Increasing the detection distance of remote NMR using wireless inductive coupling coil

Unilateral nuclear magnetic resonance (UNMR) spectrometers have been applied in a variety of fields such as petrochemistry, materials science, and process control1. In UNMR measurements the sample is placed outside of the UNMR sensor and the signal intensity is reduced almost exponentially as the sample-to-sensor distances increases. To expand the detection limits of remote UNMR sensors, wireless inductive coupling was proposed and tested. This strategy was proved to reduce signal attenuation due to sample detachment from sensor, resulting in an increase in detection distance by one order of magnitude (i.e., from few millimeters to few centimeters). This novel approach broadens the potential applications of UNMR sensors and opens new opportunities in several areas, from chemical to biomedical applications.


Results
Secondary coil coupling to the unilateral NMR device. Fig. 1 illustrates the apparatus applied in this work. The secondary coil (S c2 ) is composed of a thin copper coil etched on a printed circuit board. This coil was tuned by soldering a chip capacitor onto it. The capacitor was chosen based on the primary coil frequency that maintained the so-called 'over coupling' regime wherein all the dissipated power in the primary coil is essentially dissipated in the secondary circuit. To reach as higher SNR values as possible, the coupled system was also matched to 50 Ω [12][13][14][15] .
In a typical single-sided magnet, the coil is placed close to the magnet surface, as depicted by S C1 in Fig. 1. When the region to be analyzed is far from the S C1 coil, the signal induced by nuclear spin precession and relaxation usually has remarkably low intensity. A straightforward means of increasing signal intensity is by surrounding the sample region with a second coil S C2 , which in turn is coupled by mutual-inductance to S C1 .
Computational simulations were carried out using FEMM 4.2 software Y20 in order to estimate the relative magnetic flux in the S C1 and S C2 coils generated by the nuclear spins. Thus, homogenously narrow disks with width similar to the diameters of coil wire, magnetized perpendicularly to the coil surface, were positioned concentrically to the coil axis. The magnetic flux perpendicular to the coil surface Φ m (d) was then calculated as a function of the distance d from the coil to the magnetized region. Figure 2 presents Φ m (d) normalized by the flux m 0 , which corresponds to d = 0 mm, for three different magnetized disk diameters: 6.7, 13.3 and 20 mm.
Although single-sided magnets do not feature a homogeneous circular region, calculations exploiting the code tridimensional feature provide an idea of the behavior of induced signal amplitude when only the primary coil (S C1 ) is used in the measurement. This decay is denoted by the function f m (d), which can be fitted exponentially. The amplitude of the induced voltage V 1 in the S C1 coil is thus given by V 0 1 f m (d), where in V 0 1 is V 1 at d = 0 mm. In other words, f m (d) directly shows the decay of the signal amplitude of S C1 coil in a circuit without the secondary coupling coil (S C2 ).  Coil coupling was also simulated using FEMM 4.2 software. In this situation, one coil was fed with a current of 1 Amp and the normal magnetic flux was assessed in the second one as a function of distance d. Figure 2 presents the ratio (Φ 12 /Φ 11 ) between the flux Φ 12 created by coil S C1 in the coil S C2 as well as the flux Φ 11 , generated by S C1 itself. The flux Φ 12 is related to mutual inductance M 12 and the ratio Φ 12 /Φ 11 is the coupling factor "k". The flux Φ 11 corresponds to self-inductance L 1 or, for Φ 22 , L 2 . As L 1 = L 2 = L in this study, M 12 = k (L 1 .L 2 ) 1/2 = k.L. Because of the magnetic field linearity generated by these coils, the self-inductance is directly obtained when the current is set to 1 Amp. Figure 2 also shows that the fluxes of magnetized disks decay like the flux created by one coil in the other one. This happens because the homogeneously magnetized disk can be replaced by the magnetization current density, what makes the magnetic field of the disk equals to that of a coil with one turn.
Circuitries for excitation/detection of coupling coil regarding both high and 50 Ω impedances may be found in the literature [15][16][17][18] . The circuits chosen in the experiment reported here are illustrated in Fig. 3. If one considers only the physically connected left side, it would be a common circuit typically used in NMR devices, applying tuning and matching capacitors (C 2 and C 3 ) as well as R Q resistor for circuit quality factor (Q) adjustment. T means the coaxial cable (50 Ω) and the output voltage is on R R . Rc indicates the resistances for both coils. The entire circuit was then used for inductive coupling. It also consisted of capacitors for impedance matching and resonance frequency tuning.
Since the voltage induced in the coil S C1 is not negligible, the voltage source V 1 was included in the circuit topology in addition to V 2 , which is induced in the coil S C2 . These circuits were analyzed through LTspice code 19 . Although there was not a rigorous modeling taking into account the exact coil geometries, copper shielding, the ferromagnetic influence of the carbon steel base magnet, and the dynamic analyses, the gains associated to coupled coil signal and its quasi-constant behavior could be seen.
If the sub-circuit that contains the S C1 coil has a high impedance, as the S C1 coil terminals are open, the tuning is obtained by C 2 capacitor and the mutual inductance does not influence the current in the coupled circuit. The maximum current I 2 is given by V 2 /R 2 at the resonance frequency (w r ). In this situation, the voltage between the S C1 coil terminals (V 0c ) is then the voltage of the coupled coils subtracting the voltage directly induced by the nuclear spins in S C1 , since they produce opposite magnetic fluxes. Thus, V 0c can be expressed by Eq. 1.
On the other hand, the voltage V 0 of the uncoupled circuit is obtained by Eq. 2 and the gain is the ratio V 0c /V 0 .
Intensity of the NMR signal versus sample distance (d) from the sensor. To evaluate the improvement of signal intensity due to the implementation of a secondary inductive coil coupled to the UNMR sensor, NMR spin echoes of a thin automotive lubricant oil layer were recorded at different distances d from the sensor surface using surface coil and the wireless inductive coupled coil. d was varied through the sequential addition of microscopy glass sliders (1 mm in thickness) between the sensor and the sample. It is worth mentioning that, for the inductive coupled experiments, d reflects the distance between Sc 1 and Sc 2 coils, being the sample positioned right above the Sc 2 coil. Figure 4 shows the maximum intensities of the NMR echoes recorded at different distances d.
As evidenced in Fig. 4, the intensities of the NMR signals using the surface coil Sc 1 (squares) and the remote coil Sc 2 (circles) are remarkably different at distances from the sensor higher than 2 mm. At approximately 6 mm, the signal resulting from Sc 1 was within the detection limit and presented a SNR equal to 3, whereas the intensity measured at the same distance with Sc 2 was identical do the Sc 1 on the surface. The intensity of the signal at 20 mm using the wireless remote coil was equal to that at 2 mm using the surface coil. This is equivalent to a one order of magnitude enhancement in signal intensity, indicating the greater advantage of this coupling. Although this advantage is not universal, we can envisage numerous applications for the wireless remote inductive coupled coil, which can boost the use of remote NMR.
Monitoring plaster curing. The secondary coil was also used to monitor the curing process of plaster.  Even though discussing mass transport and water mobility (curing process) on a time course in not the goal of this work, one may observe in Fig. 5b that the signal intensity related to water content decays faster on the surface than in the center of the plaster block. The difference between such positions was not larger because the glass sliders used to protect the S c1 coil limited water evaporation. Water loss during the experiments was approximately 25%.
Larger differences between T 2eff were observed in the two positions (Fig. 5b). The lower T 2eff values on the surface can be explained by fast decay of CPMG signal caused by water diffusion in the presence of larger magnetic field inhomogeneity at the magnet surface 4 . At 16 mm, the magnetic field inhomogeneity is smaller than on the magnet surface and the effect of water diffusion is less pronounced. The smaller decay of T 2eff values on the surface than at 16 mm can be explained by the reduced water diffusion due to hydration process that takes place concomitantly to water evaporation 20 .

Discussion
In summary, a simple, efficient means of enhancing the detection distance of small UNMR sensors based on wireless inductive coupling sensor, involving neither coils featuring sophisticated designs nor larger magnets and  coils, was demonstrated. The proposed configurations increased the detection distance by more than one order of magnitude, opening new opportunities for field applications of UNMR sensor. Although this advantage is not universal, several applications of the wireless remote inductive coupled coil may be envisaged, boosting the use of remote NMR. Some potential applications are listed below: a) Monitoring chemical reactions that need to be isolated from the NMR sensor. The remote wireless sensor can also be applied to reduce the effect of magnetic field on electrochemical reactions 21 , as the electrochemical cell can be positioned in an area of low magnetic field. b) Biomedical applications, in which the Sc 2 coils could be applied as bandages on specific regions of the body to evaluate the evolution of bone or soft tissue lesions caused by traumatic and infectious processes or even tumoral lesions. c) Materials Engineering, to monitor polymerization reactions either in laboratory or pilot scales as well as in manufactured products. Civil Engineering, to monitor curing and degradation processes of cement. In the latter, embedding Sc 2 coils into a concrete structure could provide valuable internal chemical and physical information concerning the sample.
Moreover, the simple S C2 design, built on the thin-coppered print circuit board, keeps the instrumentation costs low, which creates the possibility to make disposable coils depending upon the application.

Methods
Home-built UNMR sensor. A more detailed description of the UNMR sensor construction can be found elsewhere 22 . Basically, it was built using four axially magnetized NdFeB alloy blocks (2.54 × 2.54 × 1.27 cm 3 ) mounted on a carbon steel yoke base. Each pole was constructed with two blocks with the same orientation and separated by a 2-mm gap. The separation between the two poles was 14 mm 6,22,23 . The coil probe (Sc 1 ) was built in 20 awg copper wire with 9 turns and having an external diameter equal to 20 mm. Matching and tuning variable capacitors (Cs) ranging from 5 to 25 pf and from 5 to 50 pf, respectively, were used to adjust the probe between 25.550 MHz (0.6 T on sensor surface) and 10.650 MHz (0.25 T, 20 mm above sensor surface), where the system showed Q values around 50. For frequencies lower than 24.000 MHz, chip ceramic capacitors up to 300 pf were added in parallel to tune the circuit at the desired frequency. The UNMR sensor was connected to a NMR console CAT-100 (Tecmag, Houston, USA), a 3205 AMT power amplifier, and an AU 1114 preamplifier.
Secondary coil fabrication. The wireless remote coil Sc 2 was etched in a 0.2-mm thick, double-sided, coppered printed circuit board (55 × 25 mm 2 ). The resonance circuit was tuned to each frequency by a specific chip ceramic capacitor (C s2 ). The S C2 coil had 9 turns with an external diameter of 20 mm. As previously stated, the chip capacitor soldered to it was intended to keep the coupled system working on the over coupling regime, e.g. for 11.010 MHz at 20 mm, whereas the primary coil was set at 10.912 MHz, the secondary coil was set at 11.287 MHz. Figure 6 shows a picture of the secondary coil. NMR experiments. The intensities of the NMR echo signals were acquired using a spin echo sequence with 2-μs-long RF pulses separated by a time τ of 512 μs and averaged with 200 scans. The intensities of the echo signals were measured with an automotive lubricant oil sample (0.5-mm-thick layer). For the analyses without the remote coil, the sample distance to the sensor varied up to 6 mm, while for the remote coil it ranged up to 20 mm. CPMG pulse sequence was used to monitor the plaster curing process using 2-μs-long RF pulses separated by a time τ of 500 μs, 1200 refocusing pulses, and an average of 300 scans.
Plaster curing experiment. The plaster was bought in a neighborhood market as plaster of Paris powder. It was previously prepared in a beaker by mixing powder and tap water at a 1:0.8 weight ratio. Then, it was transferred to an acrylic box of 40 × 40 × 35 mm 3 (l x w x h) with a 1-mm glass slider at the bottle, for molding and setting on the UNMR sensor. To monitor the curing process on the surface, a sample of freshly prepared plaster was placed on the surface of the Sc 1 coil. For remote analyses, the Sc 2 coil was embedded in the center of the plaster. Subsequently, 43 CPMG experiments were performed during 9 hours. To accelerate the curing process, a fan was placed 50 cm away from the experimental set-up and the room temperature was maintained at 25 ± 1 °C.