorption potentials caused by overlap of the force fields from opposite pore
213
walls, (2) activated diffusion effects caused by constrictions in the microporous network, and (3) molecular size and shape selectivity, with preferential adsorption of flat molecules. These properties have enabled molecular sieve carbons to be developed for the separation of gases. Fractal analysis of adsorption in microporous carbons suggests that the surface fractal dimension D, decreases from about 3 to about 2 with increasing activation, indicating that activation smoothens pore surfaces. Adsorption potentials may be calculated for slitshaped model micropores formed between singlelayer planes. These calculations show that adsorption potentials in micropores are enhanced by a factor of up to 2 compared to the free surface and lead to critical dimensions for diffusion of gases through micropores. The nature of the adsorption process in micropores renders the Brunauer-Emmett-Teller (BET) equation unsuitable for analyzing adsorption isotherms with a significant microporous contribution. The BET equation can be used to estimate the nonmicroporous surface area, provided that the microporous contribution to adsorption can be removed. Various techniques have been developed to do this such as t plots, LYplots, n-nonane preadsorption, and isotherm subtraction. The Dubinin-Radushkevich (DR) and DubininAstakhov (DA) equations have been more successful when applied to adsorption on microporous carbons, because they reflect the influence of adsorbent heterogeneity on the adsorption process. The DR and DA equations result from an approximation to the generalized adsorption isotherm (GAI); more exact solutions of the GA1 enable site-energy distribution functions for microporous carbons to be obtained. Micropore size distributions for molecular sieve carbons can be obtained from measurements of adsorption of molecules of different size. Single parameter estimates of pore sizes can be obtained from the DR constant E,,. In principle, micropore size distribution functions can also be obtained from the energy distribution function f of the GAI. Acknowledgments-Thanks go to T. J. Mays for valuable discussions, to S. Ah for the use of unpublished data. and to J. Wang for help in the production of the figures. REFERENCES
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