Kinetics of Catalytic Peroxide Oxidation of Phenol ... - ACS Publications

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Kinetics of catalytic peroxide oxidation of phenol over three-dimensional fractals Želimir Jel#i#, Karolina Maduna, and Stanka Zrncevic Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b01182 • Publication Date (Web): 27 Jun 2017 Downloaded from http://pubs.acs.org on July 1, 2017

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Industrial & Engineering Chemistry Research

Kinetics of catalytic peroxide oxidation of phenol over threedimensional fractals Želimir Jelčić¥,*, Karolina Maduna# and Stanka Zrnčević§ ¥

PLIVA Croatia Ltd. TAPI, R&D, Prilaz baruna Filipovića 25, HR10000 Zagreb, Croatia. E-

mail: [email protected] #

Faculty of Chemical Engineering and Technology, University of Zagreb, Zagreb, Croatia,

HR10000 Zagreb, Croatia. E-mail: [email protected] §

Faculty of Chemical Engineering and Technology, University of Zagreb, Zagreb, Croatia,

HR10000 Zagreb, Croatia. E-mail: [email protected]

1

Abstract

The aim of this work was to develop fractal-like kinetic model for describing hydrogen peroxide oxidation of phenol over Cu/ZSM-5 catalyst of different fractal forms caused by thermal treatment of the catalysts. Pseudo-first order generalisations of the apparent kinetic rate (Kopelman fractal-like, Brouers-Sotolongo fractal-fractional, Weibull and stretched exponential models) allowed describing the kinetic of reaction. These suggested mathematical models of the phenol oxidation plausibly depict the experimental data and correctly reproduce oxidation process. Fractality of the catalysts exerts a pronounced effect on catalysts activity as well as on the apparent kinetics of the process. The maximum ability toward phenol oxidation has been detected for the Cu/ZSM-5 catalyst with more fractality.

Keywords: fractal, phenol, catalytic oxidation, Cu/ZSM-5, reaction kinetics, modelling, Kopelman, Weibull, Brouers-Sotolongo

*

Corresponding author: Želimir Jelčić, PLIVA Croatia Ltd. TAPI, R&D, Prilaz baruna Filipovića

25, HR10000 Zagreb, Croatia. E-mail: [email protected]

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Introduction

Water pollution by phenol bears important environmental toxic effect towards life in the aquatic environment1,2. Phenolics have been of great concern in view of adverse toxic effect and slow degradation by spontaneous routes 3 . Catalytic reaction rate on zeolites is governed by the intricate relationship of rate constants of the elementary reactions and constitution and construction of the catalyst’s surface. However, the surface may change with reaction settings, such as the pressure and temperature. The outcomes of these effects on overall kinetic behaviour are often very complex. Heterogeneous oxidative catalysis by copper containing MFI zeolite (Cu/ZSM-5) utilizing hydrogen peroxide (H2O2) is a recognized promising method for the efficient elimination of organic chemicals in water 4 . The alumina-silicate ZSM-5 microporous zeolite (IUPAC code MFI), shows high adsorption capability to organic chemicals, and, thus, consistent catalytic efficiency. However, decreases of the effective surface area by rapid leaching in Cu/ZSM-5 suspension results in low catalytic efficiency. Nevertheless, this disadvantage can be improved by catalyst calcinations 5 ,9. However, the real catalysts with obvious pore shape and size are not simplified two-dimensional surfaces. Hence, geometrical shape of the catalyst’s surface surely has impact on the reaction kinetic. However, until now, there was no fundamental relation between catalysts' morphology, calcination and catalytic reaction. Therefore, we prove, first, that the zeolite crystal voids space, as well as the catalyst’s solid surface, is fractal6. In order to do so, zeolite porous surface is appropriately regarded as fractal lattices7,8. By virtue of the high fractal dimension of the voids, the void channels criss-cross the zeolite in a nearly space-filling manner and generate high porosity. Hence, the fractal analysis theory provides a new approach to study the reaction kinetic on porous catalysts. In some of our previous works, we already had investigated the peroxide (H2O2) oxidation kinetic models of phenol (PhOH) over Cu-containing zeolites 9 . In this ongoing study, the catalytic activity of non-calcined and calcined Cu/ZSM-5 supports on peroxide H2O2 oxidation of phenol is evaluated. Some important operational parameters, such as reaction temperature, calcination temperature, catalyst dose, is researched in this work. Thus, the prime objective of the present work was to model catalytic process using fractal Cu/ZSM-5 catalysts. Heterogeneous catalysis, where reactant and catalyst separated in different phases, can be quite different from its homogeneous equivalent, because the diffusion and reactions are restricted to porous catalyst fractal space with dimensions less than three in which the mobility restricts the rate. Fractal geometry is essential part of characterization of catalysts10,11. Fractal analysis, with Page 2 of 42


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inherent irregularity and complexity, can explain the variation in reactivity of many heterogeneous catalytic processes12,13. The effect of irregular catalyst pore fractal structure on the diffusive transport14 and reaction in a porous media15 have long been explored in heterogeneous catalysis, like percolation model 16 stochastic pore network model 17 , pore network- continuum model18. The fractal geometrical description of the pore networks is given for diffusion limited aggregation (DLA) clusters19, regularly symmetric fractal structures20, and statistically symmetric fractal percolating pore networks 21 . Anomalous behaviour of a wide variety of reactions on fractals have led to the so called “fractal reaction kinetics.” In the present work, our focus is the fractal-like and the new Brouers-Sotolongo fractalfractional models of the kinetics of the phenol oxidation reaction catalysed by Cu/ZSM-5 catalysts. A rigorous kinetic study of the phenol oxidation reaction is a complicated topic due to the porous structure of the catalyst and irregular exposition of catalyst surface to the chemicals (H2O2, phenol) along the reaction. Fractal-like kinetic has offered the means to describe kinetics that deviate from the classical exponential law and include the signature behaviour of power‐law. Fractal chemical reaction kinetic, originated by Kopelman, requires heterogeneous or fractal conditions, where a power law time dependent coefficient is introduced. This equation has led to the stretched exponential or the Weibull equation used extensively as empirically derived kinetic. The assumption of Fickian diffusion dominates mathematical modelling in reaction kinetics. However, there is strong experimental evidence demonstrating significant deviation from this behaviour in some cases. The signature of anomalous kinetics is considered to be the presence of power laws instead of the usual exponential kinetics. The reason behind deviations from Fickian diffusion can be attributed to the constrained or fractal topology of the reaction medium . More recently, the Brouers-Sotolongo fractional model has offered a more elegant way of describing the anomalous kinetics by replacing the first- or second-order derivative by fractional derivative in the classical kinetic equation. The Brouers-Sotolongo fractional kinetic equation represents an appropriate model to describe physical phenomena such as diffusion in porous media with fractal geometry22 . This approach has turned out to be successful in modelling anomalous diffusion processes and/or anomalous kinetics.

2.1.1

Catalyst fractality

The catalyst function within the total kinetics can be inferred by “catalyst descriptors”, like catalysts crystal void or pore fractality. There are many diverse perceptions of the fractal

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dimension reliant on how it is ascertained. For catalyst surface, many approaches were anticipated to determine this factor. 2.1.1.1 Pore/ void fractality Many porous catalysts were shown to have a surface that is fractal23,24. The accessible surface is the fractal with the dimension in a range between 2 (smooth surface) and 3 (space-filling surface). A very convoluted internal catalyst surface provides high fractal dimension. The established approach of mapping void space is by rolling a probe sphere of variable radius over a sphere-like depiction of a molecular crystal giving the solvent-accessible surface area, a geometric descriptor25. The fractal dimension, D, is determined from the slope of solvent-accessible surface (SAS) area dependence on the probe radius. Methods for the computation of a fractal dimension index D are proposed and applied to calculate the solvent-accessible surfaces of molecules,26. However, here, as novelty, we want to present a new approach for the determination of pore fractal dimension that is related to the internal catalyst’s electron density structure. Based on isosurfaces of the pro-crystal electron density, an alternative approach27 can be used to localise and visualise the void space in crystals, as well as readily chart surface areas and volumes of the voids. Many aromatic sorbate-ZSM-5 structures have been investigated by single-crystal X-ray diffraction: benzene, p-xylene, p-nitroaniline, p-di-chlorobenzene, toluene, pyridine. Briefly, there are also numerous articles on the synthesis of ZSM-5 handling diverse organic molecules such as amines and alcohols. Volumes and surface areas are the most basic geometric properties of crystal structures. However, the zeolites cannot be viewed as Euclidean object, which minimizes the void space, but as inherently fractal28. The properties of the zeolites are proportionately dependent on the empty space in crystal as well as on the space filled by molecule. The essential property of a series of fractal voids is that their volume and surface area decrease as a power law with iso-surface values. The fractal dimension of zeolites’ crystals voids is computed from the scaling of crystals voids volume vs. electron density iso-values 29 . The mapping of the voids in the crystalline material is created by the Crystalexplorer software at different iso-surface values (default at 0.002 e-.Å-3, that produces similar representation as the Corey–Pauling–Koltun (CPK) surfaces) of procrystal electron density. The void surface is set where the sum of the pro-molecule densities is less than a user-definable iso-value. The pro-molecular surface is used to reveal the surface that belongs to the molecule as well as to the empty space in the crystal27. Crystal voids in ZSM-5 crystals represent a fractal network of voids with fractal rough interfaces. Fractal relations of topological crystal voids vs. iso-values are considered. Such relations generate Page 4 of 42


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predictable power-like “reduced“ graphs, which specify separations in connectedness of nonoverlapping, separable topological subspaces in a crystal structure. The void volume defined equivalent crystal void radius of the ZSM-5 catalysts was between 0.1-0.4 nm over the range of iso-densities studied and was found to increase with iso-density values. The volume fractal dimension, indicative of the void arrangement, mirrored the changes in the mean void size. Small crystal voids surfaces appear in sequence by a sweep from low iso-values to high iso-values. One may imagine the (separated and singular) crystal voids (at low iso-values, less than 0.0001 e-.Å-3) as expanding balloons merging each other as the iso-values approaches to 0.01 e-.Å-3, forming a continuous and connected crystal void. The first, “continuous” void subspace, includes the system of “open“ channels or pores, and, the second, “point-like“ void subspace, comprises the void centres and conglomerates. This method admits proper visualization of crystal voids, and provides an evaluation of their size and shape. 2.1.1.2 Fractality in SEM/ EDS images Surface structures of the zeolite catalysts and dispersal of the copper on surface is related through the fractal dimension to the reaction rate 30 . Scanning electron microscopy (SEM) provides the topographic view of surface of a real catalyst surface. However, EDS elemental map images expose some data about the interior structure while do not present relief features. Catalyst surface morphology, one of the major structural distinctions of practical catalysts, have been explored in terms of fractal theory. This paper proposes use of fractal analysis in order to study the dispersal of active sites for a reaction of phenol and hydrogen peroxide. D(q) and f(α) for several values of reaction conditions are calculated, analysing dispersal of active sites relative to multi-fractal properties. In particular, by determining the dispersal of Al and Cu atoms in the copper alumina-silicate zeolite (Cu/ZSM-5) catalyst, we have aimed to indicate the maximum working Cu/ZSM-5 catalyst in the catalytic oxidation of phenol. The multi-scale spreading of pixels in the SEM and EDS images at respective magnification (scale) is studied with fractal and multi-fractal method. With multi-fractal analysis, it is common practice to evaluate the f(α) spectrum31. The research on catalyst surface morphology with monoand multi-fractal methods explicates the power of fractal theory and advances an approach for studying catalysts surfaces morphologies. 2.1.2

Fractal-like reaction kinetics

The irregular surface of a catalyst can be modelled as a fractal and, as such, the total available surface area depends on the size of the reactant 32 . There is experimental verification for the Page 5 of 42



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fractal roughness of the pore surface of various catalysts over a limited scaling span that embraces the size of usual diffusing molecules33. The rough catalyst texture and its control on diffusion and reaction can be, thus, reasonably modelled using fractal geometry. 2.1.3

Fractal model kinetic

The prominent fractal kinetics developed by Kopelman 34 has been proposed to deal with heterogeneous reactions. Fractal reaction kinetics provides a novel view for heterogeneous chemical reaction kinetic, even in a reaction medium that is not a geometrical fractal. The fractal kinetic model is a phenomenological description of the relationship between microscopic properties and the global macroscopic observables35. The complex reactions over catalyst are limited by the catalysts accessibility due to molecular obstructions. Fractal-like effective kinetic rate analysis based on the first-order kinetic empirical model can be useful to describe the catalytic oxidation of phenol. Accordingly, the catalytic oxidation of phenol in an ideal aqueous solution without molecular obstructions supposedly follows the first order kinetic. However, on a heterogeneous catalytic surface, which exposes fractal character, the rate of chemical reactions fails to follow the mass–action law. The timedependent effective rate constant is now, in the fractal kinetics, time-dependent and is linked to the fractal exponent:

= ×

Equation 1

where k(t) is the time-dependent rate constant, and h is the fractal exponent (where h ≠ -1). The residual phenol concentration in the catalytic degradation of phenol can be expressed as:

=

, × −

× 1−ℎ

Equation 2

where cPhOH,0 is the initial phenol concentration, and c(t) is the persisting phenol concentration at certain reaction time. Oxidation of phenol improves with the rise of rate constant k(t) while reduces with the raise of fractal exponent h. Only for the diffusion-limited reactions h>0, and therefore, h can be used to measure deviations from the law of mass action. The fractal time exponent h is a fractional reaction order, which follows from the impenetrability of the catalyst; not all the reactive sites might contribute to the reaction progression. At initial times, the kinetic is dictated by the reaction on the rather scarce and favourably reactive sites. Thus, at a particular temperature, h quantifies the energetic inconsistency in the catalyst.

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2.1.4

Brouers-Sotolongo model

The statistical Brouers-Sotolongo macroscopic model generally merges the fractal diffusion and kinetic, irreversibility, and the nature of birth and death of the process36,37. The initial point of the fractal kinetic formal description is the differential equation, where fractal time was empirically introduced. −

= ,

Equation 3

where cPhOH(t) is the phenol concentration at t time, n is the apparent reaction order, and α is a global fractal time index (fractional time index) arising from the assumed fractal diffusion and phenol degradation kinetics due to the geometric and energetic heterogeneity of the catalyst and this exponent appraises the breadth of the adsorption energy distribution and energy heterogeneity of the catalyst surface. In the result of Equation 3, respecting the starting physical restrictions, the subsequent equation is gotten:

=

, × !1 − "1 + $ − 1 ×

%

,

&

' Equation 4

where cPhOH,0 is the initial phenol concentration, and τn,α=[ Κn,α(cPhOH,0) n−1]−1/α stand for the representative time of the kinetics. The fractional order (n) and fractal time parameter (α) indicate the rate constant variations in time, and τn,α is a scale factor36. When n and α are ≠1, time-dependent rate constant should be specified and the appropriate measure indicating the time evolution of the reaction is the specific time τn,α. Diverse limits of Brouers-Sotolongo model between the first- and second-order kinetics can arise 38: a)

First-order kinetics with the rate constant, k1: cPhOH(t) = cPhOH,0 ×exp(−k1t), when n=1, α=

1, and the corresponding pseudo-first order kinetic may be re-written as: -(dcPhOH /dt) = k1 cPhOH. b)

second order kinetics with the second order constant, k2: -(dcPhOH /dt) = k2 cPhOH2, when

α=1, n=2, and the corresponding pseudo-second order kinetic may be re-written as:

=

1

( (

,

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+

,


Equation 5


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c)

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Weibull model kinetic, with “half-reaction time” τ½= τα [ln(2)]1/α, in the case where n →

1 and α ≠1, and

=

, × 1 − −

%

Equation 6

Overall, the Brouers-Sotolongo model is more proper for expressing the kinetic data as it covers all possible variations in kinetic orders for the heterogeneous processes at the liquid-solid borderline, and where the diffusion process occurs in a complicated environment with fractal outline.

3

Experimental

3.1

Catalyst preparation and characterization

Complete description of copper exchanged MFI preparation can be found elsewhere 39 . The protonic form of commercial ZSM-5 zeolite (Leuna Werke) was passed through ion exchange with copper acetate solution at 298 K over 24 hours, and then the sample was dehydrated for 10 hours at room temperature. The ion exchanged samples required thermal treatment by the calcination of at different temperatures (773, 1023, and 1273 K) for at least 5 h. The specific surface area and pore size distribution were determined by nitrogen sorption using ASAP 2000 (“Micromeritics”) automatic apparatus. X-ray powder diffraction of powder zeolite samples was accomplished using Philips PW 1065 with Ni-filtered CuKα radiation in the 2θ range of 5° to 40°. Before measuring, the samples were degasified at 473 K for 24 hours. SEM images were taken on a JEOL JSM-5800 model equipped with X-ray energy dispersive spectrometer Oxford Aztec X-max 20mm2. The mono-fractal distribution has been determined by the Harfa software40, in the whole range of thresholding conditions, which produces the fractal spectrum as a criterion for copper and aluminium distribution. Also, the multi-fractal distribution has been determined by the FracLac41, an ImageJ add-in, and variogram analysis. The physico-chemical properties of the zeolites and catalysts samples, and the codes, are summarized in Table 1. 3.2

Catalytic measurement

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The batch catalytic trials were taken out in a stainless steel Parr reactor at atmospheric pressure, in the temperature range from 323 to 353 K, and at stirrer speed 200 rpm. Phenol oxidation tests involved an aqueous phenol solution (volume 200 cm3, phenol concentration 0.01 mol dm-3). Solid catalyst (at loadings 0.1 or 0.5 g dm-3) was suspended in the solution under continuous stirring. After the phenol solution was warmed to the desired temperature, hydrogen peroxide (at final concentration 0.1 mol dm-3) was added and thus the reaction was initiated. Aliquots were withdrawn during the reaction run at selected times and filtered by means of 0.2 µm nylon membrane to evaluate remaining phenol in the reaction mixture. Phenol was detected and measured by UV/vis absorbance at 254 nm wavelengths by standard 4-aminoantipyrine colorimetric method. Hydrogen peroxide was detected by UV/vis absorbance at 450 nm wavelengths by ammonium-metavanadate colorimetric method. 4

Results and discussion

4.1

Physico-chemical properties of Cu/ZSM-5

The physico-chemical properties of ZSM-5 zeolites and calcined and non-calcined Cu/ZSM-5 catalyst are showed in Table 1. As can be seen, all the samples indicated reduced copper content than the achievable maximum (i.e. 5.2 w/w% Cu for the Na/ZSM-5 with a Si/Al = 12), which could be attained when all the sodium cations are exchanged. XRD patterns presented in Figure 1 confirm that every sample exhibit the features of a greatly crystallized MFI type zeolites,. Low intensity peaks at 2θ= 20.8º and 26.6º correspond to the reflections related to the α-quartz. The XRPD pattern of Cu/ZSM-5 matches with the pattern of ZSM-5, which preserves all the distinctive diffraction peaks (2θ=7.8, 8.8, 24.4, 24.8º). After ion exchange, no phase transition of Cu/ZSM-5 was detected, which implies that the copper inserting did not damage the structure of ZSM-5. The Cu/ZSM-5 catalysts represent the typical XRPD outline for MFI structure with no extra unrevealed phase. Absence of additional peaks discloses homogeneous dispersion of copper. The intensity of characteristic peaks around 2θ = 7-8o is slightly decreased for through impregnation, for non-calcined Cu/ZSM-5 catalyst, which can be assigned to removal of Al from the framework , and then substantially for the calcined catalysts Cu/ZSM-5-K1273, with complete damage of the lattice. In addition, the peak position around 2θ=23.9o in the XRD patterns of modified catalysts shifts to the higher values which agrees with reduction of aluminium content in the lattice. Thus, modified Cu/ZSM-5-K1023 shows excellent stability and activity due to the de-alumination and thus elimination of part of the Brønsted acid sites. Page 9 of 42



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Copper oxide CuO may form during the thermal treatment at high temperature and can be indicated in XRPD by diffraction peaks at 2θ= 35.7° and 38.5°. However, as can be detected in Figure 1, presence of CuO in Cu/ZSM-5 samples were not confirmed by XRPD. Furthermore, the copper oxide in the calcined Cu/ZSM-5-K1273 is not obviously verified, as the peaks’ intensity is very low with a slight increase in the baseline. Consequently, this result does not reject the chance the CuO, with size ≤ 3 nm, were made that are non-detectable, either amorphous and/or well dispersed in the external surface or in the pores of the zeolite crystallites42. BET surface area of H/ZSM-5 was only marginally varied after inclusion of Cu. Differences in the surface areas of these materials are negligible (Table 1). Pore volume exhibited of H/ZSM-5 is in accord with the literature findings43. Nitrogen adsorption is almost finalised at (p/p0) values lower than 0.1, indicating the main involvement of the micro-porosity (Supporting information, pp.13-16). Minor reduction in the total pore volume observed for Cu/ZSM-5 is a consequence of both, the porosity decreases and the bulk density increase. However, on the other hand, a considerable reduction in the total pore volume of the Cu/ZSM-5-K1273 has been distinctly noted as the crystallinity rises.

Figure 1 XRPD graph of: H/ZSM-5, Cu/ZSM-5 (non-calcined), Cu/ ZSM-K773, Cu/ ZSMK1023, Na/ ZSM-5 (pentasil), and Cu/ZSM-5-K1273 (from top to down).

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Table 1 The physico-chemical properties of the zeolite catalysts. The copper content, Si/Al ratio and Cu/Al ratio (average ± st.dev.) are derived by SEM-EDS method (mag. 100x-20000x).

H- ZSM-5 Na/ ZSM-5 Cu/ZSM-5, noncalcined Cu/ZSM-5-K773 Cu/ZSM-5-K1023 Cu/ZSM-5-K1273 4.1.1

Specific surface, BET, m2 g-1 307.7 -

Average pore diameter, nm 1.88 -

300.4 315.5 321.9 16.3

Cu, wt. %

Si/Al ratio

Cu/Al ratio

-

12.0 ±0.8 12.0 ±0.7

-

1.53

4.13 ±0.40

12.5 ±0.4

1.16 ±0.11

1.63 1.60 3.19

4.42 ±0.28 4.32 ±0.41 4.50 ±1.23

12.3 ±0.5 12.0 ±0.6 11.4 ±0.7

1.32 ±0.06 1.23 ±0.09 1.22 ±0.42

SEM and EDS mapping

Outer appearances of the Cu/ZSM-5 catalysts are relatively uniform aggregates of 10–20 µm in diameter of individual aggregates. SEM images, at high magnification, of the ion-exchanged zeolites revealed aggregates that resulted from small-sized crystals aggregation. The morphology of the zeolites was confirmed by SEM (Table 2) and EDS mapping (Table 3, Supporting information, pp.17-23). It is worth noting that the impregnation and calcination do not change crystal morphology. As can be seen, the Cu/ZSM-5 catalysts exhibit typical elongated prismatic shape of the ZSM-5 crystals. The distinguished morphology of the Cu/ZSM-5-K1273 catalyst seen in Table 2 is responsible for the exceptionally low surface area and pore volume of this catalyst. However, it has also the comparable activity in phenol degradation decomposition (as will be discussed later), due the fact that the amount of dispersed copper and degree of its dispersion are similar to those of other Cu/ ZSM catalysts (Table 1). SEM micrographs of the precursors, H/ZSM-5 and Na/ ZSM-5, are showed also in Table 2. Selected areas were analysed by EDS, which showed that Cu was regularly distributed at the zeolite framework. EDS analysis (Table 1, Table S4-Table S10) indicated that Cu/ZSM-5 was constituted of Cu, Si, Al, and O. However, catalysts surfaces are non-uniform; compare the EDS copper elemental maps for Cu/ZSM-5-K1273 (Table 3). Overlay of copper elemental mapping and SEM micrographs at different magnifications show the differences in the surfaces of different catalysts and illustrate the irregular geometry, pores and the catalytic active places which may be conveniently, described in fractal terms.

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Table 2 SEM images of ZSM-5 zeolite and Cu/ZSM-5 catalysts calcined at different temperatures, magnification 10000x, image size 13.4 × 10.1 µm. H/ZSM-5 pentasil

Na-ZSM-5 pentasil

Cu/ZSM-5

Cu/ZSM-5-K773

Cu/ZSM-5-K1023

Cu/ZSM-5-K1273

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Table 3 Overlay of SEM images and added copper (Cu), aluminium (Al), silicone (Si) and oxygen (O) EDS elemental maps of Cu/ZSM-5 catalysts calcined at different temperatures, magnification 10000x, image size 13.4 × 10.1 µm. Sample Cu/ZSM-5-K1273 shows obvious copper (Cu) expulsion to the surface of particles. Cu/ZSM-5

Cu/ZSM-5-K773

Cu/ZSM-5-K1023

Cu/ZSM-5-K1273

4.2

Fractality in catalysis

4.2.1

Fractality of crystal voids

The pores of Cu/ZSM-5 catalysts (Table 1) remain in the micro-pore range (< 2 nm), except for the meso-porous Cu/ZSM-5-K1273 with a pore diameter > 2 nm. Uninterrupted structure of pores is crucial for zeolite catalytic efficiency, since it facilitates free transference of both reactants and products from bulk solution to active centres inside catalyst.

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The simplified Euclidean, cylindrical shape of the zeolite micro-pores is usually used for calculation of effective diffusion and kinetics of sorption and catalytic processes 44. However, here, the fractal dimensions were calculated from the crystal void surfaces shaped by the geometrical outlines of the building units of zeolites. Structural crystals’ data listed in Table 4 can be retrieved from the Cambridge Structural Database (Cambridge Crystallographic Data Centre). Figure 2 shows the voids in the crystal structure of ZSM-5 and toluene/ZSM-5. Crystal voids presentations have been derived by Crystalexplorer software, at 0.002 e-·Å-3 iso-value, view along b-axis and presented for all ZSM type zeolites (Table S1, Supporting information, pp. 4-7). Catalysts’ voids fractal dimensions are derived from the scaling of crystals voids volume vs. electron density iso-values (Table S2) or from crystals voids surface area versus crystals voids volume (Table 4).

Figure 2 Crystal voids representation (along b-axis, iso-values = 0.002 e-.Å-3) of ZSM-5 (CCDC code 1540267) (left), and toluene/ZSM-5(right).

As consequence, the fractal dimension values of the zeolites mostly vary in significant extent within the used range of iso-values, especially for the comparatively greater iso-values (> 0.001 e-.Å-3) that are similar to the sizes of existent adsorbates (Figure 3). The fractal dimension of crystal voids of ZSM catalysts types falls in the range 2 < Df < 3 (Table 4). Fractal dimension values found by the suggested approach appear to be coherent with those settled by using experimental adsorption data in their comparative sizes. Results match well with backing calculations executed with program Mercury45 (Figure 4). Thus, fractality is applicable to real catalyst void structures.

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Figure 3 Crystal voids volume vs. iso-values for various catalysts: ■ ZSM-5, code1540267, ▲ ZSM-5, code1505106, ∆ ZSM-5, code calcined, ♦ ZSM-10, code 8103691, ● ZSM-11, code 1541697, □ ZSM-12, code 1537207

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Table 4 Fractal dimensions Df,void,SV from the fractal relationship of crystal voids area vs. crystal voids volume. Porosity, %, is given as ratio of crystal voids volume, at 0.002 e-.Å-3 iso-value, to the cluster volume (crystal unit cell+ 5 Å). Coefficient of determination R2 for power fit of crystal voids area vs. crystal voids volume. CCDC

Fractal dimension,

code

Df,void,SV

ZSM-5

1540267

ZSM-5

R2

porosity, %

2.2364 ± 0.0115

0.9948

6.15

1505106

2.3091 ± 0.0236

0.9693

13.97

ZSM-5, calcined, ref.46

-

2.2846 ± 0.0117

0.9911

13.89

ZSM-10

8103691

2.1945 ± 0.0070

0.9972

15.35

ZSM-11

1541697

2.2948 ± 0.0129

0.9913

10.82

ZSM-12

1537207

2.2220 ± 0.0362

0.9447

8.43

GUS-1 (ZSM-12)

7118391

2.1993 ± 0.0317

0.9592

7.59

ZSM-39

1530728

2.2500 ± 0.0086

0.9962

13.48

p-nitroanline/ ZSM-5

1526069

2.1759 ± 0.0262

0.9742

5.94

Cs/ ZSM-5

1521690

2.1509 ± 0.0326

0.9782

5.96

toluene/ ZSM-5

bs5009

2.2260 ± 0.0123

0.9959

3.26

tetrapropylammonium /ZSM-5

1505105

2.2440 ± 0.0237

0.9845

6.66

1522289

2.2732 ± 0.0199

0.9888

5.81

-

2.2168 ± 0.0136

0.9948

4.44

tetrapropylammonium / ZSM-5, Si/Al=23 tetraethylammonium/ ZSM-12, ref.47

Cavity-like globularity and amorphicity of crystal voids (parameters derived by the Crystalexplorer software) show sharp discontinuities. The majority of cavity-like voids express low fractal character (approaching Df=2.7 and, thus, approach the Euclidean volume limit of d=3). However, the ZSM type catalysts void spaces show fractal dimension values resting in the range Df=2.3-2.5, at lower iso-values. The 6-unit cavity-like space appears with the maximal fractal dimension and is anticipated to be the most reactive. Fractal catalyst has an accessible surface area that declines or rises with the decreasing iso-values (or, enlarging dimensions of the probe molecules), for fractal dimension above and, even, below 2, respectively. For fractal dimension Df >2, the minor molecules have access to the catalyst surface that is not accessible for bigger molecules. Fractal dimensions Df 200 for D[BW] indices (Figure 5) is well related to the reaction activity of Cu/ZSM-5 catalysts. Also, the step “transition” in the inter-facial fractal D[BW] indices of copper EDS elemental maps’ threshold m~40 for inter-facial D[BW] indices is well related to the reaction activity of Cu/ZSM-5 catalysts (Figure 6). Focal fractal index spectra for SEM images (Figure S32-Figure S35) and copper elemental EDS “maps” images (Figure S36-Figure S39) of Cu/ZSM-5 catalysts are not so conclusive; most probably due to larger “window” over which the fractal dimension is calculated, around 1 µm2. Nevertheless, the values of Dff in the range of focal fractal index Dff around 2.595-2.64, are related to the reaction activity sequence of Cu/ZSM-5 catalysts. Also, the surface fractal dimensions by the classical Frenkel–Halsey–Hill (FHH) equation from the single nitrogen adsorption isotherm can be evaluated 48 (see Supporting information, pp. 1316, Table S3).

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Figure 5 Inter-facial fractal index D[BW] spectra for SEM images of Cu/ZSM-5 catalysts: ♦ Cu/ZSM-5, ▲ Cu/ZSM-5-K773, ● Cu/ZSM-5-K1023, ∎ Cu/ZSM-5-K1273; (mag.1000x, image size 124×101 µm2).

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Figure 6 Inter-facial fractal index D[BW] spectra for copper elemental EDS “maps” images of Cu/ZSM-5 catalysts: ♦ Cu/ZSM-5, ▲ Cu/ZSM-5-K773, ● Cu/ZSM-5-K1023, ∎ Cu/ZSM-5K1273; (mag.1000x, image size 124×101 µm2).

4.2.2.2 Multi-fractal analysis of copper and aluminium density distributions Amount and type of the Brønsted acid sites, the position and dispersal of which varies the actual diffusional directions of the reactant molecules, essentially determines the catalytic behaviour of ZSM-5. As a result, diffusional restrictions play a decisive role in the catalytic capability and in the eventual deactivation. Further, this model relates to quantitative resolve of geometrical distribution arrangements by multi-fractal analysis of non-calcined and calcined ZSM-5 catalysts. The multi-fractal spectra of the generalized fractal dimensions, D(q), do not differ much for information dimension (q=1) and correlation dimension (q=2), which reflects the similar surface topography of the catalysts at low magnifications, except for the Cu/ZSM-5-K1023. For higher magnifications, significant differences occur for non-calcined and for calcined catalysts, especially Cu/ZSM-5-K1023. These multi-fractal characteristics, which are due to different probabilities of calcination induced morphology changes, were observed over a spatial range calcination promotes processes which lead to a smoother topography, thus enhancing the stabilizing effect and lessening the reactivity. This argument indicates that considerable capacity Page 20 of 42


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dimensions relate to increased porosities. This is a likely outcome, as the pore spaces structure is more dense for images with great porosity, which increases the capacity dimension. More, this example concerns quantitative determination of geometrical distribution patterns by multi-fractal analysis of copper and aluminium on the ZSM-5 catalysts. The multi-fractal spectra of the generalized fractal dimensions, D (q) decrease with magnification for non-calcined and calcined Cu/ZSM-5 catalysts and do not differ much for dimensions at q>0, D(1) and D(2) ≈ 0.65-0.7 (Table 5). For q 15 min) 0.013 ± 0.043 (t > 60 min) 0.238 ± 0.498 0.342 ± 0.070 (t < 60 min) (t >15 min) 0.193 ± 0.688 (t > 60 min) 0.732 0.997 (t< 60 min) 0.908 (t > 60 min)

353

0.076 ± 0.081 0.327 ± 0.045 0.989

0.117 ± 0.008 0.238 ± 0.044 0.996 0.089± 0.008 0.433 ± 0.041 0.988 0.092 ± 0.009 0.347 ± 0.049 0.991 0.077 ± 0.028 (t > 10 min)

0.335 ± 0.104 (t > 10 min)

0.992

Temperature dependence of the initial rate k0 and fractal exponent h have been calculated from the least square fitting of data given in Table 7. The fractal form of the catalyst surface alters both the apparent activation energy Ea and the pre-exponential factor A of the fractal reaction model parameters (Table 8). The activation energy Ea of the phenol degradation rises with

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intensification in the non-uniformity of the catalyst surface, distinguished by the fractal dimension Df. Table 8 Apparent activation energy Ea and pre-exponential factor A for fractal model terms for phenol oxidation over calcined and non-calcined Cu/ZSM-5 catalysts (cPhOH,0 =0.01 mol dm-3, cH2O2,0 = 0.1 mol dm-3). fractal model terms Catalyst Non-calcined Cu/ZSM5 Non-calcined Cu/ZSM5 Cu/ZSM5K773 Cu/ZSM5K1023 Cu/ZSM5K1273

Fractal exponent, h

Initial rate, k0 Ea,k kJ mol-1

63.5 ±13.1

63.3 ±4.5 102.9 ±4.0 103.0 ±25.9 87.3 ± 24.3

A R2 mcat = 0.1 g dm-3 1.8×108 0.921 ±8.5 ×108 mcat = 0.5 g dm-3 2.6×108 0.994 ±4.2×108 1.3 ×1014 ± 0.998 1.9×1014 1.7×1014 ± 0.940 1.5×1015 6.4×1011 ± 0.927 6.4×1012

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Ea,h, kJ mol-1

5.6 ±6.2

0.67 ±16.65 68.9 ±11.9 79.3 ±41.9 27.2 ± 16.2


A 0.2×101 ±0.4×101 2.0×10-1 ±1.2×100 6.9×109 ±2.8×1010 2.2 ×1011 ±3.3×1012 3.9×103± 2.2×104

R2

0.450

0.992 0.971 0.781 0.736

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Figure 8 Fractal kinetic model fit (lines) for phenol concentration cPhOH decay over Cu/ZSM-5K1023 catalyst at reaction temperatures: ▲ 333 K, ● 343 K, ■ 353 K. (mCAT = 0.5 g dm-3, cPhOH,0 =0.01 mol dm-3, cH2O2,0 = 0.1 mol dm-3) 4.3.4

Brouers-Sotolongo kinetic model

The results of the fit with the Brouers-Sotolongo kinetic model produced extremely close results to the phenol oxidation (Figure 9, Figure S92 - Figure S100). As previously indicated, the improvement of the Brouers-Sotolongo fractal kinetics is that this model can be extracted as a first-order kinetic with time-dependent rate, k(t). The phenol oxidation exposed rapid initial loss of phenol, trailed by moderately reduced elimination, and, lastly, by the reaching of balance. This tendency can be assigned to the existence of more Brønsted acidic sites on the Cu/ZSM-5 surface in the initial stage. This rapid initial degradation is one of the appealing qualities of catalytic degradation for real-world uses. The approximated parameters of the kinetic models are listed in Table 9. Apparent activation energy Ea and pre-exponential factor A for Brouers-Sotolongo model terms for phenol oxidation kinetics over calcined and non-calcined Cu/ZSM-5 catalysts are given in Table 10. Apparent activation energies for terms fractional reaction order n and fractal time exponent α are only significant for the non-calcined Cu/ZSM-5 catalyst, while these activation energies for calcined Cu/ZSM-5 catalysts are low and negligible. The apparent activation energies for terms τα for calcined Cu/ZSM-5 catalysts are almost the same. Hence, Page 29 of 42



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centred on the kinetic reaction data, the phenol oxidation was well differentiated by the BrouersSotolongo model.

Figure 9 Brouers-Sotolongo kinetic model fit (lines) for phenol concentration cPhOH/ decay over Cu/ZSM-5 catalyst at reaction temperatures: ♦ 323 K, ▲ 333 K, ● 343 K, ■ 353 K. (mcat = 0.1 g dm-3, cPhOH,0 =0.01 mol dm-3, cH2O2,0 = 0.1 mol dm-3)

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Table 9 Brouers-Sotolongo model terms, fractional reaction order n, fractal time exponent α and characteristic time τα, for phenol degradation over calcined and non-calcined Cu/ZSM-5 catalysts. (mcat = 0.1 g dm-3, and mcat = 0.5 g dm-3, cPhOH,0 =0.01 mol dm-3, cH2O2,0 = 0.1 mol dm-3) Term

τα

Reaction temperature, K 333 343 -3 mcat = 0.1 g dm Cu/ZSM-5 2.142 ± 0.317 1.435 ± 0.160 50.6 ± 6.0 28.6 ± 2.4

2.486 ± 0.529 17.4 ± 2.9

α

-1.062 ± 0.109

-0.917 ± 0.055

-1.240 ± 0.163

τα

mcat = 0.5 g dm-3 Cu/ZSM-5 1.000 ± 0.345 1.976 ± 0.348 24.4 ± 5.3 16.9 ± 2.3

2.681 ± 0.438 8.7± 0.9

α

-0.830 ± 0.121

-1.018 ± 0.102

-1.481 ± 0.125

n

τα

2.651 ± 0.823 107.6 ± 21.2

Cu/ZSM5-K773 2.168 ± 0.214 48.2 ± 4.1

3.087 ± 1.696 20.1 ± 9.7

α

-1.499 ± 0.413

-1.118 ± 0.073

-1.220 ± 0.338

n

τα

Cu/ZSM5-K1023 1.652 ± 0.395 2.566 ± 0.320 65.7 ± 10.6 30.3 ± 3.2

1.451 ± 0.400 10.3 ± 1.4

α

-1.151 ± 0.184

-1.207 ± 0.089

-1.137 ± 0.087

n

τα

Cu/ZSM5-K1273 1.000 ± 0.610 1.119 ± 0.141 130.3 ± 33.2 44.7 ± 2.8

1.090 ± 0.110 25.3 ± 1.1

α

-1.279 ± 0.512

-1.390 ± 0.055

n

n

-1.245 ± 0.077

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Table 10 Apparent activation energy Ea and pre-exponential factor A for Brouers-Sotolongo model terms, fractional reaction order n, fractal time exponent α and characteristic time τα, for phenol oxidation kinetics over calcined and non-calcined Cu/ZSM-5 catalysts (mcat = 0.1 g dm-3 and mcat = 0.5 g dm-3, cPhOH,0 =0.01 mol dm-3, cH2O2,0 = 0.1 mol dm-3) Brouers-Sotolongo model terms

n

τα α

A

mcat = 0.1 g dm-3 Cu/ZSM-5 -0.6 ± 12.91 0.2×101 ± 1×101 71.2 ± 10.5 4.7×10-10 ± 1.7×10-9 -3.1 ± 6.0

0.3×101± 0.6×101

Coeff. Det. R2

0.984 0.982 0.964

τα

mcat = 0.5 g dm-3 Cu/ZSM-5 -48.4 ± 9.8 4.0×107 ± 1.3×108 49.9 ± 8.9 4.0×10-7 ± 1.2×10-6

0.960 0.968

α

-31.8 ± 3.6

4.6×10-6±5.9×10-6

0.987

n

τα

Cu/ZSM-5-K773 -7.1 ± 15.7 3.2×101 ± 1.7×102 81.7 ± 3.3 1.6×10-11± 1.9×10-11

α

10.2 ± 10.5

n

Cu/ZSM-5-K1023 5.8 ± 28.7 2.3×10-1 ± 2.3×104 90.6 ± 10.2 4.6×10-13 ± 3.5×101

n

τα α n

τα α 4.3.5

Ea, kJ mol-1

0.5 ± 3.0

3.4 ×10-2± 1.2×10-1

9.6×10-1 ± 2.8×100

Cu/ZSM-5-K1273 -4.2 ± 3.8 4.7 ± 3.8 80.5 ± 12.8 3.1×10-11 ± 8.9×101 -3.9 ± 3.9

5.2 ± 3.9

0.171 0.998 0.486 0.040 0.988 0.031 0.555 0.975 0.507

Iso-conversional apparent activation energy

In thermally activated processes, reaction rate is temperature dependent, following the Arrhenius equation, and usually assumed conversion-independent. However, the catalytic degradation of phenol cannot be explained within the model assuming static distributions of the Arrhenius parameters determining the reaction rate. Thus, one should seek another explanation, the most obvious one being conversion-depending reaction rate. In other words, one should assume that the reaction changes micro-environment of unreacted molecules, hence dynamically modifying Page 32 of 42


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the activation energy Ea and pre-exponential factor A as the reaction progresses. In the following, we shall adopt a simple phenomenological model assuming a non-linear dependence of Ea and A on conversion. Iso-conversional apparent activation energy Ea,α is deduced from the temperature dependence of reaction times t for some predetermined conversion α (=constant) as: /, 3 = 4$5 = 6 × exp −

-, ./

Equation 9

If Ea,α values were independent of phenol conversion α, the phenol oxidation process would be dominated by a single reaction step. Apparent activation energy Eα is not a constant value, but changes with the extent of the reaction process. The variation in iso-conversional apparent activation energy Ea,α for phenol oxidation by H2O2 over Cu/ZSM-5 catalysts can be taken as a clear example. The dependence of Ea,α on conversion α for phenol degradation is presented in Table 11. Obviously, three different regions can be marked in each case of calcined Cu/ZSM-5 catalysts. Therefore, from Table 11, it was obvious that the first region ranges from 0 to 0.2 of phenol conversion α provides information about initial phenol conversion that could be due to the interactions present in catalyst structure. The curve of Eα vs. α is characterized with a roughly “V” shape for Cu/ZSM-5-K1273 catalyst. The Ea,α values are fairly stable in second region from conversion α =0.2 up to α =0.5-0.6 which could be due to the principal catalytic reaction between phenol and H2O2: Ea,α showed an almost stable behaviour with the approximate average around Ea,α = 70 kJ mol-1. The third region is found within conversion range (α > 0.6) representing an abrupt change in Ea,α values which can be referred to the breakage of strongly restricted phenol in catalyst pore. The reaction under consideration seems to involve at least two different competitive reaction pathways consistent with what expected from the initial dual phase (pore and mass) microstructure of the investigated Cu/ZSM-5 catalysts. A similar pattern of the variance in Ea,α with conversion α has been previously seen in other kinetic studies. Similarly, to the iso-conversional analysis, iso-chronal apparent activation energy Ea,t can be deduced from the plot of the temperature dependence of conversion α at pre-set reaction time t=constant. However, just the first region that ranges from zero to 20-30 min of reaction time provides information about initial phenol conversion that is strongly thermally activated (Supporting information, p. 167, Figure S136).

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Table 11 Effect of calcination of Cu/ZSM-5 catalyst mass on the iso-conversional apparent activation energy, Ea,α, of phenol conversion (cPhOH,0 = 0.01 mol dm-3, cH2O2,0 = 0.1 mol dm-3, mcat = 0.5 g dm-3).

4.3.6

Relations of structural fractality and reactivity

Fractal dimensions of Cu/ZSM-5 zeolites estimated from SEM images and EDS copper (Cu) elemental maps were utilised to differentiate the alteration in their texture reliant on different calcination thermal treatments. These fractal dimensions are correlated to the activity of these zeolites in the phenol oxidation by hydrogen peroxide; fractal dimensions and multi-fractal spectra of SEM and EDS images at small scales (high magnifications) are good related to the activity of catalysts. Non-calcined Cu/ZSM-5 demonstrated fractal dimensions lesser than that of the calcined samples. Conversely, calcined Cu/ZSM-5-K1023 samples also had activities in the phenol degradation somewhat higher than zeolites activated by calcination at 773 K or 1273 K. This signifies the value of the zeolite fractality for the reaction of sizeable phenol molecule within a restricted space. Resolving the fractal character of zeolites may be of fundamental significance for the extrapolation of the scaling behaviour faced in catalysis. The fractal outlines of the pore surfaces and the comparative vicinity of the molecule dimensions to the structural Page 34 of 42


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units are essentially accountable for the fractality of zeolites. With high-temperature calcinations, the pore size spreading in the modified zeolite turns out to be of great consequence. Wider pore size spreading indicates the incidence of elevated fractal dimension. All the copper loaded catalysts, when interact with H2O2, enhanced the oxidation of phenol. These results disclosed that the operational surface area and H2O2 adsorption capability of the Cu/ZSM-5 favour fast oxidation of phenol. The studies of the non-calcined and calcined catalysts with different fractality have demonstrated catalytic activity for the phenol conversion on these catalysts sequence: Cu/ZSM1273< Cu/ZSM-5-K773 < Cu/ZSM-K1023< Cu/ ZSM5. This sequence appears analogous to the sequence of the fractality of the catalysts. Rational associations related the fractality of heterogeneous catalyst and the rate of a catalytic reaction on its surface 53 , 54 . Fractal dimensionality of the catalyst surface is related to both the apparent activation energy and the pre-exponential coefficient of the rate. The apparent activation energy of the reaction rate intensifies with spread in the non-uniformity of the catalyst surface, distinguished by the fractality Df. Cu/ZSM-5 catalysts with the lower widths of multi-fractals generalized dimensions (derived from the SEM images) have better reactivity (Table 5). Some non-linear kinetic model parameters are inter-related. For instance, the fractal exponent, h is correlated strongly with the stretched exponential model exponent term β (R² = 0.964) and Weibull parameter dw (R² = 0.627, excluding the data for Cu/ZSM-5-K1273), and just weakly to the Brouers-Sotolongo term τα scale/rate parameter (R² = 0.515) (Figure 10). Therefore, the Weibull scale/rate parameter, cw, is, also, linearly related with fractal exponent, h (R² = 0.5062). The Brouers-Sotolongo model term τα is related logarithmically to the Weibull parameters t50 and cw for phenol oxidation over Cu/ZSM-5 catalysts (Supporting information, Figure S107).

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Figure 10 Relations of fractal-like model exponent, h with the stretched exponential model exponent term β (♦), and Weibull scale/rate parameter, dw (■). The Weibull shape parameter, dw and the fractal-like model exponent, h are related to the order of reaction: the first-order reaction is approximated by dw ≈ 1, and h≈ 0, where the model functions are reduced to an exponential function. Hence, it is not speculative that the fractal-like model exponent, h is related to the stretched exponent β and Weibull shape parameter, dw. The BrouersSotolongo apparent reaction order term n is, also, related to fractal-like model exponent, h, although just weakly. This is most probably due to more disperse and more exact values for the BrouersSotolongo term n (average ≈ 2.14 ± 0.60) in comparison to the narrow range of fractal-like model exponent, h (average ≈ 0.27 ± 0.10) (excluding the un-realistic data for Cu/ZSM-5-K1273 catalyst). Brouers-Sotolongo term τα is, as expected, inversely related to the fractal initial rate k0. Also, Weibull parameters t50 and cw are logarithmically related to the Brouers-Sotolongo term τα(R² = 0.7-0.8). Stretched exponential λ and Weibull shape t50 models parameters are inversely related as expected, λ ≈ 0.66 × t50 -0.94 (R² = 0.937).

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5

Conclusions

Current work elucidates wet oxidation of aqueous solutions of phenol with hydrogen peroxide using heterogeneous calcined and non-calcined Cu/ZSM-5 catalyst under mild conditions by the Kopelman-type fractal-like, and general Brouers-Sotolongo fractal models approach. The proposed fractional-fractal Brouers-Sotolongo kinetic model of the phenol oxidation process constructed on the pseudo-first order kinetic provides reasonably accurate description of the experimental data and reproducing all important process regularities. The results clearly show that the Brouers-Sotolongo model is appropriate for expressing the phenol oxidation kinetic data. Furthermore, the Brouers-Sotolongo fractal kinetic model covers even the change in the kinetic order, demonstrating that the fractal kinetic model is appropriate for expressing the catalytic kinetic data than the classical first-order kinetic model. Catalysts’ voids fractal dimensions have been derived from the scaling of crystals voids volume vs. electron density iso-values and from the scaling of crystal voids surface area vs. voids volume. To the best of our knowledge, there is no report on fractality of Cu loaded ZSM-5 catalysts for catalytic applications, particularly for the oxidation of phenol. The fractal dimensions of the zeolites extensively vary within the range of iso-values used, especially for the relatively outsized iso-values (> 0.001 e-·Å-3). Increase of the fractal dimensions SEM images of the calcined Cu/ZSM-5 catalysts with the calcination temperature indicates the roughness step-up of their surfaces. Also, the shape of the “dark” areas captured more accurately in the highest threshold setting of threshold m>200 for D[BW] indices (from SEM images) is well related to the reaction activity of Cu/ZSM-5 catalysts Apparent activation energy of phenol oxidation increases with spread in the non-uniformity of the fractal catalyst surface, with increase of Df. The highest efficiency toward phenol destruction was observed for the catalysts with the lowest multi-fractal width. Key findings are: a) the crystal voids of various ZSM zeolites are fractal, with different fractal dimensions, and the crystal voids scale with the iso-values; b) the Brouers-Sotolongo fractalfractional model is most general and provides the best description of various possible kinetic models; c) Structural fractality of various Cu/ZSM-5 catalysts, determined from the SEM imaging and copper EDS elemental maps, are related to their catalytic activity.

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Acknowledgments

The authors thank the Croatian Ministry of Science, Education and Sport for the financial support of this study: “Preparation and Characterization of Zeolite Based Catalysts for Phenolic Wastewater Treatment (ZCat4Water)”.

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Associated content

Supporting Information : Crystal voids presentations; Fractal relationship of crystal voids volume vs. iso-values (Crystalexplorer software) and crystal voids volume by contact surface vs. probe radius (Mercury software); Fractal dimensions Df,void from the power scaling of crystal voids volume vs. iso-values; Surface fractal dimension by adsorption–desorption analysis; Nitrogen adsorption–desorption analysis; Fractal dimensions from the analysis of N2 gas adsorption isotherms; SEM images, copper (Cu) and silicone (Si) elemental EDS maps; Mono-fractal indices threshold spectra of SEM images; Mono-fractal indices threshold spectra of copper (Cu) elemental EDS map images; Focal fractal dimensions frequency distributions of SEM images; Focal fractal dimensions frequency distributions of copper (Cu) and aluminium (Al) EDS maps; Multi-fractals generalized dimensions D(q); Comparison of Multi-fractals generalized entropy dimensions; Multi-fractals spectral terms; Mass transfer; Rotation speed; Catalyst loading; Kinetic model fits; Langmuir-Hinshelwood model; Fractal kinetic model; Brouers-Sotolongo kinetic model; Weibull model; Stretched exponential kinetic model; Parity plots; Iso-chronal apparent activation energy; Variation of activation energy with temperature and catalyst loadings (PDF).

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Crystal voids volume vs. iso-values for various catalysts 344x225mm (72 x 72 DPI)


Kinetics of Catalytic Peroxide Oxidation of Phenol ... - ACS Publications

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