diffusion of volatile organic chemicals in porous media. 1

Diffusion of Volatile Organic Chemicals in Porous Media. 1.

Alcohols and Aromatics/MCM-41 Mesoporous Materials

Journal: Industrial & Engineering Chemistry Research

Manuscript ID: Draft

Manuscript Type: Article

Date Submitted by the Author: n/a

Complete List of Authors: Nalbant Ergun, Asli; Sabanci University, Faculty of Engineering and Natural Sciences Kocabas, Zuleyha; Sabanci University, Faculty of Engineering and Natural Sciences Yurum, Alp; Sabanci University, Sabanci University Nanotechnology Research and Application Center

Yurum, Yuda; Sabanci University, Faculty of Engineering and Natural Sciences

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research

Diffusion of Volatile Organic Chemicals in Porous Media.

1. Alcohols and Aromatics/MCM-41 Mesoporous

Materials

Asli Nalbant Ergün1, Züleyha Özlem Kocabaş1, Alp Yürüm2 and Yuda Yürüm1,2*

1Faculty of Engineering and Natural Sciences, Sabanci University,

Tuzla, Istanbul 34956, Turkey

2 Sabanci University Nanotechnology Research and Application Center,

Tuzla, Istanbul 34956, Turkey

*Corresponding Author:

Yuda Yürüm Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, Istanbul 34956, Turkey [email protected]

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ABSTRACT: The aim of the present paper was to measure the apparent coefficients of

diffusion, Knudsen diffusivities, pore diffusivities and activation energies of diffusion at 26-

32 oC and to determine the modes of transport of some alcohols (methanol, ethanol, propanol,

n-butanol) and aromatics (benzene, ethylbenzene, propylbenzene, toluene, o-xylene, m-

xylene, p-xylene) into the porous structure of MCM-41 mesoporous material synthesized. The

diffusion coefficients of alcohols and aromatics were calculated from the slope of graphs of

Mt/M∞ versus t1/2. As the molecular weight of the alcohols and aromatics increased, apparent

coefficients of diffusion decreased, the activation energy for diffusion increased. Lower

molecular weight alcohols and aromatics had higher coefficients of diffusion compared to

those with higher molecular weight alcohols at the same temperatures. The diffusion of

isomeric molecules within the mesoporous channels were affected 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 temperature, raised the

kinetic energy of the molecules which resulted increases in the coefficients of diffusion of the

alcohols and aromatics in the MCM-41 material. Diffusion rate constants of alcohols and

aromatics increased with temperature within the range of 26-32 °C, and decreased as the

molecular weight of the diffusing chemical increased. The diffusion of alcohols and aromatics

in the MCM-41 obeyed the anomalous transport mechanism. 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 or non-

Fickian/super-Case II depending on the substitution to the benzene ring. Activation energies

of alcohols and aromatics were also in good agreement with the values of coefficients of

diffusion of alcohols and aromatics such that larger activation energies resulted in smaller

diffusion coefficients.

Keywords: MCM-41 mesoporous material; diffusion; coefficient of diffusion; Knudsen

diffusion; pore diffusion; activation energy of diffusion; modes of transport

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1. INTRODUCTION

Diffusion is the random transfer of molecules or small particles, occurring due to

thermal energy. In a more simple way, diffusion is a spontaneous tendency of all systems to

equalize concentration, if any external influence does not slow down this process. That is,

atoms, molecules, or any particle moves chaotically in the direction where fewer elements of

its own type are located. Diffusion of gases and vapors in porous materials is a very important

subject, since this effect is important in catalysis, gas chromatography, and gas separation

processes. From an industrial angle, it is noteworthy to be able to predict and explain the mass

transfer through the packed-bed absorption towers and reactors used in the chemical

industries. A better understanding of this phenomenon will aid in the optimization and

development of industrial applications of these materials in separation, catalytic processes,

and kinetics-based pressure swing adsorption. In separation processes, for example, the

necessity of a comprehension of diffusion phenomena is obvious. Membrane-based

separations also rely on the diffusion properties of the applied membrane. Therefore, to

advance practical applications, diffusion must be precisely explained.

The diffusion of small molecules in the intracrystalline void volume of porous media

has been a research topic for many years. To obtain information about the transport properties

of gases and vapors in zeotype crystals is important in order to understand the dynamics

fundamentals of small molecules inside a zeolite, which is relevant for all applications,

including catalysis for energy production. The size, shape and adsorptive selectivities of both

natural and synthetic zeolitic materials have been used in a wide variety of heterogeneous

catalytic processes. As an example, zeolite is used as a catalyst in the methanol-to-gasoline

conversion process, which is of major commercial importance. This process has been the

subject of numerous experimental1,2 and theoretical studies3,4 but it is still not particularly well

understood.

Diffusion plays an essential role in most phenomena occurring to molecules in porous

media, e.g., it favors adsorption, makes effective separation of similar molecules, and drives

chemical reactions both on the reagent side to lead the reactants into the active sites and on

the product side to select and extract the species resulting from the reaction. Various

techniques for the measurement of intracrystalline diffusion have been developed5-10 which

widely vary in scope, degree of experimental and theoretical sophistication, and range of

applicability. For a large number of the indirect methods, the diffusing species, or its

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concentration profile in the microporous material, is not directly observed; the diffusivity is

rather calculated from the external measurement of pressure, concentration, or sample weight.

Such computations require suitable models which describe all transport phenomena and

possible sorption processes that can occur in the experimental setup.

Seferinoglu and Yürüm11 recently measured the coefficients of diffusion of pyridine in

raw and acid-washed low-rank coals. The method they used was simple and precise for the

measurement of diffusion coefficients of solvents in coals. Ritger and Peppas12 and Howell

and Peppas13 studied diffusion processes in describing the transport kinetics for pyridine in

coal using the same empirical equation 1. This method can also be used for the measurement

of diffusion constants of several solvents in natural and synthetic zeolites. Bludau et al.14

studied the uptake of pyridine into mordenite and H-ZSM-5. Their data evaluation was based

on the solution of Fick’s second law, using diffusion coefficients for the whole process. Dyer

and White15 studied cation diffusion in a natural zeolite clinoptilolite and compared three

different approaches to determine diffusion coefficients, including Fick’s second law of

diffusion (equation 3), which was found to produce similar results with other approaches. The

applicability of various models to the determination of ion exchange diffusion coefficients in

clinoptilolite was examined in another study16 in which equation 3 was found to be acceptable

for the calculations. Marecka and Mianowski17 used Fick’s second law to determine sorption

of carbon dioxide and methane on a highly metamorphosed coal, and the results of the model

are compared with the experimental kinetics of nitrogen sorption on type A zeolite.

Seferinoglu and Yürüm11,18 and Sakintuna et al.19,20 proposed a calculation method for

the measurement of coefficients of diffusion of volatile chemicals into porous media. The

calculations of diffusion coefficients, modes of transport, and activation energies of some

alcohols and aromatics into the MCM-41 mesoporous materials in the present study are based

on these reports11,18-20.

The determination of diffusion coefficients is based on uptake measurement of the

volatile component by sorbents. Analysis of the sorption data can be accomplished by various

means. A convenient method of analysis involves fitting the sorption data to empirical eq 1. It

is possible to express the initial rate of diffusional solvent penetration in terms of the

equation:

(1)

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where Mt is the amount of solvent diffused in the macromolecular structure at time t, M∞ is

the amount of solvent diffused at a steady state, t is the release time, k is the rate constant

which depends on structural characteristics of the system, and n is an exponent characteristic

of the mode of transport of the solvent in the porous structure and varies with the diffusion

mechanism and particle geometry.

Sorption mechanisms in macromolecular systems such as solid coals may be defined

in terms of two limiting cases of Fickian diffusion and Case II transport.21 When n = 0.5, the

solvent diffuses through and is released from the adsorbent with a quasi-Fickian diffusion

mechanism. For values of n > 0.5, non-Fickian solvent diffusion is observed. When n = 0.85,

Case II transport occurs and values of n between 0.5 and 1.0 indicate anomalous transport.

Values above n = 0.85 are possible and are termed “super-Case II”. It is important that cited

work showed that the expected values of n are sensitive to the assumed particle shape. For an

infinite plane sheet, the values would be 0.5 and 1.0 for Fickian and pure Case II,

respectively, and in the case of an infinite cylinder, 0.45 and 0.89, respectively.21 There may

be differences in the diffusion behavior of different sections of the zeolite. Thus, the values of

n can be used only as a rough guide to the nature of the process. Different n and k values can

be found in the literature.22 Eq 1 is useful for preliminary analysis of sorption data, although it

may be used up to 60% of the final weight of the penetrant imbibed and it has no provisions

for the analysis of details, such as inflections or penetrant loss with time.23,24 In the graph of

ln (Mt/M∞) versus ln t, ln k is the intercept and n is the slope.11,16

When a porous adsorbent system is placed in contact with a solvent (penetrant) gas,

diffusion of the penetrant in the porous material may be followed by measuring the uptake of

the solvent. Diffusion in the silicalite crystals can be described by Fickian diffusion with

concentration-independent diffusivity, D. In Fick formulation, the driving force for diffusive

transport is the gradient of chemical potential of concentration, rather than the gradient of

concentration.25 The kinetics of the diffusion into the sphere in Fick formulation is expressed

by equation 3.26

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

coordinates, to be solved is

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(2)

with the initial conditions

CA = C∞ for r = r0 at t > 0

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

where CA is the solid-phase concentration (mol cm-3); D is the diffusion coefficient, constant

throughout the process (m2 s-1); t is the time (s); r is the distance from the particle center (m);

C is the initial solid-phase concentration (mol cm-3); and r0 is the particle radius (m). The

exact solution of equation 2 is equation 3 for gas-phase diffusion to the solid solute.16

Assuming the zeolite particles are of spherical shape, the solution of Fick’s second law

of diffusion in spherical systems gives.24,27

(3)

where Mt and M∞ represent the amount of solvent diffused entering the spheres with radius a,

at times t and steady state, respectively, and n is an integer coming from the solution of Fick’s

second law. D is the coefficient of diffusion of the solvent vapor. This equation is based on

the assumption that the particle radius does not change, which is true for zeolite particles. The

solution to equation 3 is given by equation 4.28

(4)

For short times, equation 4 approximates to

(5)

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Neglecting the contribution of the term 3Dt/a2, the value of D is found from the slope

of a plot of Mt/M∞ versus t1/2.

If the diffusion process takes place at sufficiently high temperatures, there are

essentially three regimes with different diffusivities according to the pore diameter.29 For

macropores (i.e., pores with diameters of 50 nm or larger), collisions between the molecules

generally happen much more frequently than collisions with the wall, and molecular diffusion

is the dominant mechanism. At the same time as the pore size decreases, the number of

collisions with the wall increases; at this point, Knudsen diffusion takes over, and the mobility

starts to depend on the dimensions of the pore. At even smaller pore sizes, in the range of 2

nm or less (i.e., when the pore diameter turns out to be similar to the size of the molecules),

the molecules will constantly experience the interaction with the pore surface. Thus, diffusion

in the micropores of a zeolite or related materials, as was stated before, typically occurs in the

configurational diffusion regime.30

Configurational diffusion is the term used to describe diffusion in zeolites and related

materials and is characterized by very small diffusivities (10–12 to 10–18 m2/s) with a strong

dependence on the size and the shape of the guest molecules, high activation energies (10 to

100 kJ/mol), and strong concentration dependence.29 Zeolites and related materials are

microporous crystalline solids of special interest in the chemical and the petroleum industries

as catalysts and sorbents. For these applications, migration or diffusion of sorbed molecules

through the pores and cages within the crystals plays a dominant role.

As the pore dimension decreases, or the mean free path of the molecule increases,

owing to pressure lowering, the flowing species tend to collide more and more with the pore

walls than among themselves; then molecules are flowing almost independently from one

another according to the Knudsen flow.31,32

The movement of fluids (gas or liquid) into the interstices of porous solids or

membranes is called pore diffusion. Pore diffusion occurs in membrane separation, zeolite

adsorption and reverse osmosis. Diffusion inside particles is complicated because molecules

not only diffuse through pores but also interact with the solid surface. Pore structure and

interaction between the fluid and solid phases influence the overall diffusion rate, and

therefore intraparticle diffusivity is usually system-dependent and has to be estimated

experimentally. The pore diffusivity is calculated from the following equation 633

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(6)

where,

DK : Knudsen diffusivity, for a vapor of molecular weight M, which diffuses along the pore

with rp cm radius, the value of DK (cm2/s) is

�� 9700� �� /�

(7)

τ : tortuosity factor, has been measured experimentally by Salmas et al.34 as 2.40, for MCM-

41 materials of pore volume of 0.54 cm3/g. So we used this value, τ = 2.40, in our

calculations.

Diffusion is an activated process; that is, to occur, it requires overcoming an energy

barrier. Other activated processes are found in zeolites, the most common examples being the

adsorption of a molecule which, from a gas or a liquid, enters into the micropores and,

especially, chemical reactions occurring in the channel and cavities. If the activation energy is

smaller than, equal to, or slightly larger than the available thermal energy kBT, the probability

of overcoming the energy barrier is sufficiently high to allow the activated process to occur

for a statistically meaningful number of times during a reasonably long simulation. Activation

energies of diffusion are calculated using the equations 8 and 9 below:

� � ��/�� (8)

�� (9)

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

for diffusion.35

For the calculation of diffusion coefficients, the following assumptions are made: the

diffusion mechanism obeys Fick’s law of diffusion, the crystallites possess a spherical shape,

and the concentration profile of the sorbed gas in these spheres shows radial symmetry. The

diffusion is assumed to be isotropic; it can be described by a single diffusion coefficient rather

than a diffusion tensor, and the diffusion coefficient does not depend on sorbate

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concentration. It is proposed that there are at least five limiting types of diffusion for the

molecules flowing through the zeolitic material:36

Case a. Unrestricted intracrystalline diffusion: the molecule moves in the channels and

cavities of a crystallite without crossing the surface of the solid or extended crystal defects.

Case b. Modified intracrystalline diffusion: the particle crosses extended (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 is reflected at the crystal boundary

because of a very low probability of desorption.

Case d. Intercrystalline diffusion: the molecule migrates between different crystals, so it is

sorbed most of the time but not confined to the same crystal. Sometimes this type of diffusion

involves surface film formation and diffusion on the zeolite surface.

Case e. Diffusion in the fluid phase: the particle remains in the gas or liquid phase, confined

only by the walls of the vessel containing the sample.

The aim of the present paper was to measure the apparent coefficients of diffusion,

Knudsen diffusivities, pore diffusivities and activation energies of diffusion and to determine

the modes of transport of some alcohols (methanol, ethanol, propanol, n-butanol) and

aromatics (benzene, ethylbenzene, propylbenzene, toluene, o-xylene, m-xylene, p-xylene) into

the porous structure of MCM-41 mesoporous material synthesized. The present paper is the

first of a series of experimental investigations which will report the transport of volatile

organic compounds in porous media.

2. EXPERIMENTAL SECTION

2.1. Materials and Synthesis of MCM-41 Material. The synthesis procedure for MCM-41

material was a modified method described by Davis et al.36 6.6 gr of

hexadecyltrimethylammonium bromide was dissolved slowly in 43 ml of deionized water at

40°C and 5.65 ml of sodium silicate solution was added dropwise to the clear solution with

continuous stirring at the same temperature. After stirring for 1 hour, the pH of the mixture

was adjusted to 11 by adding sufficient amount of 1 M H2SO4. The resulting gel is stirred for

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1 hour before being transferred to a 120 ml Teflon autoclave. The autoclave was placed in a

Delonghi EMD MW 311 model microwave oven with a Velp Scientifica VTF Digital

Thermoregulator. The microwave oven operated at 230 V, 50 Hz, with adjustable power

output of 800 W. The gels under autogeneous pressure were allowed to absorb microwave

energy of 120 W to achieve the desired reaction temperature of 120°C, for 30 minutes. The

resultant solid was recovered by filtration, washed thoroughly with distilled water until the pH

got neutralized and dried at room temperature. Before calcination step the solid was kept at

40°C for 24 hours. The as-synthesized MCM-41 was finally calcined inside a quartz filter

installed quartz tube (120 cm long x 1 cm diameter) which was placed in a tubular furnace, by

heating from ambient temperature to 550°C at a rate of 1°C/min and kept at 550°C for 6 hours

in a flow of dry air.

2.2. Surface Area Measurements. The surface area and porosity properties of the

mesoporous materials were determined using NOVA 2200e Surface Area and Pore Size

Analyzer by Quantachrome Instruments Co., USA. The measurement was performed at the

liquid nitrogen boiling point of 77 K. The samples were outgassed at 150°C overnight. The

BET surface area was determined by a multipoint BET method using the adsorption data in

the relative pressure (P/P0) range of 0.05–0.3. The pore volume and pore size distributions

were calculated using a procedure developed by BJH method.

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 mesoporous media were investigated in detail in an adiabatic

isothermal setup. The alcohols and aromatic solvents were purchased from Aldrich, and they

were used as received. The adiabatic isothermal setup19 designed and built in our laboratories,

was used in the diffusion experiments. A Sartorius CP 124S analytical balance with 0.0001 g

accuracy was placed in a Memmert model 300 laboratory oven. At the start of the experiment,

approximately 0.2 g of degassed MCM-41, or metal incorporated MCM-41 sample was

evenly distributed in a Petri dish and its initial weight was recorded. Four wide beakers filled

with a total of 200 ml of the alcohol (methanol, ethanol, propanol, n-butanol) or the aromatic

solvent (benzene, ethylbenzene, propylbenzene, toluene, o-xylene, m-xylene, p-xylene) were

used in each experiment, and they were placed in the closest vicinity of the balance pan. The

temperature of the experiment was set to 26, 28, 30 and 32°C, and the system was closed.

After the temperature reached the constant set value between 26°C and 32 °C, the weight

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increase of the mesoporous material as a result of alcohol or aromatic solvent vapor uptake

was recorded every 5 s with the aid of Sarto Connect software installed on the PC. The

experiment was continued until the software collected 2000 data points and a constant weight

was attained. All experiments were repeated at least five times. For the calculation of the

diffusion coefficients, the following assumptions were made: the diffusion mechanism obeys

Fick’s law, the crystallites possess a spherical shape, the concentration profile of the sorbed

vapor in these spheres shows radial symmetry, the diffusion is assumed to be isotropic and it

can be described by a single diffusion coefficient rather than a diffusion tensor, and the

diffusion coefficient does not depend on sorbate concentration.

RESULT and DISCUSSION

3.1. Physical and Structural Properties. MCM-41 type material synthesized with low power

(120 Watt) microwave assisted direct synthesis method at 120oC and in 30 minutes are

presented in Table 1. The BET surface area of the MCM-41 used in the present study was

1438 m2 g-1. The mean pore diameter and pore volume of the MCM-41 material were

measured as 4.0 nm and 0.53 cm3g-1, respectively. The MCM-41 material used therefore

could be classified as mesoporous according to the classification scheme proposed by the

International Union of Applied Chemistry (IUPAC). The agglomerate size was 0.5 µm.

Nitrogen adsorption/desorption isotherms and pore volume distribution of the MCM-41

sample are given in Figure 1.

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

microwave assisted direct synthesis method

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

BET

Surface Area, (m2/g)

Pore Volume, (cm3/g)

Pore Radius,

rp, (nm)

Interplanar Spacing,

d100, (nm)

Lattice

Parameter, a,

(nm)

Pore Wall Thickness,

δ, (nm)

Particle Porosity,

εm

MCM-41 (120/30)

1438 0.53 2.00 3.64 4.20 0.38 0.54

Surface Analysis by Porosity Type, %, by volume

Micropores 31.6 Mesopores 64.8 Macropores 3.6

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-Figure 1-

3.2. Apparent Coefficients of Diffusion. The uptake measurements of volatile solvents into

the mesoporous structures were recorded until the equilibrium was attained. As an example,

ethanol uptake measurement in MCM-41 at 26 ºC was given in Figure 2. The apparent

coefficients of diffusion and activation energies were calculated from the region where

diffusion was assumed to be linear during the first 60 percent of the ramp of uptake versus

time graph. Graphs of Mt/M∞ versus t1/2 for the solvent diffusion in mesopores were plotted in

order to calculate the apparent coefficient of diffusion, Figure 3. The slope of this graph was

used to calculate the apparent diffusion coefficients. The type of transport mechanisms of

volatile solvents in the mesopores of MCM-41 materials were predicted from the values of

diffusion rate constants, k, and diffusion exponents, n, which were calculated from the graphs

of ln(Mt/M∞) versus ln t, Figure 4.

-Figure 2 – Figure 3 – Figure 4-

Diffusion of vapors inside zeolites is complicated because molecules not only diffuse

through pores but also interact with the solid surface. Pore structure and interaction between

the fluid and solid phases influence the overall diffusion rate, and therefore intraparticle

diffusivity is usually system-dependent and has to be estimated experimentally. Diffusion of

volatile alcohols and aromatic solvents in the mesoporous structure of the MCM-41material

were investigated. The MCM-41 material used had a specific surface area value of 1438 m2/g

and mean pore diameter of 4 nm. The MCM-41 material has high potential as an adsorbent for

small and bulky adsorbate molecules due to its mesoporous structure and high surface area.

Adsorption of N237-43 and water 39,44- 46 on MCM-41 has been thoroughly investigated. There

are also some studies based on heavier hydrocarbons, such as benzene47,48, toluene49,

cyclopentane50,51, cyclohexane50-53, propane, and methane54 on MCM-41. However, there are

very few studies on the diffusion properties of MCM-41.

The change in apparent coefficients of diffusion of methanol, ethanol, n-propanol and

n-butanol at 26, 28, 30 and 32 ºC were presented graphically in Figure 5. The numerical data

were given in Table 2. Lower molecular weight alcohols had higher coefficients of diffusion

compared to those with higher molecular weight alcohols at the same temperatures. For

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example, the diffusion coefficients of methanol, ethanol, n-propanol and n-butanol were

measured as 4.01 x10-13, 1.83 x 10-13, 8.26 x1 10-14 and 2.51x 10-14 m2/g at 26 ºC,

respectively. Thus, smaller amounts of high molecular weight alcohols diffused in the MCM-

41 material relative to the low molecular weight alcohols due to steric hindrances at the same

temperature.

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

different temperatures

Alcohols 26 °C 28 °C 30 °C 32 °C

Methanol 4.01 x 10-13 4.38 x 10-13 8.43 x 10-13 9.99 x 10-13

Ethanol 1.83 x 10-13 2.34 x 10-13 2.70 x 10-13 3.38 x 10-13

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

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

-Figure 5-

Increasing the temperature raised the kinetic energy of the molecules which resulted

increases in the coefficients of diffusion of the alcohols in the MCM-41 material. For

instance, the coefficients of diffusion of methanol at 26, 28, 30, and 32 °C were measured as

4.01 x 10-13, 4.38 x 10-13, 8.43 x 10-13, 9.99 x 10-13 m2/s respectively. The coefficients of

diffusion of the other alcohols, ethanol, n-propanol and n-butanol, used also increased as the

temperature was increased to 28, 30, and 32 °C.

Sakintuna et al.19 studied the diffusion of methanol, ethanol, n-propanol, i-propanol

and n-butanol in a natural zeolite with 40.2 % micropores, 57.9 % mesopores and 1.9 %

macropores and 59 m2/g surface area. The coefficients of diffusion of methanol, ethanol, n-

propanol, i-propanol and n-butanol were 10 times lower than those measured in the present

work. It is clearly seen that, larger pore diameter and higher surface area values of MCM-41

was more accessible for the alcohols used. Wang et al.55 studied the diffusion of N2 and CO2

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in γ-alumina within limited volume of a stiff container. The diffusion coefficients were in the

order of 10-7 m2/g.

The change in apparent coefficients of diffusion of benzene, toluene, ethylbenzene,

propylbenzene, o-xylene, m-xylene and p-xylene at 26, 28, 30 and 32 ºC are presented

graphically in Figure 6(a-b). The numerical data are given in Table 3. The experimental

results can be discussed in terms of two groups: benzene, toluene, ethylbenzene and

propylbenzene as one group and benzene, toluene, o-xylene, m-xylene, p-xylene as another

according to organic structures.

Table 3. Apparent diffusion coefficients (m2/g) of aromatic solvents in MCM-41

measured at different temperatures

Aromatic

solvents 26 °C 28 °C 30 °C 32 °C

Benzene 3.96 x 10-14 5.47 x 10-14 7.38 x 10-14 9.52 x 10-14

Toluene 3.79 x 10-14 4.35 x 10-14 5.94 x 10-14 7.85 x 10-14

Ethylbenzene 3.74 x 10-14 4.12 x 10-14 5.87 x 10-14 6.64 x 10-14

Propylbenzene 3.26 x 10-14 3.52 x 10-14 3.90 x 10-14 4.41 x 10-14

o-Xylene 3.68 x 10-14 3.96 x 10-14 5.21 x 10-14 6.50 x 10-14

m-Xylene 3.42 x 10-14 3.79 x 10-14 4.65 x 10-14 6.01 x 10-14

p-Xylene 3.11 x 10-14 3.47 x 10-14 4.35 x 10-14 5.67 x 10-14

- Figure 6 –

The apparent coefficients of diffusion of benzene were the highest in both of the

groups and increased from 3.96 x 10-14 to 9.52 x 10-14 m2/g as the temperature was increased

from 26 to 32 °C. As the molecular weight of the aromatic compound increased, diffusion

coefficients decreased. For instance, diffusion coefficients of benzene, toluene, ethylbenzene

and propylbenzene were 3.96x10-14 m2/g, 3.79x10-14 m2/g, 3.74 x10-14 m2/g and 3.26x10-

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14m2/g at 26 °C, respectively and o-xylene, m-xylene and p-xylene were 3.68x10-14, 3.42x10-

14, 3.11x10-14, at 26 °C, respectively.

As the chain length of the alkyl group attached to the benzene ring increased, the

coefficients of diffusion slightly decreased, i.e. 3.96x10-14 m2/g (benzene) and 3.26x10-14 m2/g

(propylbenzene) at 26 °C. Within the xylenes, there were some differences in the coefficients

of diffusion at the same temperatures depending on the position of the alkyl substitution.

Among ortho, meta and para isomers of xylenes, the biggest apparent coefficient of diffusion

was measured with p-xylene. This was probably due to the increase of molecular diameter

that decreased the diffusion of p-xylene through the channels within the MCM-41. It can be

concluded that, the diffusion of isomeric molecules within the mesoporous channels were

affected 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.

Hoang et al.56 investigated the diffusion of aromatic solvents (n-Heptane, toluene and

oxylene) in bi-porous nano-materials using zero length column (ZLC) method and compared

the results with pure silicate crystal. The coefficients of diffusion were in the order of 10-16

m2/g at 70 °C and increased with temperature. The coefficients were higher than the pure

silicate due to the presence of mesoporous channels.

3.3. Knudsen and Pore Diffusion Coefficients. Knudsen and pore diffusion coefficients of

alcohols and aromatics are presented in Table 4 and Table 5, respectively. The values of

Knudsen and pore diffusivities of the alcohols and aromatics in the MCM-41, presented in the

Tables 4 and 5, are in the order of 10-7 m2/s. Diffusion of molecules in porous systems is

highly dependent on the dimensions of the pore network. Transport of molecules in very large

pores is essentially governed by molecular diffusion since collisions with other molecules are

much more frequent then collisions with the pore walls. As the pore dimension reduces and

the mean free path of the molecule increases the flowing species tend to collide more and

more with the pore walls than among themselves; then molecules flows almost independently

from one another according to the Knudsen flow.31,32 In the Knudsen regime molecule-wall

collision are dominant and the diffusivity decreases with the pore size.

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Table 4. Knudsen 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 5.93x10-7 5.95x10-7 5.97x10-7 5.99x10-7 2.47x10-7 2.48x10-7 2.49x10-7 2.49x10-7

Ethanol 4.94x10-7 4.96x10-7 4.98x10-7 4.99x10-7 2.06x10-7 2.07x10-7 2.07x10-7 2.08x10-7

n-Propanol 4.33x10-7 4.34x10-7 4.36x10-7 4.37x10-7 1.80x10-7 1.81x10-7 1.82x10-7 1.82x10-7

n-Butanol 3.90x10-7 3.91x10-7 3.92x10-7 3.94x10-7 1.62x10-7 1.63x10-7 1.63x10-7 1.64x10-7

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

Knudsen Diffusivity (m2/s) Pore Diffusivity (m

2/s)

26 °C 28 °C 30 °C 32 °C 26 °C 28 °C 30 °C 32 °C

Benzene 3.80x10-7 3.81x10-7 3.82x10-7 3.83x10-7 1.58x10-7 1.59x10-7 1.59x10-7 1.60x10-7

Toluene 3.50x10-7 3.51x10-7 3.52x10-7 3.53x10-7 1.46x10-7 1.46x10-7 1.47x10-7 1.47x10-7

Ethylbenzene 3.26x10-7 3.27x10-7 3.28x10-7 3.29x10-7 1.36x10-7 1.36x10-7 1.37x10-7 1.37x10-7

Propylbenzene 3.06x10-7 3.07x10-7 3.08x10-7 3.09x10-7 1.28x10-7 1.28x10-7 1.28x10-7 1.29x10-7

o-Xylene 3.26x10-7 3.27x10-7 3.28x10-7 3.29x10-7 1.36x10-7 1.36x10-7 1.37x10-7 1.37x10-7

m-Xylene 3.26x10-7 3.27x10-7 3.28x10-7 3.29x10-7 1.36x10-7 1.36x10-7 1.37x10-7 1.37x10-7

p-Xylene 3.26x10-7 3.27x10-7 3.28x10-7 3.29x10-7 1.36x10-7 1.36x10-7 1.37x10-7 1.37x10-7

Types of porosities present in the MCM-41 material were given in Table 1. The

MCM-41 material contained 31.6 % micropores, 64.8 % mesopores and 3.6 % macropores.

The values of the apparent diffusion coefficients presented in the Tables 2 and 3, for alcohols

and aromatics, respectively, are in the order of 10-13-10-14 m2/s while the values of Knudsen

and pore diffusivities presented in the Tables 4 and 5 are in the order of 10-7 m2/s. From these

tables it can be clearly seen that Knudsen diffusion values are significantly higher than

apparent diffusivities. This indicated that adsorption of solvents was the dominant process

during the diffusion in micropores. On the other hand, the relatively lower values of the

apparent coefficients of diffusion of the alcohols and aromatics included also the diffusion in

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the microporous structure of the MCM-41besides diffusion in mesopores and macropores. So

the diffusion of alcohols and aromatics in the MCM-41 was therefore controlled by the

configurational molecular transport mechanism that mostly occurred in the micropores.

Configurational diffusion is the type of molecular transport found in zeolites and zeotypes and

is characterized by small diffusivities, strong dependence on the size and shape of the guest

molecules, high activation energies and strong concentration dependence.57

3.4. Diffusional Rate Constants and Mode of Transport in MCM-41. The type of transport

mechanisms of aromatics in the zeolitic porous structure can be speculated by the values of

the diffusion rate constants, k, and diffusion exponents, n, which were calculated using ln

(Mt/M∞) versus ln t graphs. The diffusion rate constants, diffusion exponents and transport

mechanism of alcohols and aromatics in MCM-41 were given in Table 6 and Table 7,

respectively. Linearity analysis of the data gave acceptable regressional coefficients, R2 with

values greater than 0.98 indicating a linear relationship between ln (Mt/M∞) vs. ln t for

diffusion of alcohols and aromatics in mesoporous media.

Table 6. Diffusion rate constants, diffusion exponents, transport mechanism and

activation energy of diffusion of alcohols in MCM-41

Alcohol

T, ºC

k, s-1

n

R2

Transport

Mechanism

Ea,

Activation

energy of

diffusion,

kJ/mol

Methanol

26 2.56 x 10-4 1.00 0.999 Non-Fickian/ Super-Case II

65 28 2.93 x 10-4 1.00 0.985 Non-Fickian/

Super-Case II



Ethanol


76




n-Propanol


93




n-Butanol 26 8.84 x 10-5 1.00 0.993 Non-Fickian/

Super-Case II 118


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Table 7. Diffusion rate constants, diffusion exponents, transport mechanism and and

activation energy of diffusion of aromatics in MCM-41

Aromatics

T, ºC

k, s-1

n

R2

Transport

Mechanism

Ea,

Activation

energy of

diffusion,

kJ/mol

Benzene


48




Toluene


91




Ethylbenzene


98 28 1.55 x 10-3 0.78 0.999 Non-Fickian

30 1.61 x 10-3 0.81 0.999 Non-Fickian

32 2.80 x 10-3 0.75 0.999 Non-Fickian

Propylbenzene

26 1.67 x 10-3 0.76 0.999 Non-Fickian 112

28 1.81 x 10-3 0.76 0.998 Non-Fickian

30 1.84 x 10-3 0.74 0.998 Non-Fickian

32 2.36 x 10-3 0.72 0.999 Non-Fickian

o-Xylene

26 2.20 x 10-3 0.77 0.999 Non-Fickian 121

28 1.49 x 10-3 0.83 0.999 Non-Fickian

30 2.05 x 10-3 0.80 0.998 Non-Fickian

32 2.73 x 10-3 0.76 0.999 Non-Fickian

m-Xylene

26 1.12 x 10-3 0.86 0.999 Non-Fickian 126

28 2.71 x 10-3 0.73 0.999 Non-Fickian

30 3.55 x 10-3 0.70 0.998 Non-Fickian

32 3.62 x 10-3 0.71 0.995 Non-Fickian

p-Xylene

26 1.08 x 10-3 0.86 0.999 Non-Fickian/ Super-Case II 133

28 2.85 x 10-3 0.74 0.998 Non-Fickian

30 3.14 x 10-3 0.76 0.997 Non-Fickian

32 4.41 x 10-3 0.73 0.997 Non-Fickian

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Diffusion rate constants of alcohols and aromatics increased with temperature within

the range of 26-32 °C, and decreased as the molecular weight of the diffusing chemical

increased. The diffusion rate constant of methanol in MCM-41 increased from 2.56 x10-4 to

1.50 x 10-3 s-1 when diffusion temperature was increased from 26 to 32 °C. For the case of

benzene, diffusion rate constant increased from 1.06 x10-4 to 2.44 x 10-4 s-1 when diffusion

temperature was increased from 26 to 32 °C.

Diffusion exponents 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 or non-Fickian/super-Case II depending on the substitution to the benzene

ring. The diffusion exponents of methanol, ethanol, n-propanol, i-propanol and n-butanol in

natural zeolite systems were measured by Sakintuna et al.19 were between 0.96-1.00

indicating an anomalous diffusion mechanism.

3.5. Activation Energies of Diffusion of Alcohols and Aromatics in MCM-41. The

activation energies of diffusion for alcohols and aromatics were calculated from the slope of

the Arrhenius graph of ln D versus 1/T. The results were given in Table 6 and Table 7 for

alcohols and aromatics, respectively. The activation energies of diffusion of methanol,

ethanol, n-propanol, n-butanol were calculated as 65, 76, 93 and 118 kJ/mol, respectively and

the activation energies of diffusion of benzene, toluene, ethylbenzene, propylbenzene, o-

xylene, m-xylene and p-xylene were calculated as 48, 91, 98, 112, 121, 126 and 133,

respectively. It is observed that an increase in molecular weight (or chain length) resulted in

increases in activation energy. It seemed that there were influence of chain length, polarity,

critical molecular size and configuration of diffusing molecules on the diffusion coefficients

and activation energies. The activation energies measured were also in accord with the values

of coefficients of diffusion of alcohols and aromatics for different temperatures. The

activation energies might be thought of as the energy required to produce the diffusive motion

of 1 mole of penetrant molecules. Large activation energies resulted in relatively small

coefficients of diffusion. The activation energy of methanol in the MCM-41 was measured to

be the smallest among those of alcohols, and of benzene was measured to be the smallest

among those of aromatics. With increasing molecular weight of the alcohols and aromatics

the activation energies also increased. Larger activation energies resulted in relatively small

diffusion coefficients for alcohols and aromatics diffusion measurements in mesoporous

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media. It can be concluded that there should be a strong relationship between the chain length,

critical molecular size on the diffusion coefficients and activation energies. Activation

energies of alcohols and aromatics were also in good agreement with the values of

coefficients of diffusion of alcohols and aromatics such that larger activation energies resulted

in smaller diffusion coefficients.

It is interesting that Sakintuna et al.19 calculated the activation energies of the volatile

alcohols diffusion within the natural zeolites as 18.3, 46.4, 79.7 and 90.1 kJ/mol, respectively.

Although the operating conditions were the same, the diffused molecules in the MCM-41

have to overcome an energy barrier higher than the natural zeolites. Once the molecules

overcome this energy barrier, they move more easily within the mesoporous channels of

MCM-41 than microporous channels of zeolites which explain the higher diffusion

coefficients of alcohols within MCM-41.

The activation energies of aromatics were 48, 91, 98, 112, 121, 126 and 133 kJ/mol for

benzene, toluene, ethylbenzene, propylbenzene, o-xylene, m-xylene and p-xylene,

respectively. With increasing molecular weight of the volatile aromatics, the activation

energies also increased. The activation energy of benzene in the mesoporous channels of

MCM-41 was estimated to be the smallest among those of aromatic solvents and as discussed

above, diffusion coefficients of benzene were the highest at all temperatures.

4. CONCLUSION

Coefficients of diffusion, modes of transport, and the activation energies of some

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 from 0.7 to 1.00 indicated that the diffusion mechanisms

were either non-Fickian or non-Fickian/super-Case II depending on the substitution to the

benzene ring. These indicated anomalous diffusion mechanism, which might be assumed to

be presented by Case b, c, or d or any of the combinations of the limiting types of diffusion of

the molecules flowing through the zeolitic material.36 It was concluded that, as the molecular

weight of the solvent increases, diffusion constants decrease, the activation energy for

diffusion increases, and the time necessary to come to equilibrium increases. The diffusion of

n-butanol in the zeolite seemed to be less, compared to those of the smaller alcohols. In all of

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the samples, the diffusion constants increased linearly with an increase in the temperature.

The diffusion of alcohols in the zeolite obeyed an anomalous transport mechanism. Diffusion

rate constants slightly increased as the temperature was increased.

References (1) Seiler, M.; Schenk, U.; Hunger, M. Conversion of methanol to hydrocarbons on zeolite

HZSM-5 investigated by in situ MAS NMR spectroscopy under flow conditions and online

gas chromatography. Catal. Lett. 1999, 62 (2-4), 139-145.

(2) Bjørgen, M.; Kolboe, S. The conversion of methanol to hydrocarbons over dealuminated

zeolite H-beta. Appl. Catal., A 2002, 225 (1), 285-290.

(3) Stich, I.; Gale, J. D.; Terkura, K.; Payn, E. M. C. Dynamical observation of the catalytic

activation of methanol in zeolites. Chem. Phys.Lett. 1998, 283 (5-6), 402-408.

(4) Hutchings, G. J.; Watson, G. W.; Willock, D. Methanol conversion to hydrocarbons over

zeolite catalysts: comments on the reaction mechanism for the formation of the first carbon-

carbon bond. J. Microporous Mesoporous Mater. 1999, 29 (1), 67-77.

(5) Kainourgiakis, M. E.; Stubos, A. K.; Konstantinou, N. D.; Kanellopoulos, N. K.; Milisic,

V. A network model for the permeability of condensable vapours through mesoporous media.

J. Membr. Sci. 1996, 114 (2), 215-225.

(6) Domontis, P.; Suffritti, G. B. Structure and Dynamics of Zeolites Investigated by

Molecular Dynamics. Chem. Rev. 1997, 97 (8), 2845-2878.

(7) Haberlandt, R. Transport processes in porous media: diffusion in zeolite, Thin Solid Films

1998, 330 (1), 34-45.

(8) Rallabandi, P. S.; Ford, D. M. Permeation of small molecules through polymers confined

in mesoporous media. J. Membr. Sci. 2000, 171 (2), 239-252.

(9) Quintard, M.; Bletzacker, L.; Chenu, D.; Whitaker, S. Nonlinear, multicomponent mass

transfer in porous medias. Chem. Eng. Sci. 2006, 61 (8), 2643-2669.

(10) Valdes-Parada, F. J.; Goyeau, B.; Ochoa-Tapia, J. A. Diffusive mass transfer between a

microporous medium and an homogeneous fluid: Jump boundary conditions. Chem. Eng. Sci.

2006, 61 (5), 1692-1704.

(11) Seferinoglu, M.; Yürüm, Y. Diffusion of Solvents in Coals: 1. Measurement of

Diffusion Coefficients of Pyridine in Elbistan Lignite. Energy Fuels 2001, 15 (1), 135-140.

(12) Ritger, P. L.; Peppas, N. A. Transport of penetrants in the macromolecular structure of

coals, 7. Transport in thin coal sections. Fuel 1986, 66 (6), 1379-1388.

Page 21 of 35



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

(13) Howell, B. D.; Peppas, N. A. Transport of penetrants in the macromolecular structure of

coals ii. Effect of porous structure on pyridine transport mechanisms. Chem. Eng. Commun.

1985, 43 (4-6), 301-315.

(14) Bludau, H.; Karge, H. G.; Niessen, W. Sorption, sorption kinetics and diffusion of

pyridine in zeolites. Microporous Mesoporous Mater. 1998, 22 (1-3), 297-308.

(15) Dyer, A.; White, K. J. Cation diffusion in the natural zeolite clinoptilolite Thermochim.

Acta 1999, 340-341, 341-348.

(16) Inglezakis, V. J.; Grigoropoulou, H. P. Applicability of Simplified Models for the

Estimation of Ion Exchange Diffusion Coefficients in Zeolites. J. Colloid Interface Sci. 2001,

234 (2), 434-441.

(17) Marecka, A.; Mianowski, A. Kinetics of CO2 and CH4 sorption on high rank coal at

ambient temperatures. Fuel 1998, 77 (14), 1691-1696.

(18) Seferinoglu, M.; Yürüm, Y. Diffusion of Solvents in Coals: 2. Measurement of Diffusion

Coefficients of Pyridine in Çayirhan Lignite. Energy Fuels 2006, 20 (3), 1150-1156.

(19) Sakintuna, B.; Fakioglu, E.; Yürüm, Y. Diffusion of Volatile Organic Chemicals in

Porous Media. 1. Alcohol/Natural Zeolite Systems. Energy Fuels 2005, 19 (6), 2219-2224.

(20) Sakintuna, B.; Çuhadar, O.; Yürüm, Y. Diffusion of Volatile Organic Chemicals in

Porous Media. 2. Alcohol/Templated Porous Carbon Systems. Energy Fuels 2006, 20 (3),

1269-1274.

(21) Otake, Y.; Suuberg, E. M. Temperature Dependence of Solvent Swelling and Diffusion

Processes in Coals. Energy Fuels 1997, 11 (6), 1155-1164.

(22) Gao, H.; Nolura, M.; Murata, S.; Artok, L. Statistical Distribution Characteristics of

Pyridine Transport in Coal Particles and a Series of New Phenomenological Models for

Overshoot and Nonovershoot Solvent Swelling of Coal Particles. Energy Fuels 1999, 13, 518-

528.

(23) Peppas, N. A.; Franson, N. M. The swelling interface number as a criterion for prediction

of diffusional solute release mechanisms in swellable polymers. Polym. Phys. Ed. 1983, 21

(6), 983-997.

(24) Peppas, N. A.; Lucht, L. M. Transport of penetrants in the macromolecular structure of

coals. I. Anomalous transport in untreated and pyridine-extracted coals. Chem. Eng. Commun.

1985, 37 (1-6), 333-354.

(25) Ruthven, D. M. Sorption kinetics for diffusion-controlled systems with a strongly

concentration-dependent diffusivity. Chem. Eng. Sci. 2004, 59 (21), 4531-4545.

Page 22 of 35



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

(26) Hall, P. J.; Thomas, K. M.; Marsh, H. The relation between coal macromolecular

structure and solvent diffusion mechanisms. Fuel 1992, 71 (11), 1271-1275.

(27) Crank, J. The Mathematics of Diffusion; 2nd ed.; Clarendon Press: London, 1976.

(28) Ndaji, F. E.; Thomas, K. M. The kinetics of coal solvent swelling using pyridine as

solvent. Fuel 1993, 72, 1525-1530.

(29) Post, M. F. M., Diffusion in Zeolite Molecular Sieves. Stud. Surf. Sci. Catal. 1991, 58,

391-444.

(30) Xiao, J.; Wei, J., Diffusion mechanism of hydrocarbons in zeolites—I. Theory. Chem.

Eng. Sci. 1992, 47 (5), 1123-1141.

(31) Wang, M. R.; Li, Z. X. Nonideal gas flow and heat transfer in micro- and nanochannels

using the direct simulation Monte Carlo method. Phys. Rev. E 2003, 68, 046704/1-6.

(32) Hwang, S.-T. and Kammermeyer, K., Techniques in Chemistry: Membranes in

Separation, John Wiley and Sons, New York. 1975.

(33) Prasetyo, I.; Do, H. D.; Do, D. D. Surface diffusion of strong adsorbing vapours on

porous carbon. Chem. Eng. Sci. 2002, 57 (1), 133–141.

(34) Salmas, C. E.; Stathopoulos, V. N.; Pomonis, P. J.; Rahiala,; Rosenholm, J. B.;

Androutsopoulos, G. P. An investigation of the physical structure of MCM-41 novel

mesoporous materials using a corrugated pore structure model. Appl. Catal., A. 2001, 216 (1-

2), 23-39.

(35) Callister, W. D. Material Science Engineering, 2nd ed.; Wiley & Sons: New York,

1991.

(36) Caro, J.; Hocevar, S.; Kaerger, J.; Riekert, L. Intracrystalline self-diffusion of H2O and

CH4 in ZSM-5 zeolites. Zeolites 1986, 6 (3), 213.

(37) Davis, M. E.; Saldarriaga, C.; Montes, C.; Garces, J.; Crowder, C. VPI-5: The first

molecular sieve with pores larger than 10 Ångstroms. Zeolites 1988, 8 (5), 362-366.

(38) Kresge, C. T.; Leonovicz, M. E.; Roth, W. J.; Vartuli, J. C.; Beck, J. S. Ordered

mesoporous molecular sieves synthesized by a liquid-crystal template mechanism. Nature

1992, 359, 710-712.

(39) Branton, P. J.; Hall, P. G.; Sing, K. S. W.; Reichert, H.; Schüth, F.; Unger, K. K.

Physisorption of argon, nitrogen and oxygen by MCM-41, a model mesoporous adsorbent. J.

Chem. Soc., Faraday Trans. 1994, 90, 2965-2967.

(40) Liewellyn, P. L.; Grillet, Y.; Schüth, F.; Reichert, H.; Unger, K.K. Effect of pore size on

adsorbate condensation and hysteresis within a potential model adsorbent: M41S. Microp.

Mesop. Mater. 1994, 3 (3), 345-349.

Page 23 of 35



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

(41) Zhu, H. Y.; Zhao, X. S.; Lu, G. Q.; Do, D. D. Improved Comparison Plot Method for

Pore Structure Characterization of MCM-41. Langmuir, 1996, 12 (26), 6513-6517.

(42) Kruk, M.; Jaroniec, M.; Sayari, A. Adsorption Study of Surface and Structural Properties

of MCM-41 Materials of Different Pore Sizes. J. Phys. Chem. B 1997, 101 (4), 583-589.

(43) Ravicovitch, P. I.; Wei, D.; Chuch, W. T.; Haller, G. L.; Neimark, A. V. Evaluation of

Pore Structure Parameters of MCM-41 Catalyst Supports and Catalysts by Means of Nitrogen

and Argon Adsorption. J. Phys. Chem. B, 1997, 101 (19), 3671.

(44) Chen, C-Y.; Li, H-X.; Davis, M. E. Studies on mesoporous materials: I. Synthesis and

characterization of MCM-41. Microporous Mater. 1993, 2 (1), 17-26

(45) Llewellyn, P. L.; Schüth, F.; Grillet, Y.; Rouquerol, F.; Rouquerol, J.; Unger, K. K.

Water Sorption on Mesoporous Aluminosilicate MCM-41. Langmuir 1995, 11 (2), 574-577.

(46) Cauvel, A.; Brunel, D.; Di Renzo, F.; Garrone, E.; Fubini, B. Hydrophobic and

Hydrophilic Behavior of Micelle-Templated Mesoporous Silica. Langmuir 1997, 13 (10),

2773-2778.

(47) Janchen, J.; Stach, H.; Busio, M.; van Wolput, J. H. M. C. Microcalorimetric and

spectroscopic studies of the acidic- and physisorption characteristics of MCM-41 and zeolites.

Thermochim. Acta 1998, 312 (1-2), 33-45.

(48) Nguyen, C.; Sonwane, C. G.; Bhatia, S.K.; Do, D. D. Adsorption of Benzene and Ethanol

on MCM-41 Material. Langmuir, 1998, 14 (17), 4950-4952.

(49) Boger, T.; Roesky, R.; Glaeser, R.; Ernst, S.; Eigenberger, G.; Wietkamp, J. Influence of

the aluminum content on the adsorptive properties of MCM-41. Microporous Mater. 1997, 8

(1-2), 79-91.

(50) Rathousky, J.; Zukal, A.; Franke, O.; Schulz-Ekloff, G. Adsorption on MCM-41

mesoporous molecular sieves. Part 2.—Cyclopentane isotherms and their temperature

dependence. J. Chem.Soc., Faraday Trans. 1995, 91, 937-940.

(51) Franke, O.; Schulz-Ekloff, G.; Rathousky, J.; Starech, J.; Zukal, A. Unusual type of

adsorption isotherm describing capillary condensation without hysteresis. J. Chem. Soc.

Chem. Commun. 1993, 724.

(52) Chen, C.Y.; Xiao, S.-Q.; Davis, M.E. Studies on ordered mesoporous materials III.

Comparison of MCM-41 to mesoporous materials derived from kanemite. Microporous

Mater. 1995, 4 (1), 1-20.

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(53) Glaser, R.; Roesky, R.; Boger, J.; Eigerberger, G.; Ernst, S.; Weitkamp, Progress in

Zeolite and Microporous Materials. J. Stud. Surf. Sci. Catal. 1997, 105A, 695.

(54) Maddox, M. W.; Sowers, S. L.; Gubbins, K. E. Molecular simulation of binary mixture

adsorption in buckytubes and MCM-41. Adsorption 1996, 2 (1), 23-32.

(55) Wang, S.; Fei Ma Z.; Yao H. Fractal diffusion model used for diffusion in porous

material within limited volume of stiff container. Chem. Eng. Sci. 2009, 64 (6), 1318-1325.

(56) Hoang, V-T.; Huang, Q.; Malekian, A.; Eic, M.; Do OT.; Kaliaguine, S. Diffusion

characterization of a novel mesoporous zeolitic material. Adsorption, 2006, 11 (1), 421-426.

(57) Roque-Malherbe, R.; Ivanov, V. Study of diffusion and counter-diffusion of para- and

ortho-xylene in H-SSZ-24 and H-ZSM-11 zeolites. Microp. Mesop. Mater. 2001, 47 (1), 25.

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Table List

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

microwave assisted direct synthesis method

Table 2. Apparent diffusion coefficients (m2/g) of alcohols in MCM-41measured at different

temperatures

Table 3. Apparent diffusion coefficients (m2/g) of aromatic solvents in MCM-41 measured at

different temperatures

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

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

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

energy of diffusion of alcohols in MCM-41

Table 7. Diffusion rate constants, diffusion exponents, transport mechanism and and

activation energy of diffusion of aromatics in MCM-41

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Figure Captions

Figure 1 a) Nitrogen sorption isotherm obtained at 77 K and b) pore size distribution of the

MCM-41 sample.

Figure 2 Ethanol uptake of MCM-41 at 26 ºC

Figure 3 Mt/M∞ versus t1/2 graph of ethanol diffusion in MCM-41 at 26 ºC

Figure 4 ln (Mt/M∞) versus ln t graph of ethanol diffusion in MCM-41 at 26 ºC

Figure 5 Apparent diffusion coefficients of alcohols in MCM-41

Figure 6 Apparent diffusion coefficients of a) first group aromatics and b) second group aromatics in MCM-41

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Figure 1 a) Nitrogen sorption isotherm obtained at 77 K

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Figure 1b. and b) pore size distribution of the MCM-41 sample. 238x198mm (72 x 72 DPI)

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Figure 2 Ethanol uptake of MCM-41 at 26 ºC

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Figure 3 Mt/M∞ versus t1/2 graph of ethanol diffusion in MCM-41 at 26 ºC

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Figure 4 ln (Mt/M∞) versus ln t graph of ethanol diffusion in MCM-41 at 26 ºC

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Figure 5 Apparent diffusion coefficients of alcohols in MCM-41

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Figure 6 Apparent diffusion coefficients of a) first group aromatics

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Figure 6. b) second group aromatics in MCM-41

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diffusion of volatile organic chemicals in porous media. 1

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