Ecole Polytechnique Fédérale de Lausanne Section de Physique Travaux Pratiques III Electron Paramagnetic Resonance Responsable : Dr. Arnaud Magrez Superviseur : Felix Blumenschein Lausanne, 6 juin 2017 TP III Electron Paramagnetic Resonance 1 Introduction This TP III experiment is about electron spin resonance (ESR) spectroscopy, in english more often called electron paramagnetic resonance (EPR) and in french résonance param- agnétique électronique (RPE). In EPR spectroscopy we measure the energy differences between the discrete energy states of quasi-free electrons in form of free radicals and paramagnetic centres by measuring their absorption of electro-magnetic radiation. In our present set-up a continuous wave EPR set- up is used. By modulating the magnetic field in combination with the continuous electro- magnetic (EM) microwave (MW) field one can gain insight into the molecular structure, chemical configuration and dynamics of the studied substrate. EPR spectroscopy is used for the detection of free radicals and paramagnetic centres in biology, chemistry and physics. In medicine the application of ESR is rather difficult, as radicals are reactive. 2 Basic ESR theory 1 Electrons have a spin quantum number of s = 2 and corresponding magnetic moment 1 of ms = ± 2 . Without an external field, the spin-orientation is randomly distributed. However, in the presence of an external magnetic field of strength B0, the spin orientates 1 1 itself parallel (− 2 ) or antiparallel ( 2 ) to B0 with corresponding energy E = msgeµBB0, with the Landé g-factor (ge = 2.0023 for free electrons) and the Bohr magneton µB = e¯h = 9.2740 × 10−24 J=T 2me . This splitting of the Energy within an external magnetic field is called Zeeman-Effect and leads to a separation of ∆E = geµBB0 (1) between the lower and upper energy state for free electrons, which is directly linear pro- portional to B0, as depicted in figure 1. According to Planck’s law, a free electron can be transferred between the two levels by emission or absorption of an photon of frequency v and energy ∆E = hv. This leads to the fundamental equation of EPR spectroscopy, the resonance condition hv = geµBB0. (2) ms = +1=2 j"i ∆E = E+1=2 − E−1=2 Energy ms = −1=2 j#i B0 = 0 B0 6= 0 Figure 1: Splitting of the electron spin state in an external magnetic field, Zeeman effect. 1 TP III Electron Paramagnetic Resonance Most of the standard EPR experiments happen in the MW range of 9 GHz to 10 GHz (≈ 33 mm to 30 mm). Regarding the resonance condition, this corresponds to fields of around 0.35 T. In most EPR experiments, the MW frequency is kept constant and the magnetic field is increased between an interval (sweeping) around the expected signal (continuous wave, "CW" EPR). Reaching the resonance condition, the gap-energy ∆E(B0) matches the MW energy hv and the electrons can transit between the two spin states. The Maxwell- Boltzmann distribution predicts a higher population of the lower energy state nlower than the upper energy state nupper, which leads to more absorption than emission: nupper Eupper − Elower ∆E hv = exp − = exp − = exp − , (3) nlower kBT kBT kBT −23 with the Boltzmann constant kB = 1.3806 × 10 J=T. This net resonant absorption due to spin-flip is what we observe in EPR-spectroscopy. An example EPR scan for DPPH is shown in figure 2 on the right in blue, as absorption signal over the swept external magnetic field B0. The basic set-up consists of an electro-magnet for B0 and a MW generator. The MW are guided through wave-guides (metallic, hollow tubes), which allow only single modes. To optimise the EPR absorption, a resonator (cavity) is used. The MW are guided into the resonator where they are reflected from the walls, forming a standing wave. The MW reflected out of the cavity is detected with e.g. a shottky-diode. The dimensions of the cavity therefore have to be adjusted, such that at a certain MW frequency no signal is reflected out of the chamber anymore. Figure 3 shows the reflected signal of the cavity for a frequency sweep. The resonance frequency, where no MW is reflected out of the chamber anymore is visible as the dip in that scan. The adjustment process to find this resonance frequency of the cavity is called matching and tuning. For the EPR spectrum of a sample in the matched and tuned cavity, the MW frequency is kept constant, while B0 is swept. The sample absorbs MW energy at the field corresponding to the resonance condition (eq. 2), B0,res.(hv). The absorption changes the cavity impedance and therefore the coupling condition of the cavity. As the cavity at B0,res.(hv) is now no longer critically coupled, MW is reflected out of the cavity. However, this absorption induced reflection-signal is very small. Therefore, we measure the derivative signal with a Lock-In detector by additional B-field variation coils which induce a sinusoidal field parallel to B0. This corresponds to the red signal on the left in figure 2. Figure 2: EPR spectroscopy signal of DPPH, taken with the MS400. Shown is the absorption signal over the swept external magnetic field B0, on the left as direct Lock-In derivative absorption signal in red and on the right the integrated absorption signal in blue. 2 TP III Electron Paramagnetic Resonance The set-up sensitivity depends strongly on cavity, MW frequency v, MW power P and sample volume V . The quality of the cavity system is defined through the unloaded quality factor Q0 of the microwave cavity and the filling coefficient kf . Q0 indicates how efficiently the microwave energy is stored (reflected) by the cavity and is defined as 2πEstored Q0 = . (4) Edissipated Estored and Edissipated correspond to the energy stored and lost while sweeping once over the resonance frequency. The loss for a perfectly matched and tuned cavity is due to the electrical currents generated in the cavity walls by the MW, which again produce heat. Effectively Q0 is found by measuring the position of the resonance frequency vres. and the width ∆v of the absorption signal at half it’s height in fig. 3, together with formula 4 rewritten as vres. Q0 = . (5) ∆v A high Q0 value is important for a good spin sensitivity. The lowest number of detectable spins Nmin is calculated as k1V Nmin = , (6) 2 1 Q0kf v P 2 with constant k1. A good set-up sensitivity is achieved with a large number of spins and small Nmin. Obviously in equation 6, also higher MW power and lfrequency is of advantage for a good Nmin value. The signal’s size, i.e. the integrated signal intensity, is proportional to the concentration of unpaired electrons. The MW intensity in combination with the electron relaxation time τ has another influence on the signal. The absorbed energy is mostly emitted again in form of phonons, which happens with the rate 1/τ. Too large an MW intensity can lead to an slower relaxation rate compared to the MW excitation rate, i.e. a [ saturation] of the upper level, which -0.5 0.0 Amplitude of the reflected signal [V] 9.30 9.35 9.40 9.45 9.50 Frequency [GHz] Figure 3: Reflected signal for a MW frequency scan to find the resonance position of the cavity. 3 TP III Electron Paramagnetic Resonance again leads to a decrease of the MW absorption. Increasing saturation appears in the EPR spectra as decreasing absorption lines. The theory above is explained for the case of free electrons. In reality however, we look at radicals or paramagnetic centers, the electrons are under the influence of one or more atoms. The influence of the molecule on the electron is visible in the EPR signal, as a change of the g-value, the line-shape, and hyper-fine coupling: g-factor and line shape In the presence of an atom or molecule, the electron possesses, besides its spin s, some orbital momentum L, changing its total angular momentum. This spin-orbit coupling leads to a change of the g-factor away from ge of an unpaired electron. Effectively, the local magnetic field is changed from B0 to Beff = B0(1 − σ). σ is hereby the influence of the magnetic fields from atoms and molecules. By applying this on equation 2, we get hv = geµBB0(1 − σ) ) hv = g · µBB0. (7) σ is the difference of g from the free electrons value ge and is easily determined from the EPR spectrum. Moreover, σ contains information about the substrates’ orbital-structure, as the coupling magnitude depends on the masses. Organic free radicals, with only hydrogen, oxygen, carbon and nitrogen, only have small deviations from ge, while e.g. metals having a more significant influence. For e.g. DPPH, the influence of the molecule is on average zero, leading to an EPR signal for DPPH corresponding to g = 2.0036, which is quasi-free. In general g is a 2nd order tensor with three main or principal components (of the diag- onalised tensor) gx, gy and gz. In the case of an anisotropic electronic structure of the molecule or atomic structure, g is such a tensor. This leads to a signal structure for such anisotropic orbital molecules, which is dependent on their orientation to the direction of B0. By measuring different orientation of the substrate in the external field, additional informations about the substrates structure can be collected. For single crystals, all the molecules are in the same orientation. A molecule with e.g. two different principal compo- nents (e.g. an axial-symmetric crystal with the main-axis gx = gk and gy = gz = g?) will have different signals, depending on the crystals orientation to B0 at Bx or By,z.