J. CHEM. SOC. FARADAY TRANS., 1994, 90(11), 1487-1493 Grand Canonical Monte Carlo Study of Lennard-Jones Mixtures in Slit Pores Part 3.t-Mixtures of Two Molecular Fluids: Ethane and Propane Roger F. Cracknell and David Nicholson* Department of Chemistry, Imperial College of Science, Technology and Medicine, London, UK SW72AY Mixtures of ethane and propane in a slit micropore at ambient temperatures have been simulated in the grand ensemble. Ethane was modelled as two Lennard-Jones sites and propane as three Lennard-Jones sites. A new type of selectivity-pressure profile, outside the Tan-Gubbins classification, has been noted. The mixed adsorp- tion of the two gases was found to be thermodynamically ideal. Molecular shape and pore size were found to play an important role in determining the extent of adsorptive separation.Much of the observed behaviour is shown to be entropy driven. For adsorptive separation of particular gaseous mixtures to be a viable industrial process, one component must be selec- tively adsorbed on a suitable microporous adsorbent relative to the other. Selectivity is controlled by a number of factors: the adsorbate-adsorbate interactions for like and unlike mol- ecules including the strength of adsorbate-adsorbent inter-actions, as well as geometric considerations such as micropore width and the size and shape of the adsorptive species. The techniques of molecular simulation are ideally suited to discriminate between the relative importance of these factors since model micropores and adsorbents can be defined in an unambiguous fashion on the computer.Molec- ular dynamics' and Monte Carlo have been used to model physisorbed mixtures. Other workers have used mean field density functional theory for the same Density functional theories have the advantage of being computationally faster than full molecular simula- tions; however, studies are at present limited to spherical par- ticles and effects due to molecule shape cannot be probed. On the basis of extensive DFT calculations, Tan and Gubbins' have introduced a classification scheme for selectivity iso- therms; in their class I, for cases where the temperature is significantly greater than the capillary critical temperature of the mixture, the selectivity isotherm shows a single maximum.Class I1 selectivity isotherms occur where the temperature is just above the capillary critical temperature and have double maxima. Class I11 and IV selectivity isotherms occur at tem- peratures below the capillary critical temperatures and are characterised by discontinuities corresponding to capillary condensation and layering transitions. This is the third of a series of papers from an ongoing study of various fluid mixtures in slit-shaped micropores. In the first paper,g we presented results for a grand canonical study of Lennard-Jones mixtures of methane and ethane in graphitic slit pores using spherical models for both com-ponents in order to facilitate comparison with the density functional theory calculations of Tan and Gubbim8 In that paper we established a methodology for performing GCMC simulations of mixtures in an efficient manner by using par- ticle interchange trials in addition to the familiar move, cre- ation and deletion trials.Comparison was also made between our simulation results and predictions made from the ideal adsorbed solution theory (IAST)' derived from single-component isotherms of the model ethane and methane; it t Part 1 :ref. 9. Part 2: ref. 11. was found that the IAST worked well for the system under study. In the second paper' ' we used a two-centre Lennard-Jones model for ethane and a spherical Lennard-Jones model for methane. Ethane molecules in the first adsorbed layer tended to lie with their axes either parallel or perpendicular to the wall, the relative distribution of orientations of molecules being strongly dependent on pore size.This was consistent with Sokolowski's observations for a two-centre Lennard- Jones model of oxygen in slit pores.12 For a full pore, a plot of ethane-methane selectivity us. pore size showed an oscil- latory behaviour as was also noted for the spherical ethane and methane. However, when elongated models of ethane were used, there were significant differences in the positions of maxima and minima. A logical extension of previous work is to study a mixture of two non-spherical particles; in this paper we present results for an adsorbed mixture of ethane, modelled as before by a two-centre Lennard-Jones particle, and propane, model- led as a non-linear three-centre Lennard-Jones particle.Method Potentials The Lennard-Jones (12-6) potential between sites i and j on two molecules is given by uij = -4Eij[($ -(?2)12] The interactions were cut (but not shifted) at 1.756 nm (five times the ethane CT parameter). The parameters used in the simulation are given in Table 1; E, CT are the usual Lennard- Jones parameters defined in eqn. (l),1 is the bond length and 8 is the bond angle. The model of ethane is due to Fischer et ~1.'~and that of propane is due to L~stig.'~ Both models have been shown to reproduce bulk thermodynamic properties accurately,' although we note that for propane other models exist with different geometries and energy parameters, which also accord with experimental thermodynamic properties;" the Lustig potential, however, has the advantage of having three identical Lennard-Jones sites, making it simpler to use from a computational standpoint.The graphitic surface was treated as stacked planes of Lennard-Jones atoms. The interaction energy between a fluid particle and a single graphite surface is given by the 10-4-3 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 potential of Steelel' 4 u,Xz) = 2xpsESf a:f A{ 1(3)"-(2r-52 3A(0.616 + z)~ (2) where A is the separation between graphite layers (0.335 nm) and ps is the number density of carbon atoms in graphite (1 14 &sfnm-3). osf and are the solid-fluid Lennard-Jones param- eters which were calculated by combining the graphite parameters in Table 1 with the appropriate fluid parameters using the Lorentz-Berthelot rules.The external field for a single Lennard-Jones site, dl),in a slit pore of width, H, is the sum of the interaction with both graphitic surfaces and can be expressed mathematically as U(l) = usf(z)+ u,(H -z) (3) (H is the C centre-(: centre separation across the pore). Since our immediate interest here is in equilibrium adsorption at ambient temperatures, we have not accounted for the surface structure of the graphite planes on the pore walls. It should be stressed that a slit pore bounded by stacked parallel layers of graphite represents only a model of a porous carbon, and it is not clear that this is necessarily the best representation; for example, some workers have considered a pore of triangu- lar cross-section to be a more appropriate representation of porous carbon~.'~ Comparison with Experimental Values of & To test the potentials for the simulation, we calculated values for the isosteric heat of adsorption at zero coverage for both propane and ethane on a single graphitic surface using the relationship j$ry w)exp[:-Pu(r, @I dt- do 4&= RT -L (4) exPC-P%(rY 41 dr do In eqn.(4), us is the energy of interaction between the pore and a molecule located at position r with orientation o, j9 = l/kT and L is Avogadro's constant. We used a Monte Carlo integration method with 1 x lo7 trial insertions in order to evaluate eqn.(4). In the limit of large H, there is no pore enhancement effect and the potential represents two separate isolated graphitic surfaces; it was necessary to evalu- ate 4& for single surfaces in order to facilitate unambiguous comparison with experimental data. Our results are sum- marised in Table 2. La1 and Spencer2' have collected various literature values for isosteric heats of adsorption of hydrocarbons on non- porous carbons; our calculated values for both ethane and propane fall within the scatter of the various experiments which gives us confidence in the potentials we are using. GCMC Technique The GCMC method is ideally suited to adsorption problems because the chemical potential of each adsorbed species is specified in advance.The chemical potential can then be Table 1 Potential parameters used in the simulations pair o/nm (E&) 0 I/nm ref. C,H,-C,H, 0.3527 119.57 90 0.216 14 C2H6--c2H,(2CLJ) 0.3512 139.81 -0.2352 13 C(graphite)-C(graphite) 0.340 28.0 --18 Table 2 4& values for adsorption on non-porous carbons; compari- son of potentials used in this work us. experiment adsorbate T/K theoretical experimental" C3H8 300 24.9 24.8-27.3 C2H6 300 18.6 16.0-19.7 a From ref. 20. related to the external pressure by use of an equation of state or by running GCMC simulation of bulk homogeneous adsorbate. We note that the isothermal-isobaric (NPT) Monte Carlo method has been successfully applied to the study of mixtures on a single s~rface;~ however, extension to problems involving pores is problematic because the pressure tensor normal to the walls cannot be equated to the bulk pressure.As in both of our previous papersg*" we used four types of trial, attempts to move particles, attempts to delete particles, attempts to create particles and attempts to swap particle identities. A detailed discussion of the method is given in ref. 9 and 11. The z dimension of the simulation box was equal to the pore width. Periodic boundary conditions were applied in the x and y directions; for a given simulation the x and y dimensions of the system were chosen so that ca. 100-250 molecules were present in the simulation. The minimum x and y box size was 3.527 nm, which is the minimum image distance for the potential used.No significant system size effects were observed. The simulations were generally run for 5 x lo6 configurations on Intel i860 processors in a Trans- tech 'parastation' with a PC front end acting as host. Sta- tistics were not collected over the first 2 x lo7configurations. The simulations took between 2 and 8 h for a single point depending on the number of particles in the system. The acceptance rate was particularly low for the smaller pore sizes studied (H < 0.762 nm) and 1 x lo7configurations were required for adequate convergence of the simulation (error bars are shown for the selectivities in Fig. 1). It is clear that studies of more complex mixtures in pores will require a biasing technique' to be computationally viable.II40 S 30 20 nL-0.0 0.1 0.2 0.3 0.4 0.5-10 0' I I 0 5 10 P/bar Fig. 1 Separation us. pressure profiles for a propaneethane mixture of equal bulk mole fraction at pore sizes H/nm = 0.763 (O),0.9525 (V), 1.143 (0)and 3.048 (A). The inset shows the low-pressure region in greater detail. T = 296.2 K. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Selectivity at Zero-pressure Limit The selectivity in the limit of zero pressure can be determined from extrapolation of low-pressure GCMC results. Alterna- tively, it can be deduced from the ratio of the one particle configurational integrals. Thus $ exp[ -/?u~RoPANE(r,o)]dr du, so = $riJva)]dr do (5) exp[ --fiuFTHANE(r, The integrals were calculated by Monte Carlo numerical inte- gration using 1 x 10’ trial insertions. Results and Discussion Selectivity Isotherms We use the conventional definition of selectivity22 as the ratio of the mole fractions in the pore to the ratio of the mole fractions in the bulk, thus the selectivity of propane over ethane is defined as where x refers to a pore mole fraction and y to a bulk mole fraction.Fig. 1 shows the selectivity us. pressure profile for various pore sizes at 296.2 K with equal bulk absolute activities [the absolute activity, z = exp(/3p)/(A3A,), with A the thermal de Broglie wavelength, and Ar the reciprocal of the rotational molecular partition function]. In the low-pressure limit, this is equivalent to equal bulk mole fractions (ye = y, = 0.5).At higher pressures there is some densification of propane in the bulk relative to ethane; thus, for example, at a pressure of 8.7 bar, y, = 0.54 with equal bulk absolute activities. Density functional calculations* show weak dependence of selectivity on mole fraction and the small difference in bulk mole frac- tions would not be expected to have a significant effect on selectivity. The simulated propane-ethane selectivity isotherms for the three largest pores in Fig. 1 would all be classified as type I in the classification scheme of Tan and Gubbins,” with the selectivity going through a maximum before decaying with additional pressure. The small pore (H = 0.762 nm) does not show the maximum and does not conform to any isotherm in the Tan-Gubbins classification.Experimentally, however, it is quite common: for example, Fig. 10 of the original paper on the ideal solution theory” (see below) shows a selectivity isotherm for a C02-C2H, mixture on an activated carbon at ambient temperature which has just this shape. In our paper on mixtures of methane and a two-centre Lennard-Jones model of ethane,’ we investigated the effect of arbitrarily elongating the ethane molecule when simulating mixture adsorption in a pore of a given width. We observed that the selectivity of ethane over methane decreased mark- edly with ethane molecular length at all pressures and the maximum in the selectivity isotherm also disappeared. As the molecular length increases, the number of orientations which do not cause repulsive overlaps in the system become fewer. Consequently the number of configurations which make a positive contribution to the configurational integral become fewer, or in other words the entropy decreases.The reason for maxima in selectivity isotherms is that the more strongly adsorbed component undergoes an element of cooperative filling which increases the selectivity above that observed at the zero-pressure limit for enthalpic reasons. For molecular fluids, however, a higher pore density increases the risk of one molecule ‘interfering’ with the rotation of another thus there is an entropic penalty associated with higher pore density. For sufficiently small pores (for example, the H = 0.762 nm plot in Fig.1) the entropic effect swamps the enthalpic effect and the maximum ceases to exist. Tan and Gubbins used spherical molecules in their density functional calculations and consequently could not possibly observe an entropic effect of the type we describe. Comparison with Results from Single-component Isotherms Experimentally, multicomponent isotherms are relatively dif- ficult to measure as compared to single-component data. It is useful therefore to be able to use single-component data to be able to predict multicomponent adsorption. For a pore of width H = 0.9525 nm we used GCMC to generate single- component isotherms for ethane and propane (Fig. 2). The adsorption is plotted as a density with the pore volume in that calculation including all the space between the two opposing planes of carbon centres.The isosteric heat of adsorption, qsT, was calculated, assuming the gas phase to be ideal, using the relation where 0 is the configurational energy per adsorbed particle. The calculated values are shown in Fig. 3. The differential (derivative) molar entropy of adsorption, As, can be defined in different ways, first as the difference between the differen- tial entropy of the adsorbed phase, s,, and the molar gas entropy, s, , at a particular temperature and pressure, in which case As1 = S, -S, = -qsT/T (8) where s refers to differential entropy. An alternative definition is the difference between the differential entropy of the adsorbed phase and the molar gas entropy at a particular reference state, S; (in this work we have taken the reference state to be a pressure of 1 atm) thus (9) The differential entropies of adsorption corresponding to the two definitions are shown in Fig.4. The definition of eqn. (9) 0 0 1 2 3 Plbar Fig. 2 Single-component isotherms for propane (V) and ethane (0) in a pore of width H = 0.9525 nm. The physical width, H (the dis-tance between carbon centres in adjacent graphitic planes) is used to calculate the volume of pore for the density shown in the figure. T = 296.2 K. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 related according to 25 1n(P0)= 7rno(p) d In p It is possible for example to calculate xi for a given P and yi by first solving for Po(n)in the equation This equation follows from eqn.(10) since the sum of the mole fractions in the pore must equal unity. To implement the IAST, it is necessary to choose a suitable fitting function for the single-component isotherms. We used two alternative fitting functions, the first a Langmuir-Freundlich (LF) isotherm of the form n(P)= x (KP)” 1 +(KPp where n is the uptake for a given pressure P and X, K and a are adjustable parameters. The advantage of using an LF fit is that the integral in eqn. (11)can be carried out analytically. A disadvantage is that it does not reduce to Henry’s law in the limit of low pressure. While for certain purposes this may not be a problem, it is the loading divided by the pressure which is integrated with respect to pressure in eqn. (1 1) and the low-pressure region makes a substantial contribution to the integral.23 An alternative function for fitting single- component data to the Langmuir uniform distribution (LUD) equation, which is the Langmuir isotherm modified for a patchwise heterogeneous surface, with m, C and s adjustable parameters is: 1 This does reduce to Henry’s law at low pressure but the inte- gral to determine the spreading pressure cannot be done ana- lytically, making it more cumbersome.We adopted essentially the algorithm suggested by Myers in the Appendix to ref. 23 in order to use the LUD equation in the IAST. As shown by Fig. 5, the IAST was found to work well for the pore size we tested it on (H = 0.9525 nm), with little dif- ference observed between the LF and LUD fitted single- 35 -5 0123456 ~/nrn-~ Fig.3 Isosteric heat of adsorption (single component) for propane (V) and ethane (0)us. density in a pore of width H = 0.9525 nm. T = 296.2 K. (which is shown with filled symbols) provides the more useful comparison between ethane and propane, since both sets of data refer to the differential entropy of the adsorbed phase minus the same constant factor. The differential entropy of adsorption for propane does decrease more sharply with pore fdling than is the case for ethane. This would appear to bear out the arguments used in the proceeding section concerning an entropic effect hindering selective adsorption of propane.The extent to which single-component isotherms can give information about mixed adsorption depends on the ideality of the mixing process: The ideal adsorbed solution theory (IAST)’’ is in essence Raoult’s law applied to adsorbed mix- tures ; comparison of IAST predictions from single-component data with mixture isotherms should give a good indication of the ideality or otherwise of the mixture. For a given component i, we can write Py, = Po(n)xi (10) where yi and xi are the bulk and pore mole fractions of i, respectively, P is the total bulk pressure and Po(7t) is the bulk pressure corresponding to spreading pressure 7t in the single- component isotherm of component i, for which Po and 7t are I I I I I I I I I I II-25 I 0123456 ~/nrn-~ Fig.4 Differential entropy of adsorption (single component) of V)and ethane (0,propane (0, 0)us. density in a pore of width H = 0.9525 nm. T = 296.2 K. The hollow points are As calculated by eqn. (8); the filled points by eqn. (9) taking 1 atm of bulk gas pressure as the reference state. I I 0 5 10 P/bar Fig. 5 Separation us. pressure profiles for a propane-ethane mixture of equal bulk mole fraction at a pore size of 0.9525 nm. Comparison of results from mixture GCMC simulation (0)with ideal adsorbed solution theory calculations from the single-component isotherms of Fig. 2 which were fitted by Langmuir-Freundlich (a) and Langmuir uniform distribution (b)fitting functions. T = 296.2 K. J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 component isotherms in Fig. 2. The IAST appears to underpredict systematically the selectivity by ca. 10-1 5%, indicating a limited degree of non-ideality. It would be unwise, however, to attempt to draw too many conclusions from the discrepancy since the mixture GCMC results are subject to a certain amount of statistical error because of low acceptance rates. In our previous studies of methane and ethane, the IAST was also found to give good results; however, in that study the LUD variant gave superior results to calculations based on fits to the LF equation. Effect of Pore Size on Selectivity The zero-pressure selectivity was calculated using eqn. (5) for various pore widths at 296.6 K.Selectivities (for equal absol- ute activities) at 8.7 bar were obtained from GCMC and results for both pressures are displayed in Fig. 6. The zero- pressure plot shows a single maximum. The selectivity decreases to the right of the maximum because the depth of the potential wells become less. The selectivity decreases to the left of the maximum because of a molecular sieving effect, with propane unable to enter the smallest pores. The molecu- lar sieving effect is also observed for the higher pressure; however, the selectivity does not decrease monotonically to the right of the first maximum. To attempt to understand the 1o2 10' 1oc lo-' 0.0 0.5 1.o 1.5 2.0 8 6 \ (04 2 9 0.991 0 ,o0 L I I I 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Hlnm Fig. 6 Separation us.pore size at zero pressure (line) and 8.7 bar (0)with equal bulk mole fraction of propane and ethane. (a)Plot showing results at both pressures, (b)plot showing 8.7 bar simulation results only. The particular pore widths marked are used in the density profiles. Fig. 7 Diagrammatic representation of centre of mass and vectorial direction for (a)propane and (b)ethane. The density profiles in Fig. 8 and 10 refer to the positions of the centre of mass. The orientations in Fig. 9 and 11 show the orientation of the vectorial direction shown in this figure relative to the line normal to the pore walls. molecular features underlying the variation of selectivity with pore size, we show distribution functions and snapshots for four pore widths [those pore widths are labelled on Fig.qb)]. Two types of distribution function are plotted, the density distributions refer to the density of centres of mass of par- ticles, for a given distance, r, from the centre of the pore. The angular distributions refer to the square of the angle between a particular reference vector on each molecule and the normal to the pore walls. The particular vectors are for propane the bisector of the CCC angle and for ethane, the C-C bond. The positions of centres of mass and the refer- ence vectors are shown in Fig. 7 for propane and ethane. Fig. 8 and 9 show the density and angle profiles for ethane at 8.7 bar. In the smallest pore (H = 0.762 nm) there is a narrow density peak in the centre of the pore and the angle distribution suggests that the ethanes are constrained to lie flat against the wall.For the next size of pore in the distribu- tions (H = 0.857 nm), there is again a sharp peak in the centre of the pore but the angle profile indicates that the ethanes are orienting themselves so as to have a methyl group in the energy minimum of opposite walls. The density profile shows a shoulder, which corresponds to some ethanes lying parallel to the wall. At H = 0.991 nm, the density in the centre has diminished considerably although the molecules are oriented so as to be almost perpendicular to the wall; there is a sharp density peak corresponding to ethanes lying flat against the wall. At H = 1.238 nm, there are virtually no ethane molecule centres in the pore centre (the noise in the angle profile in the centre is a consequence of this).There is a broad peak, corresponding to molecules lying flat against the wall, and a shoulder, corresponding to ethanes perpendicular I I mI E 35 +-h 0 0.0 0.1 0.2 0.3 rfnm Fig. 8 Density profiles for ethane in pores of widths (a)0.762, (b) 0.857, (c) 0.991 and (d) 1.238 nm. P = 8.7 bar. T = 296.6 K. 0.9 1 ' 1 -.-. L " ..I 0.00.0 0.10.1 0.20.2 0.30.3 r/nm Fig. 9 Angle profiles ((cos' 0)) for ethane in pores (widths as given in Fig. 8). P = 8.7 bar. T = 296.6 K. 0 is the angle between the normal to the pore wall and the C-C bond in ethane (see Fig. 7). to the wall, but the pore is now too wide for an ethane to span it and have methyl groups in the potential minima of both walls.Fig. 10 and 11 show the density and angle profiles for propane. The propane densities are higher because propane is more strongly adsorbed than ethane giving rise to the selec-tivity. In the pore of width 0.762 nm, the propane molecules are sterically constrained to lie flat. In the pore of width H = 0.857 nm, the minimum energy occurs when all three methyl groups lie in the potential minimum of a wall. One way to achieve this is for the molecule to lie flat against one wall; there is an entropic penalty to this and few propanes do it (although ethanes will lie flat, as evidenced by the shoulder in the H = 0.857 nm density profile).The other minimum-energy positions occur when one bond is parallel to the wall and one perpendicular (that the bonds can be exactly parallel and perpendicular is a consequence of the 90" bond angle in the propane model used here). From geometrical consider-ations it can be deduced that this situation corresponds to the maximum in the density profile and the shoulder at (cos' 0) = 0.5 in the angle profile. The other minimum-energy situation is to have the middle methyl group on one wall and the other two on the wall opposite, such is likely to be the case for particles with centre of mass in the pore centre. For H = 0.991, there is a small broad peak corre-sponding to propanes lying flat and a very broad central 80 70 60 0 50 E c 40-' r-Q 30 20 10 0 0.0 0.1 0.2 0.3 rjnm Fig.10 Density profiles for propane in pores (widths as given in Fig. 8). P = 8.7 bar. T = 296.6 K. The densities refer to the centres of mass of the propane molecules (see Fig. 7). J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 0.9 I I I 0.8 -0.7 -o.6 <(W NG0.5 -1 ,.-. ...8 0.4 -\ ;' '. . ,' '..(d) .a. I. ,I' ' ' ...../0.3 -,. .,,.,; .,.. .... .;. ; . .. .. Fig. 11 given in Fig.-8).P = 8.7 bar. T = 296.6 K. 8 is the angle between the normal to the pore wall and the bisector of the C-C-C angle in propane (see Fig. 7). peak of greater maximum density than that for the propane lying flat (in sharp contrast to the behaviour of ethane). The H = 1.238 nm density profile can be interpreted in terms of some propanes lying flat against a wall and a larger number with one or two methyl groups in the potential well of the wall.It is possible to provide an interpretation of the minima in Fig. 6(b)in terms of the structure of the adsorbed phase. At H = 0.762 nm both propane and ethane are constrained to lie flat; however, it is more entropically unfavourable for propane to lie flat than for ethane. At H =0.991 nm, it is energetically favourable for the adsorbate to pack into two layers flat against the walls, again it is much more entropi-cally unfavourable for propane to do so than ethane and another minimum in selectivity is found. Fig. 12 shows snapshots for ethane-propane mixtures in the pores of width 0.762 nm (a), 0.857 nm (b), 0.991 nm (c), 1.238 nm (4. Only the bonds are shown; the bonds for propane are black, those for ethane are grey.The planes of carbon centres in the graphite are also shown in black. Snap-shots only represent a particular configuration and do not necessarily give any indication of the configurationally aver-aged adsorbate structure; nevertheless, they can be used to help visualise the profiles in Fig. 8-11. For example, one can see that the adsorbate molecules are constrained to lie rela-tively flat in Fig. 12(a). In Fig. 12(b) a number of propane molecules have one bond parallel to the wall and one perpen-dicular, as suggested by the density profiles. In Fig. 12(c) we see the propanes distributed over a wide single layer whilst in Fig.12(4 we see two distinct layers emerging. Note the lack of recognisable ordering in an individual configuration, the ordering being revealed only by statistical averages (i.e. profiles). While this may not be too surprising at the tem-perature of the simulation, it does help us to understand why entropic effects are so important in determining selectivity. Conclusions We have presented results for selective adsorption of a two-centre Lennard-Jones model of ethane and a three-centre Lennard-Jones model of propane in model microporous carbons. We have shown that adsorbed molecular fluids can give a more diverse range of selectivity isotherms than adsorbed atomic fluids, We have found a new class of selec-tivity isotherm, frequently observed experimentally, but not hitherto seen by simulation or theory.This class of isotherm appears when the entropy considerations outweigh energy considerations, leading to a monotonic decrease of selectivity J. CHEM.SOC. FARADAY TRANS., 1994, VOL. 90 Fig. 12 Snapshots of ethane and propane in pores of width 0.762 (a),0.857 (b),0.991 (c) and 1.238 nm (d). P = 8.7 bar. T = 296.6 K. Equal bulk mole fractions. Only the bonds are shown, with C-C bonds shown as black in propane and grey for ethane. The planes of C centres in the pore walls are also shown as black. with adsorption. It is clear that the Tan and Gubbins classi- fication scheme,' although a major advance in the under- 6 7 E.Kierlik and M. L. Rosinberg, Phys. Rev. A, 1991,44,5025. 2. Tan, U. M. B. Marconi, F. van Swol and K. E. Gubbins, J. standing of adsorptive separation, is incomplete. The ideal adsorbed solution theory (IAST) can provide a quite accurate description of propane-ethane mixture adsorption, suggesting a reasonable degree of ideality of the adsorbed phase for this case. 8 9 10 11 Chem. Phys., 1989,90,3704. 2. Tan and K. E. Gubbins, J. Phys. Chem., 1992,%, 845. R. F. Cracknell, D. Nicholson and N. Quirke, Mol. Phys., 1993, 90,885. A. L. Myers and J. M. Prausnitz, AIChE J., 1965,11, 121. R. F. Cracknell, D. Nicholson and N. Quirke, Mol. Sim., 1994, in The behaviour of selectivity with pore size has also been investigated. At zero pressure, a single maximum in selectivity is observed.At higher pressures, several minima have been observed which we have ascribed to entropic effects. 12 13 14 15 the press. S. Sokolowski, Mol. Phys., 1992,75,999. J. Fischer, R. Lustig, H. Breitenfelder-Manske and W. Lemming, Mol. Phys., 1984,52,485. R. Lustig, Mol. Phys., 1986, 59, 173. R. Lustig, A. Torro-Labbe and W. A. Steele, Fluid Phase This project was funded under BRITE EURAM CON-TRACT BREU-CT92-0568. The authors thank Dr. N. G. 16 17 Equilib., 1989,48, 1. R. Lustig and W. A. Steele, Mol. Phys., 1988,65,475. S. Toxvaerd, J. Chem. Phys., 1989,91,3716. Parsonage of Imperial College, Prof, N. Quirke of ECCSAT, and Mr. S. Tennison of BP for their helpful comments and encouragement. 18 19 W. A. Steele, The Interaction of Gases with Solid Surfaces, Perga-mon, Oxford, 1974. M. Bojan and W. A. Steele, Ber. Bunsenges. Phys. Chem., 1990, 94,300. 20 M. La1 and D. Spencer, J. Chem. SOC., Faruday Trans. 2, 1973, 21 70, 910. R. F. Cracknell, D. Nicholson, N. G. Parsonage and H.Evans, References 1 S. Sokolowski and J. Fischer, Mol. Phys., 1990,71, 393. 2 F. Karavias and A. L. Myers, Mol. Sim., 1970,8,51. 3 D. M. Razmus and C. K. Hall, AIChE J., 1991,37,5. 4 J. E. Finn and P. A. Monson, Mol. Phys., 1992,72,661. 5 E. Kierlik, M. Rosinberg, J. E. Finn and P. A. Monson, Mol. Phys., 1992, 75, 1435. 22 23 Mol. Phys., 1990,71,931. D. M. Ruthven, Principles of Adsorption and Adsorption Pro- cesses, Wiley, New York, 1984. A, L. Myers, in Fundamentals of Adsorption, ed. A. L. Myers and G. Belfort, Engineering Foundation, New York, 1984. Paper 4/00546E; Receiued 28th January, 1994