1. Introduction 64-311 Laboratory Experiment 11 NMR Spectroscopy Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful and theoretically complex analytical tool. This experiment will introduce to the basic theory behind the technique and determine nuclear gyromagnetic ratios for 1 H and 19 F. Note that NMR unlike Electron Spin Resonance (ESR) probes the nuclei of atoms and molecules, not their electrons. However, the chemical environment of specific nuclei is deduced from information obtained about the nuclei. This technique is now, amongst its many applications, a powerful medical imaging tool and generally referred to by the less scary name (as far as the general public is concerned) of Magnetic Resonance Imaging (MRI). 2. Theory You are already familiar with the notion of electron spin, which is one way of articulating that an intrinsic property of an electron is that it has a magnetic dipole moment (μ). Other particles - including protons and neutrons - also have magnetic dipole moments which are similarly characterized by intrinsic spin quantum numbers. In many nuclei (such as 12 C, which has 6 protons and 6 neutrons) these spins are (respectively) paired against each other, such that the nucleus of the atom has zero overall spin. However, in other nuclei (such as 1 H and 13 C) the nucleus does possess a net spin or a finite magnetic dipole moment. The rules for determining the overall spin, I, of a nucleus are: 1. If the number of neutrons and protons are both even, then the nucleus has no spin. 2. If the number of nucleons is odd, then the nucleus has half-integer spin (i.e. 1/2, 3/2, 5/2) 3. If the number of neutrons and protons are both odd, then the nucleus has integer spin (i.e. 1, 2). From quantum mechanics we know that angular momentum quantum numbers (in this case, I ) will have (2I + 1) possible I z components (or orientations) designated by a m I magnetic quantum number. Consequently, a nucleus with spin 1/2 will have 2 possible orientations and in the absence of an external magnetic field, these orientations are of equal energy (i.e. degenerate). If a magnetic field is applied, then the energy levels split and their energies depend on m I. Moreover, when the nucleus is in a magnetic field, the initial populations of the energy levels are determined by thermodynamics, as described by the Boltzmann distribution. Initially the lower energy level will contain slightly more nuclei than the higher level, but it is possible to excite these nuclei into the higher level with electromagnetic radiation. The frequency of radiation needed is determined by the difference in energy between the energy levels. 1
The nuclear magnetic moment, μ, which is proportional to its spin, I, is given by: μ = γih (1) The constant, γ, is called the gyromagnetic ratio (or magnetogyric ratio) and is a fundamental nuclear e constant which has a different value for every nucleus. Note that γ = g, where M is the mass of 2 M the extra nucleon and g the appropriate Landé g-factor. The energy perturbation (δe) of a particular energy level is given by: eh δ E = μ. B = μ B = m B = z γ I h g m I B 2M (2) where B is the strength of the magnetic field at the nucleus. The difference in energy (ΔE) between levels (the m I = +1/2 m I = -1/2 transition energy) is simply: Δ E = γhb (3) This means that if the magnetic field, B, is increased, so is ΔE. It also means that if a nucleus has a relatively large gyromagnetic ratio, then ΔE is correspondingly large. 2.1 The absorption of radiation by a nucleus in a magnetic field Taking a semi-classical view of the behaviour of a charged particle in a magnetic field, consider a nucleus (of spin 1/2) in a magnetic field. This nucleus is in the lower energy level (i.e. its magnetic moment does not oppose the applied field) and in the presence of a magnetic field, the magnetic dipole moment will precess around the magnetic field direction. The frequency of precession is termed the Larmor frequency, which is identical to the transition frequency. The potential energy of the precessing nucleus is given by Equation 2, i.e: E = - μ B cosθ Applied magnetic field direction where θ is the angle between the direction of the applied field and the magnetic dipole moment vector. If energy is absorbed by the nucleus, then the angle of precession, θ, will change. For a nucleus of spin 1/2, absorption of radiation "flips" the magnetic moment so that it opposes the applied field (the higher energy state). As absorption only occurs when the photon energy equals that of the energy difference between the spin states, the process is described as a resonance in an analogous way to classical driven oscillators. An NMR spectrometer, then, measures the exact radio wave frequency that is absorbed by the sample nuclei. It is important to realise that only a small proportion of target nuclei are in the lower energy state (and can absorb radiation). There is the possibility that by exciting these nuclei, the populations of the higher and lower energy levels will become equal. If this occurs, then there will be no further absorption of radiation as the spin system is saturated. The possibility of saturation means that we must be aware of the relaxation processes which return nuclei to the lower energy state. How then do nuclei in the higher energy state return to the lower state? Emission of radiation is insignificant because the lifetime (which is related to the classical rate of radiation emission) is 2
proportional to ν -3, where ν is the frequency. At radio frequencies, re-emission is negligible; therefore we must focus on non-radiative relaxation processes. There are two major relaxation processes, namely: (a) Spin-lattice relaxation: Nuclei in the sample lattice are in vibrational and rotational motion, which creates a complex magnetic field - called the lattice field - with many components. Some of these components will be equal in frequency and phase to the Larmor frequency of the nuclei of interest. These components of the lattice field can interact with nuclei in the higher energy state, and cause them to lose energy (returning to the lower state) in a characteristic time scale. (b) Spin-spin relaxation. This is due to the interaction between neighbouring nuclei with identical precessional frequencies but differing magnetic quantum states. In this situation, the nuclei can exchange quantum states; a nucleus in the lower energy level will be excited, while the excited nucleus relaxes to the lower energy state. There is no net change in the populations of the energy states, but the average lifetime of a nucleus in the excited state will decrease. One further point of interest (and immense practical application) is that the magnetic field at the nucleus is not equal to the applied magnetic field; electrons in their various orbitals around the nucleus shield it from the applied field. The difference between the applied magnetic field and the field at the nucleus is termed the nuclear shielding. The electron configuration can either oppose or support the applied field, resulting in so-called diamagnetic and paramagnetic shifts, respectively. [Classically the electron motion creates a current loop which produces a magnetic field.] This quantified by a Chemical shift, which is defined as nuclear shielding / applied magnetic field. The chemical shift is a function of the nucleus and its environment (neighbouring atoms); such shifts are calibrated relative to a reference compound. 3. Experiment Carefully set up the apparatus as indicated in the CWS 12-50 Operating Manual. Familiarise yourself with the software and hardware operation. (A) Continuous Wave NMR Experiment in Rubber Objective: Preparation and execution of a field sweep and a frequency sweep NMR continuous wave experiment. This will serve as a template for other NMR experiments and will produce the 1 st derivative of an NMR absorption signal. Experimental setup Check if electromagnet is connected to console. Slide the probehead into electromagnet and then insert a rubber sample in the probehead. Start control program. Activate console connection to the computer by Spectrometer/Connect Select Mode/NMR 1H. Program automatically activates connections with an electromagnet. In this introductory NMR experiment, continuous wave (CW) is used; most sophisticated NMR systems used pulsed sources and have more complex (Fourier Transforms) data analysis. 3
Figure 1. Experimental setup for acquiring NMR signal in rubber by magnetic field sweep. Procedures: (i) Field Sweep Fill parameter boxes with values shown in Figure 1. 1. To find NMR signal quickly in Modulation change: Field Sweep = 300 Gs; to cover widest sweep range, 2 nd Mod Amplit = 1 Gs; to obtain strong signal, Sweep Time select = 0.5 min; to acquire preliminary result fast. 2. Begin an experiment by clicking on Start. Look at the acquired signal and adjust the following: Magnetic field BB0 to position signal on the display window center, Receiver Gain to fill at least half of the display window vertical scale, Reduce Field Sweep to cover about ¼ of horizontal scale by resonance signal, Detector Phase to get maximum signal or to chose between +/- or -/+ pass, Measure line width by DB function available on auxiliary tool bar and lower 2 nd Mod Amplit to reduce line broadening. Higher value of 2 nd modulation increases signal-to-noise, but broadens the line. Find compromise between low line broadening and low noise amplitude, Increase Sweep Time to find if signal increases. Samples with long relaxation times may require longer sweep time. 4
3. If signal is still weak, select number of accumulation Acc higher than 1. Note that signal-tonoise ratio increases as square root of number of accumulations. 4. Repeat adjustments to obtain satisfying results. 5. Store experiment in the file by File/Save Data As, or fill Acquisition/Store in file with file name and repeat experiment to store data automatically (ii) Frequency Sweep For frequency sweep experiment in Modulation, select Frequency Sweep with widest Frequency Sweep available 1,000 khz and repeat whole procedure described above. Remember to reduce Frequency Sweep to conduct final experiment. Usually 50-100kHz sweep is enough. Follow parameters setting from Figure 2. Note that the signal acquired with frequency sweep is affected by limited frequency sweep resolution (frequency synthesizer limit) and therefore is less smooth than the signal acquired with field sweep. Figure 2. Experimental setup for acquiring NMR signal in rubber by frequency sweep. 5
Using the samples available find the NMR resonance profiles for 1 H in (a) acrylic (which has a wide line width), (b) Delrin (which has wide and narrow components to its linewidth), (c) Glycerin (a liquid-like sample). Now observe the NMR resonance profiles for 19 F in Fluoroboric acid (HBF 4 ) and Teflon. Use whatever analysis tools are available and comment on your observations. (B) Nuclear Gyromagnetic Ratio Measurements with CW NMR Objective Experiment To determine nuclear gyromagnetic ratio of protons ( 1 H) and 19 F nuclei (recall equation 1). The gyromagnetic ratio (γ) can easily be determined by measurement of the resonant frequency for different magnetic field magnitudes and performing a linear regression analysis. Recall equation (3): Δ E = γ hb ΔE = hω = γhb ; hence: ω = γb. Therefore measurements of f (or ν = ω/2π) as a function of B will result in a slope of γ. Obtain 10-20 data points of NMR resonances at different magnetic fields with corresponding frequencies. Operate in a narrow frequency and field range to see changes of resonances on the same screen (see Figure 3). First determine γ for 1 H. Figure 3. Experimental setup for determination of 1 H NMR resonance frequencies for different magnitudes of magnetic field in glycerin sample. 6
Keep the Field Sweep of 50 Gs and set BB0 field to see resonance signal on the right margin of the screen. Decrease Frequency by 10.0 khz and perform field sweep. With Pass Display set for 5 observe how resonance moves towards lower magnetic filled (left side of the screen). Record f 0 and corresponding BB0 at which resonance occur. Operate in wider frequency and field range to determine the gyromagnetic ratio of 19 F in HBF 4. With Sweep of only 10 Gs (helps to measure magnetic field very accurately) change field by about 25 Gs Adjust frequency to see signal visible on the screen. If necessary, temporarily expand Sweep Width to localize the line. Change frequency to shift the line to the center of the screen and reduce Sweep Width. Record f 0 and corresponding BB0 at which resonance occurs. How do your values compare with the accepted values? [ 1 H: γ = 2.675 s -1 T -1 ; 19 F : γ = 2.518 s -1 T -1 ] Comment on any discrepancies. (C) Electron Spin Resonance in DPPH. Figure 4. Setup parameters for an ESR experiment in DPPH 7
The principles behind ESR are analogous to NMR although pertaining to unpaired atomic electrons rather than nucleons. Most ERS spectroscopy takes place at microwave frequencies; however ESR in DPPH does give a radiofrequency signal which this equipment can observe. DPPH is diphenyl picrohydrazyl and contains a nearly free unpaired electron on one it s the nitrogen atoms. You will first need to prepare the hardware and software for this CW ESR experiment and data acquisition. Experimental Setup and Procedure Check if Helmholtz coil is connected to console s Coils output. Slide probehead into coils (horizontal slot from the side opposite the cable) and then insert a sample in the probehead from the opposite side. Start control program. Activate console link to the computer by Spectrometer/Connect. Select Mode/ESR. Program automatically redirects current to Helmholtz coils. Obtain DPPH s ESR resonance profile and (again) use whatever analysis tools are available to quantify your results. What is the g factor for DPPH? Questions: What is the hyper-fine interaction? How do you relate the Landé g-factor for a whole atom with total electronic angular momentum (J = L+ S) and the nuclear spin I? [Hint: consider F = I + J.] For information, note the following g-factors: Elementary Particle g-factor Uncertainty Electron g e -2.002 319 304 3718 0.000 000 000 0075 Neutron g n -3.826 085 46 0.000 000 90 Proton g p 5.585 694 701 0.000 000 056 References: Theory section was based on lecture notes from Sheffield University (UK). Experimental Section was based on the CWS 12-50 Operating and Experimental Manual. 8