Probing Interactions between Electron Donors and the Support in MgCl₂-Supported Ziegler–Natta Catalysts

Abstract

Olefin polymerization using Ziegler–Natta catalysts (ZNCs) is an important industrial process. Despite this, fundamental insight into the inner working mechanisms of these catalysts remains scarce. Here, we focus on the low-γ nuclei ²⁵Mg and ³⁵Cl for an in-depth solid-state NMR and density functional theory (DFT) study of the catalyst’s MgCl₂ support in binary adducts prepared by ball-milling. Besides the bare MgCl₂ support and a MgCl₂–TiCl₄ adduct, samples containing donors that are part of the families of 2,2-dialkyl-1,3-dimethoxypropanes and phthalates used in fourth- and fifth-generation ZNCs are studied. DFT calculations indicate that the quadrupolar coupling parameters of the chlorines differ significantly between bulk and surface sites. As a result, the NMR visibility of the chlorine sites correlates with the particle size except for the adduct with 2,2-dimethyl-1,3-dimethoxypropane donor. The DFT calculations furthermore show that the surface sites are fairly insensitive to binding of different donor molecules, making it difficult to identify specific binding motives. The surface sites with large ³⁵Cl NMR line widths can be observed using high radio frequency field strengths. For the 2,2-dimethyl-1,3-dimethoxypropane donor, we observe additional surface sites with intermediately high quadrupolar couplings, suggesting a different surface structure for this particular adduct compared to the other systems. For ²⁵Mg, pronounced effects of donor binding on the quadrupole interaction parameters are observed, both computationally and experimentally. Again the adduct with the 2,2-dimethyl-1,3-dimethoxypropane donor shows a different behavior of the surface sites compared to the other adducts, which display more asymmetric coordinations of the surface Mg sites. Identifying specific binding motives by comparing ²⁵Mg NMR results to DFT calculations also proves to be difficult, however. This is attributed to the existence of many defect structures caused by the ball-milling process. The existence of such defect structures both at the surface and in the interior of the MgCl₂ particles is corroborated by NMR relaxation studies. Finally, we performed heteronuclear correlation experiments, which reveal interactions between the support and Mg–OH surface groups, but do not provide indications for donor–surface interactions.

Introduction

Ziegler–Natta catalysts (ZNCs) play an important role in the worldwide production of polyolefins. Modern catalysts are composed of a disordered MgCl₂ support with co-adsorbed TiCl₄ and an organic electron donor. This system is activated by an Al-alkyl, often together with a second donor (in most cases, an alkoxysilane).^1,2 Still, these catalysts hold many secrets at the molecular level. The important surface structures are not well understood, due to the complexity of the system and the absence of significant experimental studies. Yet, fundamental understanding of the active constructs is crucial for further catalyst design.

The last decade yielded a significant number of theoretical contributions aimed at finding the most stable surface constructs for MgCl₂–donor or MgCl₂–TiCl₄ binary adducts.³⁻¹⁶ Thermodynamically, (104)-surface sites have been found to be the most stable. However, coordination of electron donors can reverse the relative stabilities so that the (110)-surface sites become more stable than the (104)-surface.^5,7,14,17,18 Some computational studies go one step further and look at the role that the donors play in the whole catalytic cycle.¹⁹⁻²¹

Recent years have seen more experimental studies that focus on structure–function relationships, for both traditional MgCl₂-based ZNCs²²⁻²⁴ and new MgCl₂-derived support materials.²⁵⁻²⁹ Still, many studies try to investigate the produced polymer in intricate ways to learn more about these elusive catalysts via an indirect approach.³⁰ It is our belief that the final answers about the working mechanisms of ZNCs will primarily be found when studying the catalysts themselves.³¹

This calls for a wide range of experimental studies making use of the strengths of different spectroscopic techniques, including solid-state NMR spectroscopy. A few recent studies³²⁻³⁴ have shown the potential of a combined ¹H and ¹³C solid-state NMR/density functional theory (DFT) approach for the study of the organic donors on the catalysts’ surface, giving valuable experimental proof for standing hypothesis about preferred coordination modes. The surface structures in Ziegler–Natta catalysts can be studied from two sides. Besides the donor, the support can be studied. One of the strengths of NMR spectroscopy is its ability to study interactions between different components, such as donor–support interactions, making it a suitable tool for the study of heterogeneous catalysis.^35,36 Such insight into donor–support interactions should give a more complete picture of the coordination of donors on the MgCl₂–support. In this article, we will present a detailed investigation of the MgCl₂ nanoparticles’ surface. Subsequently, we will present an in-depth study of the interactions between the donors and the surface. To this end, we make use of correlation experiments, such as cross-polarization (CP), rotational-echo double-resonance (REDOR),^37,38 and transfer of populations in double resonance (TRAPDOR).³⁹⁻⁴¹

In a previous study, we showed the feasibility of ²⁵Mg and ³⁵Cl solid-state NMR for the study of the neat support material MgCl₂ (α-MgCl₂) as well as the ball-milled equivalent (δ-MgCl₂).⁴² The results indicated that the bulk of MgCl₂ nanoparticles is readily observed; however, more advanced schemes are necessary to study the catalytic relevant surfaces because of their large quadrupolar interactions. Here, we will use ¹H, ²⁵Mg, and ³⁵Cl solid-state NMR to study the support with its surfaces and support–donor interactions in Ziegler–Natta catalyst model systems. We will make use of a variety of sensitivity enhancement schemes and correlation experiments to yield information about the surface structures. The interpretation of the NMR results is supported by DFT calculations of both ²⁵Mg and ³⁵Cl quadrupolar interaction parameters.

Results and Discussion

A series of ball-milled binary adducts between MgCl₂ and industry-relevant electron donors and an adduct between MgCl₂ and TiCl₄ are studied. The investigated samples have been introduced by us elsewhere³⁴ and studied with ¹³C NMR spectroscopy to identify the preferences for particular surfaces depending on the donor type. The samples contain donors that are part of the families of 2,2-dialkyl-1,3-dimethoxypropanes and phthalates: 2,2-dimethyl-1,3-dimethoxypropane (DMDOMe, Do1), 9,9-bis(methoxymethyl)-9H-fluorene (DMFluo, Do2), and diisobutyl phthalate (DiBP, Do3) used in fourth- and fifth-generation ZNCs.^43,44 The binary adducts are coded as Do“x”_“y”, where Do“x” refers to the donor type and _“y” refers to the donor loading (in percentage). Table 1 gives the sample characteristics showing the particle size as determined from powder X-ray diffraction (XRD), where ⟨L_c⟩ and ⟨L_a⟩ are the average particle dimensions perpendicular and parallel to the basal (ab) plane, respectively. Ball milling MgCl₂ in the presence of electron donors yields nanoparticles with much smaller dimensions. On the basis of previous results,³⁴ we printed the most likely surface type for each sample in bold.

Table 1. Sample Properties.

samples code	donor loadinga	⟨Lc⟩ (nm)	⟨La⟩ (nm)	Cl surf. frac.b (%) (104)/(110)	rel. int.c (%)	Mg surf. frac.b (%) (104)/(110)
dry MgCl2d		n.d.e	n.d.e		100
MgCl2 DCMd		12.6	13.0	5.3f/6.2	96	10.5/6.2
MgCl2/TiCl4	4.3	6.34	7.88	8.4/10.2	92	16.8/10.0
Do1_4	4.0	4.24	7.70	8.6/10.3	94	17.0/10.0
Do1_10	10.0	2.84	4.37	14.3/17.2	93	28.3/17.0
Do2_2.5	2.5	4.98	8.41	8.0/9.3	91	15.8/9.5
Do3_2	2.1	7.35	7.76	8.5/10.3	87	16.9/10.0
Do3_7	6.7	n.d.e	3.93	15/19	82	31.0/19.5

^a(% mol adsorbate/mol mg).

^bThe fraction of surface sites is given for particles exposing either (104)- or (110)-surface sites, see text.

^c35Cl intensities from solid-state NMR experiments are an average between magic-angle spinning (MAS) and static relative intensities, where the difference between MAS and static was never more than 3%.

^dSee ref (42).

^eThe average size could not be determined because the XRD resonances were too narrow (dry MgCl₂) or too broad (Do3_7).

^fNumbers in bold face indicate most probable exposed surface.

The MgCl₂ nanoparticles can be studied by ²⁵Mg and ³⁵Cl NMR. We compare the binary adducts to neat MgCl₂ as well as the ball-milled equivalent (MgCl₂ DCM) for quantitative measurements of the ³⁵Cl NMR signal intensity. Despite large surface areas, these particles still have a dominant “bulk” phase, which will be the predominant species in ²⁵Mg and ³⁵Cl spectra. Therefore, we will first characterize the bulk phase in detail before performing dedicated NMR experiments that are necessary to look at the surfaces. With the surface sites revealed, correlation experiments can be performed to probe interactions between donor and support.

In studies of Ziegler–Natta catalysts, there are two types of surfaces of the MgCl₂ nanoparticles that are most commonly considered: the (104)- and (110)-surfaces. The (104)-surface is supposedly the most stable lateral surface of MgCl₂ in the absence of donors. It exposes pentacoordinated magnesium sites as well as coordinatively unsaturated chloride sites that are bound to only two magnesium. On this surface, donors might bind monodentately, although bivalent donors are more inclined to bind in a bridging mode. In the presence of electron donors, also the (110)-type of surfaces might become exposed because of the stabilizing effect of the donor. The (110)-surface exposes tetracoordinated magnesium sites on which bivalent donors coordinate in a chelating mode. Again, there are coordinatively unsaturated chloride sites as well.

Ball milling MgCl₂ yields nanoparticles with the high surface areas needed for catalysis. The fraction of surface sites/exposed sites (also called “surface fraction” in short) is defined as the number of coordinatively unsaturated Mg or Cl atoms (the outermost layer) divided by the total number of Mg or Cl sites in the nanoparticles. An estimation of this fraction of surface sites can be made for particular particle geometries from the given ⟨L_c⟩ and ⟨L_a⟩ dimensions, and the results are shown in Table 1 for hexagonal particles exposing either (104)- or (110)-type surfaces. Figure S1 shows the crystallographic morphology of such a hexagonal particle.

For chlorine, particles with only (110)-type surface sites yield a 20–30% higher fraction of surface sites than equisized particles with only (104)-type surfaces, depending on the exact particle size (see Table 1). For example, with a particle size of 13 nm, the ball-milled sample has an estimated chlorine surface fraction of 5.3% (considering only (104)-surfaces) or 6.2% (assuming only (110)-surfaces), so the adduct with the smallest particle size (Do3_7) has a surface fraction of 15–19.5%. The difference in the fraction of exposed surface sites between both surface types is significantly larger for magnesium (vide infra).

Bulk ³⁵Cl NMR

Despite the large surface areas, most of the chlorine (and magnesium) spins are still in sites with a bulklike conformation, where each magnesium is surrounded octahedrally by six chlorides. As a result, both ²⁵Mg and ³⁵Cl NMR spectra will be dominated by signal from the bulk or bulklike sites. The results of solid-state ³⁵Cl NMR measurements obtained at 15.625 kHz MAS at 20.0 T can be found in Figure 1A. It shows the central transition (CT) center band with two sets of spinning sidebands on both sides. For all samples, the CT only shows one component.

Figure 1.

³⁵Cl NMR Hahn-echo spectra of MgCl₂ binary adducts (A) at 15.625 kHz MAS, rotor-synchronized and (B) under static conditions, B₀ = 20 T.

Compared to the neat material (dry MgCl₂), the sharp features of the quadrupolar powder pattern broaden and are smeared out. This has already been observed before for ball-milled MgCl₂⁴² and is explained by a distribution in quadrupolar parameters that result from a disorder in the local environment. Such a distribution manifests itself in typical line shapes, such as the asymmetric broadening of the MAS spectra. The line shape is mainly the result of a distribution in quadrupolar parameters without much chemical shift broadening. This is most obvious examining the static experiments (Figure 1B), in which it can be seen that the discontinuity at the isotropic chemical shift position is present in all samples, while the two horns on the left and right are increasingly smeared out. The spectra of the binary adducts show the presence of larger distributions in quadrupolar parameters than those found for MgCl₂ DCM, which indicates a larger heterogeneity in these samples. This is not surprising given the smaller particle dimensions. Along the sample series, as shown in Figure 1, there is a gradual increase in the distribution in quadrupolar parameters. The smallest particles with the highest donor loading (Do1_10 and Do3_7) give rise to the largest distribution in quadrupolar parameters.

³⁵Cl (and also ²⁵Mg) experiments were performed with long relaxation delays (5 × T₁) and in the weak radio frequency (RF) regime (ν_RF ≪ ν_Q) to ensure quantitative conditions and avoid line shape distortions.⁴⁵ Quantification of the spectral intensities (see Table 1) shows that the spectra of some samples lack a significant fraction of the anticipated signal. This is most prominent for the DMFluo (Do2) and DiBP (Do3) adducts, for which 10–20% of the ³⁵Cl signal is not detected. For Do3_7, a sample with a high donor loading and the smallest particle size, the largest fraction of ³⁵Cl signal escaped detection. It is also the sample with the least-defined line shape and thus the largest distribution in quadrupolar parameters. This loss of signal can pertain to sites with large quadrupole interactions, which consequently yield resonances that are broadened beyond detection (at least under the experimental settings used to acquire the spectra in Figure 1).

In general, there is a correlation between particle size (in the lateral dimension) and intensity loss in the chlorine Hahn-echo spectra (see Table 1). This strongly suggests that the surface sites in the lateral dimension are missing from the spectra. Such an observation is in agreement with the results from DFT calculations (vide infra) that predict large quadrupolar parameters for these surface sites, even after binding of donors. Remarkably, the samples containing DMDOMe (Do1) fall outside this trend (Figure 2). In particular, the spectrum of Do1_10 shows only a relatively low fraction of signal loss, despite a large surface area (small particle size), high donor loading, and a line shape showing a large distribution in quadrupolar parameters.

Figure 2.

Missing intensity in quantitative ³⁵Cl NMR spectra vs fraction of Cl surface sites. ³⁵Cl intensities from solid-state NMR experiments are an average between MAS and static relative intensities, where the difference between MAS and static was never more than 3%.

Line Shape

For neat ball-milled MgCl₂,⁴² we previously described the distribution in quadrupolar parameters of the bulk-phase signal to be induced by surface effects (i.e., lack of long-range order) and fitted its line shape using the extended Czjzek distribution.^46,47 The much larger surface areas of the smaller nanoparticles of the adducts explain the larger distribution in quadrupolar parameters observed.

The Czjzek model^48,49 can be used to describe a distribution in quadrupolar parameters for a disordered system. For systems with an intrinsic quadrupole moment, such as MgCl₂, a more elaborate model is necessary that can describe long-range disorder around a locally ordered site. For such situations, the so-called extended Czjzek model has been introduced.^46,47 Here, C_Q,0 and η₀ are the quadrupolar parameters for the well-defined first-order coordination sphere and, similar to the Czjzek model, the distribution in quadrupolar parameters caused by structural variations in the higher coordination spheres is described by the parameter σ.

A distribution in quadrupolar parameters as the result of ball milling was observed earlier by Bureau et al.⁵⁰ for GaF₃ and by Scholz et al.⁵¹ for Al₂O₃. In both studies, the particle size is around 13 nm, very similar to what we obtain for neat ball-milled MgCl₂. In contrast to our ³⁵Cl spectra, bicomponent line shapes are observed, in particular for GaF₃. Because of a weak quadrupolar interaction in the ⁷¹Ga spectrum prior to ball milling, the authors model their experimental spectra using two Czjzek distributions, with different σ-values. The site with the lowest σ is attributed to “crystalline grains” (i.e., bulk sites that are slightly more distributed than crystalline GaF₃), while the site with the largest σ is attributed to “grain boundaries” (i.e., surfaces). The latter corresponds to 70% of the intensity, showing that ball-milling impacts much more than just the outer shell. For Al₂O₃, Scholz et al. used a combination of Czjzek distribution and well-defined resonance to describe their spectra, again assigning the two components to grain boundaries/surfaces (referred to as “amorphous phase” in their contribution) and crystalline grains/bulk. The fraction of the amorphous phase even reaches 80%, again showing the far-reaching impact of ball milling. Just like MgCl₂, Al₂O₃ already has a quadrupolar interaction before ball milling and we therefore believe that an extended Czjzek model (which had not yet been introduced at that time) would be better suited to model the spectra of ball-milled Al₂O₃, in particular because the experimental spectrum shows no sign of two components (which clearly is the case in GaF₃). It is important to realize for our study that the ball milling affects a significantly larger fraction of the Mg and Cl sites in the nanoparticle than just those in the outer shell. This is something which becomes apparent in the analysis of our relaxation data (vide infra).

We tried to describe our experimental line shapes using extended Czjzek distributions. Using the EGdeconv program,⁵² the MAS spectra could be modeled reasonably well with a single component exhibiting an extended Czjzek distribution, as can be seen in Figure 3. The overall experimental line width (in both the static and MAS spectra) does not increase along the sample series, despite the increasing distribution in quadrupolar parameters. The fitting results show that a larger distribution is compensated by a somewhat smaller C_Q,0, e.g., while the ³⁵Cl sites in neat MgCl₂ have a quadrupolar coupling constant, C_Q, of 4.61 MHz, adduct Do3_2 gives C_Q,0 = 4.36 MHz and Do3_7 C_Q,0 = 4.16 MHz (see Table 2). The decrease in C_Q can be attributed to the increased contribution of (001)-surface sites, which have slightly smaller quadrupolar coupling parameters compared to the bulk (see Table 3). For robustness, the fitting routine has a lower limit of 0.5 for the σ parameter. As a consequence, the actual distribution is slightly overestimated for some of the least disordered samples, in particular MgCl₂ DCM. The best agreement is found for the most disordered samples Do1_10 and Do3_7. Unfortunately, the static spectra could not be satisfactorily simulated using the parameters following from the MAS fit, nor could they be fitted properly to the extended Czjzek model (see Figure S2). It could be that some CSA is present in the static spectra, which prevents fitting them to a model only taking into account the quadrupolar interaction. Alternatively, even the extended Czjzek model may not be sophisticated enough to describe the distribution that results from the effects causing both variation in first and higher coordination spheres of the chlorines. Although it would undoubtedly give a better fit, we do not think it is justified to include a second component into the fitting procedure, as was done in the studies of GaF₃ and Al₂O₃ because we see no features of a well-defined crystalline fraction (with pronounced quadrupolar features) in the spectra.

Figure 3.

Fit of the ³⁵Cl MAS spectra (B₀ = 20 T) to the extended Czjzek model.

Table 2. Results from Fitting to the Extended Czjzek Distribution.

samples code	CQ,0 (MHz)	η0	σa (MHz)
MgCl2 DCM	4.34 ± 0.10	0.0	0.50 ± 0.05
MgCl2/TiCl4	4.46 ± 0.10	0.0	0.51 ± 0.05
Do2_2.5	4.36 ± 0.10	0.0	0.51 ± 0.05
Do3_2	4.36 ± 0.10	0.0	0.54 ± 0.05
Do3_7	4.16 ± 0.10	0.0	0.65 ± 0.05
Do1_4	4.40 ± 0.10	0.0	0.51 ± 0.05
Do1_10	4.22 ± 0.10	0.0	0.68 ± 0.05

^aLower limit of the fitting routine is σ = 0.5 MHz.

Table 3. DFT Calculations of the ³⁵Cl and ²⁵Mg Quadrupole Parameters for Various Neat MgCl₂ Species and MgCl₂-H₂O Adducts, at B3LYP-D2/pob-TZVP Level.

species	atom	35Cl CQ (MHz)	η	atom	25Mg CQ (MHz)	η
MgCl2 bulk	Cl	4.4	0	Mg	1.62	0
MgCl2(001)	Cl	4.9	0	Mg	1.51	0
MgCl2(104)	Cl	15.0	0.7	Mg	11.2	0.3
	Clcs	6.7	0
MgCl2(110)	Cl	18.3	0.5	Mg	6.6	0.4
MgCl2(104)–H2O	Cl-1	10.5	0.7	Mg	2.3	0.8
	Clcs-2	5.7	0.9
MgCl2(110)–H2O	Cl-1	19.7	0.4	Mg	10.5	0.1
	Cl-2	16.7	0.6
MgCl2(110)–2H2O	Cl-1	13.6	0.3	Mg	6.5	0.6
	Cl-2	13.6	0.3

Relaxation

A strong reduction in the ³⁵Cl T₁ relaxation times is found for the binary adducts with respect to neat MgCl₂ (see Table S1). The relaxation times show a correlation with ⟨L_c⟩ in particular. In the following discussion of quadrupolar relaxation behavior, chlorine relaxation data are leading, as they are determined more reliably, but all conclusions appear to be valid for ²⁵Mg T₁ relaxation as well. Ball-milling neat MgCl₂ already has a small effect on the relaxation time and T₁ decreases further for the adducts. This suggests that fast relaxation is taking place at the surfaces, but also the relaxation rate of the bulk is increased as a result of local distortions. Due to the weak dipole–dipole interaction and the low natural abundance of, in particular ²⁵Mg, we exclude the option that spin diffusion governs the enhanced relaxation for the bulk. This is corroborated by the fact that the relaxation behavior under MAS is equal to that under static conditions.

The relaxation behavior of our particles can be fitted with a biexponential function, with the exception of neat MgCl₂, which shows monoexponential behavior. Although quadrupolar relaxation is intrinsically multiexponential; in practice, it is often monoexponential for a spin I = 3/2,⁵³⁻⁵⁵ in agreement with the relaxation behavior of neat MgCl₂. Therefore, the relaxation behavior of our binary adducts would suggest the presence of two phases, such as surfaces and bulk, each having its own typical relaxation. However, in the discussion about the distributed line shapes, we argued against such a distinction in two different phases because we find no evidence for a crystalline fraction. In analogy to a distribution in quadrupolar parameters to describe the observed line shape, a distribution in relaxation times seems more appropriate, and this can be modeled using a Weibull distribution (“stretched exponential”), as can be seen in Figure S3. Ideally, both distributions would even be connected, as 1/T₁ ∝ ω_Q². Along the samples series, the distribution in ω_Q does not change dramatically, but T₁ times decrease drastically. Quadrupolar relaxation is often overwhelmingly dominated by fluctuating electric field gradients. This suggests that motion-driven relaxation processes play a crucial role and we hypothesize that defect-induced dynamics govern the fast relaxation. Surface sites have largest ω_Q (vide infra) and probably highest dynamics as well, resulting in the fastest relaxation. To fully understand the relaxation behavior, extensive field- and/or temperature-dependent relaxation measurements have to be performed, which is beyond the scope of this contribution.

The relaxation times of ²⁵Mg and ³⁵Cl appear to be strongly correlated. This again suggests that their relaxation is influenced by the same defect-induced dynamics. Mobility of donor molecules could also contribute to enhanced relaxation at the surfaces, but the reduction of T₁ for sample MgCl₂ DCM indicates that there is already enhanced relaxation in the absence of a donor.

DFT Calculations of ³⁵Cl Sites

The surfaces are, at least partially, covered by donor molecules. Intuitively, it would be expected that coordination of these molecules to the unsaturated (104)- and (110)-surfaces would have a large impact on the quadrupolar parameters. To interpret the quadrupolar NMR parameters, we calculated quadrupolar coupling constants (C_Q) and asymmetry parameters (η) for the binary adduct systems. As a test case to see if this hypothesis is true, we first calculated the ²⁵Mg and ³⁵Cl quadrupolar parameters for adsorbed water on the surface. We choose water because it is a small molecule with few degrees of freedom, as well as because water adsorption is known to occur in these kinds of samples. For the (110)-surface, binding of both a single water and a full coordinative saturation by the binding of two water molecules was considered (see Figure 4).

Figure 4.

Optimized structures of H₂O (A) on the (104)-surface surfaces of MgCl₂ and (B, C) on the (110)-surface; Mg atoms are colored in yellow, Cl atoms in green, O atoms in red, H atoms in white. Cl-2 on the (104)-surface is in the Cl_cs position.

Furthermore, we calculated quadrupolar parameters for MgCl₂(110)–TiCl₄, MgCl₂(104)–DMDOMe, and MgCl₂(110)–DMDOMe adducts using periodic calculations. We used cluster models that were introduced in ref (34), for the calculations of the quadrupolar parameters for DiBP adducts and for a high-coverage model of DMDOMe. In the calculations, the donor molecules are coordinated in either the “bridge” or the “chelate” mode (see Figures 5, S8, and S9) and TiCl₄ adopts the so-called Corradini site (see Figure 6). For DMDOMe, also a monodentate coordination is considered to check the outcome for a pentacoordinated magnesium.

Figure 5.

Optimized structures of DMDOMe on the surfaces of MgCl₂, showing a bridging conformation on the (104)-surface (A) and a chelating binding mode on the (110)-surface (B). For the sake of clarity, the picture shows only a few surface atoms close to the donor molecules; Mg atoms are colored in yellow, Cl atoms in green, O atoms in red, C atoms in gray, and H atoms in white.

Figure 6.

Optimized structures of TiCl₄ on the (110)-surfaces of MgCl₂; Mg atoms are colored in yellow, Cl atoms in green, and Ti atoms in gray.

The results of the calculations are summarized in Tables 3–6, and we will initially discuss the results concerning ³⁵Cl. As a reference, Table 3 also includes the quadrupolar parameters for exposed surface sites, which have been calculated before.⁴² One addition is the inclusion of the (104)-Cl_cs sites. These correspond to chlorine sites on the (104) surface, which are bound to the unsaturated magnesium surface sites, but are coordinatively saturated (hence “cs”) themselves. This sets them aside from the “real” surface chlorines that are bound to only two magnesium atoms; compare Cl-1 and Cl-2 in Figure 4A. The bulklike coordination of the Cl_cs sites is reflected in the C_Q, indeed being much closer to the bulk than to real surface sites. These Cl_cs sites have not been included in the calculation of the chlorine surface fraction in Table 1.

Table 6. DFT Calculations of the ³⁵Cl and ²⁵Mg Quadrupole Parameters for MgCl₂(110)–TiCl₄, at the B3LYP-D2/pob-TZVP Level.

species	atom	35Cl CQ (MHz)	η	atom	25Mg CQ (MHz)	η
B3LYP-D2/TZVP	Clsurf-1	8.9	0.6	Mg-1	2.05	0.7
	Clsurf-2	8.9	0.6	Mg-2	2.05	0.7
	Cl-1	17.8	0.1
	Cl-2	17.8	0.1
	Cl-3	21.1	0.8
	Cl-4	21.1	0.8

As expected, the quadrupolar parameters of the bare surface sites differ strongly from those of the bulk sites. The coordination of water has little effect on the ³⁵Cl quadrupole parameters of the surface sites, however. It does not really matter whether a pentacoordinated or hexacoordinated Mg site is formed or whether the (104)- or the (110)-surface is considered; in all situations, the ³⁵Cl C_Q of the surface sites remains very close to the values found for the bare surfaces. Only a small reduction in C_Q is observed for the Cl_cs sites.

Figure 5 shows structures of DMDOMe on MgCl₂. On the (104)-surface of MgCl₂, binding takes place via both oxygen in a bridging coordination and this restores the coordinative saturation of two surface magnesium sites, although no perfect octahedron is formed. The calculated quadrupole parameters at the B3LYP-D2/TZVP level are shown in Table 4. We note that for the bulk phase, slightly better agreement with experimental results was obtained at the B3LYP-D2/pob-TZVP level, although the results at the B3LYP-D2/TZVP level were comparable to this computational more demanding calculation. Moreover, the coefficients of the TZVP basis set were specifically optimized for MgCl₂ adducts¹¹ and hence we performed the calculations at the B3LYP-D2/TZVP level. Considering that we used slightly different approaches, we will mainly look at trends in the calculated C_Q values and do not focus too much on their absolute values. The results for the ³⁵Cl C_Q in the bridging coordination mode show no significant effect for Cl-4–Cl-6, while Cl-1–Cl-3 (Cl_cs) have again a reduced, bulklike C_Q-value. For binding of water, the most pronounced effect was observed for these Cl_cs sites as well. Also the coordination of DMDOMe to the (110)-surface does not affect the chlorine C_Q. There is hardly any difference between a monodentate and a chelating binding mode, similar to the case where water was considered.

Table 4. DFT Calculations of the ³⁵Cl and ²⁵Mg Quadrupole Parameters for MgCl₂(104)–DMDOMe and MgCl₂(110)–DMDOMe Adducts, at B3LYP-D2/TZVP Level.

species	atom	35Cl CQ (MHz)	η	atom	25Mg CQ (MHz)	η
MgCl2(104)–DMDOMe	Cl-1	6.1	0.3	Mg-1	2.81	0.3
	Cl-2	4.2	0.0	Mg-2	2.91	0.3
	Cl-3	6.0	0.3
	Cl-4	11.1	1.0
	Cl-5	12.1	1.0
	Cl-6	11.2	0.1
	Cl-1	13.5	0.4	Mg-1	11.9	0.2
MgCl2(110)–DMDOMe	Cl-2	15.2	0.5
monodentate	Cl-3	14.9	0.6
	Cl-4	15.1	0.6
	Cl-1	13.5	0.5	Mg-1	3.42	0.7
MgCl2(110)–DMDOMe	Cl-2	13.4	0.6
chelate	Cl-3	14.9	0.5
	Cl-4	14.8	0.6
high-coverage clu_27u_110 3Do1A	Cl	13.1	0.6	Mg-l	2.1	0.7
				Mg-m	1.8	1.0
				Mg-r	2.2	0.9
high-coverage clu_27u_110 3Do1C	Cl	13.5	0.6	Mg-l	3.2	0.6
				Mg-m	2.9	0.9
				Mg-r	3.2	0.6

The presented periodic calculations have some conceptual problems, as the small MgCl₂ nanoparticles lack long-range crystalline order. In ref (56), an alternative cluster description has been presented that should be better suited to describe such disordered systems. On the basis of this cluster approach, we proposed some high-coverage models³⁴ that were indeed found to better describe the MgCl₂–DMDOMe adducts as far as ¹³C chemical shifts of the donor are concerned. Quadrupole parameters have been calculated for the optimized cluster model with three donors on the surface that has been shown in ref (34) and is reproduced in Figure S6. Two different conformers, namely, Do1A and Do1C, are considered and their presence have been indicated by ¹³C NMR. For both conformations considered, this high-coverage cluster model does not result in significant changes in the chlorine quadrupole parameters and we report only the average ³⁵Cl C_Q. The conformation considered in the periodic calculation (chelate binding mode) corresponds to conformer Do1C from the cluster calculations.

Optimized cluster models for the DiBP donor in different conformation on both (104)- and (110)-surfaces were presented in ref (34) as well. The structures of these models are reproduced in Supporting Information Figure S7. The five different models consider a symmetric and an asymmetric conformation of the DiBP molecule on the two different surfaces. However, in none of the considered models, we find a significant effect of donor coordination on the ³⁵Cl C_Q for the surface sites (Cl-4–Cl-6) (see Table 5). These results are in line with the other calculations and indicate that the quadrupolar parameters of surface chlorines are insensitive to binding of molecules. After binding, the chlorines in the Cl_cs position (Cl-1–Cl-3) have their C_Q reduced from 6.7 MHz toward the bulk value, in agreement with the other calculations. The chelating coordination of DiBP on the (110)-surface of MgCl₂ also restores the coordinative saturation for magnesium. However, the surface chlorines Cl-1–Cl-2 again yield C_Q values close to the bare surface chlorines and appear to be only marginally influenced, in both the symmetric and asymmetric conformers.

Table 5. DFT Calculations of the ³⁵Cl and ²⁵Mg Quadrupole Parameters for MgCl₂–DiBP Adducts, from Cluster Calculations.

species	atom	35Cl CQ (MHz)	η	atom	25Mg CQ (MHz)	η
clu_24u_110 Do3S	Cl-1	6.1	0.4	Mg-1	1.8	0.4
	Cl-2	3.2	0.7	Mg-2	1.8	0.4
	Cl-3	6.1	0.4
	Cl-4	10.8	1.0
	Cl-5	13.3	0.4
	Cl-6	10.8	1.0
clu_24u_110 Do3A	Cl-1	5.4	0.2	Mg-1	2.0	0.8
	Cl-2	4.9	0.8	Mg-2	2.1	0.6
	Cl-3	5.9	0.3
	Cl-4	11.6	1.0
	Cl-5	12.6	0.8
	Cl-6	11.0	0.9
clu_24u_110 Do3A1	Cl-1	5.7	0.4	Mg-1	2.5	0.9
	Cl-2	5.6	0.6	Mg-2	1.7	0.9
	Cl-3	5.5	0.2
	Cl-4	11.4	1.0
	Cl-5	12.0	0.8
	Cl-6	12.0	1.0
clu_27u_110 Do3S	Cl-1	13.3	0.5	Mg-1	2.5	0.6
	Cl-2	13.9	0.4
clu_27u_110 Do3A	Cl-1	13.9	0.5	Mg-1	2.6	0.5
	Cl-2	13.4	0.5

Some effects on the chlorine quadrupolar parameters are seen for the binary system MgCl₂–TiCl₄ (see Table 6). In particular, the two chlorine surface sites that are directly involved in TiCl₄ coordination (see Figure 6) are calculated to have a reduced C_Q (from 18 to 9 MHz), although it remains significantly large. The other chlorine atoms (Cl-1–Cl-4) are exclusively bound to Ti. They are calculated to have C_Q values of 18 and 21 MHz, which are in the same order of magnitude as, or even larger than, the exposed MgCl₂ surfaces. The observation of the titanium-bonded chlorines with solid-state NMR suffers therefore from the same difficulties as observation of the surface sites: both belong to diluted species and will give very broad lines and hence are difficult to observe in the bulk MgCl₂-dominated spectrum. Johnston et al.⁵⁷ showed a ³⁵Cl solid-state NMR spectrum for TiCl₄ grafted on SiO₂, an experiment that obviously benefits from the lack of a chlorine-containing substrate. They observed a ∼400 kHz broad pattern and simulated that with C_Q = 14.3 MHz and η = 0.15, which seem in line with our calculations for the titanium-bonded chlorides. However, it should be noted that the coordination mode of TiCl₄ on SiO₂ is different from the coordination mode on MgCl₂.

Our calculations of the ³⁵Cl quadrupolar coupling parameters show that they are hardly affected by various donor molecules and coordination modes. In some cases, η changes slightly, but in all considered structures (for both (104)- and (110)-surfaces), the ³⁵Cl C_Q appears to be unperturbed by surface binding of donor molecules, with the exception of chlorines coordinating to TiCl₄ and chlorines in the Cl_cs position. In our previous study, the Cl_cs position was not primarily considered as a surface site because it has, in first approximation, a bulklike coordination. Similar to the (001)-surface, it should therefore have quadrupole parameters similar to the bulk. In the case of an uncoordinated surface, its parameters are calculated as C_Q = 6.7 MHz and η = 0. After coordination of donors, the quadrupolar parameters for the Cl_cs sites are almost restored to bulk values. The ³⁵Cl C_Q for the real surface sites are hardly influenced by absorption of a donor on either the (104)- and (110)-surface and still yield large C_Q (<12 MHz). Hence, these chlorine sites remain “invisible” also after coordination of a donor. Consequently, the loss of intensity in the chlorine spectra could therefore still pertain to distorted surface sites, similarly to what has been found for the bare surfaces in MgCl₂ DCM. The low signal loss for Do1_10 suggests the formation of surface sites with a smaller ³⁵Cl C_Q. However, the calculations of the ³⁵Cl C_Q for the proposed chelating binding mode on a (110)-surface give large C_Q values, suggesting that different structural models should be considered, e.g., relating to specific defects generated as a result of the ball-milling process.

³⁵Cl NMR Spectra of Surface Sites

The single resonance that is observed in ³⁵Cl spectra is assigned to the bulk phase of the MgCl₂ nanoparticles, although it might also include contributions from well-defined surface sites such as (001)-terminations. The signal from surface sites is not observed in Figure 1A or B because it is broadened beyond detection as follows from the calculated quadrupolar parameters. In an attempt to observe and characterize these surface sites with large C_Q, we acquired rotor-synchronized sideband-selective double-frequency sweep quadrupolar Carr–Purcell–Meiboom–Gill (ssDFS-QCPMG) (MAS) and QCPMG (static) spectra to increase sensitivity. In the case of ²⁵Mg spectra (vide infra), these methods allowed the detection of additional signal, but in ³⁵Cl, we did not observe a second signal, while we did get some line shape distortions (see Figures S4 and S5).

In a previous publication⁵⁸ we showed that the use of high-RF fields, which enable broadband excitation, makes broad resonances visible for Do1_10. Using a static home-built probe with a 1.2 mm inner diameter coil, we reached an RF field strength of 500 kHz for ³⁵Cl at a static magnetic field strength of 18.8 T (ν_L = 78.3 MHz). We showed that this led to the detection of part of the satellite transitions from the MgCl₂ bulk, but also to the observation of signal from the surface sites, which will be discussed in more detail here. Using nutation NMR and variable offset cumulative spectra, we showed the absence of other, much broader, components for Do1_10. The high RF experiment is now also applied for Do3_7 and MgCl₂ DCM. Figure 7 compares the spectra of Do1_10 and Do3_7, where clearly a ∼350 kHz broad resonance is detected for both adducts. The control experiment for MgCl₂ DCM gives a flat baseline.

Figure 7.

(A) Static ³⁵Cl NMR spectra of MgCl₂ Do1_10 (black) and Do3_7 (red) obtained at B₀ = 18.8 T and 500 kHz RF. (B) Zoom of the surface site, cutoff vertical scale at 0.20.

For both samples, the resonances show a somewhat asymmetric line shape, but they do not show well-defined quadrupolar features. This suggests the presence of a distribution in quadrupolar parameters, which is expected given the supposed heterogeneous nature of the surfaces. The two samples do give distinctly different spectra, where Do1_10 appears to give additional signals compared to Do3_7. The experiments at high-RF field are not performed under quantitative conditions, prohibiting the ability to retrieve absolute intensities. Nevertheless, the spectra in Figure 7 can still be interpreted semiquantitatively, given that the sample amount (±1 mg) and relative MgCl₂ content of the samples are very comparable. This shows that Do1_10 has more intensity in the broad signals. For Do3_7, there are two signals: besides the bulk phase signal, there is one broad resonance spanning about 350 kHz that should result from a surface site. After comparison with Do3_7, it becomes clear that the spectrum of Do1_10 actually has three resonances. Besides the bulk phase signal and the ∼350 kHz broad resonance, there is also a less intense resonance spanning about 170 kHz. From the span of this resonance, a C_Q of ∼8 MHz is estimated, which is significantly smaller than any of the calculated C_Q values.

An ∼350 kHz broad resonance corresponds to a C_Q of ca. 10–11 MHz. Although a bit lower, this is in the range of calculated C_Q’s for the surfaces (ca. 12–14 MHz, whether coordinated with donors or not, Tables 3–5). As none of the adducts have a full surface coverage of the donor, uncoordinated surface sites remain present for both Do1_10 and Do3_7. We can therefore not be certain whether the signal in the spectrum of Do3_7 originates from exposed or coordinated surface sites or both. For Do1_10, the ∼350 kHz broad resonance corresponds most likely to exposed surface sites. A T₁ measurement for Do3_7 under the high ν_RF conditions shows that the ∼350 kHz broad surface site has a short T₁: spectral integration of part of this signal, outside the span of the bulk signal, shows a monoexponential behavior with a T₁ of around 10 ms. The combination of large ω_Q and dynamics at the surface can explain this short relaxation time of the surface sites. It is remarkable that no broad signal is observed for MgCl₂ DCM at all, as this has surface sites (±5%) as well. We do note that weak X-band electron paramagnetic resonance signals are observed for MgCl₂ DCM, indicating the presence of some radicals, which are most likely formed during ball milling. These sites could induce very fast relaxation, which can explain the absence of detectable surface sites for the ball-milled samples. We consider potential radical sites to be quenched in the presence of donors.

The calculations indicate only small effects of donor coordination on the ³⁵Cl quadrupolar parameters and consequently the difference between both donors should be small. However, this is not in line with the ³⁵Cl visibility (Table 1). Also, the high ν_RF experiments are not in agreement with this, as is clear from the detection of the additional resonance with reduced C_Q for Do1_10. Both experiments suggest that for Do1_10 a surface structure is formed, in which the surface chlorines are affected by the donor coordination in such a way that their C_Q becomes lower (8 MHz), explaining both the observed additional resonance as well as the relative high ³⁵Cl visibility for this sample. This particular surface construct is consequently different from the suggested models as the C_Q calculated for the models are too high. The high-coverage model 3Do1A has shown good agreement with experimental ¹³C NMR results, however giving rise to some inconsistencies. More evidence of the surface structures might follow from the calculation of ²⁵Mg C_Q and the detection of surface sites via ²⁵Mg NMR.

Bulk ²⁵Mg NMR

While ³⁵Cl is considered an insensitive nucleus, the sensitivity of ²⁵Mg NMR is generally even lower due to its lower gyromagnetic ratio and low natural abundance. Nevertheless, ²⁵Mg NMR might be more sensitive to changes on the surface because it should be directly involved in the binding of the donors. ²⁵Mg Hahn-echo spectra for selected adducts are shown in Figure 8A. Again, the quadrupolar powder pattern features are most pronounced in MgCl₂ DCM, but the line shapes look rather comparable for all samples. Also in the static spectra (see Figure 8B) the signal is rather similar for all samples with comparable levels of distribution in the quadrupolar parameters. This is in contrast to the ³⁵Cl measurements, where there was a clear difference in the level of distribution in quadrupolar parameters for the different samples. The larger the distribution, the less well-defined the line shapes get and the longer the observed tailing of the signal. However, the ²⁵Mg C_Q (≈1.65 MHz) is much smaller than the ³⁵Cl C_Q.

Figure 8.

(A) ²⁵Mg rotor-synchronized Hahn-echo NMR spectra of selected MgCl₂ binary adducts obtained at MAS speeds of 10 or 15.625 kHz, B₀ = 20 T. The shoulder observed on the left-hand side of the main resonance in some of the spectra (marked by an asterisk for DCM) originates from the satellite transitions. (B) Static ²⁵Mg Hahn-echo NMR spectra of selected MgCl₂ binary adducts. The top spectra in blue are a 10× enlargement of MgCl₂ Do3_7 emphasizing the broad component.

The ²⁵Mg MAS spectra indicate the presence of additional site(s), which show up as a pronounced tailing on the right-hand side and actually differs significantly between the samples. The strongest tailing, and thus the largest distribution in quadrupolar parameters, is observed for Do3_7 and it stretches out as far as −8 kHz (−150 ppm), as is shown in the blown-up top trace in Figure 8A. A significant tailing is also observed for Do3_2 and MgCl₂/TiCl₄, stretching to ca. −5 kHz (−100) ppm. For MgCl₂ DCM and Do1_10, the asymmetric line is more narrow and slopes down to −2.5 and −4 kHz (ca. −50 and −75 ppm), respectively. In the static spectra, there are clues for the presence of a broader component as well, as can be seen in the rescaled top trace in Figure 8B. Again, this underlying component is broadest for Do3_7.

Spectral overlap makes it difficult to exactly identify this second component. An experiment that might help to alleviate this issue is the multiple-quantum MAS (MQMAS) experiment^59,60 thanks to its ability to separate overlapping quadrupolar broadened resonances in a two-dimensional fashion. Unfortunately, we were not able to observe the second site in MQMAS experiments (see Figure S8) due to the limited RF field strength (ν_RF), which hampers the excitation and conversion of the triple-quantum coherence.

Similar to the fraction of chlorine surface sites, the fraction of magnesium surface sites can be estimated from the particle dimensions. In contrast to the chlorine case, the fraction of magnesium surface sites differs a lot between the (104)- and (110)-surfaces. Particles having mostly (104)-surfaces expose 60–70% more surface sites than the equisized particles exhibiting (110)-surfaces (see Table 1). For example, if it would exhibit (104)-surfaces, the Do3_7 adduct would feature 31% surface sites, compared to 19.5% in case it exhibits (110)-surfaces. The difference between both surfaces might therefore seem to be an easy handle to interpret the ²⁵Mg spectra. However, the quadrupolar couplings of the coordinated surfaces are much closer to the bulk value (vide infra), meaning that surface sites should not be broadened beyond detection in ²⁵Mg spectra and they might significantly overlap with the bulk. On the other hand, only a part of the surface sites is actually covered with donors. Exposed surface sites with large quadrupole parameters are still present as well. For reasons not fully understood, the magnesium intensities from Figure 8 could not be reliably determined. Although the spectral quality appears high enough, no consistent magnesium intensities were found. Both spectral integration as well as the FID maximum did not result in reproducible relative intensities over different measurement sessions.

DFT Calculations of ²⁵Mg Sites

Binding of donor molecules to the unsaturated (104)- and (110)-surfaces restores coordinative saturation which will (partially) recover local symmetry. It is therefore expected to have more pronounced impact on the quadrupolar parameters for magnesium than what was found for chlorine. The binding of molecules has indeed various effects on the calculated quadrupole parameters for ²⁵Mg, as tabulated in Tables 3–6. The extent to which C_Q is reduced varies between the different models and coordination modes. For example, the interaction with water (see Table 3) leads to a significant reduction of ²⁵Mg C_Q when octahedral coordination is restored. Moreover, there is a significant difference between the (104)- and (110)-surface. The coordination of a single water on the (110)-surface, giving a pentacoordinated magnesium, also has an effect on the C_Q, but it remains large (<10 MHz).

The bridging coordination of DMDOMe on (104)-surfaces leads to restoration of coordinative saturation. The consequence is a strongly reduced C_Q for both coordinated magnesium sites, with values that approach the bulk (see Table 4). On the (110)-surface, the ²⁵Mg C_Q is strongly reduced as well, but only in the case of a chelating binding mode. The monodentate binding of DMDOMe on (110) gives similar results to the coordination of a single water where the C_Q remains large.

High-coverage models, which we introduced in ref (34), allowed for a better description of the system, based on a comparison of the ¹³C chemical shifts. Comparing the quadrupolar parameters of the high-coverage model to a single donor model shows interesting differences for ²⁵Mg C_Q (Table 4) again in contrast to the chlorides where no effect was observed. We focus on the central Mg site (Mg-m) as this should be most representative, although the results are actually rather comparable to the left- and right-hand-side Mg sites. Interestingly, the exact conformation considered in the high-coverage model is of significant influence on the ²⁵Mg C_Q. On the basis of ¹³C chemical shifts, Do1A was identified as the sole conformer in Do1_10 and the major component in Do1_4. This conformer yields a C_Q that is very close to the bulk value of 1.65 MHz. Do1C, which was found to be present as a minor component in Do1_4, gives a C_Q of 2.9 MHz, again a strong reduction compared to the bare surface, but significantly larger than Do1A. These differences should result in significant differences in the line widths of the respective resonances.

In the case of the bridging coordination of DiBP (Do3) on the (104)-surface of MgCl₂, also coordinative saturation is restored. This is directly reflected in the quadrupolar parameters for the two involved surface magnesium sites (see Table 5). Remarkably, conformer A1 appears to induce a difference between the two Mg surface sites, while conformer A does not. All in all, in both the symmetric and asymmetric conformers, C_Q is strongly reduced to values close to the bulk C_Q. The chelating coordination of DiBP on the (110)-surface of MgCl₂ leads to a reduction of ²⁵Mg C_Q as well. Again octahedral coordination is restored and thus the corresponding C_Q shows a significant reduction, but appears to be slightly larger than at the (104)-surface (see Table 5). Also in this case there is no significant difference between the symmetric and asymmetric conformers.

The MgCl₂–TiCl₄ binary adducts show pronounced effects on the ²⁵Mg C_Q as well (see Table 6). Binding of TiCl₄ generates magnesium surface sites with an octahedral coordination by chloride ligands, very similar to the bulk, although this is only true for a high TiCl₄ loading. At lower loadings, the resulting Mg sites will be pentacoordinated. Alternatively, TiCl₄ molecules might coordinate on steps or holes^9,56 with structures locally resembling the structural motive, as shown in Figure 6, so that for at least one of the two magnesium sites octahedral coordination is restored. C_Q for the octahedral magnesium sites comes down to approximately 2 MHz, which is very close to the bulk value. The results are in line with the results from the donors, but this is the only case where the binding does not take place to an oxygen, but to a chlorine.

Our calculations of the ²⁵Mg quadrupolar parameters show that they are affected to a different extend by various coordination modes. Coordination of one oxygen to the (110)-surface (a single H₂O or monodentate coordination of a donor), leading to pentacoordinated magnesium, already lowers ²⁵Mg C_Q, but it remains significantly higher than in the case of hexacoordinated magnesium. In all considered structures (for both (104)- and (110)-surfaces), ²⁵Mg C_Q reduces strongly after restoration of the octahedral surrounding with both oxygen and chlorine ligands. In the case of MgCl₂–H₂O and MgCl₂–donor adducts, ²⁵Mg C_Q generally becomes 2–6 MHz, but only when octahedral coordination is restored. Despite a clear reduction compared to the exposed surfaces, the resulting C_Q generally remains somewhat larger than the bulk. The high-coverage model 3Do1A on the (110)-surface results in the largest reduction of C_Q for the covered surfaces and it almost reaches bulk values.

²⁵Mg NMR Spectra of Surface Sites

The calculated quadrupole coupling constants of coordinated magnesium surface sites (2–4 MHz) correspond to resonances with line widths (3–18 kHz at 20.0 T) that should be detectable under regular conditions. However, sensitivity could be an issue because only a small fraction (2–10%) of the spin pool is a covered surface site. ²⁵Mg Hahn-echo experiments already showed the presence of additional components. To increase the sensitivity of ²⁵Mg NMR experiments, we obtained static QCPMG and ssDFS-QCPMG spectra under MAS. The ssDFS sequence⁶¹ gave enhancements in the S/N ratio of up to ∼2.7. The ssDFS-QCPMG experiments actually emphasize the broad signal on the right-hand side over the bulk phase signal. Moreover, the spikelet spectrum allows for an easy differentiation between baseline and the broad components of the signal. Due to increased sensitivity, the tailing is observed to span an even larger frequency range compared to the spectra in Figure 8. For TiCl₄ and DiBP adducts, the signal extends beyond −10 kHz (−200 ppm). For the Do1_10 sample, it only tails to −5 kHz (−100 ppm, see Figure 9). The broad signal lacks well-defined features, and the asymmetric featureless tailing is again indicative of a distribution in quadrupolar parameters reflecting disorder.

Figure 9.

Rotor-synchronized ²⁵Mg ssDFS-QCPMG NMR spectra of selected MgCl₂ binary adducts: (A) Do1_10, (B) MgCl₂/TiCl₄, and (C) Do3_7, B₀ = 20 T.

Also in static QCPMG experiments, the additional broader component can easily be detected in the spikelet spectrum. The sensitivity for static QCPMG experiments could be boosted with a double-frequency sweep (DFS) prepulse, giving enhancements of ∼2.9 for DCM, Do1_10, and Do3_7 with line shapes similar to the experiments without DFS (see Figure S9). Clearly, this second broad component is detected for most samples, but not for Do1_10 (see Figure S10). Generally, the relative intensities in the QCPMG spectrum are the same as in a spectrum obtained by a Hahn echo, with the exception of Do1_10, where the QCPMG spectrum is actually narrower than that obtained by Hahn echo. For that sample, the Hahn echo shows some broadening due to a distribution in quadrupolar parameters, but this is not very apparent in the QCPMG spectrum.

The DiBP adduct with the smallest particles (Do3_7) gives the broadest QCPMG spectrum, spanning almost 25 kHz (from ∼200 to −250 ppm). Additional QCPMG experiments were performed at higher ν_RF of 20 kHz for this sample. This is no longer in the low ν_RF nutation regime for the signal of the bulk phase (C_Q ≈ 1.65 MHz). Therefore, it led to some line shape distortions as well as signal loss for the narrow signal. The signal intensity of the broader component is very similar in both experiments. Importantly, the higher ν_RF did not lead to the excitation of further, even broader, resonances (see Figure S11). QCPMG experiments were also performed at a second magnetic field strength of 14.1 T. At the lower field, the line widths naturally increase due to stronger quadrupolar broadening. However, after scaling the axis for the field difference, the spectra for 14.1 and 20.0 T can be overlaid and show identical line shapes. This proves that the line shapes of the resonances are purely of quadrupolar origin.

The additional resonances that are detected have significant intensities, which impose some problems. Due to the potential difference in T₂ between different components, QCPMG experiments are in first approximation no longer quantitative. However, comparison between the first echo and the sum of all echoes shows only small difference in the line shape and thus relative intensities comparable to a single Hahn echo. The high intensity of the broad resonances can therefore not completely be explained by T₂ effects. For Do3_7, the broad component corresponds to a much larger fraction of the signal than can be accounted for by the donor loading. Also, calculated C_Q’s of ca. 2–2.5 MHz are actually too small to account for the observed span of the resonance, in particular if we consider that larger ν_RF might give somewhat broader lines. This is also true for the TiCl₄ adduct, the C_Q of the surface magnesium for the TiCl₄ adduct is calculated as 2 MHz (Table 6). This value underestimates the width of the experimental spectrum, which indicates a C_Q of up to ∼3.5 MHz. These differences might be related to the accuracy of the calculations. Also here, the second site represents much more spins than the 8% that can account for TiCl₄-bound sites (since per TiCl₄, there are two surface chlorine sites involved in the binding). On the basis of relaxation data, we concluded earlier that the surfaces might affect a much larger fraction of the spins than just the outer shell, e.g., due to defects caused by the milling process.

For Do1_10, no broad component is detected, suggesting that the quadrupolar parameters of covered surface sites are very close to the bulk and those sites will (practically) overlap. This is in agreement with the C_Q value (1.8 MHz) calculated for Do1A, which is the main surface structure, as followed from ¹³C experiments. However, ³⁵Cl NMR results suggest a different surface construct. For Do1_4, on the other hand, a second surface structure was identified using ¹³C NMR: Do1C, for which a larger quadrupole parameter of 2.9 MHz is predicted. The presence of Do1C can explain the second site that is indeed found in the QCPMG experiments for this sample. In fact, the calculated quadrupolar parameters match the experimental span, although the accuracy of the calculations does not allow for such a specific agreement. Again, there is a problem with the intensities though. The ¹³C NMR results indicate that Do1C is only a minor component³⁴ and it can therefore not account for such an intense signal.

Donor–Surface Interactions

Since the surfaces are covered with organic donors and thus with protons, this should offer the possibility to do correlation experiments between the donors and the surface sites. To this end, we performed ¹H–³⁵Cl and ¹H–²⁵Mg double-resonance experiments to probe potential interactions.

¹H–³⁵Cl Correlation Experiments

¹H–³⁵Cl cross-polarization (CP) experiments were employed with the aim to selectively get signal for those sites in the vicinity of donors (i.e., surface sites) and suppress the signal from the bulk phase. However, the resulting ¹H–³⁵Cl CP spectra showed signals very comparable to the direct excitation (see Figure S12). Moreover, these measurements proved to be very time-consuming because of low CP efficiencies⁶² and also because ¹H T₁ times (2–3 s) are significantly longer than the T₁’s of the quadrupolar nuclei (150 ms for smallest nanoparticles).

³⁵Cl–{¹H} REDOR and ¹H–{³⁵Cl} TRAPDOR experiments have been performed to get a deeper insight into the donor–surface interactions. The REDOR sequence has been combined with signal enhancement schemes to give an ssDFS-REDOR-QCPMG pulse sequence for enhanced sensitivity. ³⁵Cl–{¹H} REDOR experiments show a clear Cl–H interaction (see Figure 10). The REDOR fraction reaches 40% for most of the samples after a dephasing time of ∼65 ms. This includes the MgCl₂ DCM sample, which has no donor protons. Previously, we did observe that this sample contains Mg–OH groups.⁴² The other donor-free adduct, MgCl₂–TiCl₄, only reaches a REDOR fraction of 11%, thus clearly having less or weaker Cl–H dipolar interactions.

Figure 10.

Results of ³⁵Cl–{¹H} ssDFS-REDOR-QCPMG experiments for MgCl₂ adducts obtained at 15.625 kHz MAS, B₀ = 20 T. The black lines are the reference spectra (S₀), while the blue lines are the REDOR spectra (S) at a REDOR time of 65 ms.

Due to the relative high natural abundance (75%) of ³⁵Cl, it should be possible to perform the reverse experiment, ¹H–{³⁵Cl} REDOR, to get more insight into the protons responsible for the observed Cl–H REDOR effect. Due to the strong ³⁵Cl quadrupole interaction, the REDOR-type experiment is not feasible, but alternatively a ¹H–{³⁵Cl} TRAPDOR can be used as shown in Figure 11. The ¹H spectrum of MgCl₂ DCM shows a sharp signal at 1.66 ppm, which has been assigned to a Mg–OH surface group.^42,63−65 This signal shows a clear TRAPDOR effect. After 12.5 ms of chlorine irradiation, the TRAPDOR effect, ΔS/S₀, is 95%. The broad signal around 4 ppm, most likely related to some H₂O, has a much shorter T₂, but shows a TRAPDOR effect as well. In MgCl₂–TiCl₄, there is also a pronounced TRAPDOR effect, again for the signal at 1.66 ppm as well as the signal at 3.8 ppm (most likely some H₂O-related signal), as shown in Figure S13. The proton spectrum shows two resonances at 1.26 and 0.84 ppm that can be assigned to hydrocarbons physisorbed to the MgCl₂ particles. These narrow signals have a long T₂ and dominate the ¹H spectrum at longer echo times, but clearly do not show any TRAPDOR effect.

Figure 11.

TRAPDOR curve of ¹H–{³⁵Cl} TRAPDOR experiment for MgCl₂ DCM (full spectrum, red triangles), Do1_10 (Mg–OH signal, green stars), and Do3_7 (Mg–OH signal, blue squares). The right column shows spectra after 12.5 ms dephasing time, where the black lines are the reference spectra (S₀) and colored traces are the TRAPDOR spectra (S). MAS speed = 12.5 kHz, ν_RF³⁵Cl = 30 kHz.

The signals from physisorbed hydrocarbons and Mg–OH are also the relevant proton signals in the TRAPDOR experiments of the DMDOMe (Do1) adducts. The signals from the donor have a short T₂ (and are therefore not visible in the spectra for Do1_10 in Figure 11) as they have decayed before any TRAPDOR effect could be observed. What is left at longer dephasing times are again hydrocarbon signals that do not show any TRAPDOR effect and a Mg–OH peak with a relatively strong TRADPDOR effect (see Figure 11). Similar reasoning applies to the TRAPDOR experiment for Do3_7, although the hydrocarbon peaks show up at slightly lower ppm values and also the intensity of the hydrocarbons as well as the Mg–OH group appears to be much lower.

The TRADPOR effect was monitored as a function of the offset of the chlorine transmitter to probe the strength of the quadrupolar parameter of the site that couples to the Mg–OH protons (Figure S14). From 2.25 MHz onward, no detectable dephasing occurs anymore, indicating the TRAPDOR cutoff frequency, ν_C, which equals ν_Q in the case of a spin S = 3/2 nucleus.^41,66 From this, the C_Q of the coupled ³⁵Cl can be determined, which is found to be 4.5 MHz. This matches perfectly with the ³⁵Cl C_Q of MgCl₂, indicating that the Mg–OH protons have an interaction with bulk or bulklike chlorine atoms. Our TRAPDOR experiments fail to show an interaction between the donor and MgCl₂. Due to the short T₂ of the donor resonances, the peaks have already dephased completely at longer echo times and potential TRAPDOR effects cannot be observed.

¹H–²⁵Mg Correlation Experiments

Static ²⁵Mg QCPMG experiments yield better signal with ¹H decoupling. In particular for Do3_7 and Do1_10, significantly more echoes can be acquired using decoupling (Figure S15). The line shape, on the other hand, does not seem to be influenced by the decoupling. Also MQMAS experiments performed better using ¹H decoupling. These are the first, rudimentary, proofs of an interaction between ²⁵Mg and protons in these systems. To further investigate this, we attempted to perform ¹H–²⁵Mg CP measurements (see Supporting Information (SI)) initially on samples MgCl₂ DCM, Do1_10, and Do3_7. The ¹H–²⁵Mg CP spectra of the adducts look very comparable to the bulk, although the S/N ratio is too low to warrant that there are no additional broader signals present. For MgCl₂ DCM, a signal could only be detected after 68 h of experimental time (because proton relaxation times were found to be very long (<1 min)), in which 4096 scans were acquired using 20 ms of contact time (see Figure 12A). The spectral quality is poor. Nevertheless, it is remarkable that this intrinsic proton-free sample is able to give a CP signal that looks quite similar to the direct excitation spectrum.

Figure 12.

(A) Static ¹H–²⁵Mg CP spectrum of MgCl₂ DCM (room temperature) and (B) comparison of the ¹H–²⁵Mg CP spectrum (black, −40 °C) of Do3_7 to a QCPMG spectrum (red, room temperature), B₀ = 20 T.

An ¹H–²⁵Mg CP spectrum of Do3_7, acquired in 91.5 h at −40 °C, is shown in Figure 12B. While the line shape of the bulk signal appears slightly broader than the QCPMG echo, the overall line shape agrees very well with the QCPMG echo. Both the CP and QCPMG spectrum show the broad component between −200 and 200 ppm with the same relative intensities (see also Figure S16A). All in all, this correspondence in line shape and long relaxation times discouraged us to continue with CP experiments. However, the similarity between DP and CP spectra requires an explanation. Also, the observation of CP signal for MgCl₂ DCM is unexpected due to the low proton content in this sample. Clearly, bulklike sites are in the vicinity of some source of protons. These bulklike sites could either be the layers just below the surface or perhaps the (001)-surfaces. The latter surface sites have quadrupole parameters close to the bulk, yet no donors or −OH groups should coordinate to these (001)-surfaces. The protons that are involved in the CP were further probed using correlation experiments.

Correlation experiments such as ²⁵Mg–{¹H} ssDFS-REDOR-QCPMG, ¹H–{²⁵Mg} REDOR, and ¹H–²⁵Mg HETCOR experiments have been performed to study the H–Mg interaction(s) (see SI). Similar to the ³⁵Cl–{¹H} REDOR experiment, the ²⁵Mg–{¹H} REDOR experiments show clear X–H interactions (Figure S17), while for technical reasons, no interactions could be seen in ¹H–{²⁵Mg} REDOR and HETCOR experiments (Figures S18 and S19).

For the ²⁵Mg–{¹H} REDOR experiments, there is quite a difference between the samples, with some showing a pronounced REDOR effect, while for others, the effect is only small. The REDOR fraction, ΔS/S₀, goes up to 17 and 24% for Do1_10 and Do3_7, respectively. For MgCl₂ DCM and MgCl₂–TiCl₄ adduct, the REDOR effect is only marginal, showcasing a much weaker ¹H–²⁵Mg dipolar interaction.

Remarkably, MgCl₂ DCM showed a significant effect in the ³⁵Cl–{¹H} REDOR experiment. Owing to the ssDFS and QCPMG elements, the ²⁵Mg spectra show both the bulk signal and the surface site for Do1_4, Do3_7, and the TiCl₄ adduct. This clearly shows that only REDOR effects are observed for the signal from the bulk phase, and the surface sites are never influenced by the refocusing pulses on the proton channel. Also in ³⁵Cl–{¹H} REDOR experiments (vide supra), an X–H interaction (resulting from −OH groups) with the bulk was found. As the surface sites could not be observed in the ³⁵Cl REDOR experiments, we cannot establish if there is an interaction between protons and chlorines at the surface.

Implications

The analysis of ²⁵Mg/³⁵Cl–¹H correlations experiments gives some intriguing results. An H–X interaction between Mg–OH protons and the bulk of MgCl₂ is detected, while interactions between the donor and the support could not be established. Only in the case of ¹H–²⁵Mg CP experiments, there is a correlation between the surface sites and protons, which was not found in the ²⁵Mg–{¹H} REDOR experiments.

Most intriguing results have been obtained for sample Do1_10. Both ²⁵Mg and ³⁵Cl show interesting differences compared to the other adducts. The absence of surface sites in ²⁵Mg QCPMG experiments can still be explained by the formation of surface sites with low C_Q (of similar value as the bulk), in agreement with computational results for the suggested model, which was identified based on ¹³C NMR results. However, the spectrum of Do1_4 is significantly different, which is unexpected since ¹³C NMR results suggest that both samples have predominantly the same surface structure for the donor, with Do1_4 only having a minor contribution of an additional conformer. The high ³⁵Cl visibility of Do1_10 is not in line with its large surface area, suggesting the formation of surface sites with lower ³⁵Cl quadrupolar coupling parameters that are indeed detected using ³⁵Cl Hahn echoes at high RF power. These findings do not conform to the calculated quadrupolar coupling parameters from the suggested surface structure. All in all, there are some inconsistencies in the results from quadrupolar NMR studies that do not allow us to either confirm or reject the proposed surface model for DMDOMe. One explanation for this might lie in the dynamics at the surface. This is very demanding to accommodate into DFT calculations, but it could have pronounced influence on some spectral aspects.

Considering the other adsorbates, the ³⁵Cl NMR results are in agreement with the large C_Q values for the exposed surface sites (either coordinated or not). However, the unresponsiveness of the ³⁵Cl C_Q to donor adsorption makes it impossible to detect coordinated and bare surface sites independently. The observation of surface sites in ²⁵Mg QCPMG experiments is interesting and confusing at the same time. In particular, the span of these resonances indicates larger quadrupole coupling parameters than what have been calculated. Also, the high relative intensities of these resonances do not conform to the fraction of coordinated surface sites. It could very well be that also magnesium sites in the next shell contribute to the broader signals. Surface deformations can change the local symmetry of these otherwise coordinatively saturated sites, increasing their quadrupolar coupling parameters. Moreover, there may well be many defects in the sample induced by the ball milling.

Despite different approaches, we have not been able to measure interactions between the donor and the support. Although protons have shown interactions, the observed effects did not originate from the donors. Low resolution and short T₂ hamper the further application of proton NMR, and more demanding experiments, involving, for example, ¹³C, are required. Intrinsically, ¹³C–²⁵Mg/³⁵Cl correlation experiments sound very appealing; unfortunately, they are not feasible. The main limitation for this is the sensitivity, due to the dilution of the relevant species, low natural abundance of the involved nuclei (¹³C, ²⁵Mg), and their low gyromagnetic ratio leading to low receptivity. Although costly, a boost in the sensitivity could be obtained by (selective) isotope labeling of ¹³C and/or ²⁵Mg.

Conclusions

We showed DFT calculations of the ²⁵Mg/³⁵Cl electric field gradient (EFG) tensor and ²⁵Mg/³⁵Cl solid-state NMR spectra for a series of binary adducts between MgCl₂ and TiCl₄ or MgCl₂ and electron donors. These samples have been investigated as model systems to Ziegler–Natta catalysts. In particular, we have been looking into the surface structures formed by different donors to find experimental evidence for suggested models. Correlation experiments clearly show X–H interactions, but they ultimately involved the Mg–OH surface group as source of the proton polarization. The interactions were found to occur between the OH group and bulklike sites.

In general, for magnesium, DFT calculations show pronounced reduction of the quadrupolar interaction (C_Q) for each case, where octahedral coordination is restored at the surface. In some cases, the resulting C_Q becomes almost the same as the bulk value. For chlorine surface sites, on the other hand, the coordination of adsorbates has only a minor effect, which means that chlorine surface sites will continue to give broad lines also after coordination of a donor. This is in line with the visibility of Hahn echoes of the central transition (low ν_RF), in which up to 20% of the expected signal intensity is missing. Echo experiments, obtained using high RF fields, indeed show the presence of chlorine sites with low local symmetry, i.e., large quadrupole parameters (C_Q > 10 MHz) for the small-particle DiBP adduct (Do3_7).

The DMDOMe adduct behaves quite differently compared to the other adducts. In ²⁵Mg QCPMG and ssDFS-QCPMG experiments, the spectra of all adducts clearly indicate the presence of a second component for most samples, but this is absent in Do1_10. Also, it has a surprisingly high ³⁵Cl visibility given its small particle size. Besides sites with large quadrupole parameters, echo experiments obtained at high RF power show an additional signal with an intermediately large quadrupole parameter (C_Q ∼ 8 MHz) for this sample. This is not in line with calculated NMR parameters from the suggested model. We should therefore consider a notably different surface structure for Do1_10, in which both ²⁵Mg and ³⁵Cl C_Q are affected by the donor coordination.

We found that it is not feasible to use ³⁵Cl C_Q for the interpretation of specific structural models. In that respect, the ²⁵Mg quadrupolar interaction parameters seem much more promising as they are strongly influenced by donor binding, both experimentally and computationally, and also show significant structural variations. Further research employing solid-state NMR should focus on ²⁵Mg NMR as a very valuable source of structural information.

Identifying specific surface structures by comparing NMR results to DFT calculations proved to be difficult in all cases. This is partly attributed to the existence of many defect structures caused by the ball-milling process used to prepare the samples. The existence of such defect structures both at the surface and in the interior of the MgCl₂ particles is obvious from T₁ relaxation studies of the adducts, which display large difference in relaxivity as a function of particle size/ball-milling time.

Experimental Section

Sample Preparation

The preparation of the samples studied in this contribution is described elsewhere.³⁴ In short, dried MgCl₂ and the respective donors were ball-milled for 8 h. The resulting solid was then washed with one or more aliquots of dry heptane and pentane under vigorous stirring at room temperature and finally dried under vacuum at 50 °C overnight.

Computational Details

Quadrupolar parameters were calculated by means of a well-known periodic ab initio software package, namely, the CRYSTAL09 suite,⁶⁷ which uses atom-centered (Gaussian) basis sets.

Geometry optimizations and electric field gradient (EFG) calculations were carried out at the B3LYP⁶⁸ level of theory, including Grimme’s (D2) semiempirical correction⁶⁹ for dispersion (with the modification proposed by Civalleri and co-workers⁷⁰), using the TZVP basis set¹¹ for Mg, Cl, and Ti, and Ahlrichs VTZ plus polarization basis set⁷¹ for the C, H, and O atoms (optimized in a previous work¹²). In the case of MgCl₂–nH₂O, the EFG calculations were carried out using the pob-TZVP basis set⁷² for Cl atoms. The positions of all atoms were fully relaxed along with the cell parameters. With reference to the CRYSTAL09 user manual,⁶⁷ in the evaluation of the Coulomb and Hartree–Fock exchange series, the five threshold parameters determining the level of accuracy were set at 7, 7, 7, 7, and 18 values. The threshold on the self-consistent field energy was set to 10^–8 Ha for the geometry optimizations. The reciprocal space was sampled according to a regular sublattice with shrinking factor equal to 6.

In the case of the DiBP adducts and the high-coverage model of the DMDOMe adduct, we adopt the cluster approach described elsewhere.^34,73 The optimized cluster structures are reproduced in the SI. The EFG calculations were carried out at the TPSSTPSS⁷⁴ level using the 6-31+G(2d,p) basis set⁷⁵ for Mg and Cl, and the IGLO-II basis set⁷⁶ for H, C, and O atoms.

NMR

²⁵Mg and ³⁵Cl spectra were recorded at room temperature on a Varian VNMRS 850 MHz spectrometer (20 T, 52.0 MHz for ²⁵Mg, 83.25 MHz for ³⁵Cl) using a triple-resonance 4.0 mm Varian T3 MAS probe at 15.625 kHz MAS. ²⁵Mg and ³⁵Cl spectra have been obtained using a Hahn echo with short echo times: 1 rotor period (64 μs) or 16 μs (static). Recycle delays were long enough (3–5 times T₁) to ensure quantitative measurements. Shifts were referenced to solid NaCl (δ_iso = −45.37 ppm with respect to infinitely dilute solution of NaCl(aq) (δ_iso = 0.0 ppm)) or a saturated solution of MgCl₂(aq) (set to 0.0 ppm).

We used the sideband-selective double-frequency sweep (ssDFS) pulse scheme⁶¹ to transfer population from the satellites into the central transition to increase the signal. A theoretical maximum enhancement of 2I can be obtained using this technique. We also used the QCPMG detection scheme.⁷⁷⁻⁷⁹ A series of echo pulses is applied with signal detection between the echoes. This leads to the so-called spikelet spectrum, in which the regular Hahn-echo signal is split into a manifold of sharp lines (spikelets), which resembles the envelope of the echo spectrum. Since the intensity of the echo is distributed over a few spikelets, the signal-to-noise ratio increases significantly. As shown before,⁸⁰ we combined ssDFS and QCPMG to get maximum enhancement.

Supporting Information Available

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.8b05123.

• Additional solid-state NMR spectra and optimized structures of cluster models (PDF)

The authors declare no competing financial interest.