Electron spin resonance electron paramagnetic resonance

Electron spin resonance electron paramagnetic resonance

1. Electron Spin Resonance Electron Paramagnetic Resonance BY- KANHAYA LAL KUMAWAT INSTITUTE OF CHEMICAL TECHNOLOGY MUMBAI

2. 2 ESR Spectroscopy Electron Spin Resonance Spectroscopy Also called EPR Spectroscopy Electron Paramagnetic Resonance Spectroscopy Non-destructive technique

3. NMR and ESR/EPR EPR focuses on the interactions between an external magnetic field and the unpaired electrons of whatever system it is localized to, as opposed to the nuclei of individual atoms. The electromagnetic radiation used in NMR typically is confined to the radio frequency range between 300 and 1000 MHz, whereas EPR is typically performed using microwaves in the 3 - 400 GHz range.  In EPR, the frequency is typically held constant, while the magnetic field strength is varied. This is the reverse of how NMR experiments are typically performed, where the magnetic field is held constant while the radio frequency is varied. Due to the short relaxation times of electron spins in comparison to nuclei, EPR experiments must often be performed at very low temperatures, often below 10 K, and sometimes as low as 2 K. This typically requires the use of liquid helium as a coolant. EPR spectroscopy is inherently roughly 1,000 times more sensitive than NMR spectroscopy due to the higher frequency of electromagnetic radiation used in EPR in comparison to NMR.

4. Applications of ESR Electronic state of magnetic materials and semiconductors Electron state of semiconductor lattice defects and impurities (dopants) Structure of glass and amorphous materials Tracking of catalytic reactions, changes in charge state Photo-catalytic reactivity and photochemical reaction mechanisms Radicals of polymer polymerization processes (photo-polymerization, graft polymerization) Active oxygen radicals related to aging in disease in living organisms Oxidative degradation of lipids (food oils, petroleum, etc.) Detection of foodstuffs exposed to radiation Measurement of the age of fossils and geological features using lattice defects

5. 5 What compounds can you analyze? Applicable for species with one or more unpaired electrons Free radicals Transition metal compounds Useful for unstable paramagnetic compounds generated in situ Electrochemical oxidation or reduction

6. An electron is a negatively charged particle with certain mass, it mainly has two kinds of movements. Spinning around the nucleus, which brings orbital magnetic moment. "spinning" around its own axis, which brings spin magnetic moment. Magnetic moment of the molecule is primarily contributed by unpaired electron's spin magnetic moment. M S =√S(S+1) h/2 π M S  is the total spin angular moment, S is the spin quantum number and h is Planck’s constant. 

7. In the z direction, the component of the total spin angular moment can only assume two values: M SZ = m S ⋅h /2 π The term m s  have (2S + 1) different values: +S, (S − 1), (S − 2),.....-S. For single unpaired electron, only two possible values for m s  are +1/2 and −1/2.  The magnetic moment, μ e  is directly proportional to the spin angular momentum and one may therefore write μ e=− g e μ B M s The appearance of negative sign is due to the fact that the magnetic momentum of electron is   antiparallel  to the spin itself. The term ( g e μ B ) is the magnetogyric ratio. The Bohr magneton, μ B , is the magnetic moment for one unit of quantum mechanical angular momentum: μ B =eh/4 π m e where e is the electron charge, m e  is the electron mass, the factor g e  is known as the free electron g-factor with a value of 2.002 319 304 386 (one of the most accurately known physical constant). 

8. This magnetic moment interacts with the applied magnetic field. The interaction between the magnetic moment ( μ) and the field (B) is described by  E=− μ⋅ B For single unpaired electron, there will be two possible energy states, this effect is called Zeeman splitting. E +1/2 =1/2g μ B B E −1/2 =−1/2g μ B B In the absence of external magnetic field, E +1/2 =E −1/2 =0 However, in the presence of external magnetic field , the difference between the two energy states can be written as Δ E= hv =g μ B B

9. 9 energy levels Resulting energy levels of an electron in a magnetic field

10. 10 Energy Transitions ESR measures the transition between the electron spin energy levels Transition induced by the appropriate frequency radiation Required frequency of radiation is dependent upon strength of magnetic field Common field strength 0.34 and 1.24 T 9.5 and 35 GHz Microwave region Because of electron-nuclear mass differences, the  magnetic moment of an electron is substantially larger than the corresponding quantity for any nucleus, so that a much higher electromagnetic frequency is needed to bring about a spin resonance with an electron than with a nucleus, at identical magnetic field strengths. For example, for the field of 3350 G, spin resonance occurs near 9388.2 MHz for an electron compared to only about 14.3 MHz for  1 H nuclei.

11. 12 Describing the energy levels Based upon the spin of an electron and its associated magnetic moment For a molecule with one unpaired electron In the presence of a magnetic field, the two electron spin energy levels are: E = g m B B M S g = proportionality factor m B = Bohr magneton M S = electron spin B = Magnetic field quantum number (+ ½ or - ½ )

12. EPR is often used to investigate systems in which electrons have both orbital and spin angular momentum, which necessitates the use of a scaling factor to account for the coupling between the two momenta. This factor is the g-factor, and it is roughly equivalent in utility how  chemical shift  is used in NMR. The g factor is associated with the quantum number J, the total angular momentum, where  J=L+S . g J = 1+[J(J+1)+S(S+1)-L(L+1)]/2J(J+1) Here,  g L  is the orbital g value and g s  is the spin g value. For most spin systems with angular and spin magnetic momenta, it can be approximated that g L  is exactly 1 and g s  is exactly 2. This equation reduces to what is called the Landé formula:  g J = 3/2−L(L+1)−S(S+1)/2J(J+1) And the resultant electronic magnetic dipole is: μ J =− g J μ B J In practice, these approximations do not always hold true, as there are many systems in which J-coupling does occur, especially in transition metal clusters where the unpaired spin is highly delocalized over several nuclei. But for the purposes of a elementary examination of EPR theory it is useful for the understanding of how the g factor is derived. In general this is simply referred to as the  g-factor  or the  Landé g-factor .

13. The g-factor for a free electron with zero angular momentum still has a small quantum mechanical corrective g value, with g=2.0023193. In addition to considering the total magnetic dipole moment of a paramagnetic species, the g-value takes into account the local environment of the spin system. The existence of local magnetic fields produced by other paramagnetic species, electric quadrupoles, magnetic nuclei, ligand fields (especially in the case of transition metals) all can change the effective magnetic field that the electron experiences such that  B eff =B +B local The g-factor must then be replaced by a variable g factor g eff  such that: B eff =B ⋅(g/ g eff ) Many organic radicals and radical ions have unpaired electrons with  L  near zero, and the total angular momentum quantum number J becomes approximately S. As a result, the g-values of these species are typically close to 2. In contrast, unpaired spins in transition metal ions or complexes typically have larger values of L and S, and their g values diverge from 2 accordingly.  After all of this, the energy levels that correspond to the spins in an applied magnetic field can now be written as: E ms = m s g e μ B B And thus the energy difference associated with a transition is given as: Δ E ms = Δ m s g e μ B B

14. 15 Proportionality Factor Measured from the center of the signal For a free electron 2.00232 For organic radicals Typically close to free- electron value 1.99-2.01 For transition metal compounds Large variations due to spin-orbit coupling and zero-field splitting 1.4-3.0

15. 16 Spectra signal is the first derivative of the absorption intensity

16. 17 Proportionality Factor MoO(SCN) 5 2 - 1.935 VO(acac) 2 1.968 e - 2.0023 CH 3 2.0026 C 14 H 10 (anthracene) cation 2.0028 C 14 H 10 (anthracene) anion 2.0029 Cu(acac) 2 2.13

17. 18 How does the spectrometer work?

18. KLYSTRONS Klystron tube acts as the source of radiation. It is stabilized against temperature fluctuation by immersion in an oil bath or by forced air cooling. The frequency of the monochromatic radiation is determined by the voltage applied to klystron. It is kept a fixed frequency by an automatic control circuit and provides a power output of about 300 milli watts.

19. WAVE GUIDE OR WAVEMETER The wave meter is put in between the oscillator and attenuator. To know the frequency of microwaves produced by klystron oscillator. The wave meter is usually calibrated in frequency unit (megahertz) instead of wavelength. Wave guide is a hollow, rectangular brass tube. It is used to convey the wave radiation to the sample and crystal. ATTENUATORS The power propagated down the wave guide may be continuously decreased by inserting a piece of resistive material into the wave guide. This piece is called variable attenuator. It is used in varying the power of the sample from the full power of klystron to one attenuated by a force 100 or more.

20. ISOLATORS It’s device which minimizes vibrations in the frequency of microwaves produced by klystron oscillator. Isolators are used to prevent the reflection of microwave power back into the radiation source. It is a strip of ferrite material which allows micro waves in one direction only. It also stabilizes the frequency of the klystron. SAMPLE CAVITIES The heart of the ESR spectrometer is the resonant cavity containing the sample. Rectangular cavity and cylindrical cavity have widely been used. In most of the ESR spectrometers, dual sample cavities are generally used. This is done for simultaneous observation of a sample and a reference material. Since magnetic field interacts with the sample to cause spin resonance the sample is placed where the intensity of magnetic field is greatest.

21. MODULATION COIL The modulation of the signal at a frequency consistent with good signal noise ratio in the crystal detector is accomplished by a small alternating variation of the magnetic field. The variation is produced by supplying an A.C. signal to modulation coil oriented with respect the sample in the same direction as the magnetic field. If the modulation is of low frequency (400 cycles/sec or less), the coils can be mounted outside the cavity and even on the magnet pole pieces. For higher modulation frequencies, modulation coils must be mounted inside the resonant cavity or cavities constructed of a non-metallic material e.g., Quartz with a tin silvered plating.

22. CRYSTAL DETECTORS Silicon crystal detectors, which converts the radiation in D.C has widely been used as a detector of microwave radiation. MAGNET SYSTEM The resonant cavity is placed between the poles pieces of an electromagnet. The field should be stable and uniform over the sample volume. The stability of field is achieved by energizing the magnet with a highly regulated power supply. The ESR spectrum is recorded by slowly varying the magnetic field through the resonance condense by sweeping the current supplied to the magnet by the power supply.

23. 25 Hyperfine Interactions EPR signal is ‘split’ by neighboring nuclei Called hyperfine interactions Can be used to provide information Number and identity of nuclei Distance from unpaired electron Interactions with neighboring nuclei E = g m B B M S + aM s m I a = hyperfine coupling constant m I = nuclear spin quantum number Measured as the distance between the centers of two signals

24. 26 Which nuclei will interact? Selection rules same as for NMR Isotopes with even atomic number and even mass number have I = 0, and have no EPR spectra 12 C, 28 Si, 56 Fe, … For isotopes with odd atomic numbers and even mass numbers, the values of  I  are integers. 2 H, 10 B, 14 N, … For isotopes with odd mass numbers, the values of  I  are fractions. For example the spin of  1 H is 1/2 and the spin of  23 Na is 7/2.  1 H, 13 C, 19 F, 55 Mn, …

25. 27 Hyperfine Interactions Interaction with a single nucleus of spin ½

26. 28 Hyperfine Interactions More common to see coupling to nuclei with spins greater than ½ The number of lines: 2 NI + 1 N = number of equivalent nuclei I = spin Only determines the number of lines--not the intensities

27. 29 Hyperfine Interactions Relative intensities determined by the number of interacting nuclei If only one nucleus interacting All lines have equal intensity If multiple nuclei interacting Distributions derived based upon spin For spin ½ (most common), intensities follow binomial distribution

28. 30 Relative Intensities for I = ½ N Relative Intensities 1 1 1 : 1 2 1 : 2 : 1 3 1 : 3 : 3 : 1 4 1 : 4 : 6 : 4 : 1 5 1 : 5 : 10 : 10 : 5 : 1 6 1 : 6 : 15 : 20 : 15 : 6 : 1

29. 31 Relative Intensities for I = ½

30. 32 Relative Intensities for I = 1 N Relative Intensities 1 1 1 : 1 : 1 2 1 : 2 : 3 : 2 : 1 3 1 : 3 : 6 : 7 : 6 : 3 : 1 4 1 : 4 : 10 : 16 : 19 : 16 : 10 : 4 : 1 5 1 : 5 : 15 : 20 : 45 : 51 : 45 : 20 : 15 : 5 : 1 6 1 : 6 : 21 : 40 : 80 : 116 : 141 : 116 : 80 : 40 : 21 : 6 : 1

31. 33 Relative Intensities for I = 1

32. 34 Hyperfine Interactions Example: VO( acac ) 2 Vanadyl acetylacetonate , C10 Interaction with vanadium nucleus For vanadium, I = 7/2 So, 2 NI + 1 = 2(1)(7/2) + 1 = 8 You would expect to see 8 lines of equal intensity

33. 35 Hyperfine Interactions EPR spectrum of vanadyl acetylacetonate

34. 36 Hyperfine Interactions Example: Radical anion of benzene [C 6 H 6 ] - Electron is delocalized over all six carbon atoms Exhibits coupling to six equivalent hydrogen atoms So, 2 NI + 1 = 2(6)(1/2) + 1 = 7 So spectrum should be seven lines with relative intensities 1:6:15:20:15:6:1

35. 37 Hyperfine Interactions EPR spectrum of benzene radical anion

36. 38 Hyperfine Interactions Coupling to several sets of nuclei First couple to the nearest set of nuclei Largest a value Split each of those lines by the coupling to the next closest nuclei Next largest a value Continue 2-3 bonds away from location of unpaired electron

37. 39 Hyperfine Interactions Example: Pyrazine anion Electron delocalized over ring Exhibits coupling to two equivalent N ( I = 1) 2 NI + 1 = 2(2)(1) + 1 = 5 Then couples to four equivalent H ( I = ½) 2 NI + 1 = 2(4)(1/2) + 1 = 5 So spectrum should be a quintet with intensities 1:2:3:2:1 and each of those lines should be split into quintets with intensities 1:4:6:4:1

38. 40 Hyperfine Interactions EPR spectrum of pyrazine radical anion

39. 41 Conclusions Analysis of paramagnetic compounds Compliment to NMR Examination of proportionality factors Indicate location of unpaired electron On transition metal or adjacent ligand Examination of hyperfine interactions Provides information on number and type of nuclei coupled to the electrons Indicates the extent to which the unpaired electrons are delocalized