F18_NMR

Abstract

Pulsed nuclear magnetic resonance was used to measure the spin-lattice relaxation time (T1) for the phases of water from solid to ice. The method was also used to observe temperature dependence of T1 as liquid water warmed to room temperature. For the case of ice, at a temperature of -196℃, T1 was measured to be 4.38 ± 1.21s. During the melting stages of ice, temperature remains at 0℃ and T­1 was measured to be 3.11 ± 0.26s. Finally, T1 for room temperature (25℃) water was measured to be 1.98 ± 0.097s, which was the lowest relaxation time among the other phases measured.

Results and Data Analysis

The measured proton Larmor frequency was approximately 21.18518 ± 0.00150 MHz for water, this can be confirmed when the beat frequency comparing the frequency from the precessional motion of the sample and the output frequency from the mainframe. Error in the Larmor frequency was obtained by making five measurements and taking the standard deviation. The figure below shows our measured data for liquid water at room temperature following equation 3. Using MATLAB to fit the data to an exponential trend, we obtained a relaxation time of 1.98 ± 0.097s.

Figure 2

Introduction

In 1946 Purcell and Bloch placed a sample containing magnetic nuclei in a uniform magnetic field and exposed it to a continuous radio frequency (RF) magnetic field. While being tuned to resonance, they observed characteristic properties of said sample, and in doing so, developed a new type of spectroscopy, nuclear magnetic resonance (NMR). In 1950, Erwin Hahn, further improved NMR by exploring the response of the sample magnetic nuclei after applying pulsed RF magnetic fields. He observed a ‘spin echo’ signal that emerged after a two pulsed sequence. With Ernst’s and Anderson’s analysis of Fourier transform and transient responses, high resolution NMR spectroscopy were made more efficient with the help of computers [1]. Now pulsed NMR has become the most used spectroscopic tool for many research applications.

Theory

Materials with magnetic constituents that have both a magnetic moment, µ and an angular momentum, J, have an intrinsic property called spin. In the absence of a magnetic field, the spins of these materials are oriented randomly and vectorially, cancel out. This means there are no net magnetization. With an applied constant and uniform external B-field (which we orient in the z-axis and denote it as Bo), a net magnetization occurs in the same direction as the applied field, Mo. The Bo-field supplies energy to particles such that the particle absorbs a photon of frequency ωo to transition to higher states. It is a valuable quantity in the technique of NMR because it represents the frequency in which the magnetic moment of the nuclei, precesses about an external magnetic field (shown in figure below), this is better as Larmor precession/frequency.

Figure 6 below shows our measured data for solid ice when submerged with liquid nitrogen. Following equation 3, we obtained a relaxation time of 4.38 ± 1.21s

Figure 3

From the moment the uniform Bo-field is applied to the nuclei system, the occurrence of thermal equilibrium happens in some interval of time. The spin-lattice relaxation time, T1, is defined as the time it takes for the magnetization to reach equilibrium along the direction of the magnetic field when a 180ᵒ pulsed RF frequency is applied to the system. T1 is mathematically defined as

Finally, figure 7 shows our measured data for melting ice when frozen in the freezer. Once again, following equation 3, we obtained a relaxation time of 3.11 ± 0.26s.

Figure 4

(1)

With a solution of,

To collectively get a better view, the spin-lattice relaxation time for the different phases of water were graphed with temperature as shown in figure 5. We expected to see a kink from where ice transitioned to water, which is what the graph seems to claim. However, since the melted ice data had too many errors in terms of temperature, we can’t make the conclusion.

Figure 5

Ice has some crystalized structure that limits atomic motion in the lattice. Since the physical definition of T1 is the time it takes for energy within the nucleus, to dissipate energy into its surroundings, we can think of this as vibrational motion between atomic neighbors which are fixed in space. The crystal lattice of ice restricts vibrational motion of atoms and therefore, takes much longer to reach thermal equilibrium [5].

Liquid water, on the hand have the motion of atoms no longer restricted to one location and moves freely within the volume with some speed [5]. Therefore, energy dissipation from the nuclei to its surrounding occurs much quicker than that of ice. And of course, melting ice is a mixture of both liquid and solid ice structures, therefore T1 of the melting phases should be between Ice and water, which was what we observed.

Conclusion

The goal of this project was to measure the spin-lattice relaxation time (T1) for the phases of water from solid to ice using pulsed nuclear magnetic resonance techniques and observe temperature dependency of T1. Note that the relaxation time vs temperature graph (figure 5) is simply an approximation. We know that the liquid water was approximately 25℃ and the iced water is approximately -196 ℃, however there was not an efficient way to measure it.

Improvements on the project due to time constraints would be to measure the spin-spin relaxation time (T2) that describes how the neighboring nuclei’s magnetic field affect one another. We could have also observed chemical shifts between ice and water themselves using pulsed NMR techniques. For the scope of this project, we could measure the resonant frequency of water and ice, then compare the difference between the two to understand how the motion of the electrons makes its own magnetic field that shields the externally applied one (Bo) [6].

(3)

We determined T1 by measuring the initial amplitude of the FID signal (Mz as a voltage signal) as a function of delay time and plotting equation 3 to an exponential fit on MATLAB.