ISSN 00360236, Russian Journal of Inorganic Chemistry, 2015, Vol. 60, No. 12, pp. 1514–1517. © Pleiades Publishing, Ltd., 2015. Original Russian Text © P.R. Smirnov, O.V. Grechin, 2015, published in Zhurnal Neorganicheskoi Khimii, 2015, Vol. 60, No. 12, pp. 1655–1658.
THEORETICAL INORGANIC CHEMISTRY
Structural Parameters of the Nearest Surrounding of Ions in Aqueous Solutions of Erbium Chloride According to Xray Diffraction P. R. Smirnova and O. V. Grechinb a
b
Krestov Institute of Solution Chemistry, Russian Academy of Sciences, Ivanovo, Russia Research Institute of Thermodynamics and Kinetics of Chemical Processes, Ivanovo State University of Chemistry and Technology, Ivanovo, Russia email:
[email protected] Received July 17, 2014
Abstract—The radial distribution functions of aqueous solutions of erbium chloride determined from Xray diffraction data in a broad range of concentrations under standard temperature and pressure were analyzed using the simulation approach. Based on the identified optimal models of structural units for the systems under study, it was found that the coordination number of erbium ion in concentrated and saturated solutions is close to six and increases to eight as solutions are diluted. A reduction in concentration causes the forma tion of a second coordination sphere around the cation and the formation of a first hydration sphere for the anion. All the systems contain noncontact ion associates. DOI: 10.1134/S0036023615120256
The structural characteristics of the nearest sur rounding of lanthanide ions in various solutions have been attracting researchers' attention both due to their practical significance (e.g., these ions are used in med icine) and their unique properties that are of interest for fundamental science (a long series of chemically similar ions exhibiting the lanthanide contraction effect). Hence, a number of studies have focused on this topic; Smirnov and Trostin made a review of these publications [1]. However, almost no data on the con centration dependence of the nearest surrounding of ions in aqueous solutions of lanthanide salts are cur rently available. With this in mind, we are performing a series of studies aimed at investigating the effect of concentration on the structural features of aqueous solutions of lanthanide salts [2–4]. This work aimed at determining the quantitative parameters of structural units in aqueous erbium chloride solutions over a broad range of concentrations under standard temper ature and pressure. Erbium chloride solutions were studied by Xray diffraction earlier [5, 6], but the con centration dependence of their structure has never been discussed in these works. The following averaged description of the hydrate structure is presented in [1]: the coordination number (CN) of Er3+ ion is 8.3, and the distance to the first coordination sphere Er3+–OH2 is 0.235 nm. This cat ion forms a second coordination sphere consisting of 14–16 water molecules that lie at an average distance of 0.449 nm. Solutions of erbium salts typically form ion pairs, both contact and noncontact.
tions were analyzed in [7]. The predominant coordi nation numbers of Cl– ion among the large range of the determined values were six and seven. The number of water molecules in the hydration sphere of the anion decreases with increasing concentration. The distance to them is 0.310–0.320 nm. The anion does not form a second coordination sphere. The chloride anion is prone to forming ion pairs. CALCULATIONS In order to solve the problem, we used simulated the experimental radial distribution functions (RDFs) of saturated solution (molar ratio: 1 : 14.7, concentra tion: 3.322 mol/L) and erbium chloride solutions with molar ratios 1 : 20 (2.54 mol/L), 1 : 40 (1.34 mol/L), and 1 : 80 (0.68 mol/L) derived from primary Xray data [8]. The simulation consisted in developing vari ous models of structural organization of the solutions under study, calculating theoretical structural and cor relation functions for each model, and elucidating optimal models based on the best fit between the the oretical and experimental functions. We used the mathematical tool built in the KURVLR software algorithm to calculate the experimental and simulated functions [9]. The structure functions i(s) were determined using the equation
The extensive available data on the structure of the nearest surrounding of chloride ion in aqueous solu 1514
i(s) = I coh(s) −
∑x f
i i
i
2
(s),
(1)
STRUCTURAL PARAMETERS OF THE NEAREST SURROUNDING OF IONS
where Icoh(s) is the coherent radiation scattering inten sity, fi(s) are the scattering factors of the ith atom, and s is the wave vector (s = 4πλ–1sinθ). The RDFs were calculated using the Fourier trans form according to the formula
1515
4πr 2 (ρ – ρ0) 50 0
s max
D(r ) = 4π r ρ 0 + 2r π 2
−1
∫
si(s)M (s) sin rsd s,
(2)
0
0
where ρ0 is the average scattering length density; M(s) is the modifying function determined as
∑
∑
M (s) = ⎡⎣ xi f i2(0) xi f i 2(s)⎤⎦ exp(− 100s 2 ), and smax is the maximal experimentally achievable value of s. The models of the nearest surrounding of ions in the solution were developed using data obtained by us and the available literature. The theoretical structural functions were calculated using the formula
i(s)calc =
∑∑ x n
i ij f i (s) f j (s)sin(rij s)(rij s)
i j i≠ j 2
× exp(−bij s ) −
∑∑ x x i
i
−1
3 −1 j f i (is) f j (s)4 j πR jV
(3)
j
× {sin(R j s) − R j s cos(R j s)} (R j s) exp(−B j s ). −3
2
The first term of the equation refers to shortrange interactions characterized by distance rij, temperature factor bij, and the number of interactions nij between atoms i and j. The second term of the equation corre sponds to the interaction between the spherical vol ume and the continuous electron density beyond this volume. Rj is the radius of spherical volume around the jth atom; Bj is the parameter describing the attenuation of continuous electron density. RESULTS AND DISCUSSION Saturated solution was initially considered to determine the base model. We used the available liter ature data and the experimental range of interatomic distances to develop the model that included the hydrate complex of erbium ion consisting of eight water molecules located at the distance 0.235 nm and hydrated chlorine ion with six solvent molecules lying at a distance of 0.310 nm from the anion. The counte rions formed the noncontact ion pair Er3+–H2O–Cl–. The cation in the model of the saturated solution lacked a second coordination sphere. In order to describe the excess electron density manifesting itself in the experimental functions at distances larger than 0.6 nm and being caused by the longrange order, we included various types of scattering species (e.g., cat ion–cation, cation–anion, and anion–anion) with large interparticle distances what was analyzed in pre vious work [8]. However, the RDFs calculated for that model did not agree with the experimental ones. The RUSSIAN JOURNAL OF INORGANIC CHEMISTRY
0 0 –50 0.2
0.4
0.6
0.8 r, nm
Experimental radial distribution functions (points) of aqueous erbium chloride solutions with molar ratios (1) 1 : 14.7 (saturated solution); (2) 1 : 20; (3) 1 : 40; and (4) 1 : 80 and the theoretical functions (solid curves) calcu lated for the optimal models.
first peak showing that the cation had the first coordi nation sphere and the shoulder on the righthand side of the peak, corresponding to the hydration surround ing of the anion, had far greater intensities in the cal culated functions compared to the experimental ones. This fact unambiguously indicated that the coordina tion numbers of the cation and anion in that specific system differed from those employed in the first model. Contrariwise, the second major peak was less intense in the calculated function. The intensity of the peak of the corresponding function could not be achieved when the model comprised the ion pair alone. We then developed a series of models with consec utively decreasing coordination numbers of the cation and anion and increasing number of chloride ions in the ion associate. The second coordination sphere of Er3+ ion was also included. What we mean by ion asso ciates in this study is ion pairs between cations and anions as well as more complex structures such as con tact and noncontact ion triplets. As a result, we eluci dated the model whose calculated functions provided the best fit with the experimental ones (figure). The parameters of the optimal model are listed in the table. Based on these findings one can draw a conclusion that the nearest surrounding of the cation includes six water molecules located at a distance of 0.235 nm from the cation; the cation starts to form a second coordi nation sphere, which consists of 4.2 solvent molecules in this system and lies 0.433 nm away. The anion starts to rearrange its own hydration shell that consists of 3.7 water molecules in a saturated solution. A noncon tact ion triplet with the distance between the cation and anions of 0.482 nm is formed in the system. It can be easily seen that the total number of water molecules Vol. 60
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SMIRNOV, GRECHIN
The main structural parameters of the nearest surrounding of ions in aqueous solutions of erbium chloride
Molar ratio Interaction type
1 : 14.7 r
1 : 20 n
r
1 : 40 n
Er3+–O
0.234
6.0
0.235
6.3
Er3+–OII Cl––O Er3+–Cl–
0.435 0.310 0.482
4.2 3.75 2.0
0.437 0.315 0.484
6.1 4.15 1.7
1 : 80
r
n
r
n
0.235 0.260 0.436 0.315 0.490
6.0 2.1 6.8 6.0 1.5
0.235 0.265 0.438 0.319 0.492
6.0 2.3 12.5 6.5 1.1
r is the interparticle distance (nm); n is the number of pairwise interactions at this distance.
in the surrounding of the ions (21.3) is greater than the molar ratio in the experimental solution (14.7). There is no contradiction, since some water molecules are shared with the neighboring ions; thus, a solvent mol ecule can be a component of both the second sphere of the cation and the hydration shell of the anion. When working with the model, we also considered the possibility that a contact ion pair where chloride ion is comprised by the first coordination sphere of the Er3+ ion could be formed in the solution. The distance between the cation and the anion Er3+–Cl– in this case was set close to the sum of ion radii of erbium and chloride ions (0.265 nm). Thus, the ion associate Er3+–Cl– contributed to the first RDF peak rather than to the second one. The number of solvent mole cules in the first coordination sphere of the cation in this case decreased assuming that they were replaced by the anion. In the functions calculated for this model, however, the first peak was shifted toward greater distances relative to the experimental values due to the significant contribution from interionic interactions. Hence, it follows that the structure of sat urated solution is independent of contact ion associ ates. They can be present in the solution but at a very low concentration so that it makes no contribution to the total scattering pattern and has no effect on the RDFs. The nonexistence of contact associates in this concentrated system was supported by numerous studies. Most experimental studies focused on lan thanide chlorides provide evidence that only non contact ion pairs are formed even in concentrated solutions of these ions [10–13]. The simulation approach was then used to analyze the solution with the 1 : 20 molar ratio. The optimal model obtained for the saturated solution with proper variation of concentrations of its components was used as the initial variant. The calculations demonstrated that the theoretical functions show good fit to the experimental ones. However, some correction was still needed. The model was improved by slightly changing the coordination number and interparticle distances, which yielded the optimal result (table). The structure of this system was similar to that of saturated solution.
Dilution insignificantly increased the average number of water molecules in the nearest surroundings of the cation and anion and reduced the number of chloride ions forming an associate with the cation. The next step was to analyze the functions of the solution with the 1 : 40 molar ratio. We calculated the functions for the model considered to be optimal for the solution with the 1 : 20 molar ratio. There was no fair agreement between the theoretical and experi mental RDFs. The peaks of the calculated functions were less intense. In the next model, the coordination number of the cation was increased to eight, but it did not yield the desired result either. The major peak of the calculated function was shifted toward smaller dis tances. Calculation of different variants while slightly correcting the model failed to find the proper coordi nation number. As a result, the model with distorted coordination sphere of the cation was developed, where six water molecules were located at a closer dis tance, while the remaining two lay farther away. It was not a fundamentally new idea for describing the near est surrounding of a lanthanide ion, since modern studies provide evidence that the coordination sphere of a light lanthanide is a threecap trigonal prism, where three water molecules occupying the “cap” positions also lie at greater distances [14, 15]. When moving toward heavy lanthanide ions, the binding between one of the molecules and the cation becomes weaker, so that this molecule leaves the coordination sphere of the cation, thus yielding the coordination number of the ion equal to eight. All these observa tions indicate that the first coordination sphere of a lanthanide ion can be conventionally subdivided into two portions: the stronger one consisting of six water molecules and the weaker one comprising two or three water molecules lying at greater distances. This assumption well explains why the coordination num ber of erbium ion decreases with rising concentration. At high concentrations, the cation retains the stronger coordination sphere, while losing two water molecules from the weaker portion. Next, we developed a model for the system with the 1 : 80 molar ratio. As in the previous cases, the model
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considered to be optimal for the previous solution was used as the base one. Although the calculated and the experimental functions were similar, the model still needed some optimization. It turned out in the opti mal variant that the number of water molecules in the second coordination sphere of the cation increased significantly. The number of chloride ions in the ion associate decreased and the associate became a hydra tionseparated ion pair. Hence, the saturated and concentrated (1 : 20 molar ratio) aqueous solutions of erbium chloride are struc turally a combination of noncontact ion associates of cations and anions with the average distance between them being 0.484 nm. The first coordination sphere of Er3+ ion includes six solvent molecules lying at dis tances of 0.234–0.235 nm away from the cation. The second coordination sphere of the cation and the hydration shell of the anion only start to be formed. In more dilute solutions, the number of water molecules in the first coordination sphere increases and can be as high as eight; two water molecules lie at greater dis tances (0.260–0.265 nm). The number of solvent mol ecules in the second sphere of the cation also becomes greater. The anion forms its own hydration shell. Non contact ion pairs continue to be a decisive factor for the structure of the systems with the molar ratios 1 : 40 and 1 : 80. REFERENCES 1. P. R. Smirnov and V. N. Trostin, Russ. J. Gen. Chem. 82, 360 (2012).
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Translated by D. Terpilovskaya
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