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Nanoscale nuclear magnetic resonance with chemical resolution

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Science  07 Jul 2017:
Vol. 357, Issue 6346, pp. 67-71
DOI: 10.1126/science.aam8697

NMR on diamonds gets down to chemistry

Nuclear magnetic resonance (NMR) spectroscopy is immensely useful for chemical characterization, but it requires relatively large amounts of sample. Recent studies have leveraged nitrogen vacancy centers in diamond to detect NMR signals from samples of just a few cubic nanometers, but with low resolution. Aslam et al. optimized this technique to achieve a resolution of 1 part per million—sufficient to distinguish among alkyl, vinyl, and aryl protons in solution (see the Perspective by Bar-Gill and Retzker). They also demonstrated solid-state implementation and fluorine detection.

Science, this issue p. 67; see also p. 38

Abstract

Nuclear magnetic resonance (NMR) spectroscopy is a key analytical technique in chemistry, biology, and medicine. However, conventional NMR spectroscopy requires an at least nanoliter-sized sample volume to achieve sufficient signal. We combined the use of a quantum memory and high magnetic fields with a dedicated quantum sensor based on nitrogen vacancy centers in diamond to achieve chemical shift resolution in 1H and 19F NMR spectroscopy of 20-zeptoliter sample volumes. We demonstrate the application of NMR pulse sequences to achieve homonuclear decoupling and spin diffusion measurements. The best measured NMR linewidth of a liquid sample was ~1 part per million, mainly limited by molecular diffusion. To mitigate the influence of diffusion, we performed high-resolution solid-state NMR by applying homonuclear decoupling and achieved a 20-fold narrowing of the NMR linewidth.

Nuclear magnetic resonance (NMR) spectroscopy is among the most widely used analytical techniques, with applications in materials science, biology, chemistry, and medicine (13). Its versatility stems from minimal invasiveness and chemical specificity. In addition, NMR underlies magnetic resonance imaging (MRI), one of the most important diagnostic tools in medicine (46). A drawback of NMR-related techniques is their relatively low sensitivity, which requires nanoliter-sized sample volumes (7). Given the increased importance of nanoscale analytics across all areas of science, and in particular in biology and medicine, increasing NMR sensitivity is highly desirable.

Various approaches to increase sensitivity include magnetic resonance force microscopy (8), superconducting quantum interference device (SQUID)–based MRI (9), optical detection of NMR (10, 11), and external high-quality-factor resonators for low field detection (12). Recently, the nitrogen vacancy (NV) center in diamond has demonstrated its outstanding capability as a NMR sensor (1315). NMR detection of 0.1-zl samples with the NV center as well as imaging of nuclear spins has been demonstrated (1618). Compared with conventional NMR, the number of nuclear spins required to generate a detectable signal is reduced by 12 orders of magnitude.

Full functionality of NMR requires high spectral resolution. The resonance frequency of every nuclear spin is determined by its neighboring nuclear spins (J-coupling) and the surrounding electron distribution. Specifically, the electron density at the nuclear spin location leads to modification of the experienced magnetic field. This so-called chemical shift is conventionally defined as a relative shift to the Larmor frequency of a reference molecule in parts per million (ppm): δ = (νsamp – νref)/νref. For example, a relative shift of δ = 0.8 ppm in 1H NMR corresponds to an absolute frequency shift of δν = 1 Hz at 30 mT and δν = 100 Hz at 3 T. Consequently, NMR spectroscopy is preferably, but not exclusively, carried out at elevated fields in order to resolve such shifts (12), with resolution limited by the decoherence or dephasing times Embedded Image of the sample spins. The spectral resolution of our nanoscale NMR method is challenged by additional factors. First, the spin relaxation time of the sensor electron spin Embedded Image limits the achievable phase acquisition time τ and hence spectral resolution (19). Second, the nanoscopic sample volume itself imposes further constraints. For liquid samples, molecular diffusion through the (5 nm)3 large sample volume on time scales TD of a few tens of microseconds, as in (14), restricts the interaction time of the sample molecule with the sensor and hence limits the relative spectral resolution toEmbedded Image(1)Here, γ is the corresponding nuclear spin gyromagnetic ratio, and T limits the phase acquisition time τ. In previous NV nanoscale NMR studies, linewidths of 12,000 ppm have been achieved (19, 20), mainly limited by low magnetic fields, short Embedded Image, and short TD. By comparison, the chemical shift range of proton spins in organic molecules is ~13 ppm. Hence, distinguishing such protons and identifying and characterizing the related molecules typically requires a spectral resolution of 1 ppm (Fig. 1A), a factor 10,000 smaller than previously achieved. For NMR spectroscopy of molecules, it is therefore essential to increase the relative frequency resolution. We tackled this problem first by increasing the magnetic field to 3 T (21). At 3 T, the required phase acquisition time T for resolving chemical shifts in a 1H NMR spectrum is reduced to a few milliseconds (Fig. 1A). The high magnetic field in our experiments is not required for thermal spin polarization because detection relies on statistical spin polarization (8, 13, 14). Second, the intrinsic nitrogen nuclear spin was included as a quantum memory (22, 23). At 3 T, the spin relaxation time of the memory spin (Embedded Image) lengthens to ~260 s. With the use of this quantum memory, Embedded Image is replaced by the much longer Embedded Image in Eq. 1, yielding a potential maximal spectral resolution of ~1 mHz or Embedded Image ppm at 3 T (Fig. 1A), which is comparable with conventional NMR. As a result, the achievable resolution is limited only by diffusion (TD of liquid samples) or by dipolar broadening, such as in the case of solid-state samples (Embedded Image).

Fig. 1 Nanoscale NMR sensor and its functionality.

(A) Phase acquisition time T required to resolve chemical shift and J-couplings for 1H NMR according to Eq. 1 at an applied magnetic field B of 3 T (with γ = γH = 2π · 42.576 MHz/T). The bottom light-blue arrow marks the phase acquisition time required to resolve different proton chemical shifts (Δδ < 13 ppm). The top two arrows indicate the required phase acquisition time for resolving proton-proton and proton-carbon J-couplings (JHH and JCH). The red line marks the maximum phase acquisition time (spectral resolution limit) imposed by the spin-lattice relaxation time of the memory spin. The gray vertical lines mark the resolution achieved in the present work. (B) Schematic representation of NV diamond–based nanoscale NMR probe setup. The probe and sample are located in the room-temperature (RT) bore of a 3-T superconducting vector magnet. The probe is optically excited, and its fluorescence response is detected via a confocal microscope. MW waveguides and RF wires provide the oscillating magnetic fields for spin manipulation. (Right) Zoomed-in view illustrating the nanoscale probe-sample arrangement. The nanoscale NMR probe consists of a NV electron spin quantum sensor in diamond with an intrinsic 15N nuclear spin quantum memory. It detects sample spins within the indicated detection volume. The probes used in this study had a distance to the sample ranging from 34 to 95 nm. (C) The nanoscale NMR probe detection scheme relies on in situ correlation of sample magnetization from the initialization and readout stages. During the phase acquisition time, arbitrary NMR pulse sequences alter sample spin magnetization (for example, Ramsey spectroscopy, magnetization decay measurement, homonuclear decoupling, or higher-dimensional spectroscopy). While the sensor detects, the memory preserves sample magnetization information for later correlation via efficient quantum algorithms. Hence, the memory lifetime determines spectral resolution [see (A)]. Quantum nondemolition measurement of the memory state yields measurement data bit by bit with high fidelity (details are provided in the supplementary materials).

We used the NV center in diamond as a nanoscale NMR probe, optically detected with a confocal microscope. A high magnetic field along the NV center axis was provided by a 3-T superconducting vector magnet with a room-temperature bore. We conducted electron spin manipulation with a microwave (MW) antenna capable of operating at up to 90 GHz (Fig. 1B) (21). We manipulated the nitrogen nuclear spin of the NV center acting as the memory spin via radio frequencies (RFs) applied by a copper wire that also excited the sample spins. The sensor-sample distance governs the strength of the detectable NMR signal and also defines the detection volume. Long sensor coherence times allow for large sensor-sample distances in the first place. To this end, we used an isotopically purified, high-quality type IIa diamond substrate to eliminate the deleterious effects of 13C-spins and paramagnetic defects (24).

Measuring NMR spectra with the nanoscale NMR probe was separated into three experimental steps (Fig. 1C): initialization, application of the NMR pulse sequence, and readout. During initialization, a snapshot of the sample spin statistical polarization was acquired for time t/2 by the electron spin sensor and stored on the nuclear spin memory via an entanglement-based algorithm (22, 23). During the phase acquisition time, different NMR pulse schemes can be applied to the sample spins [one-dimensional (1D), 2D, or higher-dimensional NMR sequences]. In a concluding sequence of duration t/2, the effect of the sample spin NMR was detected and finally read out (Fig. 1C).

Different nuclear sample spin species (such as nitrogen, carbon, protons, and fluorine) were selectively addressed via resonant RF excitation exploiting their vastly different Larmor frequencies. We detected their response signal with the probe (Fig. 2A). The intrinsically broadband RF-excitation wire and the wide bandwidth of our nanoscale NMR probe allow for multispin species detection. Detailed spin Hamiltonian and measurement sequence description are provided in the supplementary materials.

Fig. 2 NV nanoscale NMR of multiple nuclear spin species.

(A) Normalized signals from 13C (in diamond), 1H [in polyvinylidene fluoride (PVDF)], and 19F spins (in PVDF) spectrally separated via their differing gyromagnetic ratios. For 13C spins, the normalized signal can become larger than 1 because of coherent interaction with only a few close spins as opposed to an incoherent interaction with a 1H or 19F spin bath. On top of the three spectra, the measurement scheme is depicted (compare Fig. 1C and supplementary materials). (B) The circle and dark gray line show the dependence of measured and extrapolated diffusion-related NMR linewidth on sensor-sample distance as d−2 for polybutadiene (1H) on diamond (2/γBTD with B = 3 T) (Eq. 1). Pale blue line indicates the depth-scaling of the detection volume (≈0.49d3), which contains half of the detected sample spins that contribute to the signal Embedded Image. (C) Depth determination of nanoscale NMR probe. NMR contrast increases with sensing time t and depends on the sample spin density ρ and the distance d between the sample spins and the NV sensor (details available in the supplementary materials). Different samples are used for this purpose: polybutadiene oil (1H, dark red), cyanoacrylate solid glue (1H, light red), and PFPE oil (19F, light and dark green). Vertical dashed lines indicate the required sensing time to reach 50% signal strength (horizontal dashed line) for each NV-sample combination.

For liquid-state samples, the time TD for diffusion through our nanoscale detection volume limits the achievable spectral resolution (19, 20, 25). In essence, diffusion changes the distribution of spatially inhomogeneous statistical polarization and thus diminishes the correlation between the sensor signal of the “init” and “read” parts (Fig. 1C). To mitigate this effect, one could increase the viscosity of the host medium for the molecule under study. However, for large viscosity, NMR spectra broaden because of a lack of molecular mobility (19). As a result, a further parameter to optimize is the detection volume. With growing sample-sensor distance d, the spin signal per volume decreases, and the sensor acquires substantial spin signals from larger volumes (Fig. 2B). The diffusion time is thus prolonged as Embedded Image, where D relates to the diffusion coefficient of the sample spins (supplementary materials) (25). To achieve a spectral resolution of 1 ppm for the D of the substances we used (Fig. 3F), we require an effective sample volume of (20 nm)3 corresponding to an NV depth of d ≈ 25 nm (Fig. 2B). To reach sufficient signal strength S, we need to increase the total sensing time t (Fig. 1C, “init” and “read”) according to Embedded Image(2)where γ is the gyromagnetic ratio of the sensor spin, Embedded Image is the variance of the sample spin magnetic field at the sensor (the effect of statistical polarization), and Embedded Image is the coherence time of the sensor electron spin. Embedded Image, on the other hand, is proportional to 1/d3. The measured proton and fluorine signal strengths (1H and 19F, respectively) are shown in Fig. 2C for different depths up to ~100 nm and varying total sensing time t up to ~0.6 ms, corrected for the coherence decay of the sensor. The sample spin density ρ and the sensor’s coherence time Embedded Image limit the practical sensor distance (supplementary materials). For the present case, because of the long Embedded Image (>200 μs), we were able to detect even diluted samples of proton and fluorine spins in principle up to a distance of 100 nm (supplementary materials).

Fig. 3 Chemical shift resolved liquid-state NMR for 1H and 19F.

(A) Ramsey measurement of 19F spins in PFPE (fomblin). We fit two exponentially decaying cosine functions with Embedded Image and Embedded ImagekHz to the data (details available in the supplementary materials). The insets in (A), (D), and (F) show the measurement scheme (compare Fig. 1C and supplementary materials). (B) FFT power spectra of data (green line) and fit (bold light green line) from (A) together with the results of a conventional NMR spectrum (dark green line, 400-MHz NMR spectrometer) of our sample. Chemical structure of PFPE is shown. Pale green and blue areas under the curve mark signals of individual 19F atoms with different chemical shift. The corresponding positions within the PFPE molecule are highlighted by identical colors. For better visibility, conventional NMR and nano-NMR signals are enhanced by factors of 5 and 10 for the chemical shift range 130 to 160 ppm. (C) Enlarged view of the NMR resonance peak from (B) around 80 ppm. Here, the phase acquisition time τ is increased to 5 ms, yielding a full width at half maximum (FWHM) of the NMR peak of 1.3 ppm (decay time 2.5 ms). Conventional NMR yields a FWHM that is an order of magnitude smaller. (D) Ramsey measurement of 1H spins in liquid polybutadiene. Measured data are fitted with a superposition of two cosine functions with 1.7 and 2.2 kHz (details available in the supplementary materials). (E) FFT power spectra of 1H spins in liquid polybutadiene. Chemical structure of polybutadiene reveals two subgroups: CH and CH2. The corresponding NMR peaks are detected with a FWHM of 1.3 and 1.4 ppm, respectively. Examples of conventional NMR spectra can be found in (26). The FFT of data and fit from (A) and (D) displayed in (B), (C), and (E) were all obtained by zero-filling and therefore represent interpolated FFT spectra. (F) Magnetization decay of 1H spin signal in liquid polybutadiene. An exponential decay fit function yields a decay time of TD = 5.4 ± 0.9 ms owing to diffusion of sample molecules out of the detection volume.

For the present experiments, we chose highly viscous fluids: polybutadiene [(CH2CH = CHCH2)n] with about n = 90 subunits per polymer strand in the case of 1H NMR, and perfluoropolyether {PFPE; CF3O[–CF(CF3)CF2O–]x(–CF2O–)yCF3} with about x = 140 and y = 13 subunits per polymer strand in the case of 19F NMR. The polymer strands are on the same length scale as our detection volume. Ramsey experiments for these two fluids are shown in Fig. 3, A and D. The data reveal multiple frequency oscillations (Fig. 3, A and D). In the case of PFPE, the fast Fourier transformed (FFT) data in Fig. 3B exhibit two peaks arising from fluorine spins with different chemical shifts, which match the reference NMR spectrum obtained with a conventional 400-MHz NMR spectrometer. The linewidth of the major peak is 1.3 ppm (Fig. 3C) for the NV nanoscale NMR. By comparison, conventional NMR yields a 10-fold narrower line. Furthermore, the FFT of the polybutadiene 1H NMR measurement in Fig. 3E shows two peaks, as expected (26). The proton chemical shift of the CH2 groups (Fig. 3E, inset, chemical structure) is dominated by the sp3 hybridized neighboring carbon atom and thus shows a chemical shift similar to alkanes (~1 to 2 ppm), whereas the chemical shift of protons in the CH group is dominated by the sp2 hybridized neighboring carbon atom that is typical of alkenes (~6 ppm). The linewidths of 1.3 and 1.4 ppm are five orders of magnitude larger than the nanoscale NMR probe’s intrinsic frequency resolution. We attribute these linewidths mainly to the diffusion of the molecules out of the detection volume within TD (Eq. 1). This is supported by the decay of the sample spin magnetization (Fig. 3F). Rather than being on the order of seconds, as measured on bulk liquid samples, we measured a time constant of 5.4 ms. This is close to what is expected for the diffusion of polybutadiene molecules through a detection volume of (28 nm)3 corresponding to a diffusion-related coefficient of D = 223 nm2 ms–1 (Figs. 2B and 3F) (20, 25). In liquids close to the diamond surface, however, residual dipolar broadening that is not fully averaged out by molecular motion also contributes to linewidths (19). Therefore, the lines in Fig. 3, B, C, and E are slightly broader than 2/γBTD = 0.5 ppm (Fig. 3F).

By fixing the position of the detected spins, translational diffusion of spins can be mitigated. We investigated solid poly(ethyl 2-cyanoacrylate) deposited on the diamond surface. The magnetization of the sample spins decayed on a time scale of T = 94 ± 11 ms (Fig. 4A), which is about 20 times slower than for the liquid phase. In fact, dipolar spin-spin interaction—averaged out in liquids—causes spin diffusion with a coefficient on the order of D ~ 1 nm2/ms, which is about three orders of magnitude slower than for translational diffusion (27). In conventional solid-state NMR, two methods are used to effectively remove dipolar broadening and achieve high-resolution spectra: magic-angle spinning and homo- or heteronuclear decoupling sequences (28). We performed two homonuclear decoupling sequences (WAHUHA and MREV-8) to demonstrate high-resolution solid-state nanoscale NMR. Both sequences consisted of a train of phase-shifted π/2 pulses (each ~3 μs in duration), separated by free evolution times (Fig. 4B). The dipolar coupling between spins is refocused, whereas the phase signal Embedded Image is accumulated (for example, because of nuclear Zeeman interaction), albeit with a certain scaling factor cdec < 1, which depends on the sequence and the duty cycle and affects the effective free evolution time τeff = cdecτ. In Fig. 4, C and D, the sample spins’ Ramsey oscillations and the corresponding Fourier transform are shown without and with homonuclear decoupling (here, MREV8 is used). We prolonged the effective phase evolution time by a factor of 17, resulting in a linewidth of Embedded Image kHz in the FFT spectrum. In order to evaluate the factor cdec, we introduced a frequency offset between the sample spins’ Larmor frequency and the RF driving field. As expected, the NMR signal exhibits a frequency that shifts with the detuning scaled with the factor cdec,WAHUHA = 0.57 and cdec,MREV8 = 0.46 (Fig. 4, E and F), which agrees with theoretical predictions (28).

Fig. 4 Solid-state 1H NMR with homonuclear decoupling.

(A) Magnetization decay of 1H spins in poly(ethyl 2-cyanoacrylate). The decay time is determined by an exponential fit to be 94 ± 11 ms. (Inset) The measurement scheme (compare Fig. 1C and supplementary materials). (B) Pulse sequence of WAHUHA and MREV-8 homonuclear decoupling methods acting on the sample spins during a Ramsey measurement. The broadening due to dipole-dipole interaction among sample spins is reduced while maintaining a certain fraction of susceptibility to static magnetic fields. (C) Top curves and bottom curve show Ramsey measurement with and without homonuclear decoupling (MREV-8) of 1H spins in poly(ethyl 2-cyanoacrylate), respectively. For the measurement with homonuclear decoupling, the waiting time is already corrected by the factor cdec obtained from the control experiment [see (F)]. For better visualization, the topmost graph shows the measurement without homonuclear decoupling with an adjusted time axis (details available in the supplementary materials). (D) The FFT reveals a 17× increase of the frequency resolution by the MREV-8 homonuclear decoupling from 26 kHz (206 ppm) down to 1.5 kHz (12 ppm). (E and F) Reduction of magnetic field susceptibility for WAHUHA and MREV-8 sequences. Detuning of the frequency in the Ramsey measurement is varied, and the corresponding frequency shift according to the phase acquisition time is monitored. The ratio between the sensing time and the total sequence length is determined via the slope to be cdec,WAHUHA = 0.57 ± 0.01 and cdec,MREV8 = 0.46 ± 0.01. The intercept reveals information on the resonance frequency of the sample spins in poly(ethyl 2-cyanoacrylate). The displayed FFT spectra in (D) to (F) are obtained by zero-filling of corresponding data.

The enhanced spectral resolution demonstrated here comes at a cost. During the phase acquisition time τ, the sensor is idle. Discriminating sample spin NMR frequencies, the required resolution scales as δν = 1/τ and hence improves for long τ. On the other hand, the NMR signal strength (Embedded Image) for a required spectral resolution δν exhibits a sensitivity scaling Embedded Image (t < 500 μs is the sensing time; details are available in the supplementary materials). Hence, the sensitivity deteriorates for higher required spectral resolution because of increased phase acquisition time τ and thus reduced measurement rate. Last, τ and therefore δν are limited by T, the decay time of phase correlation of the sample spins. For the present experiments, T is shorter than the readout time of the memory Tread ≈ 8 ms (Fig. 1 and supplementary materials). As a consequence, the sensitivity is reduced by less than Embedded Image in our experiments and will start scaling as ∝δν–1/2 for τ >> 8 ms or δν << 100 Hz.

To enhance sensitivity, Tread can be shortened by increasing the collection efficiency of NV fluorescence photons (29, 30). On the other hand, application of compressed sensing would reduce the overall measurement repetitions needed to reach a certain signal-to-noise ratio (31). Further enhancement can be achieved by incorporating more memory spins (proximal host 13C spins), which would allow the use of quantum algorithms such as quantum Fourier transform or quantum error correction, resulting in measurement speed-up and more robustness (32).

The discrepancy in spectral resolution of the present nanoscale NMR measurement and the measured bulk NMR linewidth can be overcome, for example, in liquid-state NMR by immobilizing sample molecules in nanocapsules such as liposomes, micelles, or polymer shells (33). Although such immobilization techniques might have an impact on molecular structures, they will prevent translational diffusion out of the detection volume and still allow averaging out of dipolar interactions through motional narrowing. However, for solid-state NMR the measured linewidth was limited by the finite pulse length in the homonuclear decoupling sequence. An optimized RF microstructure and higher RF power equipment would thus further improve resolution, enabling chemical structure analysis experiments. Additionally, in NV nanoscale NMR there is no need for a reference molecule because the host 13C spins can be used to determine the magnetic field very precisely (<0.03 ppm) (23).

This work paves the way for numerous applications of nanoscale NMR. For instance, imaging of sample spins’ chemical shift Embedded Image and T1 in cells with nanometer spatial resolution would open a promising contrast mechanism for optical microscopy.

Supplementary Materials

www.sciencemag.org/content/357/6346/67/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S5

Tables S1 to S3

References (3448)

References and Notes

  1. Acknowledgments: We thank S. Zaiser, N. Abt, and A. Momenzadeh for fruitful discussions and technical advice. We acknowledge I. Jakobi for graphics design. The NMR measurements with the 400-MHz NMR spectrometer were acquired by K. Dirnberger and B. Omiecienski from the Institute of Polymer Chemistry, University of Stuttgart. We acknowledge financial support by the German Science Foundation (SFB-TR 21, SPP1601), the EU (DIADEMS, SMel), the Max Planck Society, the Volkswagen Stiftung, and Japan Science and Technology Agency and Japan Society for the Promotion of Science KAKENHI (nos. 26246001 and 26220903). F.F.O. acknowledges the financial support by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) project no. 204246/2013-0. Data supporting the findings of this study are available within the article and its supplementary materials and from the corresponding authors upon reasonable request.
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