NMR+course.docx
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NMR+course.docx
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NMR+course
NMR
Spin
Allnucleihaveapropertycalledspin.Spindescribesthenatureofthatnucleus'magneticfield.Spinischaracterizedbyaspinnumber,I,whichcanbezeroorsomepositiveintegermultipleof1/2(e.g.1/2,2/2,3/2,etc.).Nucleiwhosespinnumber,I,equalszerohavenomagneticfield,whilenucleiwithnon-zerospinnumbersdohavemagneticfields.Highervaluesofspinnumberimplymorecomplexmagneticfields.
Somecommonnuclei,suchas12Cand16O,haveI=0andhavenomagneticfield.ThismakesthesenucleiinvisibletoNMRspectroscopy.Otherelementssuchas1H,13C,19Fand31PhaveI=1/2,whileothershaveevenhigherspinnumbers:
I=114N,2H
I=3/211B,35Cl,37Cl,79Br,81Br.
AsthevaluesforIincrease,theshapesofthemagneticfieldsbecomeprogressivelymoreandmorecomplex.
Whiletheshapeofanucleus'magneticfieldisdescribedbyI,it'sstrengthisdescribedby
themagnetogyricratio.Anucleuswithalargemagnetogyricratiohasastrongermagneticfieldthananucleuswithasmallmagnetogyricratio.Thestrongestmagneticfieldisconvenientlypossessedby1H,themostcommonisotopeofthemostcommonelement.ThesesimplefactsexplainwhyhydrogenNMR(alsocalledprotonNMR)isthemostpopularformofNMRtoday.Carbon-13andphosporus-31NMRareprobablycloseseconds.Throughoutthisseries,youshouldassumethatunlessotherwisespecifiedtheexampleswillrefertoprotonNMR.
TheExternalMagneticField
Iftwomagnetsarebroughtneareachothertheywillexertaforceoneachotherandwilltrytoalignthemselves.Forsimplebarmagnets,thefavouredalignmentisparallel(northpoleofonemagnetfacesthesouthpoleofthesecond).
Similarly,whenamagneticnucleus(I>0)isplacedbetweenthepolesofanexternalmagnet,ittoowilltrytoalignitselfwithrespecttothisexternallyappliedmagneticfield(Ho).Inthemacroscopicworld,twomagnetscanbealignedinaninfinitenumberoforientations.Attheatomiclevel,thesealignmentsarequantized.Thereareonlyafinitenumberofalignmentsanucleuscantakeagainstanexternalmagneticfield.Thisnumberdependsontheshapeofthenucleus'magneticfieldandthereforedependsonthevalueofitsspinnumberI.EachpossiblealignmentisassignedavaluecalledIzwhichrangesfrom-Ito+Iinstepsof1.Theseorientationsarereferredtoasspinstates.Thediagramillustratesthepossiblespinstatesforaspin1/2andaspin1nucleus.
NucleiwithI=1/2haveasimplemagneticfieldandcanalignWith(Iz=1/2)orAgainst(Iz=-1/2)theexternalmagneticfieldyieldingtwospinstates.NucleiwithI=1haveamorecomplexmagneticfieldandcanhaveoneofthreeorientations(Iz=1,0,-1).Ingeneral,anucleuswillhave2I+1orientations(spinstates)withrespecttotheexternalmagneticfield.
Precession
Classicalmagnets,whenbroughttogether,willalignexactlyparalleltoeachotherandwillmaintainthisalignmentinastaticfashion.Magneticnuclei,duetorestrictionsdescribedbyquantummechanics,donotalignexactlyparalleltooragainsttheexternalmagneticfieldbutrather,theyalignatanangle.Thishasanimportantconsequencethatcanbeillustratedbyconsideringagyroscope.
Agyroscopeisausefuldeviceandwhileithasmanyimportantapplicationsinnavigation,itisfirstencounteredbymanypeopleasachild'stoy.Agyroscopeistypicallyaspinningmasssupportedinaframe.Aspinninggyroscope,whenplacedinaspecificorientation,willtendtoholdthatorientationdespitetheeffectsofexternalforceslikegravity.
Inaverticalgravityfield(gravitypullingstraightdown)agyroscopeplacedverticallywillmaintainthisorientationmotionlessly.Ifthegyroscopeisplacedatanangletothegravityfield,itwillrotateaboutanaxisparalleltothisfielddemonstratingsomethingcallprecession.Thefrequencyofthisprecessiondependsontwofactors,theforceexertedbythegravityfield,andtheforceexertedbythegyroscope.Thiscanbeillustratedintwoways.Amassplacedontheuppertipofagyroscopewillincreasetheforceexertedbythegravityfieldandtheprecessionfrequencywillincrease.Increasingthespeedormassofthegyroscope'sspinnerwillincreasetheforceitexertsand,again,theprecessionfrequencywillincrease.
Amagneticnucleusinanexternalmagneticfieldbehavesverymuchlikeagyroscopeandprecessesabouttheexternalmagneticfield.Theangularfrequencyatwhichthisprecessionoccursisgivenby
andiscalledtheLarmorfrequency.Thevalue,
isthemagnetogyricratioandischaracteristicforeachtypeofnucleus.Itrelatestothestrengthofthenucleus'magneticfield.Histhestrengthoftheexternallyappliedmagneticfield.Forexample,a1HatominamagneticfieldH=1.41TeslahasaLarmorfrequencyof60megahertz(MHz).TheconceptofprecessionisimportantinunderstandingpulseNMRexperimentsareconducted.
Energies
Theorientationsamagneticnucleuscantakeagainstanexternalmagneticarenotofequalenergy.Spinstateswhichareorientedmorenearlyparalleltotheexternalfieldarelowerinenergythanintheabsenceofanexternalfield.Incontrast,spinstateswhoseorientationsmorenearlyopposetheexternalfieldarehigherinenergythanintheabsenceofanexternalfield.
Whereanenergyseparationexiststhereisapossibilitytoinduceatransitionbetweenthevariousspinstates.Byirradiatingthenucleuswithelectromagneticradiationofthecorrectenergy(asdeterminedbyitsfrequency),anucleuswithalowenergyorientationcanbeinducedto"jump"toahigherenergyorientation.TheabsorptionofenergyduringthistransitionformsthebasisoftheNMRmethod.OtherspectroscopicmethodssuchasIRandUV/Vis,alsorelyontheabsorptionofenergyduringatransitionalthoughthenatureandenergiesofthetransitionsvarywidely.
WhendiscussingNMRyouwillfindthatspinstateenergyseparationsareoftencharacterizedbythefrequencyrequiredtoinduceatransitionbetweenthestates.Whilefrequencyisnotameasureofenergy,thesimplerelationshipE=hv(whereE=energy,h=Planksconstant,andv=frequency)makesthissubstitutionunderstandable.Thestatement"thetransition(peak)shiftedtohigherfrequencies"shouldbereadas"theenergyseparationincreased".
Comparisonofvariousspectroscopicmethods
NMR
~60x106to600x106Hz
Probesnucleus'magneticfield
ESR
~1x109to30x109Hz
Probeselectron'smagneticfield
Microwave
~1x109to600x109Hz
Probesmolecularrotation
Infrared
~6x1011to4000x1011Hz
Probesbondvibrationsandbending
Ultraviolet/Visible
~7.5x1014to300x1014Hz
Probesoutercoreelectrontransitions
Mössbauer
~3x1016to300x1016Hz
Probesinnercoreelectrontransitions
Probestransitionswithinthenucleus
PopulationDistribution
Inagivensampleofaspecificnucleus,thenucleiwillbedistributedthroughoutthevariousspinstatesavailable.Becausetheenergyseparationbetweenthesestatesiscomparativelysmall,energyfromthermalcollisionsissufficienttoplacemanynucleiintohigherenergyspinstates.ThenumbersofnucleiineachspinstatearedescribedbytheBoltzmanndistribution
wheretheNvaluesarethenumbersofnucleiintherespectivespinstates,
isthemagnetogyricratio,hisPlanck'sconstant,Histheexternalmagneticfieldstrength,kistheBoltzmannconstant,andTisthetemperature.Forexample,givenasampleof1Hnucleiinanexternalmagneticfieldof1.41Tesla
ratioofpopulations=e((-2.67519x108rad.s-1.T-1*1.41T*6.626176x10-34J.s)/(1.380662x10-23J.K-1*K293))=0.9999382
Atroomtemperature,theratiooftheuppertolowerenergypopulationsis0.9999382.Inotherwords,theupperandlowerenergyspinstatesarealmostequallypopulatedwithonlyaverysmallexcessinthelowerenergystate.
Thisnearlyequalpopulationdistributionhasaveryimportantconsequence.Thesignalintensityofanyspectroscopicmethoddependslargelyonthepopulationdifferencebetweenthetwoenergylevelsinvolved.Whenasystemisirradiatedwithafrequency,whoseenergymatchesthatseparatingthelevels,transitionswillbeinducednotonlyfromthelowerenergyleveltothehigher,butalsointhereversedirection.Upwardtransitionsabsorbenergywhiledownwardtransitionsreleaseenergy.Thenumberoftransitionsineitherdirectionisgivenbymultiplyingthestartinglevelpopulationbyaprobability.Thisprobabilityisthesamefortransitionsineitherdirection.Iftheenergylevelpopulationsarethesame,thenumberoftransitionsineitherdirectionwillalsobethesame.Theabsorptionandreleaseofenergywillbalanceeachothertozeroandtherewillbenothingtoobserve.Onlywhenthepopulationsarenotequalisthereanetabsorptionorreleaseofenergytoobserve.
EnergylevelsinaspectroscopictechniquesuchasUV/Visiblespectroscopyarefarapartinenergyand,accordingtotheBoltzmanndistribution,thepopulationresidesalmostentirelyinthelowestenergystate.Asaresult,UV/Visiblespectroscopyisanextremelysensitivetechniqueandiscommonlyusedinanalyticalchemistrytodealwithverysmallamountsofsample.InNMR,theenergyseparationofthespinstatesiscomparativelyverysmallandwhileNMRisveryinformativeitisconsideredtobeaninsensitivetechnique.
NMRExperiment
Whenasampleofmagneticallyactivenucleiareplacedintoanexternalmagneticfield,themagneticfieldsofthesenucleialignthemselveswiththeexternalfieldintovariousorientations.Eachofthesespin-stateswillbenearlyequallypopulatedwithaslightexcessinlowerenergylevels.Duringtheexperiment,electromagneticradiationisapplied
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