J.C.S. Faraday I , 1980,76,2472-2485Study of Molecular Sieve CarbonsPart 2.-Estimation of Cross-sectional Diameters of Non-sphericalMoleculesBY JACOB KORESH AND ABRAHAM SOFFER*Atomic Energy Commission, Nuclear Research Center-Negev,P.O. Box 9001, Beer-Sheva, IsraelReceived 19th November, 1979The estimation of molecular dimensions by various experimental methods is discussed and theirrelevance to non-spherical molecules is evaluated. Liquid molar densities provide an average dimensionwhich is adequate for spherical molecules but completely insensitive to molecular shape. The combina-tion of bond lengths and van der Waals radii enables one to estimate satisfactorily the length of linearmolecules but not their width. The kinetic diameters calculated from different physical properties ofgases diverge significantly and are insensitive to molecular shape.Adsorption in molecular sieve(MS)solids exhibit high sensitivity to the width or smallest dimension of the molecule. Molecular sievecarbons (MSC) seem promising in this respect since their avera e pore diameter can be tailored to theexact critical dimension of any molecule in the range 3-5.51 studied so far. The combination ofadsorption stereospecificity data and liquid molar volumes provides reasonable numerical estimates ofthe width of non-spherical molecules. Polar molecules may have different dimensions depending onwhether the carbon surface is polar (oxidised) or non-polar. Hydrogen acquires a surprisingly largewidth which is in accordance with its high liquid molar volume.Adsorbent-adsorbate interactions playa crucial role in determining molecular dimensions and serve to elucidate the unusual behaviour of bothhydrogen and polar molecules. An overview of the concept molecular dimension is given in terms of theeffect of intermolecular forces.It has been shown previously' that: (1) The pore opening in molecular sievecarbon (MSC) derived from the same material can be adjusted to any desirablevalue from 3.1 8, to at least 5 8, by stepwise mild thermochemical treatments. (2) Ahigh adsorption stereospecificity, comparable with that of zeolite molecular sieves(MS), can be maintained over the entire pore dimension range. These two proper-ties enable one to sort various small molecules according to their molecular dimen-sions, by determining their penetration into an ultramicroporous structure.In thisrespect, MSC seem to have more advantages than crystalline MS, since in the lattercase the change of pore dimension involves essentially the synthesis of variouscrystalline materials. Accordingly pore dimension changes should still occur insteps while practically any value could be achieved by modifying carbons within thespecified range.In this work on the assessment of molecular dimensions, comparison with othermethods is made and any discrepancies are elucidated. Some questions, such as thatof the dependence of the results on specific adsorbent-adsorbate interactions andthe type of critical molecular dimension which determines absorbability, are thenconcerned.247J .KORESH A N D A . SOFFER 2473SOME COMMON METHODS OF ESTIMATINGMOLECULAR DIMENSIONSESTIMATION FROM MOLAR VOLUME OF THE CONDENSED PHASEThis is probably the most accepted approach to estimating molecular dimensionsin surface chemistry. It assumes a close packing of spheres2 so thatwhere d is the diameter, A4 the molecular weight, p the condensed phase densityand N is Avogadro’s number.To our knowledge, however, eqn (1) has not been applied in any systematic studyof MS absorbents, probably because it does not correlate well with the experi-mental molecular sieving sequence of non-spherical molecules. For non-sphericalmolecules, however, this approach must not be ruled out and some shape factorshave to be accounted for.ESTIMATION FROM B O N D LENGTH A N D V A N DER WAALS R A D I IIn order to obtain a molecular dimension by this method bond lengths have tobe completed by the dimensions of the non-bonding electron clouds of the outeratoms of a molecule, i.e.by the van der Waals radii3 These have been estimated forthe most abundant covalently bonded atoms and groups, as an average of values toan accuracy of kO.1 A. However, the van der Waals radii are only adequate in thedirection opposite to the covalent bond of the atom. At small angles from the bonddirection, the covalent atom radius may be as much as a few tenths of Angstromsmaller, as noted by P a ~ l i n g , ~ and it cannot then be estimated to any accuracy.This approach cannot therefore account for the width of linear molecules, althoughtheir length may be estimated from it quite successfully. This concept may alsoinclude estimations based on molecular model4ESTIMATION FROM COLLISION DIAMETERS I N THE G A S PHASEThis method is presently the most common one since it was found to correlatebetter than the former two with the sieving properties of mineral MS.5 The molecu-lar dimension is an essential parameter which appears whenever a gas propertywhich is sensitive to the “covolume” of the molecules (second virial coefficient,viscosity, diffusion) is calculated using a model of a potential energy function.Molecular dimensions considered by this approach relate to the average of allmutual orientations of the colliding molecules so that the molecules are consideredto be essentially spherical.Some studies by Kihara‘ and Corner7 allow for molecular shape in the calcula-tion of the second virial coefficient B(T) according to the Lennard-Jones potential.Kihara extended the work of Isihara and Hayashida,’ who provided a generalformula for the second virial coefficient of non-spherical rigid molecules, in the caseof “soft” interacting molecules. He obtained very satisfactory results of B against Tplots for both spherocylindrical and spheroidal H2, C02, N2 and C2H4 molecules.The obtained lengths and widths of these molecules were, however, different by afew tenths of 8, for the two models (table l), indicating that “from the second virialcoefficient alone it is impossible to assert generally which model represents rea2474 MOLECULAR SIEVE CARBONSTABLE 1 .-MOLECULAR DIMENSIONS (A) AS ESTIMATED BY VARIOUS METHODSobserved bond length and kinetic diameter (gas) liquid molar volumeincreasing van der Waals radii width and length’ average shape correctedsequence width length spherocyl ellipsoid average” (d) d/2’Ib width length3.7w 4.6W4.53 4.03 3.1 5.56 co2 2X5 5.38 5.9L 5.09L 4B00, 2.8 4.01 3.54 4.0 3.51 3.28 3.99C;H2 5.72 4.22 4.6 4.1 3.33 5.63H2 2.4516 3.15 4.06 3.62 3.44 3.852.81W 3.24W3.55L 3.32L 2.973.41 ;- 4.09W ;-N2;Ar 3.0;-’s6 4.1;- 4.57~;- 4.29~;- 3.15; 3.42 3.85; 3.6 3.59; 3.6 3.59; 3.6 4.2; 3.6SF6 4.53* 5.87* 5.51 5.63 5.02x, 4.05 4.42 3.94 3.94 3.94* Calculated from molecular model.molecules more closely”.It seems, therefore, that the second virial coefficient is, ashas been also stated by Hirshfelder et al.,9 quite indifferent to molecular shape, sothat the latter caniiot be assessed at the accuracy needed to account for the highadsorption stereospecificity of zeolites5 and MSC.’ Insensitivity to molecular shaperesults from the shape factor f of rigid non-spherical molecules derived by Isiharaand Hayashida.8 This value is obtained by integrating over all mutual positions oftwo colliding molecules allowing equal probability for all orientations.Thus, thestatistical contributions of the closest and farthest positions of non-spherical mol-ecules are only fractional and therefore a tendency for averaging should be expectedwhenever covolume dependent properties are studied.EXPERIMENTALAdsorption measurements were carried on in a volumetric high vacuum system.Pressureagainst time curves were recorded, from which adsorption against time curves were obtained.The starting amount of gas was so chosen that the initial pressure in the adsorption cell was6 M 5 Torr for all experiments. The starting material which had been treated to obtain differentpore openings was a fibrous carbon cloth TCM 128, a product of Carbon-Lorraine, France.Other experimental details were as described previously.’CRITICAL MOLECULAR DIMENSION CONTROLLINGMOLECULAR SIEVINGThe accumulated data on adsorption on solid MS indicate clearly that the mol-ecules occluded during adsorption are preferably oriented so that their passagethrough the pores is determined by their smallest dimension.For instance, pre-ferred adsorption of normal over branched paraffins occurs on both minerallo~’’and carbon MS.12313Also, Dubinin et al. found that adsorption of benzene was considerably betterthan that of cyclohexane on MSC.I4 This behaviour clearly indicates that thenarrower normal paraffin and the flat benzene molecule are aligned parallel to thepore during their migration into it. The same results are obtained from the adsorb-ability of the simpler axial molecules carbon dioxide and acetylene, which areadsorbed on NaA zeolite after partial exchange with potassi~m,~ while the“shorter” nitrogen molecule is not adsorbed.We have previously observed’ that these molecules behave similarly on our MSCand we found evidence of the parallel orientation of benzene in slit-like pores.Wehave also found that dinitrogen oxide is adsorbed in preference to nitrogen, asshown in fig. 1. In conclusion, the smallest dimension of non-spherical molecules iscritical in controlling their penetration into ultramicroporesJ . KORESH AND A . SOFFER 24750.50.44'w 0.3E-i2s 0.20.100000001 2 3 4 5 6tlminFIG. 1.-Adsorption kinetics of dinitrogen oxide on C-250-4.' In this case nitrogen as well as hydrogenare completely excluded from the pore system. V, is the initial adsorption rate, 220 pmol min- ; initialpressure 60 Torr. T,d = -80°C.OBSERVED SEQUENCE OF ADSORBABILITY I NRELATION TO MOLECULAR DIMENSIONThe experimental sequence of adsorbability is given in table 1 together withmolecular dimensions calculated by different common methods.In this table anytwo molecules are considered to have different dimensions if we could develop aMSC for which the ratio of their initial rates of adsorption into the pores was atleast one thousand.? Except for the last two columns on the right, which will bediscussed in the next section, no other columns correlate with the experimentalorder over the whole span of adsorbates studied. In the following, each columndealing with width or average dimension will be discussed in detail. The inadequacyof the van der Waals width frequently used as a measure of the smallest dimen-si0n~9~ has been shown above.By this approach carbon monoxide, carbon dioxideand oxygen would have the same dimension, namely that of a chemically boundoxygen atom (2.8 A). Also, N 2 0 would have the same width as nitrogen (3 A).However, a net preference of N 2 0 adsorption over N2 (fig. l), of C 0 2 adsorptionover O2 and of the latter over CO is manifest. An even more significant discrepancyis shown by hydrogen, which exhibits a surprisingly large dimension in completecontrast to its van der Waals radius. The last four molecules presented in table 1 fitthe experimental sequences according to all approaches presented, presumablyt Such high selectivities (hence sensitivity to molecular dimension) were obtained for a closed porestructure. Under such conditions the rate was so slow that frequently equilibrium values of adsorptioncould not be obtained after any reasonable time.Whenever these could be estimated we observed that atsimilar and fairly low pressures they differed by only a small amount, in contrast to the orders-of-magnitude ratios in the initial rate. This is in accordance with the view' that the pore volume iscomposed of relatively large, poorly stereoselective pores with few constrictions responsible for molecu-lar sieving, which is therefore mainly of kinetic origin2476 MOLECULAR SIEVE CARBONSbecause of their proximity to the spherical shape, and mainly because of the largedimensional differences between them. The kinetic diameter in the gas phasepresents a different sequence which deviates from the experimental one mainly withregard to elongated C02, C2H2 and N 2 0 (c = 3.8 A) molecules.This could resultfrom averaging the overall orientations of the linear molecules, and thereby greatlyreducing their sensitivity to shape. Beyond any shape considerations, the relativelysmall dimension of hydrogen is in complete disagreement with adsorption experi-ments. The hydrogen molecule exhibits an extraordinarily large dimension in theadsorbed state. The same behaviour is exhibited by the average dimension calcu-lated from the liquid molar density, according to eqn (1) (to be discussed later). Asin the case of the kinetic diameter the liquid molar volume sequence does notcorrespond to the observed one for the elongated C 0 2 and C2H2 molecules, whichsuggests the necessity of shape corrections.As a frame of reference for the average molecular dimension, we preferred dataobtained from liquid molar density rather than those from the kinetic theory ofgases because of (1) the better correspondence of the hydrogen dimension; (2) theadsorbed state being closer to a condensed state than to an ideal gas; (3) wideravailability of data on liquid density, especially in case of large organic moleculeswhich will be studied in the future.It is also a well accepted method of estimatingcross-sectional areas of adsorbates on open surfaces from liquid molar volumes.ESTIMATION OF MOLECULAR DIMENSIONAND GEOMETRYThe objective of this section is to assign simple, geometric shapes and numericalestimates of dimensions to adsorbate molecules in such a way that: (1) the widthcalculated will correspond to the experimental adsorbability sequence.In particu-lar, the width of the N2 molecule has to fit the argon atom dimension, since theiradsorbabilities are equal. (2) The average molecular dimension of a molecule justpassing a narrow constriction will be 21/6 smaller than its average dimension in theliquid phase.The reason for the factor 21/6 is given below. Taking the liquid phase dimensionof adsorbate as a reference, we recognise that the liquid molecular diameter standsfor the average dimension at the minimum of the intermolecular potential function.However, the critical dimension for the passage through the pores of a MS isreckoned at the zero value of the potential energy.’?Adopting the Lennard-Jones (6,12) potential for the non-polar molecules treatedin this section, the average critical dimension of molecules passing a pore would be0 = d/2Ii6.(2)We obviously attributed a spherical shape to the noble gas atoms and also to the“globular” SF6 molecule.To the linear molecules studied so far we attribute a spherocylindrical or aprolate ellipsoidal shape with the foci located at the nuclei of the edge atoms.Although arbitrary, these geometric shapes, considered also by Kihara,6 assume thegenerally accepted “shape” of linear molecules, which is sharpened at the edges andhas cylindrical symmetry. We will furthermore make use of this arbitrariness byt This implies, very reasonably, that the dimension of a molecule in contact with the walls of a narrowpassage corresponds to a nil interaction.In fact, thermal activation may enable the “squeezing” of evenlarger molecules through pores leading to a slight difference in their dimensionsJ . KORESH AND A. SOFFER 2477trying fractional contributions of spherocylindrical and ellipsoidal shapes so thatthe molecular width can fit the observed sequence of adsorbabilities. According torequirement (2) above and to eqn (2) we equalise the volume of the adsorbatemolecule to that of a sphere of diameter 0. Thus for a spherocylinder we have:where r is the radius, 1 is the sum of bond lengths and o is the average diameterfrom the liquid phase. For a prolage ellipsoidal molecule we have:a = JFZwhere b is the minor axis, a is the major axis of the ellipsoid and c is half of the sumof the bond lengths.The widths 2r and 2h can therefore be calculated from eqn (3) and (4).Thecorresponding values obtained for various molecules are given in table 2 in theobserved sequential order. The numerical width values do not agree with this order.We took, therefore, fractional contributions of spherocylinder and ellipsoid in theform of arithmetic averages of the widths and lengths of the two shapes, for alllinear molecules except C02 for which pure spherocylindrical geometry is retained.The results, which are given in the last two columns of table 1, indicate a fullcorrespondence of widths with the experimental sequence including the coincidenceof the N2 width with the diameter of argon.Another striking feature of theseaveraged values is that the lengths are similar to the van der Waals lengths within0.2 A or less, so that they are not too far from reality. The hydrogen molecule isexceptional in this respect.It appears from tables 1 and 2 that the eccentricity of the pure ellipsoid moleculeis too small to account for both (adsorption) widths and van der Waals lengths,whereas that of spherocylinder too large, so that the average has had to be used. Ifa linear molecule acquires a shape of revolution its volume is given by the followingequation, which is a generalization of the left-hand side of eqn (3) and (4).v, = 4nM3f(4 (6)where E is the eccentricity (i.e. the ratio of length to width) and f ( ~ ) is a functionwhich describes the shape of the molecule (equal to E for an ellipsoid and $ 6 - fora spherocylinder).The use of the arithmetic average is equivalent to the applicationTABLE 2.--DIMENSIONS (A) OF SPHEROCYLINDER AND ELLIPSOID MOLECULES AS OBTAINED FROMEQN (3) AND (4)ellipsoid spherocylinderwidth length width lengthadsorbate (2b) ( 2 4 (24 (2r + 1)co2 3.1 5.560 2 3.5 3.7 3.06 4.27CzH2 3.72 4.98 2.95 6.27H2 3.6 3.67 3.29 4.04N2 3.8 3.95 3.37 4.42478 MOLECULAR SIEVE CARBONS3.03'on 2.0E * *-;1 -1.0of the functionf(e), which in terms of eccentricity is somewhere between an ellip-soid and spherocylinder. The large adsorption stereospecificity of MS imposes strictlimitations with regard to the widths of the molecules but leaves freedom to choosethe lengths from considerations such as crude correspondence with the van derWaals radii.Accordingly significant freedom to choose the shape function f(c) isprovided so that the choice of a simple arithmetic averaging is as adequate as thatof more elaborate methods.I---* -1, -t -EFFECT OF THE INTERMOLECULAR POTENTIALFUNCTIONS ON MOLECULAR DIMENSIONSO F ADSORBATESThe width exhibited by a molecule passing through a pore of a MS is dependenton its interaction with the walls, so that the greater the attractive force the smalleris the apparent width sensed in an adsorption experiment. In view of the extremelysteep repulsion potential it may be possible to consider the molecule and adsorbentas rigid bodies as far as molecular dimensions are concerned.However, the tem-perature dependence of the stereospecificity of MS clearly indicates that this is notthe case since molecules can be thermally activated to overcome narrow pores, i.e.to climb up the repulsive portion of the potential. This behaviour has already beenobserved by Maggs," who showed the increasing adsorption of nitrogen on coalwhen increasing the temperature from 77 K. Dubinin et a1.,16.'7 showed that woodcharcoal MS treated to adsorb oxygen in preference to nitrogen and argon at 77 Kaccommodated nitrogen and argon at 195 K. A similar behaviour was observed forargon and nitrogen on inorganic MS.'* We have also observed thermally activatedadsorption. A carbon thermally treated at 400°C (C-400) whose pores are relativelyopen to nitrogen showed adsorption isotherms having a normal temperaturedependence, as shown in fig.2. On the other hand a carbon with a more closedIA0I 1 1 . 1 I 1 I I 1 I 1 1 . 1 I I I I 1 1 I I I10 50 100 150 200p/Torr**0 AAY aFIG. 2.-Adsorption isotherm of nitrogen at two temperatures and on two differently treated carbonsshowing the inversion of the normal dependence of isotherms for the more closed C-300 carbon due tothermal activation. *,- 196"C, C(400); U, - 196"C, C(300); A, -8O"C, C(300); @, -8O"C, C(400)J . KORESH AND A . SOFFER 2479structure (C-300) shows inversed temperature dependence so that a nitrogen iso-therm at 195 K is considerably higher than one taken at 77 K.A much more pronounced effect of the ability of molecules to be “compressed”through narrow pores is observed by comparing the behaviour of polar adsorbateson polar and non-polar carbon surfaces.As previously described’ the carbons usedso far had a substantial coverage of chemisorbed oxygen whose partial removalserved to enlarge the pore apertures. In most cases described, however, the removalof oxygen surface groups was far from complete. Degassing was mostly below500°C so that CO surface groups did not leave the surface. The various carbonsused so far should therefore be considered as having acquired polar surfaces andAAAAAa0 .AAa0aI l l l t l l l l l l l l l l ’ 1 5 10 15t/minFIG. 3.-Adsorption rates of A, HC1; I, HBr and 0, N2 on the non-polar carbon C-1100.K,,‘,, = 1100°C.will be termed polar carbons.A second way of adjusting pore dimensions is tosinter at temperatures above 800°C. Results indicating the possibility of gradualpore closure have been described previously by means of decreasing adsorptionrates of nitrogen.’ The sintered MSC differs from the polar carbon mainly in thealmost complete absence of oxygen surface groups, as is well known from otherstudies,” and it will be termed non-polar. The sequence of adsorbzbility of the fewnon-polar molecules which we examined was identical to that of the polar carbonpresented in table 1, namely C02 > O2 > H2 > N2.Highly polar adsorbates, however, behave very differently on polar and non-polar MSC.Thus, the adsorption of HBr (p = 0.8 D) on non-polar MSC is slightlyslower than that of N2, while the adsorption of HCl (p = 1.0 D) is faster, as shownin fig. 3. This indicates that the critical diameter of these two molecules is approxi-mately that of N2, i.e. slightly above and below 3.6 A, respectively (table l), inaccordance with the van der Waals (and ionic) radii of atomic chlorine (1.6 A) andbromine (1.85 A).3 These two molecules cannot be absorbed on a non-polar MSCwhich does not adsorb N2 but does adsorb H2 and C02. Polar MSC, on the otherhand, with narrow pores adsorbing only C02, does adsorb both of these gases, asshown in fig, 4, indicating that in this case a critical dimension of ~ 3 . 1 8, isexhibited by these molecules.The same effects of “shrinkage” in contact with pola2480 MOLECULAR SIEVE CARBONSMSC pores was found with methyl chloride ( p = 1.86 D). In fig. 5 the adsorptionrates of CH3C1 at 195 K and of CH3CN at room temperature are comparable withthat of H2 at 77 K, the rate ratio If,,/VcH,c, being 278. This ratio is inversed andbecomes 0.06 for polar carbon C-250-12 h* (fig. 6), indicating inversion of theadsorbability sequence of these two molecules. The sequence inversion is muchmore profound with CH3CN as observed by comparing fig. 5, where the CH3CNadsorption rate on C-1200-1/4 h is comparable with that of H2,Jf with fig.7, whereits adsorption rate on C-100-17h is faster than that of C02. In this case the“shrinkage” of CH3CN due to the polar surface may be estimated to be >0.3 A.In order to understand this behaviour, a deeper view of the role of intermolecularforces in determining the penetration of molecules into molecular sieving pores isA05 10 15 20tlminFIG.4.-Adsorption rates of A, HC1; 0, HBr and D, C 0 2 on polar carbon C-100.necessary. The adsorption energy of pores of molecular dimensions was recognizedto be considerably higher than the adsorption energy on a single plain surface.Calculations by Everett and Powel2’ based on a Lennard-Jones type potentialshow that the highest ratio of the minimum potential energy of an adsorbate withina slit shape pore to that of an open surface is 2. The maximum ratio occurs at ad/ro, for which 2d is the distance between the foci of nuclei on the opposite walls ofthe pores and ro is the regular zero-energy distance of the two-particle potentialfunction.We may generalize some of Everett’s potential-energy drawings to anyother potential-energy function, provided they exhibit a minimum and a re-pulsive portion. Fig. 8A describes various potential energy curves for a molecule* This designation implies that the high temperature treatment is degassing at 250°C for 12 h. t On a carbon with longer degassing time the C-1200-1 h adsorption of both CH,Cl and CH3CNceased completely while that of hydrogen continued. Prior to degassing at 1200°C both C-1200-1/4 hand C-1200-1 h were degassed at 1000°C for 1 h to assure the removal of surface oxygen groupsJ . KORESH AND A . SOFFER0.157 0.14n3 i2 E248 1--AA3I I I 1 1 1 1 I20 60 100 140 180t,lSFIG.5.-Adsorption rates of CH3C1, CH3CN and H2 on the non-polar carbon C-1200-1/4. @, H2,V, = 780pmol min ', rJld = -196 C; ., CH,CN, V, = 260,umol min-', T,d = 24'C; A, CH3C1,V, = 2.8 pmol min TId = -80 C.between two opposite walls of a pore. Our view is that the pores of an MSC aregenerally not dimensionally homogeneous so that constrictions are responsible formolecular sieving. Thus the distance between the walls in fig. 8A corresponds tothat existing between the constrictions in fig. 8B. The potential minima existingwhen the walls are far apart coincide with a lower minimum when they are close toeach other so that the attractive portions of the molecule for single wall interactions' AAAAAA810 30 50 701 :minFIG. 6.---Adsorption rates of CH3Cl and H2 on polar C-250-12h.A, CH3C1, V, = 31.7 pmol min-',7&,, = -80 C; @, H2, V, = 2.1 pmol min-l, Kd = - 196 C.1-72482 MOLECULAR SIEVE CARBONSAA5 10 15tlminFIG. 7.-Adsorption rates of CH3CN and COz on the polar carbon C-100. A, COz, Vo = 8.23pmolmin-', T,d = -80°C; 0, CH,CN, Vo-85.7 pmolmin-l, Kd = 24°C.overlap. As the walls come closer to each other, the minimum is raised due to theoverlap of the repulsive portions until the pore becomes impermeable. In contrastto fig. 8, fig. 9 describes the changes in potential energy when an adsorbate movesalong a pore with varying widths starting from a very wide aperture with twoseparate minima.The abscissa in fig. 9 is the adsorption coordinate which is moreor less parallel to the walls. In this figure two types of activation of passage throughconstrictions are evident : desorption activation [column (b)] and normal activationEI IIFIG. 8.-A, Potential energy E of a molecule of a diameter 2ro as a function of distance (d) between thewalls; E is the minimum potential for d 4 00. B, Lowest energy positions of the molecule in a pore withconstrictionJ. KORESH AND A . SOFFER 2483AE 0 -e2s -( a > ( b ) ( C ) ( d 1FIG. 9.-A, Potential energy E as a function of the adsorption coordinate into a pore of varyingdimensions. B, Corresponding lowest energy positions along the coordinate; dashed line, minimumenergy pathway (adsorption coordinate); (a) walls far apart compared with yo, unactivated adsorption(d > ro), (b) desorption activation from the pore (d = yo), (c) normal activation through a constriction(d < yo), (d) constriction practically impermeable (d < yo).[column (c)].In fig. 10(a) we added an attractive potential to the drawing offig. 9(d), which represents an impermeable pore, in order to account for a changefrom a non-polar to a polar surface. The resultant potential shown in fig. lO(c) has aconsiderably lower activation energy so that the adsorbate molecule can penetrateinto the pore. Such a change probably shifts the whole scale of adsorbabilitytowards smaller pores but does not eventually severely affect the sequence as longas the attractive potential added is of the same type for all adsorbates.This may bethe case if all adsorbates were non-polar and a dipole-induced-dipole attraction isadded. [Numerical estimates of widths and lengths as those given in the last twocolumns of table 1 also remain unaffected as long as the adsorbability sequence isnot changed. Moreover, molecular dimensions are scaled primarily by a property ofthe pure adsorbate (liquid molar volume) whereas the sequence is introduced onlyEI I IFIG. 10.-Interaction energy plotted against adsorption coordinate of an adsorbate in a pore near aconstriction: (a) for a non-polar surface as reproduced from fig. 9(d), (b) additional attraction due tosurface polarity, (c) resultant curve for polar surface2484 MOLECULAR SIEVE CARBONSthrough shape corrections.] If, however, a polar molecule is examined against adimension sequence of non-polar molecules, the dipole-dipole potential added isconsiderably greater and will therefore shift the location of the molecule towards asmaller dimension in the non-polar molecule sequence.This is eventually the casewith HCl, HBr, CH3C1 and CH3CN.The unexpectedly large dimension of the hydrogen molecule (table 1) demon-strates intermolecular forces behaving in a way opposite to that in polar molecules.Its interaction with the surface is very weak compared with other non-polar mol-ecules of considerably higher polarizabilit y. This molecule cannot, therefore, comeas close to the walls as other molecules do.SIGNIFICANCE OF MOLECULAR DIMENSIONSMolecular dimensions are not of a well defined magnitude.This is mainlybecause the electron distribution function +b2 ( X , Y, 2) is assymptotic and vanishesonly at infinity. The distance ro for which the intermolecular potential functionbecomes zero can provide an adequate definition. This value depends, however, onthe nature of the second body which interacts with the molecule studied and itsinfluence cannot be neglected, at least as far as polar molecules are concerned. Ourview is that the dependence of molecular dimensions on environment has to beconsidered a reality so that the above definition must be adopted. In this sense, thetransfer of adsorbate molecules through MS pores provides a means of arrangingmolecules according to their width, while the influence of environment (walls) isalready taken into consideration. The question now is whether different series ofmolecular dimensions have to be expected for each set of experimental conditions.This is not necessarily so, since it has been shown above that only the dimensionsof very polar molecules change significantly according to the polarity of the walls.One could therefore deduce with certainty that the sequence given in table 1 isgenerally adequate for non-polar molecules in either polar or non-polar environ-ments. The term “environment” may in turn be generalized to biological mem-branes, thin-layer films, diffusive solids, gas mixtures etc.CONCLUDING REMARKSThe ability to change continuously the average pore dimension of MSC enablesThe change of surface polarity of the carbon makes it possible to demonstrate theThe molecular dimensions of spherical molecules in the liquid phase as a stan-one to order different molecules according to their smallest dimension.influence of environment on molecular dimensions.dard can provide numerical values for molecular width.REFERENCESJ.Koresh and A. Soffer, J.C.S. Farnday I, 1980,76,2457.2S. Brunauer, P. H. Emmett and E. Teller, J . Amer. Chem. Soc., 1938, 60, 309.3L. Pauling, Nature of the Chemical Bond (Cornell Univ. Press, Ithaca N.Y., 3rd edn, 1960).4A. N. Ainscough, D. Dollimore and G. R. Heal, Carbon, 1973, 11, 189.6T. Kihara, J . Phys. SOC. Japan, 1951, 6, 297.7J. Corner, Proc. Roy. SOC. A, 1948, 19% 275.‘A. Isihara, J. Chem. Phys., 1950, 18, 1446; A. Isihara and T. Hayashida, J. Phys. SOC. Japan, 1951, 6,9J. 0. Hirshfelder, Molecular Theory of Gases and Liquids (John Wiley, N.Y., 1964), p. 206.D. W. Breck, Zeolite Molecular Sieves (John Wiley, N.Y., 1974), pp. 634-6.40, 46J . KORESH AND A . SOFFER 2485'OR. M. Barrer, Quart. Rev., 1949, 3, 293; T. G. Lamond, J. E. Metcalfe I11 and P. L. Walker. Carbon,l 1 D. W. Breck, Zeolite Molecular Seives (John Wiley, N.Y., 1974), p. 640.l 2 J. R. Dacey and D. G. Thomas, Trans Faraday SOC., 1954, 50, 740.I3S. S. Barton, M. J. B. Evans and B. H. Harrison, J . Colloid Interface Sci., 1974, 49, 462.14M. M. Dubinin, E. D. Zaverina, A. T. Kaverov and Kasatochkin, Izv. Akad, Nauk S.S.S.R., Otdel.15F. A. Maggs, Nature, 1952, 169, 793.I6M. M. Dubinin, 0. Kadlec, 1. Botlik, E. 0. Zaverina, A. Zukal and B. Sumec, Dokludy Adad. Nauk,17M. M. Dubinin, 0. Kadlec and A. Zukal, Nature, 1965, 207, 75.I'D. W . Breck, J . Chem. Ed., 1964, 41, 678."S. S. Barton, D. Gillespie and B. H. Harrison, Carbon, 1973, 11, 649; S. S. Barton and B. H. Harrison,'OD. H. Everett and J. C. Powel, Trans Faradaji SOC., 1976, 72, 619.1965, 3, 59.khim. Nuuk. V , 1961, 1, 29.S.S.S.R., 1964, 157, 656.Carbon 1975, 13,47.(PAPER 9/1843