Unilateral Nuclear Magnetic Resonance for Quality Control · uclear magnetic resonance (NMR) spectroscopy and NMR imaging require a sam-ple to be positioned in a ho-mogeneous magnetic

uclear magnetic resonance(NMR) spectroscopy andNMR imaging require a sam-ple to be positioned in a ho-

mogeneous magnetic field inside astrong magnet. The instrumentation islarge, and the sample is carried to themagnet for investigation. In unilateralNMR, the magnetic field is applied tothe sample from one side. Such NMRdevices can be built small so that theyare portable and can be carried to theobject. The magnetic field penetratingthe object is inhomogeneous, and only alimited number of the wide variety ofdifferent NMR experiments can be per-formed. Nevertheless the information

N

18 Spectroscopy 18(2) February 2003

Unilateral Nuclear Magnetic Resonance for Quality ControlThe NMR-MOUSE

B. Blümich, S. Anferova, K. Kremer, S. Sharma, V. Herrmann, and A. Segre

acquired by unilateral NMR is wellsuited for product and quality control ofsoft matter like elastomers, food,creams, biological tissue, and wetporous materials. In this article, theprinciples of unilateral NMR are intro-duced and demonstrated with applica-tions to elastomers and nondestructivein situ inspection of a wet fresco fromancient Rome, Italy.

NMRNMR is a form of radio-frequency (rf)spectroscopy (Figure 1) (1). Magneticatomic nuclei such as the proton 1H arecontacted in magnetic fields by the mag-netic component B1 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.

N

Nuclear Magnetic Resonance

Figure 1. Nuclearmagnetic resonance(NMR) is a form of radio-frequency (rf)spectroscopy in strongmagnetic fields. Thecommunicationfrequency �rf isproportional to thestrength B0 of themagnetic field. Radio-frequency impulses aresent to a sample in themagnetic field. Themagnetic atomic nucleisuch as 1H answer at anearby frequency �L withan impulse responsewhich, for soft matter inhomogeneous fields,often decays like astretched exponential A � exp{�(1/b)(t/T2)

b}.Spectrometer

Atomic nuclei ina magnetic field

B0

t t

Excitation:rf pulse at frequency �rf

Impulse response:cos{2��Lt} exp{�(t/T2)

b/b}

�L∝B0

www.spectroscopyonl ine.com

www.spectroscopyonl ine.com20 Spectroscopy 18(2) February 2003


wave. The frequency �rf of that wave isproportional to the strength B0 of themagnetic field. For a field strength of B0

� 0.5 T, the frequency for protons is �rf �20 MHz, which is a frequency in theshort-wave rf band. The contact isachieved by rf excitation pulses a few mi-croseconds long. In homogeneous mag-netic fields, the atomic nuclei respondwith an rf signal that oscillates at a fre-quency �L in the vicinity of the excitationfrequency �rf and decays with a time con-stant T2. The protons in different chemi-cal groups in a molecule have slightly dif-ferent response frequencies �L. Thedistribution of response frequencies is theNMR spectrum, which provides detailedinformation about the chemical structureof molecules. This is why NMR spec-troscopy is probably the most importantmethod for structural analysis in analyti-cal chemistry and molecular biology.

In inhomogeneous magnetic fields,the NMR frequency is different at dif-ferent locations within the sample. Thisfact is exploited in NMR imaging by ap-plying linear field variations across the

object in different directions, so that animage of the object can be recon-structed from NMR spectra measuredin such gradient fields. NMR imaginghas become an indispensable tool formedical diagnostics, with an increasingnumber of applications in material sci-ence and chemical engineering. Whenthe magnetic field does not vary lin-early across the object, images andmeaningful distributions of NMR fre-quencies �L are hard to measure, butthe decay time T2 of the impulse re-sponse in homogeneous fields can stillbe obtained by a trick (Figure 2): al-though in inhomogeneous magneticfields, the impulse response decaysmuch faster than in homogeneousfields, the signal can be made to reap-pear stroboscopically as echoes of theimpulse response by applying further rfpulses. The decay time constant T2 canthen be derived from the envelope of atrain of echoes by fitting an exponentialfunction to the experimental data. T2 iscalled the transverse relaxation time inNMR. Its value is determined by the

time scale and geometry of molecularmotion. In liquids T2 is of the order of1 s, in soft solid matter it is in the rangeof 1 ms, and in rigid polymers it can beas short as 20 �s. In general, the shorterthe T2, the harder the material. There-fore, T2 is a good NMR parameter tomeasure for materials characterization.There is another relaxation time T1 inNMR, which determines how fast thethermodynamic equilibrium is reachedafter excitation of an echo train, so thatthe experiment can be repeated. T1 islarger than or equal to T2 and typicallyin the range of 0.1 to 1 s for protons.

The NMR-MOUSENMR spectroscopy and NMR imagingrequire expensive equipment, becausethe magnetic field needs to be extremelyhomogeneous and strong to measure thediscrete distributions of frequencies inthe parts-per-million range for discrimi-nation of different chemical groups incomplex molecules (Figure 3). Further-more, in imaging, the magnets need tobe large enough to accommodate objects

TimeTransmitter

Receiver

Impulse response in homogeneous fieldsexp {�(t/T2)

b/b}

NMR echoes in inhomogeneous fields

Figure 2 (left). In inhomogeneous magneticfields, the NMR signal decays very quickly. Bymeans of echoes, the signal can be recoveredstroboscopically. The echo envelopeapproximates the signal decay in ahomogeneous magnetic field. Echoes aregenerated by trains of many rf pulses from thetransmitter.

Magnet

N

S

rf field: 20 MHz Magneticfield: 0.5 T

Antenna

Magnet

Sensitive volume

Magnet

rf transmitterand receiver

Figure 3 (left). Conventional NMR spectrometerand NMR-MOUSE. In conventional NMR, thesample is positioned inside the homogeneousregion of a superconducting magnet (left).Conventional NMR spectrometers and NMRimagers for medical tomogaphy are stationary,and the sample or the patient are brought to thespectrometer for investigation. In mobile NMR,the equipment is small and portable (bottomright). Often the magnetic fields are applied tothe object from one side. The NMR-MOUSE is amobile unilateral NMR sensor for materialsanalysis in product and quality control. Themagnet may be u-shaped or bar-shaped. Thesignal is generated and detected in a sensitivevolume above the surface of the NMR-MOUSE,where the lines of the magnetic field and the rffield have perpendicular components (top right).



the size of a human body. In unilateralNMR, a magnet and the rf communica-tion antenna — usually the coil of a res-onant rf circuit — are placed on the ob-ject, which can be much larger than themagnet. Homogeneous fields are diffi-cult to achieve, so that the relaxationtimes T2 and related parameters aremeasured by NMR echo methods. Withpermanent magnets, NMR sensors assmall as the size of a computer mousecan be built and positioned on intact ob-jects at different places to measure T2

(2). Small mobile NMR sensors of thistype have been named NMR-MOUSE,for MObile Universal Surface Explorer(RWTH, Aachen, Germany) (3). Theycan be built from u-shaped magnetswith an rf coil as an antenna positionedin the gap of the magnet (4), or from asimple magnet block with an rf coil lo-cated at the face of the north or the

south pole. Depending on the size of thecoil, different measurement depths canbe reached in the object. With a 20-mm-diameter solenoidal coil, a 10-mm depthcan be accessed; with a meander coilhaving a wire spacing of 0.5 mm, thesensitive volume is limited to a depth ofabout 0.2 mm, suitable for analysis ofmembranes and single sheets of paper.

This type of unilateral NMR hasbeen pioneered in the bore-hole inspec-tion business for oil prospecting, whereecho trains are measured from the flu-ids in the porous rocks forming thewalls of a bore hole (5). Entire NMRspectrometers are lowered down oil-well holes as much as 10 km deep. Theecho signals measured for a water- andoil-filled rock matrix with a pore sizedistribution are analyzed for a distribu-tion P(T2) of relaxation times T2 by in-verse Laplace transformation of the

echo envelope. Several studies showthat this distribution translates into adistribution of pore sizes because, inmost cases, the contact of rapidly dif-fusing fluid molecules with the porewalls governs the magnetization loss,and T2 is proportional to the pore size.

In strongly inhomogeneous fields,the measured values of T2 also dependon the particular measurement condi-tions and the geometry of the NMRsensor; however, with reference to stan-dard measurement conditions, relax-ation times and relaxation time distri-butions can be obtained that areindicative of material properties such aschain stiffness in elastomers and poresize distributions in fluid-filled porousmedia. Also in elastomers, the observedecho envelope is usually more compli-cated than a simple exponential. A goodfitting function for experimental data isthe stretched exponential function a(t)� A � exp{�(1/b)(t/T2)b} (Figure 4).Compared to an intuitively more ap-pealing biexponential function, onlythree parameters — A, b, and T2 — in-stead of four need to be fitted, and thefit is less sensitive against noise.

ApplicationsMost natural products and many syn-thetic ones are inhomogenous on differ-ent space scales. For examples, rubberproducts are 3-D networks of macromol-ecular chains filled with various addi-tives, such as waxes and mineral fillers orcarbon black. The 3-D network is formedwhile using a specified formulation ofcomponents after mixing in a processsimilar to baking bread, making thedough according to a particular recipe.The formation of cross-links and the dis-tribution of filler particles are statistical.So there are short and long intercross-link chains as well as regions with fewand regions with many filler particles. Inaddition, filler particles may aggregate,the curing temperatures may be distrib-uted unevenly, and the wrong con-stituents may have been chosen acciden-tally for compounding. For economicalreasons, mixing and curing times arekept as short as possible to meet the re-quired specifications of the product.

The consequences are twofold: First,to assure equal product quality over

10 mm

tE(ms)0 10 20 30 40 50

100

0

20

40

60

80

Rela

tive

ampl

itude

Relaxation time T2

Mean value

Relative number of counts

Measurements atthe same position

Measurements atdifferent positions

a(t) � A exp {�(1/b)(t/T2)b}

Figure 4. Analysis of transverse magnetization decays in inhomogeneous fields for inhomogeneoussamples. NMR imaging reveals that most technical rubber products are inhomogeneous, such as thesheet shown here (top left). In inhomogeneous fields, the magnetization decay is probedstroboscopically by a train of NMR echoes; for example, 800 echoes are shown for a sample ofcarbon-black filled natural rubber (top right). By fitting the experimental data with a stretchedexponential function, the amplitude A, the relaxation time T2, and the stretched exponent b areobtained. All are characteristic of the sample properties. A measures the number of signal protons inthe sensitive volume covering the sample, and T2 measures the stiffness or modulus of the material.In inhomogeneous materials such as technical rubber products, these parameters show adistribution with a mean value and a variance (bottom).



An illustrative example of productinhomogeneity on a scale of 0.1 mm isshown in Figure 4 by example of aproton-density image of a cross-linkedsample from natural rubber (NR) thatwas not filled with carbon black. Thespots that become visible in the NMRimage are agglomerates of zinc oxide,which is part of the formulation for im-proving the vulcanization process. Sim-ilar features are observed in most tech-nical rubber products. At a givenposition, the transverse relaxation timeT2 can be detected with an accuracy ofbetter than 1%, and accordingly, thedistribution of relaxation times ob-tained from repetitive measurements ofT2 is narrow. Measurement of T2 at dif-ferent but equivalent, randomly chosenspots of that sample produces a signifi-cantly broader distribution of relax-ation times. The mean of the distribu-tion is a measure of the segmentalmobility of the cross-link chains, whichis often dominated by the influence ofthe cross-link density. The variancemeasures the distribution of segmentalmobility or cross-link density valuesfrom one measurement spot to thenext. The size of each spot is deter-mined by the size of the sensitive vol-ume of the sensor. Typically it is of thesize of a small coin. A remarkable fea-ture of such NMR measurement is thatthe value of T2 scales with the chemical

16 18 20 22 24

6.6

6.8

7.0

7.2

7.4

7.6

180 °C 160 °C 140 °C

t90

tR90

T 2(m

s)

Relative number of chemical cross-links of type S1, S2, Sx

C

C

X

S S

S2S2Sx

Sx

S1

S1

Sy

Curing temperature ofcarbon-black filled NR

Figure 5 (top left). NMR relaxation time T2 andchain stiffness. Sulfur vulcanization produces avariety of chemical structures including cross-links (S1, S2, Sx) with different numbers (1, 2, x)of sulfur atoms S. The reaction products changecontinuously with increasing curing time alsobeyond reversion. For example, the rheometermoments at the curing times t90 before andtr90 after reversion are the same, but T2 isdifferent. Because T2 is a measure of thesegmental mobility, the curing process can alsobe followed beyond the point of reversion witha sensitivity different from that of swelling andrheometer measurements.

Room temperature

3,4IR

N-SBR

SBR

NR

I-BR

cis-BR (Type B)

cis-BR (Type A)

Increasing

cross-link density

Coil background

0.1

1

T 2 (m

s)

�100 �80 �60 �40 �20 0 20 40

Glass transition temperature Tg(° C) at 1 Hz

Figure 6 (bottom left). NMR relaxation timesT2 at room temperature for different technicalelastomers as a function of the glass transitiontemperature Tg (5). Tg increases and T2decreases with increasing cross-link density.

long times as personnel change or gettired and as machines wear out, contin-uous product monitoring is requiredfor comparison of the current productquality with that of a chosen referenceproduct. Second, due to the statisticalnature of cross-links, filler, and defectdistributions, a single measurement of a

product property — such as the hard-ness of a rubber part at a selected spot— will be insufficient. Rather, the prop-erty should be tested at different equiv-alent spots and its distribution shouldbe analyzed — for example, in terms ofthe statistical mean and its standard de-viation (Figure 4).



0 10 20 30 40 50

14

12

10

8

Curing time (days)

Glass with primeradhesive and iron sheet

,Glass with primerand adhesiveGlass

NMR-MOUSE with sample

Spectrometer

Rela

xatio

n tim

e (m

s)

Circle 23, 24

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.

28 Spectroscopy 18(2) February 2003


4 h 45 min

4 h 13 min

3 h 34 min

2 h 12 min

0 h 56 min

0 h 00 min

Prob

abili

ty d

ensit

y

T2 (ms)

Drying time

Large poresSmall pores

T2 pore size

Small pores

Large pores

FrescoBrick near fresco

Freq

uenc

y (n

ot n

orm

aliz

ed)

Dry brick ofnewer wall

0.1 1 10

Relaxation time (ms)

0.1 1 10

Figure 8. Pore-size distributions from the distribution of relaxation times derived by inverse Laplace transformation of experimental magnetizationdecays. 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, thesmall 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 hadless water. In another wall the large pores were dry.

www.spectroscopyonl ine.com



cross-link density, and is largely inde-pendent of the type of filler. Filler inho-mogeneities show up in the distributionof signal amplitudes A.

Usually the formulation of a techni-cal rubber product is tested on arheometer, where a test sample is vul-canized, undergoing small oscillatoryshear deformation. During curing, thetorque increases to a maximum and de-creases on further curing following re-version of the cross-linking reaction.From the theory of rubber elasticity, itis known that the torque at small defor-mation is a direct measure of the cross-link density. The degree of swelling isalso a measure of the cross-link densityand is in good agreement with torquemeasurements. Torque, as well asswelling measurements, cannot dis-criminate between rubber samplescured to assume the same cross-linkdensity, but before and after the pointof reversion. Interestingly, the NMR re-laxation times can make that discrimi-nation (Figure 5). In many cases NMR

relaxation times continue to decreasewith increasing curing time also beyondthe point of reversion of the cross-linkdensity. An explanation of the phenom-enon must be sought in the details ofthe chemistry going on during forma-tion and destruction of cross-links, andduring chain scission. Figure 6 illus-trates the range of relaxation times for anumber of technical elastomers withdifferent cross-link density cured to themaximum rheometer torque (6). Theyare shown as a function of the glasstransition temperature, where the rub-ber elasticity is lost on cooling and thematerial becomes energy elastic, likemany rigid bodies. With increasingcross-link density T2 decreases and Tg

increases. NMR relaxation measure-ments have turned out to be extremelyuseful for quality control of elastomerproducts in connection with a databaseof reference values for different formu-lations and curing parameters. More-over, with the mobile NMR-MOUSE,the properties of the final product can

be compared with those of the vul-cameter reference sample.

A related application is the monitor-ing of the curing process (7) of thick-layer polyurethane rubber adhesive(Figure 7). Such adhesives are used inthe vehicle industry — for example, toglue windshields into passenger cars.Increasing demands on shorter curingtimes and higher temperature resistanceled to more critical formulations of ad-hesives. In a pilot study, we have shownthat the state of curing can be moni-tored by the NMR-MOUSE in a glass/adhesive/sheet-iron layer composite de-spite the presence of the ferromagneticsteel representing the car frame. Supris-ingly, the adhesive takes several days tofully cure instead of only a few.

The nondestructiveness of the unilat-eral NMR analysis is of particular valuewhen historical objects are to be exam-ined. Together with Bruker Biospin(Milano, Italy, and Rheinstetten, Ger-many), and the University of Rome(Italy), we are developing and testing

Circle 26



the NMR-MOUSE for its use in assess-ing the state of preservation of objectsof cultural heritage. In a cryptoporticusat Colle Oppio in Rome, we examined awet ancient Roman fresco as well as thebricks in the surrounding walls (Figure8). Approaching the precious fresco to adistance as close as 1 mm, we measuredthe signal of the water in the poreswithout touching the fresco. Followingthe procedures developed for oil-wellanalysis, the echo envelope was then an-alyzed by inverse Laplace transforma-tion for a distribution of relaxationtimes. Although some signal loss has tobe accounted for by translational self-diffusion in the highly inhomogeneousmagnetic field of the NMR-MOUSE,the signal amplitude at short T2 cannevertheless be attributed to water insmall pores, and the signal at large T2 towater in large pores. The wet frescoshowed strong signals at both small andlarge T2, so small and large pores werefilled with water. The brick wall sup-porting the fresco gave similar results,

in particular when considering that thebricks have a pore size distribution dif-ferent from the fresco material. On theother hand, the bricks in another, dryerpart of a different wall of the crypto-porticus showed low signal at high T2.This is in line with laboratory dryingstudies, which show that during dryingthe NMR signal vanishes first from thelarge pores and only later from thesmall pores. By calibration with labora-tory samples including established mer-cury porosimetry studies on test sam-ples, the nondestructive measurementsby the NMR-MOUSE can be used toquantify the distribution of the water-filled pores. Due to magnetic impuritiesin many building materials, this is anontrivial task and the subject of ongo-ing research.

SummaryNMR is mostly known for its use inchemical analysis and medical diagnos-tics. An important but largely unno-ticed application is in well logging. The

same principle is used for the NMR-MOUSE, which is positioned at or nearan object to measure NMR parameterslike the relaxation time T2 and the sig-nal amplitude A from one side withinthe object. Unilateral NMR is particu-larly useful for quality control of tech-nical elastomer products, where thestate of processing and vulcanizationcan be assessed providing informationcomplementary to that of swelling andrheometer measurements.

In particular, cross-link density andthe revision process in curing can oftenbe followed unambiguously. Potentiallyvaluable applications are also anticipatedin food analysis. The nondestructivenessof testing is of outstanding value in theanalysis of historical treasures. Althoughthe NMR-MOUSE measures the sameparameters that determine the contrastin medical NMR images, the instrumentis small, mobile, and two orders of mag-nitude less in price.

AcknowledgmentsWork on the NMR-MOUSE has greatlybenefited from continuous support byDeutsche Forschungsgemeinschaft(DFG, Bonn, Germany). A comparativeevaluation of the use of the NMR-MOUSE in the rubber industry is con-ducted in cooperation with industrialpartners in a project supported by Bun-desministerium für Bildung undForschung (BMBF, Bonn, Germany).The experiments on Cultural Heritagewere performed as part of the EUREKAproject Eurocare �!2214-MOUSE ofthe European Community in collabora-tion with Bruker Biospin in Milano,Italy (Giovanni Bizarro and FabioTedoldi) and Rheinstetten, Germany(Dieter Schmalbein), as well as the Uni-versity of Rome (Franco de Luca andCinzia Casieri). New NMR-MOUSEsensors were developed in cooperationwith INTECH-Thüringen GmbH (Wal-tershausen, Germany).

References1. B. Blümich, NMR Imaging of Materials

(Clarendon Press, Oxford, UK, 2000).2. G.A. Matzkanin, ”A Review of

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“Unilateral Nuclear Magnetic Resonancefor Quality Control” continued on page 73

February 2003 18(2) Spectroscopy 73

The Baseline

iron nuclei back into resonance withthe emitted gamma ray photons.

Interested readers are directed to the“Suggested Reading” section for moredetailed information about this fasci-nating form of spectroscopy.

Reference1. R.H. Holm, et al., J. Am. Chem. Soc.

96(8), 2644–2646 (1974).

Circle 54

Suggested Reading1. R.S. Drago, chapter 15 of Physical

Methods for Chemists 2nd ed. Saun-ders 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 (accessedSeptember 24, 2002).

4. http://www.nobel.se/physics/laure-ates/1961/mossbauer-bio.html (ac-cessed September 24, 2002).

5. http://www.webres.com/mossbauer_detail.html (accessed September 24,2002). ■

Nondestructive Characterization ofComposites Using NMR,“ in Nonde-structive 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. Kupfer-schläger, 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 Applica-tions, (Gulf Publishing, Houston, TX,1999).

6. V. Herrmann, K. Unseld, H.B. Fuchs, andB. Blümich, Colloid and Polymer Sci-ence 280, 738–746 (2002).

7. A. Hartwig and B. Wolter, Adhäsion 12,34–38 (2001). ■

B. Blümich is a professor at the Institutefor Technical Chemistry and MacromolecularChemistry, RWTH, D-52056, Aachen,Germany, and president of AixNMR Zentrumfür Magnetische Resonanz e.V., Bergstraße31, D-52159, Rott, Germany.S. Anferova is a visiting scientist at theInstitute for Technical Chemistry andMacromolecular Chemistry and seniorlecturer at Kaliningrad State University,236041 Kaliningrad, Russia.K. Kremer is a doctoral student at theInstitute for Technical Chemistry andMacromolecular Chemistry, RWTH, D-52056,Aachen, Germany, and assistant to thedirector of AixNMR Zentrum für MagnetischeResonanz e.V.S. Sharma is a doctoral student at theInstitute for Technical Chemistry andMacromolecular Chemistry.V. Herrmann is manager in chemicaltechnology at Dunlop GmbH, Dunlopstr. 2,D-63450 Hanau, Germany.A. Segre is director of research at theInstitute of Chemical Methodologies of CNR,00016 Monterotondo Stazione, Rome, Italy.

“Unilateral Nuclear Magnetic Resonancefor Quality Control” continued from

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Documents

Unilateral Nuclear Magnetic Resonance for Quality Control · uclear magnetic resonance (NMR) spectroscopy and NMR imaging require a sam-ple to be positioned in a ho-mogeneous magnetic