s19NMR

Nuclear Magnetic Resonance of Liquids within a Porous Medium

Kalven Bonin & Charles Kemper

University of Minnesota, Methods of Experimental Physics

Abstract

Pulse nuclear magnetic resonance was used to find the spin-spin relaxation times for solutions of light mineral oil and water. Data was taken for samples which contained only the liquid and samples which contained both liquid and microscopic glass beads Using a combination of uniform and radio-frequency (RF) magnetic fields, the solution(s) were subjected to magnetic pulses to shift the orientation of magnetic moments and measure how long it took for the spins to relax. The primary focus of this experiment was to determine how the presence of the glass beads affected the spin-spin relaxation time. It was found that, due to relaxation interactions between the magnetic moments and the surface of the glass beads, the spin-spin relaxation time decreased to approximately 30% and 60% of its original value for water and light mineral oil respectively.

Introduction

Nuclear magnetic resonance is a process that exploits the magnetic moments and angular momentum of individual protons to alter their magnetic orientations for a variety of purposes. It was first introduced by Edward Purcell of Harvard University and Felix Bloch of Stanford when they exposed a sample of magnetic nuclei to a uniform magnetic field and a resonating RF magnetic field at the same time. Since then, the applications of NMR have diverged into a number of applicable fields. MRI (magnetic resonance imaging) uses this technique by immersing a patient in the necessary magnetic ﬁelds to produce a three dimensional image of their skeleton and inner tissues for study and diagnosis. NMR is also used to study the earth itself. Through the use of NMR, the composition of the earth’s crust can be determined at certain locations miles below the surface. This technique is used by researchers to measure the permeability of rock layers, fertility of soil, and contents of permanent and sea ice all over the world 3]. NMR can be used to determine where to drill for oil. If the gradient of the rock layer in the earth can be determined, oil can be successfully found and excavated without drilling through gas or water. In this experiment, water and a mineral oil will be used to test the inﬂuence of a porous medium on the magnetization properties of these liquids when immersed in the magnetic ﬁelds necessary for NMR. Samples of water and mineral oil were placed in a medium of glass beads (ground up glass reﬁned into microscopic marbles) and tested by constant and RF magnetic ﬁelds.

Theory

The theory section from out TDR (attached file) goes into copious detail in case anything is not well understood in this summary.

When the magnetic moments of nuclei are placed into a magnetic field, they being to precess about the axis parallel to the external magnetic field at the Larmor frequency. This phenomenon is described in Introduction to Quantum Mechanics by David J Griffiths in Example 4.3 from the 3rd edition. If you do not have this book, we have summarized this in the file "An Explanation of the Larmor Frequency". You can also explain this semi-classically with a geometric argument:

Gamma is the gyromagnetic ration and mu is the magnetic moment. Here is the image corresponding to this argument.

is the Larmor frequency, and this is in agreement with the value derived from the quantum mechanical approach.

We will now give a brief explanation about how the pulse from the RF magnetic field rotates the magnetic moments of the nuclei. Please refer to pages 5 and 6 in Measuring the Spin-Spin Relaxation time for Substances within Glass Pores. For a more detailed explanation.

First we imagine that we add a circularly polarized magnetic field along the plane perpendicular to the large external magnetic field. Note that the RF pulse would actually be a superposition of two counter rotating circularly polarized magnetic fields

but the physics is still the same. We move to a reference frame (the * reference frame) where the x* axis rotates with the magnetic field. The field rotates about z (the direction which we arbitrarily assign to be parallel to the large external magnetic field) . In this reference frame z=z*. Also, we must add in a 'fictitious" magnetic field to account for out change of reference frame:

. Now the total magnetic field in the rotating reference frame is:

And if we set the magnetic field to the Larmor frequency, the second term goes to zero. We are left with with an effective magnetic field which is completely in x* (a coordinate which rotates with the magnetic field). This causes the magnetic moments to precess about x* which causes them to rotate. If you apply the RF field long enough, you can create a transient magnetization along the transverse plane.

The magnetic moments will come the thermal equilibrium (you can find the energy difference between the spin-up and spin-down states and find that the majority of the moments point along the magnetic field) when the RF field is turned off. If you place matter into a magnetic field, the characteristic time for them to return to thermal equilibrium is called the spin-lattice relaxation time. Essentially, the energy decreases because more magnetic moments go to the low energy states, and the energy goes into the lattice. The spin-spin relaxation takes into account the local magnetic fields from the magnetic moments themselves. These interactions cause the transverse magnetization to decay more rapidly. However, the RF pulse actually rotates magnetic moments with a distribution of frequencies (it still only rotates the magnetic moments very close to the Larmor frequency, but there is a distribution). So when they reach the transverse plane, they precess at different phases, and the magnetization decays too rapidly. More rapidly than the spin-spin relaxation time. To fix this you have to add in a series of 180 degree pulses after the initial 90 degree pulse.

After the 180 degree pulse, the magnetization peaks and an echo is produced:

The echos for each pulse create an exponential decay curve which looks like this:

To find the exponential decay curve, we found the peaks of echo and fit the data in excel.

The purpose of this experiment was to observe the effect of the glass beads. Theoretically, the nuclei in the liquid will interact with the surface of the glass beads. These relaxation interactions are thought to cause the decay to occur more rapidly (reference 3).

Experimental Setup

This experiment was conducted using a permanent magnet, a PS2 controller which controls the temperature of the magnet, and a mainframe which consists of a receiver module, a 21MHz synthesizer, and pulse programmer. The permanent magnet consists of two magnet poles which create a constant magnetic ﬁeld of 0.50±0.01T and wire coils that surround the sample which are used to create an RF pulse on the order of 21MHz.

A glass tube vial was ﬁlled with a sample of micron-sized glass beads and water/mineral oil to create a porous sample. The vial was inserted into a sample chamber on the top end of the magnet. Each sample had no more than 0.1 grams of glass beads, and no more than 30 µL of liquid. There were coils shaped to form solenoids around the sample chamber. This coil is also how the ambient RF magnetic ﬁeld was induced. The ﬁrst step in any data acquisition process for NMR is to tune to the correct frequency. There were tuning capacitors on the magnet that acted as ﬁlters. The tuning capacitors were adjusted with a screwdriver. The capacitors were adjusted such that the signal on the oscilloscope (in the absence of any magnetized sample) was at a maximum. The oscilloscope was connected to the mainframe such that the reference signal from the synthesizer and the Lamar frequency detected by the sample coils can both be displayed. When the signal is tuned correctly, it appears almost identically to the Lamar frequency of the sample.

For both water and mineral oil, a sample of pure liquid was placed in the magnetic sample coil to ﬁnd the T2 of the liquid without any eﬀects of porous materials. Then, three samples of glass beads (each containing 70 mg of glass) mixed with 10, 20, and 30 µL of liquid respectively were tested in the magnet to ﬁnd the eﬀects of a porous medium on the spin-spin relaxation time of a liquid. This was done by applying a 90 degree pulse to flip the magnetization of the protons in the direction of the sample coil, followed by a 180 degree pulse to flip the magnetization entirely to obtain an echo; both of which where generated by the synthesizer.

Data

Analysis

If you want to see plots of weighted residuals (and analysis of those plots) please look at the analysis section of Measuring the Spin-Spin Relaxation Time for Substances within Glass Pores.

A short summary is that we did find that the presence of the glass beads reduces the spin-spin relaxation time for distilled water and light mineral oil. This effect was more significant for the distilled water. We believe that this occurred because water has an intrinsically longer spin-spin relaxation time that light mineral oil. Therefore, there is more time for the nuclei in water to diffuse (not facilitated diffusion but random from Brownian motion) to the surface of the glass. Therefore, there are more relaxation interactions for the distilled water.

There was a contamination in the magnet which caused some problems. This substance produced its own echo decay curve even when nothing was in the magnet. We think that this caused our measured T2 to be too rapid. The contamination had a T2 of about 8ms. This is very fast.

If you take data for too long, it begins to level out and you have a problem with the resolution of the oscilloscope. For example, during the very end of the decay. there may be come data point that are actually higher than the previous one. We think that this is a result of the resolution of the oscilloscope being larger than difference in induced voltage for adjacent data points. We think this is why the 10 microliter sample had the longest T2 for the distilled water with beads. We though that more water would yield a slower T2 because some may rest on top of the glass beads. However, the 10 microliter outlier may have just been a result of us taking too many data points for the 20 and 30 microliter sample. They abnormally level off (considering we are linearlizing it with the natural log) at high value of time because its just not decaying fast enough to be able to be distinguished from the noise. We recommend that you shorten the time in between pulses and take data for a shorter absolute time to get a better fit. The slow T2 for the 10 microliter sample may also be a result of some of the distilled water getting on the side of the glass tube. Please see Additional Advise for Students Planning to Do This

How can you improve this?

1) Use you data to determine the pore sizes of the glass beads. See reference 2 and 3.

2) Use more samples than just distilled water and light mineral oil. Do the glass beads always have a greater effect for substances that have a longer T2?

3) See how the glass beads effect T1.

References: