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A PULSED NMR RELAXATION AND DIFFUSION STUDYOF WATER IN TREATED AND UNTREATED WATERLOGGEDWOOD

ByDavid A Bannister

Thesis submitted to the University of Nottinghamfor the Degree of Doctor of Philosophy

January 1990


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Proton N.M.R. Relaxation and Self Diffusion in WaterloggedWoods.Contents.Abstract. Uv)Acknowledgemenis. (vi)Chapter 1. NMRnd the Study of Water in Waterloggedgood. IChapter 2. Waterloggedgoodand its Conservation.2.1 Introducion. 62.2 The Structure of Wood. 7

2.3 The Decompositionof Wood. 102.4 Methodsof ConservingWaterloggedWood. 122.5 Stabilisation of WaterloggedWoodusing Polyethylene Glycol. 14Chapter 3. The Theory of NMR elaxation and Diffusion Measurementsn

HeterogeneousSystems.3.1 Introduction. 213.2.1 FundamentalConcepts. 223.2.2 The Block Equations. 243.2.3 The Rotating Frameof Reference. 263.2.4 Spin Lattice (TI), and Spin-Spin (T2) Relaxation. 283.2.5 Pulsed Nuclear Magnetic Resonance. 29

3.3 The Interpretation of Relaxation times (TI and T2) in, Termsof 35Molecular Events.

3.3.1 Mechanismsf Relaxation and the Bloemberg,Foundand Purcell 35Theory.

3.4 HeterogeneousSystems. 403.4.1 The Discrete Multiphase Model. 413.4.2 A Distribution of Correlation Times. 453.4.3 Cross-Relaxation Effects. 493.4.4 Anisotropic Motion. 503.5 Diffusion. 52


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5.4.2 TheTemperatureontroller. 1125.4.3 TheBrukerMinispeck. 1135.5 The Diffusion Equipment. 1135.5.1 TheField GradientCoils. 1135.5.2 ThePulsedField GradientUnit. 1165.6 Data Analysis. 1175.7 Sample reparation. 1205.7.1 PolyethyleneGlycol Solutions. 1205.7.2 Xylem. 120Chapter6. A PulsedNMR tudyof Water n WaterloggedWood.6.1 Introduction. 1246.2 FreezingCurves. 1256.3 NMR elaxationof Water n WaterloggedWoods. 1336.3.1 Single Componenteasurementsf TI andT2. 1336.3.2 MulticoaponentRelaxationof Water n WaterloggedWoods. 1426.3.3 NMR elaxationTimesof Water n WaterloggedWoodsas a 145

Functionof MoistureContentandTemperature.6.4

6.4.16.4.2

6.5

6.5.16.5.26.6

NMRtudieson WaterloggedWoodmpregnated ith Polyethylene 172-Glycol Solutions.ThePolyethylene-glycol/Water ystem. 173A PulsedNMR tudyof WaterloggedWoodmpregnated ith 181Polyethylene-glycolSolution.A Studyof Self-diffusion for Water n UntreatedandTreatedWaterloggedWoods sing NMR ield GradientTechniques.Self-diffusion In UntreatedWaterloggedWood.Self-diffusion in TreatedWaterloggedWood.Conclusion.

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ABSTRACT

Freezing curve. NMRelax3tion data. 5nd Steady fieid jr3dient and Puised fieid gradientexperiments were conoucted on samplesoi water-logged woocsexcavated from the TUdorwarship.

'hehe flar- Rose. and on 3;iaiLar samples mpreqn;ted witl P-oiyethylene-Glycol solutions; 16polymer used as a buiking agent to prevent decay.

At ic3s,. two distinquis, i-,ole populations of water molecules are found in wood. Freezing

curves indicate the ? esenceof approximately 0.38 g/g of hydration water. close to that 00-servea in iresh timoers. Reiaxation measurementsn pre-treatea samplesprovides evidenceof a very tightlY tound fraction. present at water contents of below 0.14 q/g of hydration-Aater. with a secondpopul3tion of hydration water being present upto MIS 9/9. Abovethis*,.,lue a thitd. 'free' "., zuiation is observed.

The elaxation deC3YSn longitudinal andtransverseoitection havebeenanalysed nterms01 3 sumof exponentials. These ndicate the presenceof two populationsof waterinicn do not correspond to FaFulations observed in freezin; curve analysis.

Exchange echanismsominatehe temperature ependencyt the relaxation behaviour npre-treited sampis. Aich is similar to that observed in other fibrous materials such asmeat. however.he difierent componentsonot appear o correspondo the PhYsicalcharac-teriitics or the wood.andthe spin populationscannotbe associatedwith a distribution be-tweenoentifiable -compartmentsithin the.system.

In FEGmpregnatedampleshe contribution to the signal from the polymer s not resolv-able on the equipment used. Samples reated with FEGs or which the degree of polymerisationis ireater than 1540showa dependencyof relaxation characteristics on the water content Ofthe sample. At lowvater contentsPEGsof lowmolecularweight impart a mobility to the


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1 %

ABSTRACI

Freezing curve. NMR eiax3tion data. and Steady field jr3dient and Pulsed field gradientexperimentswere conouctedcn samplesof vater-logged wooosexcavated trom the Tudor uarship,the Mary Rose. and on 3laiiar 3amoies impregn;tted . itft Polyethylene-Glycol soiutions: the

poiymer used as a buikin? agent to prevent dec3y.

At lc-3st two distinguis, 61aolepopulations of water molecules are found in wood. Freezinj

curves inucate the presence of approximately 0.38 g/g of hvdration water. close to that OD-ser,,ea in iresh timoers. Reiaxation me3surements n "pre-treated samples provides evidenceoi a very tilhtlY bound raction. present at water contents of below 0.14 g/g 0i hydration'mater. uith 3 secondPopulation of hydration water beinj present upto 0.1.8 9/9. Above hisvalue a third,. 'free' PozulBtion is observed.

The elaxation deC3YSn longitudinal and ransversecitection havebeenanaiysed ntermsot a sumof exponentials. Thesendic3te the presenceoi two populationsof waterinicn do not Correspand o oplations observed in freezing curve anaiysis.

Ex.han? mechanismsominatehe temperature ependencyt the relaxation behaviour n

Pfe-tt,? ted samcles. which is similar to that observed in other fibrous materials such asmeat. however. he difterent componentso not appear o correspondo the physical charac-teristics Or the wood.andthe spin populationscannotbe associatedwith a distribution te-tween icentifiable compartmentswithin the system.

In FEGmpregnatedampleshe contribution to the signal from the polymer s not resoiv-able on the equipment sed. Samplesreated with FEGsor whichthe degreeof polymerisatiOnis greater than 140showa dependency f relaxation characteristics on the water content Ofthe sample. At low water contents FEGsof low molecular weight impart a mobility to the

Qv)


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"bound"water moleculeswhich is notseenn untreated samples.

3. eIr dirfision coetticients ror watermaieculesn woodare anisotropic, and are reauCeditom those observed.n distilled water. Ihis reau.tion is 'broughtaboutbecause; atermol-cuies are coth held in a hyd-ation a,er, ana boundeaby the cellular structure Oi thewood.

In impregnatedsampies he diffusiOnrates are lowered by a factOr Oi 10- rhOlJzq,his isnot reiiected in the relaxation benaviour. 'the anisotropy is reduced,and proton excnan?mecranisms te biocked.

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,%CKN0'jLEDGE?!T5

I ouid' like to express my appreciation to the 'Ioliowi'g;

Frof. 'W. Derbyshire - for his supervision and the provision of laborato ry facilities.Dr. J. Harvey - ior initiating the project and indentitving sampiespecies.Fror. . F.Cloqh - for his patience. '''Ir. S. Booth - for his incredible hard work in keeping the equicme,t operational.Tle113ryRoseTrust - 'for providing samples. C3Snand heiprui injor-i3tiOn.

--TheS.E. R.C. - for rinancing the case award.T ssistance.he PhononBunenana 'or. F. Zelaya - for friendsnip. en,,,usi3smand aR. Underwood'skitzhen table - for its support!Mum nd Dad.


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CHAPTERNMRND HESTUDYFVATERINATER-LOGGEDOOD.-", -I

There have been numerouseports on the study of water in heterogeneoussystems using avariety of techniques 11-11. Despite this, an understanding of the nature of water withinthese systems, and Its Interaction with these systemms,as not been well established. Onesystemwhich has received little attentici in the literature lsthat`of water-! oggedwood.

Curre:it procedures lsej In the p, eservatiCn and conse.i3tion-'of wate:-logged artefaCtsare, at best., pragmat!c, ard are certairly'rot, well underst:,cd. 'Meth,cids that have been

developedover the past thirty years or so In manycases pr: ve, u-, at! s1actory,,! arSelY be-cause It is not knownhcwthe preservatives'lnteract with the materials which they areemployed o preserve. !n order t- opt.,mllsethe processes used at present, It Is obviouslyimportantUat the penetrationprcpertles be determinedand, for thles, it !s consideredhatsomeknowledgeof the'dynamics of both the systam and the praservatIve Is necessary.

Thedynamic roperties of water In biolcgical 'systemsare modifed f: om hose .f 11,lk13 envir 'Mnater o varyingdegrees, ependingponhewatercontent, f the systemndLt or e t.

it hasnot yet beenestablishedhat to explain he propertiesof,,ater In thesesystemstis necessaryo Invoke biological effect and/or hat explanationscasedponhesystemsbeingdispersed ndheterogeneousonoCprovesufficient. In general, he applicationofthe standardnvesUgativeechnijueso suchsystemss-non-trivial, sometimesn termsoftecbrilques,but moreoften In termscf interpretation of observation.

Someof'the commonxperkental, techniquescapableof detecting different types of physi-cal processesare shown,n figure 1.1. The first class encompasseshe thermodynamicech-niquessuchas sorption Isothermsandcalorimetric a, d volumetric analysis', useful in'thestudyof bulk phercmenauchas phasechanges,energy elationships and-thedeterminationof

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fractions of unfreezablewater. However,hermodynamiceasurementso not enableus to as-sign watermoleculeso specific sites, not do they offer Informationon the kinetics, of,molecules r mechanismsf binding processes.

Lai Tint fs) OASipinj t solias,*vat] bEfraotum "T,HIM scattering Chtwal. reactionDiffasm in solid P419ykerschmi: &I reaction-'I MI ic -+--4t Rotation in SollasAcoustic DiffiLsion - PoiUmos in 5DILAtkv

loui PalmationSmf-L

1

Iq. Pa I_rpec CovjLt

- Dif rnslan m lecu ar TvIationSmall,moleculQsnelltrOnMel ic Ii Iona ibrationrra ng Triuupt U fin scalesof "Chcular Trocesms naapplication witsd amerimntal tedaims.

Thesecondgroupof techniquesexamineshe molecularstvuctural parameters ndpertLrba-tions thereof, together iith the dynamic roperties of wate- andzolecular substrates. Thegroup includes dielectric relaxation, Infa-red reflectance, photo-acoustic effects, neutronelastic scattering, nuclear magnetic resonanceand electron spin reso. ance. These techniques

can be used to monitor rotational and translational diffusion of water molecules and can dis-

criminate betweenwater In the bulk and water which Is unde: oing restricted 2otion. Of this

group,Auclear Magnetic ResonanceNMR) s possibly the most powerful and useful in the study

of water-loggedoodsnd heir preservation, s It hasseveral mportant dvantages,vertheothermethods.

,NFIRffers high selectivity- As a result, the NMRpectroscopistcan chooseo study,,,atomic, uclei of-any elementprovided hat they possessa magneticmoment., Theproton, witha nuclear spinnumber1:1/2 Is the most-commonlyxploited,, due. o its high natural abundanceand,arge magnetogyricatio (gamma- 2.673x 101 CKg)., OthersIn commonse Include ,, -deuteriumoxygen-17,ndcarbon-13.,,-- ,",:, ,., I"II

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Themagnetic field experienced by a nucle; (B) is the applied field (Bo), pertufted bysmal local magneticeffects. Someof these are induced 7 the exte",,al field and honce re-

,emer.s in Eystem, Including all otherated tc It, 4hile others are due to aal, stlc ;nun!o! ?osses3inj magnetic mozents. The local fields associated with these perturbationshave both steady and fluctuating compcnents.Consejuent Iy, 'he ", sition and width of thespectral 'lines are extremely sensitive to the environments nuclei under examination,I. e. to the structure and dynamicsof the molsc,,,es contain-ng the nuclei I'l U Ic .q est r

Vithin Efferent systems there 3re 3 variety of inter-moleciflar Interactlons, such as

molecular reorientat! on, diffusicn, and chemical exchange, which JIVe rise to different

properties of the NMRsignals. T,Nse interacti^. ns may be : ez-. ved -;lnj the versatility ofNFR. Cre can deduce ! Ifferent types and ! r. cr-. at! or. itzlit a seysts: y changing elthe. - thetype :f NMRmeasun-ment, or the system itself.

one f t1hemost mportantadvantages.n using NMRs that it is essentially a -,on-invasive andnon-destnctive probingtechnique.SamplesZaYbe sublectel to a series of NMRexperimentsithoutstructural or chemicalamage.

Thereare twomajorJisadvan'tagesn the use of NMR.Firstly, the parameters f Inter-

est, suchas chemicalshifts andmagnetisat! n decay ates, are phencmencnather thansystem-based. n other words, the res-ilts of NVRmeasurezentsequire extensiveInterpreta-tion 'Anorder to relate these derived parameterso the properties of the systemexpressednfamiliar -inits. Further complications occur because f the fifferential dependencesf thedifferent NMRechniq1jes pon he different interactions. ghilst this has been elativelydirect In the case of simplesystems, t has provedvery difficult In thoseof greater com-PIex ty. Secondly,whilst the selectivity of MR Is high, the sersitivitY Is low. Since thetechniqueInvolves ransitionsbetweenenergyevels for populationsAlch are distributed

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amongsthose levels according o Boltzmannstatistics, and he available field strengthsarelow, i. e. the magneticenergy2g.B is muchess than the thermalenergyKT, the signal IIstrengthsare Inherently poor. NMRxperimentsequire relatively large samples nd are notsuitable for trace analysis.

The low'sensitivity does not present difficulties in the study of wite r -saturated timbersandNMRignals can readily be obtained.However,n a complex ystemsuchas, hat of water-loggedwood;one Is operatingat the extremeimits, JIf not beyondhe limits, of, ap-plicability of'current NMRheories. In attempting o improveour understanding,f the Sys-tes, weare simultaneously,esting the applicability of current 111MRheories.

It should be stressed that in this work It is primarily the properties of the water inthe system hat are of Importanceo us, the emphasiseingon the mannern Alch Its Inter-actions with the cellular material of the wocd,andthe prese: atives jsed to stabilise thewoodsmodify its dynamic ehaviour romthat of bulk water. It Is considered hat thedetailed compositionof woodon a molecular evel is relatively unimportant rom this pointof view. Yhat Is of interest to us however,s the macroscopictructure of the ucodandthemethod y whichwater preservativesmaypenetrate and,eside in the wood.Onewouldexpectthe compartmentationf the water to haveprofoundeffects on Its NMRroperties. A descrip-tion of the macroscopic tructure is therefore given in chapter2.1 1

Vooddiffers from other cellular, systems*in hat the water contentsnormally encounteredare low; usually, in the order of 38% y weight, or below. Consequently,water In wood Snormally foundIn close associationwith the wood ell wall, or in vapour orm. 'in contrastfsamples f woodrom the Tudorbattleship, the ", lary Rose",are highly saturated, havingwatercontents whichare similar in magnitudeo thoseof other biological cellular systems.Onewouldexpectthe dynamic ehaviourof the water moleculesn water-logged imbers, there-tore, to be markedlydifferent from that of water In fresh wood,andthat this shouldbe

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reflected In Its NMR-propertleg-Onedoesnot necessarilyexpect o observe he behaviourwhich s shownn other cellular systems ecausehe water In woods not In equilibrium with'Its environment.

In this work measurements f TI and T2 and 'he self diffusion coefficients of the water-logged woodhave been measuredas a furction oil water content, degree of degradation -o'andtemperature of the samples lin order to characterlise its nature and contrast1ts behaviourwith that observed for vater in fresh wocder Limbers. The NMRproperties of water In samplestreated with, different Irades-of 'the stabilislng agent Polyethylene-glycol have also been ob-seryed,, and the modification of the dynamiicproperties of-dater in the treated samples15discussed. I11, ' . ..

Refererces

1. Mathur-de-VreR, "Thestudies of vater in Biological systems. Frog. Blophys.Molec.BiOl. , Vol 35, pp 103-134.,11979) ---:,, " , ,, "- 'I ,I

2. Belton P-S-,- Ratcliffe R,G. ",NMRndCompartmentationn Biological Ussues. Frog.In NMR pectroscopy.Vol 17, pp 241-279.-, 1985)

3. Lillford F.J., Clark A.H., JonesO.V. 'Distribution of water in heterogeneousoodandmodelsystems. Vater In Polymers,Chapter10. Pub.AmericanChez.Soc. (1980)

4. CookeR.,, Kuntz-1.D. "Propertles of water in Biological systems. Ann.ReviewBloph. andBloch. Vol 3,, p 95. (119714)

S. FranksF. "Vater -A comprehensivereatise. ' Pub.Plenum ress,,NewYork.(1972)

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CHAPTERVATER-LOGGGEDOODNDTS CONSERVATION

2.1 Introduction

In an archaeological coniext water-logged woodmaybe defined as that which has been com-pletely filled with water instead of'air and has been chemically broken downby the action ofmicro-organiims, 'causing considerable weakeningof, the structure of the mood.

Theability of different speciesof woodo absorbwater Is amazingly ariable; alder,

beechandmaple,for'example, take up water very rapidly andcanbecomeaturatedwithin afewhours,,while in other speciessuchas cak the processcan take weeks,cr evenyears. ''Inthe case of porous woods he chemical breakdownoccurs almost simultaneously throughout"thesample?whereasIn less hydroscopic species the breakdown s likely to occur from the out-side, onecell layer at a time.

'Despite the quite fresh appearancef mostsamples f water-loggedwood,normaldryingout procedures sually lead to the completedestruction of the samples thin a matter ofhours. Theconservationof vater-lolged wooden rtefacts is aimedatstablllslnj the sizeand'shape'of he'samplest"and"atproviding some urability, without destroying'their aes-thitic value.

Thefollowing chapterbeginswith a brief description of the structural and chemicalcom-position's of woodafid, he ways hat'these are degraded s a result of water-loggini. Ashort historlhl account s presenteddescribing attemptswhichhavebeenmadeo' conserve,asaturatedwoodenrtefacts, followedby an appraisal of the processof conservationby im-pregnationwith polyethyleneglycols, which is the mostwidely andsuccessfully usedmethodto date.

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2.2 TheStructure of Vood., -

-There Is a great'diversity In the appearanceand physical properties of different typesof wood'-II, and yet the ul tra-structure ct the dif f erent species is basical ly the same.Al I 'woods re madeup of cel Nlar tissues composedf three main constituents. - Eachcel Imaybe thought of as a lattice of crystalline cellulose encrusted by lignins and hemicel-luloses.

Cellulose is a straight, fibrous and extremely long polysaccharide madeup of severalthousand, beta-glucosemolecules that are rq-1 C-4 linked. In wood, cellulose forms a rope-like structure. - About forty-polymer chains align parallel to each other to makeup strandsknownas elementary fibrils. Several thousand of these fibrils threaded together formmicrofibrili, which themselves intertwine to form macrofibrils. The macrof!brils give formand strength to the cell wall by binding together in alignment. They are visible usingelectron microscopes, and appear as thin striations In the cell wall,

The elementary fibrils are surrounded by shor'ter' chain molecules called hemicelluloseswhich have different monomeric nits' 'with d*e-g'reesof polymerisation of around 100. Thehemicelluloses are adapted to the cellulose crystalline system, and form the most hygroscopic

fraction of the cell wall.

Lignin Is depositedonto hemicelluloseand Is bondedo it. It doesnot bondwith thecellulose itself. It is an a3orphousubstancederived from phenyl-propaneuilding blocksandgives rigidity to the wood.

- -1 1. ''I -. 1'4.

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Thecell walls are constructedof, four layers;, the primaryuall, and he outer, middleand nner layers,of the secondarywall. Theyare distinguishedby the orientation of theirmacrofibrils (See,igure 2-1). The hick secondary all Is depositedon the inner side ofthe primarywall andprovidesby far the majority of the cell wall substance.

Between'thewalls of adjacentcells is anamorphousegion packedwith lignins known sthe.middle lamella. ThecellAumina are connectedo eachother.vii pores-in-the call, wallscalled pits. In fresh wood, its act as valvesandallow for the passage f,water frcm onecell to another, but, -In deadwood,mostpits are closed.,

S3S2si

Mmarm allFigure21 Organisationf cell walls n wooailres.

Thewalls contain tanins, resins, fats andwaxes,whichoccupya proportion of the

cavities andopencapillaries existing betweenibrils, microfibrils andelementaryibrils.Thecapillary system s extensiveandmakes p about40% f the cell wall volome.For eachcubic centimetreof cell wall, It Is estimated hat there is 100-2-00squaremetersof surfacearea. A roughguide to the dimensions f pores in woods givenbelow: ,

Fissures within elementaryibrils InzCapillaries betweenelementaryibrils IODM

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Capillaries betweenibrils up to 80nmPares In pit membranes up to IsonmDiameterof-a watermolecule 0.2nm

There Is a great diversity In size, shapeand juxtaposition of cells from one species toanother. The different species of woodmaybe broadly divided Into two groups. Theseareang!osperms, knownas hardwoods,and gymnosperis,known as softwoods. Both are constructedby two Inter -penerat Ing systems f ceils; oneoriented radially andthe other lon-Zitudinally, which are Interspersed by intercellular 3pacescaUed resin canals.

The Iwogr^. ps canbe distinguishedby their different cellular ccmpcsiticns. The argepores, evident only in angiosper:s, are called'vessel3. Theseare madeup of smaller tubularunits that are-joined-end tO end to fcrz passagewayshat : an vary In length from a few cen.tIzetres to several meters. They are used In the 46aI.sportation of water. lost are oval inshape, and their spatial arrangementsare fixed, makinj themuseful when dentifying species.

I,he tissue betweenvessels Is madeup predominantly of tjo types of cells. Theseare thin

walled trachleds, -andthick walled fibres. These ypes of cells are commono both an-glosperms nd gymnosperms.n gymnosperms,s much s 90%of xylemsmade p of verticallystacked rachleds whichare elongatedcells that are arrangeduniformly, andhave engths-ofbetween and7 millimetres. Fibres resemblerachleds but have hicker walls, fewerpills,andsmaller umens. ibres erm hebulk of the solid matter oundn angiosperms.

Thereare a number f other typesof cells found n wood uchas the parenchyma,ndtheresin-producingepithelial cells. Themajority'.cf cells in woodare oriented In the longitudinal direction. Theradial elementsare called rays. Theseare composedf passagewayswhichradiate outwards ike the spokesof a wheel. Theyare usually 10 to 15 cells wide, andare often associatedwith horizontally oriented resin canals. (See igure 2.2)

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Homogeneousrivs composeaentireig of paaialIgorientatea cells.

Fivre 2.2 lag Patterns in wood

2.3 The DecOmpositionof 'Jcod

Heterigeneous ragsuntaining UPI-ightcells.

There are three methodsof attack : ausing the deccmpositlon o! -jood'"; a chemical attackcausedby -,xygen ard water, a vegetable attack by fungi, mic:o-crianisms and bacteria, and ananimal attack causedby insects.

In the first process, the long cellulose molecules are broken downAt h the result thatthe mechanical strength of the cell walls is weakened nd the woodbecomes rittle. The cel-Julose undergoesa slow, natj: al, decomposition In the presence of oxygen, heat and light.oxygen is the main deterioration agent, and tte process is accelerated by the presence ofU.V. Ilght and high temperatures. Lignin decomposesn the samemanner,but at a muchslowerrate.

Vater causes he hydrolysis of certain compoundsn xylemand canalso be the basis forother decomposingactors, suchas fungal growth. A number f fungi are able to live from'wood,using it as a nutrient. This results in the physical decayandweakeningf the wood,whlcgives"rise to both orfzontal and vertical cracks.

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Attack from micro-organisms may occur aerobically and araerobically. Anaerobic processesOcc'jrunderwater, or in the mud t the bottomof salt or ! -9shwater.,,The,micro-orlanismsattack the cellulose, breakingIt down nto ethyl alcohol, acetic acid and, finally, carbondioxide andwater. Methaneermentationprocessesmayoc=r by meansf anaerobicmicro-organicattack, andthe wood an lose up to 65-85%of Its solid cortent. Lignin is rotdecomposedirectly by methaneermentation,but xylemcanbe converted o humusIf it staysin water long enough. Enzymicattack fis least effective In acidic =rditions.

Animal decomposition arises becausemany nsects, Or'their larvae, dilest'xylem.. ""

TheProcessof deterioration of woodn wet araercbic c:-dIticns is a combination f theabove. Firstly, the readily soluble materials In the vocd! Issolve into the surroundingmedium,ollowed by readily hydrolysedcompcunc'such as pe: Ins andpentosans.,Mcrobi3logical degradationof the morestable cellulose andhemicellulosewill then follow.Finally, lignin remains, hough his too maybe deccmposed--ymicro-organismsn an anaerobicenviro-nment.Both fungi andbacteria cause he breakdownf xylem, andboth use extra-,, ',cellular enzymeso hydrolysethe cellulose, hemicalluloseand Ignin. ' Degradation preadsthrough he capillary systemof the wood s far as the ext: -cellular enzymesan penetrate.

-The degree f degradationcan husbeexpressedy the remainingellulose, hemicelluloseand119nin"'. Scanninjelectron microscopy'"' reveals that degradationoccurs InitiallyIn the secondarywall, starting in the lumen,and progressing nto the cell wall. Structuresin whichdegradation s extensivemaycontain only 30% f the original cell wall substance,with 90-95%f the,carbohydratematerial havingdisappeared. Even he middle lazella*maybecorrodeJanddissolved. As carbohydrates re removedrom t.he fibrils of the cell wall,, --cavities are producedwhichfill with water. In these structures, water acts as a bulking


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agent, which keeps the wood n shapeas long as it is kept -jet, by preventing the remainingcellulose molecules from combiningwith eachother via hydrogenbonding of adjacent hydroxylgroups.

The result of the decay of cell material Is a considerable loss of original strength. Itthe wood s extremely decomp", He uah: content can be as muchas 9095. Den In at atIS r'elative humidity, such woodAl! start to collapse. hen drying, :.,d jat? r-logled -icodS'l. ' as thehowsvery strong shrinkage, warping and cracking, and even complete disintegraticn,strength of the capillary system s exceeded Y the contracting capillary forces Of theevaporating water.

In many imbers, the decay is nor-iniftrt, and three regions of deiradaticn -.an be Iden-aatifled. The decay Is mcst advancedat the s=face ct these samples, which become xtremelysoft, and greyish-brown In colour. Belowthi's lies 3 thin ! 1brous layer In which thle break-

downof the cell walls Is less advanced han the cuter layers. 71,': luner core cf these

sampleshas the apppar:nue of fresh Ulbe,,st is .ompletely saturated with wate:. Collapse

c! the cells Is muchgreater on the outside layer due to greater voids In the cell wall,acausedby the removal of celluflose. : ells In this rellon ccwntaln ittle morethan the -middlealamella and someprimary wall. In the two less degraded layers the secondarywall is still

Present, although frequently contracted and 1osened rom its position.

2.4 Methods f ConservingWater-loggedWood

Vhen estoring water-loggedartefacts, it is the aimof the conservationist to produceafinished product that Is stable in the envircnient In ihich it Is to be kept, while maintain-tIng as many f the original aesthetic qualities of the artafacts as possible. '


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!n the : age of woodartafacts, the proble3 !s red,-, ed to Iftat of drying outthe sampleswhilst preserving their overall shape,and appearance. Oncedried, Ahe artefactsmust be able to withstand changes n the surrounding temperature and relative humidity.- Some

protection against fungal and organic attack Is also desirable.

Re first successfully employedmethodof -.onservaticn, cf. water-logled woodwas the alum

method,ntroducedby jorgensen"' In 11859.Thesampleswere soakedn boiling potassil;m-aluminium ulphateunt'j. the water In the samples adbeenreplacedby the alum,,andthe'sampleswerethen left to cool. Thealumsolidified in the pores andcapUlaries of thewood,acting as a bulking agentandtherebyprevenUngsubsequentollapse.

Themethod adseveral disadvantages.It :equiredthat the surfaceof the samples ecleanedandtreated Ath varnish, or some uch protective suter layer. It wasnot revers-ible. It was oundthat the water vas rezoved rom the sa., les faster than the alumcould

.14tresses ,mpregnatehe structure, leadingo'Internal . Someollapse. Furthermore,hesuccessf: the method asunpredictable,nddependedntheamountf alumabscrbedy thewood, nd-the onditionof thewoodtself. I -- .? ' - 1.. I

, Thedeogreef shrinkage,n woodas It dries Is proportional to the capillary forces ofthe evaporating,iquld, andshrinkage s less pronounced hen rying Is fast. It is possibleto reduce hese forces by replacing the water with volatile, low surface tension liquidswhich, uponevaporation,exert far smaller forces on the : ell wall. Ethyl ether andtertiarybutanol weresuccessfully,used n early trials In a number f caseswhere he degradationwasnot severe.

' Analternative wayof reducing hese forces Is by freeze-drying the samples. Thetech-niquedependsuponhe sublimationof ice within the Yoodbeing such hat-the drying-waterphase s avolded. -III,, 111 1-II., "I. -I I- II


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"'In general, someconsolidation will Wrequired with both of thesetechniques. Freezedrying from iater often gives rise to Innumerableracks,causedby stresses set up vhenthewater freezes. These anbe'avoided f the samples re pre-treated with bulking agents,while a final treatmentmaybe requiredwhen sing the alcohol exchange ethod.

"Consolidation of the'saturated'xylemcells has beencarried'out using a variety, of bulk-ing Iagents. Early attempts nvolvedembeddinghe woodn a hardwaxby impregnation t hightemperatures. Substitution of the water in the woodor alcohols wasnecessarywherehewaxes sedwire insoluble in wate.. 'Objacts that'are totally iimprel.ated In this waycanbeexpectedo reiain, lr a fixed state ove"r or,&'periodsof time, but the surfacesusually re-

in, but the simplest cf sur-uire extensivecleaning, which s normallydifficult on anyth,-sfaces. The'processcanbe slcw if the waxes o not readily penetratethe wood.

To speedup the rate of Impregnation, everal attemptshavebeenmadeo Impregnate hewoodwith monomersuchas vinyl acetate, methylmethacrylate,ndzoncethylene lycol, -andthen to polymerise'these nside the cell walls using catalysts. The oxicity of the monomersand ire risk ire serious drawbackso using'this method,however,andIt canbe difficilt 'toobtain a satisfactory surface. The echnique s non-:eversible, andcanresult in someshrinkage n the wood ponpolymerisation.

2.5" Stabillsation-of Vatei-'IoggedVoodusing PolyethyleneGlycol.

Themosteffective zethodof conservingwater-loggedwoodo date is by ImpregnationwithPolyethyleneglycols (PEGs)"". Theseare water soluble polymersof ethyleneoxide. PEGsare producedn different grades hat are designateda numberepresenting he averagemolecularweight of the grade. In general, PEGsvith molecularveights of between 00and


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600 are clear, viscous liquids at room emperature,while those with weights of between1000and 20,000 are white, waxy, solidsM,. At higher molecular weights, there Is a decrease Insolubility, vapour pressure and hygroscopicity. The changes n the polymer properties withmolecular weight are significant whendecidingwhich grade to use In the preservation ofwater-logged timbers. Lowhygroscopicity of the finished product is desirable but. at thesame ime, the conservationist must consider the ease with which the different grades canpenetratethe water-loggedartafacts, aswell as the effectivenessof the different grades nstabillsing the timbers.

, The treatment of water-logged artefacts using Polyethylene glycols was first IntroducedIn the early 1950's by Centerwall and Moren"'. They adopted a technique whereby he ar-tefacts were Immersedn PEG olutions at 65 degreescentigrade. The concentration of thesolution was increased daily from 0% o 100% y increments of 15%.

In early experiments,amplesreatedusingPEGSJith molecular eights etween5,000and20,000developed ollow cheeksafter beingallowed o dry for several days. Samplestreated with molecularweightsbetweei1,500and3,000underwentittle or no dimensionalchanges, ut it wasnoticed that thesesamples ecamereasyand ncreased n weightwhenhehumidityOf the air rose. -

PEGsavingmolecular eightsn the intermediateange, . e. fro: 4,000o 10,000,providegooddimensionalstability to the water-loggedwoods,whichshowno tendencyo takeup waterat relative humidities of less than 83%. Treatmentsusing PEG ,000were avoured,as the lowermolecular weightscould penetrate the woodaster than the larger molecules.


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Today he conservationist Is still dependenton the PEG-vatersystem. lt'Is relativelycheapand dces not provide a health risk to those working with it"". In most cases, PEG4,000 is still used or, for well preserved wood,PEG , Soomaybe chosen; as the smallermolecules will penetrate better into the wood.-Treatment Ath PEG 00, followed by freeze-drying, has also proved useful.

The mportant factor in addressirl'the questionof how?EGs'prevent'sh.Inkage-s todeterminehe degree o whichPEGsf different Molecularweightsoccupyhe cell wallspaces,andhow,much f the boundwater Is replaced,or howeffectively prr'-occupiescelllumina.

PEGsmpregnate ither the cell wall, the lumina,cr both. Thebulking effect thenprevents he collapse of the cellular strilcture on drying. PEGs f molecularweights n terange200to 600replace 3ome f the boundwaterduring soaking reatments,andIt is assumedthat they remain n the cell wall upondrying. ThesePEGsffer substantial dimsionalstability to the woodevenat concentrationswell below he fibre saturation point of thewood.

PEGsn the molecularweight range1000 o 3000are also expectedo infIltrate theultrastructure of the vood-but, at higher concentrations,are also expectedo bulk'the cellluminaas well. PEGs ith molecularweightss:eater than 3000are expectedo resistaashrinkage orces by bulking ol'the'cell 1umIna nly, -as their solution sphere s too large toallow them o penetratethe cell wall.

16


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The grade of PEGhat is mcst suitable for the preservation cf water-logged timbersdependsheavily on the state of the wood tself. A detailed study of the preservation ofwater-loggedwood,using PEGs,wascarried out by Hoffman"O', in whichhe attemptedo re-late the degreeof wood egradationandPEGmolecularsize to the amountofPEGakenup bythe system, the stabilltY achieved, ard the resulting hygroscopicity.

Hoffmannused PSGS ith different molevilar weights from . 00 to 4000oa voods with watercontent between120% nd 580%. The fluorescence tests develcped by youngand 'Jainwright'"'were used to assess the extent of penetration of the PEGs. AYIellow to Ir een fluorescence Isinducedn woodby shortuave ight Of wavelength 50-490n.m. The luorescenceorigirates fre:lignin. PEGstained with cobalt thio-cyanate suppresses this natural fluorescence, which canbe observed nder a microscope.

The anti-shrink efficiency (ASE)of a treatment was def! ned as:

(BO BD/BOx 100%

where30 is the shrinkageobservedn untreated wood,and31 Is the shrinkageobservedntreated samples. A good ndication"U'the rel-atlonshipbetweennitial watercontentand thedegreeof shrinkage o be expectedor the different treatments s given in figure 2,3.

Theresults showedhat some EG enetrated he wood,whichevergradewasused,but thatthe penetration, using lowmolecularweights, was superior to that when sing high molecularweights. Thevarious degreeso which he fluorescencewassuppressed as ndicative of theeasewith whichPEGspenetrateddifferent regions of the cell. The ost accessibleregionsare the corners of the cells and he middle lamella. Next is the primarycell wall, and the'Bostelusive region for the PEGmoleculess the secondarywall.

17


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C"OssSectionalShrinkage 401.4.

U-A

IdI Wl" Ix.. -I _ Itp@atnent 321 -, , .11/, PEG 9g PEG 99

PLC1590

plase 3090130 2ig 363 40 440Maxmcisture antantof imodrigure M Stabilitg acheivea reating water-loggea waacls ith Wferent PECS-

qoffmannconcluded with the following:

ID PEG ,5010 asCOnsistentlypoorat effectin., the ji. -e-S,40nalstability of water-loggedwoodo: all watercontents.

Thehygroscopicitywasgreatestwhenowmolecular 4eights were usedbut, even nthesecases, relative humidities were1'0%-80%efore there wasevidenceof leaching.

In relatively fresh timbers, wheredegradations not severe,stabilisation isbroughtabout mosteffectively by lowmolecular.welghtPEGs,. e. small moleculeswhich enter Into the'large parts of the capillary systemof the cell walls, middlelamella andeel , -corners Here hey replace the 1water,nd, on drying, keep he woodin a swollenstate. Voods avingwater contents.of up. o 160%anbe treated In thisway.

is


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In heavily: degraded'woods aving moisture,contents upwardsof, 400%,especially wherethe secondary'wall'has been destroyed, there Is evidently not enoughwoodsubstance!eft' to be kept'swollen by s2all'FEG moleculesand,thereby, stabillse the whole -car-

pus. - In this case, stabillsation is moreeffective If the wcod s bulked usinghigher'molecular weights. Concentrations,of around 70%are required In these cases.

these' woextremeshere His a region of -joodcontainingboth highlyV) 3etween%degradednd well preservedcells, eachcomponentf whichrequires a d! ferent gradeof PEG.n this case, 111tute5of different jradeszaybe used,or consecutiveap-plications of PEGmayprovide the solution.

Referenl-as

I. Stamm. WoodandCellular Ecience. Pub. RonaldPress, NewYork. (1964)2. MorleyP.R. "PowTreesGrow. Pub. Edward rnoldLtd. (1963)3. PanshinA.J. anddeZeeuw. "Textbook f 'JoodTech,nonlogy.Chapters4,5,11. Pub.

McGraw-Hill,NewYerk. (1980)BorginK. "Themechanismf breakdownf 'he structureof wood ,., to environmentalfactors. J. Inst. Vood cl. Vol. 5, pp6-30. (1971)JespersonK. "The decompositionof wood., Int. Symposiumn conservationof largeobjects of water-loggedwood. Amsterdam. Scept 977)Borlin K. "Theuse of the electron scanningmicrOSCOPeor the study of weatheredwood. J. of Microscopy.Vol 92, pp,47-55. (1970)

7. Findley G. J.D. andLevyJ.F. "Scanningelectron microscopy s an aid to the study ofwoodanatomy nddecay. I- Inst. YoodScl. Vol 4, pp 57-63. (1969)

8. OddyV.A. IED MaritimeMonographsandreports. Vol 16, pp 45-49. (19715)


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9. Christensen B.B. "The conservation'of water-logged wood n the National Museumf,Denmark. Studies in Museum ech. Copenhagen. (1970)

10. Murray H. 'Conservation of artifacts from the MaryRose. , Jagels R. "A deterior-tion evaluation procedure for waterloggedwood., Barbour R.J. wCondition anddimensional stabillsation of highly deteriorated samples. , Foffzan P."Stabilisation of water-logged woodwith PEG.- Molecular si: e v degree ofdegradation. " Proceedings of the ICOnwater-logged wood working group conference.Ottowa. (1981)

11. Union Carbide Material data safety'sheet No. F-48039A-GB.

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CHAPTERTheTheoryof NMR elaxationandDiffusion Measurements,n HeterogeneousSystems.

3.1 Introduction.

The Nuclear Magnetic Resonance henomenaccurs whennuclei possessingmagnetic momentsinteract with an applied magnetic field. The theory on which NMRs founded is well estab-

nS4 -le fract nished andhasbeenadeli; tely describedby a number. authors' ". A CC i erab ioof the theory canbe explainedusing classical ideas andthis simplifies its understandirg.In, this chaptera brief accountof the resonancehenomenas givenand he conceptsofszpin-lattice and spin-spin relaxation timesare introducedby adoptingwherepossible, "hisclassical approach.,

The Interpretation of NMRrelax3tion times in terms of real, physical, mo! cular eventsa3 that can account for all the types cf, behaviouromplicated, and ttere is no unique modelthat have been observed. An underst3nding of howmolecular motions lead to an observedrelaxation time Aas, irst prcpcsed by BloemtergentPoundand Purcell"'. Their theory couldpredict the characteristic behaviour of relaxation times observed In bulk water, but couldnot account, or those cbserved in less uniform samples, such as cellular systemsand polymer

solutions.1,1. III

For water In thesemorecomplicated ystemshere are a number f effects"', mostnotably multi-componentelaxation, an increase n relaxaticn rates relative to bulk water,and a variety of-temperaturedapendencles,whlchstem rom the modifieddynamic ehaviourofthe water molecules,and n some ases rom the magnetisationof the substrate. Thesehavenecessarily led to a number f theories which extendthe Ideasput forward by Bloambergenetal. Somef these are described n this chapter. Althoughproton resonancen water is themainconcernof this work, the description of the relaxation phenomenas kept as general35Possible.

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Self-diffusion ccefficients for water in heterogeneoussystemsare conveniently measuredusing NMRtechniques'&-". Twomethodsare used during the course Of this work, namely thesteady-field gradiert techrique and the pulsed fleld-gradient technique, and descriptionsnecessary for the Interpretation of the results from both methodsare presented in this chap-ter. The effects of anisotropy and compartzertation on the observedself-diffusion coeffi-cients are also considered.

3.2.1 Furdamental Concepts.

A nucleus is a compound yst?m which mayhave a non-z-ar: angular moment=hl, and a mag-netic moment . The two juantities are related by the equation

gammahl

Theconsiant,of proportionality -g'amma'isharacterist c of the nuclear species.Nuclei otherthan thosewith evenatomicandmassnumbersossess nuclearmagneticmomenthenn theirgroundstate.

Quantumheory predicts that for a nucleuswith spin quantimnumber , the componentfangularmomentumesolvedIn anyspecific direction (e.g. the z dire-ction),mayhaveany oneof 21+1observablevalues givenby m(l), wherem(l) canadopt.ntegral values fromm(l)to m(l) : fl. Vhenplacedin a magnetic ield of flux Bothe corresponding ermissibleenergies p3o are given by

Em= gammahm(D.Bo

idherehe energy evels are separatedby an energy

3.2

22


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9E= Es(l) EMU 1)= gammahx Bo(m(l)-m(l t D)

gammahx Bo 3.3

The probability of spontaneous ransitions betweenenergy levels is proportional to thecube of the frequency of the energy associated with such an event. The frequencies encoun-

n 'ds'avallable and areered In NOR xperiments are limited by the size of the magnetic fieltypically a factor of 101 downon those of optical spectroscopy, and thus the probability ofspontaneous ransitions are negligible. Transitions maybe Induced by the presenceofelectromagnetic radiation of angular frequency 'Jo, satisfying the rescnancecondition

hVo=U : 'iana xhx Sovo = gammaSo 3.4

For a typical laboratory field the frequencys in the r. f. range.

A first order perturbation t: eatment ields a probability of t: ansition proportional tothe strength of the perturbing r. f. field together with the selection rule of tz = 1.

anensemblef nuclei underthe Influence of a static homogeneousagnetic ield BOattemperature . the 21+1energy evels are occupiedat equilibrium according o the Boltzmannfactor

exp (-m(l). gamma..Bo)/KT

Therelative populationsNm(Dof nuclei occupyinghe m(Dth energy evel is then given bya

23


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Nm(l)/Nm(l D. 2 exp (gamma..BO)IKT , 3.5

There s there!ore.a surplus of nuclei in the lowerenergy evels a consequently net mag-netisation Mo n the direction, of, the applied, ield. As the probability 3f excitation fromagivenstate Is proportional to the populationof that state, and he lowerenergy evels aremorehighly populated here will be a net absorptionof energyon radiation. (See igure 3.1)

PCpalation

x1 4/2

2 PossJ619enerS9 evels with spinsaistrauteimongsthem ccorain,oBoltzmann'sstatistical theors.(a)figure 3.1 Theaistrilution of Parinetic pinsU. a nucleuswith 1 1/2.

TheBlochEquations3.2.2

Th observablequantity measuredn NMRpectroscopys the vectorial sumof th in-

dividual nuclear magneticmoments . The ime dependencef the magnetisation ector in amagneticield Bo Is describedclassically by the famous 1:ch"' equations.For a magneticfield in the z direction thesecanbe summarisedy a single vector equation,

dM(r,Q/dT gamma.M^Bo) (?, i + Myj)/T2 - (, ,:-Mo)k/Tl 3.6

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T;he term gazzma. Badescribes the effect of the torque experiencedby the magnetic mo3ent nthe field. This torque causes the precession of the magnetisatiOnvector about the z axis atthe Larmor frequency Vo, 'which is identical to the angular frequency of the electromagneticradiation required to match the : esonancecondition and indice %transitionsbetweenenergylevels.

The system has classical a classical analogue in a gyroscope. !Jlnena gyroscoperotatingabout Its axis initially vertical Is Ideflected ! rcm the vertical through an angle theta, thegyrosccpe, while continuint to rotate abcut Its axis, precessas about the vertical. The r3tecf precession is dependson the massdistribution within the gyroscopeand on the strength ofthe gravitational field.a

In an analogousmannerhe Individual nuclearmagneticmozents nd heir resultant, thenet magneticmoment_M_Ojhen isturbed fromequilibrium alcng the applied magneticield willprecessabout the applied magnetic ield Boat a frequencyproportional to that field, anddependentpon he 'mass' distribution within the nucleus,and herefore will be Onaracteris-tic of it. In the event, the rate of precession s given by jamma..Bowheregammaas'thesame umericalvalue as in equation3.1. Hence ammas frequently termed he gyro-magneticratio.

it is this phenomenahat allows the nuclear magnetic esonanceo be observed. t Is un-necessaryo consider the nuclei Individually; they canbe represented y the net magneticmoment o. If this is disturbed from its equilibrium along the direction of the applied mag-netic field Ro, Mowill precessaboutRo. If a coil of wire is placedwith Its axis in thex-Y plane perpendicularto the t, axis, In the direction of the applied field direction, itwill havea voltage inducedn It as the flux passing hrough t changes s Moprecesses.This Inducedvoltage signal whichIs proportional to the magnitude f Moandthe rate ofprecession,canbe amplified anddetected.

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The secondand third terms on the right of equation 2.6 were Introduced by Bloch to ac-count for the effects of spin-spin and 3pin-lattice relaxation respectively. They indicatethat the component f magnetisation in the x-y plane decays in time to zero, uhilst the com-ponent In the direction of the magneti: field relaxes to its equilibrium value Mo, as Isdeterminedby the Boltzmann'distribution of nucle! amongst he available energy levels.

3.2.3 TheRotating Frame f Reference.

Theapplication of an alternating magneticield Bly perpendic-flar463he static field 3oandat the resonant requency;o = gamma.o, will induce ransitions betweenhe energyaleyels and c3usea net absorptionof energy rom the radiation field. If the amount f energyabsorbed y the spin systemss sufficient to equallse the populations, then the systemssaid to be saturated,

In addition to disturbing the equilibrium Boltzmann ist: ibution of spins amongstheavailable energy evels, the peitur'bati-on aused y the field BI also causeshe individualspins to precessaboutthe direction of the external field 2-o n phasewith eachother toproducea net magnetisationn the x-y plane.

To'understandhe effects of the field Lt rotating at the Larmor requencyn the x-y0plane it Is convenient o considerthe behaviourof the magnetisatIon ector MIn a rotatingframeof referencerather than the laboratory frame. Observedroma referenceframerotatingat a frequency'Vr'abouthe z axis, a disturbed magnetIsationwouldappear o precessat afrequencyVo Vt. Equation3.6 Is still valid providedthat the magnetic ield Bo is re-placedby an effective field B,.LL, such hat

B.tt : Bo- Vr/gamma 3.7

04


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zp 'armor frequency 'do, the effectivehus or a frame of reference W, f,, ), rotating at the Lfield B.,, is zzero,and he mapetisation vector is stationary, existing as Mo n the z'direction at equilibrium.

The application of an oscillating magnetic field of strength 2.31 and frequency Wo n thex-y plane of the laboratory frame of reference is equivalent to applying two counter-rotating! ields each of strength 31 and rotating about the _:axis with angular frequency +Qoand -1jo.Oneof these componentsotates In the samedirection is the nuclear spins and the otherr-, at? s In the opposite direction. The latter can be Ignored as Its Interactions with the

nuclei cancel to zero over each complete cycle. Viewed n the rotating frame of : e!a7encethowever, the component otating wlt%, he nuclei is statinn-a-: , and Its lnteractln with 10 I'snot aurngad Lozero.

up

I-J. , Mo Altel. IN4 NIS@No" 3.2 vierts onma t gooanamo paiseamaimeticiemit.

The awsof mechanicsre independentof the frameof reference.Thus f B-IIs appliedalonga specified direction (e.g. the x' axis) then the magnetisationprecesses bout the xfaxis with an angular frequencyof gamma.l. In time t, the magnetisation ector precessesabout31 throughan angle

gamma.1A 3.8

No no nit

Ma fter 90#pulsexo;; oD1

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A pu se BI of suf fI cient' durat Ion to Up the zagneti sat Ion vector Into, the xI -y" pI ane fromthe equilibrium along the z' axis Is termeda 90 degree pulse. A 180 degree pulse rotates themagnetisation vector through 180 degreesabout the direction of 31.(See figure 3.2)

and Spin-Spin (M-lelaxation.,2. '4 Spin-Lattice (TI)l

,, The return of an either completely or partially saturated systemto equilibrium followingthe removal of a perturbing field LI occurs via two simultaneous processes.

Spin-Lattice Relaxation.

'Jhenattention is focused on a given spin system, all other nuclei and electrons In the

%, 'he lat-ampleare collectively referred to as the lattice. A transfer of energy to or ! rcmtice from the spin system,resulting s1romransitions of nuclei between pper and!owerenergystates, canbe Inducedby the presence f f luctuating fields in the lattice, If thereis a componentt the appropriate frequencyo Ind-ice ransitions. This enables he return toa Boltzmannistribution of the nuclel abouttheir energy evels at a rate which s charac-terised by the spin-lattice relaxation rate IM. -- .11,1 1"I" 1-11 ". I

Spin-SpinRelaxation.

Thespins return to equilibrium with eachother via'spin-spin interactions bet1jeen,n-'dividual, nuclei. 'This Involvesan exchangef energybetween-the uclei of the same pin Sys-temso-thata transition,. froman upperto a lowerstate Is, matchedy'a transition from alowerAo an upperstate. Thesimultaneousransitions cause'a loss of, phasecoherencen thespin systemwlthouta changen the net energyof the system. Further loss of, phase, ),coherence rises from local field anomalies.Eachnucleus n the spin systemwill Interact

28


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with non-zero magnetic fields producedby the lattice and other spins of the samesystem. Asa result of these Interactions there 13 a spread in the local fields, I'M, experienced by dif-ferent, nuclei, which gives rise'to a distribution of precessional frequencies.

The'effect of spin flipping and local field anomalies on a syste:a of nuclei precessing inphasefollowing the application of an r. f. field LI, Is a loss of phaseat a rate gamma..Hence he voltage induced In the deteciing coil will decrease, representing a decrease .n thecomponent f the net magnetisation in the x-y plane. There will also be an additicnal loss ofsignal in the x-y plane as Individual nuclear magnetic 3oments eturn to there equilibrium

,,distribution with the lattice. The spin-spin relaxation rate 1/(T&*), is defined as the rateof Icss of magnetisation in the x-y plane, whIchlis therefore given by

I/T24 ,Samma.+ I/Tl

3.2.5 ' 'PulsedNuclearMagnetiz. esonance.

3.9 ,

In pulsedNMRmeasurements'B-ls applied to a spin system n a series of short duration,high powered ulsesat the Larmor requency.Usually theseare in combinations f 90 degreeand180degreepulses along the x1 or j! axesof the rotating frame. Theresponse f anuclear s'pin iystes to a sequencef-such pulsesprovidesmethodsor measuring I andT2.Phaseor diode detectors are employedo monitor the behaviourof the componentf magnetisa-tion' in the'xl-y' plane. Diodedetection records the amplitudeof the net voltage induced n.he detecting coil and'is in turn proportional to the net magnetisationn the V-y''plane, :whereas hasedetection, using the r. f. 'sourcefrom which81 is derived as a reference,detects the componentf magnetisation longsome articular directionln the x'-y' plane.

Z9


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Q) TheFree induction,Decay.

For a nucleus of spin 41/21here are onlytwo possible mi components, . e. 'I/&, and -112.Thesehave different magretic energies, *Po and -gEo. The ratios of the populations of thesetwo states-is given by

II Nu/Nlz exp(-2.4o/KT) 3.10 -

In practice PBo


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Zexp -, /Tl) 1 3.12, (T) = Mo xII, t.

Tozakethe observationa 90 degreepulse is appliedwhichenablesan irstantaneousmeasumentof M;.o be cadeby rotating 11. nto the x1y' plane. Thus he Initial height ofthe decaycurve following the 90 degree . f. pulse is proportional to Mzat tIMe T.

After a time of not less than S-x 1% the spins have effectively returned to equil Ibrium

and. he sequencemaybe repeated using different, values of T. From he measurement f theinitial signal amplitude, and ising, expresslon,112 a ial,.,e of TI maybe determined.

(H) The Measurementf 1161na.pin-SpinRelaxationTime,T2.

An nitial 90 degreer. f pulse applied along the 1! axis to a spin systemn equilibriumrotates the magnetisationMo .nto the ) direction. Thephasi coherences lost as a conse-

quence f the combinationof SFID-lattice relaxation processes nd he inhomogeneitiesn thestatic field at the site of the nuclearspins, some f which are due o other surroundingnuclearmagneticmomentsndsomeo the Imperfections n the applied magnetic ield. Theob-servedFIDdoesnot therefore give a true measure f the spin-spin relaxation time T2, whichshouldbe independentof the applied field. 1

The oss of magnetisaticnn the x-y plane hasbeengivenby1/T&^* gammaEB+ IM 3.13

Incorporating the No sourcesof the spread n the local fields at the sites of the in-dividual nuclei, i. e. changesn the local field_producedby other neighbouringnuclei andfield Inhmogenelties In the applied field, equation3.13 maybe expandedhus; II

I,., - , - I/M - gammaMinhom.+'EBs)+I/Tl- 3.14

31'


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T "Bs Is determinedby the sample. Thejhe term t'Binhom. Is dependentupon the equipmentwhilst esPin-SPin relaxation rate I/T2 is defined as gamma.Bs + I/Ti. To determine the spin-spinrelaxation rate correctly somemechanismmustbe devised to eliminate the effects of applied2eld InhomogeneRles, I. e. 931nhom. This can be 3chieved './ the Hahi Spin-Echoexperiment"".

The sample is exposed o 3 90 degree :. f, pulse causing the net magnetisation to rotatefrom the +z' direction to the X1 direction. Nuclei will subsequently precess about theaxis. Nuclei In the sample'where he applied static field ;.s higher than the meanJillaprecess ! aster than those in weaker regions of the field. Viewed n the rotating frame ofreference the'spins dephaseaho-jt the :e axis. An indIvid,Ual,-it: leus will precess through anangle 0 relative to the mean.

a '23) xT Ci= 7amma I.Hinhoz. + I-

nccorporatinghe spin-lattice effects and escivinj the agnetisation long he 11 andaxes

MX'(T) MOx Isin(g3mmax Minhom SEWx T)l x exp (-T/Tl)Mox sin(e) x exp (-,r/Tl)

3.16and

Myl(i) = Mox cos(O)x exp (-T/TAI,. 3.17

'If a 180 degreepulse is applied about the xv axis, Mx1 emainsunchangedut W Isreversed;becoming-11,0.SB! homs uncharnd, but as the 1.50 eorpi p1se hasreversedthe2 11 r,I .. 14omponentf the fi. .s due o all of the resonant ucle,,,Us is also reversed.Thenew recessionate is; gammaMinhom- 3s)

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After a further timeUs) x T)i x eipo x tcos(-O Minhom -t

Mo x Iccs(gamma 2x t'Es) x Ti x exp (--!-riT1)

- Theeffects c. Uinhomhavebeeneliminated, andsuczingover all resonantnuclei, 3.13becomes:

MY'(2T) 2 Mox exp (-ZT/T2*)

Theva!ue of T2* could be derivedby repeatingthe pulse sq,, erce at. different valuesofInstead,spin-spin relaxation tizes in 'Nzz wo: weremeaswedsinj lta --ethcdof Carr andPurcel and inccrporating the MeibcomndGill"21 modificatlon,(CPMG).r4 ri.

,, AnInitial 90 degreepulse 'Is applied to the spin sYste-' n equilibrium to rotate themagnetisat'lonMa nto the f direction. Theeffects of static field inhomogeneltiesn TZ*canbe removedf after a time ra 180degree . f. Pulse is applied along the j! axis. Thisrotates the spins aboutthe V axis so that-the faster spins are now aggIng-In phase, whilethe slowspins are leading In phase.It requires a'further time before the*quickly"precess-In& spins recover their phase oss andthe slowly precessingspins lose their phaseead. Ata time 2T theref, re', the spins will refocus along',,he 4! axis andthis All be seenas aLnecho n the magnitude f the magnetisation.

After the rephasinghasoccurred he spins once againbegin -10 ephase. his processcanbe reversedby the same 80r. f. pulse alongthe V axis. A train of IN degreepulsescanbeapplied at Intervals of 2T, and echosignals observedn a cne-shotexperiment.This Is theCarr-Purcell sequence.

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This'particular sequences susceptible o a cumulativeerror. 'If'the 180degreepulsehasbeen3is-set by an amount , or Is Inhcmcgenecus,henan error of 3 degreeswill reducethe'amplitudeof the first echoby cos(O).After a second ulse the net error Is 20 and,. ereduction n signal amplitude s cos(23). After n pulses the cumulative eductionIs Costno)., singthe Meiboom-Glllmodification of the Carr-Purcell sequencehe phaseof the 180degreepulse is shifted so that the rotation Induced y the refoc-Issing,ulseoccursabout %e'f

, Itial 90 degreepulse a nucleusprecesseshro g n3linsteadof the x1 axis. After the in uhae19wouldbeof +j elative to'the f 'axis. Followinj a :ntatlon of 160 erreis the phaseang

and f the angleof rotation were o be less than 180degreesby an angle90, hen themagnetisationwouldbe SO bove he x1y' plane. After a time -r the deph'asingasbeencan-celled out, but as the magnetisaticns'at an angle 90above'thex1y' planethe signal Isreduced y a factor cOS(93).At a further' time r, the phaseangle for tine'nucleusIs again +1relative to the X! axis, but Z"Obove he Vy' plane. Rotation of an angleof 180-90'aboutthe f axis usi,.g the same 80degree . f. pulsewill take the magnetisatIon ack nto the

x yl plane and the effect of the mis-setting will havebeen eversed. (SeeFigure VD.

IL

91 91

lacl

91Xkl o=IPSw -WasowA'"--pat,ez,m,Idslesa t: 2T 0 Effugligure 3.3a nw foratin of a spineobi) tsing he CM palse5eqwrcl! cl%an enserlleof eins . EXI.rnal ritU 31) pylLodn -e 4lileotion.

990Pulse

va990puberotatesNoAm V, variation in Do

e', lm" tatst reger-SescausesSpindiituslen phaie ag at t=1

1891Pulse

t=at=7t =27 timefigure 3.3hCPKGulse equence.800 ulses phasehifteJbs980.


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ThesPin-spin relaxation ti3e may hen be calculated vla the relationshipMM z 3.Zo x exp (-t/T2) , 10

,4here11(t) Is the height of the spine echo observedat time t2'. "IT, (n

on of Relaxation imes (TI andT! 1,n termsof MolecularEv9nts-3.3 The Interpretatio 4

Mechnismsof RelaxaticnandthesA. cemberogeen,oundandPurcell"' Theory.

,Following the applicaticn of a sequenceof pulses, a spin systemwill return to an equi--he Interac-librium Boltzmanndistribution. The principle mechanism f : elaxation is throug, t

tion betweennuclear magnetic moments nd a magnetic field having a component f the correctfrequency and polarisation to induce transitions between 11re nergy levels of the spin sys-tem. In the case of dipolar spin-spin interactions these f! elds stem frcm the Interacticyn of

nuclear magnetic momentwith the fields generated by Its reighbou: inl, nuclear magnetic mo-7ments.

In the presenceof a large static magneticield, the energyof a nucleus.n the fielddue o Its, nelghbours s represented s the sumof energies of that nuclearmagneticmomentdue o its magnetic nteraction with each.The ield at the nucleus due o a neighbouringnuclei j Is liven bya

pi. bj (Lpj lrlj, ) x (3COSIM-1)gamma..11x gamma.. li

-- ----------------------- 1 OCOS20H), 3.20rij,

rij is the separationof the twonuclei, and0 Is the anglebetweenhe magneticmomentfthe Ith nuclei andthe jth nuclei.

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For nuclei of spin 1/2, mi can be +/- 1/2, leading to two quantum tates which maybecallel ii and 31. For two neighbouring,nuclei this leads to a total of ftur combinations ofspin states; lliai, ajoi, Iab Ifl-

Transitions can occur betweenall levels. The transit! on from alaJ to ii$j or $1-ij, andtransitions fros alfl or Olaj to $Uj representchangesn the state of a single nucleus hatrequiresa changen the energyof state for the twonuclei of h9o.

The transition aimi to ifl involves the simultarecus t: ansitic.., of bcth nucle;. and anenergy No. The transitions from states -xij to --2i$jand !: om3! xj to Izj involve thesimultaneous transition of both nuclel, and no net transfer in energy between he system3Tdthe lattice is required.

The local Internal field has sever3l sources Of arijin. The magnetic mc.en'.s of relaxingnuclei -maye Influencedby the fields produced y other magneticparticles suchas othernuclei of similar or different spin systems,or unpairedelectrons. The interacUonsbetweenthe moments aybe direct dipolar couplingsor Indirect scalar couplings via electrons. Each'fiucleus n a samplewill experiencea field dueto its neilhbourswhichmayaddor subtractfromthe applied field. Thedipole - dipole Interactions predominaten the caseof protonresonancepectroscopy.

The ocal field Is determined y statistical consider3tions.At normaldensities Ithewidth of the distribution is the order ef mT.In practice'-nucleiwill movo -. aL!ve to eachother andthe field experianced y a givennuclei will changs.One andefine an auto-correlation fuction 'of the forim,

B(T) X NOT)G(T) = ------------- MBIM

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whereBM is the local field experienced by a given nucleus at time t, G(T) describes thecoherenceof randommolecular processes with time. The spectral density at a frequency W,representing the component f motion at a frequency 9 is the Fourier transform of G(T);

21(w) G(, )exp(-iVt) dt 3. "--0)

it is usual to assumehat, G(T) is expandedn character so that

GW = G(O) x exp(-,T/Tc), 3

leadingto;

2TCJ(W) = G(O) x --------- 3.241+ w2TC2

TC s a function of the-temperature f the sample,andiVre 3.4 showshe form of, J(W) fcr

different values of Tc. Thecomponentf the locally oscillating field at any frequencybelowthe correlation frequencywe rc-1 Is constant. A. ovewe ,1, spectral density functionquiCkly falls to, zero.

Sectral " Low t4mpooa ape&"Si" im

fivure3.4 ]It spectralensityuction R4)skovaorMO. ovani ntentaiateemperaturvs.

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Bloembergen.ound ndPurcell consideredhe magnetic elaxaticn for a systemof similarspinswith an angular spin quantum umber= 1/2, undergoingandcm. . trcpic moticn. Theyassumedhat the only contribution to th fluctuating lattin field was romthe dipole-

dipole interactions betweenhe spins, which culd te ddescrfled y a single correlation time

-IUsing time-deFendentperturbation"'I theO"Y&,.ey s'nowedhat for such a system, .om-

pon. nts of the 1ccal field at f: equencies14c nd 2"w'ocould contribl.-te to the spin-! &ttice: elaxatlon such that

--- Z- 7-,. t Jwo) + AVII-40) : 12.1ASTIT

--------- - ---------3

whereuz = 9/160.ammaz-ij-4, and ,., is the distancebetweenhe ith and th interactingspins. zz is termedVanVleck's rigid lattice second2cment..

In addition to the ccmpo,,,nt of the sFectral density at 'JoandNo, there is a : ont: bu-tion to the spin-spin relaxation time fromthe low frequencycomponentf J(O).

rII. 11 ,,;2.13 J(O) + SJ(wo)+ 2J(i'6'wo)l 3.27TZ L331- ------------ - ----------- 3.283(l WQZTZ) 3(l + 4woZT2)1

The unctions of equations3-26and'3,8 are describedby the log-normalplot in figure ..35It hasbeenassumedhat the correlation time hasan Arrhenius emperaturedependence,. e.

7=TX eXp (E/RT) 3.29

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,heie R is the ,;niversal ps constant. T is the absolute temverature. and E is an apparent

actiation energy tor Ine motions describej oy the nuclei le3dinj to the Huctuating local

field.

RelaxationtimesT1,12(Secon,s)I

Tl anaT2TI at lowfrequencti

11 at high frequencV

12Curye

18-19 Wolz1 12-5 Correlation time (7)(seconas)Figure 3.5 Behayiourof T1anJ72with Correlation time(1) - BBPDiem.I

These urveshavebeenused o predict the behaviourof T1andTZover a rangeof tem-peraturesin liquids where3 single correlation time maybeused o describethe IOC31ieldfluctuations. It canbe seen hat TI passeshrougha minimumt the point where he rate ofmolecuiarmotionsare closest to the resonant requency. . e. whenwcT 1. At lowervaluesof T. TI is equal to T2. This is a consequencef the extrememotionalnarrowing n thisregion. As r increases, the J(O) termof equation3.27 increasingly dominateshe spin-spinrelaxation. andcausesT2 to decrease ntil the rigid lattice condition sets in.

Thecomponentsf J(w) correspondingo rapid motionsdonot contribute to the dephasingprocessbecausehey are averaged ut. Thetime scale over which he dephasing ccurs is T2.If dephasingwere he sale factor determining elaxation. then because

T2AH gamma.i(t). dt

is., h, dephasingangleof nucleus , at a.time t, T2wouldbe defined such.hat.

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T2Cos gamma. 31(t). dt] >= I/e 3.31

andonly componentsf motion ;p to a frequencyof. II/T21 ouldbe effective in the dephasingprocess. PIIZ s proportional to the integral oil J(w) ! rc2 0 to IM. "

temper3ture, s decreaseda cond! 11on s reached w1here-the orrelation frequency Iss the..less than the static line width 1/TZ, which Is prcpartional to -. 9, the sq-jare root of the

rigid lattice sec: nd moT.nt. Further ,C'In the correlation ! requncy dces ".10t result4, r, In-spin relaxation rate remains ncharged-any change In the.-rtegral, ad t', e sp,

3.4 i., Heterogenevis ystems

11heory of,,

hebehaviourof TI andT2 for bulk water Is adeqately JescriteJ by the BPIsection Hydraticn wate: in heterogeneo,,,systems,however,exists In a variety CIstates of molecularmotionarising from interactions with Its environment. A single 'zorrela-tlOn time Is no longer sufficient to characterlsethe kinetic prcpertles of such complex ys-tems,and a number f extendedheories havebeenproposedo acz^wuntor the T1 andT2 ob-servations. IIII-, I. 11 111.

Thecharacteristics are that the relaxation rates are considerablyenhancedver bulk,water.values at all frequenciesand emperatures,, l values exceedT2valuesat all tempera-tures including, thoseabove hat at which the TI value is a 2inimu,, T1 exhibits a frequencydependencehat is Inconsistent with simple BPPheory. There s also a detectableunfrozenwatercomponentInmany a2plesat temperatures elowOIC,whichcannotbe explained simplyby assuminghat the water moleculesexhibit a restricted mobillty, becausehe relaxationrates are considerableenhancedver bulk water values.

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4.1 T11-1iscrete Mfultlphasemodel.

I It hasbeenproposedhat water in heterogeneoussystems xists in a number f 'discrete

?phases',' . Twosuch phases re ncrmallyenvisaged;onecontaining 'free' water moleculeswith properties resemblingthose3f water In the bulk, 3M the other containing-dateriolec,les which interact to some egreeAth the substratezaterial. Themolecular3otions ofthis interacting water maybe restricted or modified1-1 r, -, bero* ways.For this reason thas been ermedboundwater'.

Exchangeof nuclei betweenthe two phasesproceeds at rates which determine the NMIR

relaxation characteristics of the system. In general an NIR : easurementcannot resolve apopulation of -nuclei into separate phases14' he nuclei ef! ictively experience all possiblestates during the period of zagnetlic relaxation. The two phases . der these cc..Etions aresaid, to be in : ap,Id exchange, and an observedrelaxation : ite ! /TI-js'given' by the weightedaverageof the relaxation rates cf'the individual' phases.

Pba 4+ 3.3Z,TI Ta Tb

wherePaandPbare the populations, andTa andTb are the : elaxation times of the boundandfree phases.

Watermoleculesn the bulk typically teorientate at a : ate Vc is propor-1011Hz. I/T1tional to Vc andhasa value of about I sec.,. In bulk ice the vater moleculemobility isrestricted andWe%104Hz. Thespln-sin relaxation rates are therefo'r'e n the order of 10,sec-', giving TZvaluesof a fev :aicroseconds.

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Whendjacentto a surfacecf slowmovingmacromoleculeshe watermoleculesexhibit anintermediatereorientation rate characterisedby Vcvalues in the order of 101Hz, cor-respondingo intrinsic spin-spin relaxation timesof milliseconds. Hencef a systemexists

4here1% f the water is boundand exchanles rapid betueenhe boundandfree phaseshenthe relaxation will be dominated y the boundphase.

In the limit of slow exchange he lifetimes of the spins in each environment are long

comparedo the respective relaxation Umes, and each environment effectively relaxes inde-pendently. The two phases will be observedseparately If the spectrol:eter conditions are 3P-propriate. The observed magnetisation ! ecaY s a sumof No decays such that

MR) = M(O)x pa.exp(-t/Ta) + Pb.exp(-t! Ib) 1,3.

wherefor longitudinal relaxation MM : ?,O)-Mz(t), and ! or transverse : elaxaticn M(t)My'('6j. In favourable conditions the two components f relaxation maybe resolved and thetrue value of Pa, Pb, Ta and Tb found.

TheaI tenslon of to thr'eeor morediscrete phasess straight forvard, andequation3.32tecomes

n ?ITobs i--l TI

fCr the caseof rapid exchange, ndIn the limit of slow exchangeq,.,tlon3.34 becomes ,1,

ntiNO K(O)xE Pl.exp(-t/Ti).

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For 'Intermediate rates of exchangeAere the lifetimes of the spirs within each envircn-ment are comparable with the respective intrinsic relaxation times. the decay of magnetisa-tion mayest!11be described by equation, 3.26 FrovUed that the tne values zf Pi and Ti 3-ereplaced by apparent f: 3ctional populations PI, and apparent -elaxaticn-t! mes Ill.

I- 1-1.1The case cf Intermedlate exchangehas been discussed by Zimmer-,n and Brittin. The ex-; mmims W: ne obsened relaxWon bemmes5per Qn Ta')>_W, and ?a PS A AMcase

Fb Fa--------- + 33%ios (7b 4-Tb) -a

he lifetime -of the spins -I the Cund 1hase.,ere Tb represents ,,.

In the two-phase iso R: Pa', Fbn Ta' and7b' law' t: -n etermired for anumbe:Of special Te , esullu are complex the tve pa:am.ltars, theI! fet,.. esOf the Spins In eachphase,*a and b, and he resonant : equency f eachphase.A

1:aphlcal description of the effects mof uclearexchangen, hese Pramet9: , whers t Is as-sumedhat the act of transfer is not itself a,relaxation mmechanis:,s presentedbelow.

In figure 3.6, the effects of nuclsar exchangeonhe apprent Iractional, population of- 1the slow relaing comporent al Is shownn te: msof a reducednuclear transfer rate RTbPb.Tb/Tb, for a systemn whichFra= Pb, Ta : !00.Tb, nd lJoa 'Job.UhenRTb,eachesa?proximately3, Pa' tends to unity, andSincePa+Pb' 1, the apparent ractional populationof the fast relaxing phase'Pb' ends to zero. In other words he ftst relaxing state appearsto be emptyingand n general if RTb 2 it Is not possible to detect two separaterelaxationtimes experimentally"".

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populationsP'a,P'L

0.5

FaStatewith long elaution time.la--1221h

State with short relaxation timeM4i Ig -3 19+1CM ,- fate of exchangeFigure 3.6 Apparent fractional Populations as a function of exchange ate.

Fizure 3.7 shows he effects of the reduced nuclear transfer rate RTb. on the ratio ofthe apparent spin-spin relaxation times to the true relaxation times. Similar curves arefound for spin-lattice times. The most striking feature is that both apparent relaxationtimes decreasewith increasing exchange ate. the effects on the long relaxation time beingmorepronouncedat lower exchange ates than for the fast relaxing component. t is possiblefor Pal. Pbl and Tb' to be close to their true values while Tal is several times smaller thanTa.

Figure3.7 Theeffect of nuclearexchingeon apparent relaxation timesTV of a twostate s9stem,withTh Ma= A, Pa : Ph, anJ Ta = IBM.T

T TalTNucleiexchangeettweentatesa anab at a rate Ca,anavice-Yersaat a rate Ch.(ITb

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Thebehaviour oi Ta' and TV over a, range of temperatures vi II be 'a function of 'theseparate temperature dependences f the correlations times,for phasesa and b, modiiied bythe eftects at nuclear exchangedescribed above. if nuclear exchangedominates then the

relaxation times will decreasewith increasing temperature in contradiction to the behaviourpredicted by EFP heory.

I Since T1 is usually greater than'TZ for nuclei in absorbed systems It'is possibleAhat'the exchange s rapid in comparison with T1, and yet slow comparedwith T2. In this case itis possible for two-phasebehaviour to be observed for spin-spin relaxation but not forspin-lattice relaxation. since rb may, atisfy both Pb.T2Zb/ib ( I and Pb.Tlb/,rb )) I simul-taneously.

In general, numerical' solutions'can be found'tor systems in which discrete phasesex,changemagnetisation via the transfer of n0clei- Boundwater is often Identified with non-freezing water. Typically relaxation times of non-freezatie water ,I SSas used in our ex-ample. TheTI'minimum for-non-freezable water is typically between-IO'C and -SO'Cand isfrequency dependent. Roomemperature is above the TI minima, and"exchangebetween the bound

and free phases cannot explain whyTI >> T2,and why'there is a frequency 'dependenceof T1.

3.4.2 A Distribution of'Coirelation Times.

In the discrete multiphasemodel t is assumedhat a quantity ofIhighly immobilisedwaterdetermineshe relaxation behaviourof the bulk throughexchangerocesses.A variationonBPP'theoryn'contrast with-this is one-in whichall the watermoleculesAnheterogeneous

systeasare considered o be incontinuous ong-range nteraction Atli the substrate. This111I-I. ... I- ,

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leads o a continuum t motional properties whichmaybe-described y a distribution of cor-relation times"""'. This distribution maybe expresseds a density function J(T) suchthat;

0(, ). dr 3.37

rhe relaxation times TI and TZ are then obtained by averaging the EPPexpressions over thedistrintion to gi-je;

z- UZ. T. O(T). 'r +4 -'r 0(, ) . dTTI 31+ W1, rz I+ 4W, ZlrZ00and

r. O(T). dT +5r. 0ir)dr 2 r. O(,t)dr_ 4. '3'9Td' + W.ZT 3j 1+ 4W,Zlr0 'f ,,:, 0,, -: 0' -

I",

Thedensity function which has beenmost frequently applied Is that of a log-normai dis-tribution. Here the binding energies of the water molecules are represented by a Gaussiandistribution function. (See figure 3.8). TheGaussiandistribution is specified in terms of awidth parameter 6, and a mediancorrelation time rf

i. e. 0(, )dT exp (-OIZZ) 3.40

where Z In 3.41

Other types of distribution functions have been proposed to describe the variation inbinding energies of the molecules in the system under investigation. All introduce variablesthat are analogous to r* and 0. -

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Variations of r*, with temperature are governedby thermal activation laws. Twosuch lawshave been largely considered;

(a) the Eyring form given by , r* r*.,.exo(E/RT)1. KT(b) the Arthenius form given by T, r#.. exp(E/RT)

InFigure3.8 TheGaussioOistril6utlon f correlationimes,Theeffects of increasing heterogeneityn the systems reflected In an Increasing,width

parameter . An increase in the hydration level will decrease without notably?eifect nj

Figure 3.9 showshe effect of changinghe width parameter0 on TII andT2-as a functionof reciprocal temperature,T, where he Eyring formof thermalactivation law is. assumedodescribethe behaviourof ir*.

As the heterogeneityincreases he activation enthalpyas determined.rom the.slope of T2curvedecreases.This Is matched y an increasein the ratio TIM at andabove he tempera-ture of the T1 minimum. heminimumtself becomesess pronounceds the curvesbecomeshal-lowerwith increasing 0. _ -

I'

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71,72

P2

II Ll lembpel-auLvIl -- I-, I, '.Figure3.1 Changesn TI an&12caused y an inuease in the ralve of listrilation ofceprelallen imes,T. FD F2 FL.

. In somecircumstances a mayhavea temperature dependence,and this-CauseS the minimumn

the T1 curve to be shifted from whereWT*2 0.615a. In addition TI mayvary asymmetricallY -aocut the, minimum,and the temperature dependence n T2 will be increased as comparedo thecase when0 is a constant. In modelswherea temperature dependent j) has beenrequired to

matchexperimentaldata with theory, an inverse relationship has beenused.

Resing"51.defined a cut-off valueof the correlation time To, abovewhichrigid latticebehaviours observed.On owering he temperature f a sYstemn whichthere is a continuousdistribution of correlation times there is a gradualtransition to the rigid lattice state,with thosemoleculeshavingthe longestcorrelation times reachingthe rigid lattice cut-offpoint first. Theresult is a decreasen the observed opulationof the heterogeneoushaseandhasbeenconsequently escribedas a phase ransition. To incorporate this effect intothe caicuations, or TI andT2the rangeof integration in equations3.38 and3.39 arechangedo the cut off value r,. With this modification the modelhasbeensuccessful in pre-dicting the behaviourof TI andT22.n a number f systems.

In systemswherea distribution of correlation times exist, values for VanVleck's secondmoment.he distribution width parameter0, and the activation energyof relaxationmechanismsan be theoretically determined.

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3.4.3 - Cross-Relaxation ffects. .I-I,, I

In addition to the, transier of magnetisation via the exchange of nuclei bet-ween phases.It has been acknowledged that a transfer of magnetisation can result from magnetic interac-tions between nuclei at the interfacel2l-23). Coupling by spin interactions across the inter-face results in cross-relaxation effects, including magnetisation transfer between the phases.The mechanisms of magnetisation transfer at the interface, and diffusion of magnetisationwithin the bulk phases enable the population with the greater relaxation rate to act as a

magnetic sink for the rest of the population. The driving force for this process of mag-,_,

netisation transfer is the difference in 'spin temperatures' created by the diffe! en't. intrin-

sic relaxation rates of the two phases. If the intrinsic relaxition rates of, the two Popula'tions arc similar, then there is no detectable effect unless the populations are selectivelyexcited to different magnetisations.

Vhenhe populationsare eachkept isothermalby rapid diffusion of spin mainetisation,which n liquids takes place via molecularor nucleardiffusion andexchange, nd n solidswhere here is sufficiently strong spin-spin Interaction, via spin diffusion, the contribu-tion, fromthe cross-relaxation effects maybe IncorporatedAnto, he relaxation equations orthe twopopulations I andS to give; ',- III: 1,

d( I-lo) -z -(R, - RT I-lo) +RL (S-50) 3.42dt F]2L

d(S-So) -[R, + Rj x (S-so) + Rf 1-1o) 3.43dt

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ghere lo and So are the 2agnetisation of he two phasesat equilibrium, R, and Re are therelaxation rates appropriate to isolated I and S spins, R, is the, rate of transfer of-mag-netisation between I and 5-spin systems, and F is the ratio of. the spin populations. -At equilibrium lo = So/F

The solution of these coupled equations is a two-component pin-lattice decay for the Iand 3 components.

-In most cases where data has beenanalysed by incorporating the cross-relaxation effect,

the exchangeof magnetisation and a resulting modification to the spin-lattice. relaxationtime have generally beenconsidered-to be the only consequences f the cross relaxation. Ithas beendemonstratedexperimentally, however, that direct spin-spin relaxation is also a

consequence.

3.4.4 Anisotropic Motion.

- ThecouplingswhichgovernNMRelaxation mechanismsavebeendiscussed n section3.2-1. Theyare vector quantities. In liquids, the constanttumblingmotionsof the.spinscausesan averagevalue, or their couplings.o be observed.For examplehe local, tield ex-periencedby=e nucleusas a result of the dipole momentf a second epends pon he angle0 betweenhe inter-nuclear vector andthe external field. -It mayhaveoneof two valuesdependingon the relative orientation of the two spins, givenby

9B -- t/- Ko. 3cosl(O)-I) 3.44

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whereK, is the dipolar coupling constant. An isolated water molecule would therefore yield adoublet resonancespectrum. In liquid water the local field effects are dynamically averagedto zero, and a single resonance s observed. The randomorientations of the molecules produceno preferred orientations of the inter-proton vector and so there is no angular dependenceoriplitting of the spectrm.

Whenwater molecules interact with molecular system'ssomemotional anisotropy maybe im-posedon the water. If there is Macroscopicanisotropy' of the substrate such'as occurs infibrous and laminar materials, the anisotropy will extena throughout the sampleand can be

observedas a dependence f the magnetic resonanceproperties on the orientation of thespecimen n the magnetic field"I"I".

In the caseof dipolar couplingsthe local fields given by equation3.44 mayhavea nonzero time averagevalue. Sincethe rate of T2 relaxation is determined y these dephasingfields I/TZ2 xhibits the same ependencen the angle0.

Anisotropic effects are morenoticeable In TZ than TI, since it Is the low-frequencYOm-pon'ents'afthe local fi Ie.Ids whichhavean angulardependence.f there exists macroscopicanisotropybut no long-rangeorder in the sample owderype spectra will be obtained. Ifthe scale of'the' anisotropy is suchthat the watermoleculesexperienceImany'domainsn thetime scale of the NMRxperiment n isotropic averagingwill occur, andthere will be no ob-servableangular dependenceof the magnetic esonance roperties.

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3-5 '' Ditfusion.

Diftusion maybe described as the general transDattation of matter fro& one part of asystem o another, such that molecules or ions mix, through normal thermal agitation. In woodthere exists two fundamental types of diffusion. the first being 'dynamic' or 'driven' diffu-sion causedby initial concentration gradients of the diffusing species. The second type ofdiffusion is 'static' or 'self' diffusion, wherebymolecules diffuse with respect to oneanother without any changes n the local concentrations, and is a consequence f randommo-tion.

In this work it is the latter which has been investigated. The self-diffusion coefficientD is defined by Fick's law; in a single of multi-component system where there exists uniformmacroscopicconcentrations, the one-dimensional form of Fick's, 21, second law states that;

LP (X,V Dxd2P(X,) 3.45dt dxzwhereP(x, ) is the probability that the position of oneparticular moleculeof the speciesunderconsideration is at a position x at a time t.

In an isotropic mediumhis equationmaybe extendedo a three dimensionalform;

dP (L, t)dt D del.ZF(r.,) 3.46

In an anisotropic mediumhe value of D-s often orientationly dependent

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and the equation 3.46 needsmodification. Choosinga rectangular systemof co-ordinates(xj, x:, xj) for example, with Di, D2, and D3as the principle diffusion coefficients, equation3.46 becomes;

LP(rt) DILIP+ D2LIP + D3dzP 3.47-it dxI dx22 dxl

Solutions to the Diffusion Ejuation.

Solutions to equation3.46 describingdiffusion in an isotropic medium aybe found or avariety of initial andboundaryonditions"". Themethod f separationof variables is usedwherebyhe probability density function P(r, t) is expressed s the productof a spatial anda temporal unction. For an unboundedsotropic mediumhe solutions in one, two, andthreedimensions re given below;

(a) Onedimensionalcase, , x,: x,t)--- (4nDt)'IexpE-(x-x4)2/4Dtl-A. 48

whereP(x,: x, t) is the probability that a molecule nitially at x. will diffuse to position xIn time t.,

(b) Twodimensionalcase, P(rl.:.rt) = (4nDt)*Iexp[-(r-_rL)1/4Dtl 3.49= (x,y)here

(c) Threedimensionalcase, F(rL:rt) z (4xDt)*3'2exp1-(r-ra)I/4DtI 3.50. !', - t' .I- 11 1 11' Iwhere (X'Y'Z)

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Theone dimensional solution describes diffusion in a one dimensional medium.and alsodiffusion in any specified direction within an isotropic plane (i. e. two dimensions), orwithin a three dimensional isotropic medium.Figure 3.10 describes the-shape of-the probabil-ity density iunction for any specified direction at three successive values of time t.

The.mean-square isplacement r2 of molecules

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