3. Discussion
- (1)
The information of the optimized structures of Cu-bearing species
It has been accepted that isotope fractionation can be affected by changes in the elemental compositions or structures of molecules and molecular clusters. Many previous studies have also confirmed such a phenomenon [
6,
8,
23]. Therefore, it is of great theoretical and practical significance to study the isotope effects of different Cu-bearing species in solution/hydrothermal solution systems based on first principles.
Table S1 shows the optimized energy data of potential Cu-bearing (Cu(I) and Cu(II)) complexes calculated in this study (see
Figure 1 for the inner layer coordination). The theoretical basis set for all structural optimization and energy calculation is b3lyp/6-311+g(d). The energies of clusters with 6, 12, 18, 24, 32, 36, and 42 water molecules are shown in
Table S1. To ensure the accuracy of the final calculation, four parallel calculations (represented by A, B, C, and D, respectively) were carried out when executing the energy structure optimization and the simple harmonic vibration frequency calculation. Hence, a total of more than 532 molecular clusters were optimized. The purpose of this operation is that when using the water drop method to treat solvation effects, many different conformations are used to simulate aqueous complexes, which can reduce the error that may be caused by conformational differences in a solution. The optimized structure energies of all molecular clusters are listed in
Table S1 in the
Supplementary Materials.
All Cu-bearing complex aqueous solution models with 42 water molecules are surrounded by multiple layers of water molecules. These water molecules are connected by hydrogen bonds to form four-, five-, and six-member rings. The four-, five-, and six-member rings in the optimized Cu-bearing complex aqueous solutions are very stable. This is also consistent with the previous research result that liquid water has a cyclic structure [
24]. All the calculated harmonic frequencies have no virtual frequency, which indicates that the optimized structure is at least at a local minimum on the potential energy surface.
In the theoretical study of isotope fractionation, the change in bond length is also an important factor that directly affects the isotope fractionation effect. The theoretically optimized bond lengths of four representative Cu(I) complexes ([CuCl]
0, [CuCl
2]
−, [CuCl
3]
2−, and [Cu(HS)
2]
−) and a typical Cu(II) complex ([Cu(H
2O)
6]
2+) were compared with previous theoretical and experimental results to verify the rationality of the proposed method.
Table 1 shows the comparison of species bond lengths between the theoretical and experimental results of this study and those of previous studies. For Cu(I) complexes such as [CuCl]
0, [CuCl
2]
−, [CuCl
3]
2−, and [Cu(HS)
2]
−, the corresponding bond lengths of Cu-Cl, Cu-Cl, Cu-Cl, and Cu-S are 2.101 Å, 2.167 Å, 2.408 Å, and 2.213 Å, respectively. Corresponding previous research data were 2.095 Å [
13] (2.052 Å [
21]), 2.165 Å [
13]) (2.13 Å [
22]), 2.403 Å [
13], and 2.207 Å [
13], respectively. For [Cu(H
2O)
6]
2+, the molecular cluster is a typical octahedral structure. Cu(II) is located in the center of the molecular cluster, and four oxygen atoms form a plane with Cu(II), and the other two oxygen atoms are located directly above and below this plane. In this sense, there are two different types of Cu-O bonds in [Cu(H
2O)
6]
2+. In this study, these two different types of Cu-O bonds are named Cu-O
1 and Cu-O
2, respectively. For these two different types of Cu-O bonds, the results of this study and previous studies are Cu-O
1:2.28 Å (this study), 2.30 Å [
20], and 2.28 Å [
25] and Cu-O
2: 2.02 Å (this study), 2.02–2.03 Å [
20] and 2.00 Å [
25]. Based on the existing experimental and theoretical calculation results, it can be seen that the results of this study have a good agreement with the previous studies. This also reflects from the side that this research method is correct and reasonable.
- (2)
Calculated data of Cu isotope fractionation
In simulating solvation effects, the method used is the “water-droplet” method, which adds different amounts of water molecules to the periphery of the Cu-bearing complexes. In general, the more water molecules you have, the better you can simulate a real aqueous environment. However, considering the accuracy, calculation cost, and time cost in the actual calculation process, six water molecules were chosen to add as a batch around the Cu-bearing complexes until the complex (H
2O)
42 was obtained. As can be seen from
Figure 2, whether for Cu(I) or Cu(II) complexes, when the number of water molecules exceeds 30, the change in β value is basically in a small range. In other words, when the number of water molecules exceeds 30, its β converges to a constant value. Therefore, when performing theoretical calculations, it is reasonable for us to choose a structure surrounded by 42 water molecules as the final structure to calculate the β value.
Using Equation (1), the Cu isotope fractionation parameters (i.e., 1000lnβ) of different Cu-bearing species at 0, 25, 50, 100, 150, 200, 300, and 500 °C can be calculated. The specific β values of Cu-bearing complex solutions under the corresponding temperature conditions are shown in
Table 2. For six Cu(I) aqueous solutions ([CuCl]·(H
2O)
42, [CuCl
2]
−·(H
2O)
42, [CuCl
3]
2−·(H
2O)
42, [Cu(HS)
2]
−·(H
2O)
42, [Cu(HS)(H
2O)]·(H
2O)
42, and [Cu(HS)(H
2S)]·(H
2O)
42), in the temperature range of 0–500 °C, the variation range of 1000lnβ was 2.19~0.28, 2.09~0.27, 1.67~0.21, 2.82~0.37, 2.52~0.33, and 2.51~0.32 (‰). At the same time, isotope fractionation parameters (β) considering only the inner coordination forms (without considering solvation effects) are also listed in
Table 3.
Figure 3A shows the relationship between the isotope fractionation parameter (1000lnβ) and temperature. As can be seen from
Figure 3A, the calculated results of this study show that the change order for the 1000lnβ values of the aqueous solutions of six Cu(I) complexes is [Cu(HS)
2]
−·(H
2O)
42 > [Cu(HS)(H
2O)]·(H
2O)
42 ≈ [Cu(HS)(H
2S)]·(H
2O)
42 > [CuCl]·(H
2O)
42 > [CuCl
2]
−·(H
2O)
42 > [CuCl
3]
2−·(H
2O)
42. The largest Cu isotope fractionation (in the form of
65/63Cu) occurs between species [Cu(HS)
2]
−·(H
2O)
42 and [CuCl
3]
2−·(H
2O)
42. At 25 °C, the isotope fractionation factor between the two substances can reach 0.98(‰). From this change order, it can be seen that for the ligands HS
− and Cl
−, the complexes with ligands of HS
− have a stronger ability to enrich heavy Cu isotopes than Cl
−. For the Cu(I) complex solutions with Cl
− as ligands, the ability to enrich heavy isotopes gradually decreases with the increase in the amount of Cl
−.
For Cu(II) aqueous solutions, 13 different substances were selected to study the Cu isotope fractionation effect, namely [Cu(NO
3)
2]·(H
2O)
42, [Cu(NO
3)(H
2O)
4]
+·(H
2O)
42, [CuCN]
+·(H
2O)
42, [Cu(H
2O)
6]
2+·(H
2O)
42, [CuCl]
+·(H
2O)
42, [CuCl
2]·(H
2O)
42, [CuCl
3]
−·(H
2O)
42, [CuBr
2]·(H
2O)
42, [Cu(OH)
2]·(H
2O)
42, [Cu(COOHCOO)]
+·(H
2O)
42, [Cu(CH
3CH
2COO)]
+·(H
2O)
42, [Cu(HOC
6H
4COO)]
+·(H
2O)
42, and [Cu(SO
4)(H
2O)
3]·(H
2O)
42. These species were used to simulate aqueous solution environments under different conditions. In the temperature range of 0–500 °C, the corresponding Cu isotope fractionation parameters (1000lnβ) ranged from 5.77~0.78, 5.56~0.75, 5.39~0.72, 5.86~0.79, 5.40~0.72, 4.80~0.64, 4.07~0.54, 4.29~0.57, 5.70~0.77, 5.57~0.75, 5.68~0.76, 5.73~0.77, and 5.69~0.77(‰), respectively (see
Table 2 for details). At the same time, the Cu isotope fractionation parameters (1000lnβ) without considering the solvation effect of water (that is, only considering the coordination form of the inner layers) have also been systematically studied. In the same temperature range, the isotope fractionation parameters (1000lnβ) of [Cu(NO
3)
2], [Cu(NO
3)(H
2O)
4]
+, [CuCN]
+, [Cu(H
2O)
6]
2+, [CuCl]
+, [CuCl
2], [CuCl
3]
−, [CuBr
2], [Cu(OH)
2], [Cu(COOHCOO)]
+, [Cu(CH
3CH
2COO)]
+, [Cu(HOC
6H
4COO)]
+, and [Cu(SO
4)(H
2O)
3] were 6.31–0.84, 5.46–0.73, 5.65–0.76, 5.37–0.72, 1.48–0.19, and 4.28–0.58, 3.94~0.51, 3.62~0.47, 6.79~1.00, 2.09~0.27, 2.38~0.31, 3.68~0.50, and 5.17~0.70(‰), respectively (see
Table 3 for details). Compared with the molecular clusters surrounded by water molecules on the outer side, it can be seen that the solvation effect of aqueous solutions is very significant. Taking 1000lnβ at 25 °C as an example, the values of [Cu(COOHCOO)]
+ and [Cu(COOHCOO]
+·(H
2O)
42 are 2.09 and 5.57, respectively. The difference between them could be reached up to 3.48(‰). It is well known that the isotope fractionation parameter (1000lnβ) has a good functional relationship with temperature, that is, with the increase in temperature, 1000lnβ gradually decreases. All the systems involved in this study follow this rule.
Figure 3B–D show the temperature variation of the 1000lnβ of different Cu(II)-bearing complex solutions. For the Cu(II) inorganic ligand (H
2O, OH
−, NO
3−, SO
42− and CN
−) complex solutions, the change sequence of 1000lnβ is as follows: [Cu(H
2O)
6]
2+·(H
2O)
42 > [Cu(NO
3)
2]·(H
2O)
42 > [Cu(OH)
2]·(H
2O)
42 > [CuSO
4(H
2O)
3]·(H
2O)
42 > [CuNO
3(H
2O)
4]
+·(H
2O)
42 > [CuCN]
+·(H
2O)
42 (
Figure 3B). At 25 °C, the 1000lnβ of these six Cu(II) complex solutions varied from 4.57 to 4.98, with a maximum difference of 0.41(‰). For Cu(II) complex solutions with halogen elements as ligands, the variation in 1000lnβ is [CuCl]
+·(H
2O)
42 > [CuCl
2]·(H
2O)
42 > [CuBr
2]·(H
2O)
42 > [CuCl
3]
−·(H
2O)
42 (
Figure 3C). At 25 °C, the variation range of the 1000lnβ of these four Cu(II) complex solutions was 3.45~4.58, and the maximum difference was 1.13(‰). In nature, Cu(II) is one of the important components of many organisms. To investigate the Cu isotope fractionation effect in organic life activities, three organic ligands (HOC
6H
4COO
−, CH
3CH
2COO
−, and COOHCOO
−) were selected to study this process. The results showed that the change sequence of 1000lnβ for these three Cu(II) organic complex aqueous solutions was [Cu(HOC
6H
4COO)]
+·(H
2O)
42 > [Cu(CH
3CH
2COO)]
+·(H
2O)
42 > [Cu(COOHCOO)]
+·(H
2O)
42 (
Figure 3D). At 25 °C, the 1000lnβ of the three Cu(II) organic complex solutions varied from 5.57 to 5.73, and the maximum difference was 0.16(‰). Compared with Cu(II) inorganic ligand aqueous solutions, the isotope fractionation effect between Cu(II) organic complex aqueous solutions is much smaller. To facilitate the acquisition of the 1000lnβ of Cu(I) and Cu(II) complex (solutions) at any temperature, the polynomial expansion coefficient terms of 1000lnβ for the research systems involved in this study are given in detail in
Table 4.
If the solvation effect is not considered (only the inner coordination structure is considered), the Cu isotope fractionation parameters of these six Cu(I) complexes are as follows: [Cu(HS)(H
2O)] > [CuCl
2]
− > [Cu(HS)
2]
− > [Cu(HS)(H
2S)] > [CuCl] > [CuCl
3]
2−. This change order is inconsistent with that when solvation effects are considered (
Figure 4A). For the inorganic ligand complex of Cu(II), the change order of 1000lnβ is [Cu(OH)
2] > [Cu(NO
3)
2] > [CuCN]
+ > [CuNO
3(H
2O)
4]
+ > [Cu(H
2O)
6]
2+ > [CuSO
4(H
2O)
3] (see
Figure 4B). At 25 °C, the variation range of 1000lnβ was 5.17–6.79 (‰). The sequence of the 1000lnβ of the Cu(II) complexes with halogen as ligands is [CuCl
2] > [CuCl
3]
− > [CuBr
2] > [CuCl]
+ (see
Figure 4C). At 25 °C, the range of 1000lnβ for these four species is 1.25~3.64. The sequence of the 1000lnβ of the three Cu(II) organic complexes is [Cu(HOC
6H
4COO)]
+ > [Cu(CH
3CH
2COO)]
+ > [Cu(COOHCOO)]
+ (see
Figure 4D). Although the size order does not change compared to aqueous solution species, the numerical difference between each species is huge. At 25 °C, the variation range of 1000lnβ for these three species is 2.09~3.68 (‰).
- (3)
solvation effect on the Cu isotope fractionation
In order to better understand the solvation effect on the isotope fractionation of Cu(I) and Cu(II) complexes, the Cu isotope fractionation factors between different Cu-bearing aqueous solutions and simple complexes were systematically studied. Water is the most important driving force in the migration of elements. For the Cu(I) species, [CuCl]·(H
2O)
42 is a more enriched heavy Cu isotope than [CuCl], and the equilibrium Cu isotope fractionation factor varies from 0.38 to 0.05 at the temperature range of 0~500 °C. At 100 °C, the Cu isotope fractionation factor (1000lnα (‰); similarly hereinafter) between [CuCl]·(H
2O)
42 and [CuCl] is 0.20 (‰). For the system of [CuCl
2]
−·(H
2O)
42 vs. [CuCl
2]
−, at the temperature range of 0~500 °C, the range of the Cu isotope fractionation factor between these two species is −0.93~−0.12. At 100 °C, the isotope fractionation factor between [CuCl
2]
−·(H
2O)
42 and [CuCl
2]
− is −0.52, and the isotope fractionation effect is very significant. However, for Cu-bearing species with HS
− ligands, complex solutions will deplete heavy isotopes compared with simple complexes. To be specific, the ranges of Cu isotope fractionation factors for the systems of [Cu(HS)
2]
−·(H
2O)
42 vs. [Cu(HS)
2]
−, [Cu(HS)(H
2O)]·(H
2O)
42 vs. [Cu(HS)(H
2O)]., and [Cu(HS)(H
2S)]·(H
2O)
42 vs. [Cu(HS)(H
2S)] are −0.06~−0.01, −0.77~−0.11, and −0.20~−0.03 (0~500 °C). For the system [Cu(HS)
2]
−·(H
2O)
42 vs. [Cu(HS)
2]
−, the difference in the heavy isotope enrichment capacity between the two systems is limited, that is, the solvation effect is not very obvious. For the other two systems, ([Cu(HS)(H
2O)]·(H
2O)
42 vs. [Cu(HS)(H
2O)] and [Cu(HS)(H
2S)]·(H
2O)
42 vs. [Cu(HS)(H
2S)]), simple complexes significantly preferred enrichment-heavy isotopes (
Figure 5A).
For the 13 Cu(II) complex species, at the temperature range of 0~500 °C, the ranges of the Cu isotope fractionation factors for the systems [Cu(NO
3)
2]·(H
2O)
42 vs. [Cu(NO
3)
2], [Cu(NO
3)(H
2O)
4]
+·(H
2O)
42 vs. [Cu(NO
3)(H
2O)
4]
+, [CuCN]
+·(H
2O)
42 vs. [CuCN]
+, [Cu(H
2O)
6]
2+·(H
2O)
42 vs. [Cu(H
2O)
6]
2+, [CuCl]
+·(H
2O)
42 vs. [CuCl]
+, [CuCl
2]·(H
2O)
42 vs. [CuCl
2], [CuCl
3]
−·(H
2O)
42 vs. [CuCl
3]
−, [CuBr
2]·(H
2O)
42 vs. [CuBr
2], [Cu(OH)
2]·(H
2O)
42 vs. [Cu(OH)
2], [Cu(COOHCOO)]
+·(H
2O)
42 vs. [Cu(COOHCOO)]
+, [Cu(CH
3CH
2COO)]
+·(H
2O)
42 vs. [Cu(CH
3CH
2COO)]
+, [Cu(HOC
6H
4COO)]
+·(H
2O)
42 vs. [Cu(HOC
6H
4COO)]
+, and [Cu(SO
4)(H
2O)
3]·(H
2O)
42 vs. [Cu(SO
4)(H
2O)
3] are 0.53~0.06, 0.09~0.02, 0.26~0.04 and 0.49~0.07, 3.92~0.53,0.52~0.06, 0.13~0.02, 0.68~0.10, 1.09~0.23, 3.48~0.47, 3.30~0.45, 2.05~0.27, and 0.52~0.07(‰) (
Table 5). That is, when the solvation effect is considered, the Cu isotope fractionation effect of different Cu-bearing species will change obviously. Therefore, the solvation effect is a factor that must be considered in the theoretical calculation of the Cu isotope fractionation effect of the Cu complexes’ solutions. Specifically, for the Cu(II) inorganic ligand complexes, the [Cu(NO
3)
2] phase is more heavily isotopically enriched than [Cu(NO
3)
2]·(H
2O)
42 (
Figure 5B). At 100 °C, the Cu isotope fractionation factor between [Cu(NO
3)
2]·(H
2O)
42 and [Cu(NO
3)
2] is −0.28 (‰). However, the [Cu(NO
3)(H
2O)
4]
+·(H
2O)
42 preferentially enriches the heavy Cu isotope more than the [Cu(NO
3)(H
2O)
4]
+, but there is little difference in the heavy isotope enrichment capacity between these two phases. At 100 °C, the Cu isotope fractionation factor of the system [Cu(NO
3)(H
2O)
4]
+·(H
2O)
42 vs. [Cu(NO
3)(H
2O)
4]
+ is 0.06 (‰). The Cu isotope fractionation factor of system [CuCN]
+·(H
2O)
42 vs. [CuCN]
+ is −0.16(‰), that is, [CuCN]
+·(H
2O)
42 is significantly deficient in the heavy Cu isotope compared to [CuCN]
+. Compared with [Cu(H
2O)
6]
2+, [Cu(H
2O)
6]
2+·(H
2O)
42 is a significantly enriched Cu heavy isotope, and the Cu isotope fractionation factor between them is 0.28 (‰) at 100 °C. When the ligands are halogen elements, the solutions tend to be enriched with a heavy Cu isotope compared to simple complexes (
Figure 5C). At 100 °C, the Cu isotope fractionation factors of these systems ([CuCl]
+·(H
2O)
42 vs. [CuCl]
+, [CuCl
2]·(H
2O)
42 vs. [CuCl
2], [CuCl
3]
−·(H
2O)
42 vs. [CuCl
3]
−, and [CuBr
2]·(H
2O)
42 vs. [CuBr
2]) are 2.18, 0.27, 0.08, and 0.38 (‰), respectively. Compared with [Cu(OH)
2], [Cu(OH)
2]·(H
2O)
42 is significantly deficient in heavy isotopes, and the Cu isotope fractionation factor between them is −0.76 (‰) at 100 °C. Cu(SO
4)(H
2O)
3]·(H
2O)
42 has a stronger ability to enrich a heavy Cu isotope than [Cu(SO
4)(H
2O)
3], and the Cu isotope fractionation factor between these two species is 0.29 (‰) at 100 °C. For the three organic ligand complexes involved in this study, when the solvation effect is considered, the solutions are significantly enriched with a heavy isotope compared with the simple complexes, and the ability to enrich heavy isotopes is much greater than that of the simple complexes (
Figure 5D). Taking the Cu isotope fractionation factors between complex solutions and simple complexes at 100 °C as an example, the Cu isotope fractionation factors of these systems ([Cu(COOHCOO)]
+·(H
2O)
42 vs. [Cu(COOHCOO)]
+, [Cu(CH
3CH
2COO)]
+·(H
2O)
42 vs. [Cu(CH
3CH
2COO)]
+, and [Cu(HOC
6H
4COO)]
+·(H
2O)
42 vs. [Cu(HOC
6H
4COO)]
+) are 1.95, 1.84, and 1.12 (‰), respectively (see
Table 5). To facilitate other researchers interested in this topic to obtain the Cu isotopic fractionation factors between these complex solutions and simple complexes at any temperature (0–500 °C), the exponential expansions of the Cu isotope fractionation factors of these systems are shown in
Table S2 of the
Supplementary Materials.
- (4)
Cu isotope fractionation factors (Cu(I) and Cu(II)) between different Cu-bearing complex solutions
For Cu(I) complex solutions, [CuCl]·(H
2O)
42 was selected as the reference material to facilitate the discussion of the magnitude of Cu isotope fractionation factors between different Cu(I)-bearing substances. In the temperature range of 0–500 °C, the study found that the Cu isotope fractionation factors of Cu isotopes of these systems ([CuCl]·(H
2O)
42 vs. [CuCl
2]
−·(H
2O)
42, [CuCl]·(H
2O)
42 vs. [CuCl
3]
2−·(H
2O)
42, [CuCl]·(H
2O)
42 vs. [Cu(HS)
2]
−·(H
2O)
42, [CuCl]·(H
2O)
42 vs. [Cu(HS)(H
2O)]·(H
2O)
42 and [CuCl]·(H
2O)
42 vs. [Cu(HS)(H
2S)]·(H
2O)
42) vary from 0.11~0.02, 0.52~0.08, −0.63~−0.08, −0.33~−0.04, and −0.32~−0.04 (‰). From these Cu isotope fractionation data, it can be seen that the
65Cu enrichment capacity of complex solutions with a Cl
− ligand is weaker than that with HS
− as ligand. The Cu isotope fractionation factors of systems [CuCl]·(H
2O)
42 vs. [CuCl
2]
−·(H
2O)
42 and [CuCl]·(H
2O)
42 vs. [CuCl
3]
2−·(H
2O)
42 are positive, indicating that [CuCl]·(H
2O)
42 is preferentially enriched with a heavy Cu isotope (
65Cu) (
Figure 6A. At 100 °C, the Cu isotope fractionation factors of these two systems are 0.07 and 0.30 (‰), respectively. In other words, [CuCl
3]
2−·(H
2O)
42 is the system that preferentially enriches a light Cu isotope (
63Cu). At the same temperature condition, the Cu isotope fractionation factors between [CuCl]·(H
2O)
42 and HS
−-bearing complex solutions ([CuCl]·(H
2O)
42 vs. [Cu(HS)
2]
−·(H
2O)
42, [CuCl]·(H
2O)
42 vs. [Cu(HS)(H
2O)]·(H
2O)
42, and [CuCl]·(H
2O)
42 vs. [Cu(HS)(H
2S)]·(H
2O)
42) are −0.34, −0.18, and −0.17 (‰), respectively.
For Cu(II) complex solutions, due to the large number of systems involved, to facilitate data analysis and statistics, these systems are divided into three categories according to different ligand types: inorganic ligand complex solutions (NO
3−, CN
−, H
2O, OH
−, and SO
42−), complex solutions with halogen elements as ligands, and organic ligand complex solutions. For the inorganic ligand complex solutions, [Cu(NO
3)
2]·(H
2O)
42 was selected as the reference material to discuss the Cu isotope fractionation effect between [Cu(NO
3)
2]·(H
2O)
42 and other complex solutions. Cu isotope fractionation factors between other phases can also be obtained according to this method. For the sake of article length, I will not list them here. It can be seen from the results that the ability to enrich a heavy isotope for a complex solution with a NO
3− ligand is stronger than other inorganic ligand complex solutions. At 100 °C, the Cu isotope fractionation factors of these systems ([Cu(NO
3)
2]·(H
2O)
42 vs. [CuNO
3(H
2O)
4]
+·(H
2O)
42, [Cu(NO
3)
2]·(H
2O)
42 vs. [CuCN]
+·(H
2O)
42, [Cu(NO
3)
2]·(H
2O)
42 vs. [Cu(H
2O)
6]
2+·(H
2O)
42, [Cu(NO
3)
2]·(H
2O)
42 vs. [Cu(OH)
2]·(H
2O)
42, and [Cu(NO
3)
2]·(H
2O)
42 vs. [CuSO
4(H
2O)
3]·(H
2O)
42) are 0.12, 0.23, −0.05, 0.03, and 0.04 (‰). These data size relationships indicate that for inorganic ligand complex solutions, [Cu(H
2O)
6]
2+·(H
2O)
42, [Cu(OH)
2]·(H
2O)
42, [CuSO
4(H
2O)
3]·(H
2O)
42, and [Cu(NO
3)
2]·(H
2O)
42 have a slightly different ability to enrich heavy isotopes. This phenomenon can be seen more directly in
Figure 6B. From
Figure 6B, we can see that the maximum variation range of Cu isotope fractionation factors between [Cu(NO
3)
2]·(H
2O)
42 and the other three substances is only −0.05~0.04(‰). However, the complex solution with a CN
− ligand has a special preference for a light Cu isotope (
63Cu).
When the ligands of complex solutions are halogen elements, the reference material is [CuCl]
+·(H
2O)
42. According to the study, at 100 °C, the Cu isotope fractionation factors of these isotope exchange pairs ([CuCl]
+·(H
2O)
42 vs. [CuCl
2]·(H
2O)
42, [CuCl]
+·(H
2O)
42 vs. [CuCl
3]
−·(H
2O)
42, and [CuCl]
+·(H
2O)
42 vs. [CuBr
2]·(H
2O)
42) are 0.34, 0.76, and 0.63 (‰), respectively (
Table 6). When the ligand is Cl-, as the number of Cl atoms gradually increases, its ability to enrich heavy isotopes gradually decreases, which can be clearly seen from the variation of the Cu isotope fractionation factors with temperature (
Figure 6C). When the complex solutions have the same spatial structure but the ligands are different (such as [CuCl
2]·(H
2O)
42 and [CuBr
2]·(H
2O)
42), the enrichment capacity of light or heavy isotopes is also different. To put it simply, when the ligands are elements of the same main group, with the gradual increase in atomic weight, the enrichment ability of heavy isotopes for the complex solutions with the same coordination structures gradually decreases. This law is the most common consensus of mass-dependent fractionation, and the results of this study also conform to it.
When ligands are organic ligands, [Cu(COOHCOO)]
+·(H
2O)
42 was chosen as the reference material to discuss the Cu isotope fractionation effect between [Cu(COOHCOO)]
+·(H
2O)
42 and other organic complex solutions. Compared with the Cu isotope fractionation effect between the complex solutions with inorganic ligands, the Cu isotope fractionation effect between the three organic ligand complex solutions involved is significantly smaller. At 100 °C, the Cu isotope fractionation factors of these systems ([Cu(COOHCOO)]
+·(H
2O)
42 vs. [Cu(CH
3CH
2COO)]
+·(H
2O)
42 and [Cu(COOHCOO)]
+·(H
2O)
42 vs. [Cu(HOC
6H
4COO)]
+·(H
2O)
42) are −0.06 and −0.08 (‰), respectively (
Table 6). This also points to the fact that the isotope fractionation between different organic ligand complex solutions is very small (
Figure 6D). In order to obtain Cu isotope fractionation factors at different temperatures more conveniently, polynomial expansion coefficients of these Cu isotope fractionation factors between different Cu-bearing organic complex solutions are listed in
Table S3 of the
Supplementary Materials.
- (5)
Implication for Cu isotope fractionation in different systems.
At one time, the accepted academic consensus was that the oxidation state of Cu(II) in seawater was important. Non-equilibrium processes, such as biochemical, photochemical, or thermochemical processes occurring in seawater systems, may also promote the formation of Cu(I) [
26]. This is also the original starting point for studying the isotope fractionation effect of Cu(I) and Cu(II) complexes. In the natural water body, the existence form and concentration of trace metal elements depend on various competitive processes between the same type of metal ions (such as Cu, Ag, Zn, etc.), and there will be a trade-off between each other. At the same time, the different ligand types will also affect the migration performance of metal elements, such as solubility, mobility, and so on. The complexation and chelation between ligands and Cu(I)/Cu(II) will have an important effect on the existence of metal ions. One of the most intuitive examples is the process of metal ion flow into the ocean with river water, and various physical and chemical processes that occur at the estuary will significantly affect the existence of Cu(II) species [
27]. At the estuary, the river water meets the sea water, and there will be obvious estuarine chemical reactions that will form various types of flocculation products. An important factor affecting Cu flocculation is salinity. Hence, various geochemical behaviors of Cu in estuarine play a crucial role in the geochemical cycle of Cu isotopes [
28]. The ab initio method also has been used to study the stability of aqueous solutions of various Cu complexes and has made considerable progress in this field [
29]. It is important to study the properties of metallic elements in an aqueous solution system to understand their various geochemical behaviors and help to explain various geochemical processes. The behavior of Cu is more complex than other metallic elements [
30]. Dissolved Cu
2+ in soil and natural water bodies do not exist in a single species but in the form of mixed complexes. The transport mode of metal ions in soil and natural water bodies depends on the nature and concentration of chelating agents present in the environment.
It is well known that humic acid is a widely existing organic matter in natural water and soil. Although the specific molecular structure of humic acid has not been completely determined, it has been found from the existing research results that some functional groups in the structure of humic acid are benzene ring, carboxyl group, hydroxyl group, etc. [
31]. In this study, three organic ligands were selected as examples to study the isotope effect of Cu complexes formed by metal–organic ligands. Experimentally, it is common sense that the functional groups that play a decisive role in a substance can be determined by the spectrogram of a substance [
32]. The species morphology of Cu(II) in solution/hydrothermal solution systems depends on the concentration of Cl
− and the pH of the solution system [
33]. The results of this study also support this view. The complex reaction between metal ions and ligands under hydrothermal conditions will form various types of new coordination compounds, which have very important potential applications in material science and earth science [
1,
34]. In the natural environment, the types of ligands are very diverse. Among them, the two ligands that play an important role in the migration of metal ions in the crust are HS
− and Cl
−. The formation of Cu deposits is also closely related to the existence of various ligands. This is because metal chloride or sulfide (sulfur hydride) complexes play a decisive role in the migration of metal ions. This also reflects laterally that the concentration of complexes in various aqueous solutions not only depends on their chemical stability but also has a direct relationship with the concentration of ligands [
35]. Various processes, such as chemical equilibria between minerals and chemical equilibria between aqueous substances, are affected by many factors, such as pH, oxidation states, temperature, and pressure [
2].
Many geological processes, environmental processes, and life processes can produce impressive Cu isotope fractionation. The Cu isotope fractionation will provide a good tool to study the geochemical cycle of Cu. It is found that the Cu isotope composition will have obvious difference during the formation of soil. The research of the Cu isotope fractionation in soil formed by oxidative weathering found that the variation range of δ
65Cu in the studied area was 0.57~0.44 and the Cu isotope composition was closely related to the oxygen content [
3]. Little et al. found in their research on the isotope fractionation of Cu and Zn in the process of extreme chemical weathering that heavy Cu isotopes (
65Cu) would be prefertively released during weathering under oxidation conditions and that this phenomenon is independent of the form of Cu [
36]. Previous researchers also studied the Cu isotope fractionation in porphyry Cu deposits [
37]. It was found that the total Cu isotope variation measured in the samples involved in the study ranged from −16.96‰ to 9.98‰ (expressed in the form of δ
65Cu). An experimental study on the Cu isotope fractionation between Cu(II) aqueous solution and CuS found that the average value of Δ
65Cu
(Cu(II)aq-CuS) at 20 °C was 3.06 ± 0.14‰ [
38]. This study concluded that covellite is a Cu(I)S(I) compound and the REDOX state may be an important controlling factor for abiogenic
65Cu/
63Cu differentiation in low-temperature geological environments [
38].
The variation of Cu isotopic composition (δ
65Cu) of the main terrestrial Cu-bearing sulfides is −1‰~1 ‰ and for stream waters is 1.38‰~1.69‰. In general, the Cu-bearing solutions are more enriched with a heavy Cu isotope (
65Cu) than the Cu-bearing minerals. The Cu isotope fractionation factors between mine wastewater and Cu-bearing minerals (chalcopyrite and enargite) are 1.43 ± 0.14 and 1.60 ± 0.14, respectively [
39]. Given various Cu isotope fractionations found in experiments, Liu et al. used first-principle calculations to systematically study the Cu isotope composition of different types of Cu-bearing minerals. The results showed that the Cu isotope compositions (1000lnβ) of different Cu-bearing minerals would be varied from 1‰ to 7‰ [
40]. At the same time, it also has been found that the heavy isotope (
65Cu) in the complex preferentially enriched during the formation of Cu-bearing complexes and the Δ
65Cu
complex-free value varies between +0.14 and +0.84‰ [
41]. Cu isotope fractionation not only occurs between various inorganic substances but also between different organic systems. For example, the study of Cu isotope fractionation in plants found that plants preferentially enrich the light Cu isotope (
63Cu) compared to the soil in which they grow [
42].
In conclusion, various processes in nature can lead to Cu isotope fractionation. These key parameters of Cu isotope fractionation obtained in this study will provide important theoretical guidance for explaining the mechanism of Cu isotope fractionation from the molecular level.