24 OBTAINING AN NMR SPECTRUM Bo rf oscillator Figure 3.3. Orientation of (a)the receiver coil (attached to ammeter A)around the y axis and (b) the transmitter coil (attached to rf oscillator )around the x axis. 3. 1.2 Generation of B, in the Transmitter Coil spectrum, and, of course, a sample to be analyzed. In this chapter we will refine our spectrometer design as we consider Remember from Section 2.3 that to tip M off the z axis, so it its performance and limitations has a component in the x,y plane, we need an"irradiating magnetic field (B,) that oscillates at exactly the precessional 3.2.1 The Magnet frequency of the nuclei of interest and is oriented perpendicu lar to Bo. How are we going to generate such a precessing The three most important characteristics of the magnet in any magnetic field? NMR spectrometer are the strength, stability, and homogene Suppose we orient a second loop of wire, henceforth called ity of its magnetic field Bo. Not only is the precessional the transmitter coil, so that its axis is aligned with the x axis. (resonance) frequency of identical nuclei directly propor perpendicular to both Bo and the axis of the receiver coil; see tional to the strength of Bo(Section 2.2), but so is the differ Figure 3.3b. As we saw in Figure 3. 2. passage of an rf ence in precessional frequencies(Av)of nonidentical nuclei alternating current through the transmitter coil will generate a magnetic field B) that is linearly polarized(oscillates back Av=v-v,=I Bo Y2 Bo_(Y1-Y2)Bo (3.1) and forth) along the x axis, as in Figure 3. 4a. Now here is the important part. This linearly polarized field can be viewed as if it were the vector sum of two oppositely phased, circularly Therefore, it is advantageous to use the strongest available polarized rotating magnetic fields( B, and B1), as shown in magnet to obtain the greatest separation (i. e, resolution Figure 3. 4b. Note how the two circularly polarized vectors in between NMR signals. Remember also that the stronger field Figure 3. 4b add together to generate the linearly polarized results in larger energy gaps between spin states [Eq(2. 4) vector in Figure 3. 4a. One of these, B,, is rotating clockwise, and hence greater populations in the lower energy states (Eq in the same direction as the nuclear moments precess around (2.8)]. This serves to enhance the intensity of the NMR signal, Bo(Section 2.2.2). Therefore, when viewed in the rotating which turns out to be approximately proportional to the square frame(Figure 3. 4c). B, will always be aligned with the x axis, of Bo exactly where it is needed to bring about the precession of M Magnets are of three general types: permanent magnets, compare Figures 3. 4c with 2.10 electromagnets, and superconducting magnets. There are ad vantages and disadvantages with each type. Permanent mag 3.2 THE NMR MAGNET nets are less costly, they have relatively stable fixed magnetic fields, and they require noelectric current to generate the field From the foregoing discussion we can list the basic compo- Unfortunately the strength of their fields is so limited(ca. 1.4 nents of an NMR spectrometer. There will be a magnet to T)that they were used only in the first generation of commer- generate Bo, an rf oscillator to generate B, in the transmitter cial NMR spectrometers. Electromagnets used for NMR ap coil, a receiver coil to pick up the signal, the electronics plications, on the other hand, are huge and more costly to build (including a computer and plotter) to turn the signal into a and operate, but their field strengths range up to the strongest
3.2 THE NMR MAGNET 25 B,( inear) Figure 3. 4.(a) Linearly polarized magnetic field BI(linear)oscillating along the x axis of the laboratory frame: compare with Figure 3. 2.(b)Resolution of B,(linear)into oppositely rotating circularly polarized magnetic fields, B, and B,' both oscillating at vo.(c) Orientation of B, in the rotating fram ever achieved, in excess of 34 T(which corresponds to a 'H The appropriate current is initially established in the resonance frequency of 1.45 GHz, where 1 GHz= 10 Hz). cooled solenoid with the aid of a high-voltage dc source. Then However, electrical resistance to the high current necessary to the twoends of the solenoid loop are"short circuited, remov generate strong magnetic fields generates considerable heat ing the de source. However, because the solenoid circuit has that must be efficiently dissipated to assure a stable field zero resistance, the large direct current continues coursing The superconducting magnets used in NMR spectrometers through the solenoid indefinitely (as long as the helium holds constitute a out!), thereby generating a very strong and stable magnetic perconducting magnet is designed to provide a specific nomi. field nal field strength, currently in the range of ca. 6-18 T, As strong and stable as the magnetic field is, it is still corresponding to H operating frequencies in the range of necessary to provide some mechanism by which the stability 50-750 MHz. The cylindrical solenoid through which the of the field is monitored and controlled. This can be achieved through an electronic feedback technique known as locking alloy that becomes superconducting(that is, develops zero NMR signal (the lock signal)at a diera give rise toa strong large direct current flows is made of a unique niobium-tin electrical resistance)when cooled to 4 K(4 degrees above those of the nuclei of interest. If the lock substance is kept absolute zero)by immersion into liquid helium in a cryostat physically apart from(but close to! )the sample, it is referred that includes an outer jacket filled with liquid nitrogen. Figure to as an external lock. More commonly, the lock substance 35a shows a complete Bruker DMX-500NMR spectrometer. is used as the solvent for the sample and is termed an internal The internal configuration of the magnet and probe region is lock. In either case, the frequency of the lock signal is con- detailed in the cutaway diagram of Figure 3.5b. tinuously monitored and electronically compared to a fixed
26 OBTAINING AN NMR SPECTRUM reference frequency rf oscillator. Any difference between the EXAMPLE 3.2 Suppose the lock signal frequency is k and reference frequencies causes a direct microcurrent found to be slightly less than the constant reference free to pass through a secondary coil ( known as the Z gradient of the rf oscillator, Should the magnetic field be increased ol coil, aligned with and inside the solenoid). This results in a decreased to bring it back to the nominal value? small secondary magnetic field to be generated, aligned either with B, (increasing its magnitude slightly) or against Bo O Solution: Remember Eg. (3. 1)1 that the frequency ot (decreasing its magnitude slightly)until the lock frequency any signal increases in direct proportion to the field once again matches the reference frequency. At this point the strength. Thus to increase the lock signal frequency w magnet is said to be "locked. need to increase the field strength The most common lock systems monitor the signal from deuterium (H, I= I). so it is common in NMR to use deute- Once a stable field is established. the question remains as rated solvents such as D,O or CDCh,(deuteriated chloro- form). Many such deuteriated solvents are readily available. to whether that field is completely homogeneous(uniform) throughout the region of the sample. The level of homogene ity required for a given NMR experiment depends on the a EXAMPLE 3.1 If the spectrometer's magnetic field desired level of resolution, which in turn controls the pree varied by +0.0000)1 T(that is, about 2 ppm). what magnitude sion of the measurement. In the case of h nuclei at 5.87T of change would be inlroduced in the resonance frequency of for example, Example 3. I suggests that to achieve a precision I H nuclei at 5.87T? of =l Hz at a frequency of 250 MHz (four parts per billion the field must be homogeneous to the extent of 2.35 x 10-kT O Solution: We can use a simple proportion Such phenomenal uniformity can be achieved by means of two additional instrumental techniques. First, the sample 0.00001T vessel (normally a precisely constructed glass tube)is posi 5.87T250MHz tioned along the center (: axis) of the solenoid in a region called the probe(Figure 3.5) that is separated from the △v=0.000430MHz=430Hz region cooled by liquid helium and whose tempcrature can herefore be independently controlled. The tube is spun As we will see later, this -2 ppm shift would be a very around its axis at ca. 100 Hz by mcans of an air stream that large shift indeed C turns a small plastic turbine attached to the top of the tube Figure 3.5. (a) Bruker model DMX-500 NMR spectrometer. The magnet cryostat is located on the
3. 2 THE NMR MAGNET 27 liquid helium superconducting turbine transmitter receiver coil magnet shim coils probe shim coils probe head filter commutator receiver transmitter relay Figure 3. 5.(h)Cutaway diagram of the cryostat, showing the essential parts of the magnet and probe Courtesy of Bruker Instruments, Inc) This spinning helps to"average out"any slight inhomogenei the probe cavity. The resulting small fields in these coils can ties of the field in the sample region be adjusted to further improve the homogeneity of the field Second, the contour(shape )of the field itself can be varied This process, called shimming or tuning the magnet, is ac- ( within very narrow limits) by passing extremely small cur- complished by adjustment of a dizzying series of shim con- rents through a complex series of shim coils located around trols (labeled by the field axis most affected, e. g
8 OBTAINING AN NMR SPECTRUM z2,23.X, Y. XZ. YZ, XY, X2, -Y, etc. )before each spectrum diameter of the tube, 0.42 cm. The height of the sample is taken. With the advent of microprocessor-controlled spec- cavity is given by trometers, the bulk of these adjustments are now accom- plished automatically. 0.050 We are left with a paradox. To get an acceptable signal, we =0.255cm I ratal t(0.25 cm)2 need to have as many nuclei as possible in the sample region (remember the minute difference between spin state popula tions? ) But we must restrict our sample to the smallest 042cm/2=0.21cm, possible volume in the interest of precision and resolution The eventual compromise results in a sample cavity of -0.05 cm for instruments that accommodate narrow-bore(5-mm o.d. )tubes to.0 cm3 for instruments using wide-bore h=x(0.2lcm)2(0.25cm)=0035cm3=35比L (10-20-mm-o.d ) tubes. [However, for medical use, some low-resolution NMR instruments have been constructed that Thus, only 70% of the sample cavity is filled with sample accommodate entire human bodies! ( See Chapter 16)] Typi in this case. Clearly, the thinner the wall of the tube, the cally, ' H and C spectra require ca. 5 and 15 mg of sample. more sample actually gets into the sample cavity. Further more,for samples in very limited supply(<I mg), pre cisely machined Teflon inserts for the tubes are available EXAMPLE 3.3 A typical thin-wall narrow-bore NMR to both reduce the amount of dead volume in the tube tube has an outside diameter of 5.00 mm(0.500 cm)and an below the sample cavity and prevent formation of vortices inside diameter of 4.20 mm. It is usually filled to a height of (whirlpools) of the solution within the tube when it is I in. (2.5 cm).(a)What is the wall thickness of the glass spun ube? (b)If the total volume of the sample cavity(including the tube)is 0.050 cm what are the dimensions(radius r There is one more thing you should know about the pow height h, and volume)of the space that is actually occupied erful magnets used in today s NMR spectrometers. If you get by sample? [Hint: The volume of the cylinder is rh. I too close to the magnet itself, you run the risk of demagnet izing anything on your person, such as credit cards, magnetic tapes, and computer diskettes. (This fact was central to the D Solution: Refer to Figure 3.6 plot of a recent novel by Joseph Wambaugh. )But no need to worry: it will not affect your magnetic personality (a)Wall thickness =(5.00 mm-420 mm)2=0.40 mm (b)The diameter of the sample is the same as the inside 3.2.2 Assembling the pieces We are now ready. The magnetic field is locked at 5.87T and 5.00mm a sample containing a substance with H nuclei, dissolved in a deuterium-containing solvent, is spinning in the probe. We 4.20mm activate the rf oscillator in the transmitter coil, producing a B, field oscillating at 250 MHz radiation, and . yes! A weak signal is detected in the receiver circuit! But let us not cele brate yet. What has this told us, except that we have in the sample, precessing at 250 MHz? Certainly, we would like to sectIon nmr tube be able to adjust parameters to test for nuclei precessing at other frequencies as well. How can we accomplish that? 2.5cm 3.3 SIGNAL GENERATION THE OLD WAY: THE sample cavity CONTINUOUS-WAVE(CW) EXPERIMENT Recall from Chapter 2 that, at a given field strength, each magnetic isotope (I*0)precesses at a unique frequency governed by its magnetogyric ratio[Eq (2.6)]; see Figure 3.7. Thus, if we intend to use our spectrometer to observe nuclei Figure3.6. Bottom section of an NMR sample tube and the sample other than H, there must be a way to vary either the operating cavity where the NMR signal is generated (B1 frequency or the magnetic field strength