J.C.S. Faraday I, 1980, 76, 60-70Diffusion in 4A ZeoliteStudy of the Effect of Crystal SizeBY HAYRETTIN YUCEL-~ AND DOUGLAS M. RUTWEN*Department of Chemical Engineering, University of New Brunswick,P.O. Box 4400, Fredericton, N.B. E3B 5A3, CanadaReceived 15th January, 1979Sorption rates for N2, CH4 and C2H6 have been measured in different size fractions of synthetic4A zeolite crystals. Both the form of the uptake curves and the dependence of the time constanton crystal radius are entirely consistent with the assumption that the kinetics of sorption are controlledby intracrystalline diffusion, rather than by a surface barrier. Comparisons between differentsamples of crystals show large differences in diffusivity and the diffusivities are much smaller thanthe values derived from n.m.r.measurements,The large discrepancy between intracrystalline diffusion coefficients derived fromn.m.r. and from sorption rate measurements has been noted in recent publications.'.To explain this discrepancy Karger and co-workers have suggested that uptake ratesin a sorption experiment may be controlled by a surface barrier rather than by intra-crystalline diffusion? Evidence in favour of this hypothesis was derived from theresults of a recent series of sorption measurements carried out with crystals of differentsize.'. Diffusional time constants (D/r2) calculated from the uptake curves weresmaller than the n.m.r. values and did not show the expected dependence on thesquare of the crystal radius. However, the form of the uptake curves measured inthis and in other laboratories suggests diffusion control rather than a surface barriersince the initial uptake is generally proportional to the square root of time.Inprevious kinetic studies we therefore interpreted our uptake rate data in terms of thediffusion model but we had not previously confirmed directly the dominance of intra-crystalline diffusion by varying the crystal size. In view of the anomalous resultsobtained by Karger et aZ.,l. a more detailed investigation was required.The range of crystal sizes present in most commercial type A zeolites is = 1-4 pm.Crystals of this size are not easily separated into different size fractions and for adetailed investigation of the effect of crystal size, larger crystals are desirable.TOavoid the uncertainties involved in the comparison of crystals of different origin andthe possibility of differences arising from different degrees of ion exchange in smalland large crystals, we elected to synthesize our own crystals and to examine first thekinetic behaviour of the sodium form (4A), rather than the calcium form (5A). Inorder to minimize complications arising from concentration dependence of thediffusivity we confined our studies to the low concentration region in which theisotherms are essentially linear and the diffusivities nearly constant. The results ofthese studies show clearly that for a series of crystal samples of similar origin theexpected dependence of the time constants on the square of crystal radius is indeedobserved. There are, however, large differences in diffusivity between OUT own 4Acrystals and samples from various batches of commercial Linde 4A.t present address : Chemical Engineering Department, The Middle East Technical University,Ankara, Turkey.6H.YUCEL AND D. M . RUTHVEN 61EXPERIMENTALSamples of 4A zeolite crystals were synthesized by Charnell’s method and separatedinto convenient size fractions using Nitex micro-sieves. The crystals were identified byX-ray diffraction and chemical analysis. The diffraction patterns showed no perceptibledifference from commercial Linde 4A. Crystal sizes were determined by scanning electronmicroscope and optical photo-micrography and the size distributions of the various fractionsare shown in fig.1. The 21.5, 34 and 40 pm* crystals all originated from the same batchof crystals while the 7.3pm crystals were from a different batch, synthesized by the sameprocedure. Prior to the kinetic measurements the crystals were dehydrated slowly under avacuum of w Torr. In the initial dehydration the temperature was raised slowly(2-3 deg min-l) to 400°C and maintained at that level for 48 h. For subsequent regenerationa period of 12 h at 400°C was sufficient. Transient uptake curves were measured using aCahn vacuum microbalance system to follow the change in weight of a small sample of thezeolite (m 12 mg) when subjected to a step change in sorbate pressure. Diffusional timeconstants were calculated by matching the experimental uptake curves to the appropriatedimensionless theoretical curve calculated for an assemblage of cubic particles with theappropriate size distribution.The method of calculation was essentially similar to thatpreviously reported except that in the calculation of the theoretical uptake curve we useddirectly the measured crystal size distribution rather than approximating the size distributionby a normal distribution function. To avoid possible limitations from thermal effects orbed diffusion resistance: small samples were used and the sample was spread as thinly aspossible over the balance pan.1000.01 0.1 0.2 0.5 1 2 5 10 20 30 LO 50 60 70 80 90 95 98 99 99.5 99.8 99.9cumulative vol/ %(b) 21.5, (c) 34 and (d) 40 pm.FIG. 1.-Size distribution of 4A zeolite crystal samples plotted on log-normal paper.(a) 7.3,RESULTS AND DISCUSSIONThe equilibrium isotherms for the different size fractions of our own zeolitecrystals show good agreement, as may be seen from fig. 2. Henry’s law constants* These crystal sizes refer to the volume average diameters62 DIFFUSION IN 4A ZEOLITE( K ) and limiting heats of sorption (qo), calculated from the van't Hoff equation[K = KO exp (qO/RT)] are summarized in table 1 and comparative values of qo,obtained in previous studies, are given in table 2.Fig. 3 shows a representative set of uptake curves for N2 at O'C, measured overcomparable pressure steps with the three different crystal size fractions. Also shown1.61.41.21 .o0.80.60.40.20.02.8 11.4l O 6 I '**I 1.00.80.60.40.20.00.0 100 200 300 400pressure/TorrFIG.2.-Equilibrium isotherms for different size fractions of 4A zeolite crystals ( x , 40 ; 0, 34 ;A, 21.5 ; B, 7.3 pm). (i) 243, (ii) 273, (iii) 323, (iv) 348, (v) 389 and (vi) 423 K. (a) CH4, (b) CzH6,(4 NzH. YUCEL AND D. M. RUTHVEN 63are the uptake curves calculated from the diffusion model with D = 4.05 x 10-l2cm2 s-l, which is the average of the individual values calculated for each curve.Clearly both the form of the uptake curves and the variation in rate between thethree size fractions are well correlated by the diffusion model and there is no evidenceof any significant variation in diffusivity with crystal size.TABLE HENRY'S LAW CONSTANTS FOR SORPTION IN 4A ZEOLITEK/ 1 0-3 molecule &/I 0-6 molecule 40sorbate T/K cavity-l Tom-' cavity-l Tom-l /kcal mol-l15,) N2 243273323 0.721.33CH4 273323C2H6 323 13.7348389423 1.549.87 4.21.5 4.31.39 5.9The variation of the time constants (D/r2) with pressure and with crystal size isillustrated in fig.4. The equilibrium isotherms are essentially linear over the experi-mental range (except for C2& at 323 K and N2 at 243 K) and the diffusivities aretherefore essentially independent of sorbate concentration. The diffusivities forC2H6 at 323 K show a small increase with sorbate pressure, as is to be expected fromTABLE 2.-cOMPARISON OF HEATS OF SORPTION OBSERVED IN DIFFERENT INVESTIGATIONStemperature heat of sorptionsor bate references range/K /kcal mol-l194-273194-273194-323195-22321 5-277243-323194-273195-323195-223273-323296-273298-389273-293323-4236.8-6.45.1-5.05.7-3.37.1-54.354.25.4-5.34-2.85-44.36.47.047.55.64 DIFFUSION I N 4A ZEOLITEthe non-linearity of the isotherm ( D = Do d lnp/d ln c where Do is the correcteddiffusivity, based on a chemical potential driving force and d ln p/d In c is thegradient of the equilibrium isotherm in logarithmic form).Time constants calculatedfrom adsorption and desorption curves showed no significant difference.1.00.820.61cd c&-3 0.4ct:00.200 5 10 15 20 25 30 35dtls*FIG. 3.-Representative uptake curves for N2 at 273 K for three different size fractions of 4A zeolite.A, 7.3 ; 0, 21.5 and 0, 34 pm.The points are experimental, the lines are the theoretical curvescalculated according to the diffusion equation with D = 4.05 x lO-'O cm2 s-l. The correspondingand 0 , 1 . 4 x values of D/r2 are A, 30.3 x ; 0,3.5 xFig. 5 shows the diffusivities calculated from the experimental time constants(D/r2) for the different size fractions of our own crystals plotted against mean crystaldiameter. There is no significant trend of variation of the apparent diffusivity withcrystal size and the differences between the different size fractions are within themargin of experimental uncertainty. (An error of 10 % in the average crystal sizegives a 20 % error in the calculated diffusivity). Therefore, the kinetic data forsorption of N2, C2H6 and CH4 in our own 4A zeolite crystals are entirely consistentwith the assumption that intracrystalline diffusion is the rate controlling transportprocess and there is no evidence of a surface barrier.The temperature dependence of the diffusivities is shown in fig.6 and 7 in whichdata for several different samples of Commercial Linde 4A zeolite are included.Activation energies and pre-exponential factors are listed in table 3. For all threesorbates, our own zeolite crystals show the highest diffusivities although the valuesobtained for C2H6 by Brandt and Rudloff with very small crystals (0.7 pm) are verysimilar. In general the diffusivities of the commercial samples are smaller but thedifference is not related to crystal size, since there are quite large differences betweendifferent commercial Linde samples of similar crystal size.In order to confirm thatthe difference in diffusivities between the different samples is a real effect and notsimply the result of differences in experimental technique between different labora-tories, we carried out a series of experiments with the same sample of Linde 4Azeolite as used by Eagan and Anderson.ll Our data for C2H6 confirm exactly theextrapolation of Eagan's data. Although the diffusional activation energies aresimilar, the diffusivity for this sample is about half that for our own crystals undercomparable conditionsH . YUCEL AND D . M. RUTHVEN 658 006001 1 I I 1 I I .(4 pressurelTorr0.0 50 100 150 200 25010040I I I I(4 pressure/Torr-- +--44 002004 401I I I I I I0.0 25 50 75 100 125 150(b) pressure/Torr0.0 50 100 150 200 250 300(d) pressurelTorrFIG. 4.Dressure dependence of diffusional time constants for different size fractions of 4A zeolitecrystals.(a) CZH~ at 389 K; (b) CzHs at 273 K ; (c) Nz at 273 K ; (d) CH4 at 273 K. Averagecrystal diameter in pm as follows : +, 40 ; 0 , 34 ; A, 21.5 ; W, 7.3. Top dashed lines indicateLinde 4A : (a) and (b), Kondis (2.8 pm) ; (c) and (d), Eagan (4.1 pm).1-66crystal diameterlpmFIG. 5.-Diffusivities calculated from uptake curves for different size fractions of 4A zeolite crystals.(Error bars show k 15 % which was the range of experimental scatter in the individual time constantsfor each size fraction). (a) Nz, 273 K, (b) CzHs, 389 K ; (c) CH4, 273 K ; (d) CzHs, 323 K.FIG. 6.-Arrhenius plot showing tem-perature dependence of limiting dif-fusivity for Nz-4A.0, presentstudy with own 4A crystals; A,Eagan and Anderson; A, data ob-tained in this laboratory with zeolitesample of Eagan and Anderson, 0Ruthven and Derrah (Linde pellet) ;x , Habgood ; @, KumarH . YUCEL AND D . M. RUTHVEN 672.0 2.5 3.0 3.5 4.0103 KITFIG. 7.-Arrhenius plot showing temperature dependence of limiting diffusivity for CzHa-4A andCH4-4A. Except where indicated the data are for CzHs. 0, present study with own 4A crystals ; A, Eagan and Anderson; A, data obtained in this laboratory with zeolite sample of Eagan andAnderson ; +, Kondis, 4A crystal ; x , Kondis, crushed 4A pellet ; 0, Linde 4A lot 470017,present study ; V, Taylor, Linde 4A pellet ; , OKumar, Linde 4A pellet ; +, Brandt and Rudloff,Davison 4A.The data for N2 may be interpreted in a similar way.Our data for the N2system fall below the extrapolation of Eagan’s data and suggest a lower activationenergy. However, if our own data and Eagan’s data are taken together as one setcovering the entire temperature range 190-323 K, an acceptable Arrhenius plot isobtained with an activation energy similar to that for our own zeolite crystals.Despite the similarity in the activation energies the actual diffusivity values for Eagan’ssample are lower than the values for our own crystals by a factor of z 4.The diffusivities for some other samples of Linde 4A zeolite, determined in thislaboratory, are even smaller.Indeed, for C2H6 in Linde lot 470017 and for N2 in acrushed Linde 4A pellet l2 we observe diffusivities about two orders of magnitudesmaller than the values for our own crystals. The activation energy of N2 in thisLinde sample is essentially the same as for our own crystals but in the case of C2H68 DIFFUSION IN 4A ZEOLITETABLE 3 .-ACTIVATION ENERGIES ( E ) AND PRE-EXPONENTIAL FACTORS (D,) GIVING TEMPERA-TURE DEPENDENCE OF LIMITING DIFFUSIVITIES FOR VARIOUS SORBATES IN 4A ZEOLITE[Do = D , exp (-E/RT)]zeolite and av. temperature E D*investigator crystal diameterlpm rangelK jkcal mol-1 /lo-' cm2 s-laHabgood Linde 4A (0.5)Eagan and Anderson Linde 4A (4.1)lot 450339present study same sample (4.1)Derrah l2 Linde 4A (3.4)(crushed pellet)Kumar Linde 4A (3.5)(14-30 mesh)present study own crystals(7.3, 21.5, 34)CzHs-4ABrandt and Rudloff l3Kondis and Dranoff 14* l5Davison 4A (0.7)(lot 441079)Linde 4A pelletlot 450339Eagan and Anderson Linde 4A (4.1)Taylor Linde 4A (3.6)( 8 in.pellet)present study Linde 4A (x 3.2)(lot 470017)present study own crystals(7.3, 21.5, 34, 40)CHa4AaHabgood Linde 4A (0.5)Eagan and Anderson l1 Linde 4A (4.1)Kumar Linde 4A (3.5)(14-30 mesh)present study own crystals(7.3, 21.5, 34)194-273195-233243-32321 5-277304-363243 -3 23296-373298-389298-389273-323304-352323-389323-423194-273195-223305-366273-3234.075.86.16.05.67.45.665.237.25.66.38.27.48.26.45.80.00235.30.963 .O13.21.30.0620.0060.40.0050.0044.80.06360.410.9aThe mean crystal size of Habgood's sample was determined by the B.E.T.method whichis less reliable than photomicrography. The values of D, from Habgood's data are there-fore subject to some uncertainty. bThe data of Kumar were obtained by a chromato-graphic method while the other investigators used standard gravimetric, volumetric orpressure transient me tho ds .the activation energy for the Linde crystals appears to be smaller. However,in calculating the activation energy of C2H6 Kondis and Dranoff l4 and Taylor l 7take no account of the d h p l d In c correction factor. At the lower temperatureswithin their experimental range this factor is significantly greater than 1.0 and itsinclusion would therefore increase the activation energy of the limiting diffusivityH.YUCEL AND D. M. RUTHVEN 69The data for CH4 are similar although less extensive. There appears to be a largedifference in diffusivity between our own crystals and Habgood's commercial samplewith only a comparatively modest difference in activation energy. The data ofEagan and Anderson for CH4 do not extend over a sufficiently wide temperaturerange to permit a reliable determination of the activation energy.The consistency of the diffusivity values derived from the different size fractionsof our own crystals and the marked difference in diffusivities between our own crystalsand the Linde 4A pellet is further illustrated in fig.8 which shows data for N2 andAr at 273 I<. A slight decrease in the Ar diffusivity with increasing pressure isobserved for both zeolite samples whereas the diffusivity of N2 appears to be inde-pendent of pressure in this range. For both gases the diffusivity in the Linde sampleis lower by a factor of 30 compared with the value for our own crystals under com-parable conditions.lo-' '000 00 " 0 O0 0 w0 . . 07 10-gl .I 0 - mA - DL + t+I I I I + I t IPITorrown 4A zeolite crystals. (N2: A, 7.3 ; H, 21.5 ; 0 , 3 4 pm. Ar: 0, 34 pm).FIG. 8.-Comparison of diffusivities for N2 and Ar at 273 K in Linde 4A pellet (+ , x ) and in ourCONCLUSIONSThe results of the present study of sorption kinetics in a series of size fractions of4A zeolite crystals show clearly that for the systems investigated sorption rates arecontrolled entirely by intracrystalline diffusion and there is no evidence of anysystematic variation in diffusivity with crystal size.However, there are large differ-ences in diffusivity between some of the different zeolite samples, even though thereis no perceptible difference in the X-ray diffraction patterns. In paticular, for onecommercial sample, the diffusivity was nearly two orders of magnitude smaller thanthe value for our crystals. The reduction in diffusivity is generally associated with areduction in the pre-exponential factor, rather than with an increase in diffusionalactivation energy and in most cases the diffusional activation energy is actually lowerfor the slower diffusing sample.Such differences must be due to subtle changes inthe crystal structure which are not sufficient to cause noticeable changes in the latticeparameters and which therefore do not significantly alter the X-ray diffraction pattern.The most obvious possibility is a re-arrangement of the exchangeable cations. Com-mercial zeolite samples are generally marketed in dehydrated form so that the initia70 DIFFUSION IN 4A ZEOLITEdehydration is not controlled by the investigator. The importance of the initialdehydration conditions was clearly demonstrated by Kondis and Dranoff l5 whoshowed that by exposure to steam at elevated temperatures a reduction in diffusivityby more than an order of magnitude could be achieved, with little change in thediffusional activation energy, and that under these conditions there was no loss ofcrystallinity or sorption capacity.Such “ pore closure ” effects have been discussedby Breck.lRearrangement of the cations may be facilitated by exposure to steam at hightemperatures. A difference in cation distribution can produce small changes in thewindow dimensions which may alter the diffusional activation energy. However,the main effect is likely to be the complete blockage of a certain fraction of the win-dows. This will lead to large changes in the pre-exponential factor with little changein activation energy.lg This is the pattern of behaviour suggested by the presentdiffusivity data.The results of the present study stand in marked contrast to the results obtainedby Karger et aL3 for the 5A zeolite.A further study of the 5A system using differentsize fractions of the same zeolite sample was therefore carried out and the results arereported in the next paper.Of the systems studied in the present work the only one for which n.m.r. data arealso available is CH4-4A. N.m.r. self diffusivities for this system are w lo-’ cm2 s-lat 140 K with the activation energy < 2.0 kcal mol-1.20 This is very much largerthan the corrected diffusivity extrapolated from the present sorption data(Do M 1O-l’ cm2 s-l at 140 IS). However, the zeolite sample used in the n.m.r.studies was not a pure 4A sieve but contained w 20 % Ca2+.The present resultsshow that there may be considerable differences between the diffusivities for differentzeolite samples and, although it seems unlikely that such a large difference can beexplained simply on the basis of differences in the samples, it is evident that reliablecomparisons can only be made if identical samples are used.We thank Dr. R. B. Anderson of McMaster University for providing us with asample of the 4A zeolite used by Dr. Eagan in his diffusion studies.J. Karger and J. Caro, J.C.S. Faraday I, 1977,73,1363.D. M. Ruthven, A.C.S. Symp. Series, 1977, 40, 320.J. Karger, J. Car0 and M. Bulow, 2. Chem., 1976,16, 331.J. F. Charnell, J. Cryst. Growth, 1971, 8, 291.K. F. Loughlin, R. I. Derrah and D. M. Ruthven, Canad. J. Chem. Eng., 1971, 49, 66.Lap-Keung Lee and D. M. Ruthven, J.C.S. Farudczy I, 1979,75,2406.D. W. Breck, W. G. Eversole, R. M. Milton, T. B. Read and T. L. Thomas, J. Amer. Chm.Soc., 1956, 78, 5963.H. W. Habgood, Cunad. J. Chem., 1958,36,1384.’ Lap-Keung Lee, H. Yucel and D. M. Ruthven, A.C.S. Symp. Series, 1977,40,417.lo R. J. Farper, G. R. Stifel and R. B. Anderson Canad J. Chem, 1969,47,4661.l1 J. D. Eagan and R. B. Anderson, J. Colloid Interface Sci., 1975, 50,419.l2 D. M. Ruthven and R. I. Derrah, J.C.S. Faraday I, 1975,71,2031.l3 W. Brandt and W. Rudloff, J. Phys. Chem. Solids, 1965,26,741.l4 E. F. Kondis and J. S. Dranoff, Ado. Chem., 1971, 102, 171.l5 E. F. Kondis and J. S. Dranoff, Ind. Eng. Chem., Process Design Develop., 1971, 10, 108.l6 R. Kumar, Ph.D. Thesis (University of New Brunswick, Fredericton, Canada, 1978).R. A. Taylor, Ph.D. Thesis (University of New Brunswick, Fredericton, Canada, 1978).l 8 D. W. Breck, ZeoZite Molecular Sieves (John Wiley, New York, 1974), pp. 490-494, 645.l9 D. M. Ruthven, Cunad. J. Chem., 1974,52,3523.2o J. Caro, J. Karger, G. Finger, H. Pfeifer and R. Schollner, 2. phys. Chem. (Le@zig), 1976,257,903.PAPER (9/106