Principal Features of Tetrapropylammonium Hydroxide Removal

Article pubs.acs.org/JPCC

Principal Features of Tetrapropylammonium Hydroxide Removal Kinetics from Silicalite‑1 in Quasi-isothermal Heating Regimes Olga Prokopova,*,† Bohumil Bernauer,‡ Marie Frycova,† Pavel Hrabanek,† Arlette Zikanova,† and Milan Kocirik† †

J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, Dolejškova 3, 182 23 Prague 8, Czech Republic ‡ Institute of Chemical Technology, Technická 5, 166 28 Praha 6, Czech Republic ABSTRACT: We study the time dependence of tetrapropylammonium hydroxide (TPAOH) removal from unconsolidated silicalite-1 crystal layers. The changes in the assynthesized silicalite-1 crystals caused by TPAOH removal were investigated by thermogravimetric (TG) measurements using oxidative and nonoxidative gaseous agent. TG experiments were carried out under quasi-isothermal conditions that consisted of fast heating the sample to various temperatures Tmax and keeping at those temperatures. The shape of the TG curves confirmed the key role of the mobilization reaction that controls the percolation of the mobile products of TPAOH through the zeolite channel system. Another key finding was the existence of clearly defined deviations between the TG curves for air and those for N2. On the basis of these results, we proposed a simplified kinetic model that accounts for the principal features of quasi-isothermal TPAOH removal from silicalite-1. Our model approximates the TG arrangement with a continuous stirred tank reactor, a combined effect of mobilization reaction and bond−site percolation on a diamond lattice, and also possible kinetic steps involved during transport of TPAOH decomposition products from silicalite-1 crystals into the main gas stream. Based on the analysis of the TG curves, we estimated the activation energy (Ea) of the mobilization reaction from the point of deviation as 164 kJ/mol.

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INTRODUCTION Experimental techniques used in earlier papers to study tetrapropylammonium removal from small beds of MFI zeolite crystals were mainly thermogravimetric (TG) analysis, derivative thermogravimetric analysis (DTG), or differential thermal analysis (DTA).1,2 The mechanism of tetrapropylammonium hydroxide (TPAOH) decomposition in pyrolytic atmosphere was suggested by Soulard et al.3,4 In all the above experimental arrangements, the gaseous agent passed along the zeolite crystal layer. However, for different particular types of apparatuses, the hydrodynamic conditions vary, and thus, it would be difficult to extract information on intrinsic template removal kinetics on one side and apply it to some technological process on the other. A detailed experimental study of the effect of hydrodynamic conditions and the gas atmosphere on the process of template removal from various beds of silicalite-1 crystals has been done in a recent study.5−7 It has been shown that template residues remain in/on the crystal surface and change the silicalite physicochemical properties. Quantity, nature, and stability of the deposits depends just on template removal conditions.8−11 Recently, template removal from large silicalite-1 crystals was studied by combination of sophisticated microscopy techniques by Karwacki and Weckhuysen.12 Also, template removal from giant fluorosilicalite-1 crystals was investigated by Mateo et al.13 The aim of the present study is twofold: (i) Obtaining information on rate steps of the kinetics, their relative © 2012 American Chemical Society

importance, and the physicochemical characteristics of the process; this requirement seems to be fulfilled by TG measurements at quasi-isothermal conditions. (ii) The formulation of a mathematical model of quasi-isothermal degradation kinetics that would make possible evaluation of kinetic parameters and represent a basis for prediction and optimization of the template removal under practical applications. It is assumed that at least the tetrapropylammonium cations and tripropylamine molecules are completely immobile in the zeolitic framework2,14,15 and this causes the impermeability of the channel system of MFI-type structure. This is thus obvious that template layer mobilization may result in some kind of percolation process. The channel system of silicalite-1 is topologically identical with a diamond lattice where sites are represented by channel cross sections and bonds by the corresponding channel segments between sites. The open questions are (i) what template decomposition fragments and/ or products represent the precursors of mobile pseudospecies and (ii) what elements of the percolation lattice do they block. A real process of template removal from MFI zeolites may thus involve a percolation mechanism that is near to one of the following cases: (i) site percolation on channel cross sections, Received: September 11, 2012 Revised: November 14, 2012 Published: December 13, 2012 1468

dx.doi.org/10.1021/jp3090364 | J. Phys. Chem. C 2013, 117, 1468−1476

The Journal of Physical Chemistry C

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version 10.1 (Aspen Technology) module RGIBBS. It can be seen that the system contains only ammonia, propylene, and water above 130 °C . It should be emphasized that this is a simplified concept that disregards conceivable associative reactions of template decomposition products. On the other hand, due to the restricted transition-state shape selectivity of MFI-type zeolites confirmed, for example, by Degnan,17 the association reactions in the crystal interior are assumed to be significantly suppressed. However, they proceed in a considerable extent at the outer crystal surface as it was confirmed, for example, in the referred works.9,11 Apparatuses to Study Kinetics of Template Removal. TG curves in pyrolytic TGpyr and oxidative TGox atmospheres were measured in arrangement simulating hydrodynamic conditions of the template removal process in the layer of crystals. Nitrogen or air streamed parallel to the silicalite-1 crystal layer. The instrument used was a Stanton−Redcroft TG750. The mass of the silicalite-1 sample used for the TG experiment was about 15 mg. Quasi-isothermal kinetics in TG arrangement was realized by heating the sample with the rate of 50 °C/min up to a decomposition temperature Tmax and then keeping the sample at this temperature. The temperature Tmax was a variable parameter of the study. The duration of all experiments was usually about 7−8 h except for experiments with Tmax = 330 °C where it was 25 h. The volumetric flow rate of carrier gas (air or nitrogen) was adjusted to 60 mL/min. The conditions of the experiments (i.e., volumetric flow rate and bed length) were chosen to meet requirements on a continuous stirred tank reactor (CSTR). The template removal degree α was defined as

(ii) bond percolation on the lattice of channel segments, and (iii) site and bond percolation on the lattice involving both channel system elements. As to the chemistry of the template removal from MFI zeolites, the mechanism of TPAOH decomposition was reported to proceed in the following steps suggested by Soulard et al.:3 TPAOH → TPA + CH3−CH=CH 2 + H 2O

(r1)

TPA → DPA + CH3−CH=CH 2

(r2)

DPA → MPA + CH3−CH=CH 2

(r3)

MPA → NH3 + CH3−CH=CH 2

(r4)

where TPA, DPA, and MPA are tripropylamine, dipropylamine, and monopropylamine, respectively. Due to the immobility of tetrapropylammonium and some of its decomposition products, the mobilization reactions are represented by a set of consecutive reactions r1 and r2. Thermodynamic data to analyze the reaction r1 are not available. For the set of reactions r2−r4, we performed the thermodynamic analysis to find whether some of the reactions can run in the opposite direction to produce immobile TPA.

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EXPERIMENTAL AND THEORETICAL METHODS Material. All experiments in this study were performed with large silicalite-90°- intergrowths from one synthesis batch. The silicon to aluminum molar ratio (Si/Al) was estimated to be ≈350, and the crystal size was uniform with dimensions ≈23 μm × 23 μm × 120 μm. The crystals were synthesized in our laboratory using the protocol by Kornatowski.16 Tetrapropylammonium bromide (Sigma−Aldrich) was used as the template. Thermodynamic Constraints. The temperature dependence of the equilibrium composition of the system was simulated, see Figure 1. As the initial mixture, we selected

α (t ) =

[a − aΣ(t )] m(0) − m(t ) = max m(0) − m(∞) amax

(1)

where m(0) and m(t) are the masses of the zeolite sample at time t = 0 and t ≠ 0, respectively. m(∞) is the mass of the template free crystal. The quantity α can be also expressed in terms of concentration of template species a, for example, in (mol·m−3), present in the crystal. The concept of template species will be specified in more detail in the Group Approach section. The subscript “max” relates to the initial amount of TPA+ in the zeolite and that of “Σ” to its current amount at the instant t. When m(t) = m(∞), where m(∞) < m(0) and the analysis does not show any residual organics in the sample after TG experiment, then the crystal is free of the template, and α = 1. When m(t) = m(0), then α = 0, and the crystal is full of the template. Principal Features of TG Curves Measured at Quasiisothermal Conditions. Figure 2 shows a comparison of quasi-isothermal TG curves monitored in the TG aparatuses with as-synthetized silicalite-1 in nonoxidative and oxidative atmosphere at different Tmax values. It can be seen that only small mass changes occurred during the fast heating rate of 50 K/min up to Tmax = 330 °C after 25 h regardless of what atmosphere was used. The most striking finding is a phenomenon consisting of the fact that, for a given temperature program, both TG curves (TGpyr and TGox) are identical up to a certain point of deviation. This point is characterized by a time instant t1. It means that, up to t1, the template is not perceptibly affected by oxygen presence and kinetics of template removal is the same

Figure 1. Equilibrium composition of mixture of propyl-amines as a function of temperature. The initial molar composition was TPA/ propylene/H2O = 1:1:1.

that of propylene/tripropylamine/water = 1:1:1. (see reaction r1). From the point of the thermodynamic equilibrium, the water is negligible, and thus, it is not depicted in the graph. The calculation was carried out by method of minimization of total Gibbs energy of the system involving Redlich−Kwong’s equation of state. The program used was ASPEN PLUS, 1469



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Figure 2. TG curves in air (○) and in N2 (●), with a heating rate of 50 K/min up to Tmax; dashed line and solid line simulated curves according to the presented model.

as in the pyrolytic regime. Starting from the time instant t1, the curve TGox exhibits a significantly steeper rise than the corresponding TGpyr curve that is manifested for Tmax ≤ 390 °C in a sigmoid shape of the curve. Another characteristic feature of the TGpyr and TGox curves for t < t1 is that a low step develops on TG curves with Tmax ≤ 390 °C. With increasing temperature Tmax, the inflex is more pronounced, and it is displaced to lower times. The TG curves measured with temperature program Tmax ≥ 430 °C exhibit neither low initial step nor inflex, and the dependencies 1 − α versus t approach an exponential function. Based on the TPA+ sitting in the cross sections of the channels in the MFI structure, we anticipated that the shape of TG curves was primarily determined by mobilization kinetics. Applying a simplified model of mobilization kinetics in zeolite crystals based on the assumption that the percolation lattice is infinite, one expects that template removal rate dα/dt is zero up to the concentration level of the mobilized species corresponding to the percolation threshold (its definition bellow eq 7). For zeolite crystals of finite size, however, the template removal is necessarily affected by the finite character of the percolation lattice, and thus, dα/dt > 0 for t → 0+. This is because, at the very beginning of any TG run, there are formed in the crystal subsurface layer percolating clusters of finite size that have at least one lattice point in the crystal surface.

We will disregard in this initial kinetic study the effect of crystal subsurface layers on the initial shape of TG curves and consider the ideal case of mobilization in an infinite lattice. The starting point of the analysis will be the point of deviation of the TG curves. The question arises at what conditions do oxygen molecules start to be effectively involved in oxidation of the template species. The approach consistent with disregarding the phenomena taking place in subsurface layers of crystals requires consideration of the oxidation effect from a time instant tp necessary for an infinite lattice to reach the percolation threshold via transformation of immobile template species into mobile ones. Consistent with the above statements, we assume that tp is not significantly affected by the presence of oxidation atmosphere. This is because of TPAOH decomposition takes place just in the intracrystalline space. Only reaching the percolation threshold removes a transport resistance for diffusion of reactive oxygen species into the crystal interior against mobilized template decomposition products that may cause the oxidation of these products both at the outer crystal surface and in the crystal bulk. The above oxidizing effects together with accompanied heat effects represent potential causes of the observed template removal enhancement and existence of point of deviation TG curves. It should be noted that, after reaching the percolation threshold, the crystals release a considerable amount of gaseous species (according to 1470



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reactions r1−r4); it would be in the absence of association reactions 6 mol of gaseous molecules produced from 1 mol of TPAOH. Due to this flow of species from crystals, the back flow of oxidizing agent may be considerably retarded. The oxidizing agents would act in the crystal bulk probably only in the later stages of template removal. In the simplified model of the process, we disregard a possible effect of the oxidizing agents in the crystal interior and take into account only their effect in the intercrystalline space. A reasonable assumption seems to be that time coordinate t1 of the point of deviation is determined by the rate of the mobilization reaction that requires a time tp necessary for an infinite percolation lattice occupied by immobile species to reach the percolation threshold. Thus, in the first approximation, we set tp equal to t1. We evaluated from digitalized αox, αpyr versus t plots an instant t1 where a value of (αox − αpyr)/ αpyr fell within the interval . In this way, the corresponding t1 values were obtained for decomposition temperatures 370, 380, 390, and 430 °C where the point of deviations on TG curves were well pronounced. The t1 values that meet the above condition are summarized in Table 1 Table 1. Points of Deviation t1 (Values Obtained from Experimental Data) temp (°C)

t1 ≈ tp (s)

370 380 390 430

7000 4000 2600 500

Figure 3. Schema of balanced subspaces with a schematic detail of a percolation situation in the MFI channel system; the cross-channel intersection occupied by immobile molecule (black circle), by free space (blank circle), and by mobile molecule (gray circle).

These data will be used below to determine the temperature dependence of the kinetic constant of the mobilization reaction and also its activation energy. Model to Describe Principal Features of Quasiisothermal Template Removal in TG Arrangement. The model is based on the following definition of system subspaces and assumptions leading to constitutive and mass balance equations to describe the behavior of an as-synthesized zeolite in the TG process. System Subspaces. The section of the tube containing the pan with the sample is considered to be a CSTR. The model is based on the assumption that, among reactions causing the TPAOH degradation process (cf. reactions r1−r4), a reaction exists that controls the rate of the degradation. We disregard potential association reactions giving rise to bulky immobile organic species in the crystalline space. The space of the reactor VR is considered to consist of four subspaces: (i) the reactor free space volume Vr, (ii) the intercrystalline space of the zeolite layer of the volume Vε, (iii) the space of the immobile phase (preferentially TPAOH and TPA), and (iv) the space of the mobile phase (mobile pyrolysis products) in the zeolite crystals. The immobile phase is characterized by the crystal volume Vz and an actual total concentration aim (mol·m−3) of the immobile species. The mobile phase is characterized by the crystal volume Vz and the actual concentration of the mobile molecules bj (mol·mm−3) in crystals (this is the concentration averaged over the volume of crystals in CSTR), see Figure 3. Group Approach. A group of immobile species is considered as a single pseudospecies with some average properties with respect to mobilization rate. Also, all the mobile molecules in crystals are considered as a group of

pseudospecies characterized by physicochemical properties averaged over the group. The same is valid for mobile species in other subspaces. Due to this approach, one can omit subscripts distinguishing the individual species. Thus, instead of bj we can use b. Kinetics of Mobilization and Mass Balance of Species in the Crystals. The mass balance of the component in the immobile phase of the crystals can be expressed by eq 2: da im = rm (2) dt −3 −1 where rm (mol·m ·s ) is the rate of loss of immobile pseudospecies in the crystal volume unit (i.e., the rate of mobilization). The molar concentration of immobile pseudospecies is thought to be expressed in molecular units equivalent to starting immobile TPAOH. The mass balance of the component in the mobile phase of the crystals is described by eq 3: −

Vz

db = Vzrm − Szjz dt

(3)

−3

where b (mol·m ) is the molar concentration of mobile species in the crystal expressed via molecular units equivalent to starting immobile TPAOH. Sz is the total crystal surface area in the reactor, and jz (mol·m−2·s−1) is the flow density of the component from crystal volume Vz into the intercrystalline space of the volume Vε. Mass Balance of the Mobile Species in the Intercrystalline Space of the Zeolite Layer. The mass balance of the mobile component in the intercrystalline volume Vε can be expressed by eq 4: 1471


The Journal of Physical Chemistry C Vε

dcε = Szjz − Sεjε − Vεkoxcε dt

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jz = hz(b − bs)

where bs is the concentration of the mobile species on the crystal surface that is governed by adsorption equilibrium and hz would generally be dependent on the degree of TPAOH mobilization, that is, on the parameter B = b/amax. This is because the mass transfer coefficient hz would be affected by intracrystalline diffusion of mobilized species and/or by the rate of desorption of mobile species from crystals. The intracrystalline transport of the mobile species was found to be affected by the internal crystal arrangement (the twinning constituents of the MFI-type particles9,18−20). Nevertheless, any heterogeneity of the intracrystalline space is disregarded in this study. In an ideal case (i.e., no finite subsurface clusters of mobilized species), the removal of the degradation products would start at a certain concentration bp of mobilized atoms in the crystal. The corresponding fraction Bp = bp/amax is called the percolation threshold or a critical percolation probability.21 It is a critical fraction of percolation lattice elements that must be released to create a continuous path of mobile nearest neighbors throughout the system. For b < bp, eq 2 alone controls the kinetics of template degradation. There would be no loss of organic species from the crystals during the time interval necessary to reach the concentration level bp except for some template degradation products located within a subsurface crystal layer defined by clusters of mobilized species of finite size. However, the above simplified model is based on the concept of infinite percolation lattice, and thus, we neglect the surface effect. As mentioned in the introduction, in assynthesized silicalite-1, immobile pseudospecies derived from tetrapropylammonium, tripropylamine, and possibly further template decomposition products block some channel system elements (channel cross sections, channel segments), and therefore, the mobilization of the template layer can be described by a percolation model.21,22 We consider the following as possible cases: (i) site percolation, (ii) bond percolation, and (iii) bond−site percolation. An example of a situation near the percolation threshold for the site percolation model is shown in Figure 3. The problem of the critical percolation probability for these percolation processes over a network of channel system of MFI-type structure (which is topologically equivalent to diamond lattice) was solved by Holakovsky et al.23 They found that Bp equals 0.39, 0.43, and 0.64 for bond, site, and bond−site percolation, respectively. As the first approximation, we assumed that the mobilization reaction is irreversible of the first order and the mobilization rate rm is thus independent of the concentration of the mobile species b. This is in accordance with the thermodynamic analysis given formerly that indicates the irreversibility of reactions r1 and r2 and shows that no tripropylamine is formed above 130 °C in a mixture of dipropylamine and propylene (cf. the Thermodynamic Constraints section). The rate of mobilization reaction can therefore be approximated as

where cε is the average concentration of the component in the intercrystalline space of the crystal layer, Sε denotes the effective cross-sectional area of the intercrystalline space of the layer, and jε (mol·m−2·s−1) is the flow density of the component from the intercrystalline space into the reactor free volume. The expression −Vε koxcε in eq 4 represents the source term due to the oxidation of the mobile species at the outer crystal surface that, by definition, belongs to the intercrystalline space. If the oxidizing agent is oxygen present in excess with respect to the actual molar concentration of mobile species in this space, the source term per unit volume of the intercrystalline space can be expressed as rox = −koxcε = k*ox c0O2 where k*ox is the intrinsic rate constant for the oxidation of the mobile species and c0O2 is the concentration of oxygen at the CSTR inlet. It is thus obvious that, in the pyrolytic regime, c0O2 = 0 and the source term in eq 4 vanished. Mass Balance of the Mobile Species in the Free Volume of the Reactor Vr. By assuming the CSTR model for free volume of the TG experimental setup, the mass balance of mobile species in the free volume Vr of the reactor can be written as Vr

dc r = uSrcr 0 − uSrcr + Sεjε dt

(5)

where cr0 and cr (mol·m−3) are the concentrations of the mobile species at the reactor inlet and in the reactor free space (and at the same time at the reactor outlet), respectively. The concentration cr0 is equal zero. Further, u (m·s−1) is the linear velocity of the decomposition agent medium (nitrogen or dry air), Sr denotes the cross-sectional area of the reaction tube, Sε denotes the effective cross-sectional area of the intercrystalline space of the crystal layer, and jε (mol·m−2·s−1) is the flow density of the component from the intercrystalline space into the reactor free volume. A contribution of the volumetric flow rate of the template degradation products leaving the crystal layer to that of gas stream leaving the reactor free space is assumed to be negligible. We made this premise based on considerations on the template removal stoichiometry.6 Thus, the volumetric flow rate v of the fluid phase remains approximately constant throughout the system. It should be noted that no other component of gas flow in the reactor free space is balanced because oxygen and/or nitrogen (used as the carrier gas and oxidizing agent) are used in considerable excess with respect to organic. The constitutive equations for flow densities jε and jz are expressed in our model using the approach of linear driving force. The flow density jε that describes intercrystalline diffusion can be expressed in the following form:

jε = hε(cε − cr)

(7)

(4)

(6)

−1

rm = k ma im

where hε (dm·s ) is the mass transfer coefficient of mobile species from intercrystalline space into the reactor free space volume Vr. The flow density jz is related to the flow of the mobile species through the interface between the crystal bulk and the intercrystalline space. The constitutive equation for jz is in our model also approximated by the linear driving force:

(8)

where km is a rate parameter characterizing the group of the mobilization reactions taking place in the intracrystalline space. It can be considered as the product of two inseparable parameters, that is, of an intrinsic rate constant and a stoichiometric coefficient characterizing the production of the mobile species group. Taking into account eq 8, one can write 1472



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the following for the solution of eq 2 with the initial condition specified as aim(0) = amax: a im = amax exp( −k mt ),

t≥0

b(t ) = amax [1 − exp(−k mt )]

db = Vzamax k mexp( −k mt ) − Szhz(b − bs) dt

(10)

Mass balance eq 10 is related to mass balance eq 4 via the assumption of established adsorption equilibrium between the concentration bs of the mobile species at the crystal surface and concentration cε in the intercrystalline space. This equilibrium is approximated by eq 11 (a modified Langmuir isotherm): bs = (amax − a im)

Kbcε 1 + Kbcε

Vz

+ SεhεuSr]}b = Vzamax k m exp( −k mt )

Here, aim is subtracted from amax because sites occupied by immobile species are not involved in actual Langmuir kinetics of adsorption and desorption. Because of the high-temperature region of template removal (the lowest Tmax of the TG run in this study was 330 °C), we made the approximation Kbcε ≪1, and thus, eq 11 reduces to eq 12:

for t > t p

for

α (t ) = 0

(12)

hz = hz(a im) for

0 ≤ t ≤ tp, tp < t

and ⎫ ⎪ ⎬ ⎪ ⎭

α (t ) =

0.562 , km

(18)

⎡ a (t ) amax − [a im(t ) + b(t )] b(t ) ⎤ = 1 − ⎢ im + ⎥ amax amax ⎦ ⎣ amax b(t ) amax

for

t > tp

(19)

where aim/amax and b(t)/amax mean the fraction of immobile and mobile species remaining in the crystal, respectively. When amax = a im(t ) + b(t )

(20)

then α = 0, and the crystal is full of the template. When b(t ) + a im(t ) = 0

(21)

then α = 1, and the crystal is free of the template.

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(14)

DATA TREATMENT AND DISCUSSION The mathematical simulation of both stages of the TG curves was performed by means of eqs 16, 17, and 19. For a better insight into the template removal process and to make possible an estimate of system parameters from independent data, we present here a variant of the mathematical model expressed in terms of time constants characterizing the involved kinetic steps. For the first stage of the process with no release of the template decomposition products,

The instant tp at which the concentration b reaches the percolation threshold bp, that is, b = bp = 0.39amax, b = bp= 0.43amax, and b = bp= 0.64amax, for bond, site, and bond−site percolation, respectively, can be expressed from eq 9 as tp =

t ≤ tp

= 1 − exp( −kmt ) −

(13)

db = amax k mexp( −k mt ) dt

0.494 , km

for

and

Here, hz (aim) is supposed to be generally a function of the concentration of the immobile species aim. The most simple situation is when the change of hz is realized stepwise to its maximum value hz = hz(0) (absence of immobile species). It can be seen that eq 10 reduces for 0 ≤ t ≤ tp to the following form:

tp =

(17)

The knowledge of the b(t) dependence makes it possible to express the template removal degree α(t) defined by eq 1, which represent the TG curves. Thus,

Here, Kb = ka/kd, and ka and kd are the respective rate constants of adsorption and desorption at zeolite crystal surface. The most simple way to consider the effect of percolation threshold in the template removal model is to introduce into eq 7 a change for hz in the following form: hz = 0

db + Szhz{[SεhεuSr + Vεkox(uSr + Sεhε)] dt /[Szh z(amax − a im)Kb(uSr + Sεhε) + Vεkox(uSr + Sεhε)

(11)

bs = (amax − a im)Kbcε

(16)

Equation 16 was derived from eq 9 where aim = amax − b(t). (ii) subsequent stage For this stage, b(t) can be obtained by integration of eq 17 with the respective condition b = bp at t = tp where bp = 0.39amax, 0.43amax, and 0.64amax, for bond, site, and bond−site percolation, respectively. Equation 17 was obtained by combination of eqs 4, 5, and 10 where the accumulation of mobile species in the fluid phase relative to that in zeolite was neglected:

Using eq 7 for the flow jz through the interface at the crystal surface, after substitution from eqs 8 and 9 into eq 3, one obtains the following expression for mass balance of the component in the mobile phase: Vz

α( t ) = 0

t ≤ tp

for

(9)

and

and

tp =

1.021 km

(15)

for bond, site, and bond−site percolation, respectively. Here, (aim)p = amax − bp. The relations of eq 13 allow splitting of the solution of the simplified model of template removal in two parts with a discontinuity of derivatives dB/dt and dα/dt at t = tp, that is, the kinetics exhibits two steps: (i) initial stage

⎛ t ⎞ B = 1 − exp⎜ − ⎟ , ⎝ τm ⎠

α=0

for

t ≤ tp

(22)

For the subsequent stage, 1473


The Journal of Physical Chemistry C dB 1 + dt (1 − e−t /τm)(VzKbamax ) =

1 −t /τm e τm

(

τε 0 Vε

+

Article

τr 0 Vr

)

B ·Ω + τz

t > tp

for

(23)

⎛ t ⎞ α = 1 − exp⎜ − ⎟−B τm ⎠ ⎝

(24)

Here, a im = e−t /τm , amax

B = b/amax , τr 0 = Vr /uSr ,

and

τϵ = Vϵ/Sϵhϵ ,

τϵ 0 = Vε/Sεhε

Figure 4. Arrhenius plot: (●) for T = 370, 380, 390, and 430 °C; (○) for T = 330 and 480 °C; T is temperature (K); km is the rate parameter of the mobilization reactions.

The symbol τ (s) denotes generally a characteristic time parameter. It can be seen that solution of the first stage (no release of the template decomposition products) depends only on τm, which was estimated from the percolation analysis. To describe the second stage of the TG curve one rewrites eq 23 as dB 1 1 −t /τm + B= e τm dt (1 − e−t /τm)β1 + β2

correspond to the value of the (αox − αpyr)/αpyr criterium that falls in the interval . The rate parameters km estimated for the temperature region 330−480 °C are summarized in Table 2. Table 2. Rate Parameters km for Bond, Site, and Bond−Site Percolation Models

(25)

where ⎛τ 0 τ 0⎞ β1 = VzKbamax ⎜ ε + r ⎟ ·Ω Vr ⎠ ⎝ Vε

(26)

β2 = τz

(27)

Ω=

temp (°C)

(τm)bond (s)

(τm)site (s)

(τm)bond−site (s)

330 370 380 390 430 480

102 844 14 170 8097 5263 1012 156

90 400 12 456 7117 4626 890 137

49 760 6856 3918 2547 490 75

1 1 τox

(τ

0

ε

+

)+1

Vε ·τ 0 Vr r

The data from Table 2 represent the starting step of the simulation strategy. As the next step, we estimated the theoretical value of the parameter β2 as (β2)th = (τz)th. As no relevant data for intracrystalline diffusion of propylene and monopropylene are available, we made the estimation for NH3 based on the diffusion coefficient Dz obtained from QENS and PFG NMR measurements by Jobic et al.24 The silicalite crystals were approximated by a cylinder infinite in length with R = 1.5 × 10−5 m. The theoretical value of (τz)th = (β2)th for crystals free of immobile obstacles is given by eq 31:25,26

(28)

here, τox = (kox)−1 = (k*oxc0O2)−1 is the characteristic time parameter for oxidation (cf. the Group Approach section). It can be seen that, when kox → 0, for example, due to the absence of the oxygen, τox → ∞ and Ω → 1. For an oxidative regime, there is always Ω less than 1. The key characteristic time of the process is the time constant τm of the mobilization reaction that determines the time scale of the kinetic process. It is defined by eq 29:

τm = (k m)−1

(29)

(τz)th =

Using eq 15, one can express an estimate of km for respective percolation models as follows: (k m)bond ≅ 0.494t1−1 ,

(31)

th

The values of (β2) for ammonia are summarized in Table 3. As suggested by relation 13, the presence of immobile obstacles affects necessarily the diffusion coefficient Dz of the mobile species. There are fundamental studies by Kärge and Pheifer,27 Förste et al.,28 or Gupta and Snurr29 on the mobility of methane molecules in the channel system of MFI zeolite that was blocked to a certain degree by benzene molecules. A detailed analysis by Monte Carlo simulation gave universal functions Dz(αim) for a statistical blockage of channel cross sections (site percolation) and channel segments (bond percolation) and even for bond−site percolation to a defined degree blockage αim = aim/amax in a two-dimensional lattice. We used in the first approximation for our mobilization kinetics the following function:

(k m)site ≅ 0.526t1−1 ,

(k m)bond−site ≅ 1.021t1−1

Vz R2 = Szhz 8Dz (0)

(30)

The Arrhenius plot for rate parameter km based on these values is shown in Figure 4 (cf. filled symbols). It can be described by the straight line ln km = −19.674/T + 21.8 where the slope of the straight line is −19.674 that equals Ea/R. The activation energy Ea of the mobilization rate was evaluated from the plot as Ea = 164 kJ/mol. We extrapolated the Arrhenius plot in both directions (cf. dashed lines in Figure 3) and evaluated the corresponding rate parameters for temperatures 330 and 480 °C (cf. empty symbols in Figure 4). We found that also t1 values evaluated from the above extrapolated rate parameters 1474



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Table 3. Theoretical Parameters (β2)th and Parameters (β1)exp and Ω Obtained from Experimental TG Curves Using the Kinetic Model

a

temp (°C)

(β2)tha (s)

(β1)expox (s)

(β1)expN2 (s)

Ω (1)

330 370 380 390 430 480

0.1671 0.1488 0.1452 0.1418 0.1305 0.1200

12.6 6.0 5.8 5.2 5.0 4.5

16.0 14.0 14.5 12.0 10.0 −

0.79 0.43 0.40 0.43 0.5 −

The simulated TG curves are compared with the corresponding experimental ones in Figure 2. The principal phenomenological features deduced from the graphs in Figure 2 can be summarized as follows: (i) In the initial part, the experimental curves are getting ahead of theoretical ones. In the range of Tmax between 300 and 390 °C, the experimental curves even exhibit a step lying above the theoretical ones. This early species release should be attributed to formation of finite percolating clusters with at least one emptied site or bond in the crystal surface. Theoretical TG curves do not involve the effect of finite percolating clusters, and they start to increase abruptly after a delay defined by formation of an infinite percolating cluster via the mobilization reaction. This induction period decreases as the temperature increases. There is singularity on simulated TG curves associated with discontinuity of the first derivative of the TG curves at the time instant tp defined by reaching the percolation threshold. (ii) The key phenomenon is the existence of the point of deviation where the experimental TG curve measured in the flow of air starts to deviate from that measured in nitrogen. The TG curve measured in the presence of an oxidative agent lays naturally above the corresponding curve measured in the flow of nitrogen. There is no perceptible point of deviation on the experimental TG curves measured at Tmax = 330 °C although the simulation based on extrapolation of kinetic constants to 330 °C predicts a slight effect of the oxidative agent. For the TG curves with Tmax = 370, 380, 390, and 430 °C, one can determine the point of deviation. These points were used to determine the rate parameter km of the mobilization rate. The maximum effect of the presence of the oxidative agent occurs for TG curves measured at Tmax = 380 °C. This is obvious from the extent of the difference between the TG curves, and it is also manifested in the minimum value of the parameter Ω. For experiments with Tmax > 380 °C, the Ω values become again higher (cf. Table 3). The existence of the point of deviation is in accordance with the idea of the percolation threshold that is determined just by pyrolytic mobilization steps expressed by eqs 2, 8, or 9. The presence of the oxygen accelerates the template removal after attaining the point of deviation. The potential explanations of the oxidative agent effect can be (a) the driving force increase of the pyrolytic products transport by decomposition of the part molecules at outer crystal surface and (b) the oxidative reactions as a source of energy for the template decomposition in the intercrystalline space. (iii) Due to operational regulations, the duration of any TG experiment was as a rule limited to about 7 h. A significant feature of the quasi-isothermal TG experiment regards the long-term behavior of the TG curves. The shape of the theoretical (i.e., simulated) TG curves suggests that the TG curves tend for t → ∞ in accordance with the model to asymptote α = 1 (cf. Figure 2). The course of experiental TG curves suggests however a deviation of these curves (both for pyrolytic and oxidative regimes) in the direction of lower values of α(∞) < 1. It is evident that the most probable reason of such behavior is the existence of associating reactions of

Based on diffusion data for NH3 in silicalite-1 taken from ref 21.

Dz = Dz (0)(1 − αim) = Dz (0)[1 − exp( −t /τm)]

(32)

given by Barrer that is compatible with the above analysis.26 Equation 25 can be modified by introducing the expression R2{8Dz(0) [1 − exp(−t/τm)]}−1 for β2: (1 − e−t /τm) dB 1 −t /τm e B= + 2 R − t / τ 2 dt τm (1 − e m) β1 + 8D (0)

for

z

t ≥ tp

(33)

The value of the term R2/(8Dz(0)) should be compared with the minimum value of the first term in the denominator on the left-hand side of eq 33, that is, with (1 − e(−tp/τm))2β1 ≅ 0.408β1 (cf. eqs 30 and 31). It appears that, in the neighborhood of the point t = tp, the effect of intracrystalline diffusion cannot be generally neglected. For sufficiently large time, the diffusion term is compared with β1, and it can be anticipated that the term of intracrystalline diffusion is negligible. Thus, the third simulation step was the tentative simulation using values τm from Table 2 and the stepwise change of hz to hz(0) that is equivalent to the use of (β2)th from Table 3 (i.e., the value for crystals free of immobile obstacles) This simulation gave two important results: (i) The points of deviation were well reproduced on simulated TG curves only when the bond−site percolation model was applied (i.e., for the parameter (τm)bond−site). (ii) The estimates of the parameters (β1)expox and (β1)expN2 obtained from experimental TG curves were more than 35 times higher than the values of (β2)th. A comparison of the tentative values of 0.408(β1)expox and 0.408(β1)expN2 with the values of (β2)th showed that (β2)th values were still more than 15 times lower than the above tentative values. For this reason, we disregarded the effect of intracrystalline diffusion on TG curves in the final simulation step. The values of the parameters (β2)expox and (β2)expN2 obtained from the final step of the simulation are summarized in Table 3. As the group approach seems to be the only feasible method of template removal quantification, (β1)expN2, (β1)expox, and Ω are apart from km the principal system parameters accessible from experiments. It would be very difficult to predict them on the basis of sorption and texture parameters of hypothetical individual species although these parameters are expressed in detail via corresponding structural, adsorption, and kinetic parameters by eqs 26−28. 1475



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(3) Soulard, M.; Bilger, S.; Kessler, H.; Guth, J. L. Zeolites 1987, 7, 463−470. (4) Soulard, M.; Bilger, S.; Kessler, H.; Guth, J. L. Thermochim. Acta 1992, 204, 167−178. (5) Pachtova, O.; Kocirik, M.; Zikanova, A.; Bernauer, M.; Miachon, S.; Dalmon, J.-A. Microporous Mesoporous Mater. 2002, 55, 285−296. (6) Pachtova, O. The Development of Channel System Accessibility in Sorption and Membrane Materials of Silicalite-1 Type Prepared from Precursors Containing Tetrapropylammonium Hydroxide. Thesis, Institute of Chemical Technology, Prague, Czech Republic, 2000. (7) Jirka, I.; Pachtova, O.; Novak, P.; Kocirik, M. Langmuir 2002, 18, 1702−1706. (8) Brabec, L.; Kocirik, M. Mater. Chem. Phys. 2007, 102, 67−74. (9) Brabec, L.; Kocirik, M. J. Phys. Chem. C 2010, 114, 13685−13694. (10) Jirka, I.; Zikanova, A.; Novak, P.; Kocirik, M.; Weber, J.; Pelouchova, H.; Cernansky, M. Mater. Chem. Phys. 2005, 90, 116−122. (11) Jirka, I.; Sazama, P.; Zikanova, A.; Hrabanek, P.; Kocirik, M. Microporous Mesoporous Mater. 2011, 137, 8−17. (12) Karwacki, L.; Weckhuysen, M. Phys. Chem. Chem. Phys. 2011, 13, 3681−3685. (13) Mateo, E.; Paniagua, A.; Güell, C.; Coronas, J.; Santamaría, J. Mater. Res. Bull. 2009, 44, 1280−1287. (14) Soulard, M.; Bilger, S.; Kessler, H.; Guth, J. L. Zeolites 1991, 11, 107−115. (15) Parker, L. M.; Bibby, D. M.; Patterson, J. E. Zeolites 1984, 4, 168−174. (16) Kornatowski, J. Zeolites 1988, 8, 77−78. (17) Degnan, T. F. J. Catal. 2003, 216, 32−46. (18) Kocirik, M.; Kornatowski, J.; Masarik, V.; Novak, P.; Zikanova, A.; Maixner, J. Microporous Mesoporous Mater. 1998, 26, 295−308. (19) Vasenkov, S.; Böhlmann, W.; Galvosas, P.; Geier, O.; Liu, H.; Kärger, J.; Barriers. J. Phys. Chem. B 2001, 105, 5922−5927. (20) Geier, O.; Vasenkov, S.; Lehmann, E.; Kärger, J.; Schemmert, U.; Rakoczy, R. A.; Weitkamp, J. J. Phys. Chem. B 2001, 105, 10217− 10222. (21) Stauffer, D.; Aharony, A. Introduction to Percolation Theory; Taylor & Francis: London, 1992; p 65. (22) Grimmet, G. Percolation; Springer: Berlin, Germany, 1999; p 24. (23) Holakovsky, J.; Kratochvilova, I.; Kocirik, M. Microporous Mesoporous Mater. 2006, 91, 170−171. (24) Jobic, H.; Ernst, H.; Heink, W.; Karger, J.; Tuel, A.; Beé, M. Microporous Mesoporous Mater. 1998, 26, 67−75. (25) Kärger, J.; Bülow, M.; Ulin, V. I.; Voloshchuk, A. M.; Zolotarev, P. P.; Kocirik, M.; Zikanova, A. J. Chem. Technol. Biotechnol. 1982, 32, 376−381. (26) Barrer, R. M. Zeolites and Clay Minerals as Sorbents and Molecular Sieves; Academic Press: London, 1978. (27) Karger, J.; Pfeifer, H. Zeolites 1987, 7, 90−107. (28) Förste, Ch.; Germanus, A.; Kärger, J.; Pfeifer, H.; Caro, J.; Pilz, W.; Zikánová, A. J. Chem. Soc., Faraday Trans. 1987, 83, 2301−2309. (29) Gupta, A.; Snurr, R. Q. J. Phys. Chem. B 2005, 109, 1822−1833.

primary products of template decomposition that were deliberately ignored in the simplified model of the template decomposition kinetics. The associating reactions are leading to formation of organic deposits of various composition (olefinic and/or aromatic) and under circumstances rather stable (even at such high temperatures as 550 °C), which has been confirmed by chemical analysis,5−7,10,11 X-ray photoelectron spectroscopy,7,10,11 UV−visible spectroscopy,11 and light microscopy,2,5,6 and scanning electron microscopy combined also with HF etching.8,9

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CONCLUSIONS The principal features of the quasi-isothermic kinetics of TPAOH removal from a layer of highly silicious MFI zeolite crystals observed under TG experiment were revealed, and a simplified kinetic model was formulated. The important experimental finding was the existence of the point of deviation at which the TG curve measured in air started to deviate from that in nitrogen. The zeolite layer with a parallel flow of gaseous agent was described by the CSTR model. The key rate step was the mobilization reaction of the TPAOH layer in the channel system of the zeolite that rules the time instant when the percolation threshold of an infinite percolation lattice was attained for the bond−site percolation process. The rate parameter km of the mobilization reaction together with its activation energy was estimated from temperature dependence of the point of deviation. The considered rate steps following the mobilization reaction are transport of mobile species from crystals into intercrystalline space. Further rate steps considered are the diffusion of mobile species through intercrystalline space into the free space of the reactor and species flow in the free reactor space. The solution of deduced differential equation was used to simulate TG curves. The anticipated differences between experimental and simulated TG curves consist (i) in disregarding the initial template products release due to formation of subsurface percolation clusters of finite size, (ii) in disregarding irreversible organic deposits causing lower template removal in the long time region, and (iii) in disregarding dependence of the intracrystalline diffusion coefficient of mobile species on the amount of immobile species. As to our knowledge, this work represents the first quantitative description of the template removal process in zeolites. The model offers series refinement approaches for various practical applications to control template removal from crystal batches, zeolite membranes, and so forth.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by grant no. 204/11/1206 of Czech Science Foundation.

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REFERENCES

(1) Franklin, K. R.; Lowe, B. M. Thermochim. Acta 1988, 127, 319− 327. (2) Geus, E. R.; van Bekkum, H. Zeolites 1995, 15, 333−341. 1476


Principal Features of Tetrapropylammonium Hydroxide Removal

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