Low Pressure Hysteresis in the Sorption of Carbon Tetrachloride Vapour on Polymer Carbons BY BRIAN MCENANEY School of Materials Science, Bath University, Bath BA2 7AY Received April 1973 Adsorption-desorption isotherms for carbon tetrachloride vapour at 20.0"C on microporous cellulose and polyacrylonitrile carbons exhibit low-pressure hysteresis which is reduced or eliminated by widening of pores which accompanies steam-activation. Comparison of sorption of carbon tetrachloride on unactivated carbons heat-treated to 900 and 2700°C shows that the adsorbate is largely confined to external surfaces and macropores and excluded from the major part of the micro- pores by molecular sieve action. The bulk of adsorbate retained by unactivated carbons on desorp- tion to P/Po = 0.0 was adsorbed at P/Po > 0.9 indicating a pressure-threshold effect for low pressure hysteresis ; about 5 % of the micropore volume originally inaccessible to carbon tetrachloride is penetrated by the expansion-intercalation process in the case of cellulose (900°C) unactivated carbon.A model for this process is proposed based on localised fracture of the carbons. Application of the theory of adsorption-extension of Flood and Heyding shows that stresses induced in volume elements of the carbons are commensurate with or greater than measured bulk fracture strengths for carbons. Low-pressure hysteresis in sorption of organic vapours by porous carbons is usually attributed to intercalation of adsorbate molecules in micropores leading to changes in the structure of the adsorbent which are either irreversible or can only be reversed with difficulty by processes such as annealing under vacuum.Bailey et aZ.l have recently discussed this phenomenon in general thermodynanzic terms. The adsorbate plus adsorbent is considered as a two-component system and, at some point in the course of the sorption isotherm when conditions are thermodynamically favourable, an irreversible transition from the unperturbed to the perturbed (ex- panded) state occurs accompanied by intercalation of the adsorbate molecules. This paper reports measurements of sorption of carbon tetrachloride vapour at 20°C on series of steam-activated carbons prepared from cellulose and polyacrylonitrile which exhibit low-pressure hysteresis. A mechanism is proposed for the expansion- intercalation process based on the theory of adsorption-extension which is believed to be consistent with the general thermodynamic description of the phenomenon by Bailey et aZ.l EXPERIMENTAL Cellulose (Whatman's ashless powder for chromatographic purposes) and polyacrylo- nitrile powder (a laboratory sample from I.C.I.Limited) were compressed into one inch diameter pellets and carbonised in oxygen-free nitrogen at 900°C. Steam-activation was also carried out at this temperature; details of the preparation of active carbons have been reported elsewhere.2 The amount of porosity developed in carbons by reaction with steam is related to the extent of reaction. The degree of activation is, therefore, commonly expressed as the burn-off, % BO, i.e.the amount of carbon removed by the reaction expressed as a percentage. Alternatively, the degree of activation may be expressed by the comple- mentary term, the activation yield, % AY, i.e. the amount of carbon remaining after reaction, 84B. MCENANEY 85 where % BO = 100- % AY ; % BO is employed in this paper. Sorption isotherms on carbon particles of 20-40 BSS mesh were determined gravimetrically at 20.0"C in a flow system based on the method of Davie~.~ The carbon tetrachloride sorbate was prepared by fractional distillation of a commercial sample over phosphorus pentoxide ; the refractive index of the distilled sample was nio = 1.4606 in good agreement with the value given by Timmerman~.~ Desorption of carbon tetrachloride at PIPo = 0.3 to 0.0 resulted in an initial rapid weight loss followed by very slow desorption which continued for several days.It was, therefore, not possible to determine the equilibrium amount of carbon tetrachloride sorbed after desorption at PIPo = 0.3 to 0.0 in a practicable period of time. The value reported is the amount of carbon tetrachloride remaining after desorption for 24 h. Compressive fracture strengths were determined by the method of Ki~ling.~ Since the statistical variation of compressive strength for such carbons is quite large, the results are expressed as the mean and standard deviation of 25 determinations. It can be seen that for both cellulose and polyacrylonitrile carbons, compressive fracture strength decreases with increasing activation (table 1). TABLE 1 .-COMPRESSIVE FRACTURE STRENGTHS OF POLYMER CARBONS cellulose carbons ai/(MN m-2) polyacrylonitrile carbons m/(MN m-2) 25 14.8 (k3.8) 12 12.9 (k2.9) 45 10.7 (k3.0) 30 10.1 (k2.7) 60 9.8 (k2.9) 48 8.8 (k2.5) 75 8.7 (k2.6) 83 7.5 (k2.3) RESULTS Adsorption-desorption isotherms for activated cellulose and polyacrylonitrile carbons are shown in fig.1 and 2 respectively. The results for cellulose carbons are similar to those reported by Cadenhead and Everett for adsorption of benzene 1.2 1 .c n I M 3 M 0.8 9 W \ 04 0 *4 60% BO 45 % BO 25 % BO FIG. 1.-Sorption of carbon tetrachloride vapour on activated cellulose carbons at 20.0"C. 0, adsorption ; 0, desorption .86 LOW PRESSURE ADSORPTION HYSTERESIS vapour on coconut shell activated carbons. The occurrence of low-pressure hysteresis in these carbons appears to require the presence of micropores or micropore entrances which are similar in size to the adsorbate molecule.The low-pressure hysteresis found in the 25 % BO cellulose carbon may, therefore, be attributed to intercalation of the carbon tetrachloride molecule (diameter ca. 8 A) in commensurate micropores which molecular probe measurements have shown to be present. The molecular probe measurements also show that the principal effect of steam activation is to increase the mean micropore width to values greater than 12& the upper limit in the study. 48 % BO 30%BO I I I I 1 1 0-2 0.4 0-6 0.8 FIG. 2.-Sorption of carbon tetrachloride vapour on activated polyacrylonitrile carbons at 20.0"C. 0, adsorption ; e, desorption. PIP0 BO/ % FIG.3.-Adsorptive capacities for water vapour and carbon tetrachloride vapour at 20.0"C on cellulose (A) and polyacrylonitrile (B) carbons 0, HzO ; a, CCL.B. MCENANEY s7 The elimination of low pressure hysteresis in the 45 % BO and 60 BO cellulose carbons may be associated with this process. The closed hysteresis loops in the range PIPo = 0.35 to 1.0 which are found for the highly activated carbons may be attributed to reversible capillary condensation in transitional pores (meso-pores) which have been developed by the activation process. The results for activated polyacrylonitrile carbons (fig. 2) are similar to those for activated cellulose carbons except that, although low pressure hysteresis is reduced by activation, it is not entirely eliminated.This suggests that widening of micropores by steam-activation of polyacrylonitrile carbons does not occur to the same extent as in activation of cellulose carbons. This view is supported by a comparison of adsorptive capacities of the two activated series at PIPo = 1 .O for carbon tetrachloride and water vapour (fig. 3). In harmony with the previously reported density measurements,2 these results show evidence of molecular sieve action between these adsorbates in unactivated cellulose carbon, which is eliminated by activation beyond 25 % BO. Molecular sieve action is also found in the case of unactivated polyacrylonitrile carbon (fig. 3) but this effect, although reduced by activation, is not entirely eliminated until ca. 80 % BO. I' I I I I 24 f PIP0 FIG. 4.-Sorption of carbon tetrachloride vapour on unactivated cellulose carbons at 20.0"C.Open points, adsorption; closed points, desorption. 0, 0, heat treated to 900°C; A, A, heat treated to 2700°C. Sorption of carbon tetrachloride on unactivated cellulose and polyacrylonitrile carbons is of particular interest since comparison of adsorptive capacities for carbon tetrachloride and water vapour (fig. 3) indicates that the major part of the micropore volume is inaccessible to the larger molecule. In fig. 4 and 5 sorption on unactivated cellulose and polyacrylonitrile (900OC) carbons is compared to sorption on unactivated carbons which have been heat-treated to 2700°C in a graphite-resistance furnace. The effect of such heat-treatment has been shown by a variety of measurements to be a reduction in open microporosity and the development of a significant amount of closed microporosity in both carbons.For both cellulose and polyacrylonitrile carbons it can be seen that the amounts of carbon tetrachloride vapour adsorbed in the range PIPo = 0.0 to 0.9 on 900 and88 LOW PRESSURE ADSORPTION HYSTERESIS 2700°C carbons are similar (fig. 4 and 5). This result together with the observations that carbon tetrachloride is largely excluded from micropores in the case of the 900°C unactivated carbons (fig. 3) and that heat-treatment to 2700°C reduces micropore sizes,7 suggests that adsorption on unactivated carbons in the range PIP, = 0.0 to 0.9 is occurring on the surfaces of macropores and the external surface of the carbons. If this analysis is correct, then application of the B.E.T.equation to adsorption in the range P/Po = 0.0 to 0.6 gives surface areas available to carbon tetrachloride of 4.8 m2 g-l for unactivated cellulose carbons and 2.5 m2 g-1 for unactivated poly- acrylonitrile carbons. These surface areas have been obtained using a cross-sectional area for the carbon tetrachloride molecule of 32 A2, which was calculated assuming two-dimensional close-packing of the sorbate. I 1 I I I I I 1 0 *2 0 '4 0.6 0.8 PiPo FIG. 5.-Sorption of carbon tetrachloride vapour on unactivated polyacrylonitrile carbon at 20.0"C. Open points, adsorption ; closed points, desorption. 0, a, heat treated to 900°C ; A, A, heat treated to 2700°C. Fig. 4 and 5 show that for both cellulose and polyacrylonitrile carbons the amount of carbon tetrachloride retained by the 2700°C carbon after desorption to PIP, = 0.0 is less than that retained by the 900°C carbon.This effect may be associated with the reduction in the volume of micropores originally inaccessible to carbon tetrachloride produced by heat-treatment to 2700°C. For example, the micropore volume which is inaccessible to carbon tetrachloride has been shown to be 0.22ml/g for the 900°C cellulose carbon (ref. 2, table V) and 0.03 ml/g for the 2700°C cellulose carbon (ref. 7, table VI). From fig. 4, the amounts of carbon tetrachloride retained after desorption to PIPo = 0.0 are 0.01 1 ml/g (900°C carbon) and 0.004 ml/g (2700°C carbon). Thus, in the case of the 900°C unactivated cellulose carbon, about 5 % of the micropore volume originally inaccessible to carbon tetrachloride vapour is irreversibly penetrated by the intercalation process.A further feature of sorption on unactivated carbons is that the major part of the adsorbate retained after completion of the adsorption-desorption cycle was originally adsorbed at P/po>o.9, i.e. in large macropores and on the external surface of the carbons. Thus, adsorbate which is retained at P/P, = 0.0 in micropores which haveB. MCENANEY 89 been made accessible by expansion of the adsorbent was originally adsorbed in much wider pores. This observation also suggests that the process which caused low pressure hysteresis was initiated at high relative pressures ; this deduction would be consistent with the occurrence of pressure-threshold effects reported by other workers for low-pressure adsorption hysteresis.’ *- DISCUSSION Bailey et a2.l have given a general description of low-pressure adsorption hysteresis in which the phenomenon is associated with irreversible transitions from unperturbed to perturbed (expanded) states within domains in the solid adsorbent.They have suggested that such transitions may occur when local regions of the solid are strained beyond their elastic limit. In this paper the latter view of the process is developed by considering the application of the theory of adsorption-extension of Flood and Heyding.lo” If the carbons are considered as brittle materials containing micro- cracks (pores) of different sizes, then it may be proposed that the stresses induced in the solid by adsorption eventually cause localised fracture thus changing the structure of the adsorbent. Low-pressure hysteresis then occurs because micropore entrances which were previously inaccessible to adsorbate molecules are revealed and/or entrances to micropores filled with adsorbate are blocked by the localised fracture process. It has been shown above that only a small fraction ( 5 %) of the available closed porosity is penetrated by carbon tetrachloride in unactivated cellulose carbon indicating that the process may be confined to a relatively small proportion of the micropore volume.The stresses which cause low-pressure hysteresis are essentially those which cause dimensional changes in porous solids during adsorption. The lowering of the surface free energy of a solid which accompanies adsorption of a gas at pressure, P, causes dilational stresses.According to Flood and Heyding lo-’ the resultant strain, dV/Vt, is given by where K is the compressibility of the adsorbent, 4 = Va/Vc where Va and V, are adsorbate and adsorbent volumes respectively and K, is a structure factor. (Since carbons are not homogeneous solids, the distribution of stresses and strains throughout a carbon depends upon structure.) dV/V, = K $ K , ~ P (1) In the absence of directional stresses in the adsorbate CXP is given by : pa = spp”dP = aP (2) 0 P g where pa and pg are the densities of adsorbate and free gas respectively and pa is termed the mean volumetric stress intensity of the adsorbate. While dilation is the normal consequence of adsorption on a free surface, con- traction may occur in the case of porous adsorbents.If capillary condensation occurs in meso-(transitional) or macro-pores, contractional stresses may result from concave meniscus effects in the condensed adsorbate. In micropores (width < 10 A) contrac- tion has been attributed l1 to bridging of pores by adsorbate molecules. Since micropores fill at low relative pressures, dimensional changes in microporous carbons are characterised by an initial shrinkage followed by expansion at higher relative pressures. Thus at intermediate relative pressures there is presumably a complex distribution of compressive and dilational stresses in a microporous carbon. Adsorption of gases in microporous carbons is well described by the Polanyi potential theory of adsorption particularly if the adsorption temperature is much less90 LOW PRESSURE ADSORPTION HYSTERESIS than the critical temperature of the adsorbate.Adsorption of carbon tetrachloride on activated cellulose and polyacrylonitrile carbons obeys the Dubinin-Kaduskevich equation l4 : where the adsorption potential E = RTlog P,/P, V = volume adsorbed at P/Po, Vo is the micropore volume and p is a constant. Fig. 6 and 7 show typical isotherins plotted according to the linear form of eqn ( 3 ) from which V, may be estimated assuming that pa = p l , the density of the liquid adsorbate. Assuming that the potential theory of adsorption is appropriate and with the additional assumption of ideal behaviour by the free adsorbate gas, eqn (2) becomes V = V, exp( - fie2) (3) pa = (RTlog P)/V (4) where Vis the molar volume of the liquid-like adsorbate.Flood and Heyding lo have shown that for a volume element, Vt = V,+ V,, of the adsorbate-adsorbent system or where pc is the mean volumetric stress intensity of the adsorbent in the volume element. In this context, the volume element of Flood and Heyding l o may be equated to the domain of Bailey et a2.I V,P,+ VCP, = (Va+ VCP P c = P(1 + 4 > - 4 P a ( 5 ) I I I 1 0.4 0.8 1.2 1- log* POiP 60 7; BO 45 % BO 25 % BO FIG. 6.-Adsorption of carbon tetrachloride vapour on activated cellulose carbons at 20.0"C plotted according to the Dubinin-Radushkevich equation.B . MCENANEY 91 . 30% BO 12% BO log2 P,lP FIG. 7.-Adsorption of carbon tetrachloride vapour on activated polyacrylonitrile carbons at 20.0"C plotted according to the Dubinin-Radushkevich equation.The relatively small increases in adsorption of carbon tetrachloride at P/Po > 0.3 on the activated carbons (fig. 1 and 2) support the view that the majority of micropores are filled in these carbons at P/Po<o.3. Accordingly for microporous volume elements of carbons, 4 is effectively constant in the range P/Po = 0.3 to 1.0 and may be estimated from # = VOpHc where pHe is the helium density of the carbon corrected for adsorption.2* The values of 4 so calculated must be regarded as typical, since, in practice, a range of values of 4 would be expected in the various domains or volume elements of the solid adsorbent. If eqn (4) defines pa then for adsorption of carbon tetrachloride at 20°C in the range P/Po = 0.3 to 1.0 (P = 3.5 to 10.6 kN m-2) pa%P and thus from eqn ( 5 ) : Values of pc estimated from eqn (6) for adsorption of carbon tetrachloride on cellulose and polyacrylonitrile activated carbons are given in table 2, where it can be seen that pc increases with activation, reflecting the increase in 4.Externally applied compressive stresses, CJ, in porous carbons may be separated into stresses transmitted through adsorbate, CJ,, and adsorbent, nc, by an analogue of eqn (5). If it is assumed that stresses transmitted through adsorbate may be neglected under the conditions of the compression test on the carbons, then compressive fracture strengths, cf, (table 1) may be corrected for the presence of porosity by pc 21 -(+ RTlog P ) p .(6) c c = q ( l + 4). (7)92 LOW PRESSURE ADSORPTION HYSTERESIS Values of oc for the activated carbons are also included in table 2, where it can be seen that although of decreases with increasing activation (table 1) values of o - ~ are inde- pendent of the degree of activation within experimental uncertainty. TABLE 2.-CALCULATED STRESSES IN POLYMER CARBONS volume -pcKMNm-2) BO/( %) ratio, d* n,/(MN in-2) (PIP0 = 0.3) (PIP,, ~ 1.0) cellulose carbons 25 0.59 23.6 I22 138 45 1.04 21.7 214 243 75 1.79 24.3 3 69 41 9 60 1.44 23.9 297 337 pol yacryloni tri le carbons 12 0.07 13.8 14.3 16.1 30 0.14 11.5 28.2 32.0 83 0.77 13.3 157 179 48 0.21 10.7 42.3 47.9 *PHe = 1.9 8 ~ ~ l i - ' . ~ As previously mentioned, compressive stresses resulting from bridging of micro- pores may occur in carbons in addition to dilational stresses such as those calculated from eqn (6).Flood has shown l 2 that where directional stresses occur in an adsor- bate such as those resulting from bridging of micropores eqn (2) must be modified to and, applying the same assumptions as before, eqn (6) is modified to pc 21 - ( 4 RTlog P)/V+6$ (9) where, in this case, $ is the contribution to pa due to bridging potentials. It is expected that the Contribution of $ to pc will increase in the range P/P, = 0.0 to 0.3 as micropores fill but make a constant contribution to pc at higher relative pressures. The fact that volume contractions for microporous carbons are found at low adsorbate pressures suggests that $ > (RT log P ) / B in the early stages of adsorp- tion, and assuming this to be so, an estimate of @ may be obtained from measured volume contractions.Dacey and Evans l 3 have recently reported maximum volume contractions dV/Y, = for adsorption of benzene, methanol and water vapour on microporous Saran carbons which they attribute to bridging in micropores. For small volume contractions dV/V, = ti$' where $' is the bulk compressive stress of the adsorbate-adsorbent system due to bridging potentials and, using a value of the compressibility (K = m2 N-l) intermediate between those for single crystal graphite and diamond l5 a value of @' = lo8 N mA2 is obtained. The compressive stress calculated above and the dilational stresses estimated from eqn (6) may be compared with the values of 0, for cellulose and polyacrylonitrile carbons (table 2) and with the range of bulk fracture strengths found for carbons and graphites in general (from lo6 N m-2 in tension to lo8 N m-2 in compre~sion).l~-'~ It can be seen that the calculated stresses are either greater than or approximately equal to the bulk fracture strengths. Thus the proposition that low-pressure adsorp- tion hysteresis in microporous carbons is caused by localised fracture is consistentB.MCENANEY 93 with the finding that calculated compressive and dilational stresses induced in volume elements or domains in carbons by adsorption are commensurate with or greater than stresses which are found to cause bulk fracture. In additional support of this view, bulk fracture resulting from adsorption on poly(viny1idene chloride) carbon pellets which exhibit low-pressure hysteresis has been reported. Although localised fracture may occur as a result of adsorption, it does not follow that bulk fracture will always occur since the work expended in localised fracture in volume elements or domains within the carbon may reduce the stresses induced by adsorption to a value below the minimuin fracture stress for further crack propagation.Additionally, it may be necessary for adsorption-induced stresses in adjacent domains to act co-operatively before bulk fracture can occur. It has been noted that the extent of low-pressure hysteresis decreases with increas- ing activation for cellulose and polyacrylonitrile carbons (fig. 1 and 2) although, with apparent lack of correlation, the calculated values of adsorption-induced stress, pc, increase with activation (table 2). This is because low-pressure hysteresis is only observed if localised fracture reveals microporosity which was previously inaccessible to the adsorbate molecule and, as previously noted for cellulose carbons, microporosity which was inaccessible to the carbon tetrachloride molecule is progressively reduced by activation.2 CONCLUSIONS It is concluded that the theory of adsorption-extension of Flood and Heyding offers an interpretation of low-pressure adsorption hysteresis. Application of the theory to sorption of carbon tetrachloride in microporous polymer carbons has shown that calculated stresses in carbons induced by adsorption are commensurate with experimental bulk fracture strengths.The theory appears capable of accounting for pressure and temperature threshold effects associated with low-pressure hysteresis, since, from eqn (6), the adsorption-induced stress, pc, is directly ,proportional to temperature and the logarithm of pressure. The apparently anomalous adsorption effects which Bailey et al.' have attributed to collapse of pores due to compressive stresses may be understood qualitatively in terms of eqn (9) when $%(RTlogP)/F Further work is necessary to determine the extent to which the theory of adsorption- extension can be quantitatively applied to low-pressure adsorption hysteresis. For example, further theoretical work is required to describe the development of compres- sive stresses due to bridging of micropores by adsorbate molecules and experimental work is required to test the ability of the theory to accurately describe presssure and temperature threshold effects.NOTATION dV/Vt volumetric strain induced by Pa,pc K compressibility of the adsorbent Va, Vc, Vt volume of adsorbate, adsorbent adsorption (m2 N-l) and adsorbate+ adsorbent res- pa, pe, pl pectively (ml g-l) = VJV, PHe a dimensionless structure factor P, Po vapour pressure and saturated vapour pressure of the adsorbate, respectively (N m-2) a 4 Ks for porous adsorbents v V mean volumetric stress intensity of the adsorbate and adsorbent, respectively induced by adsorp- tion (N m-') density of adsorbate, gas and liquid respectively (g ml-l) helium density of the adsorbent (g ml-l) molar volunie of the adsorbate (ml mol-l) volume of micropores filled at PIP0 (ml g-9 = Pa/P94 LOW PRESSURE ADSORPTION HYSTERESIS N 0 TAT I 0 N-continued vo micropore volume of the adsorb- oar oC, 0 volumetric stress intensity of ent (ml g-l) adsorbate, adsorbent and adsorb- constant of the Dubinin-Radush- ate+ adsorbent respectively due kevich equation (mol" J-") to externally applied stresses contribution to pa due to bridging compressive fracture stress of the potentials in micropores (N m-") adsorbent (N m-").bulk compressive stress due to bridging potentials (N m-") P $ $' & adsorption potential (J moI-') (N m-2) of A. 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Flood, Proceedings of the 4th Conference on Carbon (Pergamon, New York, 1960), p. 3. l3 J. R. Dacey and M. J. B. Evans, Carbon, 1971,9, 579. I4 M . M. Dubinin, Chemistry andPhysics of Carbon, ed. P. L. Walker Jr. (Arnold, London, 1966), vol. 2, p. 51. W. N. Reynolds, Physical Properties of Graphite (Elsevier, London, 1968), p. 35. l6 R. E. Nightingale, Nuclear Graphite (Academic Press, New York, 1962), p. 150. C. L. Mantell, Carbon and Graphite Handbook (Interscience, New York 1968 ), p. 24.