J.C.S. Faraday I, 1980,76, 71-83Diffusion in 5A ZeoliteStudy of the Effect of Crystal SizeBY HAYRHTTIN YUCELt AND DOUGLAS M. RUTHVEN*Department of Chemical Engineering, University of New Brunswick,P.8. Box 4400, Fredericton, N.B. E3B 5A3, CanadaReceived 15th January, 1979The kinetics of sorption of CF4 and n-C4Hlo have been investigated in different size fractionsof two different 5A zeolites with different Ca2+ contents. The results show that in the larger crystalsthe uptake rate is controlled entirely by intracrystalline diffusion while, in the small crystals, ratesare controlled by the combined effects of external heat transfer and intracrystalline diffusion.Diffusivities are independent of crystal size but there are larger differences between the differentzeolite samples.For both CF4 and n-C4Hlo, diffusion in conimercial Linde 5A crystals is verymuch slower than in the laboratory synthesized zeolite samples. Corrected diffusivities for butanein the fastest diffusing zeolite sample are within an order of magnitude of the values estimated fromn.m.r. relaxation measurements.The need for additional detailed studies of diffusion in 5A zeolite to clarify thediscrepancy between the results of Karger et aZ.lS who, in a study of the sorptionkinetics of CzH6, C3HS and n-C,H,, in 5A zeolite, observed a strong dependenceof the apparent diffusivities on crystal size and our own results, for the 4A zeolite,which show no such variation of diffusivity, was noted in the preceding paper.3The results of such a study are reported here for two sorbates (CF4 and n-C,H,,)in two different 5A zeolites with different Ca2+ contents.CF4 diffuses quite slowlyin 5A zeolite and, since the heat of sorption is relatively small (w 5 kcal mol-l),thermal effects are negligible and the uptake curves can be analysed according to thesimple isothermal diffusion model. Within the experimental range of temperatureand pressure the CF4 isotherms deviate only slightly from linearity and the diffusivityis therefore not strongly concentration dependent. By contrast n-C4Hl, is morestrongly adsorbed. Diffusion is faster and, since the isotherms are highly non-linear, diffusivities vary strongly with concentration. The Beat of sorption is higher(m 11 kcal mol-l) and uptake rates in the smaller zeolite crystals are stronglyinfluenced by heat transfer limitations.EXPERIMENTALThe experimental procedure was similar to that described in the preceding paper.3Details of the zeolite samples are given in table 1.The 34 and 7.3 pm crystals (samplesla and lb) were prepared by Ca2+ exchange from the appropriate size fractions of the 4Acrystals used in the preceding study. The 55 and 27.5 pm crystals (2a and 2b) were alsoprepared from the same original batch of 4A crystals as sample l a (34pm). In order toachieve a high degree of Ca2+ exchange (> 95 %) the crystals were contacted with calciumchloride solution for a prolonged period and then separated by sedimentation into two sizefractions with mean crystal diameters 55 and 27.5pm.The crystal size distributions areshown in fig. 1.t Present address : Chemical Engineering Department, Middle East Technical University,Ankara, Turkey.772 DIFFUSION IN 5A ZEOLITEElectron micrographs showed that the crystals of samples l a and 16 were well formedcubes with no noticeable cracks or defects whereas surface striations and defects were clearlyevident in the crystals of samples 2a and 26. It is not known whether these occurred duringion exchange or sedimentation. Details of the chemical analysis, as well as SEM photo-micrographs are given in the thesis of Y u ~ e l . ~TABLE DE DETAILS OF ZEOLITE SAMPLESmean crystal sidesample % Ca2+* /Pm originl al b2a 26 {>%by ion exchangepreceding paper7.3 from 4A samples ofby ion exchange andsedimentation from4A sample l a ofpreceding paper* Expressed as % of original Na+ ions replaced by Ca2f.crystal size/pm16 are as shown previously.)FIG. 1.-Crystal size distribution for samples 2u and 26.(The size distributions of samples la anH . YUCEL AND D. M. RUTHVEN 73.3I xY .As1 .a1.61 . 41 . 21 . o0.40.20.00.0 50 100 150 200pressure/TorrFIG. 2.-Equilibrium isotherms for CF4 in 5A zeolite crystals (0, 55 pm ; A, 27.5 pm).values of the Henry constants (molecule cavity-' Torr-') are : (a) 273 K, 0.021 ; (b) 323 K, 4.7 xI I(c) 362 K, 2.0 x 10-3.11 .O[The10-3;0 10 20 30 40 502/^f/S+FIG. 3.-Comparison of uptake curves for CF4 in samples 2a and 2b (55 and 27.5 pm crystals of 5Azeolite) measured over comparable pressure steps at 323 K.The theoretical curves are calculatedaccording to the isothermal diffusion model with the time constants D/r2 = 4.3 x loe4 (26) and9.1 x s-l (24. p = 41-24 Torr (2b) and 38-27 Torr (k)74 DIFFUSION I N 5A ZEOLITERESULTS AND DISCUSSIONSORPTION A N D DIFFUSION OF CF4The equilibrium isotherms for CF4 on the 27.5 pm and 55 pm 5A crystals areshown in fig. 2. There i s good agreement between the data for the two size fractionsand, except at the lowest tempzrature (273 K), the isotherms are nearly linear overthe entire pressure range. Correlation of the Henry constants (K, defined by c = Kp)according to a van't Hoff equation [K = KO exp (qo/RT)] gave KO = 1.49 x(molecule cavity-l Torr-l) and qo = 5.17 kcal mol-l.These values may be com-pared with the values obtained previously for Linde 5A zeolite (lot no. 550 045) : 5KO = 3 . 8 ~ qo = 5.9 in the same units. Over the experimental temperaturerange the Henry constants for our own zeolite sample are thus slightly higher thanthe values for the Linde sample.Representative uptake curves for the two different size fractions (samples 2aand 2b), measured over similar pressure steps, are shown in fig. 3. The curvesconform well to the simple isothermal diffusion model and the difference in uptakerates is essentially as expected from the difference in crystal size.(4 (b) (c)." 5 10 40 100 10 40 100 10 40 100p/TorrFIG. 4.-Variation of diffusional time constants and diffusivities for CFq in 27.5 pin (0, 0 ) and55 pm ( x ) crystals of 5A zeolite (samples 2a and 2b) with sorbate pressure.(a) 273, (6) 323 and(c) 362 KH. YUCEL AND D. M. RUTHVEN 75Fig. 4 shows the diffusional time constants, calculated by matching the experi-mental uptake curves to the appropriate solution of the diffusion equation, dulycorrected for the distribution of crystal size, plotted against sorbate pressure. At362 K the time constants are essentially independent of pressure but at the lowertemperatures there is a small increase with pressure which can be satisfactorilyexplained by the non-linearity correction (D = Do d lnpld la c). The time constantsfor the two size fractions show the expected difference (by a factor of w 4) so thatat all temperatures diffusivities calculated for the two size fractions are essentially thesame.The temperature dependence of the limiting diffusivity (Do), correlatedaccording to an Arrhenius expression [Do = D* exp (-E/RT)], is given in fig. 10and in table 3.50 100 0 50 100 150 0 50 100 0plTorrFIG. 5.-Equilibrium isotherms for n-C4Hlo in 5A zeolite crystals. (Sample la, x ; lb, 0 ; k, 6 ;2b, 0 ; Linde lot 550 045, +). (a) 50, (b) 82 and (c) 87°C.SORPTION AND DIFFUSION OF n-C4H,,The equilibrium isotherms for n-butane in the four samples of 5A zeolite areshown in fig. 5. The isotherms for samples la and lb (65 % Ca2+) and for 2a and2b (> 95 % Ca2+) are consistent but there is a significant difference between samples1 and 2, presumably reflecting the difference in Ca2+ content.The isotherm forcommercial Linde 5A crystals is considerably lower.The analysis and interpretation of the uptake curves for samples 2a and 2b isstraightforward. Diffusion in these samples is sufficiently slow that thermal effectscan be neglected, at least in the early stages of the uptake, and the time constantsmay therefore be calculated, as for the diffusion of CF4, from the simple isothermaldiffusion model. Both the form of the uptake curves, illustrated in fig. 6, and thedifference in the time constants for the two different size fractions are consistent withthe simple diffusion model. Over the entire pressure range the time constants forthe smaller crystals are about four times as large as for the larger crystals so that thediffusivities for both size fractions are essentially the same as may be seen from fig.7.Comparisons are made at constant pressure rather than at constant sample loadin76 DIFFUSION IN 5A ZEOLITEto avoid any errors arising from differences in the isotherms. As has been previouslynoted for this system the concentration dependence of the diffusivity appears to bedue entirely to the non-linearity correction (d In p/d In c) and the corrected diffusi-vities (Do) are essentially constant.0 1 2 3 4 5 6 7 8 9 10 11 12 13 1 4 1 5 1 6l/t/s+FIG, 6.-Experimental uptake curves for n-butane in difference size fractions of 5A zeolite crystals(sample 2a and 2b). (a) 360K, pressure step 13-9Torr; (b) 323K, pressure step 7.5-5Torr.0, 55; A, 27.5 pm.The interpretation of the kinetic data for sample l a (34 pm) is similar. Uptakecurves measured under comparable conditions with two different sample quantitieswere essentially the same showing that uptake rates are controlled by intracrystallinephenomena rather than by bed diffinsion or external heat transfer limitations.Thevariation of time constants with butane concentration, illustrated in fig. 8, is similarto that observed for samples 2a and 2b. However, under comparable conditions,the diffusivities for sample l a are lower than those for 2a and 2b and this differenceappears to reflect a real difference in mobility, rather than a difference in the non-linearity correction factors, as may be seen from fig. 10 and table 3.The behaviour of the smaller (7.3 pm) crystals (lb) is more complicated.If theuptake curves for this sample are interpreted according to the isothermal diffusioH. YUCEL AND D. M. RUTHVEN(A) (B)..INLQ\ Eu7 10-2- - 1r/) --- na. W10-377- I-0 - - x x : XX - o( OX - x o x-1s - g os i o O Po xX - o xx a- - o xO X -I I I I I I l l 1 I I 1 I 1 1 1 1 I I I I l l l l l I I I I 1 1 1 100 - 0 0-0 o o0 0 00 x x r - XX0 XX00XXX 0 xX 0X XXX XXX Xt 1 I I I l l l l I I I I I I l l I I I I I l l l l I I 1 1 1 1 1 1 ,1 10 100 2 10 100p/TorrFIG. 7.-Variation of diffusional time constants and diffusivities for n-butane in 5A zeolite crystals[sample 2u (55 pm), x ; 2b (27.5 pm), 03. (A) 50 ; (B) 87°C.model one obtains time constants which show a much smaller increase with sorbateconcentration than for the other three zeolite samples under comparable conditions.At low pressures the time constants for sample l b (7.3 pm) are about twenty timeslarger than the values for sample l a (34 pm) and this difference is approximatelyconsistent with the square of the crystal radius, in accordance with the simple diffusionmodel.However, at higher pressures this ratio falls to about 5.0. Under theseconditions the initial uptake rates for the 7.3 pm sample are very rapid and the formof the uptake curves no longer conforms to the simple isothermal diffusion model.This anomaly can be quantitatively accounted for if thermal effects are considered.Non-isothermal sorption kinetics have been discussed in detail in a previouspublication in which the following expression for the uptake curve was derived interms of two dimensionless parameters a and p :1-co = c n= 1where qn is given by the roots of the equation :In eqn (1) mJm, represents the fractional approach to final equilibrium in responseto a small differential increase in sorbate pressure. The parameters a and p aredefined by a = (ha/pc,)/(D/r2) and p 3 (AH/cJ(dq*/dT),, where h is the external3P(q,cotq,-l) = 4:-a.(278 DIFFUSION IN 5A ZEOLITE1.0 5 10 50 1.0 5 10 50 100p/TorrFIG. 8.-Variation of diffusional time constants and diffusivities for n-butane in 5A zeolite crystalswith 65 % Ca2+. [la (34 pm), 12 mg sample wt., 0 ; 30 mg sample wt., x .lb (7.3 pm), fromisothermal model, sl ; from non-isothermal model, e.] (A) 50, (B) 82°C.TABLE 2.-PARAMETERS FOR NON-ISOTHERMAL ANALYSIS OF UPTAKE CURVES FOR BUTANE INSAMPLE 1b AT 50°Cpressure step/Torr(Dlr 2)/s-1(is0 t hermal values)62-4141-25.525.5-1515-85.4-3.73.7-2.92.9-2.52.5-2.0a-5.40.0340.0270.0220.020.01 70.01 60.01 30.0120.01 1P0.250.260.270.300.290.280.280.270.26U(D/r 2) Is-1(non-i so thermal)0.881.111.542.43 .O4.05.06.78.30.1 10.090.0660.0420.0330.020.0250.0150.012(ha/pcs = 0.1 s-l ; c, = 0.5 cal g-l K-lH . YUCEL AND D. M. RUTHVEN 79heat transfer coefficient, a is the external surface area per unit volume of the sample,pc, is the effective thermal capacity of the sample plus the containing pan, -AH isthe heat of adsorption and (aq*/aT), is the temperature derivative of the equilibriumadsorbed phase concentration. In order to apply this model to the analysis of theuptake curves for sample 16 we take (ha/pcJ = 0.10 s-l, as determined from experi-mental uptake curves, measured under similar conditions using small crystals of 13Xzeolite, in which diffusion is very rapid and heat transfer is rate controlling. Valuesof /? were calculated from the equilibrium isotherms with c,, the effective heat capacityof sample and pan, taken as 0.5 cal g-l K-l which is the value obtained from analysisof the thermally limited uptake curves for the 13X crystals.Using these values ofhafpc, and p the experimental uptake curves were matched to the theoretical non-isothermal curves to determine the diffusional time constants (D/r2).The time1.0; 2 aI40.10.020 4 8 12 16 20 24t l sFIG. 9.-Experimental uptake curve (0) for butane in sample lb (7.3 pm) at 50°C, pressure step15-9 Torr, compared with theoretical curve for non-isothermal sorption calculated from eqn (1)and (2) with cx = 2.4, B = 0.3, D/r2 = 0.042 s-I. Also shown are the theoretical curve for isothermalsorption with the same time constant (-), the theoretical curve for complete heat transfer controland the experimental (isothermal) curve (0) for sample la (34 pm) measured over a similar pressurestep (17.5-12.3 Torr) (D/r2 = 2.2 x s-l)80 DIFFUSION IN 5A ZEOLITEconstants derived in this way are shown in fig.8 and the relevant parameters axe givenin table 2. In fig. 9 the experimental uptake curve for one of these experiments iscompared with the theoretical curve calculated from eqn (1) and (2) (the non-isothermal model). The expected curve for isothermal diffusion with the same timeconstant is also indicated as well as the very much slower (isothermal) uptake curveobtained at similar sorbate concentration with the 34 pm sample (la). It is evidentthat the uptake rate for the 7.3 pm sample under these conditions is significantlyreduced by heat transfer limitation and the non-isothermal model provides a verygood representation of the experimental curve. Clearly, if uptake curves measuredunder non-isothermal conditions are interpreted according to the isothermal modelerroneously low values of D/r2 will result.The values of D/r2, for sample lb,derived from the non-isothermal analysis show the same concentration dependenceas was observed for the larger crystals. At low pressures the correction for thermaleffects is ininor but at high pressures the true values of DJr2 are about twice theapparent values derived on the basis of the isothermal assumption. The apparentdifferences in behaviour between samples l a and l b can thus be explained by theintrusion of thermal effects and diffusivities for the 7.3 pin crystals, calculated accord-ing to the non-isothermal model, are in good agreement with the values for the larger34 ,urn crystals.DIFFUSIONAL ACTIVATION ENERGIESArrhenius plots showing the temperature dependence of the corrected diffusivities(Do) are shown in fig.10 and the activation energies and pre-exponential factors forboth CF4 and n-C4H,, are given in table 3 together with the values obtained inearlier studies of diffusion in commercial Linde 5A crystal^.^^ The diffusivities forthe Linde crystals are very much smaller than the values for our own crystals andthis difference is of the same order as that noted for 4A zeolite in the preceding paper.We have confirmed by replicate experiments using different depths of crystal sampleand also by chromatographic measurements that uptake rates in the Linde sieve areindeed controlled by intracrystalline diffusion, so that this difference represents a realdifference in the diffusional properties of the crystals and cannot be explained byextraneous effects such as external heat or mass transfer limitations.Despite theTABLE 3 .-ARRHENIuS PARAMETERS GIVING TEMPERATURE DEPENDENCE OF LIMITING DIF-FUSIVITY Do ACCORDING TO Do = D* exp (--E/RT)D,/cm2 s-l E/kcal mol-l1.9 x 10-52 . 5 ~2a (55 ym)2b (27.5 ym) 6.69.151 (lot 550 045) .I la(34Dm) . 9~ 10-7 4.52a (".bm) } 3.1 x 10-6 n-C4Hlo 2b (27 5 pm) 4.6Linde (3:6 pm) 7.3 x 10-9 4.0 I (lot 550 045H. YUCEL AND D . M. RUTHVEN 81very large difference in diffusivities, the diffusional activation energies (for butane)are practically the same for all samples. The much lower diffusivity for the Lindecrystals is due to a lower pre-exponential factor as observed previously for N2 andC2H6 in the 4A zeolite.This suggests that the lower diffusivity is due to completeblockage of some of the zeolite windows in the Linde crystals rather than to partialblocking or changes in the effective dimensions of the windows. For CF4 the differ-ence in intrinsic diffusivities between the Linde crystals and our own sample 2 crystalsis even greater than for butane but in this case there appears also to be a difference inactivation energy.2.8 3.0 3.2 3.4 3.6 3.8 - 2.8 3.0 3.2 3.4 3.6 3.8103 KIT(A) CF4; (€3) n-C4HIo.FIG. 10.-Arrhenius plots showing temperature dependence of corrected diffusivity (Do). x ,2a (55 pm) ; 0, 2b (27.5 pm) ; 0, la (34 pm); B, l b (7.3 pm); - - -, Linde 5A (lot 550 045).CONCLUSIONSAnalysis of experimental uptake curves shows that in the larger crystals (la, 2aand 2b) the kinetics of sorption of both CF4 and n-C,H,, are controlled by intra-crystalline diffusion.The diffusional time constants show the ercpected variationwith the square of the crystal radius and there is no significant difference in diffusivitybetween different size fractions of similar zeolite crystals. The apparent anomal82 DIFFUSION IN 5A ZEOLITEin the behaviour of the smallest zeolite crystals (lb) can be satisfactorily explainedby the intrusion of heat transfer effects and when these effects are properly accountedfor the diffusivities derived from the uptake curves for this sample are found to beessentially the same as for the larger (34 pm) crystals of similar composition.Thereis, however, a considerable difference in intrinsic diffusivity between the two differentbatches of crystals. The batches have different Ca2+ contents but it has not beenestablished whether this difference is due directly to the difference in Ca2+ contentor to some other difference in sample preparation.To explain the large difference between diffusivities derived from n.m.r. and fromsorption rate measurements it has been suggested that uptake rates may be con-trolled by a surface barrier rather than by intracrystalline diffusion. In contrastwith the results of Karger et al., which show a strong increase in apparent diffusivitywith crystal size,2 the present results show no variation of diffusivity with crystal size,and therefore do not support the surface barrier hypothesis.An apparent variationof diffusivity with crystal size can arise from the intrusion of heat transfer resistanceand such effects, which become progressively more important as the crystal size isreduced, are not always easy to detect without very detailed experimentation. Anyexternal mass transfer resistance or other time delays will also become more significantas the crystal size is reduced and it seems possible that the anomalous behaviour pre-viously observed may be due to such effects. However, the present study was con-cerned mainly with larger zeolite crystals (7.3-55 pm) and one cannot completelyexclude the possibility that surface effects may be more important in the smallercrystals studied by Karger et a2.l'Most of the earlier studies of uptake kinetics in the A zeolites, both in this labora-tory and elsewhere, were carried out on commercial Linde crystals whereas the n.m.r.measurements, which require in general larger crystals, have been carried out ex-clusively on laboratory synthesized samples.The present results indicate thatdiffusivities for the laboratory synthesized crystals are very much higher than for thecommercial Linde crystals. For butane at 25°C in the fastest diffusing sample(sample 2) the present results suggest a corrected diffusivity of z 1.3 x cm2 s-lcompared with the value of w 4 x cm2 s-1 estimated from n.m.r. relaxationmeasurements with the jump distance taken as 12.3 r f .This difference is verymuch smaller than was formerly supposed on the basis of comparisons with the uptakedata for Linde crystals.2* A difference of this order could well be due to differencesin the zeolite samples. In the comparison between sorption and n.m.r. diffusivitiesthe results for CH4-4A and butane-5A appear to point to opposite conclusions sincein the case of CH4-4A the discrepancy appears to be too large to explain simply bydifferences in the zeolite sample whereas for butane-5A this seems possible. However,the present results show clearly that the differences in diffusivity between differentsamples sf both 4A and 5A zeolites are very much greater than was formerly supposedand it is evident that the comparison between n.m.r. and sorption diffusivities canonly be resolved by comparing identical samples.We thank Jar. J. Karger (K.M.U., Leipzig) for providing us with advance copiesof ref. (1) and (2) and for helpful and informative discussions. The type A zeolitecrystals used in these studies were synthesized in these laboratories by Dr. W. I.Derrah according to Charnell's method. loJ. Karger, J. Caro and M. Bulow, 2. Chern. 1976,16, 331.J. Karger and J. Caro, J.C.S. Faraday I, 1977, 73, 1363.H. Yucel and D. M. Ruthven, J.C.S. F'raday I, 1980,76,71H. YUCEL AND D. M. RUTHVEN 83H. Yucel, Ph.D. Thesis (University of New Brunswick, Fredericton, N.B., Canada, 1978).D. M. Ruthven and R. I. Derrah, J.C.S. Faraduy I, 1972, 68,2332.D. M. Ruthven, R. I. Derrah and K. F. Loughlin, Canad. J. Chem., 1973,51, 3514. ’ Lap-Keung Lee and D. M. Ruthven, J.C.S. Favaday I, 1979,75,2406. * L. Labisch, R. Schollner, D. Michel, H. Rossiger and H. Pfeifer, 2. phys. Chem. (Leezig),1974,255, 581.D. M. Ruthven, Amer. Chem. SOC. Symp. Series, 1977, 40,230.l o J. F. Charnell, J. Crystal Gruwth, 1971, 8,291.(PAPER (9/107