Approaches to NMR sensitivity enhancement based on theoretical analysis

Nuclear magnetic resonance (NMR) has been broadly investigated and applied in many industries (e.g., medical treatment, food safety and materials) as a powerful approach to explore the internal structure and composition of substances. However, the need for more sensitivity has been one of the most severe problems hindering the practical application of NMR. This paper suggests various approaches to deal with this defect, from adjusting factors based on the theoretical principle to the progressive hyperpolarization method. Classified by polarization sources, several representative sub-fields of hyperpolarization are further interpreted and analyzed, including Dynamic Nuclear Polarization (DNP), Optical Pumping (OP) and Parahydrogen Induced Polarization (PHIP). Based on the analysis and prospect of the aforementioned feasible methods, the main factors that restrict the sensitivity of NMR will be identified. Moreover, the prospects and new technologies brought by the methods based on different theoretical foundations have been considered to improve these factors and make NMR apply to a broader range of fields. Overall, these results not only indicate the current research status but also shed light on guiding further exploration of methods of enhancing NMR sensitivity and usability.


Introduction
Nuclear magnetic resonance (NMR), a widely applied physical process, has played an essential role in many sectors, such as medicine, analytical chemistry and environmental monitoring [1].Since 1946, when Nuclear Magnetic Resonance was demonstrated by Felix Bloch and Edward Mills Purcell with the induction method and absorption method, respectively, it has gradually become one of the most practical analytical techniques to obtain properties of molecules in composition, framework and dynamics [2].
However, the low sensitivity restricts the work of NMR, making the concentration of samples required high and the collection time long [3].Consequently, some methods for solving the sensitivity problem have been discovered, such as Hyperpolarized NMR and Detector Optimization.These means with various theoretical basis have distinct focuses of application with different preponderance and drawbacks.Moreover, there are few articles regarding analyzing and summarizing the existing methods for the sensitivity problem of NMR.Therefore, it is necessary to identify the main reasons leading to the insensitivity with the physical meaning behind it and suggest relevant approaches by explaining the scientific mechanism, main application fields and its potential reliability.
On this basis, this study investigates ways to solve these grave problems.To be specific, means for improving the sensitivity of NMR will be identified with the explanation of theoretical principles, research status and its future development trend.The topics of the rest of the paper will be described accordingly.The Sec. 2 will give the background information of NMR, consisting of both principles and the main application field.The Sec. 3 will identify the inherent factors leading to the insensitivity and provide basic approaches to dealing with these discovered elements.Moreover, the Sec. 4 will explain and analyze the powerful hyperpolarization methods by first indicating the classification and then interpreting the essential methods in these branches orderly.Finally, the Sec. 5 will suggest the limitations of this research as well as discuss the outlook of further studies, and then the conclusion will be illustrated in the last section.

Theoretical principle and practical application of NMR
NMR is a well-known physical phenomenon based on the charge and spin properties of nuclei.Unlike the charge property, not all the nuclei could have spin as their intrinsic property, which could be divided into three separate cases.Firstly, the amounts of protons and neutrons are both even, and nuclei, including Carbon-12 and Oxygen-16, have zero spins.Secondly, when the numbers of protons and neutrons are both odd, it has an integer spin, including Boron-10 and Nitrogen-14.Finally, nuclei with an odd mass number, such as Carbon-13 and Oxygen-17, have half-integer spin [4].It is essential to mention that only a nucleus with non-zero spin could be used in NMR, so nuclei with the first situation should be excluded.The conforming magnetic spin is always distributed randomly of the same energy without an external magnetic field.When the magnetic field occurs, the magnetic spin of nuclei will align with the field, which means they will either parallel or anti-parallel to each other.The parallel will have lower energy, and the anti-parallel spin will have higher energy.Consequently, the split of energy levels has occurred.At the same time, this axis of rotation of magnetic spin also precesses around the direction of the magnetic field, as shown in Fig. 1.The angular frequency of this kind of precession is called the Larmor frequency.After separating the energy level, radio-frequency pulses are introduced, which match the value of the Larmor frequency.The nucleus at a lower energy level will absorb this radiation and go to the higher energy level with resonance occurring.It is notable that the energy of the radio-frequency pulse is the same as the energy gap between the parallel as well as anti-parallel energy states.This is the main principle of NMR.
As a widely used technique, NMR could be applied in scientific research to equipment in real life.For instance, NMR is a standard tool for analyzing matter structures at the molecular level and studying reaction mechanisms and kinetics in analytical chemistry [6].As a medical application of NMR, Magnetic Resonance Imaging (MRI) is a medical imaging technology applied to produce detailed images of the human body in order to detect tumors and lesions.NMR could also be used in quality Figure 1.Precession of the axis of spin for non-relative case in the applied magnetic field [5].
control in the food industry to detect protein structure and trace water mobility [7].Moreover, as presented in Fig. 2, there are other current applications in the scientific field of NMR.

Traditional approaches for inherent insensitivity
The low sensitivity property of NMR is inherent due to the small number of population differences, also known as polarization of nuclei spins at thermal equilibrium [9].In order to improve this kind of inherent problem, aspects determining the insensitivity need to be identified.The sensitivity of NMR is a commonly used but less intuitive term, so it is always related to another concept of signal processing: the Signal-to-noise ratio (SNR).SNR has the definition of the peak height divided by the root mean square of the noise [10].To increase the sensitivity of NMR, terms leading to the increment in SNR should be found: The Eq. ( 1) indicates the proportional relationship between SNR and several terms.Here, B 0 and B 1 are the magnetic flux density of the external magnetic field and Radio Frequency Field with input current I, respectively; N s refers to the number of protons in the sample with temperature T; γ is the Gyromagnetic ratio which refers to the ratio of nuclear magnetic moment to spin angular momentum, which varies with different nuclei.Moreover, h is Plank's constant and k refers to the Boltzmann's constant.The last term, V noise , relates to the random thermal noise voltage.Therefore, two common strategies for increasing the sensitivity of NMR are to increase the term B 0 and to decrease the sample temperature T.However, the increment of B 0 is restricted owing to imperfect superconducting technology, which leads to high costs and a complicated manner.The decrement in T to a significant amount is only possible for particular sample types [11].The limitations of these two traditional approaches encourage the discovery of further methods, which will be discussed in the next section.

NMR hyperpolarization
A hyperpolarization method is introduced to increase the sensitivity of NMR further.It increases the population difference between higher and lower energy levels from thermal equilibrium by transferring the hyperpolarized state of exogenous particles to the atomic nucleus of the target molecule [12].The NMR hyperpolarization could mainly be divided into two general cases according to the polarization sources: transferring the polarization of the electron spin to the atomic nucleus and using specific molecules polarization to induce polarization of the atomic nucleus [13].They could also be classified into more branched fields, as depicted in Fig. 3.In this section, three representative and frequently used ways of hyperpolarization will be introduced and analyzed, which are DNP, OP and PHIP.

Dynamic nuclear polarization (DNP)
The principle of DNP is mainly the polarization transfer from electron to nucleus.To be precise, the electron and the surrounding nucleus have dipole-dipole interaction.When the microwave irradiation near Larmor frequency applies, the spin direction of both nuclei and electrons will undergo reverse if their initial spin directions are opposite.For this case, the difference between the number of particles between the energy levels increases, and the polarization hence to be increased.Nevertheless, the considered electron could also undergo the same reverse in spin direction with other nuclei around it.Hence, the nucleus will return to its original state, and the polarization increment could not be achieved.This resistive process is impossible due to the relaxation time of the nucleus is much larger than that of the electron, which keeps the nucleus in the polarization state.To achieve it practically, one needs to put the sample into a radical molecule at a low temperature under a magnetic field to obtain large electron spin polarization.Consequently, the polarization transfers to the nearby nucleus under continuous microwave.In fact, the polarization of electrons is about 660 times that of protons, and the spin-polarization of nuclei is greatly strengthened by the higher polarization of corresponding electrons [11].Thus, this kind of change in the distribution of nuclear spin energy level has led to greater polarization and better sensitivity of NMR.
The DNP could be divided into four mechanisms which are the Overhauser effect (OE), Solid effect (SE), Cross effect (CE) as well as Thermal Mixing (TM), depending on different environments of uncoupled electrons and nuclei.The electron of OE has a short correlation time, which should fulfil ω e τ <1 where ω e is the Larmor frequency of the electron and τ refers to the correlation time [14].It is mainly applied in liquid in a weak magnetic field, organic conductor and metal with free electrons.Meanwhile, the other three mechanisms are considered principles for solid samples [15].SE requires the line width of electron resonance spectra to be smaller than the Larmor frequency of nuclei (ω n ).It mainly takes place in solid samples with fixed paramagnetic centers at low temperatures, for instance, paramagnetic impurity centers in the diamond lattice.At that time, the free electrons are localized in an atom or lattice which cannot move.By contrast, the line width of spectra is larger than the Larmor frequency for CE.It not only involves coupling between nucleus and electron but also has coupling of two dipole-coupled electrons.It should obey the equation |ω e2 -ω e1 | = ω n where ω e1 and ω e2 refer to the Larmor frequencies of the coupled electrons.For the last mechanism, TM occurs when free radicals take up a relatively high concentration and broadened linewidth is close to ω n .It introduces the concept of spin temperature to describe the term spin polarization, and the polarization transfer could mainly be considered as the heat exchange between spin heat reservoirs.That are the four mechanisms of DNP.
For application, owing to the high sensitivity provided by DNP, MRI could obtain high-resolution 13C images in a small-time interval, and SNR has improved by a factor of one thousand [11].It could also be well applied in analyzing material structure with active surface sites of low area and concentration, which are usually trapped in the spectra resolution.

Optical pumping (OP)
To illustrate the hyperpolarization of hyperpolarized electrons, a branch of a method called optical pumping is introduced.OP changes the nuclear spin distribution in thermal equilibrium and uses circularly polarized light to realize nuclear spin hyperpolarization.Due to the broad concept of OP, a widely-applied sub-field called Spin exchange optical pumping (SEOP) is interpreted as an example involving a spin exchange process.SEOP is an indirect method that uses alkali metal gas (usually Rubidium) as a medium to realize the hyperpolarization of the noble gas.With the existence of magnetic field, the electronic energy level of the rubidium atom is divided into 2J+1 sublevels, where J is the quantum number of the angular momentum of the electron [16].The electron transitions from the ground state (mj=-1/2) to the higher energy level (mj=+1/2) occur when the laser is turned on.The Rb atom then returns to the two sub-levels of the ground state (mj=±1/2), emitting fluorescence during the transition.Therefore, the number of electrons with mj=+1/2 at the ground state will ascend while that with mj = -1/2 will descend.Moreover, the electronic spin of Rb atoms and the nuclear spin of noble gas atoms would form van der Waals molecules in the process of spin exchange.Thus, the detection sensitivity of noble gas would consequently be increased.Due to its high natural abundance and fast spin exchange rate of 129 Xe, it is usually used as the aforementioned noble gas in SEOP.Because of its strong sensitivity, this method is often used to detect in situ catalytic processes and the structure and connectivity of porous material in the chemistry industry.Moreover, it is also a potential technique for medical use and research in biological protein.

Parahydrogen induced polarization (PHIP)
One of the techniques of molecular-induced polarization will be mentioned in this section: Parahydrogen Induced Polarization (PHIP).Attributed to the different nuclear spin states of the same kind of atom at the symmetrical position of the same molecule, the hydrogen molecule has two nuclear spin variants: ortho-H 2 , where the nuclear spin wave function is symmetric, and that of para-H 2 is anti-symmetric.At room temperature, the proportion of ortho-H 2 to para-H 2 is about three-quarters [17].In order to increase the small ratio of a required substance, the sample is supposed to cool down with catalyst FeO(OH) because the para-H 2 is in the rotational ground state.Moreover, the PHIP is to increase the sensitivity of NMR by adding enriched para-H 2 to the unsaturated group of the substrate molecule through catalytic hydrogenation.Depending on the magnetic environment of the addition reaction, it could be divided into two situations: PASADENA for a high magnetic field and ALTADENA for a relatively low magnetic field.For PASADENA, two hyperpolarized hydrogen atoms could have two spin states αβ and αβ and could produce two antiphase doublets.For ALTADENA, two hydrogen atoms only possess one αβ spin state and could produce one negative and one positive peak.These two situations all increase the spin population differences and hence achieve the effect of hyperpolarization.Taking advantage of low equipment cost, simple operation and high polarization efficiency, it could be utilized to study hydrogenation reactions, catalytic mechanisms, biological metabolic reactions, and enhance contrast medium in MRI.

Limitations & prospects
This paper mainly studies the factors leading to the low intrinsic sensitivity of NMR and how to adjust them, as well as the powerful hyperpolarization method, which primarily analyzes three typical branches: DNP, OP and PHIP.However, the researches could also be extended to other hyperpolarization aspects like chemically induced dynamic nuclear Polarization (CIDNP), which occur in optical excited or thermal excited chemical reactions, and photo-CIDNP where occur non-Boltzmann nuclear spin polarization under illumination.Although hyperpolarization plays a vital role in improving sensitivity, it could also have some drawbacks that restrict its further promotion and development and could be considered feasible in future investigations.Firstly, the lifetime of hyperpolarization should be extended and prevent premature relaxation.For instance, a method that contains a long-lived state (LLS) could achieve this goal because of its symmetry of the spin system, which could last around 10 minutes [18].Another limitation of hyperpolarization is that it cannot provide the relative concentration of a particular substance by simply integrating peaks because it involves polarization transfer and relaxation [19].Therefore, it should be reformed to retain this valuable property.Moreover, expensive and bulky NMR equipment for hyperpolarization occurs, and the store could be another severe problem.Hence, finding ways to increase the sensitivity of NMR and simultaneously have a low-cost and portable form could be worthy of consideration to prompt more comprehensive application.

Conclusion
In summary, NMR plays an essential role in both scientific research and life applications.However, its sensitivity is considered the main factor hindering the development and better real-life application.This paper begins with an explanation of the concept and application of NMR and describes the basic methods and powerful approach, hyperpolarization, to improve the sensitivity of NMR.For each section, its theoretical principles, application branches and prospects are analyzed successively.From the discussion in this paper, the high cost and inconspicuous increase brought by the uplift of the magnetic field strength and reduction of the temperature can be well solved by the hyperpolarization method, and the further innovations could solve specific deficiencies which enhance the detected sensitivity.Nevertheless, this paper only has the occasion of mentioning some hyperpolarization methods; other approaches, including CIDNP, ONP and QRIP, could also be included for a more comprehensive understanding.As more precise instruments and more advanced methods have been used, the problems that restrict the further improvement of sensitivity will be solved more effectively.These progressive methods will be more extensive and more practical in distinct fields.