+ All Categories
Home > Documents > Electron Spin Resonance Experiment

Electron Spin Resonance Experiment

Date post: 28-Apr-2015
Author: atiq-ur-rahman
View: 54 times
Download: 2 times
Share this document with a friend
Embed Size (px)
of 19 /19

Electron Spin Resonance by Using Organic compound (DPPH)

Su m dto b itte :Sir Arif Mumtaz Sir Ghullam Hussain Jafferi

Su m dBy b itte :Atiq ur Rahman M.Sc 3rd Semes




IntroductionOne of the intrinsic quantum-mechanical characteristics of fundamental particles is that they have "spin," or intrinsic angular momentum. As with many quantities in the quantum mechanics realm, the energy states associated with the spin are quantized. The spin of a charged particle, like an electron, becomes evident when the particle is placed in a magnetic field. A charged particle with a "spin" has an associated magnetic dipole moment and, when placed in an external magnetic field, the energy of the particle will depend on the orientation of its spin relative to the magnetic field. In electron spin resonance, electrons in an external magnetic field absorb energy from an applied oscillating electromagnetic field and change from one spin orientation to another. The spins of particles and their interaction with magnetic fields provides a useful modern-day experimental tool for studying their environment. Electron spin resonance (ESR), also known as electron paramagnetic resonance, uses the spin of electrons. The resonance frequency is sensitive to the local environment of the electrons. In chemistry and medicine the resonance frequency of a proton give information about the local environment (magnetic field) of the proton. This is the key to nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI). In this experiment, you will produce electron spin resonance to show that the electron has two discrete spin energy states and you will measure the value of the electron's magnetic moment. ESR in Research In research, ESR measurements are considerably more complicated that equation 2 would indicate. The electrons and protons in an atom or molecule form a complicated electromagnetic environment, which is affected by the externally applied magnetic field. The various energy splittings and shifts that show up in ESR measurements can therefore provide sensitive information about the internal structure of the atoms and molecules. The test sample included with the PASCO ESR Apparatus DPPH, is a particularly simple substance for ESR measurements. It has an orbital angular momentum of zero, and only one unpaired electron. Therefore, for a given value of the external magnetic field, it has only a single resonant frequency. This makes it possible to investigate some of the basic principles of electron spin resonance, without (or before) getting into the more complex world of ESR analysis.

BackgroundAn electron bound to an atom can absorb a photon (or packet of electromagnetic energy) of the right energy and make a transition to a higher energy state, provided2

that the photon energy precisely matches the energy difference between two allowed states. The energy of a photon depends on its frequency (which can also be considered in a semi classical picture to be the frequency of oscillation of the electric and magnetic fields) by E = h. Thus, an electron bound to an atom can absorb or emit only photons that have specific frequencies (Figure 1).

Figure 1. Electrons bound to atoms can emit or absorb electromagnetic energy (photons) only in discrete quantities corresponding to the different allowed energy states in the atom. (a) emission, (b) absorption. When free electrons (or nearly free electrons in a solid) are placed in a magnetic field, the z-component of the spin angular momentum (the component parallel to the magnetic field) can take on two values, and these two spin orientations correspond to different energies. These two energy states are due to the magnetic dipole moment of the electron and its orientation relative to the external magnetic field (see Figure 2). A classical analogue of this phenomenon is the current loop in a magnetic field: To rotate the magnetic dipole moment of the loop opposite to the applied field, work must be done. For the spinning electron, there are only two allowed energy states associated with its interaction with the magnetic field, whereas the energy for a macroscopic current loop is continuous. (a)



(b) Figure 2. (a) Two spin states of electron in a magnetic field (b) This image shows the energy splitting due to a magnetic field for any spin particle, such as electrons,3

protons, neutrons or certain nuclei. (http://www.shu.ac.uk/schools/sci/chem/tutorials/molspec/nmrlev1.gif)

Figure 3. Energy of a classical current loop in a magnetic field The magnetic moment of the electron differs from the classical analogy of a current in a loop in one other aspect. The classical magnetic moment is easily calculated from the circulating current. The electron, on the other hand, is a point charge so its magnetic dipole moment cannot be viewed simply as a classical circulating charge. The magnetic moment of an electron is a fundamental, quantum mechanical property of the electron. As for the current loop, the magnetic moment and the spin angular momentum of the electron are proportional, but the constant of proportionality is different.

Prelab question:The magnetic moment of a current caused by a charge circulating in a loop is given by = IA where A is the area of the loop. Show that in this case = (q/2m)L , where q is the charge, m the mass of the charges, and L the angular momentum associated with the circling charges. For electron spins, a correction factor, known as the g-factor, must be included in the above equation, and we refer to the component of the magnetic moment along the z axis by substituting h/4 for the magnitude of the angular momentum along this axis, so that e = ge(q/2m)(h/4). The g-factor for the electron is now known to high accuracy through both experiment and theory to be 2.002319134. The energy associated with a classical magnetic dipole, of moment , in a magnetic field B (oriented along the z-axis) is given by E = - B = -zB. The two allowed quantum spin energy states of the electron, then, are eB, with the lower state corresponding to parallel alignment of the magnetic moment with the B-field, or when the spin of the negative charge is anti-aligned. (Note that the when there is no external magnetic field, i.e., B = 0, the two states have the same energy and are therefore indistinguishable. In quantum mechanical terms, we say that these states are degenerate.) Since the magnetic dipole moment of an electron along the magnetic field axis is given by e, as defined above, the energy difference between the two allowed energy states, and therefore the energy that can be absorbed by the electrons4

is 2eB. The requirement for electrons to absorb a photon and flip its spin, then, is that h = 2eB. This is considered a resonance situation because the natural response frequency of the system (the frequency of radiation that the electrons will absorb) equals the applied frequency (of the oscillating EM field). In this experiment, the oscillating electromagnetic field is in the radio frequency range, and is created by an oscillating current in a coil. A quantum of this oscillating electromagnetic field has energy h, where is the frequency of oscillation. The electrons will be located inside this coil and inside a larger-scale external magnetic field, created by a set of Helmholtz coils. When h = 2eB the electrons will absorb energy from the oscillating EM field.ESR in Theory The basic setup for electron spin resonance is shown in Fig 1. A test sample is placed in a uniform magnetic field. The sample is also wrapped within a coil that is connected to an rf oscillator. The smaller magnetic field induced in the coil by the oscillations of the oscillator is at right angles to the uniform magnetic field.

Consider, for the moment, a single electron within the test sample. The electron has a magnetic dipole moment ( s ) that is related to its intrinsic angular momentum, or spin, by the vector equation:

s = g s B s / (1)


g s = a constant characteristic of the electron, the g-facotr

B = the Bohr magneton =s = the spin of the electron

eh = 5.788 10 9 eV / G 2 me

= Plancks constant = 6.582 10 16 eV sec .The magnetic dipole moment of this electron interacts with the uniform magnetic field. Due to its quantum nature, the electron can orient itself in one of only two ways, with energies equal to

E 0 g s B / 2 ; where E0 is the energy of the electron before the magnetic field was applied. The5

energy difference between these two possible orientations is equal to magnitude of the magnetic field.

g s B B ; where B is the

Resonance occurs when the rf oscillator is tuned to a frequency f, such that the energy of the irradiated photons,

hf , is equal to the difference between the two possible energy states of the electron.

Electrons in the lower energy state can then absorb a photon and jump to the higher energy state. This absorption on energy effects the permeability of the test sample, which effects the inductance of the coil and thereby the oscillations of the rf oscillator. The result is an observable change in the current flowing through the oscillator. The condition for resonance, therefore, is that the energy of the photons emitted by the oscillator match the energy difference between the spin states of the electrons in the test sample. Stated mathematically:

hf = g s B B ESR in Practice


For an electron with only two energy states, in a magnetic field of a given magnitude, it would be necessary to set the rf frequency with considerable accuracy in order to observe resonance. In practice, this difficulty is solved by varying the magnitude of the magnetic field about some constant value. With the PASCO ESR Apparatus, this is done by supplying a small ac current, superimposed on a larger dc current, to a pair of Helmholtz coils. The result is a magnetic field that varies sinusoidally about a constant value. If the rf frequency is such that equation 2 is satisfied at some point between the minimum and maximum values of the sinusoidally varying magnetic field, then resonance will occur twice during each cycle of the field. Resonance is normally observed using a dual trace oscilloscope. The oscilloscope traces, during resonance, appear as in Fig. 2. The upper trace is a measure of the current going to the Helmholtz coils, which is proportional to the magnetic field. The lower trace shows the envelope of the voltage across the rf oscillator, which dips sharply each time the magnetic field passes through the resonance point.

The ESR Equipment6

Included Equipment The ESR Apparatus is available in three separate packages (see Fig. 3): The ESR Probe Unit (SE-9634) includes: The probe Unit with base Three rf Probes and a DPPH sample in a vial The passive Resonant Circuit The current Measuring Lead for the Probe Unit The ESR Basic System (SE-9635) includes: The ESR Probe Unit (se-9634) A pair of Helmholtz Coils with bases The ESR Adapter (SE-9637) The Complete ESR System (SE-9636) includes: The ESR Probe Unit (SE-9634) A pair of Helmholtz Coils with bases The Control Unit



Control Unit Technical Data: Power Requirement: 120 or 240 VAC; 60Hz Fuse: 1.6A, 220V (sil-bio) for 120VAC; 0.8A, 220V (sil-bio) for 120VAC Magnetic Field Supply: 0-10 VDC; 0-5 VAC; maximum current 3A (not overload protected) Phase Shifter: 0-90 Digital Frequency Display: 4 digits ESR Adapter If you are not using the Control Unit, the ESR Adapter can bs used to connect the probe Unit to the necessary power supply, frequency meter, and oscilloscope. See the section, Setup with the Basic ESR System, for details of the connections. See the Appendix if you would like details for building your own adapter.

Helmholtz Coils The Helmholtz coils provide a highly uniform magnetic field in which to place the sample material for the ESR measurement. They should be connected in parallel and placed so that the separation between them is equal to the radius (see Fig. 7). When this is the case, the magnetic field in the central area between the two ciols is highly uniform, and is equal to the value shown in Fig. 7. The Passive Resonant Circuit can be used to demonstrate resonant energy absorption in a non-quantum system. It is just an LC circuit with an adjustable capacitance. It replaces the test sample and the Helmholtz coils in the ESR experiment.


Required EquipmentTo perform ESR experiments with the Complete ESR System, youll need the following additional equipment: A DC ammeter capable of measuring up to 3A A dual trace oscilloscope Connecting wires with banana plug connectors


Connect the Helmholtz coils to the Control Unit, as shown in Fig. 9. (The coils should be connected in parallel-terminal A to terminal A, and Z to Z.) Connect an ammeter in series, as shown, to monitor the current to the coils. Important: the DC current supply in the Control Unit is not overload protected. Do not let the 10

current to the Helmholtz coils exceed 3A. Position the Helmholtz coils so that they are parallel and facing in the same direction, and their separation is equal to approximately one half their diameter. Connect the X output of the Control Unit to channel 1 of a dual trace oscilloscope. Set the oscilloscope controls as follws: Sensitivity: 1 or 2 V/div Sweep Rate: 2 or 5 ms/div Coupling: DC Set

U mod the center knob on the Control Unit, to zero, then slowly vary U 0 , the left knob, from 0 to

10V and observe the trace on the oscilloscope. It should be a clean, straight line, showing that the DC component of the current to the Helmholtz coils is constant. ( U 0 controls the DC current going to the Helmholtz coils.) Note: If the oscilloscope trace is not straight your Control Unit is probably not set for the proper line voltage. Set U 0 at approximately midscale, then turn U mod clockwise, to increase the AC component of the current to the Helmholtz coils. The trace on the oscilloscope should now show a smooth sine wave, as in Fig. 10, corresponding to an AC magnetic field that is superimposed upon a constant DC field.

Fig 10 Oscilloscope current to the Helmholtz coils

Connect the Y output of the Control Unit to channel 2 of the oscilloscope. Set the oscilloscope controls for channel 2 as follow: Sensitivity: 0.5 or 1 V/div Coupling: DC Connect the Probe Unit to the Control Unit, as shown in Fig. 9. Plug the medium sized rf Probe into the Probe Unit, and insert the sample of DPPH into the coil of the probe. Turn on the Probe Unit by flipping the On/Off switch to the up (I) position. Then turn the Amplitude knob on the Probe Unit to a medium setting. The Frequency meter on the Control Unit should now indicate the frequency of the rf oscillations. Adjust the Frequency control knob on the Probe Unit to produce an output of approximately 50MHz.

U mod to about the 4th position above zero (at about the 11 oclock position). Increase U 0 from zero to a medium value, so the Helmholtz coil current is about 1.0 A. TheSet oscilloscope traces should now look as in Fig. 11. Then channel 1 trace shows the current to the 11

Helmholtz coils, which is proportional to the magnetic field produced by the coils. The channel 2 trace shows the envelope of the voltage across the rf oscillator, with the pulses showing the points of resonance absorption. If you see no resonance pulses, slowly vary do.

U mod or the rf frequency, until you

Fig. 11 the Oscilloscope Display

Your traces may not be symmetrical, as they are in Fig. 11. This is because of the inductance of the Helmholtz coils, which causes the current through them, and therefore the magnetic field they produce, to lag the voltage that drives them. You can compensate for this delay by adjusting relationship between the modulating magnetic field and the resonant pulses. ESR in the X-Y Mode ESR is often observed with the oscilloscope in the X-Y mode. For this mode of observation, connect the X and Y outputs of the Control Unit to the X and Y inputs of the oscilloscope, respectively. In this mode, the horizontal displacement of the trace indicates the magnitude of the magnetic field between the Helmholtz coils. The vertical displacement indicates the signal from the Prob Unit. As before, two resonance pulses can be observed since the magnetic field passes through the correct value twice each cycle. By adjusting the Phase Shifter, the two peaks can be brought into coincidence. The resulting trace will appear as in Fig. 12.

, the Phase

Shifter control knob, until the traces are symmetrical. When symmetrical, the traces properly reflect the

Fig. 12 the Oscilloscope Display


Fig. 13 Using the Control Unit

Making ESR MeasurementsWhether you are using the Complete ESR System of the ESR Basic System, the same technique is used for making measurements. Setup the apparatus as described in the appropriate section. Adjust the rf frequency and the DC current to the Helmholtz coils until you locate the resonance pulses. Adjust the phase shifter so that the resonance pulses are symmetric with respect to the oscilloscope trace that shows the current to the Helmholtz coils. Refine the adjustment of the DC current until the resonance pulses occur when the AC component of the current to the Helmholtz coils is zero. To do this: Making sure that channel 1 of the oscilloscope (the trace showing the current to the Helmholtz coils) is in the AC coupled mode. Using the oscilloscope controls, ground the input to channel 1, zero the trace, and then un-ground the input. Adjust the DC current. As you do, notice how the resonance pulses move closer together or farther apart. Adjust the DC current, and the phase shifter if necessary, until the pulses occur just when the AC current to the Helmholtz coils is zero. (This is most accurately accomplished if you adjust the vertical position of the channel 2 trace so that the bottom of the resonance pulses are just at the zero level of the channel 1 trace.) With these adjustments, the oscilloscope traces should appear as in Figure 17. Everything is set for 13

making ESR measurements. Since the current has been adjusted so that the resonance pulses occur when the AC current to the coils is zero, the current to the Helmholtz coils at resonance is just the DC value indicated by the ammeter. The resonant frequency is equal to the value on the Control Unit display (or the value indicated by your frequency meter multiplied by 1,000).

Fig. 17 Scope Display

Measure the rf frequency and the DC current. Then vary the current and find the new resonance frequency. Do this for several values of the frequency. The magnitude of the magnetic field between the Helmholtz coils is directly proportional to the current supplied to the coils. You can determine the magnitude of the field using the following equation (easily derived from the Biot-Savart Law):

4 B = 0 5where:


NI / R

0 =

1.256 10 6 Vs / Am

N = number of turns in each coil R = the radius of the Helmholtz coils (which is equal to their separation when they are properly arranged) I = current passing through the coil If you are using the test sample of DPPH, you can now determine the g-factor for the electron using the equation

hf = g s B B .

you might damage the oscillator. CURRENT(A) .26 .35 .44 .51 MAGNETIC FIELD(mT) .55 .74 .93 1.O8 FREQUENCY(MHz) 15.3 20.6 25.2 30.1


.60. .69 .77 .86 .94 .1.0 1.10 1.20 1.30 1.35 1.45 1.55 1.60 1.70 1.80 1.90 1.95 2.00 2.10 2.20

1.27 1.46 1.63 .1.82 1.99 2.12 2.33 2.54 2.75 2.85 3.07 3.28 3.38 3.60 3.81 3.02 4..12 4.23 4.44 4.65

35.7 40.4 45.1 50.5 55.7 60.6 65.2 70.8 75.0 80.7 85.3 90.5 95.1 100.3 105.0 110.7 115.3 120.8 125.2 130.0

Reference:Griffiths, Introduction to Quantum Mechanics, 4.4 (pp. 171 on), Eisberg and Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles, Sec. 8.1 to 8.3.

www.wikipedia.com www.hyperpysics.edu.org www.wikianswers.com