# April 24, A Classical Perspective. Exam #3: Solution Key online now! Graded exams by Monday!

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1 April 24, 2015 Exam #3: Solution Key online now! Graded exams by Monday! Final Exam Monday, May 4 th, 10:30 a.m. Room: Perkins A Classical Perspective A classical view will help us understand the measurement process. Consider a spinning charged particle in a magnetic field: Particle will precess at a characteristic frequency (Larmor Frequency) ν o : ν o = γb o /2π (where γ = magnetogyric ratio) 2 1

2 Classical view of Absorption Application of another magnetic field (B 1 ) perpendicular to B o and at a frequency = ν o results in: Absorption of applied EMR Spin flip of particle to excited state 3 Instrumental Continuous Wave (CW) NMR original instruments used: Electromagnets (14-23 kg; MHz) Fixed frequency RF source Swept (variable) magnetic field -measure absorption of applied RF not very sensitive... Why? 4 2

3 Back to Boltzmann! Using Boltzmann statistics, we can determine the relative populations of each of the two spin states: N 2 /N 1 = e - E/kT E is very small (relative to optical EMR) for RF EMR As E, N 2 /N 1 1 (so, N 2 N 1 ) BUT: for absorbance, we want N 1 >> N 2 If absorption rate > decay rate, not much absorbance can occur before N 1 = N 2 (saturation) When transition is saturated, NO MORE ABSORPTION! 5 Decay (relaxation) Processes Two decay routes (non-radiative): 1. Spin-Lattice Relaxation (T 1 ) -also called: longitudinal relaxation -due to interactions between nuclear spin states and magnetic micro environments in the sample -magnetic micro environments must be at the Larmor Frequency of the absorbing nuclei in order to couple -what will affect coupling efficiency? 6 3

4 Coupling Efficiency: T 1 T 1 is the excited state lifetime associated with spinlattice relaxation (it is inversely proportional to the extent of spin-lattice relaxation) Temperature effects -at some temperature, the frequency of molecular motion matches the Larmor frequency for a nucleus and coupling efficiency is at a maximum (T 1 is at a minimum) -any change in temperature will result in an increase in T 1 (decreased coupling efficiency) Any (e.g., viscosity) changes in lattice mobility will have a similar effect 7 More on T 1 Processes Other lattice components that can reduce T 1 : unpaired electrons (from radicals and paramagnetic species, like O 2 ) nuclei with I 1 Efficient Spin-Lattice Relaxation results in: Decreased likelihood of saturation Larger absorption signal (CW NMR) Other effects? 8 4

5 Spin-Spin Relaxation: T 2 Energy transfer with other magnetic nuclei Nuclei must be in close proximity Very efficient coupling in solids (T 2 ~ 10-4 sec) Has no effect on saturation Will cause line broadening: ν = (2π t) -1 so: linewidth 1/T 2 (T sec ν 10 3 Hz) (according to Heisenberg) In solutions: (< 1 sec)t 2 < T 1 (1-10 sec) Controls linewidths (~1 Hz) Affects saturation 9 How can S/N be increased? Increase B o -increases E, increasing population difference between spin states, so more nuclei can undergo transitions -How? Superconducting Magnets Multiplex Signal Measurement -small signal makes measurement limited by detector noise, so a multiplex measurement method should improve S/N -How? Fourier Transform 10 5

6 Pulsed FT-NMR At fixed B o, irradiate sample with a range of RF EMR frequencies... How? -by pulsing a fixed frequency (ν o ) RF source, a range ( ν) of RF frequencies is generated. -the extent of the range is determined by the pulse width: ν = 1/4τ (according to Heisenberg) where: τ is the pulse width (seconds) 11 The Pulsed FT-NMR Measurement RF Excitation Pulse Free Induction Decay 12 6

7 FT-NMR: Obtaining a Spectrum Obtain maximum number of excited nuclei during the RF pulse (saturation) Measure RF Emission (signal generated by nuclei spin flips back to ground state) when RF source is off - FID FID contains emission from all excited nuclei all at their characteristic (Larmor) frequencies Use Fourier Transform to convert time domain FID to frequency domain spectrum 13 FT-NMR: Instrumentation 14 7

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