Kinetic and Thermodynamic Control in Rare Earth Cyamelurates Synthesis

Albina S. Isbjakowa Lomonosov Moscow State University Department of Chemistry: Moskovskij gosudarstvennyj universitet imeni M V Lomonosova Himiceskij fakul'tet Vladimir V. Chernyshev Lomonosov Moscow State University Department of Chemistry: Moskovskij gosudarstvennyj universitet imeni M V Lomonosova Himiceskij fakul'tet Victor A. Tafeenko Lomonosov Moscow State University Department of Chemistry: Moskovskij gosudarstvennyj universitet imeni M V Lomonosova Himiceskij fakul'tet Leonid A Aslanov (  aslanov.38@mail.ru ) Lomonosov Moscow State University Department of Chemistry: Moskovskij gosudarstvennyj universitet imeni M V Lomonosova Himiceskij fakul'tet https://orcid.org/0000-0002-0614-2902


Introduction
Heptazine-based compounds, mostly polymer melon (known as graphite-like carbon nitride g-C 3 N 4 ), have gained great popularity in recent years due to their promising practical applications in catalysis, including photocatalysis, preparation of hybrid membranes, sensors, materials for bioimaging etc. [1][2][3][4]. Also noteworthy are compounds with monomeric analogs of heptazine, for example, with 2,5,8-trihydroxy-sheptazine or cyameluric acid. Recently obtained metal-organic frameworks (MOFs) based on lanthanide ions and cyamelurate anion linkers showed high selectivity in the separation of a CO 2 /CH 4 gas mixture [5]. In addition, cyameluric acid derivatives exhibit reversible chromic behaviour [6] and have thermal stability up to 500°C [7].
Metal cyamelurates are interesting not only because of their properties, but also due to the variety of substances that exist in the metal cation -cyamelurate anion -water system. By slightly changing the synthesis conditions, completely different products can be obtained. For example, we isolated manganese cyamelurate KMn(C 6 N 7 O 3 )·5H 2 O [8], the composition and diffraction pattern of which is similar to the results of the work [9], but different from the crystals described in [6]. On the other hand, samples of cobalt cyamelurate synthesized in [9] and [8] are divers: energy dispersive spectroscopy indicates the absence of potassium cations in the cobalt cyamelurate sample [9], whereas in our case the composition corresponds to KCo(C 6 N 7 O 3 )·5H 2 O [8]. Most likely, the reaction time, which was various in these three works, is the main parameter determining the synthesis of a particular substance.
Short reaction times as well as low temperatures are the main characteristics of kinetic control, allowing the isolation of metastable substances that precede the thermodynamically stable phase [10,11].
Accordingly, long reaction times and high temperatures result in thermodynamically stable products. The diversity of metal cyamelurates can be explained from the point of view of kinetic and thermodynamic control. Low solubility of cyameluric acid salts, which complicates the dissolution-recrystallization processes, promotes the release of kinetic products, but at the same time complicates the study of their structures due to the absence of large single crystals and, frequently, due to the presence of other coprecipitating phases.
In our previous studies, most of the samples obtained at room temperature (i.e. under kinetic control) contained an impurity amorphous phase [8,12]. This fact, as well as the difference in the structure and composition of zinc cyamelurates depending on the reaction time, allowed us to put forward a hypothesis about the nonclassical nucleation of crystals inside micelles surrounded by an electric double layer [12].
This hypothesis can also be applied to lanthanide melonates. It is clearly shown in the work [13] that the as-synthesized neodymium and praseodymium melonate precipitates contain an amorphous phase, and after a several days of aging at room temperature samples transform into phase isostructural to LnC 6 N 7 (NCN) 3 ·8H 2 O. The fraction of the amorphous phase during aging is signi cantly reduced, which is very similar to slow transformation of amorphous phase to crystalline one or crystal-amorphous-crystal phase transition [14].
One gets the impression that the isotypic rare-earth melonates LnC 6 N 7 (NCN) 3 ·8H 2 O (Ln=La, Ce, Pr, Nd, Sm) are thermodynamically stable, since LaC 6 N 7 (NCN) 3 ·8H 2 O crystals suitable for X-ray diffraction analysis can be grown by the slow diffusion technique (provides equilibration), and LnC 6 N 7 (NCN) 3 ·8H 2 O (Ln=Nd, Pr) precipitate at a synthesis temperature of about 80 °С. In addition, SmC 6 N 7 (NCN) 3 ·8H 2 O phase is formed under hydrothermal conditions using sample prepared at room temperature as starting material. The authors also note that kinetic products contain more water molecules and correspond to the composition LnC 6 N 7 (NCN) 3 ·12H 2 O (Ln=Pr, Nd, Sm, Eu) [13]. But as in the case of metal cyamelurates obtained under kinetic control [8,12], polycrystalline samples of lanthanide melonates did not contain crystals, large enough for single-crystal X-ray diffraction analysis. Therefore the structure of LnC 6 N 7 (NCN) 3 ·12H 2 O is not solved.
Another example of thermodynamic control in synthesis of cyameluric acid salts is preparation of lanthanide MOFs [5]. Keeping the reaction mixture at 80°C for 24 hours followed by slow cooling resulted in a single-phase sample containing crystals of identical morphology, 50-150 µm in size. MOFs with common formula [Ln(H 2 O) 2 C 6 N 7 O 3 ] n (Ln=La, Ce, Pr) are isostructural and crystallize in the tetragonal P4 3 22 space group.
As in the case of lanthanide melonates, metastable cyamelurates are likely to exist, which can be isolated under kinetic control using room temperature and short reaction times. It is also interesting whether compounds similar to MOFs [5] can be obtained using increased temperatures but with the same reaction time as in kinetic control synthesis. Therefore the aim of this work is synthesis and structural study of lanthanide cyamelurates obtained under kinetic and thermodynamic control.

Synthesis of potassium cyamelurate
Potassium cyamelurate (K 3 C 6 N 7 O 3 ) was obtained by re uxing melon powder in aqueous KOH solution (2.5 molar) for several hours as described in [17]. The reaction mixture was exposed to hot ltration. After cooling to 0 ˚C colorless precipitatewas ltered and washed with ethanol, acetone and dried in air at 180 C.

Synthesis of rare-earth cyamelurates
Dry potassium cyamelurate was used in the synthesis. To obtain cyamelurates of rare-earth metals either nitrates or chlorides of the corresponding elements were used. All reactions were carried out both at Characterization Powder X-ray Diffraction. Powder X-ray diffraction measurements were carried at ambient conditions at two laboratory diffractometers -Huber G670 Guinier camera (CoK α1 radiation) and EMPYREAN (PANalytical, Ni-ltered CuK α radiation). Data collection details for Er1, Gd1, Pr1, Er2, Nd2 and La2 are given in Table S1. Unit cell dimensions were determined using three indexing programs: TREOR90 [18], ITO [20], and AUTOX [21,22]. The unit cell parameters and space groups were tested with the use of the Pawley t [23] and con rmed by the crystal structure solution. We came to the crystal structures for Er1, Gd1, Pr1, Er2, Nd2 and La2 by using a simulated annealing technique [24]. The model used for the cyamelurate molecule, in a direct space search without H atoms, was taken from the literature [1]. A bondrestrained Rietveld re nement implemented within MRIA [25]  Chemical analysis turned out to be ineffective for determining the compositions of the obtained polycrystalline samples due to presence of unknown amorphous phase; therefore, the chemical compositions of the crystalline phases were determined solely by the results of X-ray diffraction analysis.

Er1 structure
The formula of erbium cyamelurate synthesized at room temperature can be represented as , since Er1 contains neutral complexes. The coordination number of metal atom is 9, it is surrounded by 7 water molecules and is coordinated by the cyamelurate anion through the oxygen O2 and nitrogen N2 atoms (Fig. 1).
In the Er1 structure, at anions are arranged in stacks, which are displaced and rotated relative to each other by an angle of 180° (Fig. 2a). The distances between two neighbor anions in the stack are 3.19 Å and 3.36 Å (Fig. 2b). Adjacent stacks are arranged so that an angle of 34.13° is formed between the anions.
It is interesting to note that cyamelurate anions do not form endless chains typical for known cobalt(II) and cupper(II) cyamelurates [8], arising due to the polydentity of C 6 N 7 O 3 3− anion, and hence the ability to act as a bridging ligand. Hydrogen bonds connect individual [Er(H 2 O) 7 C 6 N 7 O 3 ] molecules together, and they are formed between all water molecules and oxygen and nitrogen atoms of the anion (except N1, N2, N4 atoms).

Er2 structure
The structure of erbium cyamelurate Er2 obtained at elevated temperatures is shown in Figure 3.
Erbium atom is surrounded by 4 water molecules and is bound to two cyamelurate anions through the oxygen atoms O3, O2 and nitrogen atoms N5, N2 (coordination number is 8). The angle between the planar cyamelurate anions bound to the erbium cation is 75.26°. Such self-organization of alternating cations and bridging cyamelurate anions leads to endless undulating chains (Fig. 4a). The distance between planar anions of adjacent chains is 3.19 Å (Fig. 4b). Outer-sphere O8 water molecules are located between the chains. Although this complex is also neutral, but it consists of in nite polymer-like chains, therefore it can be represented by the formula [Er(H 2 O) 4 C 6 N 7 O 3 ] n ·nH 2 O.

Nd2 structure
The structure of neodymium cyamelurate N2 obtained by boiling the reaction mixture is shown in the Figure 5.
The chains are tied together by hydrogen bonds between nitrogen (except N1, N2) and oxygen atoms of anions and all ve water molecules.
La2 structure The structure of lanthanum cyamelurate is shown in Figure 7. The composition of La2 based on structural data corresponds to the formula [La(H 2 O) 6 C 6 N 7 O 3 ]·H 2 O.
One lanthanum atom is coordinated by two cyamelurate anions through O1, O1 iv and N2, N2 iv atoms (where iv = x, -y, 0.5-z). Six water molecules complete the rst coordination sphere. The coordination number of central atom is 10. One water molecule is located in the cavities formed between the stacks of anions and is held in the structure via hydrogen bonding O7-H7…O2, O7-H7…N3, O4 ii -H4A ii …O7 (Fig. 7).
Neighboring lanthanum polyhedra have one common O1 vertex. Flat ribbons are realized in the structure (Fig. 8a). The ribbons are stacked (Fig. 8b), and the adjacent anions are located one above the other so that the distance between the ribbons displaced relative to each other is roughly equal to 3.3Å or 0.5a, where a -unit cell parameter.

Structure comparison
As in the case of lanthanide melonates [13], some rare-earth cyamelurates have different structures depending on the synthesis temperature. Both thermodynamic and kinetic products were isolated in the case of Nd, Pr,Y, Ho, Er, Tm, Yb, Lu cyamelurates.
Despite the variety of structures, it is possible to distinguish common features among kinetic and thermodynamic products. as a bridging ligand and binds neighboring cations. Also, metastable phases of lanthanide cyamelurates (as well as melonates [13]) contain more water molecules compared to thermodynamically stable ones.
In the case of yttrium and heavy lanthanides Ho and Er, the ion radius most likely affects the decrease in the coordination number from 9 to 8 with an increase in the reaction temperature. Since the central metal atom is surrounded by two large anions, and not one, as in the kinetic product, steric hindrances arise. The water molecule, which could be in the rst coordination sphere, is held by hydrogen bonds in the second coordination sphere. On the other hand, the coordination number of neodymium and praseodymium cations is maintained as in the structure obtained at room temperature, although each atom is coordinated by three anions.
In each groups of isostructural complexes, from light to heavy lanthanides, the unit cell parameters decrease (Tables S2-S4), which is consistent with a lanthanide contraction. Also, powders of the rst group, obtained at room temperature have unit cell parameters slightly less (by a few hundredths of an angstrom) as those synthesized at elevated temperatures.
Powders of samarium, europium, gadolinium, terbium, and dysprosium cyamelurates obtained both at room and elevated temperature have the same structure, isotypic to Er1. Therefore, this crystalline modi cation for the listed lanthanides is stable and rapidly forming, and this is the common case when thermodynamic and kinetic products are the same [11]. This also applies to lanthanum cyamelurate, which differs from the other rare-earth cyamelurates presented in this work. On the other hand, it is possible that the boiling point of the reacting mixture is insu cient to obtain the most stable modi cation, and, as in the case of samarium melonate [13], hydrothermal conditions are required. However, our attempt to synthesize nickel cyamelurate under hydrothermal conditions led to the hydrolysis of the cyameluric acid residue [12]. For this reason, we abandoned this type of synthesis.
It is possible that nucleation of rare-earth cyamelurates, as well as zinc cyamelurates [12], takes place in colloidal electric double layer micelles formed in solution. Sequential complexation reactions occur inside such micelles. First, coordination of one anion to the cation aqua-complex lead to the gradual displacement of water molecules, and second, with an increase in temperature, the monomeric complex is transformed into polymeric one due to binding of neighboring monomers via polydentate bridging anions. The second stage also proceeds with the displacement of water molecules from the inner sphere of the complexes. This is clearly seen when comparing the structures of Er1 and Er2, Nd1 (isostructural to Er1) and Nd2.
The π-π stacking of anions in the crystal structures of different metal and ammonium cyamelurates was already mentioned in this article as well as in our previous ones [1,8,12]. Coulomb interactions between cations and anions and hydrogen bonds present in all obtained structures, but in Ni(C 6 N 7 O 3 H)·5H 2 O [12] Coulomb interactions make a crucial contribution to the crystals potential energy; as a result, this crystal structure is a derivative of the CsCl-type structures (Fig. S14). Other studied structures (Fig. S15-S19) could not be attributed to known structural types, which is inevitable if Coulomb interactions exist not between individual cations and anions, but between ion aggregates collected in stacking columns under the in uence of quadrupole [29] or diradicaloid interactions [30], as well as hydrophobic-hydrophilic balance. This means that relatively weak stacking effect can determine the type of crystal structure without a determinative contribution to the potential energy of crystals.

Conclusion
Lanthanide cyamelurates demonstrate the in uence of kinetic and thermodynamic factors on crystal composition and structure, similar to the previously observed regularities [8,12]. The assembly of cyamelurate anions into stacking columns generally determines the peculiarities of their interaction with cations and the formation of hydrogen bonds.

Declarations
Funding This work was nancialy supported by Russian Foundation for Basic Research (grant 20-08-00097) and by M.V. Lomonosov Moscow State University Program of Development.
Con icts of interest The authors have no con icts of interest to declare that are relevant to the content of this article.  Numbering of atoms in a structure of Nd2. Symmetry codes: i = -x, 1-y, 1-z; ii = x, y, -1+z Structure of La2. For visual perception of the polyhedron, the coordination bonds of the central atomligand are not shown. Hydrogen bonds are indicated by black dashed lines. Symmetry codes: i=1-x, 0.5y, z; ii=1-x, 0.5+y, 0.5-z; iii=1-x, 1.5-y, z; iv=x, -y, 0.5-z; v=1-x, -0.5+y, 0.5-z; vi=x, 1-y, 0,5-z