**5. Crystallization mechanism**

274 Advances in Crystallization Processes

Fig. 16. PSDs by volume of the products obtained by hydrothermal treatment (at 483 K for 2 h) of the reaction mixture (A = 0.008; [Na+/SiO2]b = 0.64) aged at room temperature for 5 (A), 20 (B), 48 (C) and 120 h (D) before addition of seeds and heating. (Adopted from Ref.

On the other hand, the influence of the hydrogel ageing on the PSDs of the crystalline end products is probably connected with the change (increase) of the concentration of Si (most probably in the form of low-molecular weight silicate species) in the liquid phase of the reaction mixture with prolonging ageing duration (Fig. 17). Although the increase of the concentration of Si in the liquid phase during ageing (Fig. 17) does not cause the formation of the growth precursor species at the ageing (room) temperature, it certainly facilitates the formation of the growth precursor species during heating of the reaction mixture, i.e., higher starting concentration of low-molecular weight silicate species causes higher rate of formation of the growth precursor species and thus, higher rate of growth of zeolite ZSM-5 on the silicalite-1 crystals. From this reason, particle (crystal) size at given crystallization time increases with increasing time of hydrogel ageing (Fig. 16). Since, on the other hand (i) crystal growth and agglomeration take place simultaneously and (ii), the rate of agglomeration increases with decreasing particle size [65], tendency of agglomeration

[55] with permission of Publisher)

decreases with increasing time of hydrogel ageing (Fig. 16).

With the above studies, the influence of various parameters on the three most important properties (phase purity, particulate properties and chemical composition) of ZSM-5 zeolites can be clearly concluded in Table 2. From this summary, the most pronounced influence is attributed to the batch alkalinity, which changes all the relevant properties of the crystallineend product. In the large-scale synthesis of ZSM-5 zeolites for application, the batch alkalinity should be strictly controlled to obtain the qualified product. On the other hand, among the mentioned three properties of ZSM-5 zeolites, the particulate properties are most sensitive to the change of the environment of crystallization. Thus, the synthesis of ZSM-5 zeolites with controllable uniform crystal sizes is always a hot, attractive and enduring topic in the field of zeolites.


a. The influences are expressed as pronounced influence (+), less influence (-), and influence depends on the detailed condition

Table 2. Summary of the influences of synthetic parameters on the properties of ZSM-5 product. *a*

Crystallization of Sub-Micrometer Sized ZSM-5 Zeolites in SDA-Free Systems 277

Fig. 19. TEM images of the samples obtained by using 4 wt. % of 260 nm silicalite-1 seed crystals at *t*c = 0.5 h (a), *t*c = 1.0 h (b), *t*c = 1.5 h (c), and *t*c = 2.0 h (d). The scale bars in (a), (b), (c), and (d) are of 0.2 μm, 0.2 μm, 0.2 μm, and 0.5 μm, respectively. (Adopted from Ref. [50]

Fig. 21 displays the PSD curves (by number) of the 260 nm silicalite-1 seed crystals (Fig. 21A) and that of the ZSM-5 zeolites obtained using same type of seeds (Fig. 21B). It can be observed that both curves possess almost the same shape and trend. The only difference is the size of crystals. Such phenomenon, although simple, clearly revealed the fact that the total number of crystals during the process of crystallization remains unchanged. It can be deduced that the nucleation process is completely suppressed under the current synthesis condition (SDA-free system with the presence of seed crystals), further proves the only

In addition, the post-synthesis alkaline treatment was carried out on the obtained samples. Since the tetrahedral aluminium centres are relatively inert to hydroxide attack due to the negative charges associated with these centers, and the aluminum atom protects not only the adjacent silicon atoms but also those in the positions of next nearest neighbours [17, 57, 58], it could be expected that, after the alkaline treatment of the final products, the all-silica seed crystals would be dissolved away, leaving behind the aluminium-containing framework of ZSM-5. To check this assumption, the samples are treated with 0.8 M sodium carbonate solution at 80 oC for 36 h under stirring. Fig. 22 shows the TEM images of the alkaline treated samples. By comparison of untreated and alkaline-treated samples, it can be found that both the size and crystal structure remains unchanged, but the hollow core appears in the centres of particles (crystals) after alkaline treatment. This finding indicates that the crystallization takes place on the surface of seed crystals, which is in accordance

occurrence of the growth of ZSM-5 zeolites on the surface of silicalite-1 seeds.

with permission of Publisher)

with the analysis of the results of kinetic study.

The systematic analysis of the parameters governing the crystallization of zeolite ZSM-5 also makes a chance to define the crystallization mechanism of ZSM-5 zeolites in SDA-free system. To achieve the controllable synthesis of ZSM-5 zeolites with designed particulate and chemical properties, the thorough understanding of the critical processes during the crystallization is the only way. Such goal is achieved by both efforts, the kinetic analysis of crystallization processes and the alkaline, post-treatment of final products.

Fig. 18 shows the crystallization curves of the systems containing various amounts (expressed as the weight percentage of silica amount in the batch) of silicalite-1 seed crystals of different sizes. It can be clearly observed that the rate of crystallization considerably depends on both the size and the amount of the added silicalite-1 seed crystals. The time for the completion of crystallization decreases with both decreasing seed size (at constant amount) and increasing amount of seeds (at constant seed size). Furthermore, the crystallization process of the system with 4 wt.% of 260 nm seed crystals was followed by TEM observations (Fig. 19). At the initial stage of crystallization, the seed crystals and amorphous precursors (existing as small particles) can be identified clearly (Fig. 19a). At prolonged hydrothermal treatment, the amorphous precursors start to stack onto the surface of seed crystals and agglomerate together (Figs. 19b and c), followed by depleting of the amorphous precursors and complete ordering of the structure into ZSM-5 crystals (Fig. 19 d). High magnification TEM image (Fig. 20) shows a "core-shell" transformation process of amorphous to crystalline phase (zeolite ZSM-5), which happens at the seed-amorphous interface.

Fig. 18. Crystallization curves of systems with using silicalite-1 seeds of 90 nm-4wt.% (a), 260 nm-4wt.% (b), 690 nm-4wt.% (c), 260 nm-8wt.% (d), 260 nm-16wt.% (e), and 260 nm-32wt.%(f). *t*c is the time of crystallization. The percent crystallinity was calculated from the corresponding XRD patterns. (Adopted from Ref. [50] with permission of Publisher)

The systematic analysis of the parameters governing the crystallization of zeolite ZSM-5 also makes a chance to define the crystallization mechanism of ZSM-5 zeolites in SDA-free system. To achieve the controllable synthesis of ZSM-5 zeolites with designed particulate and chemical properties, the thorough understanding of the critical processes during the crystallization is the only way. Such goal is achieved by both efforts, the kinetic analysis of

Fig. 18 shows the crystallization curves of the systems containing various amounts (expressed as the weight percentage of silica amount in the batch) of silicalite-1 seed crystals of different sizes. It can be clearly observed that the rate of crystallization considerably depends on both the size and the amount of the added silicalite-1 seed crystals. The time for the completion of crystallization decreases with both decreasing seed size (at constant amount) and increasing amount of seeds (at constant seed size). Furthermore, the crystallization process of the system with 4 wt.% of 260 nm seed crystals was followed by TEM observations (Fig. 19). At the initial stage of crystallization, the seed crystals and amorphous precursors (existing as small particles) can be identified clearly (Fig. 19a). At prolonged hydrothermal treatment, the amorphous precursors start to stack onto the surface of seed crystals and agglomerate together (Figs. 19b and c), followed by depleting of the amorphous precursors and complete ordering of the structure into ZSM-5 crystals (Fig. 19 d). High magnification TEM image (Fig. 20) shows a "core-shell" transformation process of amorphous to crystalline phase (zeolite ZSM-5), which happens at the seed-amorphous

Fig. 18. Crystallization curves of systems with using silicalite-1 seeds of 90 nm-4wt.% (a), 260

nm-4wt.% (b), 690 nm-4wt.% (c), 260 nm-8wt.% (d), 260 nm-16wt.% (e), and 260 nm-32wt.%(f). *t*c is the time of crystallization. The percent crystallinity was calculated from the corresponding XRD patterns. (Adopted from Ref. [50] with permission of Publisher)

crystallization processes and the alkaline, post-treatment of final products.

interface.

Fig. 19. TEM images of the samples obtained by using 4 wt. % of 260 nm silicalite-1 seed crystals at *t*c = 0.5 h (a), *t*c = 1.0 h (b), *t*c = 1.5 h (c), and *t*c = 2.0 h (d). The scale bars in (a), (b), (c), and (d) are of 0.2 μm, 0.2 μm, 0.2 μm, and 0.5 μm, respectively. (Adopted from Ref. [50] with permission of Publisher)

Fig. 21 displays the PSD curves (by number) of the 260 nm silicalite-1 seed crystals (Fig. 21A) and that of the ZSM-5 zeolites obtained using same type of seeds (Fig. 21B). It can be observed that both curves possess almost the same shape and trend. The only difference is the size of crystals. Such phenomenon, although simple, clearly revealed the fact that the total number of crystals during the process of crystallization remains unchanged. It can be deduced that the nucleation process is completely suppressed under the current synthesis condition (SDA-free system with the presence of seed crystals), further proves the only occurrence of the growth of ZSM-5 zeolites on the surface of silicalite-1 seeds.

In addition, the post-synthesis alkaline treatment was carried out on the obtained samples. Since the tetrahedral aluminium centres are relatively inert to hydroxide attack due to the negative charges associated with these centers, and the aluminum atom protects not only the adjacent silicon atoms but also those in the positions of next nearest neighbours [17, 57, 58], it could be expected that, after the alkaline treatment of the final products, the all-silica seed crystals would be dissolved away, leaving behind the aluminium-containing framework of ZSM-5. To check this assumption, the samples are treated with 0.8 M sodium carbonate solution at 80 oC for 36 h under stirring. Fig. 22 shows the TEM images of the alkaline treated samples. By comparison of untreated and alkaline-treated samples, it can be found that both the size and crystal structure remains unchanged, but the hollow core appears in the centres of particles (crystals) after alkaline treatment. This finding indicates that the crystallization takes place on the surface of seed crystals, which is in accordance with the analysis of the results of kinetic study.

Crystallization of Sub-Micrometer Sized ZSM-5 Zeolites in SDA-Free Systems 279

Fig. 22. TEM images of ZSM-5 samples, synthesized from the reaction mixture containing 4 wt. % of 260 nm seed crystals, before (a) and after (b) alkaline treatment. The scale bars in (a) and (b) are of 0.5 μm and 0.2 μm, respectively. (Adopted from Ref. [50] with permission of

Taking into consideration of all the relevant mechanistic studies, the crystallization process of SDA-free seed-induced approach can be described as the growth of active species on the surface of seed crystals without formation of new nuclei. All the synthetic parameters influence the properties of the final products by changing either the relative rate or the

After the relevant mechanistic studies, the mathematical analysis of the growth step of ZSM-5 zeolites on the surface of silicalite-1 seed crystals becomes possible. Compared with the phenomenological description, the quantitative explanation of the crystallization step makes the further control of the process much easier and convenient. On the basis of above presented data, it can be assumed that the crystallization process is a typical seed-induced

where *m*t is the mass of zeolite crystallized up to the time *t* and *m*0 is the mass of the seed crystals added into the reaction mixture. From the above observations and general knowledge on the crystal growth of zeolites [61], it can be assumed that the crystallization proceeds by a linear, size-independent growth of seed crystals and thus, that the crystal size,

where, *d*0 represents the size of the seed crystals and *K*g is the growth rate constant. Taking into consideration that the formation of nuclei in the crystallizing system is depressed by both by the absence of SDA [50] and presence of seed crystals [50, 59, 60] it is reliable to

(1)

(2)

one which can be mathematically expressed by a cubic function [50, 59, 60], i.e.

environment of the growth step during crystallization process.

*d*t, at the crystallization time t, can be expressed as:

Publisher)

**6. Modeling approach** 

Fig. 20. High magnification TEM image of the sample separated from the reaction mixture containing 4 wt. % of 260 nm silicalite-1 seed crystals at *t*<sup>c</sup> = 1 h. The scale bar is of 20 nm and the crystalline lattice can be identified from the indicated area. (Adopted from Ref. [50] with permission of Publisher)

Fig. 21. The PSD curves (by number) of silicalite-1 seed crystals (A) and ZSM-5 product (B) synthesized using 4 wt.%% of the same seed crystals.

Fig. 22. TEM images of ZSM-5 samples, synthesized from the reaction mixture containing 4 wt. % of 260 nm seed crystals, before (a) and after (b) alkaline treatment. The scale bars in (a) and (b) are of 0.5 μm and 0.2 μm, respectively. (Adopted from Ref. [50] with permission of Publisher)

Taking into consideration of all the relevant mechanistic studies, the crystallization process of SDA-free seed-induced approach can be described as the growth of active species on the surface of seed crystals without formation of new nuclei. All the synthetic parameters influence the properties of the final products by changing either the relative rate or the environment of the growth step during crystallization process.

#### **6. Modeling approach**

278 Advances in Crystallization Processes

Fig. 20. High magnification TEM image of the sample separated from the reaction mixture containing 4 wt. % of 260 nm silicalite-1 seed crystals at *t*<sup>c</sup> = 1 h. The scale bar is of 20 nm and the crystalline lattice can be identified from the indicated area. (Adopted from Ref. [50]

Fig. 21. The PSD curves (by number) of silicalite-1 seed crystals (A) and ZSM-5 product

(B) synthesized using 4 wt.%% of the same seed crystals.

with permission of Publisher)

After the relevant mechanistic studies, the mathematical analysis of the growth step of ZSM-5 zeolites on the surface of silicalite-1 seed crystals becomes possible. Compared with the phenomenological description, the quantitative explanation of the crystallization step makes the further control of the process much easier and convenient. On the basis of above presented data, it can be assumed that the crystallization process is a typical seed-induced one which can be mathematically expressed by a cubic function [50, 59, 60], i.e.

$$
\mu m\_t = \varkappa a\_0 + K\_1 t + K\_2 t^2 + K\_3 t^3 \tag{1}
$$

where *m*t is the mass of zeolite crystallized up to the time *t* and *m*0 is the mass of the seed crystals added into the reaction mixture. From the above observations and general knowledge on the crystal growth of zeolites [61], it can be assumed that the crystallization proceeds by a linear, size-independent growth of seed crystals and thus, that the crystal size, *d*t, at the crystallization time t, can be expressed as:

$$d\_t = d\_0 + \mathcal{K}\_\mathbf{x} t \tag{2}$$

where, *d*0 represents the size of the seed crystals and *K*g is the growth rate constant. Taking into consideration that the formation of nuclei in the crystallizing system is depressed by both by the absence of SDA [50] and presence of seed crystals [50, 59, 60] it is reliable to

Crystallization of Sub-Micrometer Sized ZSM-5 Zeolites in SDA-Free Systems 281

Fig. 23. Correlation between measured kinetics of crystallization of zeolite ZSM-5 from the reaction mixture containing 1 wt. % of 260 nm silicalite-1 seed crystals (points) and the kinetics of crystallization calculated by Eq. (5) (dashed curve). (Adopted from Ref. [50] with

On the other hand, an almost perfect correlation can be observed between measured sizes, *d*t(det), of the crystalline end products and the corresponding sizes, *d*t(cal), calculated by Eq. (2), using the value *K*g = 0.15 μm/h, and the corresponding seed sizes, d0 (Table 3). This phenomenon is an additional evidence to prove that the process of crystallization takes

> *a* (h)

*d*t(cal)*<sup>b</sup>* (nm)

*d*t(det)*<sup>c</sup>* (nm)

place by the mechanism mathematically described by Eqs. (1) – (6).

90 4.0 1.5 315 270 690 4.0 2.5 1065 1100 260 4.0 2.0 560 520 260 8.0 1.5 485 440 260 16.0 1.0 410 410 260 32.0 0.75 373 350 *a.* determined from the corresponding crystallization curve in Fig. 18 by choosing the first 100%

Table 3. The comparison of measured, *d*t(det), and calculated, *d*t(cal), final crystal sizes of zeolite ZSM-5 synthesized from the reaction mixtures containing different amounts of

Seed addition amount (wt.%) *t*<sup>c</sup>

*b.* calculated from Eq. (2) using crystal growth rate of 0.15 μm/h

*c.* determined from the corresponding SEM images (Adopted from Ref. [50] with permission of Publisher)

silicalite-1 seed crystals having different sizes.

permission of Publisher)

crystallinity data point

*d*0 (nm)

assume that the number of growing crystals, *N*t, is constant and equal to the number, *N*0, of the added seed crystals. Then, the change of the mass, *m*t , of the crystallized zeolite ZSM-5 with the crystallization time *t*, can be expressed as,

$$m\_t = G\rho N\_t (d\_t)^3 = G\rho N\_0 (d\_0 + K\_\mathbf{g}t)^3 = G\rho N\_0 \left(d\_0\right)^3 \left(1 + \frac{K\_\mathbf{g}}{d\_0}t\right)^3 \tag{3}$$

where, *G* is the geometrical shape factor of the growing crystals, ρ is the density of crystalline phase (zeolite), and the mass, *m*o, of seed crystals can be expressed as:

$$
\rho \eta\_0 = \mathbb{G} \rho \mathcal{N}\_0 (d\_0)^3 \tag{4}
$$

The Eq. (3) can be transformed into

$$m\_{\mathbf{r}} = m\_0 \left(1 + \frac{K\_{\mathbf{g}}}{d\_0} t\right)^3 = m\_0 \left[1 + \Im(\frac{K\_{\mathbf{g}}}{d\_0}) t + \Im(\frac{K\_{\mathbf{g}}}{d\_0})^2 t^2 + (\frac{K\_{\mathbf{g}}}{d\_0})^3 t^3\right] \tag{5}$$

where,

$$K\_1 = \Im(\frac{K\_\mathbf{g}}{d\_0}) \cdot \mathcal{m}\_{0\_{\text{s}}} \ K\_2 = \Im(\frac{K\_\mathbf{g}}{d\_0})^2 \cdot \mathcal{m}\_0 \text{ and } \ K\_3 = (\frac{K\_\mathbf{g}}{d\_0})^3 \cdot \mathcal{m}\_0$$

Since the total silica-alumina source in the reaction mixture is constant during the synthesis, the values of *m*t and *m*0 can also be expressed as the fractions *x*t and *x*0 of aluminosilicate material in the reaction mixture at different crystallization time *t.* Thus, the Eq. (5) can also be expressed as [59]:

$$\mathbf{x}\_t = \mathbf{x}\_0 \left( 1 + \frac{K\_\mathbf{g}}{d\_0} t \right)^3 \tag{6}$$

.

where, x0 is fraction of aluminosilicate material contained in seed crystals at *t* = 0, and *x*t is the fraction of aluminosilicate material in the crystalline phase (seeds + newly crystallized zeolite) at *t* > 0.

Then, the crystal growth rate constant, *K*g, can be obtained by solving the Eq. (6), e.g.,

$$K\_{\mathbf{z}} = \sqrt[4]{\frac{\mathbf{x}}{\mathbf{x}\_0}} - \lg \frac{d\_0}{t} \tag{7}$$

Thus, the value of *K*g can be calculated by Eq. (7) using *d*0 = seed size and *x*/*x*0 = (crystallinity at *t*/crystallinity at *t* = 0) (see Fig. 18); *K*g = 0.15 μm/h for all investigated system. Then, inserting the calculated value of *K*g = 0.15 μm/h and the appropriate values of *d*0 = 0.26 μm and x0 = 1 wt. % into Eq. (5), the kinetics of crystallization of zeolite ZSM-5 from the reaction mixture containing 1 wt. % of 260 nm silicalite-1 seed crystals is calculated (curve in Fig. 23) and compared with the measured kinetics (points in Fig.23). Almost perfect agreement between calculated and measured kinetics indicates that the crystallization process proceeds in expected way, namely by a linear, size-independent growth of silicalite-1 seed crystals.

assume that the number of growing crystals, *N*t, is constant and equal to the number, *N*0, of the added seed crystals. Then, the change of the mass, *m*t , of the crystallized zeolite ZSM-5

where, *G* is the geometrical shape factor of the growing crystals, ρ is the density of

, and

Since the total silica-alumina source in the reaction mixture is constant during the synthesis, the values of *m*t and *m*0 can also be expressed as the fractions *x*t and *x*0 of aluminosilicate material in the reaction mixture at different crystallization time *t.* Thus, the Eq. (5) can also

where, x0 is fraction of aluminosilicate material contained in seed crystals at *t* = 0, and *x*t is the fraction of aluminosilicate material in the crystalline phase (seeds + newly crystallized

Thus, the value of *K*g can be calculated by Eq. (7) using *d*0 = seed size and *x*/*x*0 = (crystallinity at *t*/crystallinity at *t* = 0) (see Fig. 18); *K*g = 0.15 μm/h for all investigated system. Then, inserting the calculated value of *K*g = 0.15 μm/h and the appropriate values of *d*0 = 0.26 μm and x0 = 1 wt. % into Eq. (5), the kinetics of crystallization of zeolite ZSM-5 from the reaction mixture containing 1 wt. % of 260 nm silicalite-1 seed crystals is calculated (curve in Fig. 23) and compared with the measured kinetics (points in Fig.23). Almost perfect agreement between calculated and measured kinetics indicates that the crystallization process proceeds in

Then, the crystal growth rate constant, *K*g, can be obtained by solving the Eq. (6), e.g.,

expected way, namely by a linear, size-independent growth of silicalite-1 seed crystals.

crystalline phase (zeolite), and the mass, *m*o, of seed crystals can be expressed as:

(3)

(5)

(4)

.

(6)

(7)

with the crystallization time *t*, can be expressed as,

The Eq. (3) can be transformed into

where,

be expressed as [59]:

zeolite) at *t* > 0.

Fig. 23. Correlation between measured kinetics of crystallization of zeolite ZSM-5 from the reaction mixture containing 1 wt. % of 260 nm silicalite-1 seed crystals (points) and the kinetics of crystallization calculated by Eq. (5) (dashed curve). (Adopted from Ref. [50] with permission of Publisher)

On the other hand, an almost perfect correlation can be observed between measured sizes, *d*t(det), of the crystalline end products and the corresponding sizes, *d*t(cal), calculated by Eq. (2), using the value *K*g = 0.15 μm/h, and the corresponding seed sizes, d0 (Table 3). This phenomenon is an additional evidence to prove that the process of crystallization takes place by the mechanism mathematically described by Eqs. (1) – (6).


*a.* determined from the corresponding crystallization curve in Fig. 18 by choosing the first 100% crystallinity data point

*b.* calculated from Eq. (2) using crystal growth rate of 0.15 μm/h

*c.* determined from the corresponding SEM images

(Adopted from Ref. [50] with permission of Publisher)

Table 3. The comparison of measured, *d*t(det), and calculated, *d*t(cal), final crystal sizes of zeolite ZSM-5 synthesized from the reaction mixtures containing different amounts of silicalite-1 seed crystals having different sizes.

Crystallization of Sub-Micrometer Sized ZSM-5 Zeolites in SDA-Free Systems 283

This work is realized in the frame of the projects: NSFC (20803010), "Chen Guang" project supported by Shanghai Municipal Education Commission and Shanghai Education Development Foundation (09CG02), 'Brain Gain' Post-Doc project (I-668-2011) supported by Croatian Science Foundation and the project 098-0982904-2953, financially supported by the

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**8. Acknowledgement** 

**9. References** 

Based on the analysis of experimental data in both phenomenological and mathematical way, the crystallization mechanism and the corresponding critical processes occurring during crystallization are depicted in Fig. 24. These processes are: (i) dissolution of amorphous silica and/or alumina sources, (ii) formation of alumino(silicate) gel by polycondensation reactions and the partial deposition of gel onto the surface of seed crystals, (iii) formation of growth precursor species in the gel matrix at high temperature, (iv) deposition of growth species onto the surface of seed crystals, and (v) final ordering of growth species to form the crystalline end products.

Fig. 24. Schematic presentation of the crystallization process of seed-induced SDA-free approach for the synthesis of sub-micrometer sized ZSM-5 zeolites. (Adopted from [50] with permission of Publisher)
