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ContentsMaterials and Methods ...................................................................................................................................... S3
Preparation of PDMS-sticks. ............................................................................................................................. S4
RDC structure elucidation for (+)IPC-OAc .................................................................................................... S16
NMR Studies of PDMS-decomposition .......................................................................................................... S17 29Si NMR spectroscopy of PDMS and oligodimethylsiloxanes .................................................................. S17
DOSY-study of PDMS-decomposition. ...................................................................................................... S18
Predicting solvent quadrupolar splitting in a swollen gel ............................................................................... S19
References and Notes ...................................................................................................................................... S38
S3
MaterialsandMethods General. All reagents were used as received from commercial suppliers unlessotherwisestated.Reactionprogresswasmonitoredbythinlayerchromatography(TLC)performedonMachereyNagelaluminumplatescoatedwithsilicagelcontaininggreenfluorescence indicator for shortwave UV (254nm). Visualizationwas achieved by UVlight(254nm),saturatedaqueouspotassiumpermanganateor5%ethanolicsolutionofphosphomolybdicacidandsubsequentheating.NMRexperiments.AllNMRexperimentswereobtainedonBrukerDRX‐400,Avance‐IIIHD‐400andAvance‐III‐600spectrometers.Chemicalshifts(δ)arereferencedfromTMS(0ppmin1H,13Cand29SiNMR)orresidualCDCl3signal(7.27ppmin1HNMRand77.3in 13C NMR spectra). Assignment of NMR spectra of (+)‐isopinocampheol and β‐(–)‐cariophyllene was performed using standard 1D‐ and 2D‐NMR techniques (includingH2BC)[1].Diastereotopicprotonsofβ‐(–)‐cariophyllenewereassignedusing3J‐couplingsanalysisobtainedfromDQF‐COSYexperiment.ThePDMSwasanalyzedusing1Dand2D29SiNMR (1D‐inept, 1D‐ig, 1H‐29SiHMBC). Decomposition of PDMS in the presence of(+)‐isopinocampheol was investigated by 1H DOSY experiment (stimulated echo withbipolargradients,Brukerpulsesequencelibrarystebpgp1s)[2]performedonAvance‐IIIHD‐400NMRspectrometerequippedwitheither5mminverseprobewithZ‐gradientor5mmmicroimagingprobeequippedwithDiff30LZ‐gradientwithlockchanneland60AGREAT amplifier. The RDC data (DC‐H) were extracted from CLIP‐HSQC,[3] scaled F1‐coupledBIRD‐HSQC[4]andscaledF1‐coupledBIRD‐HSQCspectrawithMQ‐evolution[5] .These were recorded for isotropic and anisotropic samples and RDCs are calculatedaccordingtotheformula:1DC‐H=(1TC‐Haniso‐1JC‐Hiso)/2For the methyl groups the DC‐C rather than DC‐H was used for the spatial structureelucidation.Thefollowingequationwasapplied[6]:1DCC=1DCH3(‐3ɣC/ɣH)(r3CH/r3CC)
S4
PreparationofPDMS‐sticks.
1.Cross‐linker(Bis‐D4).
Tomoderately stirredneatoctamethyltetrasiloxane [D4 (17.3 g)] at120 °C freshly re‐crystallized (ethanol‐water) dry benzoyl peroxide (450 mg) was gradually added(CAUTION!avoidanadditionofbigchunks/portions;intotalitmaytakeabout1h;thesmoothertheadditionis,thehigheristheyield).Aftercompletion,thereactionmixturewasheatedforanadditional30min,cooledtoroomtemperatureandpassedthroughaplugofactivatedalumina(2.5×3cm)andwashedwithpetrolether.Afterremovingofsolventsunderreducedpressure,D4wasrecoveredbydistillationinavacuumofwater‐jet pump (b.p. 62–64°C/~10 Torr). The residue was purified by multiple Kugelrohrdistillations collecting amiddle fraction boiling between 100–120 °C/0.01mbar untiltheproductisfreeofaromaticcontaminationsandcrystallizesascolorlessneedles(m.p.55°C).Yield:353mg.1HNMR(600MHz,CDCl3,300K)δ=0.47(s,2H,CH2),0.1–0.08(m,18H,6CH3),0.08(s,3H,CH3)ppm. 13CNMR(150MHz,CDCl3,300K)δ=8.2 (2CH2),0.8(6CH3),–1.6(CH3)ppm.29SiNMR(119.3MHz,CDCl3,300K)δ=–19.15,–19.24,–19.37ppm.
2.PolymerizationCatalyst.
A mixture of 3.3 mL (11 mmol, 1.1 equivalents) of D4 and tetramethylamoniumhydroxidepentahydrate(1.8g,10mmol)wasrefluxedinbenzene(60mL)withDean‐Starktrapuntilthewaterdoesn'tseparatedanymore(typicallyovernight).Atthispoint,the solution should be completely homogeneous. Then, the majority of benzene wasdistilled off at atmospheric pressure and the rest of volatilematerialwas removed inhighvacuum to result ina colorlesswaxy semisolid. Itwas transferred inaglove‐boxand used there without additional purification. The puritiy is estimated to be ~75%fromitscrude1HNMRspectra.1HNMR(400MHz,CDCl3,300K)δ=2.79(s,24H,2NMe4),0.44(s,12H,4CH3),0.36(s,24H,8CH3)ppm.
S5
3.Polymerization.
A 5‐mL round‐bottom flask was weighed in a glove‐box and a little crumble of thepolymerisationcatalyst (seeabove)wasstuck to the internal surfaceof the flaskwithspatulatip.APTFE‐coatedstirringbarfollowed,theflaskwasclosedwithaseptumandremovedfromtheglove‐box.4wt%‐stocksolution(4wt%=2mol%)ofbis‐D4inD4wasdilutedwithD4toreachtherequiredcross‐linkerconcentration(seeabove0.5‐2mol%)and added by stirring to the polymerisation catalyst in such amount to adjust thecatalystsconcentrationexactlyto0.12mol%.Aftercompletehomogenization(about30min; don't wait any longer if you see it's dissolved, otherwise it might become tooviscous for subsequent sampling with the syringe), the polymerizing mixture waswithdrawnwithsyringeandevenlydistributedwithinthearrayofsemi‐closedpiecesofPTFEtube(ID3or3.2mm,l~25‐30mm)packedintheSchlenktubeunderargon.TheSchlenkwas carefully (CAUTION!DO IT SLOWLY!) evacuated, purgedwith argon andplacedinanovenpre‐heatedto90°C.Toequalizethepressureinthereactionflaskonecan pierce the septumwith a thin needle, or,more correctly, use any kind of "CaCl2–tube"packedwithactivatedmolecularsieves.Afterthetimerequired(typically,5h),thetemperature was raised to 150 °C and polymerization was terminated (decatalysed,removal ofNMe3) by heating for at least 3 h. Then, the reaction vesselwas cooled toroomtemperatureunderargon,thetippedendsofthePTFE‐tubeswerecutwitharazorbladeandthuspreparedPDMS‐stickswerepushedoutby2.5‐3mmrod.Toprotectthesurfaceofthestick,apieceoffinger‐rolledcottonwasplacedbetweenrodandstick.ThefreshlypreparedPDMSsticksweredriedatambienttemperatureinvacuo(0.002mbar)overnight.
Previously, NMR experimental data[7] in Me2O‐d6 or DFT calculated chemical shifts[8]were published. Herewe provide the full NMR attribution of BCP in CDCl3, includingassignmentofdiastereotopicprotons.For thespatialstructurerepresentationonecanuse the Cartesian coordinates for the three naturally populated conformers providedherebelow.For the isotropic sample 50 µL of BCPwas dissolved in 0.5mL of CDCl3. Anisotropicmeasurementswere performed for a PDMS gel sample containing 1.3mol%of cross‐linkerandsolutionof5µLofBCPin1mLofCDCl3.AbouthalfoftheBCPsolutionwasplacedatthebottomofan5mmODNMRtube,thenaPDMSstick(length14mm)waspushed insideusingarodsuchthat thegelwouldbe in thecoilofNMRspectrometer.TherestofBCP/CDCl3solutionwasaddedtothetopofthePDMSstick(thestickfloatsinCDCl3andneedstobeholdcoveredby thesolutionbyputtingarodonthe topof thestickuntil thestickswells–usuallyamatterof1‐2minutes).Theanisotropicgelwasthen equilibrated at 279K.AllNMRmeasurements forboth isotropic and anisotropicsampleswereperformedat279KonAvance‐III‐600spectrometer.
Cartesiancoordinatesfor‐CaryophylleneconformersStructuralmodels for theRDC fitswere generated computationally by geometry optimizationusing density functional theory as implemented in ORCA v3.0.1.[9] While the previouslypublishedstudiesbyAlagonaetal.[8]givesometorsionangles,electronicenergiesandpredictedNMRchemicalshifts,noCartesiancoordinatesoftheconformersarereported.StartingfromageometryusedbyKruppetal.,[10]bondswererotatedmanuallyintogeometriesresembling the , , and conformers reported by Alagona et al. These startinggeometries were subsequently re‐optimized at the B3LYP/def2‐TZVP[11] level of theory.Numerical frequency analysis was performed to confirm the local minimum nature of therespectivegeometries.TableSI‐3comparestherelevanttorsionanglesandrelativeconformerpopulations(derivedfromBoltzmannweighting)tothosereportedpreviouslybyAlagonaetal.ThegeometryisnotexpectedtobepopulatedsignificantlyatroomtemperatureandisnotobservedintheNMRmeasurements.TableSI‐3.ComparisonofDFT‐optimizedgeometriescalculatedinthisworkwiththose
Anisotropicalignmentstudyof(+)‐isopinocampheolanditsacetylester Isopinocampheol (IPC) has been traditionally used as a test small molecule for theperformanceofnewalignmentmediainourandothergroupsdevelopingRDCmethodsforsmallorganicmolecules.Technically,onecanprepareanalignedsampleintwoways.First, the gel can be pre‐swollen in pure solvent up to its equilibration point, whenneither lengthnorΔνQofthegelchangesanymore.Thesolutionofasmallmolecule isthenappliedonthetopofapre‐swollengelandallowedtodiffuse.Thesecondoptionisto achieve simultaneous gel equilibration and analyte diffusion. The latter approachimpliesthatthedegreeofalignmentofagelinthepuresolventisknown.We prepared samples either by simultaneous gel swelling and diffusion of the smallmoleculeordiffusionof(+)‐IPCintopre‐swollenPDMSgelbeingappliedinsolutiononthetopofthegel.InbothcasesdegradationofΔνQwasobserved,seenin2HNMRspectraandimages(Fig.SI‐2).[12]Forthesample,inwhich(+)‐IPCdiffusedfromthetopofthegel, 2H NMR images indicate a ΔνQ reduction at the analyte location, propagatingtogetherwith(+)‐IPCdiffusion(Fig.SI‐3).
Weobservedanelongationofthegelin(+)‐IPCsolutiontothevalueshigherthanthoseseen in pureCDCl3. This processwas accompaniedby gradual reduce of ΔνQ until thevalue of 0 Hzwas reached,which is characteristic for isotropic systems.Moreover, aPDMS gel contacted with (+)‐IPC for more than one month shortened in length andreleasedviscous liquid,which later onbecame significantly fluid.The gel could eithershrunkordepolymerize in the(+)‐IPCsolutionat theconcentrationsof9mg/mL.The29Si 1D and 2DNMR examination of the liquid, released from an (+)IPC/PDMS/CDCl3sample, evidences for thepolymerchemicaldegradation:both liquidandan intactgelshow a 29Si NMR signal of dimethylsiloxanes at ‐21 ppm (Fig. SI‐6) A 7‐month oldsamplebecamecompletelyisotropic.
InteractionofPDMSwithIPCThechemicaldegradationofPDMSgelinthefinesolutionsof(+)‐IPCwassurprisingforus,especiallybecausesimilarsticksearlierwerereportedtobesuccessfullyappliedinanumberofstudies[13]butnotforisopinocampheol.Asynthesized(+)‐IPC‐derivative,O‐capped with acetyl group, did not prevent the reduction of the ΔνQ but degradationseemedtoslowdownsuchthatwewereabletoget10RDCs(intherange‐4…+2Hz)alreadyaftertwodaysofdiffusion.TheexperimentalandtheoreticalRDCvaluesareinagreementwiththespatialstructureofthemolecule(TableSI‐4andFig.SI‐4).The ability of PDMS to swell differently in solvents is of great concern in thedevelopment ofmicro devices and their components. Alcohols are not reported to begoodsolvents forPDMS, i.e.donot showhighvaluesof volume increase[14].Thus,ourresults showing the independence of PDMS gel extension from alcohol or esterfunctionalitiesof (+)‐IPC,on theonehand, coincidewellwith thegeneraldata for thepolymer swelling properties. On the other hand, the information on chemicalincompatibility of (+)‐IPC and PDMS is potentially of big importance for furtherapplications.(+)‐Isopinocampheol acetate ((+)‐IPC‐OAc). 1M solution of (+)‐isopinocampheol in
pyridinewaschilledonanicebathand2eq.ofaceticanhydridewereaddedviaseptum.Thereactionmixturewasstirredfor5hrs. on the ice‐bath and then kept in a fridge until reactioncompletion.ThereactionprogresswasmonitoredviaTLC.Themixture thenwas poured on an ice coldHCl solution and theproductwas extracted in diethyl ether. The combinedorganic
extractionswerewashedwith 1MHCl, water and brine. The final ether solutionwasdried over MgSO4 and the organic solvent was removed on a rotary evaporatorproviding dark‐yellow liquid. Yield: 80%. Rf (EtOAc‐PE, 1:5) 0.6. 1H NMR (400 MHz,CDCl3,300K)δ=0.89(CH3‐9,3H,s),0.98(H‐7a,1H,d,9.9Hz),1.02(CH3‐10,3H,7.4Hz),1.15(CH3‐8,3H,s),1.58(H‐4a,1H,ddd,14.3x4.2x2.8Hz),1.75(H‐1,1H,dd,5.9x2.1Hz),1.86(H‐5,1H,m),1.99(Ac‐12,3H,s),2.04(H‐2,1H,m),2.30(H‐7s,1H,m),2.52(H‐4s,1H,m),4.96(H‐3,1H,m)ppm.13CNMR(100MHz,CDCl3,300K)δ=20.5(CH3‐10),21.5(Ac‐12),23.7(CH3‐9),27.5(CH3‐8),33.4(C‐7),35.9(C‐4),38.3(C‐6),41.3(C‐5),43.6(C‐2),47.5(C‐1),74.1(C‐3),177.0(CO‐11)ppm.
Fig. SI‐5. Correlation between calculated andexperimental RDCs for (+)‐IPC‐OAc (Q‐factor0.108).
S17
NMRStudiesofPDMS‐decomposition
InourexperimentsonPDMSgelsequilibrationwith(+)‐IPCand its acetyl ester we noticed the reduction of the lengthanddecreaseoftheΔνQofthealignmentmedium.Thesamebehavior is true not only for our chemically synthesizedPDMS gels but also for a sample prepared by β‐irradiation[10a]. On the photo (Figure SI‐6) one can see thefirststepofvisiblegelchanges,whenitstartstobefluid.Toprobewhether chemical degradation or gel shrinkage tookplace, we analysed by NMR spectroscopy methods the‘supernatant’–theliquidabovethegellevel.
The‘supernatant’solutioninCDCl3wasanalysedby1Dand2D29SiNMRspectroscopy.In (1H‐29Si) HMBC spectra of the liquid released from the (+)IPC/PDMS/CDCl3anisotropic system(Fig.SI‐7a) and spectraof the intactPDMS/CDCl3 (Fig.SI‐7b)onecan clearly see that ‘supernatant’ contains dimethylsiloxanes (‐22 ppm in 29Si), i.e.chemical changes occur leading to the loss of the anisotropic properties of the gel.MeasurementswereperformedonAvance‐III‐600NMRspectrometer.
DOSY‐studyofPDMS‐decomposition. A 2D DOSY spectrum (Bruker pulse program stebpgp1s, Δ = 200ms, δ = 2ms, lineargradient2‐95%in32incrementalsteps,Gmaxoftheprobeheadinthez‐directionis50Gcm‐1)[2]ofthe‘supernatant’solutionofa(1%PDMSgel/(+)‐IPC)wasobtainedat300KonAvance‐IIIHD‐400spectrometer(seeFigureSI‐8).Theself‐diffusioncoefficientsDofTMS,(+)‐IPC,residualCHCl3andoligodimethylsiloxanesweredeterminedviastandardmonoexponential fitting analysis in Topspin 3.2. With D = 1.93·10‐9 m2s‐1, theexperimentalvalueforTMSinCDCl3islowerascomparedtothemeasuredatthesametemperaturepreviouslypublished[15]valueof2.92·10‐9m2s‐1,whichmightbeduetothepresenceofhighcontentofoligomersinthemixtureandthusahigherviscosity.ForthedepolymerizedPDMSgel the estimated rangeofD is about (2.00‐2.76)·10‐11m2s‐1, i.e.two orders lower values than TMS corresponding to much slower diffusion.Unfortunately, the more precise determination of the self‐diffusion coefficient, whichcouldallowadeterminationofthemolecularweightofthedepolymerisationproducts,wasnotpossibleduetothebroadMWdistributionoftheoligodimethylsiloxanes.
Fig.SI‐8.1HDOSYexperimentsconfirmthepresenceofthede‐polymerizationproductsinCDCl3solution.Thus chemical incompatibility of the PDMS gels and the bicyclic monoterpene (+)‐isopinocampheol leadtochemicaldegradationofthegel,asseenin2HNMR,29SiNMRspectra and 1H DOSY experiments. Esterification of the alcohol functionality allowsperforming RDC analysis but does not fully prevent degradation of anisotropicproperties.The latter cannotbe accounted foronlyby the alcohol functionalityof theanalyte.Thereasonforthechemicalincompatibilityofthepolymergelandthe(+)‐IPCesterisnotyetknown.
We consider a polymer network swollen by a deuterated solvent. Each molecule ofsolventdiffuses throughout thegel, interactingoccasionallywith themonomersof thepolymerchains.Duringtheseencounters,theinteractionsbetweenthepartiallyalignedmonomersofthechainsandthesolventbiastheorientationofthesolventmolecule.Thequadrupolarsplittingofthesolventcanthusbewrittenas:
∆ Δ (1)
where is the chain monomer volume fraction accounting for the probability of asolventmoleculetoencounterachainmonomer,SistheaverageofthesecondLegendrepolynomial of monomer orientations, Δ is the quadrupolar splitting of perfectlyalignedsolventmolecules(forinstanceΔ =168kHz[16]forCDCl3)and isanefficiencyfactoraccountingforthetransferoforientationbetweenthemonomersandthesolventmolecules during a solvent‐monomer encounter. Equation (1) can be equivalentlyunderstood by considering the time average of the second Legendre polynomial ofsolventorientations.Whenthemoleculediffusesfreelyawayfromthepolymerchains,themolecularorientationstateisdescribedbyanisotropicorientationdistribution,andthemeasureofthesecondLegendrepolynomialisaveragedtozero.Duringafraction ofthetotalaveragetime,whenthesolventencountersamonomerofthepolymerchain,itsdistributionisbiasedproportionallytotheorientationstateofthechainmonomers.Theefficiencyofsolventorientationduringthistimefractionisafunctionofthedetailedmicroscopic interactions between the chain monomers and the solvent molecules.Maximal quadrupolar splitting of the solvent ∆ Δ would require thus smallamounts of solvent ≅ 1, completely aligned chains 1 and a perfectly efficienttransfer of orientations 1. Note that while and are determined by theexperimental conditions, is an intrinsic property of a given solvent/monomer pair.Tabulated values of for different solvent/monomer pairs would therefore allowpredicting the expected quadrupolar splitting for experiments performed undercontrolled swelling and stretching conditions. In the following we first reviewtheoretical predictions for in stretched polymer gel networks, then provide explicitexpectationsinthecasewheregelstretchingiscausedbyswellinginatube.Finally,wecompareourpredictionswiththedatafromtheexperimentsdiscussedinthispaperandextractthevalueoftheorientationtransferefficiencyforthepairPDMS/CDCl3.
WhereR istheend‐to‐enddistanceofapolymerchainofNmonomersconnectingtwocross‐linkingpointsand theaveragesizeofthatchain inagivenreferencepolymersolutionwith the samemonomervolume fraction.Note that the averagevalueof is
S20
relatedtothecrosslinkingmolarfraction by 2/ where isthecrosslinkerfunctionality.Inourcasewhere 4onehas 1/ 2 .
Swelling ina tube.A typicalNMRexperiment isperformedby insertinga cylindricalpieceofadrygelofdiameter andlength inanNMRtubeofinternaldiameter .The gel is then exposed to solvent and let swell to a length . The polymer volumefraction isgivenby
Comparisonwith experiments. PDMS gels of diameter D0=3 or 3.2 mm and lengthL0=14mmwith different degrees of cross‐linking (0.5 1.0, 1.3, 1.5 and 2.0mol% or,equivalently,X 0.005,0.010,0.013,0.015and0.020correspondingtoN=100,50,38,33and25)wereswolleninNMRtubeswithinternaldiametersDT=4.20mmforthetwomostcross‐linkedsamplesandDT=4.09forthethreeothers.Swellingandequilibrationofthegelisrelativelyfast,∆ reachingstablevaluesafteroneweekformostcases.AstheFig.1inthemainpapershows,allsamplesswollenforaperiodoffourdaysormoreexhibithomogeneous∆ intheregioncapturedbytheNMRcoil.Thevaluesof∆ firstincreasewithtime,eventuallyreachingtheplateauvalueoffullyequilibratedgels.
WefirstplotinFigs.SI‐(9‐12)thebaredatafromPDMSsticksanisotropicswolleninanNMR tube, while one monitors the length of the gels and the values of quadrupolarsplittingofCDCl3in2HNMRspectra.Fig.SI‐9plotstheincreaseinrelativelengthL/L0ofthe gel sticks as a function of time. After a period of 20 to 40 days all samples havereachedplateauconditionscorrespondingtomaximumrelativeextensionsintherange2‐4,withlargerextensionsbeingachievedforgelswithsmallercrosslinkingfractions.
S22
Fig.SI‐9.Relative lengthL/L0asa functionof time t, indays (0.5mol%cross‐linker ‐squares,1.0mol%‐triangles,1.3mol%‐circles).
For the relative extension values L/L0 in Fig. SI‐9, we display in Fig. SI‐10 thecorrespondingevolutionofthemonomervolumefractioninthegel,asgivenbyEq.(7).Undertheexperimentalconditionsofthispaper,asthegelsswell,theyspanmonomervolumefractionsfrom 1inthedrystatedownto ≅ 0.15forthelesscross‐linkedsamplesinthefullyswollenstate.
Fig.SI‐11showsthetimeevolutionofthemeasuredvaluesforthequadrupolarsplitting∆ .Notethatthemeasuredquadrupolarsplittingvaluesareintherange5‐25Hz,tensof thousand times smaller than the maximum possible values (Δ =168 kHz) forperfectlyalignedCDCl3molecules.
0 10 20 30 400
1
2
3
4L/L0
t
0 10 20 30 400.00
0.05
0.10
0.15
0.20
0.25
0.30
Φ
t
S23
Fig. SI‐11. Quadrupolarsplitting∆ inHzas a functionof time t, in days (0.5 mol%cross‐linker‐squares,1.0mol%‐triangles,1.3mol%‐circles)
WeplotalsoinFig.SI‐12theevolutionofquadrupolarsplittingvalues∆ asafunctionofrelativegelextension.Thefigureshowswellthatundertheseexperimentalconditionsof constrained gel swelling, the measured ∆ values are not a function of chainstretchingalone,sincethelargerstretchingratios,achievedforlesscross‐linkedgels,donottranslateintohigher∆ values.
Wenowanalyze thebaredata inFigs.SI‐(9‐12) according to theprescriptionsof thetheoretical arguments presented above.We first characterize the prevailing statisticalconditionsofthechainsinthegelnetwork,byplottingtheequilibriumswellingfractions
inFig.SI‐13asa functionof themolarcross‐link fraction :we foundthat theyfollow the standard Flory‐Rehner[18] predictions for the swelling of gels in an ideal
solvent ‐seeEq. (4) ~X / .ThisshowsthatN, theaveragesizeofpolymerstrandsbetween crosslinking points, spans a value range not large enough for reachingconditionswhereexcluded‐volumestatisticsapplies.ThelargervalueN=100isobtainedforthelower 0.005,whilethelargercross‐linkingfraction 0.02correspondstoN=25.
0 10 20 30 400
5
10
15
20D
t
1.0 1.5 2.0 2.5 3.0 3.50
5
10
15
20
L/L0
S24
Fig.SI‐13. Equilibriumvolume fraction of PDMS in a gel as a function of themolarfractionofthecross‐linker .Note,thattheaverage chain length N between two cross‐linking points is given by N 1/ 2X andthus varies here between N=25 for
0.02and N=100 for 0.005. Theline is the best power‐law fit to the data
1.05X / .
WeplotinFig.SI‐14∆ asafunctionofpolymervolumefractionforthefivedifferent values available. Interestingly, for samples with N=50 and N=38, ideal statistics
provides the best fit with Eq. (9a), while for the largest N value, excluded volumestatistics applies [19] as described in Eq. (9b). This is consistent with ideal swellingconditions applying throughout most of the explored cross‐linking density range, thesamplewithN=100beingatthecrossoverbetweenidealandexcludedvolumestatistics.For the two samples where only equilibrated properties have been measured
0.015 and 0.020, we assumed ideal conditions and extracted thecorresponding values by assuming Δ =168 kHz. Fitted efficiencies for the fivesamplesrangefrom 5.9 10 to 7.1 10 .
Fig.SI‐14. Quadrupolar splitting∆ in Hz as a function of thevolume fraction . The lines arebest fitsaccording to theEqs. (9)with Δ =168kHz, providing
OurresultsarethuswelldescribedbyEq.(1)andtheassociated dependentcurvesofEqs.(9),confirmingthephysicalpicturedevelopedabove.Inparticular,itisclearfromour data, that solvent quadrupolar splitting in gels swollen in a tube cannot beunderstoodbygelstretchingalone,sincelargerstretchingisachievedformoredilutedgels,wheretheprobabilityofencountersbetweenthesolventandthechainmonomersissmaller.Ourargumentsaccountfortheinterplaybetweenthesetwoopposingeffectsandquantitativelydescribethedata.Theanalysisfurtherstressesthe importanceof ,theefficiencyoftransferoftheorientationfromthemonomerstothesolventmolecules.This parameter, found here for PDMS and chloroform to be of the order of 1/150, isexpectedformostsystemstobeanintrinsicpropertyofagivensolvent/monomerpair,but otherwise independent of experimental conditions. Anticipated exceptions arebrieflydiscussedattheendofthissection.
0.000 0.005 0.010 0.015 0.020 0.025
0.05
0.10
0.15
0.20
0.25
0.30Φ
eq
XCR
S25
Aclearpictureemergesfromourdescriptionthataccountsforthequadrupolarsplittingvaluesobservedunder these experimental conditions.The reference value for solventquadrupolarsplitting, itsmaximumattainablevalue, isoforderofacoupleofhundredkilohertz.Dilutionofthegeltotherangeof10%volumefractionreducesthisamounttotheorderofacoupleoftensofkilohertz.MonomerorientationorderparametersS,evenforgelsstretchedinthetubebya factorfour,donotriseabout0.2,bringingfortheseexperimental conditions the maximum orientation power of the gel network to therangeofafewthousandhertz.Howmuchthisorientationpotentialcanbetransferredtothe solvent depends on the microscopic nature of the interactions between themonomersandthesolventduringthetimelengthofanencounter.WefoundherethatsuchtransferissmallerthanapercentforthePDMS/CDCl3pair,bringingthusthefinalobservedvaluestotherangeofafewtensofhertz.
In practice we expect, as values of the efficiency of orientation transfer will becomeavailable for other monomer/solvent pairs, that our approach will provide a widelyapplicable,quantitativepathwaytounderstandandpredicttheamountofquadrupolarsplitting that one can expect for a given experimental geometry. Indeed, given theefficiencyofthegel/solventpair,thesimpleknowledgeofthegelsizeandcross‐linkingratiowillallowpredictingquadrupolarsplittingvalues.
Note thatour treatmentof solventquadrupolar splittinggivenbyEq. (1) is similar toothers[20], but introduces explicitly the probability of interaction between solvent andchains,givenbythedilutionfactor intheequation,andidentifies theefficiencyfortransferoforientation.Amorein‐depthstudyofthevalidityofEq.(1),andinparticularonitsdependenceontheorderparameterSofthemonomers,isinprinciplepossiblebyusingacombinationofdeuteratedsolventswithnon‐deuteratedchains,anddeuteratedchains with non‐deuterated solvents. This might be crucial if, as we anticipate here,therearecertaincaseswhere mightbeS‐dependent,forinstancewhenthesizeofthesolventmoleculeismuchlargerthatthesizeofthechainmonomers,andtheresultinginteractionsbetweenthechainmonomerandthesolventloosetheirlocalcharacter.
Being able to quantitatively treat quadrupolar splitting in anisotropically swollen gelswill not only provide an operational framework for dealingwith orientationmedia inRDCexperiments,butwillalsoopenaspectrumofnewinterestingpossibilitiestostudythe interactions of gels with different molecules. A particularly relevant exampleconcernsgel swelling insolventmixtures, say for thesakeof clarity, inbinarysolventmixtures.Sincethevalueofquadrupolarsplittingdependsexplicitlyontheprobabilityof encounter between a given solvent molecule and the chain monomers, thedependenceofmeasuredvaluesofquadrupolarsplitting∆ asafunctionofX,themolarratioofoneofthesolventsinthemixture,shouldbeverysensitivetophenomenaakintopreferentialsolvation.Thus,wewouldexpectasmoothlinearinterpolationbetweentwovaluesfor∆ asafunctionofXifthetwosolventsareequallygoodforthepolymer,whileanypreferentialsolventcharacterwillincreaseitsprobabilityofcontactwiththechainsaboveitsaveragevalue,promotingmarkedlynon‐linearvariationsof∆ withX.
S26
NMRspectra
1HNMRofBCP/CDCl3,279K
7 6 5 4 3 2 1 0 ppm
0.
97
1.
00
1.
43
1.
46
1.
47
1.
50
1.
58
1.
61
1.
66
1.
68
1.
91
2.
00
2.
08
2.
20
2.
24
2.
32
2.
34
2.
42
2.
51
4.
82
4.
94
5.
26
5.
31
1.07
3.81
2.85
4.12
2.61
3.20
0.47
1.26
1.84
1.31
1.25
1.82
0.56
0.27
1.16
1.14
1.00
Current Data ParametersNAME yulia-600_b-caryophylleneEXPNO 10PROCNO 1
ReferencesandNotes 1 N.T.Nyberg,J.Ø.Duus,O.W.Sørensen,J.Am.Chem.Soc.2005,127,6154.2 a) D. H. Wu, A. Chen, C. S. Johnson, J. Magn. Reson. Ser. A 1995, 115, 260; b) M. D. Pelta, H. Barjat, G.
A. Morris, A. L. Davis, S. J. Hammond, Magn.Res.Chem. 1998, 36, 706. 3 A.Enthart,J.C.Freudenberger,J.Furrer,H.Kessler,B.Luy,J.Magn.Reson.2008,192,314.4 a)K.Fehér,S.Berger,K.E.Kövér,J.Magn.Reson.2003,163,340;b)C.M.Thiele,W.Bermel,J.Magn.