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Shell Versus Core Dy Contributions to NMR Water Relaxation in Sodium Lanthanide Fluoride Core-Shell Nanoparticles – An Investigation Using O-17 and H-1 NMR Rohan D. A. Alvares, Anurag Gautam, Robert Scott Prosser, Frank C.J.M. van Veggel, and Peter M. Macdonald J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b06954 • Publication Date (Web): 20 Jul 2017 Downloaded from http://pubs.acs.org on July 25, 2017

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The Journal of Physical Chemistry

Shell versus Core Dy3+ Contributions to NMR Water Relaxation in Sodium Lanthanide Fluoride Core-Shell Nanoparticles – An Investigation Using O-17 and H-1 NMR

Rohan D. A. Alvares1†, Anurag Gautam2†, R. Scott Prosser1,3γ, Frank C. J. M. van Veggel2γ and Peter M. Macdonald1γ*

1

Department of Chemistry, University of Toronto, Mississauga, Ontario, Canada, L5L 1C6 2

Department of Chemistry and Centre for Advanced Materials and Related Technologies, University of Victoria, Victoria, BC, Canada, V8W 2Y2 3

Department of Biochemistry, University of Toronto, Toronto, Ontario, Canada, M5S 1A8

Author Contributions: † Rohan D. A. Alvares and Anurag Gautum contributed equally to this work. γ R. Scott Prosser, Frank C. J. M. van Veggel and Peter M. Macdonald are co-corresponding authors

*To whom correspondence should be addressed: Department of Chemical and Physical Sciences, University of Toronto Mississauga, 3359 Mississauga Road North, Mississauga, Ontario, Canada L5L 1C6. Telephone 905 828-3805. Fax: 905 828-5425. E-mail: [email protected]

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Running Title: Core versus Shell Contributions to NMR Water Relaxation in NaLnF4 CoreShell Nanoparticles

Abbreviations Dy

dysprosium

NMR

nuclear magnetic resonance

MRI

magnetic resonance imaging

OA

oleate

PMAO-PEG

poly(maleic anhydride-alt-1-octadecene)-polyethylene glycol

T1

longitudinal relaxation time

Y

yttrium

Abstract Lanthanide nanoparticles (NPs) are useful as paramagnetic contrast agents in MRI, generating contrast through enhanced relaxation of signals from water protons in their vicinity. The overall relaxation depends on the proximity of the water, so that lanthanides at the NP surface would be expected to make a greater contribution than those buried in the core. NPs are usually coated with an organic layer to attain colloidal stability, which will influence the access of water to the lanthanide constituents. Here, we interrogated the relative contributions of NP core versus surface lanthanides to overall water relaxation using a series of core-shell lanthanide fluoride NPs (typical core dimension of 15.5 – 19.5 nm, and typical shell dimension of 0.5 nm) wherein the core and/or shell regions contained either a contrast-active lanthanide (paramagnetic; dysprosium, Dy3+) or a contrast-inactive lanthanide (diamagnetic; yttrium, Y3+), variously


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designated Dy-Dy, Dy-Y, Y-Dy or Y-Y core-shell NPs. The organic coating in each case consisted of a monolayer of oleate (OA) bound to the positively charged nanoparticle surface, intercalated with an outer layer of poly(maleic anhydride-alt-1-octadecene)-polyethylene glycol (PMAO-PEG). Paramagnetic influences were assessed via changes in water 17O chemical shift and 1H T1 relaxivity.

17

O chemical shift changes were minimal, even for Dy-Dy and Y-Dy NPs,

consistent with a limited access of water to the NP surface, likely due to occlusion by the OA portion of the organic coating. Nevertheless, water 1H T1 relaxivity was enhanced by a factor of 40 for Dy-Dy relative to Y-Y NPs, reflecting the predominant through-space 1H dipolar relaxation mechanism. Both Y-Dy and Dy-Y core-shell NPs exhibited water 1H T1 relaxivity intermediate to that of Dy-Dy and Y-Y core-shell NPs. Modelling of the 1/r6 dependence of the dipolar coupling between lanthanide and water indicates that in the presence of the OA/PMAOPEG organic coating only the outer most layer of NP lanthanides contributes to the relaxation. This suggest that for the Y-Dy and Dy-Y core-shell NPs the as-prepared shells may not be of homogeneous composition and/or thickness.

Introduction Core-shell nanoparticles (NPs) are used in various applications including drug delivery, multimodal biosensing, and theranostics.1–4 In many cases, the core provides a key diagnostic or therapeutic functionality, as exemplified by CdSe quantum dots or surface functionalized gold NPs intended for fluorescence-based detection of specific targets.5,6 The shell may perform a number of different functions including: improving colloidal stability, preventing leaching of toxic constituents, avoiding quenching or improving diagnostic efficiency of the core, adding an additional diagnostic function, coupling to a probe species for target-specific interactions, or



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simply creating an appropriate biological interface. Core-shell NPs consisting of lanthanide oxides, or lanthanide fluorides, have found many applications in luminescence-based biosensing7,8 and as contrast enhancers in both magnetic resonance imaging (MRI) and computed tomography (CT) imaging.9–19 In the case of MRI, the interaction of water with paramagnetic NP constituents is a key determinant of any enhancement of the longitudinal (1/T1) or transverse (1/T2) relaxation rates of bulk water, these being the source of contrast enhancement. Among the lanthanide-based NPs, sodium lanthanide fluoride matrices have been shown to exhibit useful optical properties as potential biosensors or therapeutic materials. Monodisperse NaGdF4 NPs can be prepared with controlled diameters between 2 and 10 nm and are colloidally stabilized in water by an oleate (OA) / poly(maleic anhydride-alt-1-octadecene)polyethylene glycol (PMAO-PEG) organic layer.12 Excitation of these nanomaterials at 980 nm results in near-infrared (NIR) upconversion emission at 800 nm, all within the so-called therapeutic window. The upconversion efficiency of such matrices depends to a great extent on the crystal phase and the population of dopants in the crystal. Thus, their performance is improved through the use of NaGdF4 core-shells in which the core is doped with Yb3+ and Tm3+. 7,8,20–22

The NaGdF4 shell in such core-shell NPs is coincidentally convenient as a T1-contrast agent in MRI, where it has been shown that the fraction of paramagnetic surface Gd3+ ions and NP size strongly dictate the water relaxation rate, and therefore contrast.12 Similarly, dysprosium-based NPs have been proposed as T2-contrast agents for ultrahigh field MRI.23 Since the overall relaxation rate depends on the proximity of the water, lanthanides at the NP surface would be predicted to make a greater contribution than those buried in the core. The presence of an organic layer coating the NP, required for colloidal stability, will influence the


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access of water to the lanthanide constituents and introduce a confounding factor. Thus, it is of interest to dissect out the relative contributions of core versus shell lanthanides to water relaxation in order to guide optimization of performance in such applications. Here, we investigate the relative contributions of core versus shell constituents to paramagnetic dysprosium-driven contrast in lanthanide-based core-shell NPs using 17O NMR chemical shift and 1H T1 relaxation rate measurements on water. A series of core-shell NPs were synthesized in which either the core, or the shell, or both, contained either a paramagnetic (Dy3+) or a diamagnetic (Y3+) lanthanide. All four core-shell NPs, designated Dy-Dy, Y-Dy, Dy-Y and Y-Y, were colloidially stabilized with an organic coating consisting of OA bound to the positively-charged NP surface, intercalated with the amphiphilic macromolecule PMAO-PEG as shown schematically in Fig. 1a. For each of the four core-shell NPs in aqueous solutions, 17O NMR chemical shifts and 1H NMR T1 relaxation rates of water dispersions were measured and compared.

Figure 1 Experimental Materials. Yttrium (III) oxide (99.9%), dysprosium (III) oxide (99.9%), yttrium (III) acetate hydrate (99.9%), dysprosium (III) chloride hexahydrate (99.9%), sodium trifluoroacetate (98%), ammonium fluoride (≥ 99.99%), technical grade oleic acid (90%), technical grade 1-octadecene (90%), and hexanes were purchased from Sigma-Aldrich. Oleylamine (97%) from Acros, trifluoroacetic acid, anhydrous ethanol and methanol from Caledon laboratories were used. All chemicals were used as supplied.



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Synthesis of sacrificial cubic (α) phase NaLnF4 NPs. Sacrificial NPs were first synthesized for subsequent use as a starting material to form the shell of the core-shell lanthanide NPs. Cubic phase NaLnF4 (Ln3+ = Y3+ or Dy3+) NPs were synthesized based on a method reported earlier.10 Typically 1 mmol of Ln2O3 was mixed with 10 mL of 50 % aqueous trifluoroacetic acid in a 100 mL three neck flask and refluxed at 85 °C overnight. Subsequently the excess of water was removed at 65 °C yielding Ln(CF3COO)3 as a white powder. To this precursor powder, 2 mmol of sodium trifluoroacetate was added, along with 5 mL oleic acid, 5 mL of oleylamine, and 10 mL of 1-octadecene, and the mixture was stirred and heated to 120 °C rapidly (~15 °C/min) for 45 min under vacuum to remove residual water and oxygen. The resulting transparent solution was further heated to 285 °C (~15 °C/min) with vigorous stirring under argon for 45 min. The solution was cooled to room temperature and the NPs were precipitated by addition of 60 mL ethanol, collected by centrifugation at 2700 rcf, washed again three times with 40 mL ethanol and finally dispersed in hexane (10 mL). Synthesis of hexagonal (β) phase NaDyF4 (Dy-Dy), NaYF4 (Y-Y), NaDyF4/NaYF4 (Dy-Y), and NaYF4/NaDyF4 (Y-Dy) NPs. In this synthesis of Dy-Dy NPs, 0.78 mmol dysprosium (III) chloride hydrate, 1.5 mL of oleic acid, and 7.5 mL of 1-octadecene were added to a 50 mL round bottom flask, and the mixture was heated to 140 °C under vacuum with stirring for 0.5 hrs to produce the dysprosium oleate complex. The complex was cooled to room temperature followed by the addition of 2.8 mmol of sodium hydroxide and 4 mmol of ammonium fluoride dissolved in 7.5 mL of methanol. After stirring the reaction mixture for 3 hrs at room temperature, the mixture was heated slowly to 90 °C (~3 °C/min) to remove the methanol. Once the methanol was removed, the solution was heated rapidly to 306 °C (~15 °C /min) for 1.5 hrs in an argon atmosphere, which produced (β) phase Dy-Dy NPs.


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Dy-Y core-shell NPs were synthesized in the same way as Dy-Dy NPs but after 1.5 hrs the pre-synthesized sacrificial cubic NaYF4 NPs, dispersed in hexane, were injected into the reaction mixture. The reaction was allowed to proceed for another 10 min to produce the Dy-Y core-shell NPs. Subsequently, the reaction was cooled to room temperature and the NPs were precipitated by addition of 30 mL ethanol, collected by centrifugation at 2700 rcf, washed twice with 30 mL ethanol and dispersed in 10 mL of cyclohexane. The synthesis of Y-Y NPs was performed in a 100 mL round bottom flask containing 1 mmol yttrium (III) acetate hydrate, 6 mL of oleic acid, and 17 mL of 1-octadecene. Subsequently, the mixture was heated to 130 °C rapidly (~15 °C/min) for 0.5 hrs in vacuum with continuous stirring to form a transparent, colorless yttrium oleate complex. The complex was cooled to room temperature followed by addition of 2.5 mmol of sodium hydroxide and 4 mmol of ammonium fluoride dissolved in 10 mL of methanol. After stirring at room temperature for 3 hrs the reaction mixture was heated to 90 °C (~3 °C/min) to remove the methanol. Once the methanol was removed, the reaction mixture was heated rapidly to 300 °C (~15 °C /min) for 1 hr in an argon atmosphere, which produced the (β) phase Y-Y NPs. Y-Dy core-shell NPs were synthesized in a similar way to Y-Y NPs but after 1 hr of reaction the pre-synthesized sacrificial cubic NaDyF4 NPs, dispersed in hexane, were injected into the reaction mixture. The reaction was allowed to proceed for another 5 min to produce the Y-Dy core-shell NPs. Subsequently, the reaction was cooled to room temperature and the NPs were precipitated by addition of 60 mL ethanol, collected by centrifugation at 2700 rcf, washed twice with 30 mL ethanol and dispersed in 10 mL of cyclohexane. Surface modification of NPs. In a 50 mL round bottom flask poly(maleimide-alt-1-octadecene) (PMAO), functionalized with poly(ethylene glycol) amine (PEG-NH2) and ethanolamine (6 mg)



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were dissolved in 6 mL chloroform. Subsequently, chloroform dispersed NPs (2 mL) were added to the above flask and the solution was shaken for 1 - 2 hrs at room temperature. The chloroform was removed slowly using rotary evaporation at room temperature, forming a thin film of NPs on the inner surface of the flask. Subsequently, the desired amount of distilled water was added to the flask and sonicated for 6-7 minutes to disperse the NPs in water. The dispersion was then filtered through a 0.2 µm syringe filter. Any excess of uncrosslinked polymer was removed using preparative centrifugation at 30,000 rcf. The pellet of NPs was redispersed in the desired amount of distilled water. Transmission electron microscopy (TEM). TEM images of NPs were acquired prior to surface modification with PMAO-PEG using a JEOL JEM-1400 microscope operating at 80 kV. NPs dispersed in hexane were drop-cast onto a formvar carbon film (Electron Microscopy Science) supported on a 300 mesh copper grid (3 mm in diameter) and allowed to dry in air at room temperature before TEM imaging. The size distribution was obtained from averaging a minimum of 150 NPs using ImageJ software. Powder X-ray Diffraction. Approximately 10 drops of the NPs dispersed in hexane were added on a zero-background sample holder (with indent). Step-scan X-ray powder-diffraction data were collected over the 2θ range 20-100° with CrKα radiation ( λ = 0.2290 nm, 30 kV, 15 mA) on a Rigaku Miniflex diffractometer with a variable divergence slit, 4.2° scattering slit, and 0.3 mm receiving slit. The scanning step size was 0.02° 2θ with a counting time of 6 s per step. Three XRD peaks ([100], [200], and [201]) were used to calculate the size of the NPs and their standard deviation. Dynamic light scattering (DLS). DLS measurements were performed on NPs in water, subsequent to surface modification with PMAO-PEG, using a Brookhaven Zeta PALS


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instrument with a 90Plus/BI-MAS Multi Angle Particle Sizing option, equipped with a 15 mW solid-state laser (658 nm). All data were obtained at a single scattering angle (90°) and averaged over three scans. Inductively coupled plasma mass spectrometry (ICP-MS). The concentration of Dy3+ and Y3+ ions in the samples was determined using a Thermo X-Series II (X7) quadrupole ICP-MS. The water dispersed NPs (~ 50 µL) were digested in nitric acid (5 mL, 16 N environmental grade) at 135 °C, for 72 hrs, in sealed Teflon vials and diluted with ultrapure water (125 mL, 18.2 MΩ) before analysis. Calibration was done by analyzing serial dilutions of a mixed element synthetic standard containing a known amount of dysprosium, and yttrium (High Purity Standards, Charleston SC). Each sample, standard and blank, were spiked with indium (to a concentration of ∼7 ppb) as the internal standard to correct for signal drift and matrix effects. Accuracy was confirmed with analysis of a standard reference material (SLRS-4). 17

O NMR. Dy3+:DTPA and the synthesized core-shell NP samples were prepared in aqueous

solutions containing 10 % D2O and 4 % 17O-enriched water. The Dy3+:DTPA concentration was 17.3 mM, while NP dispersions ranged in concentrations from 35 – 90 nM (i.e. the total lanthanide atomic content was roughly 2 mM).

17

O NMR spectra were acquired on a Varian

Inova 500 MHz spectrometer equipped with a HX broadband probe (Agilent Inc., Santa Clara, CA), operating at the 17O Larmor frequency of 67.752 MHz referenced to 1H217O and using a single pulse excitation scheme. Typical experimental parameters were: a 90° pulse of 10.75 µs, an acquisition time of 90 ms, and a repetition time of 100 ms. The frequency was locked to D2O and 256 transients were acquired for each free induction decay. The data was processed with standard zero filling and 25 Hz Lorentzian apodization prior to the Fourier transform. For all NP aqueous dispersions, the 17O chemical shifts were measured at 25, 50 and 70 °C, with a second



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25 °C point collected to observe hysteresis effects. These values were then normalized for differences in NP concentration. 1

H NMR T1 relaxation. The water 1H longitudinal relaxation time (T1) was measured for each

NP dispersion at 25, 50 and 70 °C (also 25 °C hysteresis) using a saturation recovery sequence on the same 500 MHz spectrometer operating at a 1H frequency of 499.788 MHz. For each experiment, sufficient data points (6 – 10) points were collected after achieving at least a 90 % saturation of signal intensity. Two scans were collected for each recovery time point (), while the recycle time was sufficient to achieve full relaxation (18 – 36 s). The T1 was extracted by fitting the water integrals () to the function, () = 1 −

[1]

where is the integral of the fully relaxed signal. The relaxivity was calculated as the

difference in the relaxation rate ( = 1/ ) (s-1) relative to bulk water, divided by the NP concentration (mM).

Results and Discussion NP Characterization Fig. 1b shows a TEM image of the core of the Dy-Y NPs prior to the addition of the Y3+ shell, while Fig. 1c shows the core-shell NPs formed upon subsequently adding the Y3+ shell, but prior to the addition of the organic coating. In this case the core NPs exhibited diameters of 15.5 ± 1.0 nm, which increased to 16.5 ± 1.1 nm after adding the Y3+ shell, as determined from such images. The thickness of the shell (~ 0.5 nm) roughly corresponds to a monolayer of Y3+ shell deposited on the Dy3+ core. Comparable dimensions were obtained for the Dy-Dy, Dy-Y, Y-Dy


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and Y-Y core-shell NPs, as detailed in Table 1. Fig. S1 provides TEM images of the other three core-shell NPs, as well as corresponding size distribution bar graphs obtained by image analysis.

Table 1

The X-ray diffraction (XRD) patterns of the four core-shell NPs, Dy-Dy, Dy-Y, Y-Dy and Y-Y (see Fig. S2) confirm their hexagonal crystal structure. Specifically, the XRD profiles of Dy-Dy and Dy-Y core-shell NPs were in good agreement with the JCPDS standard spectrum of NaDyF4 (JCPDS#00-027-0687), while the Y-Y and Y-Dy XRD profiles agreed well with the JCPDS standard spectrum of NaYF4 (JCPDS#00-016-0334). The average crystallite size, as calculated by applying the Scherrer equation to the XRD profiles, was 18.2 ± 1.2 nm for all four NPs samples, consistent with the TEM results. The Dy/Y molar ratios determined via ICP-MS, listed in Table 1, are also consistent with deposition of approximately a monolayer shell of Y3+ atoms on the Dy3+ core, or of Dy3+ atoms on the Y3+ core. DLS measurements on aqueous suspensions of these various NPs stabilized with an OA/PMAO-PEG organic coating yielded diameters on the order of 30-40 nm. Estimating the inner OA layer thickness at 2.5 nm, corresponding to the length of a fully extended C18 acyl chain, indicates that the outer PMAO-PEG region extends considerably from the NP surface into the aqueous medium, likely in a random coil configuration.

17

O NMR of Core-Shell NPs in Water



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The association of water with lanthanides is conveniently studied via 17O NMR chemical shift and 1H NMR relaxation rate measurements. Changes in both 17O NMR chemical shifts and 1

H NMR relaxivity (the relaxation rate enhancement per mole of lanthanide) of bulk water occur

through exchange with water coordinated to (i.e. inner sphere), or in the vicinity of, the lanthanides. In the case of fast exchange on the 17O NMR time scale, the number of such inner-sphere water molecules, , may be determined via 17O NMR chemical shift measurements, per Eq. 2,24 − = ∙ ∙ ! + #$ + %# &

[2]

where the observed chemical shift , relative to any bulk magnetic susceptibility induced

shift, (this being accounted for by use of an internal reference), is a function of the molar ratio of exposed lanthanides to water molecules, , and the chemical shift of a water molecule bound to a particular lanthanide, . The latter is partitioned into diamagnetic, i.e. non-paramagnetic, shifts ( ! ), contact, i.e. through-bond, shifts (#$ ), and pseudocontact, i.e., dipolar throughspace, shifts (%# ). For dysprosium, the 17O contact shift contributes roughly 85% of any observed lanthanide-induced change in the chemical shift of dysprosium-bound water.24 The contact shift may be expressed as a product of two terms, one specific to a given lanthanide, 〈)* 〉, and the other specific to the nucleus of interest, ,, as per Eq. 3. #$ = 〈)* 〉 ∙ ,


[3]

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For Dy, 〈)* 〉 = 28.565, while for 17O, , ≈ −2.407 ∙ 103 /, yielding #$ = -2307 ppm at = 298 K.24 To verify the reliability of the 17O NMR method in our hands, measurements were initially conducted with a Dy3+:DTPA complex, where, using the established values of the parameters pertinent to the various contributing factors in Eqs. 2 and 3 as above, the value of was confirmed to be 1.1 ± 0.2, in accord with published values.24 17

O NMR spectra of water were acquired for aqueous dispersions of the various core-

shell NPs, each stabilized by an OA/PMAO-PEG organic coating in water, examples of which are shown in Fig. S3 for the 50 ºC case. The full-width-at-half-height (fwhh) in each such spectrum was on the order of 150 Hz at 25 ºC, decreasing to 50 Hz at 70 ºC. There was little or no temperature dependence to the chemical shifts over the range between 25 and 70 ºC (Table S1). Table 2 lists the median 17O NMR water chemical shift changes observed across all temperatures, where the relative magnitude of the chemical shift change decreased in the order: Dy-Dy > Dy-Y > Y-Dy > Y-Y, when normalized for nanoparticle concentration differences. However, in absolute terms (Hz), the chemical shift changes were small relative to the large chemical shift uncertainties, the latter being proportional to the fwhh values.

Table 2

At the NP concentrations employed, the molar ratio of lanthanides to water molecules, , as it appears in Eq. 2, has an upper limit imposed by the total Ln3+ concentration, namely, the sum of the Dy3+ and Y3+ concentrations. For a 2 mM total Ln3+ concentration typical of these measurements, is on the order of 3.6×10-5. Assuming = 1, one predicts a contact shift of 13 ACS Paragon Plus Environment


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8.3×10-2 ppm at such concentrations, equivalent to 5.6 Hz at our magnetic field strength. However, for an intact NP only the surface layer would coordinate with water, thus reducing the effective lanthanide concentration by roughly a factor of 6, given the dimensions of the NPs employed here. Moreover, the OA portion of the organic coating forms a hydrophobic sheath that would tend to occlude water molecules from the NP lanthanide surface, thus producing an effective ≪ 1. Hence, the small and somewhat erratic 17O chemical shift changes observed here conform to these expectations.

1

H NMR Relaxivity of Core-Shell NPs in Water The interaction of water with paramagnetic lanthanides also influences its 1H NMR

relaxation rates, = 1/ and 6 = 1/6 , often expressed in terms of the relaxivity, i.e., the change in relaxation rate per mmol of lanthanide. Fig. 2 compares the water 1H NMR relaxivities obtained with aqueous dispersions of the various core-shell NPs, expressed in terms of the relaxation rate change per mmol of NPs. In contrast to the small effects on 17O NMR chemical shifts, the differences in water relaxivity were pronounced, with Dy-Dy NPs exhibiting relaxivities on the order of 40× those found for Y-Y NPs, demonstrating the profound influence of paramagnetic versus diamagnetic interactions. The hetero core-shell NPs, Dy-Y and Y-Dy, both exhibited relaxivities intermediate to those of the purely paramagnetic and the purely diamagnetic NPs. In all cases, there was little or no temperature dependence of the relaxivity across the three temperatures at which measurements were made (25, 50 and 70°C).

Figure 2


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For aqueous-complexes in solution, one may factor the relaxivity into contributions from waters associated with different coordination spheres.25 The inner sphere (IS) is the water coordinated directly to the ligand-lanthanide complex. The secondary coordination sphere (SS) consists of water hydrogen bonded to the ligand-lanthanide complex or to counter ions in its vicinity. Such SS waters are defined by a residence time, τm, that is longer than the diffusion correlation time of bulk water. Finally, the outer hydration sphere (OS) consists of freely diffusing, relatively disorganized water molecules. These rates are additive so that for longitudinal relaxation,

= 78 + 88 + 98

[4]

where each contribution is scaled according to the number of water molecules in that coordination sphere. The 17O chemical shift data above suggest that inner sphere water molecules are not a consideration here. For each coordination sphere, most generally three potential nuclear spin relaxation mechanisms contribute: dipole-dipole coupling between the water protons and the paramagnetic ion, scalar or contact coupling, and Curie spin coupling. For longitudinal relaxivity, at high fields, only dipolar relaxation makes an appreciable contribution.25 The relevant expression is:

1 2

Shell versus Core Dy3+ Contributions to NMR ... - ACS Publications

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