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Journal o f Structural Chonis~, VoL 37, No. 1, 1996

COMPUTER

SIMULATION OF THE STRUCTURE

OF THE HYDRATION SHELLS OF CALCIUM AND CALCIUM-WATER-ZEOLITE

A

G. G. Malenkov and M. M. Frank-Kamenetskii

UDC 514.183

A potential function is suggested to descdbe the interaction of the calcium ion with the water molecule using the tetrahedral model of the water molecule. Monte Carlo simulations of small clusters Ca(H20)n (n < 20) and analyses of the resulting F-structures showed that the coordination number of Ca is 8. The structure of water adsorbed in the a-cavity of zeolite CaA depends predominantly on interactions with Ca2+ ions. The water molecule forms one hydrogen bond with an oxygen atom of the framework; the molecules are not hydrogen-bonded with each other. In this respect the structure of water in the Ca form of zeolite A resembles that in the Na form but differs from that in the K form.

INTRODUCTION Na + and Ca 2+ are classical illustrations to the crystal-chemical law of diagonal series (e.g., [1]), which states that atoms of elements lying on a diagonal in the periodic table form similar crystal structures and can substitute each other in crystals. Indeed, an increased ionic charge seems to compensate the increased number of electrons, due to which the distances from the "diagonal" atoms to the same ligands are similar. Thus according to [2], in crystalline polyhydrates the average Na-O (with oxygen belon#ng to water) distance is 2.44/~,, and the Ca--O distance is 2.42/~. Analysis of a wider set of structural data for Na-containing crystalline hydrates [3] yielded an average Na--O distance of 2.41/~,. Ca-containing crystalline hydrates were reviewed by Eimpahr and Bugg [4]; the value given by these authors (2.41/~) is close to the value given by Drakin in [2]. However, the equality of distances between the ion and its neighbors does not imply that the ions have identical environments. It would be natural to expect that the increased ionic charge will compensate ligand repulsion in the first coordination sphere by enhancing the interaction of the ion with the neighboring ligands; as a result, configurations with higher coordination numbers are thought to be preferable. Indeed, in [2] the most probable coordination numbers of Na and Ca in aqueous solutions are stated to be 6 and 7, respectively. As follows from the histograms in [4], the coordination number of Ca is 8 (48%), 7 (37%), 9 or 6 (15% divided equally). In the overwhelming majority of sodium crystaillne hydrates, the coordination number of Na is 6 (with octnhedron as a coordination polyhedron) [2, 3], the exceptions being 5 and 8 [5]. We undertook a computer simulation to investigate the charge effect on the environment in a pair of "diagonal" ions. Earlier, we studied Na-H20 [3, 6, 7] and Na-H20-zeolite A [8, 9] systems. In this paper we report on the results of modeling of analogous systems containing Ca 2+ ions. Aqueous solutions of CaCIz were modeled by HeinTinger et al. [10-12]; they used a modified model of central forces. Dynamic modeling of the 4Ca-SCI--200H20 system in [11] gave the coordination number of Ca2+ (9); it was determined from the area under the first maximum of the pair radial distribution function of Ca--O (the maximum corresponds to the distance of 2.39/~). The coordination numbers obtained by different authors differ .~i~ificanfly (from 6 to 10), as foUows from the review [11] of experimental diffraction studies of the aqueous solutions of Ca 2+ salts. The data reported in [13] seem to be most reliable; it is shown that the coordination number of the Ca 2 + ion strongly depends on concentration, approaching 10 in diluted solutions (see also [14]). The potential used by Hein71nger et al. as well as other potentials based on quantum chemical calculations lead to slightly underestimated cation--oxygen distances [3], although they are less underestimated than the distances for Institute of Physical Chemistry, Russian Academy of Sciences. Translated from Zhurnal Strulaumoi Khimii, Vol. 37, No. 1, pp. 88-97, January-February, 1996. Original article submitted February 14, 1995. 76

0022-4766/96/3701-0076515.00 ~

Plenum Publishing Corporation

univalent ions. Bounds [15] modeled electrolyte (indudlng CaC12) solutions in the framework of molecular dynamic theory, using the TIP4P model of water and his own quantum chemical calculations. For Ca 2+ he obtained the coordination number 9.3 and the Ca-O distance of 2.54/~, which seems to be overestimated. In this paper we suggest semiempirieal potentials based on the interaction model that we used for modeling other systems [3, 5-8, 9, 16] and on structural data for crystal phases. POTENTIAL OF Ca 2 +-WATER INTERACTION The Bjerrum tetrahedral model with the parametrization proposed in [16] is used as a model of the water molecule. The interactions of the Ca 2 + ion with the water molecule include electrostatic interactions and nonvalent interactions of the ion with the oxygen atom, which are defined by the equation E = - A / R 6 + B. e x p ( - C / K ) .

TheA and C parameters were taken equal to the parameters of K + found earlier, which is isoelectronic to Ca 2+. The B parameter was determined in a series of Monte Carlo simulations of Ca(H20)n (n = 1-8) clusters at 300 K and znalyses of the corresponding F-structttres (for F-structures, see [3, 6, 7, 17]. We took two values of the B parameter, 210,000 (1) and 205,000 (2) (the distance R is measured in JL, and the energy E is given in kcal/mole; with the energy measured in kJ/mole, the B parameter will be 876,640 and 857,720, respectively). Value (2) seems to be closer to experimental data on the structure of the hydration shells of Ca in crystalline hydrates, with both potentials obviously leading to a stronger dependence of the average Ca-O distance on coordination number in the range of its values from 6 to 8 than the dependence expected from the experiment of [4] (Table 1). Probably, the model of interaction between water molecules employed by us leads to excessively strong repulsion between the molecules of the first hydration shell. It should be emphasized that the orientations induced by the strong repulsion between these molecules were not found in the ice modifications used for the refinement of the parameters of the water interaction model and hence were not included in the refinement. Nevertheless, the data on the structures of the Na and K hydration shells obtained with this model proved to be reliable [3, 6, 7]. STRUCTURE OF THE Ca HYDRATION SHELL. F-STRUCTURES The procedure for the construction ofF-structures is described in [3, 16, 17]. One of the conflgatrations obtained by modeling the Ca(H20 ) system was chosen as an initial configuration to construct the Markov chain of states corresponding to low temperatures. In this work we choose only the states with lower energies than the energy of each preceding state, i.e., the modeling actually corresponds to 0 K. Table 1 lists the data on the F-structures of Ca(H20), clusters [coordination number (CN) = n -< 8].

TABLE 1. Energies and Structural Parameters of the F-Structures of the Ca(H20), Clusters in Which All Water Molecules Lie in the First Coordination Sphere I Eto t n

Ew-i

Ew-w

(Rca-O)

(1)

(2)

(1)

(2)

(1)

(2)

(1)

(2)

-339.0 -501.6 -657.1 -812.6 -944.7

-349.4 -517.1 -676.7 -831.8 -969.8 1096.4 -1208.9

-342.3 -511.2 -675.5 -842.7 -1006.5 1165.0 -1312.5

-353.2 -527.1 -696.8 -868.2 -1035.8 -1198.0 -1346.0

3.3 9.2 18.8 34.3 61.9 94.5 135.0

3.3 9.6 20.1 36.4 63.5 101.6 137.1

2.39 2.39 2.40 2.42 2.45 2.48 2.52

2.35 2.36 2.37 2.38 2.42 2.46 2.50

2 3 4 5 6 7

-

1070.5

8

-

1177.5

-

-

Note. (1) B = 876,640; (2) B = 857,720. The energies are given in kJ, and the distances are given in ~. 77

"Freezing" of the/-structures of clusters with n > 8 usually give F-structures with CN 8. The coordination polyhedron of Ca is a more or less distorted tetragonal antiprism ("twisted" cube, Fig. 1). F-Structures with CN 6, 7, and 9 were obtained rather rarely. If the F-structure of the Na(H20) n cluster with CN 6 or 7 is chosen as an initial configuration for obtaining an F-structure, then "freezing" usually yields an F-structure of Ca(H20)n with CN 8. Thus the initial configurations with low coordination numbers are often found far from the local minima of potential energy, and during the search for such minima the structure of the hydration shell of the ion undergoes sitmificant rearrangements. The CN 9 is encountered in the F-structures of clusters with large n. Such configurations are stabilized by molecules forming the second hydration shell. During further "freezing" of the F-structure with n = 9 derived" from the F-structure with n = 20 and CN = 9 and after the removal of all molecules except those in the first hydration shell, one of the molecules withdrew from the ion to a distance of 3.44/~ and formed two hydrogen bonds. In this way we obtained the F-structures of hydration shells with the same coordination numbers as those found experimentally in crystalline hydrates. Table 2 gives the data on some F-structures of Ca(H20)n clusters with n > 8 and with different coordination numbers, and the structures are shown in Figs. 2 and 3 [calculations with potential (1)].

STRUCTURE OF Ca HYDRATION SHELLS. ENSEMBLES OF/-STRUCTURES The modeling at 300 K also testifies that a natural coordination number for our model is 8. This follows not only from the values given in the CN column but also from the sharp increase in the number of hydrogen bonds on going from n = 8 to n = 9. The second peak on the distribution functions of Ca-O distances becomes pronounced at n = 9. We do not give the functions here, since they are trivial. For the Ca(H20)n clusters (n >_ 12), the first peak of the function is observed at Rca_ 0 = 4.475-4.50 A. In most/-structures under analysis, the first coordination sphere of the hydration shell is revealed unambiguously, and the CN is 8. As in the case of Na(H20)n and K(H20)n model systems [6], we observe a tendency toward a certain increase in the coordination number (see the CN column~ Table 2) as the number of molecules increases (n > 8). With Ca this tendency is more pronounced than with Na or K. Therefore, at large n, configurations with CN = 9 are expected more frequently. The same is indicated by the relatively low energy of the F-structure of the Ca(H20)20 cluster with CN = 9 (Table 3). Recall that the calculations of the N a - H 2 0 systems using a similar model gave 6 as the most probable CN of Na and octahedron as a coordination polyhedron. Thus, according to experimental results, when Na is replaced by its nearest neighbor on the diagonal, the coordination number of the ion increases, whereas the ion-oxygen distances remain nearly the same. This increase is a consequence of the enhanced ion-water interaction, which compensates the mutual repulsion of excess water molecules forming the first hydration shell. Indeed, for the Na(H20)n model clusters, the energies of water-water interactions become negative at n >_. 11 [6], whereas in the case of the Ca cluster this energy is positive even at n = 20.

b

~1

C

Oe

Fig. 1. Coordination polyhedra for Ca surrounded by eight water molecules: a) ideal antiprism; b) in the F-structure of Ca(H20)20; c) in the F-structure of Ca(H20)16; 1 - oxygen of the water molecule; 2 - Ca 2 +. 78

TABLE 2. Energies and Structural Characteristics of the F-Structures of Ca(H20)n Clusters with Different

Coordination Numbers n

CN

E,o,

E~_~

E~_w

(Rc~_o)

Nim

8

6 7 8

- 1179.6 - 1188.8 - 1208.9

- 1206.8 - 1274.5 - 1346.0

27.2 85.7 32.8

238 2.45 2.51

4 2 0

- 1662.4

14

7 8 9

- 1693.7 - 1675.3

- 1662.8 - 1761.5 - 1772.7

0.4 67.8 97.4

2.44 2.50 2.57

14 12 10

16

8 9

- 1817.9 -- 18033

- 1802.0 - 1846.4

-15.9 43.1

2.50 2.60

16 14

-2008.8 -2041.1

- 1882.3

-126.6 10.4

2.51 2.58

22 21

20

-2051.5

Note: energies given in kJ, and distances in /~; NHB is the number of hydrogen bonds in the cluster.

S T R U C T U R E O F W A T E R A D S O R B E D IN T H E CAVITIES OF T H E CaA Z E O L I T E

Experimental investigations of water adsorption in zeolite A cavities revealed certain tendencies due to the presence of pronounced adsorption sites. Analysis of the experimental dependence of the heat of adsorption on occupation [18] for zeolite NaA and the results of the computer simulation of adsorption in the cavities of NaA and KA zeolites [8, 9] show that the structural and energy characteristics of the adsorption sites are determined mainly by the number, location, and nature of exchange cations. The numerical experiment is characterized by the possibility to separate different contributions to the total potential energy of the system and to analyze the geometrical peculiarities of the structure directly from the set of coordinates. We analyzed the results of previous computer simulations for the NaA and KA zeolites; it appeared that some adsorption characteristics such as the total potential energy of the system, the order of occupation of adsorption sites, and some other characteristics depend predominantly on the energy of interactions between the adsorbed water molecules and the exchange cations. Molecular orientations, the types of interactions with the framework, the number of water molecules in the first hydration shell of ions, and the energies of interactions between the water molecules are determined mainly by the effective radii of the exchange cations. K + and Na + are charged equally and, consequently, have close energies of interactions with water molecules but very different effective radii. To examine how the relationship between the geometries and energies of the exchange cations affect the adsorption characteristics, it is interesting to compare the data on the water adsorption on the Na and Ca forms of zeolite A, which have ions with close sizes but very different "energies of interactions with water

b

o

Fig. 2. Coordination polyhedra for Ca surrounded by 7 (a), 8 (b, in

a different aspect compared to Fig. 1), and 9 (c) water molecules. 79

a

L;

r

d

Fig. 3. F-structures of Ca(H20)n clusters: a) n = 14, CN = 7; b) n = 1 4 , CN = 8;c) n = 16, C N = 9 ; d ) n =20, CN = 8 .

molecules (25 and 82 kJ/mole). For that purpose we performed Monte Carlo simulations of the state of water in the large (a) cavity of zeolite A. As in previous works [8, 9], the model system is represented by one zeolite unit cell: 48 oxygen atoms and 24 silicon and alumlnttm atoms. The thermal motions of the framework atoms were ignored. For interactions with Si and AI atoms, we used the same potential functions; in other words, these atoms were not discriminated. The charge of the Ca ion is + 2; therefore there are six ions per unit cell (based on the electroneutrality analysis). According to X-ray diffraction studies [19], the ions are arranged as follows: one ion lies at the base of the 8-membered ring, occupancy 1/12; one ion lies in the vicinity of the 4-membered ring, occupancy 1/12; four ions lie in the vicinity of the the 6-membered ring, occupancy 1/2. In our calculations we used an initial arrangement of ions with which all six ions are located near the 6-membered rings so that the two unoccupied sites lie on the diagonal of the large cavity. This arrangement corresponds to the potential energy mininimum of the system. For Monte Carlo simulations, we employed the algorithm described in [8, 9]. The simulation was performed to examine the state of water adsorbed in the large cavities of the zeolite with occupancies (n) from 0 (completely dehydrated zeolite) to 24 water molecules per trait cell (mol./u.c.) at 300 K. 80

TABLE 3. Characteristics of Ca(HzO)n Clusters Obtained by Simulation at 300 K CN*

Etot

Ew-i

8

-266.6

9 10 12 14 16 20

-291.3 -302.7 -334.9 -361.9 -386.9 -436.5

-299.3 -322.7 -330.1 -360.6 -385.2 -406.4 -451.0

32.7 31.4 27.5 25.7 23.3 19.5 145

7.93 7.87 7.79 8.03 8.06 8.13 8.23

0.05 1.6 2.2 6.2 8.5 ~ 15.6

*The average number of oxygen atoms lying not farther than 3/~. from Ca. **Criteria for hydrogen bonds: Roo < 3.3 ~, ROH < 2.6 A, E < - 4 kJ/mole.

Figure 4 shows the plots of different energy terms of the total potential energy of the system

(Ew-i, Ew-z,

E,j_~) and the difference between the potential energy of the zeolite with the given occupancy and that of the completely dehydrated zeolite per water molecule (E0) versus the number of water molecules adsorbed in the zeolite cavity. As in the case of the Na and K forms, the main contribution to the potential energy of the system is from the interaction of water molecules with exchange cations (Ew-i). The total contributions of the interactions of the water molecules with the zeolite framework (Ew_z) and with each other

(Ew-w)is only 20% of the total potential energy. The inflection

of the curve at 3-4 mol./u.c., which is typical for the Na and K forms, is absent; this is explained by the fact that in the case of Ca all ions are in crystaUographicaUy equivalent positions and at the initial stages of adsorption the water molecules sequentially occupy the most advantageous sites in the vicinity of each of the six ions. The slight inflection

-220.0-

Eo

-

a

180.0

-14~l~

i

"

o

'2

'

'4

'

b

'

3 Ew -z

-JO.O

-70,C Ez~-w

0-

0

I

~

~

~

l

76

,'7

Fig. 4. Contributiom to the potential energy (kJ/mole) vs the number of H20 molecules (n) adsorbed in a large cavity of zeolite CaA per molecule. E 0 is the difference between the potential energies of a system with a given occupancy and a completely dehydrated system; Ew-i, Ew-z, and Ew-w are the energies of water interactions with the Caz+ ions, zeolite framework atoms, and with each other, respectively. 81

TABLE 4. Energies of Water Interactions with the Silicon-Oxygen Framework for Different Cationic Forms of Zeolite A (per molecule) Eve-z, kJ/mole

2 4

6 8

12

Ca

Na

K

-30.6 -30.1 -28.4 -25.9 -23.5

-32.3 -31.4 -30.9 -29.7 -27.4

-39.1 -39.1 -38.6 -37.0 -36.8

of the E 0 and Ew_ i curves in the region of occupancies 6-8 mol./u.c, corresponds to the start of the addition of the second water molecule to the hydration shell of Ca 2 + ions. The pronounced increase in the energies of interactions of adsorbed water molecules with each other and the slight decrease in the energies of water-zeolite interactions (Ew_ w and Ew_ z in Fig. 4b) in the region 12-15 mol./u.c. mean the start of the addition of the third water molecule to the hydration shell of Ca ions. As with the Na and K forms of the zeolite, only two water molecules with optimal orientations relative to the framework atoms can lie near the ions located in the vicinity of the 6-membered rings. In the case of other ionic forms, at high occupancies the water molecules may be located near the ions lying in the vicinity of the 8-membered rings. In our model of the Ca form, such ions are absent, and there are fewer ions. Therefore, the effect of decreased Eve_ z and increased Eve_ve will be more pronounced. Notwithstanding the high total energy of the water-water interaction in the Ca form, the number of molecular pairs forming hydrogen bonds (i.e., such molecules whose pair energy of interaction is less than - 12 lO/mole) is the same for all ionic forms, being not more than four pairs at the maximal occupancy (24 molecules/unit cell). Table 4 lists the average energies of water interactions with zeolite frameworks of different ionic forms. For the Na and K forms, the table gives data .only for the water molecules that lie near the ions located in the vicinity of the 6-membered rings, so that the numbers of molecules indicated in the table correspond to high occupancies. It can be seen that the values of Eve-z are very close for the Na and Ca forms. The lower absolute values of Eve_z of the Ca form are explained by the stronger interaction with the ion, which hinders the optimal orientation of water molecules relative to the framework atoms to a greater extent. This effect is of the same character as the above increase in the coordination number on going from the Na to Ca form in solution. In general, an analysis of instant configurations (Fig. 5) shows that in both cases an absorbed water molecule forms one hydrogen bond with oxygen of the zeolite framework, whereas in the KA zeolite the water molecule of the hydration shell of the ion lying near the 6-membered ring forms two hydrogen bonds and the energies of water interactions with the zeolite framework are sis higher. Thus the orientation of water molecules relative to framework atoms is determined mainly by the ratio of the effective radius of the exchange cation and the geometrical characteristics of the silicon-oxygen framework but not by

HzO ,,

2.85 A

Fig. 5. Characteristic orientation of the water molecule relative to the Ca 2 + ion and atoms of the 6-membered ring of the zeolite framework (different projections). 82

the value of the interaction energy. The structural similarity of the water adsorbed in the cavities of NaA and CaA, observed in the simulation, is one more example of the action of the diagonal series law, since the similarity between the radii of the "diagonal" ions in this case is responsible for some structural distinctions of the system. Tiffs work was accomplished with financial support from the Russian Fund for Basic Research (Grant No. 94-03-08996). REFERENCES 1~

2. . 4.

5. . 7. .

9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

G. V. Bokii, in: Introduction to Crystal Chemistry [in Russian], Moscow State University, Moscow (1954), p. 177. S. I. Drakin, in: Problems of Solvation and Complexation [in Russian], G. A. Krestov (ed.), Ivanovo Chemical Technological Institute, Ivanovo (1978), pp. 56-61. G. G. Malenkov, in: The Chemical Physics ofSolvation, PartA, R. Dogonadze et al. (eds.), Elsevier, Amsterdam (1985), pp. 355-389. H. Einspahr and C. E. Bugg, Acta Crystallogr., B36, 264-271 (1980). G. G. Maleakov, in: The Chemical Physics of Solvation, Part C, R. Dogonadze et al. (eds.), Elsevier, Amsterdam (1988), pp. 665-682. G. G. Malenkov, in: Water in Disperse Systems [in Russian], B. V. Deryagin et al. (eds.), Khlmiya, Moscow (1989), pp. 89-97. G. G. Malenkov, Conference Proceedings Series, Italian Physical Society, Vol. 43, M. U. palma et al. (eds.), Roma (1993), pp. 37-40. M. M. Frank-Kamenetskii and G. G. Malenkov, Dotd. Akad. Nauk SSSR, 299, No. 5, 1182-1185 (1988). M. M. Frank-Kamenetskii and G. G. Malenkov, Izv. AkacL Nauk SSSR, Set. Khim., No. 8, 1724-1738 (1989). M. M. Probst, P. Bopp, K_ Heinzlnger, and B. M. Rode, Chem. Phys. Lett., 106, 317-320 (1984). M. M. Probst, T. Radnai, K. Heinrlnger, P. Bopp, and B. M. Rode, J. Phys. Chem., 89, 753-759 (1985). K. Heinzinger and G. pallnkas, Chem. Phys. Lett., 126, 251-254 (1986). N. A. Hewish, G. W. Neilson, and J. E. Enderby, Nature, 297, 138-141 (1982). G. W. Neilson, Z. Naturforsch., 46a, 100-106 (1991). D. G. Bounds, Mol. Phys., 54, No. 6, 1335-1355 (1985). L. P. Diyakonova and G. G. Malenkov, Zh. Strulct. Khim., 20, No. 5, 854-861 (1979). G. G. Malenkov, A. V. Teplukhin, and V. I. Poltev, ibid., 30, No. 5, 89-97 (1989). M. M. Dubinin, A. A. Isirikyan, G. U. Rakhmatkariev, and V. V. Serpinskii, Izv. Akad. Nauk SSSR, Set. Khim., 1269 (1972). V. Subramanian and K. Serf, Z Phys. Chem., 81, No. 24, 2249 (1977).

Translated by L. Smolina

83