Pulsed Nuclear Magnetic Resonance Spectrometry

Pulsed Nuclear Magnetic Resonance Spectrometry

Nuclear Magnetic Resonance (NMR) is a phenomena that can be induced in materials and used to characterize some of their physical and chemical properties. NMR occurs on the nucleus constituents (protons and neutrons) after the system is first placed in an applied electromagnetic field and then excited using a selected radio frequency pulse. The frequency of this pulse is chosen according to the constituent of interest. Once the excitation is removed, the collective system is monitor over time to obtain information about the system.

This section is dedicated to low-resolution pulsed nuclear magnetic resonance using the frequency that excites thr hydrogen nucleus. Since there is no neutron in a hydrogen atom, it is common to refer to this technique as one that excites the hydrogen proton. Since a pulse is used, the technique is refered as pNMR.

pNMR has evolved to become a standard laboratory technique in the study of fats and oils. Some of the benchtop equipments, like the Bruker Mini-spec, had been fine-tuned by the manufacture to target precisely the hydrogen’s protons. This allows the manufactures to create different routines that can compute, for example, the amount of solids in fats and oils. Another application of the Bruker Mini-Spec that is gaining popularity is the study of the mobility of water and or oils.

Important Aspects of pNMR

The main important aspect of the pNMR technique and the Bruker Mini Spec equipment are introduced in the following summary table.

Summary Table 

Principle of the pNMR technique

The pNMR process can be summarized in the following four steps:

Step 1: The sample is subjected to a permanent external magnetic field, Bo which affects the nuclei spin moments.

Step 2: The spin system responds to Bo, generating an internal net magnetization  which reaches an equilibrium state in a matter of milliseconds.  Mo is not a static vector, but rather the sum from all the spins that are precessing around the Bo direction.

Step 3: An oscillating magnetic field RF of a specific frequency is applied during a limited time causing  to move to a non-equilibrium state.  

Step 4: Mo relaxes back to its equilibrium state after the RF is removed. The relaxation process is monitored over time to obtain information about the system. Due to equipment set up, Mo is monitored only along one of its two Cartesian components, the transverse one. The transverse magnetization Mr and the longitudinal magnetization Mz, are defined as Mr and Mx x^+My ŷ   and M= Mz ẑ.

Mz gives information about the interaction of the nuclei with the “environment”, the network of nuclei that surround it. Mz is referred as the spin-lattice relaxation component and is associated with a characteristic time called T1, the spin-lattice relaxation time.

Mr gives information about the lack of coherence of all spins making Mo. Not all protons will precess in unison causing a de-phasing of the spin projection into the XY plane until eventually the phases are disordered and there is no net magnetization in the XY plane. The decay of Mr happens at another time scale compare with Mz. The characteristic time for this relaxation involves only the phases of the nuclear spins and T2 is called spin-spin or transverse relaxation time.

What follows describes in more detail each of the above steps.

Step 1:
We focus of this discussion is on the Bruker Mini spec which targets the hydrogen’s protons.

Step 2:
The insertion of the sample into the external magnetic field Bo causes the NMR-active nuclei (hydrogen protons) to go to quantized energies according to their spin values. The spin can possess quantized values, I = 0, 1/2, 1, 3/2 in units of ħ. Nuclei with I = 1/2 possess a magnetic dipole moment and no higher multipoles. Each nuclear dipole in an external magnetic field like Bo possesses two quantized energy states defined by whether the Z-component of the dipole moment points in the direction of Bo (spin up) or in the direction opposite to Bo (spin down). The spin up state possesses lower energy than the spin down state so that, at any finite temperature, the spin up state will be more populated than the spin down state. This implies that the magnetic dipole will preferentially be aligned along the Z-axis, in the direction of the external field Bo. The contribution of all dipoles moments generate Mo (Fig. 1), the total magnetization moment due to all the protons' moments.

Figure 1

Step 3:
At this step, the radio frequency RF pulse is applied. It is directed at right angles to the Z-axis (Fig. 1). The energy that is provided by the RF pulse causes some of the nuclei in the spin up state to flip to the spin down state and vice versa. When a specific excitation frequency is used, during a defined time interval, it is possible to “tip over” Mo and bring it from its original Z direction to the Y direction in the (X,Y) plane. The RF is selected to have a value close to the Larmor frequency for the nuclei under study. The Larmor frequency (ωL) is related to the applied magnetic field Bo as seen in  Eq. 1

ωLBo
(Eq. 1)

 

where γ is the gyromagnetic ratio. The theoretical value for a hydrogen proton is  42.576 MHz/T. It can be seen that once the value of Bo is set , the Larmor frequency can be obtain and the RF pulse set accordingly.

Step 4:
After the radio frequency pulse is removed the nuclei realign ("relax") to be oriented in the original direction of Bo.

The signal detected by the instrument is an alternating voltage. This voltage appears in a receiver coil surrounding the sample. The voltage (V) arises from Faraday’s law V = dΦ/dt and thus the coil axis is oriented perpendicular to Bo to maximize the change in the magnetic flux, Φ, through the coil. Due to constrains in the equipment, the only signal detected is the one that is generated in the XY plane.

Free Induction Decay

The signal that the coil detects as Mo goes back to its original equilibrium state is called the Free Induction Decay (FID). Due to restrictions in the set-up of the electronics in the instrument, only the Mr component is measured. For example, the FID after a 90° pulse is a voltage signal that oscillates between positive and negative values at the Larmor frequency as seen in Fig. 2. The oscillations diminish over time, indicating that Mr is getting smaller. Usually, the FID is studied using the envelope that gets defined by the maximum of the oscillations (Fig. 2B).

Figure 2

“Free Induction Decay” (FID) is the name given to the time-domain signal obtained during the relaxation process. Some authors called FID the envelope of the FID. And to complicate matters, the relaxation process itself is sometimes referred as the free induction decay.

Equipment

Instrument Description
Our laboratory is equipped with a Bruker mq20 Series PC 120 NMR analyzer, Minispec (Bruker Optics, Milton, Ontario, Canada), shown in Fig. 3. The data acquisition is performed using the MiniSpec software V2.51 Rev 00/NT by Bruker Biospin Gmbh 2002 with Bo = 0.47 T. Using Eq. 1,  a value of 20 MHz  is obtained for the hydrogen protons Larmor frequency. This is the value used for the RF pulse. 

Calibration
Every 24 hours the routine ‘Daily Check’ is performed for the measurements of SFC. After a successful execution of this routine, the Minispec software will indicate “validated”, which indicates that the instrument is running within specifications and that the necessary parameters to perform a correct measurement were recorded. The Daily Check routine requires three standard calibration samples – polymers that will produce an FID corresponding to specific SFC values - supplied by Bruker. A problem that might arise is that the Daily Check routine does not ask for the three standard calibration samples. This can be solved by enabling the “SFC” option into the “Instrument Settings” in the Minispec menu. It is during the daily check that the correction factor (F) and digital offset factor (D) are calculated.

The calibration for relaxation experiments is performed by running the sample of interest, using “Update Settings” from the Instrument menu. This will allow the instrument to automatically set the values of the gain, the magnetic field and the length of the 90° and 180° pulses. Once the specific test-sample has been used to characterize all parameters in the instrument,  similar samples can be studied without any further adjustments.

Sample Preparation
The instrument uses NMR glass tubes that are inserted into the measuring cell (Fig. 3) for a predetermined time period (ranging from seconds to minutes) in order to perform the measurement. These tubes are 10 mm in diameter and 180 mm in height. Depending on the protocol followed, the sample is deposited into the NMR tube from the melt or from its original semisolid state.

Figure 3 

The amount of sample introduced in the NMR tube and the position of the tube in the measurement cell are very important, especially when working with relaxation measurements. A sample that is not completely located within the coil will give an erroneous result. In the Minispec instrument, the coil generates a RF pulse that extends 1.25 cm to each side of the coil’s center. The coil is 1.5 cm in height, which means that the signal extends beyond the coil. If the sample extends beyond these limits, part of it will not have interacted with a full 90° or 180° pulse, resulting in erroneous measurements. It is thus recommended (Minispec User’s Manual, 1989) to have less than 2.5 cm of sample inside the NMR tube. Care must be taken to center the sample properly in the coil, having in mind that the coil is 1.5 cm in height. The user should check with the manufacturer where the center of the coil is in relation to either the bottom or top of the measurement cell.

Depending on the scope of the experiment, an already crystallized fat or a melted one might need to be introduced into the NMR tube. Introducing a crystallized fat into the bottom of an NMR tube is not easy, if not impossible. Different strategies have been used, such as filling up another reservoir that gets dropped into the NMR tube. The back of a glass pipette, a clear glass shell vial, as well as a short Teflon tube have been successfully used for this purpose. Bruker now sells a tool that consists of two concentric cylinders of which the inner one can be lifted up and down to pick up the sample and introduce it into the glass NMR tube. They recommend the use of this tool for samples like margarine, mayonnaise or any others with similar properties. Bruker also sells small vials with plastic lids, 3 cm in height, that easily slide inside the glass NMR tubes.

Once the fat is inside the NMR tube and properly positioned in the Bruker measurement cell, specific protocols must be followed before a pNMR measurement is performed. The protocol depends on the type of fat under study and the kind of experiment to be performed. The measurement cell inside the NMR must be dry and clean before insertion of the NMR tube to prevent hardware damage. Care must be taken when inserting NMR tubes that have become wet from water baths. As well, rubber or plastic stoppers are recommended to prevent the entry of dust, solvent vapours, or moisture into the NMR tube.

Solid Fat Content

Nuclei in solids interact more strongly with other solid neighbouring nuclei than with liquid ones because of their slower nuclear dynamics. This means that solid nuclei will relax very quickly (<10 µsec) and can easily be distinguished from the slower-relaxing nuclei of more mobile atoms or molecules in the liquid state.

The solid fat content measurement looks for the number of “solid” nuclei versus the “liquid” ones. The application requires only one 90° RF pulse. Information is obtained from the NMR signal that the coil records at different times. The FID envelope shown in Fig. 4 is due to the relaxation of the system after the application pf only one RF pulse. The RF was applied for ~3 µs, followed by a dead time of the receiver of about 7 µs (Van Putte and van den Enden, 1974). Immediately after the receiver is operational, the signal collected is due to the spins in both solid and liquid state, SS-SL. The signal collected at 70 µs is due only to the spins in liquid state, as the ones in solid state had already relaxed.

Figure 4

The American Oil Chemists’ Society (AOCS) suggests two methods to calculate the solid fat content: the direct method and the indirect method.

Direct NMR method (AOCS Official Method Cd 16b-93)
This methodology separately measures the NMR signals from nuclei in the solid and liquid state and the liquid state alone from the same FID. The solid-liquid signal measurement is carried out at 10 µsec after the RF pulse is terminated, while the solid measurement is obtained 70 µsec after the RF pulse ceased (Fig. 4).

The solid fat content is calculated from the ratio of these two measurements. Most commercial instruments possess software that carries out this calculation after the data is collected. Eq. 2 is used to find the solid fat content as:

SFC = [(Ss-SL -SL)F]/[SL + (SS-SL -SL) F+D]
(Eq. 2)
 

 where SS_SL is the NMR signal due to both liquid and solid nuclei (recorded 10 µsec after the pulse), SL is the NMR signal due to liquid nuclei (recorded 70 µsec after the pulse), F is an empirical correction factor (established during calibration) to account for the detector dead time, and D is the digital offset factor (also established during calibration).

Indirect NMR Method (AOCS Official Method Cd 16-81)
Only the signal due to the liquid SL is measured (Fig. 4) when using this method. The SFC is calculated by comparing the signal of a completely melted sample with the signal of the same material after tempering. To account for the effect of temperature on instrument sensitivity, it is also necessary to measure a standard oil known to be completely liquid at both temperatures. Eq. 3 is used in this case:

%SFC=100- (Oil60 SampleT/Sample60 OilT) 100
(Eq. 3)
 

The subscripts indicate the temperature at which the FID is obtained (60 for 60°C and T for the temperature at which the measurement is performed). This calculation is based on the assumptions that both the standard oil and the sample are completely liquid at 60°C, and that the standard is completely liquid at the final measurement temperature. Although these assumptions are probably justified in many cases, they may not always be correct, particularly when making measurements at low temperatures. In the case of fats that melt above 60°C, the official method gives no provisions, but common sense indicates that the sample and oil temperature at which the reference measurement is performed (Oil60, Sample60) needs to be adjusted accordingly.

Sample Condition and Amount
Details about sample conditioning for the direct or indirect method can be found either in the AOCS or the International Union of Pure and Applied Chemistry (IUPAC) methods. Slight variations in the sample conditioning are necessary when one is dealing with fat materials that require tempering.

Depending on the scope of the experiment, an already crystallized fat or a melted one might need to be deposited inside the NMR tube. Introducing a crystallized fat into the bottom of an NMR tube is not easy, if not impossible. Different strategies have been used, such as filling up another reservoir that gets dropped into the NMR tube. The back of a glass pipette, a clear glass shell vial, as well as a short teflon tube have been successfully used for this purpose. Bruker commercializes small vials with plastic lids, 3 cm in height that easily slide inside the standard glass NMR tubes.

It is important to position the sample in the right place in the measuring cell.  Care must be taken to centre the sample properly within the coil, having in mind that the coil is 1.5 cm in height. The user should check with the manufacturer where the center of the coil is in relation to either the bottom or top of the measuring cell.

The measuring cell in the NMR must stay dry and clean while performing the measurement. Care must be taken to dry the NMR tubes if they were kept in a water-bath to prevent hardware damage. As well, rubber or plastic stoppers are recommended to prevent the entry of water, dust or any other liquid into the NMR tube.

Protocols for Sample Preparation for the Direct Method
The protocol starts by melting the fat using a temperature of 100 ± 2°C for less than 5 min. No suspended solids should be visible. If necessary, the fat can be passed through a paper filter and then melted again. After thorough mixing, the sample is transferred to the glass NMR tube, filling it to the correct height and keeping it capped. The fat is then tempered following the protocols given in Table 1. The tempering is different depending upon whether a stabilizing fat is being studied or not. Stabilizing fats are those for which the polymorphic form must be stable before reproducible SFC results can be obtained (i.e. cocoa butter) (Timms, 2001; AOCS Official Method Cd 16b-93).

After tempering is complete, the measurements are started. The selected temperatures depend on the needs and interests of the investigator. Temperatures of 10, 21.1, 26.7, 33.3, and 37.8°C are used in the AOCS Official Method, while the IUPAC Standard Method indicates measurements at 10, 20, 25, 30, 35, and 40°C. A systematic description of this methodology can be found in both the AOCS Official Method Cd 16b-93 and the IUPAC Standard Method 2.15.

Other temperatures could be sampled as well. We usually measure SFC between 10°C to 60°C in 5°C increments to obtain higher-resolution melting profiles, although the final temperature might be dictated by the fat and whether it has completely melted or not. To measure a full profile from a single tempering sequence, it is necessary to have a pre-equilibrated tempering block or a water bath for each temperature under investigation. If a dry tempering block is unavailable, then after removing the sample from the water bath, rapid and complete drying of the tube must be carried out before significant temperature drift has occurred. Tempering blocks can be easily made by drilling holes in a stainless steel block or other suitable conductive metal. If the blocks are to be used in a water bath, it is worthwhile to select a metal that is not prone to rust.

A parallel setup is generally recommended for the measurements, in which a different NMR tube is used for each temperature (Table 1) to be measured.

Table 1 

 

However, when the amount of sample, or water baths, is limited, it may be necessary to use a serial setup. In this kind of setup, after measuring SFC at the first lowest temperature, the temperature of the water bath or tempering block is increased to the next temperature of interest. After a 30 minute incubation at that temperature, the next SFC measurement is made, and so on, until the sample is melted. Note that the solid fat content of a given sample is a function of thermal history, so serial and parallel measurements may not give similar results.

Protocols for Sample Preparation for the Indirect Method
This technique is used to measure the protons in the liquid phase of the sample. The Indirect method is not as rapid as the direct method. Four measurements must be performed at two temperatures in order to calculate the percentage of solids. The Indirect method starts in the same fashion as with the direct method by melting both the standard oil and the fat at 100 ± 2°C for less than 5 min. After thoroughly mixing the sample, both sample and oil are poured into glass NMR tubes. They should be filled to the correct height and kept capped. The temperature of both tubes is brought to 60°C and after equilibration, the SFC is measured. This will give two of the values to be used in Eq. 3: Oil60 and Sample60. The next step is to temper both the standard and the fat, following the tempering steps in Table 1. After finishing the tempering, both tubes are brought to the desired measuring temperature. After 30 minutes of equilibration (60 minutes when working with stabilizing fats), the SFC is measured to give the values of OilT and SampleT to be used in Eq. 3. The final step is to use Eq. 3 with the measured values to obtain the % SFC.

Measuring the SFC to monitor Isothermal Crystallization
This section does not follow an official protocol, but it is one followed by many laboratories. During an isothermal crystallization, the sample is melted and then incubated at the desired crystallization temperature. Melting at 80°C for 15 minutes should be sufficient to melt the sample and erase all crystal memory. The SFC is then measured at particular intervals of time, while keeping the samples inside the water bath at the desired crystallization temperature. Care should be taken to wipe dry the NMR tubes before inserting them into the NMR cell. The time intervals chosen for the measurement and duration of the experiment depend on the fat and temperature of crystallization. One common protocol is to measure every 30 seconds for the first 15 minutes, every minute for the following 15 minutes and every 10 minutes for the remaining 60 minutes. After this, readings are made at intervals of 1 hour.

Case Study: Hydrogenated Palm Kernel Oil Stearin and Sorbitan Monostearate

SFC melting profile 
The direct parallel AOCS method (Cd 16b-93) was followed to temper samples made with hydrogenated palm kernel oil stearin and sorbitan monostearate (SMS) in different percentages (0, 25, 40, 50, 60, 80, 100% of SMS). After the tempering process the serial protocol for the measurement was followed. Measurements started at 5°C and finished at 70°C with 5°C intervals. The melting profile was constructed by plotting the SFC as a function of temperature (Fig. 5).

Figure 5

A sharp reduction in the SFC takes place between 25°C and 35°C for blends containing SMS. Pure SMS retains a high value of SFC until 45°C above which it decreases as the temperature increases until it falls to 0% at 60°C.

The Avrami Model
A kinetic theory of phase changes was developed by Avrami (1939, 1940, 1941) which describes changes in the volumes of crystals. This theory has been modified for fats and the volume converted to solid fat content. The Avrami equation is written as (Marangoni, 2013):

SFC (t)/SFCmax = 1 – e-ktn 

(Eq. 4)
 

where SFC(t) is the percentage of solid fat content (SFC/100) at time, t, SFCmax is the value of SFC/100 as time approaches infinity. k is the Avrami constant (units of t-1) and represents the crystallization rate constant, and n is the Avrami exponent (no units), which defines the crystal growth mechanism (Marangoni, 2005). Table 2 explains the possible values of n and their significance. Eq. 4 was used to fit data collected under the isothermal crystallization protocol. This protocol was followed for blends of palm kernel oil stearin with SMS at a crystallization temperature of 25°C. The data was then plotted as % of SFC versus time and a nonlinear regression algorithm was used. GraphPadTM was used for this purpose, but other software such as, SigmaPlotTM or OriginTM can be used. Fig. 6 displays the results for the first 133 minutes of crystallization for blends containing 0, 25, 40, 60, 100% of SMS.

Figure 6

Table 2

The Avrami model takes into account that crystallization occurs by both nucleation and crystal growth and is based on the assumptions of isothermal transformation conditions, spatially random nucleation and linear growth kinetics.

The Avrami parameters obtained for the data in Fig. 6 were: n = 1.1 ± 0.1 for the blends containing 0% to 60% SMS, and n = 3.8 ± 0.1 for 100% hydrogenated palm kernel oil. This indicates two different nucleation and growth mechanisms. The presence of SMS seems to change the mechanism of growth for the samples: the small, almost unitary value of n indicate a needle-like growth from instantaneous nuclei for samples with SMS, to a spherulitic growth from sporadic nuclei for palm kernel oil stearin with n ~ 4. The values obtained for the crystallization constant k were ~ 1.2 × 10-2 ± 0.005 min-1 for the samples from 0% to 60% mixes, but 3.3 x 10-2 min-1 for 100% palm oil. These results show that the crystallization rate for the mixtures containing SMS is faster than for pure palm kernel oil stearin, but no observable differences were detected among the different percentages of SMS.

Melting Profiles for Blends
The construction and analysis of an iso-solid phase diagram (temperature vs. composition) helps to elucidate whether the components of blends of two different fats, are soluble in each other or not. These diagrams are useful to observe any incompatibility between the two fats (eutectic or peritectic) or compatibility (monotectic). Monotectic systems are those in which the components have similar melting points, molecular volumes, and polymorphic forms.

The same experiment as the one presented in the SFC melting profile section was followed; in this case, fourteen mixes of hydrogenated palm kernel oil stearin and SMS were prepared containing 0, 5, 10, 15, 20, 25, 30, 40, 50, 60, 70, 80, 90, 100% SMS, and the melting profiles of SFC versus temperature were obtained. The points obtained were fitted to a cubic spline (which interpolates points between the data) curve with the assistance of the curve-fitting software GraphPadTM. From the interpolated points, a new graph was constructed for temperature versus SMS composition (Fig. 7).

Figure 7

The temperatures corresponding to SFC were extracted in increments of 5% for the SFC. This is a tedious work that needs to be done by hand. Notice that each line in Fig. 7 represents a particular SFC %. The original Figure would have displayed only scattered points, but Fig. 7shows the data already manipulated with another cubic spline curve. The results in Fig. 7 show a monotectic partial solid solution behaviour between palm kernel oil stearin and SMS.

Relaxation

Relaxation measurements carried out with the Minispec monitor the decay curve of a NMR signal over time after a sequence of pulses are applied. The relaxation experiment differs from the SFC in two aspects: the signal is measured continuously over a period of time, and more than one RF pulse are applied. The difference between a solid fat content measurement and a relaxation one is that the signal collected in the latest case needs to be processed. Bruker provides a software called CONTIN to extract the desire information.

Nuclear relaxation takes place via two processes which are characterized by two times, T1 and T2 (Deleanu and Pare, 1997). The T1 process is concerned with spin-lattice or longitudinal relaxation, which looks at the relaxation of the magnetic moment of a nucleus in relation to the magnetic field set up by the lattice of other nuclei around it. The T1 process can be viewed as the measurement of the signal in the Z direction only.

The Tprocess of relaxation is characterized by the decay as shown in Eq. 5, with T1 being the characteristic time of the process:

Mz = Mo (1 – exp (-t/T1))
(Eq. 5)
 

One of the oldest methods for measuring T1 is called the inversion recovery method. This method consists of the following events: 1- apply an RF pulse at 180°, 2-  wait for certain time τ , 4- apply a second RF pulse at 90°, 5- detect the FID. Which can be viewed as

RF 180°-τ- RF 90°-FID detection

The 180° pulse causes Mo to be inverted in such a way that Mz = - Mo. Under this circumstance, "spin down" states become more favourably occupied than the "spin up" states, and thus the Z-component of the magnetic moment is anti-parallel to the external field Bo. Upon removal of the RF pulse, the net magnetization begins to relax to its dynamic equilibrium position. An arbitrary time is allowed to pass (τ) before the next RF pulse (perpendicular to the direction of Z, hence 90°) is applied. This 90° pulse is necessary in order for the signal to be detected as it needs to be in the XY plane to be detected by the coil. Note that the experiment needs to be repeated a number of times with different values of τ, and that the time interval between repetitions should be several times the value of T1.

The second relaxation process, spin-spin or transverse relaxation, is due to de-phasing of the spins system as precession takes place.  The average spin-orientation density will spread further out in the (XY) plane thus losing coherence due to inhomgeneites in the applied magnetic field Bo. T2 is the characteristic time that governs the loss of coherence of the transverse magnetization, Mr (Forshult, 2001; Capozzi and Cremonini, 2009).

This is often modelled by an exponential

 

Mr(t)=Moe(-t⁄T2*)
(Eq. 6)
 

Where T2* is physical transverse relaxation time recorded by the instrument.

Typically, T2* is modelled as

1/(T2* )=1/T2 +1/TBo inhomogenieties
(Eq. 7)
 

Where T2 is the relaxation time constant of interest and TBo inhomogeneities = γ∆B0 is the spread in Larmor frequencies ∆ω0 which would cause spin-spin dephasing in a characteristic time of 1/Δω0. TBo inhomogeneities  is not desired. Two methods that try to eliminate this external factor are presented in what follows.

One method of measuring T2 is by following the Hahn spin-echo sequence (Hahn, 1950) that consists of the following events: 1- apply an RF pulse at 90°, 2- FID detection, 3- wait for certain time τ, 4- apply a second RF pulse at 180°, 5- wait for certain time τ 6- FID detection. It can viewed as

RF 90°- τ - RF 180° - τ - FID detection

After the 90° pulse is applied, the transverse magnetization Mr appears on the XY plane.  The protons start to precess and the de-phasing of the spins moment starts to take place. After the time = τ , which is in the order of ms, a 180° pulse is applied with the effect that the de-phase protons on the x-y planes are now moving to try to regenerate the lost coherence. Eventually, the magnetization Mr is regenerated, causing an ECHO. An spin-echo happens when the de-phased spins are brought back together using an RF pulse. The echo takes place and the NMR signal starts to increase until it reaches at maximum, at which moment in time is measured (FID  detection).

The Carr-Purcell-Meiboom-Gill (CPMG) sequence of events builds up on the Hahn spin echo. (Carr and Purcell, 1954). The spin-echo sequence of the CPMG method consists on a repeting many times the Hahn spin-echo sequence. The following succession of events takes place: 1- apply an RF pulse at 90°, 2- wait for certain time τ, 3- apply a second RF pulse at  180° 4- wait for the same amount of time τ as before 5- an Echo takes place, 6- detect the signal during another time τ 7- repeat the sequence from step 3 as many times as needed. This can be summarized as:

RF 90°- τ - [RF 180° - τ - FID detection]n

The sequence indicated with n is carried out for as many times as the user specifies. The idea is to construct a new curve by using only the strongest signal once the FID is detected and build up a new curve. This new curve resembles a decay and has a long and flat tail. Each data point on this new curve is the maximum signal detected after the echo took place. The constructed-curve, called by many FID, resembles a decay but it is not. This constructed-curve needs to be treated as the sum of decays that depends on the transverse relaxation of each of the constituents present in the material (Forshult, 2001). The T2 relaxation constant is the time that the spin coherent has been reduced to 37% (1/e) of its original value and it could be that this constructed curve contains more than one T2 relaxation constants.

Spin-spin relaxation measurements can be used to study the mobility of protons. Larger T2 values indicates that the protons are more mobile compare with smaller T2 values. This technique has been used to elucidate the degree of confinement of oils in organogels (Laredo et al., 2011; Rogers et al., 2008), as well as the water mobility in cookie dough (Assifau et al., 2006; Goldstein and Seetharaman, 2011).

Protocol for Sample Preparation for Relaxation Measurements
The preparation of the samples, amount and insertion into the measuring vessel to be used in relaxation measurements follows similar protocols to those used for measuring the SFC.   

Experimental Procedure
To perform the measurement, the glass NMR tube containing the material is placed inside the measuring cell in the instrument. The relaxation experiments require that the instrument is set for “relaxation” readings rather than SFC. This is done as soon as the connection with the instrument is established. The user also needs to load the desired relaxation application. Many applications are offered by Bruker. It is to note, that  the T1 and T2 processes require different applications.

Parameters such as recycle delay, gain, number of scan and time  need to be set. Some of them are set when a calibration sample is run using “Update Settings”, but they can also be changed manually by the user. As mentioned above, the calibration routine will tune the gain, the magnetic field, and the generation of the 90° and 180° pulses, and should be performed with the sample at room temperature and positioned properly. The recycle delay is the waiting time before a new scan is taken and needs to be 5 to 10 times longer than the anticipated longest T1. T1 is the characteristic time governing the return of the net magnetization vector Mz to the equilibrium value Mo. At 5 x T1, Mz has decayed to roughly 99% of Mo, which is good enough for most applications. The “Application Configuration Table” includes parameters that are sample dependent, like the recycle delay.

Depending on the kind of measurement to be performed, it might be necessary to refrigerate the measuring cell of the NMR so the sample doesn’t change condition while it is being measured. This is achieved by connecting a water bath to the measurement cell.

An FID curve can be seen as composed by two components (Deleanu and Pare, 1997; Minispec User’s Manual): an information-containing signal components and the noise. Enough repetitions are needed in order to reduce the noise. The amount of repetitions, for example in the cpmg sequence, can be viewed by the number of echos desired. τ is then an important parameter because the pulse must be applied at the right time. The number of echoes can be changed in the “Configuration Table”, under the entry “Number of echo points for fitting”. It is common practice to average several FIDs (done by the software) to reduce the contribution of the noise component. As the number of scans increases, the signal component increases relative to the noise component.

An inverse Laplace transform is typically used to analyse the data and find the time constants. For example, the CONTIN (Provencher, 1982) software application along with Minispec software version 2.3 (Bruker, Milton, Ontario, Canada) was designed to carry out this kind of analysis. But other programs can be used also, such as Igor (WaveMetrics, Portland, Oregon, USA).

Remarks

Developing faster and more reliable equipment is the ultimate goal of many analytical instrumentation companies. But, if the operator neglects to understand the basic theory behind the instrument’s capabilities, all the manufacturer’s efforts will be lost. It is imperative that every operator understands not only how to run a sample but also why the equipment was designed the way it was. This understanding will help the operator make educated estimates regarding the variables that need to be kept fixed and the ones that can be changed.

Every operator is then encouraged to spend some time familiarizing themselves with the equipment by thoroughly reading the manuals before performing any experiments. Investing time to understand the basic operation of the equipment, as well as the theory behind the technique, will guarantee the success of the measurements. Avoiding this step may lead to erroneous measurements that might put the validity of the results in jeopardy. Training sessions with experts in the area, specifically with the ones that built the equipment, might be a reasonable way to answer some of the inevitable questions. A good result is not equipment-dependent and its reproducibility should be universal, assuming that the correct technique has been used.

The use of pNMR to measure SFC in the fats and oils is widely used in the fat industry. This technique is non-destructive, easy to use and with excellent repeatability. Iso-solid diagrams can clarify the compatibility of fats when they are mixed.

Even though the relaxation technique is known and used in many areas, it has only recently been shown to be a useful tool to investigate the phase composition of lipids (Trezza et al., 2006). Those authors measured the T2 values for four different polymorphic forms in eleven lipid systems. They found a characteristic value of 12.1 ± 0.8 µs for the α form, a value of 17 ± 8 µs for the β form, and a value of 18 ± 3 for the β’ form. 

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