Applications of Diffusion NMR for Polymer Property Determination

1. NMR DiffusionandPDI determinationA Pair of Applications of Diffusion NMR for Polymer Property Determination Sjoerd J. Rijpkema 21-11-2018

2. Quick review of NMR basics • 1H 1D NMR • 1H – 1H COSY • 13C 1D NMR • 1H – 13C HSQC • 1H – 13C HMBC

3. More possibilities • TOCSY – Following a spin system trail • NOESY – Through spaceinteractions • DOSY – Diffusion NMR (Determine MW and speed) • EXSY – Exchange NMR (chemical exchange or conformer changes) • Allexperimentscanbedonewith X nuclei! (1H – 15N HMBC) i.e. A NOESY between1H and19F is called a HOESY • Diffusion • Polydispersityby NMR

4. Diffusion NMR spectroscopy • Diffusion is related to molecular shape via the Stokes-Einstein equation: • Assumptions: • Molecule behaves like a sphere • Radius α MW Important Considerations for NMR: • Temperature – ambient is best (lack of strong convection currents) • Solvent viscosity – DMSO > D2O > CDCl3 (keep in mind) • Molecular weight – too large and can’t measure D with conventional probes

5. What we canusediffusionfor • Sizeestimation/MW determination (hard sphereassumption) & Example: D7 = 1.15 x 10-5 cm2/s D8= 1.12 x 10-5 cm2/s D9= 0.95 x 10-5cm2/s ~1.66x largerthan7 or 8 Three intermediates were observed by 1H NMR and determined to have this formula via COSY, 1H-29Si HMBC and 1H-15N HSQC: Rijpkema, S.J.; White, P.B.; Bunschoten, R.P.; Mecinovic, J. Manuscript in progress

6. What we canusediffusionfor • Resolutionbased on physiochemicalinteractions (solute/solvent interactions; solute/gel; etc) Note: verysimilar MW Yet can all be resolved in MeOH-d4 due to differences in H-bonding to solvent (different solvates) Reile, I.; Rutjes, F. P. J. T.; et. al Magn. Reson. Chem., 2017, 55, 759-762

7. What we canusediffusionfor • Determination of cleavage of a group PEG tail is redox cleavable – NMR can Clear similarity between post-cleavage PEG (top) and demonstrate this free PEG (bottom) Note: Stomatocyte with PEG too large to measure D (< 10-7cm2/s) Tu, Y.; Peng, F; White, P. B.; Wilson, D. A. Angew. Chem. Int. Ed., 2017, 56, 7620-7624

8. What we canusediffusionfor • Determination of pore size of a (hydro)gel (κ-carrageenan) Dendritic NP with 19F labels Measure D (1H, 19F) of different sized Diffusometry (Diffusion + used to probe pore-size of the dendrimers and vary carrageenan loading Relaxometry) provides additional gel to find the diameter of the pore resolution of components Lower limit determinedtobe 5 – 7 nm Van As, H.; et. al. Anal. Chem.,2014, 86, 9229-9235

9. What we canusediffusionfor • Determination of criticalmicelleconcentration CMC = point where higher concentrations of surfactant induce micelle formation Same compound undergoes a structural transition DetectablebydiffusionNMR - individualmoleculesvsmicelles Tu, Y.; Peng, F; White, P. B.; Wilson, D. A. Angew. Chem. Int. Ed., 2017, 56, 7620-7624

10. What we canusediffusionfor • Looking at small molecules in the presence of large • Large molecules cause unwanted background signal • T2 filter! (large molecule short T2, small = long T2) Rastrelli, F.; et. al. J. Am. Chem. Soc.,2009, 131, 14222-14224

11. What we canusediffusionfor • Looking at large molecules in the presence of small • Small molecules diffuse faster Apply a short diffusion element at thebeginning of the sequence to filter out small molecules, keeping large ones. Most effective when is high H2O DMSO-d5 Espinosa, J.F.; et. al. J. Org. Chem., 2006, 71, 4103-4110

12. Diffusion NMR spectroscopy – Hardware requirements 1) An NMR 2) A gradientprobe/gradientchannel - Any probe that autoshims = gradients! BBFO: Standard probe for 400 (and 500) Gradientcapability: 5 G/cm/A Max Gradient: 50 G/cm @ 10 A Limit: Stomatocytes too big (as measured) Diff30 or Diff50 probe: Special designeddiffusionprobes Gradient capability: 30 G/cm/A (diff30) or 50 G/cm/A (diff50) Max Gradient: 1800 G/cm @ 60 A; 3000 G/cm @ 60 A Limit: < 10-12m2/s (nanoparticles)

13. Diffusion NMR spectroscopy – GradientLabeling • Simplest Pulse Sequence – Pulse-Field Gradient Spin-Echo • Intensity of signal during acquisition is given by the Stejskal-Tanner expression • D = D20 = Diffusion time • = P30*2 = length of gradient pulse • D1 + AQ > 3*T1 D = Diffusion constant g = gyromagnetic ratio g = gradient strength

14. Diffusion NMR spectroscopy – GradientLabeling First (windup) gradient labels the nuclei spatially along the z-axis of the tube

15. Diffusion NMR spectroscopy – GradientLabeling Second (unwind) gradient unlabels the nuclei spatially along the z-axis of the tube If all the nuclei “echo” perfectly, there is no dephasing of magnetization/loss of signal

16. Diffusion NMR spectroscopy – GradientLabeling Second (unwind) gradient unlabels the nuclei spatially along the z-axis of the tube If the nuclei DO NOT “echo” perfectly, there IS a dephasing of magnetization/loss of signal

17. Diffusion NMR spectroscopy – MeasuringDiffusion The molecules diffuse inside the tube, precessing at the frequency that was imposed upon them during the gradient pulse

18. Diffusion NMR spectroscopy – MeasuringDiffusion The fast-diffusing one moves the most thus does not “echo” perfectly and dephases, resulting in lower % peak intensity. Slow molecule hardly moves, “echoes” more perfectly, has larger % peak intensity

19. Diffusion NMR spectroscopy – Obtaining information D = Diffusion constant g = gyromagnetic ratio g = gradient strength • Two ways: • Vary the diffusion time at constant gradient strength Problem!Longer diffusion times  more relaxation (T2) problems and convection. • Vary the gradient strength at constant diffusion time No more convection and T2 problems. Limit to the gradient strength! Low Gradient – Lots of space between spin regimes, slow diffusing molecules don’t change much High Gradient – Less space between spin regimes, slow diffusing molecules change more

20. Diffusion NMR spectroscopy – VaryingGradientStrength 5 G Weak gradient = weak response to diffusion

21. Diffusion NMR spectroscopy – VaryingGradientStrength 5 G 18 G Stronger gradient = stronger response to diffusion

22. Diffusion NMR spectroscopy – VaryingGradientStrength 5 G 18 G 38 G Even stronger gradient = very strong response to diffusion

23. Diffusion NMR spectroscopy – VaryingGradientStrength 100 G 5 G 18 G 38 G

24. NMR Diffusion – PNIPAM 2K Jiawei Sun

25. Diffusion NMR spectroscopy – 1D vs DOSY Pseudo-2D technique: Not a real 2D technique because there is no indirect FID to transform. Can be applied to other parameters besides D (like rate constants!)

26. Radboud NMRs • Bruker400 (Ascend)

27. …ABABAB… vs …ABAABAA… NMR in Polymer Chemistry • Formula/functionalizationdetermination • Branching, substitution, tacticity • Insight into the mechanism of polymerization • Time-dependentstructuralisomerism • Averagemolecularweight (Mn) • Polydispersity/MW distribution • Structuralproperties • 3D structure (e.g. proteins) • Aggregration/CMC (micelleformation) • Solid-phasestructureanddynamics • Degreeof crystallinity • Muchmuch more… Donovan, K. J.; Griffin, R. G.; et. al J. Am. Chem. Soc., 2016, 138, 9663--9674

28. Properties of Polymers – IdentificationandQuantification X = 45 Y = 54 Z = 15 From NMR integration • Identity and quantification of Monomer repeating units • Distinct ranges of chemical shifts • “Easily” calculate number-average value of groups • Broad lines due to size (T2) and distribution of shifts Huang, X.; et. al. Sci. Rep. 2016, 6, 39504

29. Properties of Polymers – Polydispersity • Polydispersity/Distribution of Chain Lengths (PDI) • Calculatedby: Ð = Mw/Mn Mw= Weight-AverageMolecularWeight Mn = Number-AverageMolecularWeight Multiply the MW of each chain length by the number of times it is present; divide by total number of molecules Multiply the MW of each chain length by the weight/mass fraction it represents; divide by sum of weight fractions (usually 1) If all polymers were of identical length then the PDI (Ð) = 1.0 - monodisperse For Ð > 1.0, sample is more heterogeneous http://www.open.edu/openlearn/science-maths-technology/science/chemistry/introduction-polymers/content-section-2.6; En.wikipedia.org/wiki/Dispersity; http://www.pslc.ws/macrog/average.htm

30. Polydispersity by NMR 1D NMR can also be used to calculate Mn: 1) ID the end group 2) Normalize the integrals to # of 1Hs m = 86.41/4 1Hs = 21.6 units n = 180/1 1H = 180 units Mn= 21.6*MWPEG+ 180*MWPLA+ 32 (CH3+H+O) = 13,942.4 Da Mwnotdeterminable fromintegrals

31. Properties of Polymers – Polydispersity Mass percent Mn = 2150830/3795 = 566.75 Mw= 601.50/1.00 = 601.50 PDI = 601.50/566.75= 1.061 http://www.open.edu/openlearn/science-maths-technology/science/chemistry/introduction-polymers/content-section-2.6; En.wikipedia.org/wiki/Dispersity; http://www.pslc.ws/macrog/average.htm

32. Polydispersityby GPC (andOthers) • Polydispersity/Distribution of Chain Lengths (PDI) • Measured typically by GPC, MALDI or DLS • GPC –Gel PermeationChromatography • size-exclusionchromatographytechnique • small molecules are retained longer than larger ones • All information in one-go and already calculated PDI • Limited by requiring an internal standard very similar to your polymer (complex polymers are difficult) Median MW SharinBouwman

33. Polydispersityby NMR Is there a technique within NMR that can calculate PDI? YES NMR is all-powerful and unstoppable (as you should know by now)

34. Polydispersityby NMR ILT = inverse Laplace transform – used to process non-uniform exponential decay (distribution of compounds) • PDI byusingDiffusion:  <DW> = diff. coefficient of polymer body from ILT analysis <DN> = diff. coefficient of polymer ends from ILT analysis df= fractal dimension relatedto polymer-solvent interaction Diffusion of body weighted by mass of molecules Diffusion of ends weighted by # of molecules Delsuc, M. A.; et. al. J. Magn. Reson., 2011, 212, 169-173

35. Polydispersityby NMR • Fractal dimension (df) describesthepolymer-solvent interaction Infiniterod df = 1 Polymers in good solvent df = 1.7 Polymers in solvent df = 2 Polymer-polymerinteractions = solvent-polymerinteractions Sphere (solvent excluded) df = 3 Delsuc, M. A.; et. al. J. Phys. Chem. B, 2009, 113, 1914-1918

36. Polydispersityby NMR • Typically determined via SANS or SAXS experiments • Can also be determined via plotting relative diffusion constant vs MW of compound • best if monodisperse (and similarly shaped) Delsuc, M. A.; et. al. J. Phys. Chem. B, 2009, 113, 1914-1918

37. Polydispersityby NMR • Now we can determine the PDI by diffusion NMR <DW> = diff. coefficient of polymer body <DN> = diff. coefficient of polymer ends df= 1.86 was experimentally determined for PEG samples in D2O Delsuc, M. A.; et. al. J. Magn. Reson., 2011, 212, 169-173

38. Polydispersityby NMR - Limits • Method is quite accurate except when PDItrue>> 1 • Need to measure or use an estimate for the fractal dimension (df) - But has minor impact on PDI < 2 PDI < 2: accurate results PDI > 2: large deviations Delsuc, M. A.; et. al. J. Magn. Reson., 2011, 212, 169-173

39. Acknowledgements • Prof. Dr. Daniela Wilson • Dr. Paul White • JiaweiSun