Fluid Phase Equilibria 382 (2014) 169–179

Diffusion of alcohols and aromatics in a mesoporous MCM-41 material

Asli Nalbant Ergün a, Züleyha Özlem Kocabaş a, Alp Yürümb, Yuda Yürüma,*aMaterial Science and Nano Engineering Program, Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, Istanbul 34956, Turkeyb Sabanci University Nanotechnology Research and Application Center, Tuzla, Istanbul 34956, Turkey

A R T I C L E I N F O

Article history:Received 11 June 2014Received in revised form 20 August 2014Accepted 4 September 2014Available online xxx

Keywords:MCM-41MesoporousDiffusivityKnudsenTransport mechanism

A B S T R A C T

The aim of the present paper was to measure the apparent diffusivities, Knudsen diffusivities, porediffusivities and activation energies of diffusion at 26–32 �C and to determine the modes of transport ofsome alcohols (methanol, ethanol, propanol, n-butanol) and aromatics (benzene, ethylbenzene,propylbenzene, toluene, o-xylene, m-xylene, p-xylene) into the mesoporous structure ofMCM-41 synthesized. As the molecular weight of the alcohols and aromatics increased, apparentdiffusivities decreased and the activation energy for diffusion increased. Lower molecular weightalcohols and aromatics had higher diffusivities compared to those with higher molecular weight alcoholsat the same temperatures. The diffusion of isomeric molecules within the mesoporous channels wereaffected by the position of branching. The deterministic behavior depended on the molecular weight,length of side chain and ortho, meta and para isomerism of the molecule. Increasing the temperatureraised the kinetic energy of the molecules, which resulted in an increase in the diffusivities of the alcoholsand aromatics in MCM-41. Diffusion rate constants of alcohols and aromatics increased with increasingtemperature within the range of 26–32 �C, and the rate decreased as the molecular weight of the diffusingchemical increased. The diffusion of alcohols and aromatics in MCM-41 obeyed the anomalous transportmechanism. Diffusion exponents, n, being in the range of 0.99–1.07, indicated an anomalous diffusion(non-Fickian/super-Case II) mechanism for alcohol diffusion. However, for the case of aromatics,diffusion exponents, from 0.7 to 1.00, indicated that the diffusion mechanisms were either non-Fickian ornon-Fickian/super-Case II depending on the substitution to the benzene ring. Activation energies ofalcohols and aromatics were also in good agreement with the values of diffusivities of alcohols andaromatics such that larger activation energies resulted in smaller diffusivities. Alcohols and aromaticswith greater solubility parameters were found to have greater diffusivities.

ã 2014 Elsevier B.V. All rights reserved.

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Fluid Phase Equilibria

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1. Introduction

Diffusion is the random transfer of molecules or small particles,occurring due to thermal energy. A better understanding of thisphenomenon will aid in optimizing separation, kinetics, andcatalytic processes industrial applications. For example, inseparation processes, the necessity to comprehend the diffusionphenomena is obvious. In addition, membrane-based separationsalso rely on the diffusion properties of the utilized membrane.Therefore, to advance in practical applications, diffusion must beprecisely understood.

Zeolites and related materials are microporous crystallinesolids of special interest in the chemical and the petroleumindustries, which are used as catalysts and sorbents [1]. For theseapplications, migration or diffusion of sorbed molecules throughthe pores and cages within the crystals plays a dominant role.

* Corresponding author. Tel.: +90 533 6333340.E-mail address: yyurum@sabanciuniv.edu (Y. Yürüm).

0378-3812/$ – see front matter ã 2014 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.fluid.2014.09.009

Various techniques for the measurement of intracrystallinediffusion have been developed [2–7], which widely vary in scope,degree of experimental and theoretical sophistication, and range ofapplicability. For a large number of indirect methods, thediffusivity is calculated from the external measurement ofpressure, concentration, or sample weight. Seferinoglu and Yürüm[8] measured the diffusivities of pyridine in raw and acid-washedlow-rank coals. The method they used was simple and precise forthe measurement of diffusivities of solvents in coals. Ritger andPeppas [9] and Howell and Peppas [10] studied diffusion processesto describe the transport kinetics for pyridine in coal. Bludau et al.[11] studied the uptake of pyridine into mordenite and H-ZSM-5.Their data evaluation was based on the solution of Fick’s secondlaw, using diffusivities for the whole process. Dyer and White [12]studied cation diffusion in a natural zeolite called clinoptilolite andcompared three different approaches to determine diffusivities,including Fick’s second law of diffusion, which was found toproduce similar results with other approaches. The applicability ofvarious models for the determination of ion exchange diffusivitiesin clinoptilolite was examined in another study [13]. Marecka and

170 A.N. Ergün et al. / Fluid Phase Equilibria 382 (2014) 169–179

Mianowski [14] used Fick’s second law to determine sorption ofcarbon dioxide and methane in a highly metamorphosed coal, andthe results of the model were compared with the experimentalkinetics of nitrogen sorption on type A zeolite.

It is proposed that there are at least five limiting types ofdiffusion for the molecules flowing through a zeolitic material[15]:

Case a. Unrestricted intracrystalline diffusion: the moleculemoves in the channels and cavities of a crystallite without crossingthe surface of the solid or extended crystal defects.

Case b. Modified intracrystalline diffusion: the particle crossesextended (e.g., dislocations and mosaic boundaries) or localized(e.g., vacancies and cations in noncrystallographic positions)crystal defects hindering or, sometimes, enhancing its motion.

Case c. Restricted intracrystalline diffusion: the molecule isreflected at the crystal boundary because of a very low probabilityof desorption.

Case d. Intercrystalline diffusion: the molecule migratesbetween different crystals, so it is sorbed most of the time butnot confined to the same crystal. Sometimes this type of diffusioninvolves surface film formation and diffusion on the zeolitesurface.

Case e. Diffusion in the fluid phase: the particle remains in thegas or liquid phase, confined only by the walls of the vesselcontaining the sample.

Volatile organic chemicals are one of the main side products ofindustry and deserve a detailed study for the applications wherediffusion is important. Moreover, diffusion of volatile vapors insidezeolites is complicated because molecules not only diffuse throughpores but also interact with the solid surface. Pore structure andinteraction between the fluid and solid phases influence the overalldiffusion rate, and therefore intraparticle diffusivity is usuallysystem-dependent and has to be estimated experimentally. MCM-41 has high potential as an adsorbent for small and bulky adsorbatemolecules due to its mesoporous structure and high surface area.Adsorption of N2 [16–22] and water [18,23–25] on MCM-41 hasbeen thoroughly investigated. There are also some studies basedon heavier hydrocarbons, such as benzene [26,27], toluene [28],cyclopentane [29,30], cyclohexane [29–32], propane, and methane[33] on MCM-41.

For the calculation of the diffusivities, the following assump-tions were made:

i. the diffusion mechanism obeyed Fick’s law,ii. the crystallites possessed a spherical shape,iii. the concentration profile of the sorbed vapor in these spheres

showed radial symmetry,iv. the diffusion was assumed to be isotropic and it could be

described by a single diffusivity rather than a diffusion tensor,and

v. the diffusivity did not depend on sorbate concentration.

The determination of diffusivities is based on the uptakemeasurement of the volatile component by MCM-41. A convenientmethod of analysis involves fitting the sorption data to empiricalEq. (1). It is possible to express the initial rate of diffusional solventpenetration in terms of this equation:

Table 1Physical and structural properties of MCM-41 type material synthesized by microwave

Sample ID(Power/Time)(W/Min.)

BET surface area,(m2/g)

BJH des. porevolume, (cm3/g)

BJH des. poreDiameter,rp, (nm)

MCM-41 (120/30) 1438 0.53 4.00

Mt

M1¼ ktn (1)

where Mt is the amount of solvent diffused in to the macromolec-ular structure at time t,M1 is the amount of solvent diffused after asteady state condition is reached, t is the release time, k is the rateconstant which depends on structural characteristics of thesystem, and n is an exponent characteristic of the mode oftransport of the solvent in the porous structure and varies with thediffusion mechanism and particle geometry.

When a porous adsorbent material is placed in contact with asolvent (penetrant) vapor, diffusion of the penetrant in the porousmaterial may be followed by measuring the uptake of the solvent.Diffusion in the silicalite crystals can be described by Fickiandiffusion with concentration-independent diffusivity, D. In Fickformulation, the driving force for diffusive transport is the gradientof chemical potential of concentration, rather than the gradient ofconcentration [34]. The kinetics of the diffusion into the sphere inFick formulation is expressed by Eq. (2) [8].

Mt

M1¼ 1 � 6

p2 S1

n¼1

1n2expð�Dn2p2 t

a2Þ (2)

where Mt and M1 represent the amount of solvent vapor diffusedentering the spheres with radius a, at times t and steady state,respectively, and n is an integer coming from the solution of Fick’ssecond law. D is the diffusivity of the solvent vapor. This equation isbased on the assumption that the particle radius does not change,which is true for zeolite particles. The solution to Eq. (2) is given inEq. (3) [35].

Mt

M1¼ 6

Dta2

� �12

p�12

þ 2 S1

n¼1ierfc

naffiffiffiffiffiffiDt

p� �

� 3Dta2

(3)

For short periods of diffusion, Eq. (3) approximates to

Mt

M1¼ 6

Dtpa2

� �� 3Dt

a2(4)

Neglecting the contribution of the term 3Dt/a2, the value of D canbe found from the slope of a plot of Mt/M1 versus t1/2. In this study,the apparent diffusivities were calculated from the first 60% of theramp of the uptake versus time graph. Here, the diffusion wasassumed to show a linear behavior [36,37]. This linear range alsoincludes the surface barrier resistance including resistances ofreflecting boundaries and absorbing boundaries [38].

Graphs of Mt/M1 versus t1/2 for the solvent vapor diffusion inmesopores were plotted in order to calculate the apparentdiffusivities. The slope of this graph was used to calculate theapparent diffusivities. The type of transport mechanisms of volatilesolvents in the mesopores of MCM-41 materials were predictedfrom the values of diffusion rate constants, k, and diffusionexponents, n, which were calculated from the graphs of ln(Mt/M1)versus lnt.

Pore diffusion that is the movement of fluids (gas or liquid) intothe interstices of porous solids or membranes occurs in membraneseparation, zeolite adsorption and reverse osmosis. Diffusioninside particles is complicated because molecules not only diffusethrough pores but also interact with the solid surface. Porestructure and interaction between the fluid and solid phasesinfluence the overall diffusion rate, and therefore intraparticle

assisted direct synthesis method.

Interplanar spacing,d100, (nm)

Latticeparameter,a,(nm)

Pore qallthickness,d, (nm)

Particleporosity, em

3.64 4.20 0.38 0.54

Fig. 1. a) Nitrogen sorption isotherm obtained at 77 K and b) pore size distribution of the MCM-41 sample.

A.N. Ergün et al. / Fluid Phase Equilibria 382 (2014) 169–179 171

diffusivity is usually system-dependent and these parameters hasto be evaluated with experimental methods. The pore diffusivity iscalculated from the following Eq. (5) [39],

Dp ¼ DK

t(5)

where, DK is Knudsen diffusivity. For a vapor of molecular weightM, which diffuses along the pore with rp cm radius at a temperatureof T, the value of DK (cm2/s) is

DK ¼ 9700rpTM

� �12

(6)

tortuosity factor t, has been measured experimentally bySalmas et al. [40] as 2.40, for MCM-41 materials having a porevolume of 0.54 cm3/g.

Diffusion, which is an activated process, requires overcoming anenergy barrier. There are also other activated processes found inMCM-41, especially chemical reactions occurring in the channelsand cavities. If the activation energy is smaller than, equal to, orslightly larger than the available thermal energy, the probability ofovercoming the energy barrier is sufficiently high to allow theactivated process to occur for a statistically meaningful number of

times during a reasonably long simulation. Activation energies ofdiffusion were calculated using the Eqs. (8) and (9) below:

D ¼ D0e � EART

(7)

lnd ¼ lnD0 � EART

(8)

where D0 is a temperature-independent pre-exponential (m2/s)and EA is the activation energy of diffusion [41]. The activationenergies of diffusion for alcohols and aromatics were calculatedfrom the slope of the Arrhenius graph of lnD versus 1/T.

In order to obtain more information about the adsorptionmechanism and rate controlling steps, the intraparticle diffusionmodel Eq. (10), which was proposed by Weber and Morris [42], wasapplied at 32 �C;

qt¼kint 0:5 þ A (9)

where, qt is the amount of adsorbed volatile solvent by mesoporousstructure (g/g) at time t, kint (g/(g min0.5)) is the internal diffusionrate constant and A is the intercept of the linear plot of qt versust0.5.

Fig. 2. Representative XRD pattern of MCM-41 studied.

172 A.N. Ergün et al. / Fluid Phase Equilibria 382 (2014) 169–179

The aim of the present paper was to measure the apparentdiffusivities, Knudsen diffusivities, pore diffusivities and activationenergies of diffusion and to determine the modes of transport ofsome alcohols (methanol, ethanol, propanol, n-butanol) andaromatics (benzene, ethylbenzene, propylbenzene, toluene,o-xylene, m-xylene, p-xylene) in mesoporous MCM-41 synthe-sized. The present paper is the first of a series of experimentalinvestigations, which will report the transport of volatile organiccompounds in porous media.

2. Experimental section

2.1. Materials and synthesis of MCM-41 material

The synthesis procedure for MCM-41 material was a modifiedmethod described by Davis et al. [16] 6.6 g of hexadecyltrimethy-lammonium bromide was dissolved slowly in 43 mL of deionized

Fig. 3. TEM image of MCM-41 sample studied.

water at 40 �C and 5.65 mL of sodium silicate solution was addeddropwise to the clear solution with continuous stirring at the sametemperature. After stirring for 1 h, the pH of the mixture wasadjusted to 11 by adding sufficient amount of 1 M H2SO4. Theresulting gel was stirred for 1 h before being transferred to a120 mL Teflon autoclave. The autoclave was placed in a DelonghiEMD MW 311 model microwave oven with a Velp Scientifica VTFDigital Thermoregulator. The microwave oven operated at 230 V,50 Hz, with adjustable power output of 800 W. The gels underautogeneous pressure were allowed to absorb microwave energyof 120 W to achieve the desired reaction temperature of 120 �C, for30 min. The resultant solid was recovered by filtration, washedthoroughly with distilled water until the pH reached 7, and finallydried at room temperature. Before the calcination step, the solidwas kept at 40 �C for 24 h. The as-synthesized MCM-41 was finallycalcined inside a quartz filter installed quartz tube (120 cmlong � 1 cm diameter) which was placed in a tubular furnace.The calcination condition was reached by heating from ambienttemperature to 550 �C at a rate of 1 �C/min, after that thetemperature was kept at 550 �C for 6 h in a flow of dry air. Atthe end of the calcination, the system was let to cool down to roomtemperature.

Fig. 4. Ethanol uptake of MCM-41 at 26 �C.

Fig. 7. Apparent diffusivities of alcohols in MCM-41.

Fig. 5. Mt/M1 versus t1/2 graph of ethanol diffusion in MCM-41 at 26 �C.

A.N. Ergün et al. / Fluid Phase Equilibria 382 (2014) 169–179 173

2.2. Surface area measurements

The surface area and porosity of the MCM-41 were determinedusing NOVA 2200e Surface Area and Pore Size Analyzer byQuantachrome Instruments Co., USA. The measurement wasperformed at the liquid nitrogen boiling point of 77 K. The sampleswere outgassed at 150 �C overnight. The BET surface area wasdetermined by a multipoint BET method using the adsorption datain the relative pressure (P/P0) range of 0.05–0.3. The pore volumeand pore size distributions were calculated using the BJH (Barrett–Joyner–Halenda) method [43].

2.3. Diffusion experiments

Diffusional behaviors of the alcohols: methanol, ethanol,propanol, n-butanol, and the aromatics: benzene, ethylbenzene,propylbenzene, toluene, o-xylene, m-xylene, p-xylene in porousmedia were investigated in detail in an adiabatic isothermal setup.The alcohols and aromatic solvents were purchased from Aldrichand they were used as received. The adiabatic isothermal setup[8,44,45] designed and built in our laboratories, was used in thediffusion experiments. A Sartorius CP 124 S analytical balance with0.0001 g accuracy was placed in a Memmert model 300 laboratoryoven. Accuracy of the balance was sufficient to follow the uptake ofthe solvent with time. At the start of the experiment, approxi-mately 0.05 g of MCM-41 sample (100% degassed with heating)was evenly distributed in a sample holder and its initial weight was

Fig. 6. ln(Mt/M1) versus lnt graph of ethanol diffusion in MCM-41 at 26 �C.

recorded. The size of the sample was small enough to prevent heateffects that might mask the diffusion. After that, wide beakersfilled with 50 mL of the solvent were placed into the system. Whenthe temperature reached the constant set values of 26.0, 28.0,30.0 and 32.0 �C, the weight increase of the MCM-41 was recordedevery 5 s with the aid of Sarto Connect software installed on the PC.The experiment was continued until the software collected2000 data points and a constant weight was attained. Allexperiments were repeated at least five times.

3. Result and discussion

3.1. Physical and structural properties

Physical and structural properties of MCM-41 type materialsynthesized with low microwave power (120 W) at 120 �C in30 min are presented in Table 1. The BET surface area of the MCM-41 material was measured as 1438 m2/g. In the literature, BETsurface areas of various MCM-41 materials varied from 360 to1218 m2/g [17,21,46,47]. When compared with these materials inthe literature, MCM-41 prepared in this study has the highestspecific surface area value.

Nitrogen adsorption/desorption isotherms and pore volumedistribution of the MCM-41 sample are given in Fig. 1a and 1b,respectively. The isotherm was classified as type IV according to theIUPAC nomenclature. Thus, the isotherm indicated a linear increaseof adsorbed volume at low relative pressures (P/P0< 0.1) due tomonolayer adsorption on the surface of micropores, followed by asteep increase in nitrogen uptake at a relative pressure of 0.25< P/P0 due to capillary condensation inside the mesopores. Thisphenomenon is highly characteristic of MCM-41 [48]. The steepadsorption starting from 0.25 < P/P0 was associated with progres-sive filling of mesopores in the main channels (primary meso-pores) by the process of capillary condensation, and the narrow

Table 2Apparent diffusivities (m2/g) of alcohols in MCM-41 measured at differenttemperatures.

Alcohols 26 �C 28 �C 30 �C 32 �C

Methanol 4.01 �10�13 4.38 � 10�13 8.43 � 10�13 9.99 � 10�13

Ethanol 1.83 � 10�13 2.34 �10�13 2.70 � 10�13 3.38 � 10�13

n-Propanol 8.26 � 10�14 1.09 � 10�13 1.40 � 10�13 1.72 � 10�13

n-Butanol 2.51 �10�14 4.13 � 10�14 5.68 � 10�14 6.36 � 10�14

Fig. 8. Apparent diffusivities of aromatics in MCM-41.

174 A.N. Ergün et al. / Fluid Phase Equilibria 382 (2014) 169–179

hysteresis loop that occurred at 0.40 < P/P0< 0.65 are characteris-tic features of mesoporous materials having a narrow range ofuniform and cylindrical pores [49,50]. The long plateau at higherrelative pressures indicates that after capillary condensation of themesopores, multilayer adsorption continued on the surface of thematerial. The pore volume and pore size distributions wereestimated from the desorption branch of the isotherms by theBarrett–Joyner–Halenda (BJH) method. The isotherm gave a porevolume of 0.53 cm3/g. From the BJH method a pore size distributioncurve was drawn (Fig. 1b) and as can be seen from the curve theMCM-41 sample under the study exhibited a remarkable narrowpore volume distribution with a mean pore diameter of 4.00 nm.Fig. 2 presented the low-angle (2u value ranging from 2� to 7�) XRDpattern. Also, in Fig. 3, TEM image of the sample can bee seen. Asthese figures illustrates, MCM-41 samples prepared have a highly

Table 3Apparent diffusivities (m2/g) of aromatic solvents in MCM-41 measured at different te

Aromatic solvents 26 �C 28 �C

Benzene 3.96 � 10�14 5.47Toluene 3.79 � 10�14 4.35Ethylbenzene 3.74 �10�14 4.12

Propylbenzene 3.26 � 10�14 3.52o-Xylene 3.68 � 10�14 3.96m-Xylene 3.42 � 10�14 3.79p-Xylene 3.11 �10�14 3.47

ordered structure. The diffractogram of the MCM-41 produced inthe present work shows three Bragg peaks that can be indexed as(10 0), (110), and (2 0 0). The characteristic (10 0) Bragg peak islocated at 2u = 2.43�. This corresponds to a d100 value of 3.64 nm.The characteristic lattice parameter a, defined as the repeatingdistance between two pore centers, was evaluated from thefollowing Eq. (11) [51]:

a ¼ 2ffiffiffi3

p d100 (10)

and the pore wall thickness (d) was evaluated from thefollowing Eq. (12) [51]:

d ¼ a � 0:95Dpore (11)

For the MCM-41 samples prepared, the equations above gave apore wall thickness of 0.38 nm. In addition, SEM images (not shownhere) reveal that the samples have an agglomerate size of 0.5 mm.

3.2. Solvent uptake and apparent diffusivities

The uptake measurements of volatile solvents into the porousMCM-41 samples were recorded until the equilibrium wasattained. As an example, ethanol uptake measurement in MCM-41 at 26 �C is given in Fig. 4. As the molecular weight of the solventincreased, the time needed to reach equilibrium also increased.

Since it was assumed [36,37] that diffusion occurred linearlyduring the first 60% of the ramp (�20 min), all the calculations forthe coefficients of diffusion and the activation energy were basedon the data in this region. Graphs of Mt/M1 versus t1/2 for thediffusion of vapors of alcohols and aromatics in the mesoporousMCM-41 material were plotted in order to calculate the coefficientsof diffusion; Fig. 5 is presented as an example for the calculation ofthe coefficient of diffusion of ethanol at 26 �C. The slope of thisgraph was used for calculating the apparent diffusivities. The typeof transport mechanisms of volatile solvents in the mesopores ofMCM-41 materials were predicted from the values of diffusion rateconstants, k, and diffusion exponents, n, which were calculatedfrom the graphs of ln(Mt/M1) versus lnt, (Fig. 6).

The change in apparent diffusivities of methanol, ethanol,n-propanol and n-butanol at 26, 28, 30 and 32 �C are presentedgraphically in Fig. 7. The numerical data are given in Table 2. Lowermolecular weight alcohols had higher diffusivities compared tothose with higher molecular weight alcohols at the sametemperatures. For example, the diffusivities of methanol, ethanol,n-propanol and n-butanol were measured as 4.01 �10�13,1.83 � 10�13, 8.26 � 1 10�14 and 2.51 �10�14m2/g at 26 �C, respec-tively. Thus, high molecular weight alcohols diffused less in to theMCM-41 material. This relative less diffusion was due to sterichindrances at the same temperature.

Increasing the temperature raised the kinetic energy of themolecules, which resulted in an increase in the diffusivities of thealcohols in MCM-41. For instance, the diffusivities of methanol at26, 28, 30, and 32 �C were measured as 4.01 �10�13, 4.38 � 10�13,8.43 � 10�13, 9.99 � 10�13m2/s respectively. The diffusivities of the

mperatures.

30 �C 32 �C

� 10�14 7.38 � 10�14 9.52 �10�14

�10�14 5.94 �10�14 7.85 �10�14

� 10�14 5.87 � 10�14 6.64 �10�14

�10�14 3.90 � 10�14 4.41 �10�14

� 10�14 5.21 �10�14 6.50 � 10�14

� 10�14 4.65 �10�14 6.01 �10�14

� 10�14 4.35 �10�14 5.67 � 10�14

Table 5Knudsen and pore diffusivities of some aromatic solvents in MCM-41.

Knudsen diffusivity (m2/s) Pore diffusivity (m2/s)

26 �C 28 �C 30 �C 32 �C 26 �C 28 �C 30 �C 32 �C

Benzene 3.80 � 10�7 3.81 �10�7 3.82 �10�7 3.83 � 10�7 1.58 � 10�7 1.59 � 10�7 1.59 � 10�7 1.60 � 10�7

Toluene 3.50 � 10�7 3.51 �10�7 3.52 �10�7 3.53 � 10�7 1.46 � 10�7 1.4 �10�7 1.47 � 10�7 1.47 � 10�7

Ethylbenzene 3.26 � 10�7 3.27 � 10�7 3.28 � 10�7 3.29 � 10�7 1.36 � 10�7 1.36 � 10�7 1.37 � 10�7 1.37 � 10�7

Propylbenzene 3.06 � 10�7 3.07 � 10�7 3.08 � 10�7 3.09 � 10�7 1.28 � 10�7 1.28 � 10�7 1.28 � 10�7 1.29 � 10�7

o-Xylene 3.26 � 10�7 3.27 � 10�7 3.28 � 10�7 3.29 � 10�7 1.36 � 10�7 1.36 � 10�7 1.37 � 10�7 1.37 � 10�7

m-Xylene 3.26 � 10�7 3.27 � 10�7 3.28 � 10�7 3.29 � 10�7 1.36 � 10�7 1.36 � 10�7 1.37 � 10�7 1.37 � 10�7

p-Xylene 3.26 � 10�7 3.27 � 10�7 3.28 � 10�7 3.29 � 10�7 1.36 � 10�7 1.36 � 10�7 1.37 � 10�7 1.37 � 10�7

Table 4Knudsen and pore diffusivities of some alcohols in MCM-41.

Knudsen diffusivity (m2/s) Pore diffusivity (m2/s)

26 �C 28 �C 30 �C 32 �C 26 �C 28 �C 30 �C 32 �C

Methanol 5.93 � 10�7 5.95 �10�7 5.97 � 10�7 5.99 � 10�7 2.47 � 10�7 2.48 � 10�7 2.49 � 10�7 2.49 � 10�7

Ethanol 4.94 �10�7 4.96 � 10�7 4.98 � 10�7 4.99 � 10�7 2.06 � 10�7 2.07 � 10�7 2.07 � 10�7 2.08 � 10�7

n-Propanol 4.33 � 10�7 4.34 �10�7 4.36 � 10�7 4.37 � 10�7 1.80 � 10�7 1.81 �10�7 1.82 � 10�7 1.82 � 10�7

n-Butanol 3.90 � 10�7 3.91 �10�7 3.92 � 10�7 3.94 �10�7 1.62 � 10�7 1.63 � 10�7 1.63 � 10�7 1.64 �10�7

A.N. Ergün et al. / Fluid Phase Equilibria 382 (2014) 169–179 175

other alcohols (ethanol, n-propanol, and n-butanol) used alsoincreased as the temperature was increased to 28, 30, and 32 �C.

Dyer and Amin [52] studied the liquid-phase self-diffusion ofethanol and n-butanol in heteroionic zeolites; coefficients ofdiffusion measured by these workers are much lower (�1.15 �10�18 m2/s and �1.94 �10�18m2/s) than those measured in thepresent work. This is definitely due to the difference of liquid-phase uptake of ethanol and n-butanol in their work and the gas-phase diffusion of the same alcohols measured in the presentreport. Sorption/diffusion of liquid and gas (or vapor) phases inzeolites differs from each other from the intracrystalline masstransfer point of view of sorbate molecules in the zeolite channels[53].

Sakintuna et al. [44] studied the diffusion of methanol, ethanol,n-propanol, i-propanol and n-butanol in a natural zeolite with40.2% micropores, 57.9% mesopores and 1.9% macropores, and59 m2/g surface area. The diffusivities of methanol, ethanol,n-propanol, i-propanol and n-butanol were 10 times lower than

Table 6Diffusion rate constants, diffusion exponents, transport mechanism and activation ene

Alcohol T, �C k, s�1 n R2

Methanol 26 2.56 � 10�4 1.00 0.999

28 2.93 �10�4 1.00 0.985

30 3.20 � 10�4 1.00 0.993

32 1.50 � 10�3 1.00 0.997

Ethanol 26 2.16 � 10�4 1.00 0.997

28 2.23 �10�4 1.00 0.990

30 2.36 � 10�4 1.00 0.987

32 2.69 � 10�4 1.00 0.983

n-Propanol 26 8.35 �10�5 1.00 0.991

28 1.12 � 10�4 1.00 0.986

30 1.35 �10�4 1.07 0.984

32 1.70 � 10�4 1.08 0.995

n-Butanol 26 8.84 �10�5 1.00 0.993

28 9.84 �10�5 1.03 0.997

30 1.09 � 10�4 0.99 0.987

32 1.25 �10�4 1.00 0.984

the values measured in the present work. It is clearly seen that,higher surface area of MCM-41 (1438 m2/g) was more accessiblefor the alcohols used.

The apparent diffusivities of benzene, toluene, ethylbenzene,propylbenzene, o-xylene, m-xylene and p-xylene at 26, 28, 30 and32 �C are presented graphically in Fig. 8. The numerical data aregiven in Table 3. The experimental results can be discussed in twoterms of groups: benzene, toluene, ethylbenzene and propylben-zene as the first group and benzene, toluene, o-xylene, m-xylene,p-xylene as the second group according to their organic structures.

The apparent diffusivities of benzene were the highest amongthese two groups and increased from 3.96 � 10�14 to9.52 � 10�14m2/g as the temperature was increased from 26 to32 �C. As the molecular weight of the aromatic compoundincreased, diffusivities decreased. For instance, diffusivities ofbenzene, toluene, ethylbenzene and propylbenzene at 26 �C were3.96 � 10�14 m2/g, 3.79 � 10�14m2/g, 3.74 �10�14m2/g, and3.26 � 10�14m2/g respectively, and diffusivities of o-xylene,

rgy of diffusion of alcohols in MCM-41.

Transport mechanism Ea, Activation energy of diffusion, kJ/mol

non-Fickian/super-Case II 65non-Fickian/super-Case IInon-Fickian/super-Case IInon-Fickian/super-Case II

non-Fickian/super-Case II 76non-Fickian/super-Case IInon-Fickian/super-Case IInon-Fickian/super-Case II

non-Fickian/super-Case II 93non-Fickian/super-Case IInon-Fickian/super-Case IInon-Fickian/super-Case II

non-Fickian/Super-Case II 118non-Fickian/Super-Case IInon-Fickian/Super-Case IINon-Fickian/Super-Case II

Table 7Diffusion rate constants, diffusion exponents, transport mechanism and and activation energy of diffusion of aromatics in MCM-41.

Aromatics T, �C k, s�1 n R2 Transport mechanism Ea, Activation energy of diffusion, kJ/mol

Benzene 26 1.06 � 10�4 1.00 0.993 non-Fickian/super-Case II 4828 1.92 � 10�4 1.00 0.998 non-Fickian/super-Case II30 2.39 � 10�4 1.09 0.996 non-Fickian/super-Case II32 2.44 �10�4 0.98 0.999 non-Fickian/super-Case II

Toluene 26 3.04 �10�5 1.00 0.997 non-Fickian/super-Case II 9128 4.45 �10�5 1.00 0.998 non-Fickian/super-Case II30 4.93 �10�5 1.00 0.997 non-Fickian/super-Case II32 5.66 � 10�5 0.93 0.998 non-Fickian/super-Case II

Ethylbenzene 26 1.42 � 10�3 0.86 0.996 non-Fickian/super-Case II 9828 1.55 �10�3 0.78 0.999 non-Fickian30 1.61 �10�3 0.81 0.999 non-Fickian32 2.80 � 10�3 0.75 0.999 non-Fickian

Propylbenzene 26 1.67 � 10�3 0.76 0.999 non-Fickian 11228 1.81 �10�3 0.76 0.998 non-Fickian30 1.84 �10�3 0.74 0.998 non-Fickian32 2.36 � 10�3 0.72 0.999 non-Fickian

o-Xylene 26 2.20 � 10�3 0.77 0.999 non-Fickian 12128 1.49 � 10�3 0.83 0.999 non-Fickian30 2.05 �10�3 0.80 0.998 non-Fickian32 2.73 � 10�3 0.76 0.999 non-Fickian

m-Xylene 26 1.12 �10�3 0.86 0.999 non-Fickian 12628 2.71 �10�3 0.73 0.999 non-Fickian30 3.55 �10�3 0.70 0.998 non-Fickian32 3.62 �10�3 0.71 0.995 non-Fickian

p-Xylene 26 1.08 � 10�3 0.86 0.999 non-Fickian/super-Case II 13328 2.85 �10�3 0.74 0.998 non-Fickian30 3.14 �10�3 0.76 0.997 non-Fickian32 4.41 �10�3 0.73 0.997 non-Fickian

176 A.N. Ergün et al. / Fluid Phase Equilibria 382 (2014) 169–179

m-xylene and p-xylene at 26 �C were 3.68 � 10�14m2/g,3.42 � 10�14m2/g, and 3.11 �10�14m2/g, respectively.

As the chain length of the alkyl group attached to the benzenering increased, the diffusivities slightly decreased, i.e.,3.96 � 10�14m2/g (benzene) and 3.26 � 10�14m2/g(propylbenzene) at 26 �C. Within the xylenes, there were somedifferences in the diffusivities at the same temperatures dependingon the position of the alkyl substitution. Among ortho, meta andpara isomers of xylenes, the biggest apparent diffusivities wasmeasured with p-xylene. This was probably due to the therelatively more linear structure of the p-xylene compared to theother isomers. This linear structure of the p-xylene made itpossible for p-xylene to fit in to the entrance of the linear tunnelsof MCM-41 and diffuse in the tunnels more easily. It can beconcluded that, the diffusion of isomeric molecules within themesoporous tunnels were affected by the position of branching.Since ortho and meta isomers have non-linear structurescompared to the para isomer, they suffered more friction withinthe tunnels and diffused comparably slower within the tunnels. Suiet al. [54] systematically studied the adsorption and diffusionbehaviors of benzene and thiophene on NaY, Si-MCM-41,NaY/Si-MCM-41 mixtures, and Y/MCM-41 composite molecularsieve to obtain adsorption isotherm and relative diffusioncoefficient. It was found that the adsorption mechanisms ofbenzene and thiophene were different. The adsorption of benzenewas mainly by physical adsorption, while electrons played themost important role in the adsorption of thiophene.

It was established that the diffusion of the probe moleculestakes place entirely through the intrawall porous structure and iscontrolled by the combination of micropore and small mesoporeresistances. The primary mesopores may also play a role infacilitating diffusion through the mesoporous structure of MCM-

41 materials with low micropore content. With a decrease in themicropore volume, the diffusivity increases and activation energydecreases. In addition to that, the diffusion in small mesoporesplays an important role. Adem et al. [55] studied diffusionproperties of hexane in pseudomorphic MCM-41 mesoporoussilicas by Pulsed Field Gradient (PFG) NMR. The study of silicaswith different particle sizes and different pore sizes and theirMCM-41 pseudomorphs as a function of time allowed todemonstrate the possibilities of this technique. It was confirmedthat for monomodal porosities the diffusivities increases when thepore size increases: pore diameters of 3.8 nm,6.0 nm, and 18 nmlead to diffusion coefficients of 4.1 �10�10m2s�1, 5.9 � 10�10m2s�1,and 50 � 10�10m2s�1, respectively. The greater values of diffusiv-ities obtained in the work of Adem et al. [55] was probably due tothe smaller molecular size of hexane compared to the molecularsize of probe molecules used in the present work. With theincrease in the molecular size, less and less probe molecules canenter the micropores which yields a more mesopore controlledprocess and a lower activation energy.

3.3. Knudsen and pore diffusivities

Knudsen and pore diffusivities of alcohols and aromatics arepresented in Tables 4 and 5, respectively. The values of Knudsenand pore diffusivities of the alcohols and aromatics in MCM-41,presented in the Tables 4 and 5, are in the order of 10�7m2/s.Diffusion of molecules in porous systems is highly dependent onthe dimensions of the pore network. Transport of molecules in verylarge pores is essentially governed by molecular diffusion sincecollisions with other molecules are much more frequent thencollisions with the pore walls. As the pore dimension reduces andthe mean free path of the molecule increases, the flowing species

Fig. 9. Arrhenius graphs for a) ethanol and b) toluene.

A.N. Ergün et al. / Fluid Phase Equilibria 382 (2014) 169–179 177

tend to collide more and more with the pore walls. At this point,according to the Knudsen flow, the flow of molecules becomesalmost independent of each other [56,57]. In the Knudsen regime,molecule-wall collision is dominant and the diffusivity decreaseswith the pore size. At even smaller pore sizes, in the range of 2 nmor less (when the pore diameter turns out to be similar to the size ofthe molecules), the molecules will constantly experience an

Fig. 10. Intraparticle diffusion model for the methanol adsorption onto the MCM-41.

interaction with the pore surface. Thus, in the micropores ofzeolites or related materials, typically configurational diffusionregime occurs [58]. The values of the apparent diffusivities foralcohols and aromatics are presented in Tables 2 and 3 respectively.These values are in the order of 10�13–10�14m2/s. In addition, thevalues of Knudsen and pore diffusivities presented in Tables 4 and 5are in the order of 10�7 m2/s. From these tables, it can be clearlyseen that the Knudsen diffusivity values are significantly higherthan the apparent diffusivities. This may indicate that the diffusionof alcohols and aromatics in the MCM-41 was therefore controlledby the configurational molecular transport mechanism. Configu-rational diffusion is a type of molecular transport found in zeolitesand zeotypes, and it is characterized by small diffusivities, strongdependence on the size and shape of the guest molecules, highactivation energies, and strong concentration dependence [59].

3.4. Diffusional rate constants and mode of transport in MCM-41

The type of transport mechanism of alcohols and aromatics inthe zeolitic porous structure can be speculated using the values ofthe diffusion rate constants, k, and diffusion exponents, n. Theseparameters were calculated using ln(Mt/M1) versus lnt graphs. Thediffusion rate constants, diffusion exponents and transportmechanism of alcohols and aromatics in MCM-41 are given inTables 6 and 7, respectively. Linearity analysis of the data, with R2

values greater than 0.98, gave an acceptable linear relationshipbetween ln(Mt/M1) versus lnt.

Sorption mechanisms in macromolecular systems are definedin terms of two limiting cases of Fickian diffusion and Case IItransport [21]. When n = 0.5, the solvent diffuses through and isreleased from the adsorbent with a quasi-Fickian diffusionmechanism. For values of n > 0.5, non-Fickian solvent diffusion isobserved. When n = 0.85, Case II transport occurs and values of nbetween 0.5 and 1.0 indicate anomalous transport. Values aboven = 0.85 are possible and are termed “super-Case II”. For an infiniteplane sheet, the values would be 0.5 and 1.0 for Fickian and pureCase II, respectively. In addition, in the case of an infinite cylinder,these values would be 0.45 and 0.89, respectively [60]. Thediffusion exponents of methanol, ethanol, n-propanol, i-propanoland n-butanol in natural zeolite systems measured by Sakintunaet al. [44] were between 0.96–1.00 indicating an anomalousdiffusion mechanism. Diffusion exponents calculated in thepresent work, being in the range of 0.99–1.07 indicated ananomalous diffusion (non-Fickian/super-Case II) mechanism foralcohol diffusion. However, for the case of aromatics, diffusionexponents from 0.7 to 1.00 indicated that the diffusion mecha-nisms were either non-Fickian or non-Fickian/super-Case IIdepending on the substitution to the benzene ring.

Diffusion rate constants of alcohols and aromatics increasedwith temperature within the range of 26–32 �C, and decreased asthe molecular weight of the diffusing chemical increased. Thediffusion rate constant of methanol in MCM-41 increased from2.56 � 10�4 to 1.50 � 10�3 s�1 when diffusion temperature wasincreased from 26 to 32 �C. For the case of benzene, diffusion rateconstant increased from 1.06 � 10�4 to 2.44 �10�4 s�1 whendiffusion temperature was increased from 26 to 32 �C.

3.5. Activation energies of diffusion of alcohols and aromatics in MCM-41

The activation energies of diffusion for alcohols and aromaticswere calculated from the slope of the Arrhenius graph of lnD versus1/T, Fig. 9. The results are given in Tables 6 and 7 for alcohols andaromatics, respectively. The activation energies of diffusion ofmethanol, ethanol, n-propanol, n-butanol were calculated as 65,76, 93 and 118 kJ/mol, respectively. Sakintuna et al. [44] calculated

Table 8Parameters of intraparticle diffusion model for the alcohols and aromaticsadsorptions in MCM-41.

Adsorbent kp1(g/g.min1/2) kp2(g/g.min1/2) R12 R2

2

Methanol 0.0035 0.0018 0.9988 0.9500Ethanol 0.0030 0.0011 0.9973 0.9839n-Propanol 0.0056 0.0032 0.9991 0.9735n-Butanol 0.0037 0.0019 0.9992 0.9721Benzene 0.0092 0.0013 0.9996 0.8709Toluene 0.0083 0.0031 0.9992 0.8906Ethylbenzene 0.0048 0.0013 0.9995 0.8306Propylbenzene 0.0036 0.0022 0.9994 0.9865o-Xylene 0.0044 0.0021 0.9998 0.9583m-Xylene 0.0049 0.0017 0.9998 0.9156p-Xylene 0.0061 0.0020 0.9993 0.8860

178 A.N. Ergün et al. / Fluid Phase Equilibria 382 (2014) 169–179

the activation energies of diffusion of methanol, ethanol, n-propanol and n-butanol, within the natural zeolites as 18.3, 46.4,79.7, and 90.1 kJ/mol respectively. It seemed that the diffusingmolecules in the MCM-41 have to overcome higher energy barriersthan that of natural zeolites. Once the molecules overcome thisenergy barrier, they move more easily within the mesoporouschannels of MCM-41 than microporous channels of zeolites, whichexplain the higher diffusivities of alcohols within MCM-41. Theactivation energies of aromatics were 48, 91, 98, 112, 121, 126 and133 kJ/mol for benzene, toluene, ethylbenzene, propylbenzene, o-xylene, m-xylene and p-xylene, respectively.

Fig. 11. The relation of diffusivities of a) alcohols and b) aromatics with theirsolubility parameters at different temperatures.

It is observed that an increase in molecular weight (or chainlength) resulted in increases in the activation energy of diffusion. Itseemed that there were influences of chain length, polarity,molecular size and configuration of the diffusing molecules on thediffusivities and activation energies of diffusion. The activationenergies measured were also in accordance with the values ofdiffusivities of alcohols and aromatics at different temperatures.The activation energies might be thought of as the energy requiredto produce the diffusive motion of 1 mole of penetrant molecules.The activation energy of diffusion of methanol in the MCM-41 wasmeasured to be the smallest among those of alcohols, and forbenzene, it was measured to be the smallest among those ofaromatics. With increasing molecular weight of the alcohols andaromatics, the activation energies of diffusion also increased.Larger activation energies resulted in relatively lower values ofdiffusivities for alcohols and aromatics in mesoporous media. Itcan be concluded that there should be a strong relationshipbetween the chain length, molecular size and polarity of themolecule on the diffusivities and activation energies.

3.6. Intraparticle diffusion

The intraparticle diffusion model indicated the presence of twolinear sections in the experimental data, Fig. 10. At the first linearstage, fast adsorption of solvents was observed due to the externalsurface adsorption [61]. However, in the second linear stage,slower adsorption of volatile solvent into mesoporous structureindicated the intraparticle diffusion process. As shown in Table 8,values of kp1 were higher than those of kp2, both for alcohols andaromatics, signifying that the rate of adsorption was higher in thebeginning since more reactive sorption sites on the mesoporousstructure were available at the initial steps of the adsorption. Acorrelation between molecular weight and kp values wereobserved for the adsorption of aromatics, where the kp valuesdecreased with increasing molecular weights. On the other hand,such relationship could not be seen in the adsorption of alcohols.

3.7. Diffusivities and solubility parameters of solvents

The solubility parameter of a volatile solvent, d , is defined as thesquare root of the cohesive energy density (CED) whichcorresponds to the increase in the molar energy per unit volumeif all intermolecular forces are eliminated, as formulated below[62]:

dðTÞ ¼ffiffiffiffiffiffiffiffiffiffiCED

p¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiDUvap

V

s(12)

where T is the temperature, DUvap the increase in the internalenergy (energy content) per mole as a result of eliminatingintermolecular forces and V is the molar volume of the substance atthe pressure and temperature at which the vaporization occurs.Fig. 11a presents the relation of diffusivities of alcohols with theirsolubility parameters at different temperatures. As the molecularweight of the alcohols decrease, their solubility parametersincrease. Alcohols with greater solubility parameters were foundto have greater diffusivities. Assuming the solubility parameters ofthe alcohols were constant within the temperature range of26–32 �C, the effect was more pronounced at relatively elevatedtemperatures for methanol. Fig. 11b presents the relation ofdiffusivities of benzene, toluene, ethyl benzene and propylbenzene with their solubility parameters at different temper-atures. Similar results were also observed in this series of solvents;aromatic solvents with greater solubility parameters were found tohave greater diffusivities. Similarly, for the aromatic solvents,assuming constant solubility parameters within the temperature

A.N. Ergün et al. / Fluid Phase Equilibria 382 (2014) 169–179 179

range of 26–32 �C, the effect was more pronounced at relativelyelevated temperatures for benzene.

4. Conclusion

Diffusivities, modes of transport, and the activation energies ofsome alcohols and aromatics in the porous structure of an MCM-41 mesoporous material were determined. Diffusion exponents, n,being in the range of 0.99–1.07 indicated an anomalous diffusion(non-Fickian/super-Case II) mechanism for alcohol diffusion.However, for the case of aromatics, diffusion exponents from0.7 to 1.00 indicated that the diffusion mechanisms were eithernon-Fickian or non-Fickian/super-Case II depending on thesubstitution to the benzene ring. These indicated an anomalousdiffusion mechanism. It was concluded that, as the molecularweight of the solvent increases, diffusivities decrease, theactivation energy for diffusion increases, and the time necessaryto come to equilibrium increases. The diffusivity of n-butanol in thezeolite seemed to be low, compared to those of the smalleralcohols. In all of the samples, the diffusivities increased linearlywith an increase in temperature. The diffusion of alcohols in thezeolite obeyed an anomalous transport mechanism. Diffusion rateconstants slightly increased as the temperature was increased.Activation energies of alcohols and aromatics were also in goodagreement with the values of diffusivities of alcohols andaromatics such that larger activation energies resulted in smallerdiffusivities. Alcohols and aromatics with greater solubilityparameters were found to have greater diffusivities.

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