Single-Sided NMR

253 Pages·2011·7.391 MB·English

by  Casanova, Federico(Editor);Perlo, Juan(Editor);Blümich, Bernhard(Editor)

Single-Sided NMR
· ·
Federico Casanova Juan Perlo Bernhard Blümich
Editors
Single-Sided NMR
123
Editors
Dr.FedericoCasanova JuanPerlo
RWTHAachen RWTHAachen
Inst.Technischeund Inst.Technischeund
MakromolekulareChemie MakromolekulareChemie
Worringerweg1 Worringerweg1
52074Aachen 52074Aachen
SammelbauChemie SammelbauChemie
Germany Germany
[email protected] [email protected]
Prof.Dr.BernhardBlümich
RWTHAachen
Inst.Technischeund
MakromolekulareChemie
Worringerweg1
52074Aachen
SammelbauChemie
Germany
[email protected]
ISBN978-3-642-16306-7 e-ISBN978-3-642-16307-4
DOI10.1007/978-3-642-16307-4
SpringerHeidelbergDordrechtLondonNewYork
(cid:2)c Springer-VerlagBerlinHeidelberg2011
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Preface
Thestudyofcomplexmoleculesrequireshighsensitivityandresolutionforchemi-
calanalysis.ThisiswhytheNMRcommunitypushesthedevelopmentofevermore
powerful superconducting magnets that generate stronger and more homogeneous
magnetic fields every year. Today’s NMR magnets are heavy giants installed in
special NMR laboratories built to shield electromagnetic interference, control the
temperature,andreducemagneticfielddistortionsinordertoprovideidealexperi-
mentalconditionsinasmallvolumelocatedinsidethemagnet.Besidesthefactthat
samples must be taken to the magnet to be analyzed, they must fit in the limited
space available in the magnet center. Large samples cannot be investigated in this
way without cutting. This problem was already noted in the early days of NMR
when the technique was identified as a potential tool to characterize rock forma-
tions in situ. Measuring properties of the pore structure as well as characterizing
thesaturatingfluidsdownholebyNMRtriggeredthedevelopmentofwhattodayis
calledinside-outNMR.Here,insteadofplacingthesampleinsidethemagnet,the
apparatusisplacedinsideoratonesideoftheobject.
Theimplementationofthisconceptrequirestheconstructionofsensorsproject-
ing considerable magnetic and radiofrequency (rf) fields outside the magnet and
insidethesampleunderstudy.Formorethan30yearswell-loggingtoolsusedthe
earth’s magnetic field as polarization field, butthe low sensitivity and poor spatial
selectivity limited their commercial success. Potential application of open NMR
sensors to measure, for example, moisture in building materials or soil motivated
engineers to use electromagnets to increase the magnetic field strength. However,
these instruments were large, weighing up to 300 kg and operated at low frequen-
cies like 3 MHz. Perhaps the most important step toward reducing the size of the
magnetswastheuseofpermanentmagnetstogeneratethestaticmagneticfield.This
eliminatedmostofthepowerconsumptionoftheseNMRdevices.Duringthelate
1980sandearly1990svariousmagnetgeometrieshavebeenproposedbydifferent
well-logging companies, and a number of research groups proposed small single-
sided magnets generating magnetic fields of about 0.5 T external to the sensor.
AnexampleistheknownU-shapedmagnetgeometryusedbytheNMR-MOUSE,
which is obtained by opening the C-shaped geometry used in conventional closed
magnets.
v
vi Preface
Thebigchallengefacedwhenworkingoutsidethemagnetisposedbythelarge
inhomogeneities in both the magnetic and the radiofrequency fields. Under such
experimentalconditionsevenhardrfpulsesactasselectivepulsesandoff-resonance
effectsareconsiderable.Therefore,duringthe1990s,severalgroupssettheiratten-
tion on understanding the response of the spin system to pulse sequences known
from conventional NMR, like the Carr-Purcell-Meiboom-Gill (CPMG) sequence
extensivelyusedtomeasurethetransverserelaxationtimeT ,whentheyareapplied
2
inthepresenceofastronglyinhomogeneousmagneticfield.Chapter2providesthe
toolsneededtoevaluatetheevolutionofthemagnetizationtosuchpulsesequences
implemented in the magnetic field generated by open NMR sensors. Besides pro-
vidingthetimingofsomewell-knownpulsesequencesandthephasecyclefortherf
pulsesrequiredtoeliminateunwantedsignalsgeneratedbyresonanceoffsets,typi-
calfeaturesthatmustbeconsideredatthetimeofimplementingthemarediscussed.
Moreover, a general expression is derived for the sensitivity of NMR experiments
ininhomogeneousfields.Theconclusionsdrawnfromthisanalysissettherulesfor
optimizingmagnetandrfcoilstomaximizethesignal-to-noiseratioofsingle-sided
sensors.
In the presence of inhomogeneous magnetic fields, relaxation times and diffu-
sion coefficients are the key NMR parameters to assess sample composition and
dynamics.Toextractmaximuminformationfromrelaxationanddiffusionmeasure-
ments,anumberofnumericaltoolshavebeenproposed.Oneofthemostpowerful
ones is based on calculating the inverse Laplace transform of the signal decay to
obtain the relaxation time distribution from a relaxation measurement. Although
initiallythistransformationhasbeenappliedto1Ddatasets,recentlythepossibility
toextenditto2Dexperimentsinreasonablecomputationtimeshasbeenreported.
Itopenedthedoortomeasurepowerfulmulti-dimensionaldiffusion–relaxationand
relaxation–relaxationcorrelationspectrausefultodisentangleoverlappingsignalsin
a way similar to conventional multi-dimensional Fourier NMR spectroscopy. This
methodologyisdescribedindetailinChap.3.
Although initially magnets were optimized to maximize sensitivity by maxi-
mizing magnetic field strength (at the expense of a strong static gradient) or the
excitedvolume(attheexpenseoffieldstrength),later,harderconstrainshavebeen
imposed to the magnet design in order to generate convenient magnetic field pro-
files.Severalofthesemagnets,includingsuitablerfcoils,arepresentedinChap.4.
A particularly useful field profile is the one that defines a uniform gradient along
the depth direction. In the presence of such a field profile a slice parallel to the
sensorsurfacecanbeexitedatvariablepositionsinsidetheobject.Achievingdepth
resolutionisusefultoelucidatethedepthstructureoflargesamples.Moreover,fur-
nishingthesemagnetswithasetofcoilsthatgeneratepulsedgradientfieldsalong
thetwolateraldirections,3Dspatiallocalizationhasbeenachieved. Animportant
step toward a functioning open tomograph required the adaptation of single-point
imagingsequences toworkininhomogeneous fieldswheremulti-echoacquisition
is mandatory to achieve maximum sensitivity. The different methods available to
encodepositionduringCPMG-likesequencesaredescribedinChap.5,wherealso
Preface vii
suitablepulsedfieldgradientsequencesarediscussedtomeasuremolecularvelocity
inthepresenceofastrongbackgroundgradient.
Accepting the field inhomogeneities as unavoidable for open sensors, pulse
sequencesspeciallydesignedtominimizeoff-resonanceeffectshavebeenproposed.
A particularly challenging problem that attracted considerable attention over the
years was the possibility to recover spectroscopic information from experiments
performedininhomogeneousfields.Foralongtimethiswasthoughttobeimpos-
sible because the static magnetic field inhomogeneities are usually orders of mag-
nitudelargerthanthosecreatedbythemicroscopicstructureofthemoleculestobe
detected.Inaddition,termsinthespinHamiltonianarisingfromchemicalshiftsor
fieldinhomogeneitiesareformallyidentical.Asanaturalconsequence,noradiofre-
quency pulse sequence was deemed capable of differentiating both types of inter-
actions. A breakthrough was achieved in 2001 when an innovative alternative to
recover a chemical-shift resolved spectrum in an inhomogeneous magnetic field
was presented. The technique is based on matching the spatial dependence of the
static and the rf magnetic fields, to generate nutation echoes whose phase is only
sensitivetochemical-shiftdifferences.Thismethodologyanditsimplementationin
asingle-sidedmagnetarediscussedinChap.6.
Althoughfordecadesmagneticfieldinhomogeneitywasassumedtobeahand-
icapinherenttothesesensors,duringthelastyearsanimportantstepaheadtoward
recoveringspectroscopicresolutionhasbeenreported.Inparticular,ithasrecently
beenproventhathighlyhomogeneousfieldscanbegeneratedevenoutsideamagnet
by furnishing the main magnet with a shim unit built from small and adjustable
permanent magnet blocks. Moreover, a way has been suggested to combine mag-
netic materials with different temperature coefficients to build a magnet with a
temperature-compensatedmagneticfield.Thestrategyfollowedtohomogenizethe
strayfieldofasingle-sidedmagnetisdiscussedinChap.7.
Overtheyears,single-sidedsensorshavefoundapplicationsindiversefieldssuch
as the non-destructive testing of rubber and polymer products, food and life stock
analysis,aswellasthestateassessmentofobjectsofculturalheritage.Applications
in the area of biological tissue are discussed in Chap. 8, while those in the area
ofmaterialscienceandqualitycontrolarepresentedinChap.9.Finally,Chap.10
intendstofamiliarizethereaderwiththeparticularhardwarerequirementsofsingle-
sidedNMR.
Aachen,Germany FedericoCasanova
December2010 JuanPerlo
BernhardBlümich
Contents
1 Single-SidedNMR ............................................. 1
FedericoCasanova,JuanPerlo,andBernhardBlümich
1.1 DevelopmentofOpenNMRSensors ......................... 2
1.1.1 Well-LoggingTools ................................ 2
1.1.2 MobileSingle-SidedSensors ........................ 3
1.1.3 TheNMR-MOUSE ................................ 4
1.2 MethodsforMobileNMR .................................. 6
References ..................................................... 7
2 NMRinInhomogeneousFields .................................. 11
FedericoCasanovaandJuanPerlo
2.1 Introduction .............................................. 11
2.1.1 EvolutionoftheMagnetizationDuringaPulseSequence. 12
2.1.2 SeparationoftheMagnetizationintoCoherencePathways 14
2.1.3 NumericalCalculationoftheNMRSignal ............. 20
2.2 PulseSequenceAnalysis ................................... 21
2.2.1 SinglerfPulse..................................... 21
2.2.2 TheGenerationofHahnEchoes...................... 23
2.2.3 TheCPMGSequence............................... 28
2.2.4 InversionandSaturationRecovery.................... 35
2.2.5 DiffusionMeasurements ............................ 42
2.3 TheSNRinInhomogeneousFields........................... 47
2.3.1 TheReciprocityPrinciple ........................... 48
2.3.2 NumericalCalculationsoftheSNR ................... 49
2.3.3 AnAnalyticalSolutionfortheSNR................... 55
References ..................................................... 55
3 ExSituMeasurementofOne-andTwo-DimensionalDistribution
Functions ..................................................... 57
MartinD.Hürlimann
3.1 Introduction .............................................. 57
3.1.1 Relaxation........................................ 57
ix
x Contents
3.1.2 Diffusion ......................................... 58
3.1.3 Diffusion–RelaxationDistributionFunctions ........... 58
3.2 PulseSequencesandSpinDynamicsinInhomogeneousFields.... 59
3.2.1 RelaxationMeasurement:Carr-Purcell-Meiboom-Gill
Sequence ........................................ 59
3.2.2 DiffusionMeasurementswithStaticGradients.......... 62
3.2.3 T MeasurementsinInhomogeneousFields ............ 64
1
3.3 One-DimensionalDistributionFunctions ...................... 64
3.3.1 DataInversion..................................... 65
3.3.2 Regularization..................................... 67
3.3.3 SystematicErrors .................................. 68
3.3.4 Uncertainties...................................... 68
3.4 Two-DimensionalDiffusion–RelaxationDistributionFunctions ... 69
3.4.1 Two-DimensionalDiffusion-RelaxationMeasurements .. 69
3.4.2 DataAnalysis ..................................... 71
3.4.3 InterpretationofDistributionFunctions................ 73
3.5 ApplicationsofTwo-DimensionalDistributionFunctions ........ 74
3.5.1 Two-ComponentSystems ........................... 75
3.5.2 Wettability........................................ 76
3.5.3 ComplexMiscibleFluid ............................ 77
3.5.4 StructuredFluid ................................... 78
3.5.5 PoreGeometryofPorousMedia...................... 79
3.6 Conclusion ............................................... 81
References ..................................................... 82
4 MagnetsandCoilsforSingle-SidedNMR ........................ 87
JuanPerlo
4.1 Magnets ................................................. 88
4.1.1 B PerpendiculartotheSensorSurface,theBarMagnet
0
Geometry ........................................ 89
4.1.2 B ParalleltotheSensorSurface,theU-ShapedGeometry 93
0
4.1.3 MagnetsforDepthProfiling ......................... 95
4.1.4 Sweet-SpotMagnets ............................... 99
4.2 RFCoils .................................................102
4.2.1 CoilsforDepthProfiling ............................103
4.2.2 CoilsforSweet-SpotMagnets .......................105
4.3 GradientCoils ............................................107
References .....................................................108
5 Single-SidedTomography ......................................111
FedericoCasanova
5.1 DepthResolutionUsingtheStaticFieldGradient...............111
5.2 SpatialEncodingbyFourierImaging .........................113
5.3 Multi-EchoAcquisitionSchemes ............................117
Contents xi
5.3.1 RARE-LikeImagingSequence.......................117
5.3.2 CPMG-CPforQuadratureDetection ..................121
5.4 PerformanceoftheMulti-EchoDetectionScheme ..............125
5.4.1 SensitivityImprovement ............................125
5.4.2 RelaxationandDiffusionContrast ....................126
5.4.3 3DImaging.......................................128
5.5 DisplacementEncoding ....................................129
5.5.1 PFGMethodsinInhomogeneousFields ...............130
5.5.2 MeasurementofVelocityDistributions ................135
5.6 SpatiallyResolvedVelocityDistributions......................137
5.6.1 2DVelocityMaps..................................137
References .....................................................140
6 High-ResolutionNMRinInhomogeneousFields ..................143
VasilikiDemas,JohnM.Franck,JeffreyA.Reimer,andAlexanderPines
6.1 Introduction ..............................................143
6.2 ApproachesBasedonSpinInteractions .......................144
6.3 ExSituNMR:SpatiallyDependent“z-Rotations”...............145
6.3.1 Ex Situ Matching: Compensating Static Field
InhomogeneitiesviaSpatiallyMatchedrf ............. 147
6.3.2 Shim Pulses: Corrections Based on Gradient
ModulationsDuringanAdiabaticDoublePassage ...... 157
6.3.3 AdjustedChirpShimPulses .........................160
6.4 Summary ................................................162
References .....................................................162
7 High-ResolutionSpectroscopyinHighlyHomogeneousStrayFields .165
ErnestoP.Danieli
7.1 SensorDesign ............................................166
7.1.1 MainUnit ........................................166
7.1.2 ShimUnit ........................................167
7.2 ShimmingMagneticFieldswithMovablePermanentMagnets ....170
7.2.1 GenerationofLinearTermsAlong y ..................171
7.2.2 GenerationofLinearTermsAlongx andz .............172
7.2.3 GenerationofQuadraticTermsx2 andz2 ..............172
7.3 ExperimentalResults ......................................175
7.4 ShimmingtheMagnettoHigherOrder........................177
7.4.1 ImprovingResolutionandWorkingVolumeSize........178
7.5 TemperatureCompensation .................................181
7.6 Conclusions ..............................................185
References .....................................................185
8 ApplicationsinBiologyandMedicine ............................187
BernhardBlümich
8.1 Skin.....................................................188
8.2 Tendon ..................................................192
xii Contents
8.3 MummiesandBones.......................................194
8.4 UnilateralImagingofBiologicalMatter.......................196
8.5 Conclusions ..............................................198
References .....................................................199
9 ApplicationsinMaterialScienceandCulturalHeritage ............203
JürgenKolz
9.1 Elastomers ...............................................204
9.1.1 CrosslinkDensity..................................204
9.1.2 Aging............................................206
9.1.3 Imaging ..........................................209
9.2 HardPolymers............................................212
9.2.1 IngressofSolvents.................................215
9.3 CulturalHeritage..........................................217
References .....................................................219
10 SpectrometerHardware ........................................221
JörgFelder
10.1 Single-Sidedvs.Conventional:SystematicDifferences ..........222
10.2 FrontendDesign ..........................................223
10.2.1 MatchingandBalancing ............................223
10.2.2 Transmit-ReceiveSwitching.........................226
10.3 TransmitterDesign ........................................228
10.3.1 ConventionalPowerAmplifiers ......................229
10.3.2 AlternativeAmplifierDesigns .......................230
10.4 ReceiverDesign...........................................233
10.4.1 Low-NoiseAmplifier...............................234
10.4.2 FrequencyGenerationandMixing....................235
10.5 DigitalHardware ..........................................237
10.5.1 FrontendSignalProcessorSelection ..................237
10.5.2 DigitalPhaseSensitiveDetector......................239
References .....................................................239
Index .............................................................241