Conceptually, the nucleus of an atom can be described as a spherical particle that is spinning. This infers a kinetic moment of rotation called nuclear spin ( I ), which is associated with this movement. The nucleus of an atom is constituted by protons and neutrons, and has a net charge that is normally compensated by the extra-nuclear electrons. The number of all nucleons ( A ) is the sum of the number of protons ( Z ) and the number of neutrons ( N ). Depending on the number of nucleons and protons, the nucleus may possess a half-integer spin (for example I = ½ for hydrogen), an integer spin (for example I = 1 for deuterium) or zero (for example I = 0 for carbon).
The nuclear charge is due to its protons, and since magnetism arises from the motion of charged particles, a nuclear magnetic moment arises from the nuclear spin. The number of protons (Z) and the number of nucleons (A) determine whether a nucleus will exhibit magnetism. Carbon-12 (12C), for example, consists of six protons (Z = 6) and six neutrons (N = 6) and thus has A = 12. Z and A are even, and therefore the 12C nucleus possesses no nuclear magnetism. Another example of a nucleus with no residual magnetism is oxygen-16 (16O). All other nuclei with Z and A being uneven possess residual nuclear magnetism.
In chemical bonds of a molecule, the negatively charged electrons also possess spins controlled by strict quantum rules. A bond is constituted by two electrons occupying the appropriate molecular orbital. According to the Pauli principle, the two electrons must have opposite spins, leading to the term paired electrons . Each of the spinning electronic charges generates a magnetic effect, but in electron pairs the effect is almost self-cancel ling and results in a very small value of the magnetic susceptibility, which is of the order of −10−6 g−1 . This diamagnetism is a property of all substances, because they all contain the minuscule magnets, i.e. electrons. Diamagnetism is temperature independent.
If an electron is unpaired, there is no counterbalancing opposing spin and the observed magnetic susceptibility is much higher and of the order of +10 −3 to +10−4 g−1 . This effect by unpaired electrons exceeds the ‘background’ diamagnetism, and gives rise to paramagnetism . Free electrons can arise in numerous cases. The most notable example is certainly the paramagnetism of metals such as iron, cobalt and nickel, which are the materials that permanent magnets are made of. The paramagnetism of these metals is called ferromagnetism. In biochemical investigations, systems with free electrons (radicals) are frequently used as probes.
The way in which a substance behaves in an externally applied magnetic fi eld allows us to distinguish between dia- and paramagnetism. A paramagnetic material is attracted by an external magnetic fi eld, while a diamagnetic substance is rejected. This principle is employed by the Guoy balance , which allows quantification of magnetic effects. A balance pan is suspended between the poles of a suitable electromagnet supplying the external fi eld. The substance under test is weighed in air with the current switched off. The same sample is then weighed again with the current (i.e. external magnetic fi eld) on. A paramagnetic substance appears to weigh more, and a diamagnetic substance appears to weigh less.
For either electronic or nuclear magnets, two possible energy states exist in the presence of an external magnetic fi eld (Figure 1). In the low-energy state, the fi eld generated by the spinning charged particle is parallel to the external fi eld. Conversely, in the high-energy state, the fi eld generated by the spinning charged particle is anti-parallel to the external fi eld. When enough energy is input into the system to cause a transition from the low- to the high-energy state, the condition of resonance is satisfied. Energy must be absorbed as a discrete dose (quantum) h ν, where h is the Planck constant and ν is the frequency (see Equation 14.1). The quantum energy required to fulfil the resonance condition and thus enable transition between the low- and high-energy states may be quantified as:
where g is a constant called the spectroscopic splitting factor, β is the magnetic moment of the electron (termed the Bohr magneton) and B is the strength of the applied external magnetic fi eld. The frequency ν of the absorbed radiation is a function of the paramagnetic species β and the applied magnetic field B . Thus, either ν or B may be varied with the same effect.
Fig1. Energy levels of a proton in the magnetic fi eld B – 0 . The nuclear spin of a nucleus is characterised by its magnetic quantum number m (which can take the values - I , - I ±1, …, I -1, I ). For protons ( I = 1 / 2 ), m can only adopt +½ and −½. The corresponding energies are calculated by − m γh/(2π) B 0 , where γ is a constant characteristic for a particular nucleus, h is the Planck constant, and B 0 is the strength of the magnetic fi eld – B0 .
With appropriate external magnetic fi elds, the frequency of applied radiation for electron paramagnetic resonance ( EPR) is in the microwave region, and for nuclear magnetic resonance (NMR) in the region of radio frequencies. In both techniques, two possibilities exist for determining the absorption of electromagnetic energy (i.e. enabling the resonance phenomenon):
• constant frequency ν is applied and the external magnetic fi eld B is swept
• constant external magnetic field B is applied and the appropriate frequency ν is selected by sweeping through the spectrum.
For technical reasons, the more commonly used option is a sweep of the external magnetic fi eld. After the absorption of energy by the nucleus in the range of the radio frequencies, the system returns the initial equilibrium by the process of relaxation . This includes firstly the return of the nuclear spins to their low-energy levels and secondly the loss of magnetisation. The process is characterised by two time constants called spin–spin relaxation and spin–lattice relaxation. Spin–spin relaxation is attributed to a spin exchange between two nuclei in proximity, whereas spin–lattice relaxation is due to magnetic interactions between the nuclear spin and ions around atoms.
