Unilateral Nuclear Magnetic Resonance for Quality Control

Unilateral Nuclear Magnetic Resonance for Quality Control The NMR-MOUSE B. Blümich, S. Anferova, K. Kremer, S. Sharma, V. Herrmann, and A. Segre N uclear magnetic resonance (NMR) spectroscopy and NMR imaging require a sample to be positioned in a homogeneous magnetic field inside a strong magnet. The instrumentation is large, and the sample is carried to the magnet for investigation. In unilateral NMR, the magnetic field is applied to the sample from one side. Such NMR devices can be built small so that they are portable and can be carried to the object. The magnetic field penetrating the object is inhomogeneous, and only a limited number of the wide variety of different NMR experiments can be performed. Nevertheless the information acquired by unilateral NMR is well suited for product and quality control of soft matter like elastomers, food, creams, biological tissue, and wet porous materials. In this article, the principles of unilateral NMR are introduced and demonstrated with applications to elastomers and nondestructive in situ inspection of a wet fresco from ancient Rome, Italy. NMR NMR is a form of radio-frequency (rf) spectroscopy (Figure 1) (1). Magnetic atomic nuclei such as the proton 1 H are contacted in magnetic fields by the magnetic component B 1 of an electromagnetic This article discusses the principles of unilateral nuclear magnetic resonance with applications to elastomers and nondestructive in situ inspection of a wet fresco from ancient Rome. Impulse response: cos{2 L t} exp{ (t/t 2 ) b /b} B 0 Atomic nuclei in a magnetic field L B 0 t t Excitation: rf pulse at frequency rf Spectrometer Figure 1. Nuclear magnetic resonance (NMR) is a form of radiofrequency (rf) spectroscopy in strong magnetic fields. The communication frequency rf is proportional to the strength B 0 of the magnetic field. Radiofrequency impulses are sent to a sample in the magnetic field. The magnetic atomic nuclei such as 1 H answer at a nearby frequency L with an impulse response which, for soft matter in homogeneous fields, often decays like a stretched exponential A exp{ (1/b)(t/T 2 ) b }. 18 Spectroscopy 18(2) February 2003

N Nuclear Magnetic Resonance Transmitter Receiver Time Impulse response in homogeneous fields exp { (t/t 2 ) b /b} NMR echoes in inhomogeneous fields Figure 2 (left). In inhomogeneous magnetic fields, the NMR signal decays very quickly. By means of echoes, the signal can be recovered stroboscopically. The echo envelope approximates the signal decay in a homogeneous magnetic field. Echoes are generated by trains of many rf pulses from the transmitter. Magnet rf transmitter and receiver rf field: 20 MHz S Magnetic field: 0.5 T Sensitive volume Antenna Magnet Figure 3 (left). Conventional NMR spectrometer and NMR-MOUSE. In conventional NMR, the sample is positioned inside the homogeneous region of a superconducting magnet (left). Conventional NMR spectrometers and NMR imagers for medical tomogaphy are stationary, and the sample or the patient are brought to the spectrometer for investigation. In mobile NMR, the equipment is small and portable (bottom right). Often the magnetic fields are applied to the object from one side. The NMR-MOUSE is a mobile unilateral NMR sensor for materials analysis in product and quality control. The magnet may be u-shaped or bar-shaped. The signal is generated and detected in a sensitive volume above the surface of the NMR-MOUSE, where the lines of the magnetic field and the rf field have perpendicular components (top right). wave. The frequency rf of that wave is proportional to the strength B 0 of the magnetic field. For a field strength of B 0 0.5 T, the frequency for protons is rf 20 MHz, which is a frequency in the short-wave rf band. The contact is achieved by rf excitation pulses a few microseconds long. In homogeneous magnetic fields, the atomic nuclei respond with an rf signal that oscillates at a frequency L in the vicinity of the excitation frequency rf and decays with a time constant T 2. The protons in different chemical groups in a molecule have slightly different response frequencies L.The distribution of response frequencies is the NMR spectrum, which provides detailed information about the chemical structure of molecules. This is why NMR spectroscopy is probably the most important method for structural analysis in analytical chemistry and molecular biology. In inhomogeneous magnetic fields, the NMR frequency is different at different locations within the sample. This fact is exploited in NMR imaging by applying linear field variations across the 20 Spectroscopy 18(2) February 2003 object in different directions, so that an image of the object can be reconstructed from NMR spectra measured in such gradient fields. NMR imaging has become an indispensable tool for medical diagnostics, with an increasing number of applications in material science and chemical engineering. When the magnetic field does not vary linearly across the object, images and meaningful distributions of NMR frequencies L are hard to measure, but the decay time T 2 of the impulse response in homogeneous fields can still be obtained by a trick (Figure 2): although in inhomogeneous magnetic fields, the impulse response decays much faster than in homogeneous fields, the signal can be made to reappear stroboscopically as echoes of the impulse response by applying further rf pulses. The decay time constant T 2 can then be derived from the envelope of a train of echoes by fitting an exponential function to the experimental data. T 2 is called the transverse relaxation time in NMR. Its value is determined by the time scale and geometry of molecular motion. In liquids T 2 is of the order of 1 s, in soft solid matter it is in the range of 1 ms, and in rigid polymers it can be as short as 20 s. In general, the shorter the T 2, the harder the material. Therefore, T 2 is a good NMR parameter to measure for materials characterization. There is another relaxation time T 1 in NMR, which determines how fast the thermodynamic equilibrium is reached after excitation of an echo train, so that the experiment can be repeated. T 1 is larger than or equal to T 2 and typically in the range of 0.1 to 1 s for protons. The NMR-MOUSE NMR spectroscopy and NMR imaging require expensive equipment, because the magnetic field needs to be extremely homogeneous and strong to measure the discrete distributions of frequencies in the parts-per-million range for discrimination of different chemical groups in complex molecules (Figure 3). Furthermore, in imaging, the magnets need to be large enough to accommodate objects

Measurements at different positions the size of a human body. In unilateral NMR, a magnet and the rf communication antenna usually the coil of a resonant rf circuit are placed on the object, which can be much larger than the magnet. Homogeneous fields are difficult to achieve, so that the relaxation times T 2 and related parameters are measured by NMR echo methods. With permanent magnets, NMR sensors as small as the size of a computer mouse can be built and positioned on intact objects at different places to measure T 2 (2). Small mobile NMR sensors of this type have been named NMR-MOUSE, for MObile Universal Surface Explorer (RWTH, Aachen, Germany) (3). They can be built from u-shaped magnets with an rf coil as an antenna positioned in the gap of the magnet (4), or from a simple magnet block with an rf coil located at the face of the north or the 22 Spectroscopy 18(2) February 2003 10 mm Relative amplitude 100 80 60 40 20 Relative number of counts 0 Mean value Relaxation time T 2 a(t) A exp { (1/b)(t/T 2 ) b } 0 10 20 30 40 50 t E (ms) Measurements at the same position Figure 4. Analysis of transverse magnetization decays in inhomogeneous fields for inhomogeneous samples. NMR imaging reveals that most technical rubber products are inhomogeneous, such as the sheet shown here (top left). In inhomogeneous fields, the magnetization decay is probed stroboscopically by a train of NMR echoes; for example, 800 echoes are shown for a sample of carbon-black filled natural rubber (top right). By fitting the experimental data with a stretched exponential function, the amplitude A, the relaxation time T 2, and the stretched exponent b are obtained. All are characteristic of the sample properties. A measures the number of signal protons in the sensitive volume covering the sample, and T 2 measures the stiffness or modulus of the material. In inhomogeneous materials such as technical rubber products, these parameters show a distribution with a mean value and a variance (bottom). south pole. Depending on the size of the coil, different measurement depths can be reached in the object. With a 20-mmdiameter solenoidal coil, a 10-mm depth can be accessed; with a meander coil having a wire spacing of 0.5 mm, the sensitive volume is limited to a depth of about 0.2 mm, suitable for analysis of membranes and single sheets of paper. This type of unilateral NMR has been pioneered in the bore-hole inspection business for oil prospecting, where echo trains are measured from the fluids in the porous rocks forming the walls of a bore hole (5). Entire NMR spectrometers are lowered down oilwell holes as much as 10 km deep. The echo signals measured for a water- and oil-filled rock matrix with a pore size distribution are analyzed for a distribution P(T 2 ) of relaxation times T 2 by inverse Laplace transformation of the echo envelope. Several studies show that this distribution translates into a distribution of pore sizes because, in most cases, the contact of rapidly diffusing fluid molecules with the pore walls governs the magnetization loss, and T 2 is proportional to the pore size. In strongly inhomogeneous fields, the measured values of T 2 also depend on the particular measurement conditions and the geometry of the NMR sensor; however, with reference to standard measurement conditions, relaxation times and relaxation time distributions can be obtained that are indicative of material properties such as chain stiffness in elastomers and pore size distributions in fluid-filled porous media. Also in elastomers, the observed echo envelope is usually more complicated than a simple exponential. A good fitting function for experimental data is the stretched exponential function a(t) A exp{ (1/b)(t/T 2 ) b } (Figure 4). Compared to an intuitively more appealing biexponential function, only three parameters A, b, and T 2 instead of four need to be fitted, and the fit is less sensitive against noise. Applications Most natural products and many synthetic ones are inhomogenous on different space scales. For examples, rubber products are 3-D networks of macromolecular chains filled with various additives, such as waxes and mineral fillers or carbon black. The 3-D network is formed while using a specified formulation of components after mixing in a process similar to baking bread, making the dough according to a particular recipe. The formation of cross-links and the distribution of filler particles are statistical. So there are short and long intercrosslink chains as well as regions with few and regions with many filler particles. In addition, filler particles may aggregate, the curing temperatures may be distributed unevenly, and the wrong constituents may have been chosen accidentally for compounding. For economical reasons, mixing and curing times are kept as short as possible to meet the required specifications of the product. The consequences are twofold: First, to assure equal product quality over

T 2 (ms) T 2 (ms) Nuclear Magnetic Resonance 1 0.1 7.6 7.4 7.2 7.0 6.8 6.6 S 1 16 18 20 22 24 24 Spectroscopy 18(2) February 2003 S y X 180 C 160 C 140 C Relative number of chemical cross-links of type S 1, S 2, S x cis-br (Type A) I-BR cis-br (Type B) Coil background S 1 S NR S Increasing cross-link density S x SBR S x S 2 S 2 N-SBR C C tr90 t90 Curing temperature of carbon-black filled NR Room temperature 3,4IR 100 80 60 40 20 0 20 40 Glass transition temperature T g ( C) at 1 Hz long times as personnel change or get tired and as machines wear out, continuous product monitoring is required for comparison of the current product quality with that of a chosen reference product. Second, due to the statistical nature of cross-links, filler, and defect distributions, a single measurement of a product property such as the hardness of a rubber part at a selected spot will be insufficient. Rather, the property should be tested at different equivalent spots and its distribution should be analyzed for example, in terms of the statistical mean and its standard deviation (Figure 4). Figure 5 (top left). NMR relaxation time T 2 and chain stiffness. Sulfur vulcanization produces a variety of chemical structures including crosslinks (S 1, S 2, S x ) with different numbers (1, 2, x) of sulfur atoms S. The reaction products change continuously with increasing curing time also beyond reversion. For example, the rheometer moments at the curing times t90 before and tr90 after reversion are the same, but T 2 is different. Because T 2 is a measure of the segmental mobility, the curing process can also be followed beyond the point of reversion with a sensitivity different from that of swelling and rheometer measurements. Figure 6 (bottom left). NMR relaxation times T 2 at room temperature for different technical elastomers as a function of the glass transition temperature T g (5). T g increases and T 2 decreases with increasing cross-link density. An illustrative example of product inhomogeneity on a scale of 0.1 mm is shown in Figure 4 by example of a proton-density image of a cross-linked sample from natural rubber (NR) that was not filled with carbon black. The spots that become visible in the NMR image are agglomerates of zinc oxide, which is part of the formulation for improving the vulcanization process. Similar features are observed in most technical rubber products. At a given position, the transverse relaxation time T 2 can be detected with an accuracy of better than 1%, and accordingly, the distribution of relaxation times obtained from repetitive measurements of T 2 is narrow. Measurement of T 2 at different but equivalent, randomly chosen spots of that sample produces a significantly broader distribution of relaxation times. The mean of the distribution is a measure of the segmental mobility of the cross-link chains, which is often dominated by the influence of the cross-link density. The variance measures the distribution of segmental mobility or cross-link density values from one measurement spot to the next. The size of each spot is determined by the size of the sensitive volume of the sensor. Typically it is of the size of a small coin. A remarkable feature of such NMR measurement is that the value of T 2 scales with the chemical

Spectrometer NMR-MOUSE with sample Relaxation time (ms) 14 12 10 8 0 10 20 30 40 50 Curing time (days) Glass Glass with primer and adhesive Glass with primer, adhesive and iron sheet Figure 7. Moisture curing of a polyurethane adhesive in a three-layer phantom of glass/rubber-adhesive/iron sheet representing a car windshield glued into a steel frame. 26 Spectroscopy 18(2) February 2003 Circle 23, 24

T 2 pore size 4 h 45 min 4 h 13 min 3 h 34 min Drying time 2 h 12 min Probability density 0 h 56 min 0 h 00 min 0.1 1 10 T 2 (ms) Small pores Large pores Brick near fresco Fresco Dry brick of newer wall Frequency (not normalized) Small pores Large pores 0.1 1 10 Relaxation time (ms) Figure 8. Pore-size distributions from the distribution of relaxation times derived by inverse Laplace transformation of experimental magnetization decays. In a drying study of a sample from natural stone (pietra di noto), a bimodal pore-size distribution is observed (top). The large pores dry first, the small ones later. In a wet Roman fresco, we observed water in the large and the small pores (bottom). In a brick next to the fresco, the large pores had less water. In another wall the large pores were dry. 28 Spectroscopy 18(2) February 2003

cross-link density, and is largely independent of the type of filler. Filler inhomogeneities show up in the distribution of signal amplitudes A. Usually the formulation of a technical rubber product is tested on a rheometer, where a test sample is vulcanized, undergoing small oscillatory shear deformation. During curing, the torque increases to a maximum and decreases on further curing following reversion of the cross-linking reaction. From the theory of rubber elasticity, it is known that the torque at small deformation is a direct measure of the crosslink density. The degree of swelling is also a measure of the cross-link density and is in good agreement with torque measurements. Torque, as well as swelling measurements, cannot discriminate between rubber samples cured to assume the same cross-link density, but before and after the point of reversion. Interestingly, the NMR relaxation times can make that discrimination (Figure 5). In many cases NMR relaxation times continue to decrease with increasing curing time also beyond the point of reversion of the cross-link density. An explanation of the phenomenon must be sought in the details of the chemistry going on during formation and destruction of cross-links, and during chain scission. Figure 6 illustrates the range of relaxation times for a number of technical elastomers with different cross-link density cured to the maximum rheometer torque (6). They are shown as a function of the glass transition temperature, where the rubber elasticity is lost on cooling and the material becomes energy elastic, like many rigid bodies. With increasing cross-link density T 2 decreases and T g increases. NMR relaxation measurements have turned out to be extremely useful for quality control of elastomer products in connection with a database of reference values for different formulations and curing parameters. Moreover, with the mobile NMR-MOUSE, the properties of the final product can be compared with those of the vulcameter reference sample. A related application is the monitoring of the curing process (7) of thicklayer polyurethane rubber adhesive (Figure 7). Such adhesives are used in the vehicle industry for example, to glue windshields into passenger cars. Increasing demands on shorter curing times and higher temperature resistance led to more critical formulations of adhesives. In a pilot study, we have shown that the state of curing can be monitored by the NMR-MOUSE in a glass/ adhesive/sheet-iron layer composite despite the presence of the ferromagnetic steel representing the car frame. Suprisingly, the adhesive takes several days to fully cure instead of only a few. The nondestructiveness of the unilateral NMR analysis is of particular value when historical objects are to be examined. Together with Bruker Biospin (Milano, Italy, and Rheinstetten, Germany), and the University of Rome (Italy), we are developing and testing 30 Spectroscopy 18(2) February 2003 Circle 26

the NMR-MOUSE for its use in assessing the state of preservation of objects of cultural heritage. In a cryptoporticus at Colle Oppio in Rome, we examined a wet ancient Roman fresco as well as the bricks in the surrounding walls (Figure 8). Approaching the precious fresco to a distance as close as 1 mm, we measured the signal of the water in the pores without touching the fresco. Following the procedures developed for oil-well analysis, the echo envelope was then analyzed by inverse Laplace transformation for a distribution of relaxation times. Although some signal loss has to be accounted for by translational selfdiffusion in the highly inhomogeneous magnetic field of the NMR-MOUSE, the signal amplitude at short T 2 can nevertheless be attributed to water in small pores, and the signal at large T 2 to water in large pores. The wet fresco showed strong signals at both small and large T 2, so small and large pores were filled with water. The brick wall supporting the fresco gave similar results, in particular when considering that the bricks have a pore size distribution different from the fresco material. On the other hand, the bricks in another, dryer part of a different wall of the cryptoporticus showed low signal at high T 2. This is in line with laboratory drying studies, which show that during drying the NMR signal vanishes first from the large pores and only later from the small pores. By calibration with laboratory samples including established mercury porosimetry studies on test samples, the nondestructive measurements by the NMR-MOUSE can be used to quantify the distribution of the waterfilled pores. Due to magnetic impurities in many building materials, this is a nontrivial task and the subject of ongoing research. Summary NMR is mostly known for its use in chemical analysis and medical diagnostics. An important but largely unnoticed application is in well logging. The same principle is used for the NMR- MOUSE, which is positioned at or near an object to measure NMR parameters like the relaxation time T 2 and the signal amplitude A from one side within the object. Unilateral NMR is particularly useful for quality control of technical elastomer products, where the state of processing and vulcanization can be assessed providing information complementary to that of swelling and rheometer measurements. In particular, cross-link density and the revision process in curing can often be followed unambiguously. Potentially valuable applications are also anticipated in food analysis. The nondestructiveness of testing is of outstanding value in the analysis of historical treasures. Although the NMR-MOUSE measures the same parameters that determine the contrast in medical NMR images, the instrument is small, mobile, and two orders of magnitude less in price. Acknowledgments Work on the NMR-MOUSE has greatly benefited from continuous support by Deutsche Forschungsgemeinschaft (DFG, Bonn, Germany). A comparative evaluation of the use of the NMR- MOUSE in the rubber industry is conducted in cooperation with industrial partners in a project supported by Bundesministerium für Bildung und Forschung (BMBF, Bonn, Germany). The experiments on Cultural Heritage were performed as part of the EUREKA project Eurocare!2214-MOUSE of the European Community in collaboration with Bruker Biospin in Milano, Italy (Giovanni Bizarro and Fabio Tedoldi) and Rheinstetten, Germany (Dieter Schmalbein), as well as the University of Rome (Franco de Luca and Cinzia Casieri). New NMR-MOUSE sensors were developed in cooperation with INTECH-Thüringen GmbH (Waltershausen, Germany). References 1. B. Blümich, NMR Imaging of Materials (Clarendon Press, Oxford, UK, 2000). 2. G.A. Matzkanin, A Review of Unilateral Nuclear Magnetic Resonance for Quality Control continued on page 73 32 Spectroscopy 18(2) February 2003 Circle 28

The Baseline iron nuclei back into resonance with the emitted gamma ray photons. Interested readers are directed to the Suggested Reading section for more detailed information about this fascinating form of spectroscopy. Reference 1. R.H. Holm, et al., J. Am. Chem. Soc. 96(8), 2644 2646 (1974). Suggested Reading 1. R.S. Drago, chapter 15 of Physical Methods for Chemists 2nd ed. Saunders College Publishing: Philadelphia, PA, 1992, and references listed therein. 2. http://scienceworld.wolfram.com/ physics/moessbauerspectroscopy.html (accessed September 24, 2002). 3. http://hyperphysics.phy-astr.gsu.edu/ hbase/nuclear/mossfe.html (accessed September 24, 2002). 4. http://www.nobel.se/physics/laureates/1961/mossbauer-bio.html (accessed September 24, 2002). 5. http://www.webres.com/mossbauer_ detail.html (accessed September 24, 2002). Unilateral Nuclear Magnetic Resonance for Quality Control continued from page 32 Nondestructive Characterization of Composites Using NMR, in Nondestructive Characterization of Materials, eds. P. Höller, V. Hauck, G. Dobmann, C. Ruud, and R. Green (Springer, Berlin, Germany, 1989), 655 669. 3. G. Eidmann, R. Savelsberg, P. Blümler, and B. Blümich, J. Magn. Reson. A 122, 104 109 (1996). 4. S. Anferova, V. Anferov, M. Adams, P. Blümler, N. Routley, K. Hailu, K. Kupferschläger, M.J.D. Mallett, G. Schröder, S. Sharma, and B. Blümich, Magn. Reson. Eng. 15, 15 22 (2002). 5. G.R. Coates, L. Xiao, and M.G. Prammer, NMR Logging, Principles and Applications, (Gulf Publishing, Houston, TX, 1999). 6. V. Herrmann, K. Unseld, H.B. Fuchs, and B. Blümich, Colloid and Polymer Science 280, 738 746 (2002). 7. A. Hartwig and B. Wolter, Adhäsion 12, 34 38 (2001). B. Blümich is a professor at the Institute for Technical Chemistry and Macromolecular Chemistry, RWTH, D-52056, Aachen, Germany, and president of AixNMR Zentrum für Magnetische Resonanz e.v., Bergstraße 31, D-52159, Rott, Germany. S. Anferova is a visiting scientist at the Institute for Technical Chemistry and Macromolecular Chemistry and senior lecturer at Kaliningrad State University, 236041 Kaliningrad, Russia. K. Kremer is a doctoral student at the Institute for Technical Chemistry and Macromolecular Chemistry, RWTH, D-52056, Aachen, Germany, and assistant to the director of AixNMR Zentrum für Magnetische Resonanz e.v. S. Sharma is a doctoral student at the Institute for Technical Chemistry and Macromolecular Chemistry. V. Herrmann is manager in chemical technology at Dunlop GmbH, Dunlopstr. 2, D-63450 Hanau, Germany. A. Segre is director of research at the Institute of Chemical Methodologies of CNR, 00016 Monterotondo Stazione, Rome, Italy. Circle 54 February 2003 18(2) Spectroscopy 73