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
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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
30 3.20 x 10-4 1.00 0.993 Non-Fickian/ Super-Case II
32 1.50 x 10-3 1.00 0.997 Non-Fickian/ Super-Case II
Ethanol
26 2.16 x 10-4 1.00 0.997 Non-Fickian/ Super-Case II
76
28 2.23 x 10-4 1.00 0.990 Non-Fickian/ Super-Case II
30 2.36 x 10-4 1.00 0.987 Non-Fickian/ Super-Case II
32 2.69 x 10-4 1.00 0.983 Non-Fickian/ Super-Case II
n-Propanol
26 8.35 x 10-5 1.00 0.991 Non-Fickian/ Super-Case II
93
28 1.12 x 10-4 1.00 0.986 Non-Fickian/ Super-Case II
30 1.35 x 10-4 1.07 0.984 Non-Fickian/ Super-Case II
32 1.70 x 10-4 1.08 0.995 Non-Fickian/ Super-Case II
n-Butanol 26 8.84 x 10-5 1.00 0.993 Non-Fickian/
Super-Case II 118
28 9.84 x 10-5 1.03 0.997 Non-Fickian/ Super-Case II
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30 1.09 x 10-4 0.99 0.987 Non-Fickian/ Super-Case II
32 1.25 x 10-4 1.00 0.984 Non-Fickian/ Super-Case II
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
26 1.06 x 10-4 1.00 0.993 Non-Fickian/ Super-Case II
48
28 1.92 x 10-4 1.00 0.998 Non-Fickian/ Super-Case II
30 2.39 x 10-4 1.09 0.996 Non-Fickian/ Super-Case II
32 2.44 x 10-4 0.98 0.999 Non-Fickian/ Super-Case II
Toluene
26 3.04 x 10-5 1.00 0.997 Non-Fickian/ Super-Case II
91
28 4.45 x 10-5 1.00 0.998 Non-Fickian/ Super-Case II
30 4.93 x 10-5 1.00 0.997 Non-Fickian/ Super-Case II
32 5.66 x 10-5 0.93 0.998 Non-Fickian/ Super-Case II
Ethylbenzene
26 1.42 x 10-3 0.86 0.996 Non-Fickian/ Super-Case II
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.
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(41) Zhu, H. Y.; Zhao, X. S.; Lu, G. Q.; Do, D. D. Improved Comparison Plot Method for
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(53) Glaser, R.; Roesky, R.; Boger, J.; Eigerberger, G.; Ernst, S.; Weitkamp, Progress in
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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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