A Comprehensive Solution and Solid-State NMR Study of Proton Spin Lattice Relaxation in Paramagnetic Metallocenes

Abstract

Solid solutions of the metallocenes ferrocene (Cp₂Fe), nickelocene (Cp₂Ni), and cobaltocene (Cp₂Co) have been prepared by manually grinding the components together, or by co-crystallizing them from solution. In the solid solutions Cp₂Fe/Cp₂Ni and Cp₂Co/Cp₂Ni, the cyclopentadienyl (Cp) protons relax via dipolar electron–proton interactions, which represent the dominant relaxation mechanism. The ¹H T₁ relaxation times of the molecules Cp₂Ni and Cp₂Co, dissolved in CDCl₃, and in the solid solutions, show that the relaxation takes place intramolecularly. The relaxation of the protons is propagated exclusively via the unpaired electrons of the metal centers to which their Cp rings are coordinated, due to the large intermolecular distances that are greater than 3.91 Å. In contrast, the intramolecular distances between the electrons of the metal atoms and the protons of their coordinated Cp rings are merely 2.70 Å. Using these intramolecular distances and the ¹H T₁ relaxation times, the electron relaxation times T_1e have been determined as 17 × 10⁻¹³ s in CDCl₃ solutions and 45 × 10⁻¹³ s in the solid state for Cp₂Ni. The corresponding T_1e times for Cp₂Co are calculated as ca. 5 × 10⁻¹³ s and 20 × 10⁻¹³ s. Grinding Cp₂Fe and Cp₂Ni together leads to two different ¹H T₁ relaxation times for the protons of Cp₂Fe. The longer T₁ relaxation time indicates domains that consist mostly of Cp₂Fe molecules. The short T₁ times show a close contact of Cp₂Fe and Cp₂Ni molecules. An analysis of the short ¹H T₁ times reveals the presence of at least two to three short distances of 3.91 Å between Cp₂Fe and Cp₂Ni molecules. These results support the hypothesis that dry grinding of the metallocenes Cp₂Fe and Cp₂Ni in ratios that were changed in 10% increments from 90%/10% to 30%/70% leads to domains that mostly consist of Cp₂Fe molecules, and additionally to domains that contain a mixture of the components on the molecular level.

1. Introduction

The study of paramagnetic molecular systems in solution and in the solid state is an important field of NMR spectroscopy, directed at elucidating their structural and electronic properties [1,2]. Among various paramagnetic complexes, the classic 3d metallocenes, such as chromocene (Cp₂Cr), vanadocene (Cp₂V), cobaltocene (Cp₂Co), and nickelocene (Cp₂Ni), containing unpaired electrons at the metal centers, are of great interest [3,4,5,6]. Besides the phenomenological interest in their dynamics [7,8,9], surface-adsorbed metallocenes are especially important as precursors for single-atom catalysts [8] and the Union Carbide catalyst [10]. Recently, our group has investigated solid solutions [11] of Cp₂Fe, Cp₂Co, and Cp₂Ni that were obtained by co-crystallization from solutions [12,13,14], and by grinding the components together in the absence of a solvent [15,16]. While EPR spectroscopy proved to be less useful for probing the distribution of the components in the crystal lattice [16], the NMR chemical shifts, linewidths, and Chemical Shift Anisotropy (CSA) [17,18,19,20,21] could successfully be applied as criteria to study the surface-adsorbed, dissolved, and neat metallocenes, as well as their solid solutions.

The nature of the paramagnetic shifts in these metallocenes is well studied experimentally and theoretically and described in numerous publications that have been summarized in a recent review [1]. However, studies of the NMR relaxation properties of the metallocenes have been very limited, besides the common observation of the paramagnetic relaxation rate enhancement. One of the possible reasons for the limited studies and knowledge base might be the fact that most of the 3d metallocenes, like Cp₂Co and Cp₂Ni, are highly reactive and air-sensitive [15]. This feature complicates the preparation of clean samples in solutions and in the solid state, which is particularly important for collecting reliable proton NMR relaxation data with highly reproducible ¹H T₁ time measurements.

Recently, the ¹H T₁ criterion has been applied as a tool for studying solid solutions with the components Cp₂Fe/Cp₂Ni [15], as well as Cp₂Fe/Cp₂Co and Cp₂Co/Cp₂Ni [16]. These solid solutions have been prepared by manually grinding the components together with a mortar and pestle in the absence of any solvent or, alternatively, by co-crystallizing the mixed metallocenes from a solution [12,13,14]. The collected data, particularly the measured ¹H T₁ relaxation times and their changes when varying the ratios of the components, were considered mainly phenomenologically. In the presented work, these data [15,16], in combination with the results of additional ¹H NMR experiments, are discussed in a comprehensive manner. Hereby, the focus lies on the mechanisms of the proton relaxation in paramagnetic metallocenes, and the quantitative interpretation of the ¹H T₁ data. In general, this study is directed at a better understanding of the level of mixing of the components after grinding them together. Deeper insights about solid–solid mixtures will also be beneficial for other fields like heterogeneous catalysis [22,23] and mechanochemistry [24].

2. Results and Discussion

Among the various proton relaxation mechanisms effective in paramagnetic solids, generally the following relaxation pathways are discussed: (a) Proton spin diffusion, (b) Fermi-contact electron-nucleus coupling, (c) relaxation via dipolar proton-electron interactions, and (d) Curie relaxation [1,2]. Due to the high magnetic field strength and ‘high’ temperature commonly used in the NMR experiments, relaxation pathway (d), the Curie contribution, is recognized to be insignificant [1]. The relaxation pathways (a), (b), and (c) are analyzed in the following.

2.1. Proton Spin Diffusion

The spin diffusion relaxation mechanism, which is, in principle, possible for protons in the presence of paramagnetic centers, can be ruled out due to the following reasons: 1. This mechanism is ineffective for mobile solids [2]. The Cp rings in metallocenes undergo extremely fast rotation even in the solid state [3,20,25]. This rotation leads to very rapid reorientation of the intermolecular proton-proton dipolar vectors. 2. Spin diffusion generally leads to an exponential relaxation, especially at the fast spin diffusion limit [2] in contrast to the non-exponential relaxation observed in our study (see below). 3. In the presence of spin diffusion, the ¹H T₁ relaxation times in the mixtures of Cp₂Co and Cp₂Ni should be equal, or at least very close for both components. As follows from our measurements, presented below, these relaxation times are very different. 4. Spin diffusion is dependent on the spinning rates [26]. However, the T₁ relaxation times of the Cp₂Fe protons in a solid solution of Cp₂Fe and Cp₂Co (50%/50%), prepared by co-crystallization of equal amounts of the dissolved components, were determined as 9.6 ms and 8.4 ms at spinning rates of 10 kHz and 11 kHz, respectively. Since the frictional heating effect is negligible when increasing the rotational speed from 10 to 11 kHz [27], this indicates that the T₁ relaxation times are practically independent of the spinning rates. All these results speak against option (a), the spin diffusion mechanism, and leave (b) and (c) as possible relaxation pathways.

Regarding (c), in the absence of spin diffusion, unpaired electrons located at a metal center can facilitate the proton relaxation via dipolar interactions between the proton (H) and electron spins (S), as described in Equation (1) [28,29].

1/T₁(H)^dip = (2/5) × (μ₀/4π)²γ_H² × γ_S² × ħ² × S(S + 1) × r(H−S)⁻⁶ × c × (T_1e/(1+ ω_H² × T_1e²))

(1)

Furthermore, the proton relaxation can be propagated through pathway (b), Fermi-contact electron-nucleus coupling as described in Equation (2) [30].

1/T₁(H)^CON = (1/3) × (μ₀/4π)² × S(S + 1) × (A/ħ)² × T_1e{1 + (ω_H − ω_S)² × T_1e²}⁻¹

(2)

In these equations, T_1e is the electron spin-lattice relaxation time, r(H-S) indicates the proton-electron distance, A represents the Fermi-contact coupling constant, and S equals 1 and ½ for the electrons at the Ni and Co centers, respectively.

2.2. Fermi-Contact Electron-Nucleus Coupling

It is well known that in cases where the Fermi-contact coupling is the primary mechanism of relaxation, the ¹H T₂ relaxation times are dramatically shorter than the ¹H T₁ times. For example, in paramagnetic metal complexes, the T₂ relaxation times even of ¹³C nuclei, which have a smaller gyromagnetic ratio than protons, can be shorter than 5 × 10⁻⁴ s [30].

For solid paramagnetic species, the T₂ times can be obtained from the signal halfwidths Δν via the equation T₂ = 1/Δν. We estimated the ¹H T₂ times in solid solutions with different ratios of Cp₂Co and Cp₂Ni using a Gaussian line shape fit for the signals (

Table 1. Halfwidths Δν of the isotropic lines (kHz) and ¹H T₁ times (ms) determined at a spinning rate of 10 kHz for Cp₂Co and Cp₂Ni solid solutions prepared by grinding the components together [16], and ¹H T₂ times (ms) calculated from the linewidths for Gaussian line shapes.

Cp2Co/Cp2Ni (%/%)	∆ν (kHz)/T1 (ms)/T2 (ms)
	Cp2Co	Cp2Ni
70/30	1.39/2.3/0.72	2.46/0.38/0.40
30/70	1.40/2.4/0.71	2.69/0.38/0.37
20/80	1.39/2.8/0.72	2.54/0.46/0.39

). The ¹H T₂ times for Cp₂Co were in the range of 0.71 ms to 0.72 ms, and those for Cp₂Ni were between 0.37 ms and 0.40 ms (Table 1). These T₂ relaxation times are not significantly shorter than the corresponding ¹H T₁ times in the ranges of 2.3–2.8 ms for Cp₂Co and 0.38–0.46 ms for Cp₂Ni (Table 1). Therefore, the ¹H T₁ and T₂ relaxation time data show that the Fermi-contact mechanism is not dominant.

It should also be noted that a similar scenario is observed for CDCl₃ solutions of Cp₂Fe/Cp₂Ni mixtures (see below), where the halfwidth Δν of the nickelocene resonance is ca. 530 Hz, corresponding to a ¹H T₂ time of 0.6 ms. Again, this T₂ relaxation time is not significantly shorter than the measured ¹H T₁ time of about 0.94 ms.

An additional factor that is important for the interpretation of the proton relaxation times in solid paramagnetic metallocenes is the observation of MAS effects on their ¹H NMR spectra. Figure 1 shows, as an example, the ¹H MAS and static NMR spectra recorded for a 50%/50% mixture of Cp₂Co and Cp₂Ni prepared by grinding the components together.

The wideline NMR spectrum of this mixture exhibits two extremely broad resonances with estimated halfwidths of 6.8 and 9.4 kHz centered at about −58 and −250 ppm, corresponding to the paramagnetic components Cp₂Co and Cp₂Ni, respectively (Figure 1, bottom). The significant upfield shift in the resonances, compared to the diamagnetic analog Cp₂Fe, is due to the one and two unpaired electrons at the Co and Ni centers. The overall signal shapes are symmetric, with the number of rotational sidebands being larger for the Cp₂Ni signal. The changes in the spinning sideband intensities with different amounts of the components in solid solutions have been reported earlier [15,16]. The substantial line-broadening of the signals is also caused by the unpaired electrons, again via dipolar electron-nucleus interactions and/or Fermi-contact coupling [1,2]. In contrast, under MAS conditions, the ¹H NMR signals show extended sideband patterns with relatively narrow isotropic lines with Δν of 1.39 kHz for Cp₂Co and 2.45 kHz for Cp₂Ni (Figure 1, top). Since the Fermi-contact interactions cannot be reduced substantially by mechanical sample rotation, the relaxation mechanism (b) cannot be dominant.

Finally, it should be mentioned that the bulk magnetic susceptibility (BMS), which also contributes to the signal shape in the spectra of static samples and to the sideband intensities and their halfwidths in the MAS spectra, does not significantly influence the T₁ relaxation times [1,2]. Therefore, the proton relaxation data reported earlier for paramagnetic metallocenes [15,16] can be discussed in this contribution in terms of pathway (c) as the dominant relaxation mechanism. This result is in complete agreement with the literature [1,31].

2.3. Dipolar Proton-Electron Interactions

The dipolar interactions between proton spins (H) and electron spins (S) are outlined in Equation (1) above. The relaxation data of the metallocenes Cp₂Fe, Cp₂Co, and Cp₂Ni, which are most important in the context of the presented study, are summarized in

Table 2. ¹H T₁ relaxation times (ms) of the Cp resonances in solid solutions of Cp₂Ni and Cp₂Co, prepared by grinding the components together with the indicated molar ratios. The T₁ times were obtained by fitting procedures with a stretched exponential f(t) = exp(−τ/T₁)^β for the Cp signals.

Cp2Co/Cp2Ni (%/%)	1H T1 (ms) (β)
	Cp2Co	Cp2Ni
90/10	2.0 (0.65)	0.35 (0.65)
80/20	1.7 (0.60)	0.27 (0.45)
70/30	2.3 (0.74)	0.38 (0.65)
60/40	2.8 (0.69)	0.47 (0.77)
50/50	2.2 (0.52)	0.38 (0.62)
40/60	2.8 (0.64)	0.45 (0.60)
30/70	2.4 (0.55)	0.38 (0.52)
20/80	2.8 (0.62)	0.46 (0.59)
10/90	–	0.27 (0.70)

and

Table 3. ¹H T₁ relaxation times (10% accuracy) of Cp₂Fe/Cp₂Ni [15] and Cp₂Fe/Cp₂Co [16] mixtures dissolved in CDCl₃ with the indicated molar ratios. M stands for Ni or Co.

Cp2Fe/Cp2M (%/%)	Cp2Fe T1 (s)	Cp2Ni T1 (ms)	Cp2Fe T1 (s)	Cp2Co T1 (ms)
100/0	4.9	-	4.9	-
90/10	1.4	0.95	2.5	9.6
80/20	0.84	0.94	1.5	9.6
70/30	0.72	0.95	1.2	9.6
60/40	0.39	0.95	1.2	9.6
50/50	0.32	0.96	1.1	9.6
40/60	0.29	0.96	0.80	9.4
30/70	0.24	0.96	0.33	9.7
20/80	0.19	0.96	0.27	9.4
10/90	0.18	0.96	0.21	9.8
0/100	-	0.96	-	9.6

.

The data in Table 2 show that the proton relaxation in solid mixtures of Cp₂Co and Cp₂Ni is non-exponential, following a stretched exponential function f(t) = exp(−τ/T₁)^β. This behavior can be explained by the presence of a T₁ time distribution that is often observed in solids [2]. In contrast, in CDCl₃ solutions, the diamagnetic and paramagnetic components relax exponentially due to the isotropic molecular motions. In solution, the T₁ time of the Cp₂Co protons is 9.58 ms, whereas that for Cp₂Ni amounts to 0.96 ms [15,16].

To improve our understanding of the proton relaxation in solid Cp₂Ni/Cp₂Co mixtures, it is useful to consider the common crystal structure of these metallocenes [32,33], displayed in Figure 2. According to the X-ray data, the shortest average intramolecular and intermolecular metal (electron)—proton distances are 2.70 Å and 3.91 Å, respectively. In terms of the dipolar electron-nucleus relaxation corresponding to Equation (1), the difference in these distances leads to a ratio T₁(H^…S)/T₁(H-S) of (3.91/2.7)⁶, which equals 9.22. In other words, the T₁(H^…S) time due to intermolecular dipolar proton-electron interaction will be about nine times longer than the T₁(H-S) relaxation time caused by intramolecular H-S interactions.

Since the number of nearest neighbors surrounding one metallocene molecule in the crystal lattice is eight (Figure 2), the total relaxation time observed can be expressed via Equation (3).

1/T₁(obs) = 1/T₁(H-S) + 8 · 1/T₁(H^…S)

(3)

The relaxation time ¹H T₁(obs) of 0.27 ms has been measured for the Cp₂Ni signal in the 10%/90% Cp₂Co/Cp₂Ni mixture (Table 2). This solid solution contains a large excess of nickelocene. Therefore, it can be assumed that the eight nearest Cp₂Ni neighbors are present and that the intermolecular distances for nickelocene are preserved. Based on Equation (3) and the fact that T₁(H^…S)/T₁(H-S) is about 9, the relaxation time ¹H T₁(obs) corresponds to the T₁(H-S)Ni value of 0.51 ms for the intramolecular relaxation, and a T₁(H^…S)Ni relaxation time of 0.57 ms for the total intermolecular interactions.

The same calculation, performed for the 90%/10% Cp₂Co/Cp₂Ni solid solution with the measured relaxation time ¹H T₁(obs) of 2 ms (Table 2), gives a T₁(H-S)Co value of 3.8 ms for the intramolecular relaxation, and the T₁(H^…S)Co time of 4.2 ms corresponding to the total intermolecular interactions. In other words, these estimates for Cp₂Co and Cp₂Ni show that practically one-half of the observed relaxation rate can be provided by intermolecular interactions with the surrounding molecules.

Considering the data summarized in Table 2, it is obvious that the measured ¹H T₁ relaxation times of both components in the solid solutions Cp₂Ni/Cp₂Co do not change significantly even when the ratios are varied over a large range. The ¹H T₁ relaxation times show the average values of 2.5 ms for Cp₂Co and 0.38 ms for Cp₂Ni. Importantly, the ¹H T₁ times listed in Table 2 do not follow the component ratios, and their small variations can be attributed to 20–30% errors in the ¹H T₁ determinations due to the samples being highly air-sensitive. In other words, in the mixtures that were prepared by grinding Cp₂Ni and Cp₂Co together, the Cp protons of the components relax independently via the unpaired electrons of their own metal centers. This result reveals the absence of substantial intermolecular relaxation contributions. This effect is most likely caused by increased intermolecular distances because of the destruction of the crystal structures. In fact, when the intermolecular distances in a crystal of Cp₂Ni grow, for example, by a factor of 1.5, the T₁(H^…S)Ni time of 0.57 ms, corresponding to the total intermolecular interactions, will be increased by a factor of 11. In addition, the ¹H T₁ relaxation time in polycrystalline nickelocene has been measured as 0.23 ms, which is shorter than the times summarized in Table 2. Thus, the ¹H T₁ relaxation times of 2.5 ms and 0.38 ms mentioned above can be attributed to T₁(H-S)Co and T₁(H-S)Ni relaxation times that characterize the intramolecular relaxation contributions.

The conclusions drawn for solid Cp₂Co and Cp₂Ni mixtures on the basis of the relaxation data in Table 2 agree with the ¹H T₁ relaxation measurements carried out for paramagnetic metallocenes in the mixtures with diamagnetic ferrocene dissolved in CDCl₃ (Table 3). The ¹H T₁ relaxation times of Cp₂Co and Cp₂Ni have been determined as 9.6 ms and about 1 ms, respectively. They are independent of the fractions of Cp₂Fe that change over a large range from 0% to 90%. The Cp₂Fe rather plays the role of a diluting agent, like the solvent. Therefore, the ¹H T₁ relaxation times for Cp₂Co and Cp₂Ni in solution again represent the intramolecular electron-proton dipolar relaxation contributions.

The ¹H T₁ relaxation time of pure Cp₂Fe in the CDCl₃ solution (Table 3) is much shorter (4.9 s, Table 3) than that in the solid state (14–15 s) [16]. Such a shortening is expected due to the rapid isotropic reorientations of the Cp₂Fe molecules in solutions. In contrast, the ¹H T₁ relaxation times of both paramagnetic compounds grow significantly when going from the solid state (Table 2) to the CDCl₃ solution (Table 3). Based on the relaxation mechanism (c) via the dipolar electron–proton interactions, this observation can be explained by the electron relaxation time, T_1e, that can change with increasingly rigid environments [34].

Equation (1) can be used to calculate the T_1e relaxation time for Cp₂Ni in solution. The ¹H T₁ relaxation time of Cp₂Ni, determined for the CDCl₃ solution as ca. 1 ms for all Cp₂Ni/Cp₂Fe ratios (Table 3), and the intramolecular Ni(electron)—proton distance of 2.70 Å, derived from the X-ray structure, result in the T_1e relaxation time of 17 × 10⁻¹³ s. Analogously, the longer T_1e relaxation time of 45 × 10⁻¹³ s can be obtained for solid Cp₂Ni from the ¹H T₁ time of 0.38 ms (Table 2). In the same way, the T_1e relaxation time for Cp₂Co can be calculated as ca. 5 × 10⁻¹³ s and 20 × 10⁻¹³ s, characterizing the relaxation of the unpaired electrons of the Co centers in solution and in the solid state, respectively. It should be noted that the T_1e relaxation time of 17 × 10⁻¹³ s obtained here for Cp₂Ni in CDCl₃ is longer than that reported as 3 × 10⁻¹³ s for Cp₂Ni dissolved in toluene [31]. The latter value, however, has been estimated from the NMR linewidths and not based on the relaxation time.

Co-crystallization of dissolved metallocenes leads to solid solutions with a homogeneous distribution of the different molecules on a molecular level in the crystal lattice. This homogeneous distribution of different metallocenes has been proven by single-crystal X-ray analysis previously [15]. Hence, only one T₁ relaxation time is found for each metallocene. In a different approach, the migration of one metallocene into an existing crystal lattice of another in the absence of a solvent has been demonstrated by the ¹H T₁ relaxation experiments for mixtures of Cp₂Fe and Cp₂Ni prepared by grinding the components together with varied molar ratios [15]. While grinding is a complex process regarding the obtainable particle sizes [35], we could demonstrate earlier that even in the absence of a solvent and without grinding, the volatile Cp₂Ni migrates into single crystals of Cp₂Fe [15]. The main feature of the ¹H T₁ relaxation behavior of Cp₂Fe after grinding with Cp₂Ni was its bi-exponential character [15]. Two different ¹H T₁ times were obtained for Cp₂Fe molecules in domains composed mostly of ferrocene, and for Cp₂Fe molecules at the edges of these domains, and therewith close to Cp₂Ni molecules. Hereby, the long ¹H T₁ time of 14–18 s was determined for Cp₂Fe molecules residing far away from paramagnetic Cp₂Ni molecules [15]. However, it remained unclear how close the Cp₂Fe and Cp₂Ni molecules are located in the fast-relaxing domains when the mixtures are prepared by grinding the components together in the absence of a solvent. Here, we analyze these domains on the basis of the short ¹H T₁ times obtained for the fast-relaxing T₁ components with errors around 20–25% for the Cp₂Fe/Cp₂Ni mixtures that are summarized in

Table 4. The ¹H T₁ times (ms) of fast-relaxing Cp₂Fe molecules obtained with bi-exponential function treatments of the inversion-recovery experiments performed for the Cp₂Fe/Cp₂Ni mixtures prepared by dry grinding of the components [15].

Molar Ratio Cp2Fe/Cp2Ni (%/%)	1H T1 Time (Short)	Fraction
90/10	3.0	0.1
80/20	2.0	0.3
70/30	3.0	0.2
60/40	2.0	0.40
50/50	2.0	0.41
40/60	2.0	0.41
30/70	2.0	0.42

.

The data in Table 4 show that the fraction of the fast-relaxing T₁ component grows with the Cp₂Ni content and reaches a maximum of 0.40–0.42. This value can be caused by a limitation in the mixing technique. As shown above, the ¹H T₁(H^…S)Ni relaxation time in Cp₂Ni is 0.57 ms. This represents also the total intermolecular dipolar electron—proton relaxation that will contribute to the relaxation of the diamagnetic Cp₂Fe when it is surrounded by 8 Cp₂Ni molecules at a distance of 3.91 Å in a Cp₂Fe/Cp₂Ni crystal. Consequently, the short ¹H T₁ relaxation time of 2–3 ms, obtained experimentally for the fast-relaxing Cp₂Fe, will correspond to 2–3 short contacts (3.91 Å) between the Cp₂Fe and Cp₂Ni molecules. In other words, each Cp₂Fe molecule is surrounded by 2 to 3 neighboring Cp₂Ni molecules. This shows that the components are mixed in the solid solution Cp₂Fe/Cp₂Ni on a molecular level in the fast-relaxing domain. It is also possible that the number of short contacts is larger, but at increased intermolecular distances.

It is remarkable that for mixed crystals of Cp₂Fe and Cp₂Ni grown from 50/50 solutions, the ¹H T₁ relaxation time of the Cp₂Fe does not exhibit a slow-relaxing component. This indicates that large domains composed of only Cp₂Fe are absent, and a more homogeneous distribution of the Cp₂Fe and Cp₂Ni molecules in the crystal lattice prevails throughout the bulk of the material. The ¹H T₁ relaxation time of Cp₂Fe has been measured as 4 ms [15], which is close to the values of 2–3 ms reported in Table 4.

3. Conclusions

The proton T₁ relaxation times in solid solutions of Cp₂Co/Cp₂Ni and Cp₂Fe/Cp₂Ni, prepared by co-crystallization and by grinding the components together, have been analyzed. The results show that the dipolar electron—proton interactions are the dominant relaxation mechanism. It has been concluded that Cp₂Ni and Cp₂Co protons in CDCl₃ solutions, as well as in the mixtures prepared by grinding the components, relax independently via their own unpaired electrons. Intermolecular relaxation contributions are negligible due to the increased intermolecular distances that are much larger than 3.91 Å. Using these ¹H T₁ relaxation times and the intramolecular Ni(electron)—proton distances of 2.70 Å that were obtained from the single crystal X-ray structure, the electron relaxation times T_1e are determined as 17 × 10⁻¹³ s in CDCl₃ and 45 × 10⁻¹³ s in the solid state. The corresponding T_1e relaxation times for Cp₂Co are calculated as ca. 5 × 10⁻¹³ s in solution and 20 × 10⁻¹³ s in the solid.

The fast-relaxing T₁ components in mixtures of Cp₂Fe and Cp₂Ni, prepared by grinding the components together, have been analyzed with the Cp₂Ni content increasing from 10% to 70%. At least 2–3 short contacts with distances of 3.91 Å between Cp₂Fe and Cp₂Ni molecules are present. It is possible that the number of contacts is larger, but at increased intermolecular distances. Overall, the proton T₁ time analysis illustrates that the components in solid solutions, which were obtained by co-crystallization from solutions, mix on the molecular level throughout the crystal lattice. In case the solid solutions are prepared by manual grinding, domains mostly populated by one species remain, and the homogeneous mixing only takes place at the interfaces. In summary, the presented study provides new insights into relaxation mechanisms of metallocenes, and it demonstrates that paramagnetic solution- and solid-state NMR spectroscopy is a valuable method for monitoring mechanochemical processes [24,35] and for probing multi-component materials [36] on the molecular level.

4. Experimental Section

Materials and sample preparation. Cp₂Fe, Cp₂Ni, and Cp₂Co were purchased from Fisher Scientific and sublimed under an inert gas atmosphere prior to use. All metallocenes and solid solutions were stored in a glove box operated with purified nitrogen.

The solid solutions of metallocenes were obtained by co-crystallizing them from DCM solutions after weighing in the desired amounts of the components. The crystals contained the metallocenes in the same ratios as the initially prepared solution, as determined by filtering the crystals off from the mother liquor, dissolving them in a deuterated solvent, and measuring the integrals of the metallocene signals. The integrals confirmed that the compositions corresponded to the initial ratios of the metallocenes in the prepared solutions. Alternatively, the solid solutions have been generated by manually grinding the desired amounts of the solid metallocenes together for 30 min with an agate mortar and pestle that did not absorb the metallocenes. All materials were densely packed into 4 mm ZrO₂ rotors. Cobaltocene and nickelocene are air-sensitive and, therefore, nitrogen was used as the bearing and drive gas for MAS measurements.

Solid-state NMR measurements. The solid-state NMR spectra were recorded on a Bruker Avance-Neo 400 spectrometer (Bruker Biospin, Karlsruhe, Germany). The 4 mm MAS probehead was equipped with a broadband and a ¹H NMR channel. The ¹H NMR spectra were acquired using a single pulse program. Eight scans were sufficient for spectra with good S/N ratios. The spectra were processed without line broadening; however, the ¹H background signal was subtracted. TMS functioned as the external ¹H chemical shift standard. For the static regime, the temperature control unit of the spectrometer was calibrated by the standard procedure that is based on liquid methanol in a MAS rotor. When spinning, temperature corrections have been applied following the protocol for 4 mm rotors [27]. At a spinning speed of 10 kHz, 295 K of the drive and bearing gas corresponds to 298.3 K within the rotor based on the correction [27]. The frictional heating effect is negligible when going from 10 to 11 kHz according to this well-known protocol [27].

The proton T₁ relaxation times were determined at spinning rates of 10 and 11 kHz using standard inversion–recovery pulse programs (180°−τ−90°). The RF pulses were calibrated prior to the measurements (2.5 μs at 105.3 W power). The acquisition time was varied from 0.005 to 0.001 s. The τ delays increased incrementally from 0.00005 to 50 s for ferrocene/cobaltocene mixtures and from 0.000015 to 5.0 s for nickelocene/cobaltocene systems. After each pulse cycle, complete relaxation was achieved by sufficiently long recycle delays, which amounted to 50 s for mixtures of ferrocene and cobaltocene and 5 s for the solid solutions of nickelocene and cobaltocene. No linebroadening was necessary after accumulating 8 scans. Processing the relaxation time data was performed by subjecting the experimentally obtained inversion−recovery curves, featuring the signal intensities versus τ times, to a conventional nonlinear fitting computer program based on the Levenberg–Marquardt algorithm. Since the ¹H resonances of the metallocenes measured in this contribution have different chemical shifts, the T₁ times for their mixtures were determined using two carrier frequencies centered at the positions of the two resonances. The error margin of the T₁ time measurements is estimated to be about 10–15%.

The line shape analyses of the wideline signals were performed with the programs and software package of the Bruker spectrometer.