Pulsed NMR of Ferroin and Ferriin Jordan J Gosselin and Cassandra S Niman Modern Physics Lab 173 Bio Quantum University of California San Diego June 13 2008 Introduction Pulsed NMR is used to characterize spin spin and spin lattice interactions Due to our interest in the ferroin catalyzed B Z reaction we attempted to characterize ferroin and ferriin using pulsed NMR with hopes to run the pulsed NMR on a B Z reaction and observe changes from ferroin to ferriin in the reaction This reaction could not be imaged using NMRI as reported by Ying Gao et al Characterizing T2 for ferriin gave expected results while finding T2 for proved difficult due to the low signal to noise observed The FID of ferroin was observed as expected and T2 was characterized Attempting to measure T2 for ferroin lead to interesting observations of phase shifting in the spin echo which lead to an inability to properly characterize T2 and question the accuracy of the results found for ferriin T2 Background Pulsed NMR is a spectroscopy technique that takes advantage of the intrinsic particle property of spin Specifically it focuses on the spins of the protons in the nucleus The methodology involves placing a sample within a set of orthogonal coils which comprise the x y and z axis We have defined the x direction as the transmission coil the y direction as the reception coil and the z direction is our magnet coil A DC current is fed through the magnetic coils to create a magnetic field Bo in the z direction The spin state of each proton in a nucleus has a magnetic moment given by S underlined variables represent vectors S is the spin vector is the gyromagnetic ratio The energy of the state is determined by the inner product of the magnetic moment with the magnetic field E B Because Bo is only in the zdirection only the z component of is important This component is given by z m where m for protons The above is a quantum mechanical description of the system we are only concerned with the net effects of these magnetic moments so we will treat NMR classically with the exception of the preceding explanation of magnetic moments due to spin The individual magnetic moments due to spin can be summed into a net magnetic moment which is what is seen with the receptor coils The ratio of the populations of the spin up and spin down states S and S respectively can be estimated by the Maxwell Boltzmann distribution The equation is Number S Number S exp E kT where k is Boltzmann s constant Pochapsky 28 The net magnetic moment is directly proportional to this difference in the population of the spin states This net magnetic moment precesses about the z axis with an angular frequency given by Bo For the purposes of our experiment we tuned Bo to give an of 2 8 MHz This was done because we were using a function generator that generated 8 Mhz sine waves The main idea of NMR is to rotate this net magnetic moment into the x y plane here we can measure it s amplitude and determine the time it takes to relax to it s initial state This is most easily visualized in a reference frame rotating at the same frequency as In this reference frame Bo Since our reference frame rotates at with respect to the laboratory frame 0 therefore Bo 0 The net magnetic moment is stationary in this frame We apply an 8 MHz pulse in the x direction in the laboratory frame In the rotating frame this appears to be a stationary magnetic moment in the x direction due to the decomposition of the 8 MHz sine wave into two vectors rotating with opposite an interested reader should refer to the first chapter of Bruch s book all others must accept this as true This moment provides a torque on the magnetic moment for the duration of the pulse width This will rotate the magnetic moment around the x axis rotating frame an angle given by the equation Bx where Bx is the peak amplitude of the oscillating magnetic field applied in the laboratory frame The equation for can be easily derived from the equation for When the magnetic moment is rotated into the x y plane the net magnetic moment will decrease due to the phase spreading in the x y plane caused by inhomogenity of the magnetic field throughout the sample The above is the phase spreading in the rotating reference frame This relative phase spreading can be utilized to characterize a substance in pulsed NMR The main idea behind pulsed NMR is to use pulses with an angle of or 2 in sequence to measure various characteristic relaxation times Methodology For our project we used a pulse generating data acquisition MatLab code developed by Erik Flister combined with a simple averaging routine designed by Jordan Gosselin This allowed us to perform multiple trials and average the results extremely rapidly The mode of the dataset sizes was 64 trials the data taking averaging process for these trials took approximately thirty seconds to one minute We measured T2 and T2 for ferriin and ferroin respectively We applied a pulse with an angle of 2 followed by a pulse with an angle of in an attempt to recover a spin echo and measure T2 This is a common technique which is mentioned in all the books we referenced bibliographical information given following the report Another method we used was the Carl Purcell method This method uses multiple pulses following the initial 2 pulse We attempted to use this method unsuccessfully Our problems are discussed in the Experimental Results section below Experimental Results Our measurements are of ferroin and ferriin We tried to characterize T2 for these samples By changing the time the pulses were high and maximizing the amplitude of the FID and Spin Echo we found the time length of a 2 and pulse for each sample Ferroin and ferriin have a 2 pulse size of 25 s and 10 s respectively For each sample the length of the pulses stayed constant for the remainder of our measurements For each setting of the time between the pulses 64 or 128 raw data samples were acquired and averaged This produces a smooth data set to start with Fig1 64 averaged data sets taken of ferroin There is a clear FID and spin echo as expected The strange shape of the second pulse is likely due to an overlapping of the pulse and the tail of the FID Ferriin Data Analysis A 2 pulse for ferriin is about 10 s The data for the FID following the 2 pulse is shown below Because the signal is so small most of it gets lost in the noise there is no clear exponential decay of the peaks and this data could not be used to characterize T2 Fig2 FID for