Xiaoxin Chen

Guoju Yang

Valentin Valtchev
email: valentin.valtchev@ensicaen.fr

Environmentally benign synthesis of crystalline nanosized molecular sieves

Keywords: Zeolites, Organic template-free, Nanocrystals, Green synthesis

Zeolites and zeo-type materials with nanosized dimensions are of great practical interest owing to their favorable transport properties, faster adsorption kinetics, and large external surface area. This mini-review presents recent developments in the organic template-free synthesis of nanosized zeolites and related materials. The advantages and challenges of these methods are addressed with particular attention to the green synthesis of nanozeolites.

Introduction

Inorganic microporous materials with uniform pores and cages, typically known as zeolites and zeo-type molecular sieves, have been widely studied due to their widespread applications in catalysis, gas adsorption/separation and ion-exchange [1][2][3][4].

Zeolite is a class of inorganic microporous material, whose structure consists of adjacent aluminium and silicon tetrahedron to form a three-dimensional (3D) framework with uniform pores of molecular dimensions [5]. Zeo-type molecular sieves contain different tetrahedral framework cations (T = Al, Ti, P, Ga, Ge, and B).

Typical examples of zeo-type materials are the microporous aluminophosphates (AlPOs), silicoaluminophosphates (SAPOs), and metal-containing aluminophosphates (MeAPOs) [6][7][8][9]. The incorporation of heteroatoms in zeolite framework contributes to the diversification of zeolite properties and thus to their potential uses. Crystalline microporous materials with penta-or hexa-coordinated heteroatoms are also considered as zeo-types, although they do not fulfill all conditions of the strict definition for a zeolite.

A major drawback of conventional zeolites is that their native microporous channel system could cause severe diffusion limitations, thus suppressing their catalytic activity in the reactions involving bulky molecules. The two major avenues explored to decrease the impact of transport limitations are the addition of meso-and/or macro-porosity to the inherent microporosity and the reduction of the size of the crystals [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].

Zeolites possessing a secondary pore system of meso/macro-pores are usually denoted as hierarchical zeolites. These materials attracted considerable attention and consequently, different synthetic methods were developed. These approaches can be sub-divided into two major groups: (1) the use of sacrificial hard-or soft-templates [26][27][28][29][30], and (2) post-synthesis chemical etching leading to partial dissolution of zeolite framework [25,[31][32][33][34][35][36][37].

The nanosized zeolites are obtained by conventional hydrothermal synthesis [38][39][40][41][42][43]. However, the synthesis, i.e., the composition of the initial system, temperature -time conditions, are modified to facilitate the nucleation over the growth and hence to reduce the size of the crystals [12,39,[44][45]. A nanosized zeolite is essentially a result of precise engineering of synthesis protocol in order to face a very demanding application. The decrease of the crystal size changes the ratio between the fraction of atoms exposed to the crystal surface and zeolite channels, which has a straightforward effect on zeolite accessibility and activity. Furthermore, nanosized zeolite crystals have a reduced diffusion path length compared to conventional micron-sized zeolites.

First studies on the synthesis of nano-sized zeolite were published by B. Schoeman et al. [46]. These studies were extended and deepened by V. Valtchev and S. Mintova.

A characteristic feature of the early studies on zeolites is the extensive use of organic-structure directing agents (OSDAs). Nowadays, the use of OSDAs is still indispensable for the synthesis of high silica zeolites and some zeo-type materials.

However, during the last decade, numerous efforts were dedicated to the preparation of nanosized zeolites employing alkali metal cations solely as structure-directing agents. These efforts are justified by a number of drawbacks related to the use of organic templates. In general, the use of organic templates, which are namely amines, is not appreciated since these are often toxic compounds which are not environmentally benign. Besides, the organic templates are relatively expensive and increase the price of the ultimate product. Moreover, the use of an organic template requires an additional post-synthesis, which is the combustion of the template at high temperature, typically about 550°C. This energy-intensive step is highly recommended to be omitted because of the negative impact on the environment, i.e., the emission of CO 2 and nitrogen-containing compounds. Hence, the preparation of nanozeolites using an alkali metal cation solely as a structure-directing agent offer significant advantages not only from economical but also from the environmental point of view. The synthesis of nanozeolites using only inorganic compounds could be considered to be a great extent as a green zeolite synthesis, which is the topic of the present paper. Figure 1 illustrates the economic and eco-environmental strategy of the organic template-free fabrication of nanozeolites. Figure 1. A green approach to the synthesis of nanozeolites. This mini-review presents recent developments in the organic template-free synthesis of nanosized zeolites and related zeo-type molecular sieves. The strategies available for their preparation are discussed. The impact of the synthesis conditions on the physicochemical properties is also highlighted. Finally, the advantages and challenges of organic template-free synthesis of nanozeolites are addressed with particular attention to their potential applications.

Zeolite synthesisa general introduction

Microporous zeo-type molecular sieves are synthesized under low-temperature hydrothermal conditions. The syntheses are performed under autogenous pressure, which rarely exceeds 10 bars. The first zeolite syntheses mimic the conditions in nature and namely, the zeolite formation in pegmatite veins, where the temperature of hydrothermal can reach more than 400°C [47][48][START_REF] Barrer | Zeolites and Clay Minerals as Sorbents and Molecular Sieves[END_REF]. Later, Milton [START_REF] Milton | [END_REF] and Breck [START_REF] Breck | Zeolite Molecular Sieves[END_REF] found out that using highly reactive alkaline aluminosilicate hydrogels allows a reduction of the synthesis time and synthesis temperature below 100°C, which opens the route to ambient pressure synthesis of zeolites.

Zeolites are typically synthesized under low temperature (room temperature to 170 ºC) hydrothermal/solvothermal conditions. The initial synthesis system is generally an aluminosilicate hydrogel that evolves under the coaction of mineralizing (OH -, F -) and structure-directing agents (SDAs). The SDAs could be organic molecules or alkali metal cations. Promoted by the Van Der Waals interactions, arranging SiO 4 -and AlO 4 tetrahedra around the positively charged templating agent, such as organic molecules or hydrated alkali metal cations, is a generally accepted zeolite formation mechanism.

Alkali metal ions are identified to be crucial for the synthesis of aluminosilicate zeolites. They boost Al incorporation into the framework. However, the obtained zeolite has to be ion-exchanged and the alkali metal is replaced with proton before use as a solid acid catalyst. Therefore, synthesis without alkali metal cations would be highly desirable as it would bring the synthesis process more facile, thus more economical and industrially effective. Especially, the conventional synthetic approaches for preparing nanozeolites are based on the extensive applications of organic templates [START_REF] Cundy | [END_REF]. The advantages of the organic template-assisted synthesis of nanozeolites are the effective control of the particle size. A great merit of the use of OSDAs is the possibility to stabilize a precursor zeolite suspension of high uniformity.

The nucleation events in such a precursor are uniformly distributed in the system.

Thus the formation of zeolite nuclei and their growth is uniform as well, which is indispensable for the formation of discrete zeolite nanocrystals with narrow particle size distribution. The stabilization of zeolite suspension using only alkali metal is difficult because of their strong surface charge and the aggregation of the silica particles, thus breaking the uniformity of the initial system. However, the utilization of organic templates brings serious disadvantages: (1) The organic templates are usually quaternary ammonium or amines, which are not eco-friendly. An alternative route to avoid the drawbacks of organic templates is to synthesize in the absence of them.

In general, a zeolite synthesis is performed in a batch reactor, where the growth stops with exhausting of the nutrient pool. Under such synthesis conditions, the ultimate crystal size can be adjusted by controlling the nucleation rate in the system.

Increasing the number of nuclei generally results in a reduction in the final crystallite size. Therefore, the formation of small zeolite crystals requires conditions that are to nucleation rather than crystal growth. Hence, the guidance of the zeolite size requires precise control of the zeolite nucleation and the coinstantaneous crystal growth processes.

Significant effort has been focused on the development of organic template-free strategies to nanozeolites. Fine adjustment of the molar ratios of the starting gels is of particular importance in the synthesis of nanozeolites [41,43]. Other approaches, including the utilization of zeolite seeds [53][54][55][56][57], space-confining agent [58][59] into the starting gels, and employing non-conventional heating mode (microwave-assisted, ultrasonic-assisted) [60][61] are also employed. The green route without using an organic template is very important for the preparation of zeolites, especially in large-scale industrial production. In the following section, the representative organic template-free strategies to nano zeolites are presented.

Organic template-free methods applied in the preparation of nanosized molecular sieves

The synthesis of nanozeolites using alkali metal cations solely is challenging due to their strong positive charge, which generates inhomogeneities in the system.

Consequently, the nucleation events are not simultaneous, which results in crystals of different sizes. Another negative impact of the alkali cations is that the crystallites are heavy agglomerated. In such systems, a very pronounced Ostwald ripening, which accentuates the differences in the crystal size, is often observed. Upon the Ostwald effect, the larger particles continue growing at the expense of the smaller ones, introduce additional heterogeneity in the system in terms of particle size.

Aluminosilicate zeolites

LTA-type

LTA-type zeolite is widely employed in ion-exchange and humidity-control applications. The abundant nucleation is a critical factor in the quest of nanosized zeolites, which control includes many parameters, as stated above. Low-temperature conditions mostly favor zeolite nucleation and lead to smaller crystal particles. Thus many attempts to decrease zeolite synthesis temperature below 100°C, and even below 80 °C were reported. Zeolite A is probably the best example of a low-temperature synthesis of a nanozeolite since it was successfully obtained at room temperature [62]. A drawback of low-temperature synthesis of zeolites is the long synthesis time. In the case of zeolite A, the optimization of synthesis parameters, such as the composition of the starting gel and the choice of reactants, allowed it's synthesis within 3 days. This is a reasonable period of time, which is not much longer than the conventional crystallization of low silica zeolites. After 3 days of room temperature crystallization, the crystal size of zeolite A ranged from 100 to 300 nm without well-developed crystal faces (Figure 2A). The prolongation of the synthesis time up to 10 days resulted in the formation of larger well-faceted cubic crystals in the range of 400 -500 nm. Low-temperature synthesis of nanosized zeolite A was further studied by Dimitrov et al. [63]. The syntheses were performed at 35, 50, and 65 °C in the absence of OSDA. It was found that the crystal size of zeolite is a function of the crystallization temperature, as shown in Figure 2(B). The average crystal size was 30 -100, 200, and 300 -400 nm, respectively.

Another synthetic approach targeting nanozeolites is the vapor phase transport synthesis. This approach includes the use of an ultradense hydrogel offering a confined space, which is exposed to a water vapor atmosphere. This way, relatively large (∼700 nm) zeolite A particles were obtained [63]. Confined synthesis of nanozeolites using a physical barrier limiting the growth was also reported. Zeolite A nanocrystals were synthesized under organic template-free hydrogel system by using in-situ thermoreversible polymer hydrogels [58]. The general synthesis scheme is illustrated in Figure 2(C). It was found that the size of the zeolites can be effectively controlled by a polymerized hydrogel. The zeolite A nanocrystals (40 -80 nm) were prepared by using microwave-assisted heating in reverse microemulsion (water in oil)

without using organic templates. The reverse microemulsion played a role as a space-confining nanoreactor (Figure 3(D)), while the microwave provided fast, uniform, and preferential heating of the aqueous phase where the zeolite crystals grew [59]. Microreactors are widely applied in the synthesis of organic and inorganic compounds. The most important advantages of microreactors are the fast transfer of mass and heat, excellent reaction kinetics, and high safety [64][65]. Zeolite A nanocrystals (100-240 nm) with well-developed crystal faces and uniform particle size distribution were synthesized using a manipulated organic template-free synthesis solution at 80 °C for 7.5 min in a two-phase liquid segmented microfluidic reactor [66]. The scheme of a two-phase liquid segmented microfluidic reactor employed in the synthesis of zeolite A nanocrystals is shown in Figure 2(E). Bead-milling was utilized in the treatment of organic template-free synthetic zeolites. By a combination of bead-milling and post-milling recrystallization, nano-zeolite A (∼50 nm) with high crystallinity was successfully prepared in the absence of an organic template [67]. The synthetic process of nano-zeolite by bead-milling and post-milling recrystallization is illustrated in Figure 2(F). The yield of zeolite nanocrystals obtained by this method is almost 100%, since the preparation of nanozeolites by bead-milling and recrystallization treatment does not cause material loss.

EMT-type

An EMT-type framework possessing a 3D 12-member ring pore system is one of the most open zeolite structures [START_REF] Ch | Database of Zeolite Structures[END_REF]. EMT type zeolite is usually synthesized with the expensive 18-crown-6 as a template [START_REF] Delprato | [END_REF]. Due to the high cost, this material with great potential in the catalysis and separation processes has not been practically applied [70][71]. Therefore, organic template-free synthesis of EMT-type nanosized zeolite is highly appealing. Ultrasmall EMT-type material was obtained by an organic template-free approach, as shown in Figure 3 [41]. The ultrasmall (6 -15 nm) and nanosized (50 -70 nm) EMT type materials were obtained under nearly ambient temperature conditions for 36 hours under conventional heating or for 4 min under microwave irradiation, respectively. Ng et al. pointed out that under such conditions, the crystal growth kinetics was slowed down, and the crystallization temperature influenced the size of EMT zeolites. Besides the small size, another great achievement is the narrow particle size distribution in the sodium-rich system, which makes the synthesis unique. In addition, Ng et al. also develop an organic template free method by using biomass rice husk ashes as a silica source to prepare nanosized EMT-type zeolite crystals with a diameter of 15 nm. The crystallization of EMT-type zeolite was completed within 28 h at 28 °C [72]. In 2019, Xiao's group reported a sustainable and efficient synthesis of nanosized EMT zeolite under organic template-free and solvent-free systems [73]. This approach not only completely avoids the utilization of an organic template but also effectively reduces the water pollution during the post-synthesis treatment. In comparison with conventional hydrothermal synthesis, the yield of EMT zeolites was substantially increased by this approach. Reprinted with permission from ref. [41] (Copyright 2012, American Association for the Advancement of Science).

FAU-type

The importance of FAU-type zeolite for the petrochemical industry, particularly in the fluid catalytic cracking (FCC) process, has attracted worldwide research interest to its synthesis in a nanosized form. In 2014, the feasibility of FAU-type nanocrystals synthesis from an organic template-free condition was first reported by Valtchev and

Bozhilov [74]. The study focused on the formation mechanism of FAU-type X zeolite that was prepared at ambient temperature for three weeks. The particle size of the individual crystal was below 30 nm, building spherical aggregates of 150 -200 nm in size. The synthesis of even smaller crystals (10 -20 nm) was also reported. The extension of aging time increased the size of the crystallites; however, the size of the aggregate remains unchanged (Figure 4). Based on the similar gel system, Huang et al.

prepared nanosized zeolite Y crystals via a three-stage synthesis procedure [75].

Specifically, the synthesis gel was firstly aged at room temperature for 24 h, then was heated to 38 °C and kept for 24 h prior to hydrothermally treating at 60 °C for 48 h.

Hierarchical porous aggregated particles (190 and 600 nm) composed from well-crystallized zeolite NaY nanocrystals were obtained without adding any organic template. Awala et al. developed the rational design for the template-free synthesis of nanosized FAU zeolites [42]. The obtained nanosized FAU zeolites possessed ultra-small crystallites with a narrow particle size distribution (10 -15 nm), and high crystalline yield (above 80%). The micropore volume (0.30 cm 3 g -1 ) of the nano Y was typical of highly crystalline FAU-type materials. Again by regulating the synthesis temperature, the particle size was controlled from 10 nm to 70 nm keeping the particle size distribution very narrow. In comparison with the conventional micrometer-sized counterparts, the Si/Al ratios of the obtained materials could be adjusted between 1.1 and 2.1 (zeolites X or Y), and showed superior thermal stability thereby giving excellent catalytic activity in the dealkylation of a bulky molecule, such as 1,3,5-triisopropylbenzene. This result demonstrates high accessibility of the active sites in nanozeolites, in particular those with size below 50 nm.

MFI-type

MFI-type zeolites are a significant industrial catalyst and separation material [76].

Conventionally ZSM-5 (MFI-type) is synthesized with tetrapropylammonium as a template. Recently the works on nanosized MFI-type zeolites focusing on economic and eco-friendly syntheses were reported [77][78]. The preparation of ZSM-5 nanocrystals by using seeds-assisted crystallization from an organic template-free gel system was published by Majano et al. [77]. ZSM-5 nanozeolite crystals were synthesized using a gel system containing 0.1, 1.0, and 3.0 wt % of 80 nm silicalite-1 seeds for SiO 2 content in the synthesis gel. The size of resulting ZSM-5 particles (mainly aggregates) ranged from 140 to 230 nm. The seed content strongly influenced the size of the obtained crystal. Another advantage of this approach is the high yield, which is above 80%. However, a disadvantage of this method is the high aggregation of the crystals compared with the syntheses using clear sols rich in tetrapropylammonium hydroxides.

Other zeolites

The list of nanosized aluminosilicate zeolites obtained from organic template-free systems is longer. For instance, important zeolites as L [79][80], Beta [81], Mordenite [82], and others were successfully synthesized in nanosized form using some of the above approaches. The initial system employed and the synthesis conditions used for these syntheses are summarized in Table 1. The one-dimensional pore system of zeolite L was found appropriate for optical applications and crystallites with different sizes, including nanosized, were synthesized and further modified to fit to this application [83][84]. Garcia-Martinez and Rimer and their co-workers reported the preparation of ultrasmall (ca. 30 nm) zeolite L crystals with uniform size by employing an organic template-free method [80]. The homogeneous distribution of K + ions throughout the silicate precursor is related to the enhanced nucleation rate, and thus the formation of ultrasmall LTL-type nanocrystals. Zeolite Beta with 12-ring three-dimensional pore system is widely used in several important commercial processes. Zhou et al. reported a one-pot organic template-free synthesis of single-crystalline nanosized hierarchical zeolite beta with 200 -300 nm. This result was achieved by introducing sodium carbonate in the precursor solution [81]. The obtained material featured abundant and interconnected mesopores crossing the entire crystal. The obtained zeolite Beta exhibits a high BET surface area (667 m 2 g -1 ) and a high total pore volume (0.65 cm 3 g -1 ) that is due to mesopores centered at 2 -8 and 90 -150 nm. The one-pot sodium carbonate-assisted approach had also been successfully applied to other zeolites. The mordenite is an important catalyst utilized in petroleum refining. Zhang et al. proposed nano-Beta seeds and organic template-free aluminosilicate gel can be converted to mordenite with nanosized dimensions [82]. Thus obtained MOR-type zeolite possessed abundant inter-crystallite mesopores and high crystallinity (Figure 5). TEM images showed that the particles are composed of abundant mordenite nanocrystals with an average diameter of ca. 20 nm.

The above studies explicitly demonstrate the possibility of synthesizing zeolite nanocrystals from organic template-free systems with high crystallinity and yield, and often a narrow particle size distribution. Reprinted with permission from ref. [82] (Copyright 2016, The Royal Society of Chemistry.). [93]. These aluminophosphates (AlPO), similarly to zeolites, are synthesized under low-temperature hydrothermal conditions using organic amine as SDAs. As discussed in the introduction section, the elimination of the organic template requires high-temperature combustion with all undesired economic and environmental consequences. Thus, the quest for more green syntheses desires an extensive decrease or avoidance of the utilization of organic amine.

Ionic liquids have aroused great attention in many fields as a synthesis medium, especially for the replacement of organic solvents, which represent a green alternative of the conventional synthesis [94][95].

A nanosized manganese-containing aluminophosphate MnAlPO-5 (AFI-type) was prepared using this approach. This material was synthesized by ionothermal synthesis in the presence of 1-ethyl-2,3-dimethylimidazolium bromide under ambient conditions [96]. The ionic liquid was employed as both a solvent and a template. The size of the resulting particles was 80 nm. NKX-2 is an important intermediate for the synthesis of useful microporous aluminophosphates, such as SAPO-46, SAPO-31, AlPO-11, AlPO-5 and AlPO-CJ2, etc.. Aluminophosphite NKX-2 with rod-like morphology and a high c/a axis aspect ratio (~10) was ionothermally synthesized using 1-ethyl-2,3-dimethylimidazolium bromide (EMMIMBr) ionic liquid [97]. Noteworthy, the synthesis completed in an open vessel for about 3 h.

In 2016, via an organic template-free route, the NaNKX-2 aluminophosphite was prepared [98]. This non-conventional synthesis involves H 3 PO 3 as a phosphorous source and NaOH as an inorganic base and template. In 2020, an open-framework SAPO material with a composition of Cs 2 (Al 0.875 Si 0.125 ) 4 (P 0.875 Si 0.125 O 4 ) 4 (HPO 4 ) was synthesized by Fan et al. in an organic template-free caesium-containing system under hydrothermal conditions [99]. The replacement of the organic template by inorganic Cs + ions makes the current synthesis protocol eco-friendly. Notably, the incorporated Cs + endowed the material with improved thermal stability and high proton/ionic conductivity. However, it is clear that this approach cannot be applied to the synthesis of all AlPO-and SAPO-type materials.

Other zeo-type molecular sieves

Microporous manganese oxide octahedral molecular sieves (OMS) are essential materials in environmental chemistry, electrochemistry, and heterogeneous catalysis [100]. Structurally these materials are not zeolites since their framework is built of octahedral manganese units. On the other side, they are crystalline microporous materials with properties similar to zeolites, which justifies their inclusion in the present review. The structure and morphology of several OMS materials are shown in Figure 6. Most of the structures exhibit long prismatic morphology with a thickness of 50 to 100 nm.

There is also a plate-like material as gama-MnO 2 with a size of about 200 nm.

An important feature of the OMS materials synthesis is that no organic template is involved. Thus the synthesized material does not require high-temperature calcination.

Applications

Zeolite nanocrystals synthesized under organic templates-free conditions offer great potential for uses in heterogeneous catalysis, adsorption, and separation processes. Besides, the recent developments show that nanosized molecular sieves are in the focus of emerging nanotechnology applications, including sensors, medicine, biological and pharmaceutical industries [110]. There are substantial differences when nano-sized and conventional (micron-sized) zeolite crystals are used for catalytic reactions. The nanocrystals featuring large external surface areas are beneficial for the conversion of bulky molecules that cannot penetrate in zeolite channels. In addition, the nanocrystals offer the advantage of a shorter diffusion path, thus minimizing the effect of undesired side reactions [12]. The impact of the external surface of FAU-type nanocrystals in the dealkylation of a bulky molecule, 1,3,5-triisopropylbenzene was studied compared with a conventional micron-sized industrial sample [42]. All obtained nanosized zeolite catalysts showed higher catalytic activity with respect to the high-quality commercial sample.

The product selectivity at 200 ºC provided further insight into their superior catalytic performance. The excellent colloidal stability of nanosized zeolites is also useful for their uniform dispersion on supports and the preparation of thin-to-thick coatings [111][112]. Flexible nanosized RHO-type zeolite containing only inorganic cations (Na + and Cs + ) has been synthesized under an organic template-free system at 90 °C for 1 h [91]. Due to the high Cs content, the thermal stability of the RHO nanocrystals showed improved thermal stability. The flexible RHO-type nanosized zeolite showed excellent selectivity toward CO 2 over CH 4 attributed to the ability of the Cs + cation to displace out from and into the D8R window.

Different types of zeolite nanocrystals, for instance, EMT, LTA, LTL, MFI, MOR, FAU, have different sizes, compositions and shapes, their cytotoxic activity is low [110]. Thus these materials are safe for using in biological and medical applications. More specialized studies were performed on EMTand LTL-type zeolites synthesized without organic template that proved to be non-toxic to HeLa cells [110]. EMT-and FAU-type nanoparticles showed specific adsorption abilities for human plasma proteins. [113] These two zeolites exposed to high plasma concentration (100%) exhibited highly selective adsorption for polipoprotein C-III (APOC-III) and fibrinogen. At low plasma concentration (10 %), high selective adsorption for immunoglobulin gamma (i.e. IGHG1, IGHG2 and IGHG4)

proteins was observed. This study revealed the potential of nanozeolites in the therapies of hemophilia B (F-IX deficient)) with a risk of bleeding and hemophilic patients (hemophilia A (F-VIII deficient).

Nanozeolites also give promises in the preparation of selective chemical sensors for detection of exhaust gases, hydrocarbons and biomolecules [114].

Conclusion and outlook

Progresses in nanoscience are continually being implemented in industry and our everyday life This mini-review summarizes the significant issues related to the preparation of crystalline nanosized molecular sieves under the organic template-free condition. Addressing these issues will open the door to a more eco-friendly and economical design of high-performing materials and guide the future research direction in this field.

  (2) Removal of organic templates generally requires high-temperature calcination to obtain the open pores characteristic of molecular sieves. The calcination step is generally together with the release of hazardous gases (NO x ) and greenhouse gases (CO 2 ). The energy released by the combustion of the template combined with the generated water vapors can partially destroy the zeolite framework. (3) Most organic templates are expensive, and the calcination step for removing the organic agent increases the production cost.

Figure 2 .

 2 Figure 2. (A) SEM images of the zeolite A nanocrystals prepared at room temperature for 3 days (a) and 10 days (b). Reprinted with permission from ref. [62] (Copyright 2005, American Chemical Society). (B) TEM images of fully crystalline LTA-type materials obtained at 35 (a), 50 (b), and 65 ºC (c). Scale bar = 200 nm. Reprinted with permission from ref. [63] (Copyright 2011, American Chemical Society). (C) Schematic representation of the synthesis of template-free zeolite A nanocrystals by using in situ thermoreversible polymer hydrogels. Reprinted from ref. [58] (Copyright 2003, American Chemical Society). (D) Schematic representation of microemulsion-microwave synthetic method. Reprinted with permission from ref. [59] (Copyright 2005, American Chemical Society). (E) Scheme of synthesis of organic template-free zeolite A nanocrystals by employing a two-phase liquid segmented microfluidic reactor. Reprinted with permission from ref. [66] (Copyright 2009, Royal Society of Chemistry). (F) Scheme illustrating the construction process of nano-zeolite by bead milling and post-milling recrystallization. Reprinted with permission from ref. [67] (Copyright 2011, American Chemical Society).

Figure 3 .

 3 Figure 3. Ultrasmall EMT crystals with hexagonal morphology synthesized from template-free precursor suspension at 30°C for 36 hours. The individual crystals are with a size of 10 to 15 nm and a thickness of 2 to 3 nm. Scale bars represent 10 nm.

Figure 4 .

 4 Figure 4. Low and high magnification TEM micrographs of the crystals obtained after 17 days (A, B), 22 days (C, D), and 38 days (E, F) ageing. Reprinted with permission from ref. [74] (Copyright 2004, American Chemical Society).

Figure 5 .

 5 Figure 5. (A) Low and (B) high magnification TEM images of mordenite nanocrystals.Reprinted with permission from ref.[82] (Copyright 2016, The Royal Society of Chemistry.).

  also synthesized OMS-2 nanowires in a 3 days hydrothermal synthesis[107]. Microwave-assisted synthesis has also been used to prepare OMS-2 materials[108]. Through the assistance of microwaves in the hydrothermal condition, the preparation of OMS-2 can be achieved in 10 s. The formation of crystalline phase OMS-2 material occurred when the reaction temperature is higher than 100 ºC, whereas reaction temperatures below 80 ºC led to an amorphous manganese oxide material. The OMS-2 thin nanoflakes convert to nanowires with increased reaction temperature. However, this microwave-assisted hydrothermal approach still requires high temperatures (above 150 °C) and at least 2 bar pressure. The utilization of ultrasound in the synthesis of the OMS nanomaterials significantly reduced reaction times and temperatures. For instance, Dharmarathna et al. developed the ultrasonic-assisted synthesis of OMS-2 materials possessing a high specific surface area of 288 ± 1 m 2 /g[109]. In comparison with reflux methods (88 ± 1 m 2 /g), the specific surface area increased three times, while reaction time decreased by 50% under cosolvent systems.

Figure 6 .

 6 Figure 6. Structures and morphologies for various OMS materials. Reprinted with permission from ref. [100] (Copyright 2008, American Chemical Society).

  , from advanced technologies to domestic products. The growing environmental and economic concerns continuously boost the development of microporous nanomaterials. The analysis of the literature reveals that crystalline molecular sieve nanocrystals can be easily synthesized and scaled up at low temperatures without the release of any harmful compounds. These nanoscale molecular sieves materials offer bright futures for a great variety of technologies and commodity products. The possible green mass production of nanosized molecular sieves provides remarkable opportunities for applications in catalysis, adsorption, and separations involving larger molecules and for designing thin films, membranes, or emerging nanoscale devices.The industrial implementation of nanozeolite-based technology will depend on future developments in the field. The most urgent issues to be addressed are: (1) the extension of Si/Al ratio in important zeolites as FAU-, LTA-and EMT-type; (2) the development of organic template-free synthesis of nanosized zeolites without aggregation and impurities; (3) the improved colloidal stability of nanosized molecular sieves; and (4) the synthesis of various of nanosized molecular sieve materials, such as AlPO, SAPO, MeAPO, without the use of an organic template agent.

Table 1 .

 1 Synthesis conditions and crystal size of the aluminosilicate nanozeolites synthesized from organic template-free systems. AlPO and SAPO materials In 1982, Wilson et al. reported a new class of crystalline, microporous materials, which represented the first family of framework oxide molecular sieves synthesized without silica

	Framework		Temp,		Crystal size
		Molar composition of the clear synthesis solution (S) or gel (G)		Si/Al		Ref.
	type		°C		range, nm
	LTA	3.56Na 2 O: 1.59SiO 2 : 1.00Al 2 O 3 : 32.12H 2 O: 3.48MC (S)	80	-	70	[58]
	LTA	3.67Na 2 O: 1.65SiO 2 : 1Al 2 O 3 : 83.93H 2 O: 7.08MC (S)	80	-	98	[58]
		5.85Na 2 O: 2.7SiO 2 : 1.00Al 2 O 3 : 182H 2 O: 36.4CTAB: 364n-butanol:
	LTA		75	-	40-80	[59]
		4732cyclohexane (G)
	LTA	3-8Na 2 O: 0.4-0.55Al 2 O 3 : 1.0SiO 2 : 80-150H 2 O (G)	25 ± 1	-	100-300	[62]
	LTA	3-8Na 2 O: 0.4-0.55Al 2 O 3 : 1.0SiO 2 : 80-150H 2 O (G)	25 ± 1	-	400-500	[62]
	LTA	20mL MGS a + 10 mL SCS b (G)	80	1.3	60-260	[66]
	LTA	20mL MGS a + 10 mL SACS c (G)	80	1.1	80-260	[66]
	LTA	20mL MGS a + 10 mL ACS d (G)	80	0.7	80-360	[66]
	LTA	20mL MGS a + 5 mL SACS c (G)	80	1.0	80-275	[66]
	LTA	20mL MGS a (G)	80	0.8	80-320	[66]
	LTA	20mL MGS a + 10 mL SACS c (G)	80	1.1	95-230	[66]
	LTA	20mL MGS a + 10 mL SACS c (G)	80	1.1	60-430	[66]
	LTA	6Na 2 O: 0.505Al 2 O 3 : 1.0SiO 2 : 150H 2 O(G)	50	-	200	[63]
	LTA	6Na 2 O: 0.505Al 2 O 3 : 1.0SiO 2 : 150H 2 O(G)	65	-	300-400	[63]

a MGS: 6.5Na2O: 0.6Al2O3: 1.0SiO2: 150H2O, b SCS: 8.6Na2O: 1.0SiO2: 150H2O c SACS: 8.6Na2O: 0.18Al2O3: 1.0SiO2: 150H2O, d ACS: 8.6Na2O: 0.18Al2O3: 150H2O 3.2

  Shen et al. first prepared OMS-1 material by reactions of MnO 4 -and Mn 2+ under alkaline conditions [101]. OMS-1 possessed a thermally stable 3 × 3 tunnel structure, the mixed-valent semiconducting nature, excellent adsorptive properties, and remarkable activity in numerous catalytic reactions. Another OMS phase that shows interesting electrochemical and catalytic properties is the OMS-2 structure type with 4.6 Å square pores [102]. Yuan et al. reported the synthesis of mesoporous hollow nanospheres of OMS-2 type built up of nanosized particles [103]. These nanospheres with hexagonal flake shape and a size of approximately 400 nm in diameter showed excellent activity in oxidation reactions due to enhanced surface area. Later, Shen et al. developed a variety of OMS materials with different pore sizes and tunnel structures using the Na + cation as a structure-directing agent. These reports clearly demonstrated that similarly to zeolites, the synthesis of OMS materials can be controlled to a great extent using alkali metal cations solely [104]. The conventional routes for preparing OMS-2 include hydrothermal treatment using a sol-gel approach with reaction time varying from hours to days. De Guzman et al. prepared OMS-2 by using refluxing under a redox reaction in 24 h [105]. Yuan et al. synthesized OMS-2 material within 12 h by employing K 2 Cr 2 O 7 and MnSO 4 [106]. Morphologies of OMS-2 nanoparticles can be tuned by varying reaction temperatures. At low temperature (120 °C), OMS-2 exhibited dendritic nanoclusters, while at high temperature (180 °C) spherical dandelion-like microspheres are obtained. Via the utilization of K 2 S 2 O 8 and MnSO 4 , Yuan et al.

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant 21971082 and 22001090) and the Jilin Province Science and Technology Development Plan (Grant 20190201229JC and 20200201096JC). And this work acknowledges 111 Project (B17020). X.C. and V.V. acknowledge the collaboration in the framework of joint Sino-French international laboratory "Zeolites".


Saikat Das

Teng Ben

Shilun Qiu

Valentin Valtchev

Two-Dimensional COF-Three-Dimensional MOF Dual-Layer Membranes with Unprecedentedly High H2/CO2 Selectivity and Ultrahigh Gas Permeabilities

Keywords:

have emerged as state-of-the-art membranes with exceptional gas separation performances. However, the COF membranes are restricted to three-dimensional (3D) COFs, while the two-dimensional (2D) COF membrane remains a relatively uncharted territory. In addition, the major part of the scientific fraternity working in this field shares the dream to prepare 2D COF membranes with crystallographic preferential orientation. Here, we present a general strategy for the fabrication of oriented 2D COF membranes which is based on the incorporation of an intermediate metal-organic framework (MOF) layer. The 2D COF membrane is endowed with real ordered one-dimensional (1D) channels. This specially designed membrane that comprises two judiciously selected porous frameworks shows ultrahigh gas permeability and selectivity far surpassing the present Robeson upper bound. This contribution paves a new avenue to explore oriented 2D COF membranes as prospective high-performing membranes rendering a sustainable route for H 2 /CO 2 separation.

Porous organic framework membranes [1][2][3][4][5][6][7] with a preferred orientation are one of the most coveted membrane architectures in gas separation owing to highly efficient intracrystalline gas diffusion and reduced non-selective intercrystalline gas diffusion. 2D inorganic porous material such as zeolite, 8-10 MOF 11-16 etc. oriented membranes with high selectivity are routinely fabricated by secondary growth method using substrates with oriented seed layers. 17,18 Importantly, the performance of a gas separation membrane 19,20 depends not only on high selectivity but also on high permeability. 2D COFs 21- 26 have relatively large pore sizes compared to the sizes of the permeating gas molecules which contribute to high permeability. On the other hand, a membrane with preferential orientation presents high selectivity. Scientists always strive for membranes that outperform the Robeson upper bound 27 which represents the permeability-selectivity trade-off in the field of gas separation membranes.

The π-stacked columns of 2D COFs that can contribute to direct pathways for gas transport render 2D COFs as highly promising materials for gas separation membranes. However, it remains a formidable challenge from fabrication perspective to attain an oriented 2D COF membrane considering that the 2D COF layers tend to be randomly aligned to each other. A few examples of the preparation of 2D COF membranes 1,3,4 did not report preferentially oriented COF layer.

To tackle this issue, we herein adopted a specially designed MOF membrane that provides the binding sites along the vertical direction to anchor the 2D COF structural building units. Besides, the covalent bond formation between the 2D COF building units parallel to the MOF membrane surface enables the COF crystals to grow along the MOF membrane surface thereby favoring the growth of a continuous 2D COF layer. The interlayer interactions guide the development of the stacking structure thereby enabling the formation of ordered 1D channels oriented perpendicular to the MOF membrane surface. Hence the present fabrication approach allows us to effectively attain the 2D COF crystals growing along the MOF membrane surface as well as realize the COF channels oriented perpendicular to the entire membrane surface (Figure 1).

A porous silica disk employed as substrate was coated with a polyaniline emeraldine base layer which provides amine groups functionalized surface. Thereafter the polyaniline base-functionalized SiO2 disk (Figure S1a) was used for the fabrication of UiO-66 28 membrane (Figure S1b). On the surface of the UiO-66 membrane, there are many unsaturated metal sites. These unsaturated metal sites played a vital role in the growth of the 2D H2P-DHPh COF 22c film atop the UiO-66 layer. More precisely, the coordinatively unsaturated zirconium cations of UiO-66 interact with the amine groups of porphyrin as evident from the Zr-N coordinate bond at -1 of the Fourier Transformed Infrared (FTIR) spectrum Optical photographs presented in Figure S1a,b reveal that the surface of silica disc is uniformly covered with polyaniline and UiO-66 layers. X-ray diffraction analysis of the UiO-66 membrane revealed the formation of pure highly crystalline UiO-66 material (Figure S2). Scanning electron microscopy (SEM) study showed the formation of continuous and uniform layer of UiO-66 containing closely-packed 1-2 µm octahedral crystals (Figure S1b). As can be seen in Figures S1b and3a, the white surface of the UiO-66 membrane was regularly covered with a dark purple layer of H 2 P-DHPh COF. Cross-sectional SEM images and the corresponding elemental mapping (Figure 3c-e) of the composite membrane clearly distinguish the COF and MOF layers, each of them with thickness of ca. 60 μm. Figure 3b presents the XRD patterns of H 2 P-DHPh COF powder and [H 2 P-DHPh COF]-[UiO-66] composite membrane. The XRD pattern of composite membrane contains solely the Bragg peaks of COF material thereby implying that the top layer is composed of pure H 2 P-DHPh COF. In addition to 100 and 200 characteristic diffraction peaks of H 2 P-DHPh COF at 3.44 o (2θ) and 6.90 o (2θ) respectively, a strong peak at 21.34 o (2θ) is observed. The latter peak is attributed to 001 Bragg reflection, which is relatively weak in the powder XRD pattern. The crystallographic preferred orientation (CPO) 29,30 of [H 2 P-DHPh COF]-[UiO-66] composite membrane and H 2 P-DHPh COF powder (synthesized in pyrex tube) in Figure 3b is evaluated using 29,30 :

CPO 001/100 =
where denotes the integrated intensity of the corresponding reflection at the specified peak, mem denotes the [H 2 P-DHPh COF]-[UiO-66] composite membrane and pow the H 2 P-DHPh COF powder.

A membrane shows orientation when the CPO values 1.

31

The CPO for the (001) and (100) reflections is about 49. The intense 001 peak in the XRD pattern of composite membrane reveals that the COF layer is oriented along this plane. The preferential orientation of the 2D COF film along the 001 face can be explained with the plate-like crystals morphology. Consequently, the channel system runs along the normal of membrane surface. 2D COF crystals following faster growth along out-of-plane direction grow fast and overpower the slower crystals with in-plane orientations. As a result the COF crystals accompanying fastest growth along the direction perpendicular to the membrane plane dictate the preferential orientation of the 2D COF layer. To monitor the integrity of the 2D COF film in the course of its growth, we performed the XRD analyses on the COF film after 1 day, 2 days and 2.5 days of solvothermal growth. The H 2 P-DHPh COF crystals cover the UiO-66 intermediate layer with uniform and intimately intergrown 60 µm thick film.

In the present work we show that a highly oriented 2D COF layer can be synthesized. The generation of the COF layer is promoted by the chemical interaction with modified and thus highly reactive intermediate MOF layer of the composite membrane. Consequently, the interpenetration of the COF and MOF crystals leads to a thin interlayer with intimately intergrown MOF and COF crystals. Further, the growth of COF layer is controlled by the morphological feature (plate-like morphology) of H 2 P-DHPh COF. The porosity of H 2 P-DHPh COF and UiO-66 was examined from the N 2 gas sorption analysis (Figure S6). We also carried out the stability tests of H 2 P-DHPh COF and UiO-66 (Figures S4,S5).

Gas permeation through the [H 2 P-DHPh COF]-[UiO-66] composite membrane was studied using a gas chromatograph. As can be seen in Figure 4b, H 2 gas with a kinetic diameter of 0.289 nm permeates considerably faster than CO 2 (kinetic diameter 0.33 nm) through the composite membrane. In membrane-based gas separation, the membrane layer that is at the helm of permeability and selectivity is called selective layer. Hence the selective layer of the composite membrane in this study encompasses the constituent COF and MOF layers as well as the interlayer between them. The thickness of the selective layer in the [H 2 P-DHPh COF]-[UiO-66] composite membrane is ca. 120 µm. The gas separation capability of the [H 2 P-DHPh COF]-[UiO-66] composite membrane was evaluated by the separation of 1:1 binary gas mixture of H 2 /CO 2 at room temperature and 1 bar pressure. The UiO-66 membrane gives commendable performance in terms of H 2 permeability and H 2 /CO 2 single and mixture separation selectivity. 32 Notwithstanding the satisfactory performance of UiO-66 membrane, the phenomenal enhancement in gas separation selectivity was achieved after the crystallization of 2D H 2 P-DHPh COF layer. The [H 2 P-DHPh COF]-[UiO-66] composite membrane features an ideal H 2 /CO 2 selectivity of 49.1, whilst maintaining comparable H 2 permeability (253188.7 Barrer) with UiO-66 membrane. The composite membrane exhibits a H 2 /CO 2 mixture selectivity of 32.9, which is around four-fold enhancement in respect to the UiO-66 membrane in addition to increasing the H 2 permeability to 10834 Barrer. Importantly, the [H 2 P-DHPh COF]-[UiO-66] composite membrane outdoes the Robeson upper bound for H 2 /CO 2 separation. A comparative H 2 /CO 2 separation performance analysis of polymer membranes is presented in the Robeson upper bound plot (Figure 4a).

mol•m -1 •s -1 •Pa -1 )
.

ǁ ISF and SF denote ideal separation factor and separation factor, respectively.

High-resolution transmission electron microscopy (HRTEM) was employed to study the spatial organization of the composite membrane (Figure 5b). The membrane comprises two parts, the layered H 2 P-DHPh COF sheets and the MOF (as evident in the bottom of the TEM image) characterized with sharp octahedral morphology (Figure 5b). The inset of Figure 5b shows the selected area electron diffraction (SAED) pattern of the MOF part of the composite membrane. The energy-dispersive X-ray spectroscopy (EDS) spectrum presented in Figure 5d shows zirconium, thereby indicating that the crystal with octahedral features at the bottom of the TEM image is indeed UiO-66. Crystalline COF domains can be recognized by the straight porous channels with interlayer spacing of 2.0 ± 0.1 nm (Figure 5c). The intimate interaction between MOF and COF parts of the membrane can be seen from the interlayer image of the composite membrane.

The composite membrane comprises materials with pores substantially larger than the kinetic diameters of the permeating gas molecules. Thus the flux of the permeating gas is very high. In order to reach high selectivity we judiciously selected two porous frameworks so as to exhibit lower isosteric enthalpies of adsorption to H 2 than to CO 2 . The isosteric enthalpies of adsorption of H 2 for H 2 P-DHPh COF (Figure S8b) and UiO-66 (Figure S7b) are lower than those of CO 2 for H 2 P-DHPh COF (Figure S8d) and UiO-66 (Figure S7d). Consequently, high selectivity to H 2 was achieved. Besides the above factors, we ascribe the exceptional H 2 /CO 2 mixture gas separation performance of the [H 2 P-DHPh COF]-[UiO-66] composite membrane to gas transport via straight COF channels, oriented perpendicularly to the membrane surface, which helps improve intracrystalline gas diffusion 37-39 . The growth of a very compact 2D COF film helps to develop better grain structures, which productively cuts down non-selective intercrystalline gas diffusion 37-39 . Therefore by the rational selection of porous frameworks we obtained a specially designed membrane that demonstrates high gas flux combined with high selectivity.

To summarize, this study presents a general strategy for fabrication of oriented 2D COF membranes. The chemical synergy between the building components, their functionality, spatial arrangement and crystallographic orientation are the indispensable components that determine the exceptional performance of a membrane. The results of the present study illustrate that membranes with exceptional selectivity and ultrahigh permeability can be produced if the above issues are properly addressed. This research also provides a sustainable route for highly effective separation of H 2 over CO 2 .

ASSOCIATED CONTENT Supporting Information

Synthetic procedures, membrane fabrication, membrane illustration and characterization, FTIR, crystallographic preferred orientation (CPO), PXRD, TGA, BET plot, lowpressure gas sorption isotherms, gas permeation tests and results. This material is available free of charge via the internet at http://pubs.acs.org.

Figure 1 .

 1 Figure 1. Schematic representation of how to control the growth of a continuous 2D COF membrane along ab (lateral) direction as well as maintain the orientation of the COF channels along c (vertical) direction.(FigureS3). Strong chemical bonding between Zr and N seals the COF and MOF layers via a thin interlayer of interpenetrating crystals. The fabrication process of [H 2 P-DHPh COF]-[UiO-66] composite membrane is outlined in Figure2and the details are provided in the SI.

Figure 2 .

 2 Figure 2. Process flowchart illustrating the fabrication of [H 2 P-DHPh COF]-[UiO-66] composite membrane (Zr: cyan, O: red, N: blue, C: gray. H atoms are excluded for clarity).

Figure 3 .

 3 Figure 3. (a) Optical photographs of [H 2 P-DHPh COF]-[UiO-66] composite membrane. (b) XRD patterns of H 2 P-DHPh COF powder and [H 2 P-DHPh COF]-[UiO-66] composite membrane. (c) SEM cross-sectional view of [H 2 P-DHPh COF]-[UiO-66] composite membrane. (d) Energy-dispersive X-ray spectroscopy (EDS) elemental mapping of silicon. (e) EDS elemental mapping of zirconium.

Figure 4 .

 4 Figure 4. (a) Robeson upper bound plot of H 2 /CO 2 selectivity versus H 2 permeability for [H 2 P-DHPh COF]-[UiO-66] composite membrane compared with state-of-the-art membranes 7,33-36 . The enhancement in separation selectivity of the composite membrane compared to the UiO-66 membrane

Figure 5 .

 5 Figure 5. (a) COF pore channels in the composite membrane. (b) HRTEM image of the composite membrane. Inset: SAED pattern of the yellow marked area. (c) Magnified view (blue circle in b) of the COF channels with width of 2.0 nm in the composite membrane. (d) EDS spectrum of the composite membrane.

Table 1 .

 1 H 2 /CO 2 single and binary mixture (1:1) gas separation performance of [H 2 P-DHPh COF]-[UiO-66] composite membrane at room temperature and 1 bar.

	Membranes	Knudsen	Single gas	Mixture gas
		selectivity
			P (H2) ¶	ISF	P (H2) ¶	SF
			(Barrer)	(H2/CO2) ǁ	(Barrer)	(H2/CO2) ǁ
	[H2P-DHPh
	COF]-[UiO-	4.7	253188.7	49.1	108341.3	32.9
	66] composite
	membrane
	¶ P denotes permeability in Barrer (1 Barrer = 3.347 × 10	-16

ACKNOWLEDGMENT

This study was supported by the NSFC (21390394, 21471065, 21571078), Science and Technology Department of Jilin Province Foundation (20180414009GH). V.V. acknowledges the Thousand Talents program in China. T.B, S.Q. and V.V. acknowledge the support in the framework of China-French joint laboratory "Zeolites".

AUTHOR INFORMATION Corresponding Author

*tben@jlu.edu.cn

Notes

The authors declare no competing financial interests.


Stanislav Aranovskiy

Igor Ryadchikov

Nikita Mikhalkov

Dmitry Kazakov

Alexey Simulin

Dmitry Sokolov
email: dmitry.sokolov@univ-lorraine.fr

Scissored pair control moment gyroscope inverted pendulum

Keywords: Scissored-pair control moment gyroscope, inverted pendulum, bipedal gait

Motivated by non-anthropomorphic dynamic stabilization of a walking robot, we are working on a 2D inverted pendulum stabilized with a scissored pair of control moment gyroscopes. This inverted pendulum is a fair approximation of a robot, allowing us to study the dynamics in simplified settings. In this paper we propose a model for the pendulum; the model neglects all unessential terms and thus is suitable for analysis. We also propose a simple control law based on the linearization of the model and we validate it experimentally.

Introduction

The research problem of this paper is motivated by the walking robot we are currently developing in the Laboratory of Robotics and Mechatronics of the Kuban State University (refer to Fig. 1, left). This non-anthropomorphic robot has an auxiliary dynamic stabilization system which consists of two scissored pairs of control moment gyroscopes (CMG). The scissored pairs are orthogonal and thus the problem of vertical stabilization of the robot can be considered for each axis separately. Therefore, stabilization of the robot for one axis can be approximated with a simplified onedimensional prototype. In this paper we consider such a prototype, which is a control moment gyroscope inverted pendulum (Fig. 2). Note that the robot has a modular design: the biped is equipped with four identical CMG cubes.

Control moment gyroscope is a widely used technological device that uses the reaction of a spinning wheel to external torques. Due to the advantages of a large ratio of produced torque to control torque and relatively low power consumption, CMGs have a wide range of applications, including vessel stabilisation [START_REF] Inc | Anti-roll gyro[END_REF] , motorcycle and robot balancing [START_REF] Lee | Awakening strategies from a sleeping mode to a balancing mode for a sphere robot[END_REF] , balancing aid for humans and bipedal exoskeletons [START_REF] Chiu | Design of a wearable scissored-pair control moment gyroscope (sp-cmg) for human balance assist[END_REF][START_REF] Oya | Preliminary experiments for postural control using wearable-cmg[END_REF] , attitude steering system for the satellites [START_REF] Paradiso | Global steering of single gimballed control moment gyroscopes using a directed search[END_REF] and underwater vehicles [START_REF] Thornton | Zero-g class underwater robots: Unrestricted attitude control using control moment gyros[END_REF] . Fig. 1. We are developing a biped that uses four control moment gyroscopes (highlited in red) as an auxiliary stabilization system. Fig. 2. Left: inverted pendulum hardware that we study in this paper. The pendulum consists of six bodies: body A (the thrust bearing), body B (the frame), bodies C 1 and C 2 (the single-axis gimbals), and, finally, bodies D 1 and D 2 (the flywheels). Right: corresponding notations. This configuration corresponds to q b = -π/4 and q

1 c = q 2 c = π/2.
So, we are working on a 2D inverted pendulum stabilized with a scissored pair of control moment gyroscopes. This work extends the results 7,8 that were presented for a single CMG inverted pendulum. The main contribution of this paper is the model of the scissored pair system. Full Euler-Lagrange equations of the system are extremely cumbersome (few pages of fine print) even under numerous assumptions like symmetry of the bodies. We propose a much simpler model that neglects all unessential terms and thus is suitable for analysis. We validate the model by building a simple control law implemented in hardware.

The rest of the paper is organized as follows. In section 2 we present a model of the considered system. Next, in section 3 we present the state-feedback controller capable to stabilize the system if all states along with experimental validations of the results. Finally, possible further research directions are discussed in the concluding section 4.

Model Description

Mechanical system description

The considered inverted pendulum is shown in Fig. 2. In this paper we follow the notations from the manual of the model 750 control moment gyroscope commercialized by Educational Control Products company [START_REF]Model 750: Control moment gyroscope[END_REF] . The pendulum consists of six bodies: body A (the thrust bearing, shown in green), body B (the frame, shown in blue), bodies C 1 and C 2 (the single-axis gimbals, shown in red and orange), and, finally, bodies D 1 and D 2 (the flywheels, shown in brown and black). We associate a basis with each of the bodies:

{ a 1 , a 2 , a 3 }, { b 1 , b 2 , b 3 }, { c 1 1 , c 1 2 , c 3 }, { c 2 1 , c 2 2 , c 2 3 }, { d 1 1 , d 1 2 , d 1 3 } and { d 2 1 , d 2 2 , d 2
3 }, respectively. We assume that all the bodies are symmetric; so the inertia matrices are diagonal. Let us denote by diag(I c , J c , K c ) the inertia matrix (w.r.t the center of mass) of the bodies C 1 and C 2 ; and by diag(I d , J d , K d ) the inertia matrix of the bodies D 1 and D 2 . In the same manner, we denote the inertia matrix of the body A as diag(I a , J a , K a ). As for the body B, the frame consists of two identical cubes, and we denote by I b , J b and K b the principal moments of inertia of each half of the frame w.r.t. the center of mass of each cube.

We denote by q a the angle of rotation between the "north" direction and the body A; the angle of the body B with respect to the vertical is denoted as q b ; the angle of the bodies C 1 and C 2 with respect to the body B are denoted as q 1 c and q 2 c ; and the angle of the bodies D 1 and D 2 with respect to the body C 1 and C 2 are denoted as q 1 d and q 2 d . The configuration shown in Fig. 2 corresponds to the angles q b = -π/4 and q 1 c = q 2 c = π/2. Note that the equilibrium position of an actual device may be subject to external disturbances and sensor displacement; therefore, for our system we model the equilibrium point as q b = -π/4e, where e is the unknown (small) bias. The notations and the corresponding hardware parameters are summarized in the Table 1. With these definitions, the vectors of angular velocities can be found as:

ω a =           0 0 qa (t)           , ω b =           0 qb (t) 0           + R AB (q b ) × ω a , ω 1 c =           q1 c (t) 0 0           + R BC (q 1 c ) × ω b , ω 1 d =           0 q1 d (t) 0           + R CD (q 1 d ) × ω 1 c , ω 2 c =           q2 c (t) 0 0           + R BC (q 2 c ) × ω b , ω 2 d =           0 q2 d (t) 0           + R CD (q 2 d ) × ω 2 c .
where R AB , R BC and R CD are the transformations between the bases of corresponding bodies:

R AB (α) =           cos α 0 -sin α 0 1 0 sin α 0 cos α           , R BC (α) =           1 0 0 0 cos α sin α 0 -sin α cos α           , R CD (α) =           cos α 0 -sin α 0 1 0 sin α 0 cos α           .
When clear from the context, in the sequel the argument of time is omitted. Then the parallel axis theorem allows us to write the total kinetic energy of the system as:

T = 1 2 ω 1 d × diag(I d , J d , K d ) × ω 1 d + ω 1 c × diag(I c , J c , K c ) × ω 1 c + ω 2 d × diag(I d , J d , K d ) × ω 2 d + ω 2 c × diag(I c , J c , K c ) × ω 2 c + 2 ω b × diag I b , J b + 1 2 ml 2 , K b × ω b + ω a × diag I a , J a , K a + 1 2 ml 2 × ω a .
The potential energy is given by P = √ 2mlg cos(q b + π/4 + e). Therefore the Lagrangian can be written as

L = T -P. The torques τ 1 c , τ 2 c ,
                                         d dt ∂L ∂ qa -∂L ∂q a = 0 d dt ∂L ∂ qb -∂L ∂q b = 0 d dt ∂L ∂ q1 c -∂L ∂q 1 c = τ 1 c d dt ∂L ∂ q2 c -∂L ∂q 2 c = τ 2 c d dt ∂L ∂ q1 d -∂L ∂q 1 d = τ 1 d d dt ∂L ∂ q2 d -∂L ∂q 2 d = τ 2 d ( 1
)
These equations can be also written in the matrix form

M † (q) q + C † (q, q) + G † (q) = τ -F † r ( q),
where q := q a q b q 1 c q 2 c q

1 d q 2 d , τ := 0 0 τ 1 c τ 2 c τ 1 d τ 2 d ,
and F † r ( q) corresponds to friction and other resistance forces. Assumption 1 (Mechanical symmetry). We assume that the following mechanical symmetries hold

K b = J b = I b , K c = J c , K d = I d .
Under Assumption 1, the matrix M † takes the form

M † (q) =                          m 11 m 12 m 13 m 14 m 15 m 16 m 12 m 22 0 0 J d cos(q 1 c ) J d cos(q 2 c ) m 13 0 I c + I d 0 0 0 m 14 0 0 I c + I d 0 0 m 15 J d cos(q 1 c ) 0 0 J d 0 m 16 J d cos(q 2 c ) 0 0 0 J d                          , (2)
where

m 11 = (I d -J d ) cos 2 (q b ) cos 2 (q c1 ) + (I d -J d ) cos 2 (q b ) cos 2 (q c2 ) + (2 J c -2 I d -2 I c + 2 J d ) cos 2 (q b ) + m l 2 2 + 2 I b + 2 I c + 2 I d + K a , m 12 = -cos (q b ) (I d -J d ) sin (2 q c1 ) 2 + sin (2 q c2 ) 2 , m 13 = -sin (q b ) (I c + I d ) ,
m 14 = m 13 , m 15 = J d cos (q b ) sin (q c1 ) , m 16 = J d cos (q b ) sin (q c2 ) ,

m 22 = (J d -I d ) cos 2 (q c1 ) + (J d -I d ) cos 2 (q c2 ) + m l 2 + 2 I b + 2 I d + 2 J c .

Local controllers of bodies C and D

We assume that the torque τ is generated by local servo drives that operate in fast time scale compared to the dynamics of the whole system. The effect of these controllers is described in the following assumptions. Assumption 4 (Neglectable impact of m 13 , m 14 ). Formally, under Assumption 3 the accelerations of the bodies C 1 and C 2 given by q1 c = u1 and q2 c = u2 are affecting the dynamics of the body A due to the coefficients m 13 and m 14 of the matrix M (2). However, for the considered system these coefficients are small compared to other entries of the matrix M. Thus, in what follows we neglect this effect and assume m 13 = m 14 = 0.

Note that we apply this assumption for control design and model simplification, but not necessarily for simulations.

Taking into account these assumptions, the model can be reduced to qa = ω a , qb = ω b , qc,1 = u 1 , qc,2 = u 2 , M(q) ωa ωb = -C(q, q), where

M := m 11 m 12 m 12 m 22 , C := I 2 0 C † (q, q) + G † (q) + F † r ( q) = C 1 C 2 ,
and qc,1 and qc,1 denotes q1 c and q1 c , respectively.

Model simplification

Define the new parameters

p 1 = 2I b + 2I c + 2I d + K a + m l 2 2 , p 2 = 2I b + 2I d + 2J c + ml 2 , p 3 = J c + J d -I c -I d , p 4 = J d -I d p 5 = I c + J d , p 6 = I c + 2I d -J d . (3)
Rewrite now the matrix M as M := M 0 + M 1 (q), where

M 0 := p 1 0 0 p 2 , M 1 (q) :=        2p 3 -p 4 cos 2 (q c,1 ) + cos 2 (q c,2 ) cos 2 (q b ) 1 2 p 4 cos(q b ) sin(2q c,1 ) + sin(2q c,2 ) 1 2 p 4 cos(q b ) sin(2q c,1 ) + sin(2q c,2 ) p 4 cos 2 (q c,1 ) + cos 2 (q c,2 )        .
For our setup it can be shown that for all feasible q it holds

(M 0 + M 1 (q)) -1 -M -1 0 ≤ 0.04 M -1 0
Thus, for simplicity in what follows we will apply the following simplification:

M -1 (q) ≈ M -1 0 .
The vector C has the following expression:

C = f r (ω a ) -2 p 3 ω a ω b sin (2 q b ) -J d ω b ω d sin (q b ) (sin (q c1 ) -sin (q c2 )) + p 4 ω a ω b sin (2 q b ) cos 2 (q c1 ) + cos 2 (q c2 ) -p 4 1 2 ω b 2 sin (q b ) (sin (2 q c1 ) + sin (2 q c2 )) + p 4 ω a cos 2 (q b ) (u 1 sin (2 q c1 ) + u 2 sin (2 q c2 )) + 2p 4 ω b cos (q b ) u 1 cos 2 (q c1 ) + u 2 cos 2 (q c2 ) + J d ω d cos (q b ) (u 1 cos (q c1 ) -u 2 cos (q c2 )) -p 5 ω b cos (q b ) (u 1 + u 2 ) , - √ 2 g l m sin q b + π 4 + e + p 3 ω a 2 sin (2 q b ) + J d ω a ω d sin (q b ) (sin (q c1 ) -sin (q c2 )) -p 4 1 2 ω a 2 sin (2 q b ) cos 2 (q c1 ) + cos 2 (q c2 ) -p 4 ω b (u 1 sin (2 q c1 ) + u 2 sin (2 q c2 )) -J d ω d (u 1 sin (q c1 ) -u 2 sin (q c2 )) + 2 p 4 ω a cos (q b ) u 1 cos 2 (q c1 ) + u 2 cos 2 (q c2 ) -p 6 ω a cos (q b ) (u 1 + u 2 ) .
Let us define C 0 as follows:

C 0 := f r (ω a ) -J d ω b ω d sin (q b ) (sin (q c1 ) -sin (q c2 )) + J d ω d cos (q b ) (u 1 cos (q c1 ) -u 2 cos (q c2 )) , - √ 2 g l m sin q b + π 4 + e + J d ω a ω d sin (q b ) (sin (q c1 ) -sin (q c2 )) -J d ω d (u 1 sin (q c1 ) -u 2 sin (q c2 )) .
In our setup the velocities are bounded: it is reasonable to assume that |w a | and |w b | are inferior to 10 rad/s. Under this assumption it is easy to see that C -C 0 < 10 -3 and that we can apply the following simplification:

C ≈ C 0 .
Thus, the model can be reduced to

M 0 ωa ωb = -C 0 (q, q), (4)

Linearization-based stabilization

For the system (4), the desired equilibrium is defined as

Ω 0 := ω a = 0, q b = - π 4 -e, ω b = 0, q c1 = q c2 = π 2 .
In what follows we say that a control law (locally) stabilizes the system (4) if under this control law the point Ω 0 is (locally) attractive. Define

x 1 = q a , x 2 = qa , x 3 = q b + π 4 + e, x 4 = qb , x 5 = q c1 - π 2 , x 6 = q c2 - π 2 . (5)
Then the system's dynamics can be rewritten as

                         ẋ1 ẋ2 ẋ3 ẋ4 ẋ5 ẋ6                          =                          x 2 f a (x, u) x 4 f b (x, u) u 1 u 2                          , (6)
where f a ( 0, 0) = f b ( 0, 0) = 0 and the origin is an equilibrium (for zero input). The function f a and f b are defined as follows:

f a (x, u) := -f r (ω a ) + J d ω b ω d sin x 3 -π 4 -e (cos x 5 -cos x 6 ) -J d ω d cos x 3 -π 4 -e (u 2 sin x 6 -u 1 sin x 5 ) p 1 f b (x, u) := √ 2 g l m sin x 3 -J d ω a ω d sin x 3 -π 4 -e (cos x 5 -cos x 6 ) + J d ω d (u 1 cos x 5 -u 2 cos x 6 ) p 2
The control goal can be achieved if we start from the initial position x 5 (0) = x 6 (0) = 0 and impose a symmetry of control u 1 (t) = -u 2 (t). Then obviously x 6 (t) = -x 5 (t), ω a (t) = 0, and the system (6) can be reduced as follows:

          ẋ3 ẋ4 ẋ5           =            x 4 √ 2 g l m sin x 3 +2J d ω d u 1 cos x 5 p 2 u            (7)
The state variable x 5 can be computed through the measurements of the signal q c1 ; however, since the offset e is not known, the signal x 3 can not be computed. Thus, we define the vector of measurements as

y = q b + π 4 q c1 -π 2 = x 3 -e x 5 . (8)
Then the control goal is to find a control law that stabilizes (7) at the origin using the measurements y. A common practice to stabilize a (sufficiently well-behaved) nonlinear system is to linearize the system around the desired equilibrium. For the system (7) such equilibrium is given by x = 0, u = 0. Let us define

A :=            0 1 0 √ 2glm p 2 0 0 0 0 0            , B :=           0 2J d ω d p 2 1           (9)
Then the linearization of ( 7) around the origin is given by ẋ = Ax + Bu 1 . It is tempting to use the state-feedback static control

u 1 := -K y 1 x 2 y 2 = -K x -k 1 e, (10)
where K := k 1 k 2 k 3 is the gain vector. The problem, however, is that the equilibrium point would be (A -BK) -1 Bk 1 e = 0 0 -k 1 k 3 e. Therefore, the stabilization goal |x| → 0 is not achieved under the control law (10). In order to overcome the nonzero steady-state bodies C 1 and C 2 angle problem, we add an integral action. To this end, we introduce an auxiliary variable x e defined as ẋe := 0x 5 , where zero stays as the reference for x 5 . Then the extended state-space model is ẋ ẋe

= A 0 3×1 0 0 -1 0 A e x x e + B 0 B e u.
The pair A e , B e is controllable and we can design the extended control law

u 1 := -K e y 1 x 2 y 2 x e = -K e x x e -k e,1 e, (11)
where K e ∈ R 1×4 . Then the closed-loop dynamics is Thus, the state x converges to zero, while the integral action x e ensures the equilibrium offset compensation.

Experimental validation

The hardware for the tests 1 (shown in Fig. 2) is assembled from off-the-shelf components. The hardware parameters are summarized in the Table 1. A STM32F746 discovery board was chosen as the main computing unit. We have chosen a small brushless motor to drive the wheel D, the frames C 1 and C 2 are actuated by Dynamixel MX106-R servo motors. The inclination angle as well as the angular velocity of the body B are measured with an IMU.

We have implemented the control law (11), Fig. 3 provides the angle measurements y 1 and the corresponding control signal u 1 . The corresponding gain vector K e was chosen to be equal to [35, 4, -1, 0.3]. Note that after two seconds of the experiment an external force was applied for a short period of time, and the system has successfully recovered after that.

Conclusion

The main contribution of the paper is the model ( 6) simple enough for analysis on paper. We have validated the model through a hardware implementation that achieves the stabilization goal q b = -π 4e, ω a = 0, ω b = 0. Note that, while the pendulum is stabilized in the unstable equilibrium position, the proposed control law does not allow to control the angle q a . Straightforward linearization techniques fail when q a = 0 is added to the control goal; as a further research direction, we intend to study the possibility of full control of the system state.

Assumption 2 (

 2 Local control of bodies D 1 and D 2 ). For the bodies D 1 and D 2 , the local controllers ensure constant velocities q1 d = ω d , q2 d = -ω d for some constant ω d ; thus, q1 d = q2 d = 0 for all t. Assumption 3 (Local control of bodies C 1 and C 2 ). For the bodies C 1 and C 2 , the local controllers ensure the perfect reference tracking q1 c = u 1 , q2 c = u 2 , where u 1 and u 2 are further considered as the new input signals.

  ẋ ẋe = (A e -B e K e )x x e -B e k e,1 e, and the equilibrium is (A e -B e K e ) -1 B e k e,1 e = 0 0 0 -

Table 1 .

 1 Hardware parameters , J b , K b ] [13 10 13] • 10 -3 of the body C [I c , J c , K c ] [2.6 10 10] • 10 -4 of the body D [I d , J d , K d ] [5.6 11 5.6] • 10 -4

	Description

  τ 1 d and τ 2 d are applied to the bodies C 1 , C 2 , D 1 and D 2 , respectively; thus the dynamics obeys the Euler-Lagrange equations:

We have filmed the experiment, the video is available here: https://youtu.be/4eYPoMV1Sac.