Articles

Diffusion of Volatile Organic Chemicals in PorousMedia. 1. Alcohol/Natural Zeolite Systems

Billur Sakintuna, Enis Fakioglu, and Yuda Yurum*

Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla,Istanbul 34956, Turkey

Received April 4, 2005. Revised Manuscript Received September 5, 2005

The aim of the present paper was to measure the diffusion coefficients, mode of transport, andactivation energies of some alcohols into the porous structure of a Turkish natural zeolite.Diffusion coefficients, modes of transport, and activation energies of methanol, ethanol, n-propanol,2-propanol, and n-butanol into the porous structure of the Turkish Manisa Gordes natural zeolitewere measured at 24-28 °C. The diffusion coefficients of alcohols were calculated from the slopeof graphs of Mt/M∞ versus t1/2. As the molecular weight of the alcohols increased, diffusioncoefficients decreased, the activation energy for diffusion increased, and the time necessary toreach equilibrium was increased. The diffusion constants increased linearly with an increase inthe temperature. The diffusion of alcohols in the zeolite obeyed the anomalous transportmechanism. Diffusion rate constants remained unchanged as the temperature was increased.With increasing molecular weight of the volatile alcohols, the activation energies also increased.The calculated activation energies of diffusion were 18.3, 46.4, 79.7, 57.3, and 90.1 kJ/mol formethanol, ethanol, n-propanol, i-propanol, and n-butanol, respectively.

Introduction

The diffusion of small molecules in the intracrystal-line void volume of zeolites has been a research topicfor many years. To obtain information about the trans-port properties of zeolite crystals is important in orderto understand the dynamics fundamentals of smallmolecules inside a zeolite, which is relevant for allapplications, including catalysis for energy production.

The size, shape, and adsorptive selectivities of bothnatural and synthetic zeolitic materials have been usedin a wide variety of heterogeneous catalytic processes.As an example, zeolite is used as a catalyst in themethanol-to-gasoline conversion process, which is ofmajor commercial importance. This process has been the

subject of numerous experimental1,2 and theoreticalstudies,3,4 but it is still not particularly well understood.

Diffusion plays an essential role in most phenomenaoccurring to molecules in zeolites; for example, it favorsadsorption, makes the separation of similar moleculeseffective, and drives chemical reactions both on thereagent side to lead the reactants into the active sitesand on the product side to select and extract the speciesresulting from the reaction. Various techniques for themeasurement of intracrystalline diffusion have beendeveloped5-7 which widely vary in scope, degree of

* To whom correspondence should be addressed. Phone: 90-216-483 9512. Fax: 90-216-483 9550. E-mail: yyurum@sabanciuniv.edu.

(1) Seiler, M.; Schenk, U.; Hunger, M. Catal. Lett. 1999, 62, 139-145.

(2) Bjørgen, M.; Kolboe, S. Appl. Catal., A 2002, 225, 285-290.(3) Stich, I.; Gale, J. D.; Terkura, K.; Payn, E. M. C. Chem. Phys.

Lett. 1998, 283, 402-408.(4) Hutchings, G. J.; Watson, G. W.; Willock, D. J. Microporous

Mesoporous Mater. 1999, 29, 67-77.

VOLUME 19, NUMBER 6 NOVEMBER/DECEMBER 2005

© Copyright 2005 American Chemical Society

10.1021/ef050095w CCC: $30.25 © 2005 American Chemical SocietyPublished on Web 10/05/2005

experimental and theoretical sophistication, and rangeof applicability. For a large number of the indirectmethods, the diffusing species, or its concentrationprofile in the microporous material, is not directlyobserved; the diffusivity is rather calculated from theexternal measurement of pressure, concentration, orsample weight. Such computations require suitablemodels which describe all transport phenomena andpossible sorption processes that can occur in the experi-mental setup.

The determination of diffusion coefficients is basedon uptake measurement of the volatile component bysorbents. Analysis of the sorption data can be ac-complished by various means. A convenient method ofanalysis involves fitting the sorption data to empiricaleq 1. It is possible to express the initial rate of diffu-sional solvent penetration in terms of the equation:

where Mt is the amount of solvent diffused in themacromolecular structure at time t, M∞ is the amountof solvent diffused at a steady state, t is the release time,k is the rate constant which depends on structuralcharacteristics of the system, and n is an exponentcharacteristic of the mode of transport of the solvent inthe porous structure and varies with the diffusionmechanism and particle geometry.

Sorption mechanisms in macromolecular systemssuch as solid coals may be defined in terms of twolimiting cases of Fickian diffusion and Case II trans-port.8 When n ) 0.5, the solute diffuses through and isreleased from the adsorbent with a quasi-Fickian dif-fusion mechanism. For values of n > 0.5, non-Fickiansolute diffusion is observed. When n ) 0.85, Case IItransport occurs and values of n between 0.5 and 1.0indicate anomalous transport. Values above n ) 0.85are possible and are termed “super-Case II”. It isimportant that cited work showed that the expectedvalues of n are sensitive to the assumed particle shape.For an infinite plan sheet, the values would be 0.5 and1.0 for Fickian and pure Case II, respectively, and inthe case of an infinite cylinder, 0.45 and 0.89, respec-tively.8 There may be differences in the diffusionbehavior of different sections of the zeolite. Thus, thevalues of n can be used only as a rough guide to thenature of the process. Different n and k values can befound in the literature.9 Eq 1 is useful for preliminaryanalysis of sorption data, although it may be used upto 60% of the final weight of the penetrant imbibed andit has no provisions for the analysis of details, such asinflections or penetrant loss with time.10,11 In the graphof ln(Mt/M∞) versus ln t, ln k is the intercept and n isthe slope.12,13

When a porous adsorbent system is placed in contactwith a solvent (penetrant) gas, diffusion of the penetrantin the porous material may be followed by measuringthe uptake of the solvent. Diffusion in the silicalitecrystals can be described by Fickian diffusion withconcentration-independent diffusivity, D. In Fick for-mulation, the driving force for diffusive transport is thegradient of chemical potential of concentration, ratherthan the gradient of concentration.14 The kinetics of thediffusion into the sphere in Fick formulation is ex-pressed by eq 3 (below).15

The diffusion coefficient is supposed to be constant.The basic equation, in spherical coordinates, to be solvedis

with the initial conditions

where CA is the solid-phase concentration (mol cm-3);D is the diffusion coefficient, constant throughout theprocess (m2 s-1); t is the time (s); r is the distance fromthe particle center (m); C is the initial solid-phaseconcentration (mol cm-3); and r0 is the particle radius(m). The exact solution of eq 2 is eq 3 for gas-phasediffusion to the solid solute.13

Assuming the zeolite particles are of spherical shape,the solution of Fick’s second law of diffusion in sphericalsystems gives.11,16

where Mt and M∞ represent the amount of solventdiffused entering the spheres with radius a, at times tand steady state, respectively, and n is an integercoming from the solvation of Fick’s second law. D is thecoefficient of diffusion of the solvent. This equation isbased on the assumption that the particle radius doesnot change, which is true for zeolite particles. Thesolution to eq 3 is given by eq 4.17

For short times, eq 4 approximates to

(5) Domontis, P.; Suffritti, G. B. Chem. Rev. 1997, 97, 2845-2878.(6) Haberlandt, R. Thin Solid Films 1998, 330, 34-45.(7) Lood, W. P.; Verheijen, P. J. T.; Moulijn, J. A. Chem. Eng. Sci.

2000, 55, 51-65.(8) Otake, Y.; Suuberg, E. M. Energy Fuels 1997, 11, 1155-1164.(9) Gao, H.; Nolura, M.; Murata, S.; Artok, L. Energy Fuels 1999,

13, 518-528.(10) Peppas, N. A.; Franson, N. M. Polym. Phys. Ed. 1983, 21, 983-

997.(11) Peppas, N. A.; Lucht, L. M. Chem. Eng. Commun. 1985, 37,

333.(12) Seferinoglu, M.; Yurum, Y. Energy Fuels 2001, 15, 135.

(13) Inglezakis, V. J.; Grigoropoulou, H. P. J. Colloid Interface Sci.2001, 234, 434-441.

(14) Ruthven, D. M. Chem. Eng. Sci. 2004, 59, 4531-4545.(15) Hall, P. J.; Thomas, K. M.; Marsh, H. Fuel 1992, 71, 1271-

1275.(16) Crank, J. The Mathematics of Diffusion; Clarendon Press:

London, 1976.(17) Ndaji, F. E.; Thomas, K. M. Fuel 1993, 72, 1525-1530.

Mt

M∞) ktn (1)

∂CA

∂t) D(∂2CA

∂r2+ 2

r∂CA

∂r ) (2)

CA ) C∞ for r ) r0 at t > 0

CA(r) ) C ) const for 0 < r < r0 at t ) 0

Mt

M∞

) 1 -6

π2∑n)1

∞ 1

n2exp(-Dn2π2 t

a2) (3)

Mt

M∞

) 6(Dt

a2)1/2[π-1/2 + 2∑n)1

∞

ierfcna

xDt] - 3Dt

a2(4)

Mt

M∞) 6[ Dt

πa2]1/2- 3Dt

a2(5)

2220 Energy & Fuels, Vol. 19, No. 6, 2005 Sakintuna et al.

Neglecting the contribution of the term 3Dt/a2, the valueof D is found from the slope of a plot of Mt/M∞versust1/2.

Diffusion is an activated process; that is, to occur, itrequires overcoming an energy barrier. Other activatedprocesses are found in zeolites, the most commonexamples being the adsorption of a molecule which, froma gas or a liquid, enters into the micropores and,especially, chemical reactions occurring in the channeland cavities. If the activation energy is smaller than,equal to, or slightly larger than the available thermalenergy kBT, the probability of overcoming the energybarrier is sufficiently high to allow the activated processto occur for a statistically meaningful number of timesduring a reasonably long simulation. Activation energiesof diffusion are calculated using the equation below:

where D0 is a temperature-independent pre-exponential(m2/s) and EA is the activation energy for diffusion.18

Seferinoglu and Yurum12 recently measured the dif-fusion coefficients of pyridine in raw and acid-washedlow-rank coals. The method they used was simple andprecise for the measurement of diffusion coefficients ofsolvents in coals. Ritger and Peppas19 and Howell andPeppas 20 studied diffusion processes in describing thetransport kinetics for pyridine in coal using the sameempirical eq 1. This method can also be used for themeasurement of diffusion constants of several solventsin natural and synthetic zeolites. Bludau et al.21 studiedthe uptake of pyridine into mordenite and H-ZSM-5.Their data evaluation was based on the solution of Fick’ssecond law, using diffusion coefficients for the wholeprocess. Dyer and White22 studied cation diffusion in anatural zeolite clinoptilolite and compared three differ-ent approaches to determine diffusion coefficients,including Fick’s second law of diffusion (eq 3), whichwas found to produce similar results with other ap-proaches. The applicability of various models to thedetermination of ion exchange diffusion coefficients inclinoptilolite was examined in another study,13 in whicheq 3 was found to be acceptable for the calculations.Marecka and Mianowski23 used Fick’s second law todetermine sorption of carbon dioxide and methane on ahighly metamorphosed coal, and the results of the modelare compared with the experimental kinetics of nitrogensorption on type A zeolite.

For the calculation of diffusion coefficients, the fol-lowing assumptions are made: the diffusion mechanismobeys Fick’s law of diffusion, the crystallites possess aspherical shape, and the concentration profile of thesorbed gas in these spheres shows radial symmetry. The

diffusion is assumed to be isotropic; it can be describedby a single diffusion coefficient rather than a diffusiontensor, and the diffusion coefficient does not depend onsorbate concentration.

It is proposed that there are at least five limitingtypes of diffusion for the molecules flowing through thezeolitic material:24

Case a. Unrestricted intracrystalline diffusion: themolecule moves in the channels and cavities of acrystallite without crossing the surface of the solid orextended crystal defects.

Case b. Modified intracrystalline diffusion: the par-ticle crosses extended (e.g., dislocations and mosaicboundaries) or localized (e.g., vacancies and cations innoncrystallographic positions) crystal defects hinderingor, sometimes, enhancing its motion.

Case c. Restricted intracrystalline diffusion: themolecule is reflected at the crystal boundary becauseof a very low probability of desorption.

Case d. Intercrystalline diffusion: the molecule mi-grates between different crystals, so it is sorbed mostof the time but not confined to the same crystal.Sometimes this type of diffusion involves surface filmformation and diffusion on the zeolite surface.

Case e. Diffusion in the fluid phase: the particleremains in the gas or liquid phase, confined only by thewalls of the vessel containing the sample.

The aim of the present paper was to measure thediffusion coefficients, modes of transport, and activationenergies of some alcohols into the porous structure of aTurkish natural zeolite. The present paper is the firstof a series of experimental investigations which willreport the transport of volatile organic compounds inporous media.

Experimental Section

Materials. Turkish Manisa Gordes zeolite (95% clinoptilo-lite), obtained from Enli Mining Corp., Izmir, Turkey, was usedas the porous medium in the present study. Clinoptilolite wasthe predominant zeolite mineral produced in Turkey, especiallyin the Gordes area, about 130 km northeast of Manisa. Thisexperiment can be done with different kinds of natural orsynthetic zeolites that can be obtained from various zeolitesuppliers. Analyses of the zeolite used in this study are givenin Table 1.

The surface area (BET)25,26 of the natural zeolite wasdetermined using a Micromeritics ASAP 2000 instrument. Themeasurement was performed at the liquid-nitrogen boilingpoint of 77 K. The BET surface area of the zeolite wasdetermined from the adsorption isotherms for the degassedsample. Pore volume distribution was calculated using aprocedure developed by Barret et al.27

The solventssmethanol, ethanol, n-propanol, 2-propanol,and n-butanolswere purchased from Aldrich, and they wereused as received.

General Procedure. An adiabatic isothermal setup,12

designed and built in our laboratories, was used in thediffusion experiments. A Sartorius CP 124S analytical balancewith a 0.0001 g accuracy was placed in a Memmert model 300(18) Callister, W. D. Material Science Engineering, 2nd ed.; Wiley

& Sons: New York, 1991.(19) Ritger, P. L.; Peppas, N. A. Fuel 1987, 66, 1379-1388.(20) Howell, B. D.; Peppas, N. A. Chem. Eng. Commun. 1985, 43,

301-315.(21) Bludau, H.; Karge, H. G.; Niessen, W. Microporous Mesoporous

Mater. 1998, 22, 297-308.(22) Dyer, A.; White, K. J. Thermochim. Acta 1999, 340-341, 341-

348.(23) Marecka, A.; Mianowski, A. Fuel 1998, 77, 1691-1696.

(24) Caro, J.; Hocevar, S.; Kaerger, J.; Riekert, L. Zeolites 1986, 6,213.

(25) Brunauer, S.; Deming, L. S.; Deming, W. E.; Teller, E. J. Am.Chem. Soc. 1938, 60, 309.

(26) Brunauer, S.; Deming, L. S.; Deming, W. E.; Teller, E. J. Am.Chem. Soc. 1940, 60, 1723-1732.

(27) Barrett, E. P.; Jayner, L. G.; Halenda, P. H. J. Am. Chem. Soc.1951, 73, 373.

D ) D0 e-EA/RT (6)

ln D ) ln D0 -EA

RT(7)

Diffusion of Volatile Organic Chemicals in Porous Media Energy & Fuels, Vol. 19, No. 6, 2005 2221

laboratory oven. At the start of the experiment, approximately1.0000 g of a 100% degassed with heating zeolite sample wasevenly distributed in a Petri dish and its initial weight wasrecorded. Four wide beakers filled with a total of 200 mL ofalcohol were used in each experiment, and they were placedin the closest vicinity of the balance pan. The temperature ofthe experiment was set, and the system was closed. After thetemperature reached a constant set value between 24 and 28.0°C, the weight increase of the zeolite as a result of alcoholvapor uptake was recorded every 5 s with the aid of SartoConnect software installed on the PC. The experiment wascontinued until the software collected 2000 data points and aconstant weight was attained. All experiments were repeatedat least five times.

For the calculation of the diffusion coefficient, the followingassumptions were made: the diffusion mechanism obeys Fick’slaw, the crystallites possess a spherical shape, the concentra-tion profile of the sorbed gas in these spheres shows radialsymmetry, the diffusion is assumed to be isotropic and it canbe described by a single diffusion coefficient rather than adiffusion tensor, and the diffusion coefficient does not dependon sorbate concentration.

Results and Discussion

The BET surface area of the natural zeolite was 59.44m2 g-1. Nitrogen adsorption/desorption isotherms andpore volume distribution are given in Figure 1.

Alcohol Uptake and Coefficients of Diffusion.The zeolite used in the present study contains 40.2%micropores, 57.9% mesopores, and 1.9% macropores,Table 1. It seemed that the zeolite enclosed the materialdiffused in it, mainly inside the meso- and micropores.Alcohol molecules might have been sorbed on the porewalls, which were in equilibrium with the intrazeoliticfree gas phase. The sorbed molecules probably could notescape the force field of the surrounding pore-wallatoms, which might be considered as the Brønsted acidsites upon which methanol was initially adsorbed.28

Therefore, the maximum value attained could be at-tributed to the adsorption of alcohols mainly to thesurface sites of the zeolite.

The alcohol uptake of the zeolite samples was re-corded until equilibrium was attained. As the molecularweight of alcohols was increased, the time needed to

reach equilibrium also increased. The change in pro-panol uptake with time at 24.0 °C is presented as anexample in Figure 2. The steady-state value of 0.0612g was reached at about the 3 000th second. The experi-ment was continued until the 10 000th second, at whichthe uptake was recorded as 0.0631 g of propanol.

Since it was assumed10,11 that diffusion occurredlinearly during the first 60% of the ramp (≈10 min), allthe calculations for the coefficients of diffusion and forthe activation energy were based on the data in thisregion. Graphs of Mt/M∞versus t1/2 for the alcoholdiffusion in the zeolite were plotted in order to calculatethe coefficients of diffusion; Figure 3 is presented as anexample for the calculation of the coefficient of diffusionof propanol at 24.0 °C. The coefficients of diffusion weremeasured from the slope of such graphs. The coefficients

(28) Mirth, G.; Lercher, J. A.; Anderson, M. W.; Klinowski, J. J.Chem. Soc., Faraday Trans. 1990, 86, 3039.

Table 1. Analyses of Turkish Manisa Go1rdes NaturalZeolite

% clinoptilolite 95

surface analysis %, by volume

micropores 40.2mesopores 57.9macropores 1.9

chemical analysis %

SiO2 70.9Al2O3 12.4K2O 4.46CaO 2.54Fe2O3 1.21MgO 0.83Na2O 0.28TiO2 0.09P2O5 0.02MnO <0.01

Figure 1. (A) Nitrogen adsorption/desorption isotherms and(B) pore volume distribution of the natural zeolite.

Figure 2. n-Propanol uptake of the zeolite at 24 °C.

Figure 3. Mt/M∞ versus t1/2 graph of the n-propanol diffusionin the zeolite at 24 °C.

2222 Energy & Fuels, Vol. 19, No. 6, 2005 Sakintuna et al.

of diffusion of methanol, ethanol, n-propanol, 2-pro-panol, and n-butanol at 24.0, 25.0, and 26.0 °C arepresented in Table 2. It is seen that the higher themolecular weight of alcohols, the lower the coefficientsof diffusion they had; thus, lower amounts of higheralcohols were transported relative to the lower alcoholsat the same temperatures because of steric hindrances.The entry of the diffusing molecules into the zeolitechannels is strongly influenced by the critical size of themolecules.29 At sufficiently low temperatures or at shorttime scales, Case a must prevail, but at increasinglyhigher temperature and time scales, all the other caseswill eventually occur.5 Therefore, the effective relativelylonger time-scale (≈10 min) coefficients of diffusioncalculated in the present work might be the result of acomplex mechanism and will depend on the differentcoefficients of diffusion characteristic of each of theconsidered cases stated above.

Increasing the temperature increased the kineticenergy of the molecules and, therefore, caused increasesalso in the coefficients of diffusion; for example, thecoefficients of diffusion of methanol at 24.0, 26.0, and28 °C were measured as 4.53 × 10-14, 4.76 × 10-14, and5.00 × 10-14 m2/s, respectively. Dyer and Amin30 studiedthe liquid-phase self-diffusion of ethanol and n-butanolin heteroionic zeolites; coefficients of diffusion measuredby these workers are much lower (≈1.15 × 10-18 m2/sand ≈1.94 × 10-18 m2/s) than those measured in thepresent work. This is definitely due to the difference ofliquid-phase uptake of ethanol and n-butanol in thework of Dyer and Amin30 and the gas-phase diffusionof the same alcohols measured in the present report.Sorption/diffusion in the zeolite from the liquid and gas(or vapor) phases differs from each other in the intra-crystalline mass transfer for the entry of sorbatemolecules to the zeolite channels.29

The coefficients of diffusion measured in the presentwork were lower than those reported by Bludau et al.21

for pyridine diffusion into mordenite and H-ZSM-5,(D ) 1 × 10-12 m2/s and D ) 6 × 10-11 m2/s, respec-tively), who claimed the transport of pyridine into themicropores was the rate-determining step. The reasonfor the lower values of coefficients of diffusion in thecase of alcohols might be due to stronger polar interac-

tions of alcohols with the zeolitic intracrystalline sur-faces. It has been found that the occurrence of variousfactors such as intra- and interparticle transport mightaffect the overall rate of the sorption process.23 Keipertand Baerns31 also mention that zeolite crystal radiusand the length of the zeolite layer strongly affect theestimated values of the intracrystalline coefficient ofdiffusion.

Diffusional Rate Constants and Mode of Trans-port of the Solvent. The type of transport mechanismsof alcohols in the zeolitic porous structure can bespeculated by the values of the diffusion rate constants,k, and diffusion exponents, n, which were calculatedusing ln(Mt/M∞) versus ln t graphs; an example for suchgraphs is presented in Figure 4 for the diffusion ofn-propanol at 24.0 °C. The value of R2, for the graph,was 0.9997, indicating a linear relationship between ln-(Mt/M∞) and ln t. Diffusion rate constant, k, wascalculated as 1.24 × 10-3 s-1.

Table 3 presents the diffusion rate constants, diffusionexponents, and transport mechanisms of different al-cohols in the natural zeolite. Analysis of the linearityof these plots gave acceptable regressional coefficients(R2) in all cases; R2 values in all of the experiments wereequal to or greater than 0.98, indicating a linearrelationship between ln(Mt/M∞) and ln t. It seemed thatthe diffusion of alcohols in zeolite could be approximatedwith a first-order rate law for all of the alcohols studied.(29) Choudhary, V. R.; Choudhary, T. V. Chem. Eng. Sci. 1997, 52,

3543-3552.(30) Dyer, A.; Amin, S. Microporous Mesoporous Mater. 2001, 46,

163-176.(31) Keipert, O. P.; Baerns, M. Chem. Eng. Sci. 1998, 53, 3623-

3634.

Table 2. Coefficients of Diffusion of Volatile Alcohols inNatural Zeolite

alcohol type T, °C D, m2/s

methanol 24 4.53 × 10-14

26 4.76 × 10-14

28 5.00 × 10-14

ethanol 24 3.48 × 10-14

26 4.29 × 10-14

28 4.46 × 10-14

n-propanol 24 2.20 × 10-14

26 3.00 × 10-14

28 3.40 × 10-14

i-propanol 24 3.08 × 10-14

26 3.31 × 10-14

28 3.88 × 10-14

n-butanol 24 2.04 × 10-14

26 2.31 × 10-14

28 3.32 × 10-14

Figure 4. ln(Mt/M∞) versus ln t graph of the n-propanoldiffusion in the zeolite at 24 °C.

Table 3. Diffusion Rate Constants, Diffusion Exponents,and Transport Mechanisms of Volatile Alcohols in

Natural Zeolite

alcoholtype T, °C k, s-1 n R2

activation energy ofdiffusion, kJ/mol

methanol 24 1.36 × 10-3 1.00 0.988 18.326 1.65 × 10-3 0.99 0.99428 1.76 × 10-3 0.97 0.997

ethanol 24 1.27 × 10-3 0.97 0.997 46.426 1.51 × 10-3 0.96 0.99128 1.57 × 10-3 0.98 0.989

n-propanol 24 1.24 × 10-3 1.00 0.999 79.726 1.50 × 10-3 1.00 0.99728 2.17 × 10-3 1.00 0.999

i-propanol 24 6.77 × 10-4 1.00 0.998 57.326 1.07 × 10-3 1.00 0.98228 1.27 × 10-3 0.99 0.994

n-butanol 24 7.35 × 10-4 0.98 0.998 90.126 9.26 × 10-4 0.99 0.99628 9.99 × 10-4 0.99 0.998

Diffusion of Volatile Organic Chemicals in Porous Media Energy & Fuels, Vol. 19, No. 6, 2005 2223

Diffusion rate constants slightly increased as the tem-perature was increased and decreased as the molecularweight increased, for all of the samples in the range of24.0-28.0 °C. The diffusion rate constant of 2-propanolwas lower than those of n-propanol. The time scale ofthe intracrystalline diffusion is influenced by smallercrystals, leading to shorter diffusion times.31 Crystal sizedistribution and deviations from the spherical shape areassumed, further, to influence accuracy. The reason fordifferent rate constants in this paper was the zeolitetype that is used and the crystalline structures varietiesfound in this natural zeolite clinoptilolite.

The diffusion exponents, n, were calculated to bebetween 0.96 and 1.00 in all experiments done at alltemperatures, indicating an anomalous diffusion mech-anism. The calculations were done assuming that thediffusion mechanism is Fickian. Although the literatureresults are closer to our results, it is clear that thosedifferent techniques, models, and assumptions (crystalshape and size) may strongly affect the results. Furtherprogress in zeolite diffusion may be achieved by thesimultaneous fitting of experiments for different zeolitetypes.

Activation Energies of Diffusion For the Alco-hols. The activation energy was calculated from theslope of the straight line of the graph ln D versus 1/T.Calculated activation energies were 18.3, 46.4, 79.7,57.3, and 90.1 kJ/mol for methanol, ethanol, n-propanol,i-propanol, and n-butanol, respectively. There should bea strong influence of chain length, polarity, criticalmolecular size, and configuration of diffusing moleculeson the diffusion coefficients and activation energies.With increasing molecular weight of the volatile alco-hols, the activation energies also increased. The activa-tion energy of 2-propanol was lower than that ofn-propanol. Branching of the molecule resulted in higher

coefficients of diffusion. The activation energies mea-sured were also in accord with the values of diffusioncoefficients of alcohols for different temperatures. Theactivation energies might be thought of as the energyrequired to produce the diffusive motion of 1 mole ofpenetrant molecules. Large activation energy results ina relatively small diffusion coefficient. The activationenergy of methanol in the zeolite was measured to bethe smallest among those of alcohols, and of all diffusioncoefficients, methanol at all temperatures was thegreatest.

Conclusions

Diffusion coefficients, modes of transport, and theactivation energies of simple alcohols into the porousstructure of a Turkish natural zeolite were studied.

The diffusion exponents, n, were calculated to bebetween 0.96 and 1.00 in all experiments done at alltemperatures, indicating an anomalous diffusion mech-anism, which might be assumed to be presented by Caseb, c, or d or any of the combinations of the limiting typesof diffusion of the molecules flowing through the zeoliticmaterial.24

It was concluded that, as the molecular weight of thesolvent increases, diffusion constants decrease, theactivation energy for diffusion increases, and the timenecessary to come to equilibrium increases. The diffu-sion of n-butanol in the zeolite seemed to be less,compared to those of the smaller alcohols. In all of thesamples, the diffusion constants increased linearly withan increase in the temperature. The diffusion of alcoholsin the zeolite obeyed an anomalous transport mecha-nism. Diffusion rate constants slightly increased as thetemperature was increased.

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2224 Energy & Fuels, Vol. 19, No. 6, 2005 Sakintuna et al.