NMR in a low field of a permanent magnet

Transcription

1 Univerza v Ljubljani Fakulteta za matematiko in fiziko Oddelek za fiziko Seminar I a 2.letnik, II.stopnja NMR in a low field of a permanent magnet Author: Janez Lužnik Advisor: prof. dr. Janez Dolinšek Ljubljana, March 2014 Abstract In this seminar we first look at the experimental setup of nuclear magnetic resonance spectroscopy in a magnetic field of a permanent magnet at room temperature. Then we look at two possible practical applications of such a system. In conclusion we also discus some of the advantages and disadvantages of both applications.

2 Table of contents 1 Introduction Nuclear magnetic resonance Spin lattice relaxation Spin spin relaxation Experimental setup Measuring the pore size distribution of cement pastes and mortar Theoretical background Results NMR based liquid explosive detector Measurements of a series of samples Simulation of different alcoholic beverages and shielding effect Conclusions References Introduction Nuclear magnetic resonance (NMR) is a powerful non invasive technique used to measure various physical and chemical properties of molecules or materials. It usually requires strong magnetic fields generated by large superconducting magnets, which have to be cooled by liquid nitrogen and helium. The use of this technique is therefore limited to laboratories with suitable equipment. However systems that enable NMR in permanent fields at room temperature do exist. Some like the one that will be discussed in this paper are also small and portable. They broaden the use of NMR as an investigative technique as they allow on site testing and give fast results. Two practical applications of such system will also be presented. 2

3 2 Nuclear magnetic resonance Nuclear magnetic resonance is a phenomenon in which nuclei in a magnetic field absorb and reemit electromagnetic radiation. The nuclei with spin have a dipole magnetic moment [9,10]: ħ Eq Graph 1: When the external magnetic field is not present, the nuclei are randomly ordered and the sum of their magnetic dipole moments is zero [11]. Graph 2: When the external magnetic field B is present the nuclei allign wiht the filed and the sum of their magnetic dipole moments is now different from zero [11]. is the magnetic moment, ħ is Planck s constant divided by 2π and is the gyromagnetic ratio of the nucleus (the ration between the charge and mass of the nucleus). Gyromagnetic ratio is different for each isotope. For protons it is 42,6/. Nuclei with magnetic moment can only have discrete energy states in the external magnetic field. In the tha case of protons only two states are possible. Either in the direction of the filed +½ or in the opposite direction of the filed ½. The external magnetic field 0,0, determines the energy difference between these two states. ħ ħ Eq Graph 3: Two possible energy states of protons in the external magnetic field B 3

4 The occupation of both energy states is defined by Boltzmann s distribution: ħ. Eq At our conditions (frequency of 2MHz and temperature of 300K) the ratio ħ is about Therefore we can only take into account the linear part of the extrapolation of the exponential function. We can then define the difference between the occupations of both energy states as: ħ. Eq There is an initial magnetization in the sample in the thermal equilibrium, which is aligned with the direction of the field: ħ. Eq The net magnetization behaves in the external filed just as a single magnetic moment would. We can flip the magnetization out of its initial direction for an angle, using a short radiofrequency pulse (perpendicular to the initial magnetization) with the frequency. The flipped magnetization starts to precess around the external magnetic field with the frequency and induces a signal in our detection coil. Graph 4: The induction of NMR signal in the detection coil 2.1. Spin lattice relaxation After the RF pulse is turned off, the magnetization slowly returns towards the equilibrium state. During this process the spin system exchanges the energy with its surrounding and the longitudinal component of the magnetization changes. The process is called spin lattice relaxation and is characterized by the spin lattice relaxation time T 1. The relaxation is described by the following equations [11]: Typical relaxation times for protons are around 2 to 3 seconds. Eq Eq

5 2.2. Spin spin relaxation We can flip the initial magnetization (oriented along the z axis) around the x axis using the π/2 pulse. The magnetization is now perpendicular to the external magnetic filed nad we refer to it as transversal magnetization. After the pulse that was used to flip the magnetization is turned of, the spins preces around the external magnetic filed B 0 with the Larmor frequency in the shape of a cone spiral. Initiall all spins precess in phase. However as time passes the spins begin to dephase and the transverzal magnetization decays towards its equlibrium value of zero. The process is described by the following equations: Eq Eq The spin spin relaxation is characterized by the spin spin relaxation time T 2. It is usually faster than spin lattice relaxation. 3 Experimental setup In the two experiments we used a commercial system Magritek 2 MHz Rock CoreAnalyzer [1]. It is a cylindrical shaped magnet with the proton Larmor frequency of 2MHz. The system uses a heater to keep the magnet temperature at 30 C needed for field stability. The samples of maximal dimensions l = 62 mm and φ = 39 mm sit in a sample chamber, which is isolated form the magnet. All mea surements were done at room temperature. Grpah 5: The complete Magritek 2 MHz Rock CoreAnalyzer system is shown on the left. On the right is a picture of the probe and sample chamber [2]. 5

6 4 Measuring the pore size distribution of cement pastes and mortar Made by mixing water, cement and sand (mortar) or only water and cement (cement pastes), mortars and cement pastes are widely used construction materials. As they harden they become porous, which affects different properties of these materials such as strength and durability. Measuring the pore size distribution gives us information about the types of porosity present in the material and helps us determine the quality of the material [3,4]. During our experiment we analysed four different groups of samples, each group containing six samples. Types of samples are shown in the table below. Type of sample Number of sample (x) Composition cp5 (cement pastes) 1 to 6 1 kg cement paste +500 ml water cp6 (cement pastes) 1 to 6 1 kg cement paste +650 ml water mr5 (mortars) 1 to 6 1 kg cement paste +3 kg sand+500 ml water mr6 (mortars) 1 to 6 1 kg cement paste +3 kg sand+650 ml water Table 1: Sample types 4.1 Theoretical background In porous cement materials, the relaxation can be attributed to three main processes [5]: Eq Our experiment was done in a homogeneous magnetic field so that the diffusion contribution ( ) is negligible. Bulk relaxation ( ) is a slow process compared to the relaxation at the pore surface ( ), which happens much faster due to paramagnetic ions in the concrete, such as iron. Therefore we only measured the surface relaxation that is directly proportional to the pore size ratio [6,7]: Eq V is pore volume, S is the pore surface and ρ 2 is the relaxivity (μm/s), defined as the ability of magnetic compounds to increase the relaxation rates of the surrounding water proton spins. The spin lattice relaxation is also proportional to pore size distribution. Relaxivity is different but the relation is the same as for spin spin relaxation: Eq We fitted the T 2 and T 1 data to a broad distribution of relaxation times, using a NNLS (non negative least squares) algorithm. The stability and accuracy of results are better for T 2 data due to the fact that 100 points per T 2 experiment were used. For T 1 measurements only 20 points per experiment were used. 6

7 4.2 Results We measured the samples after they were immersed in the water for five days, so all the pores accessible to external water were saturated. The CPMG sequence was used in spin spin relaxation measurements. It consists of a π/2 pulse followed, after a specific time τ, by a series of π pulses. These pulses are 2τ apart from one another. Graph 6: CPMG pulse The observed NMR magnetization curve depends upon the T 2 of the broad distribution of all pores Area 1 14 Amplitude (a.u.) Area 2 Area 3 Area 4 0 1E-3 0,01 0, log T2 (ms) Graph 7: Integration areas of T 2 measurements shown on a typical cp group representative (cp53) Areas where the distribution is different form 0 represent different sized pores. We can estimate the pore size value of each area from the total T2 (Eq. 4.2.) calculated by integrating the same area. Area 1, which is the relaxation of crystal bound water, and Area 2, relaxation of capillary bound water are present in all samples. They are also comparable in size due to the logarithmic scale. Area 3 (relaxation of protons in larger pores) and Area 4 (relaxation of protons in cracks and very large pores) appear only in a few samples. The comparison of relaxations from different groups is presented in the graph below. The relaxation curves are shifted vertically for a better view. 7

8 Comparison of typical T 2 from different sample groups Graph 8: T 2 comparison We used the inversion recovery sequence (π pulse followed by π/2 pulse after specific time τ) for T 1 measurements. Graph 9: Inversion recovery sequence We also integrated areas from T 1 measurements, but the borders changed as shown on the graph below. 8

9 0,4 Area 3 0,3 Amplitude (a.u.) 0,2 Area 2 Area 4 0,1 Area 1 0,0 1E-3 0,01 0, log T (ms) Graph 10: Integration areas of T 1 measurements shown on a typical cp group The comparison of the relaxation curves from different groups are shown on»graph 6». Again we shifted them vertically for a better view. Comparison of typical T 1 from different sample groups Graph 11: T 1 comparison In»Table 2«the average values of integrated areas for each sample group are presented. Areas calculated from T2 measurements Name Area 1 Area 2 Area 3 Area 4 Area 1 Average of cp5 group Areas calculated from T1 measurements T2 T1 Area 2 Area 3 Area 4 A1/(A1+A2) A2/(A2+A3) E Average of cp6 group Average of mr5 group Average of mr6 group E E E Table 2: Integration results 9

10 As expected because of the different relaxivities, areas calculated from T 1 and T 2 do not match. Instead we compared the area ratios (last two columns in»table 2«), which matched quite well. They are important, because they offer us direct comparison between the water located in the pores (Area 2) and crystal bound water (Area 1). 5 NMR based liquid explosive detector In the past there were some attempts by terrorists to detonate liquid explosives on commercial planes. As a result of that the amount of liquid that a person can bring on board in hand luggage has been limited to several containers with a volume of 100ml each. A detector that could identify potential threats could increase security checks and possibly allow some lighter restrictions. In this experiment we tested the Magritek 2 MHz Rock CoreAnalyzer as a possible detector, which could discriminate between various liquids on the basis of spin lattice and spin spin relaxation times. 5.1 Measurements of a series of samples As in the previous experiment the spin lattice relaxation was measured with the inversion recovery sequence and the spin spin relaxation with CPMG echo train. We used a large set of samples to construct a model database of relaxation values. Both relaxations were measured in a two step procedure. The first step was a faster and less accurate measurement intended to get an estimated values of T 1 and T 2. In the second step the parameters were corrected according to the estimated values. The difference between the estimated and true values was less than 20% for T 1 measurements, while in the T 2 measurement the estimated and true value mostly matched. T 1 measurement took about 20s and T 1 measurement was significally shorter taking only a few seconds. Our results are shown in T 2 vs T 1 plot on the graph below [8]. Graph 12: T 2 vs T 1 plot of a series of samples 10

11 We divided the samples in several groups. The first group (laboratory chemicals such as ethanol, methanol, toluene, etc.) and the second group (various non alcoholic and alcoholic drinks) overlap slightly with only a few samples form the second group such as milk having shorter relaxation times. 95 and 100 octane petrol and diesel represent the next group. Here the T 1 for diesel (0,7s) was much shorter than T 1 for 95 (2,35s) and 100 (2,64s) octane petrol. Last group were viscous edible samples such as jam, honey, fruits, butter and several vegetable oils. These samples mostly had much shorter T 1 and T 2 values than the rest. 5.2 Simulation of different alcoholic beverages and shielding effect We also did two more experiments. In the first one we simulated different types of alcoholic drinks by mixing together distilled water and ethanol to get the T 1 and T 2 values as a function of ethanol concentration. Graph 13: T 1 (a) and T 2 (b) as a function of ethanol concentration. The fitted curve and some data from real alcoholic samples are added We can observe a minimum at 60% ethanol concentration. The T 1 and T 2 values for real drinks are usually smaller than those of our model system due to the presence of paramagnetic nuclei and some other molecule that affect relaxation dynamics in real drinks. The metal containers often used for liquids can present problems for NMR measurements because of the skin effect. That is the presence of magnetic screening fields generated by RF induced eddy currents in the metal. In our frequency range (2MHz) the skin depth of aluminium is about 1mm, which is close to the thickness of aluminium can. We wanted to test those effects at our system. To 11

12 do that we used a 40ml sample of water with added CuSO 4. First we measured the unshielded bottle. Then the bottle was wrapped with aluminium foil 30μm thick. It was still possible to measure both T 1 and T 2 after wrapping the bottle in though the signal was two times smaller than without the shield. The problem was that we could not tune the resonant circle after adding two layers of foil due to the limited range of capacitors. Graph 14: T1 (left) and T2(right) relaxation curves with and without aluminium shielding 6 Conclusions Measuring the pore size distribution of cement pastes and mortar It is essential to know the properties of mortars and concretes to guarantee their stability and durability. NMR spectroscopy is an ideal tool with which we can inspect such materials without influencing their structure. The pore size distribution ratios were not very specific. We can distinguish among different groups but not among individual samples. Another useful measurement would be effective porosity, which could be done by modifying our system with gradient coils allowing us to measure diffusion constant of water saturated samples. NMR based liquid explosive detector As a liquid explosive detector our system offers simple T 1 and T 2 measurements of large sample volumes. Though the measurements are quite fast for an efficient use they would still need to be faster. Other disadvantages are the lack of spatial resolution and that the proton density cannot be determined. Again as was the case in the first experiment we could benefit from diffusion measurements which are not possible without the gradient coils. 12

13 7 References [1] [2] aachen.com/halbach_magnets.html [3] McCain & Dewoolkar : Porous Concrete Pavements: Mechanical and Hydraulic Properties pdf [4] Hildegard Westphal, Iris Surholt, Christian Kiesl, Holger F. Thern, Thomas Kruspe; Pure appl. geophys. 162 (2005) p.549 [5] NMR Petrophysics. [6] J.H. Strange, J. Mitchell, J.B.W. Webber; Magnetic Resonance Imaging 21 (2003) p.221 [7] R M E Valckenborg, L Pel and K Kopinga; J. Phys. D: Appl. Phys. 35 (2002) p.249 [8] A. Gradišek, J.Luzar, J.Lužnik, T. Apih; Magnetic Resonance Detection of Explosives and Illicit Materials, NATO Science for Peace and Security Series B: Physics and Biophysics 2014, pp. 123 [9] M. H. Levitt: Spin dynamics: Basics of Nuclear Magnetic Resonance; Wiley, Chichester, UK (2008) [10] C. P. Slichter: Principles of Magnetic Resonance; Springer Verlag, Berlin (1996) [11] J. Dolinšek (2012); Spektroskopija trdne snovi, p.33 13