Recent Advances in the Low-Field NMR Characterization of Polymeric Soft Materials Kay Saalwächter Low-resolution proton time-domain NMR Basic experiments and industrial applications - Chemometrics - NMR cryoporometry Advanced experiments Examples: - polymer crystallization - domain sizes in block copolymers - structure and dynamics of elastomers - gelation Conclusions
Time-domain NMR typical FID of a liquid or a rubber: T 2 * 0.5 1 ms (1/πT 2 * 0.5 khz) shim- (B 0 homogeneity-) limited! compare: σ = 5 ppm 20 MHz 5 ppm = 100 Hz! most important aspect: initial FID intensity = integrated signal! FT
Mobility contrast reflected in the FID frequency domain rigid organic solid (crystalline, below T g ) ~ 20 khz liquid, oil, polymer melt, elastomer ~10-1000 Hz time domain ~ 10 µs ~ 500 µs (shim!) e.g. semicrystalline polymer, block copolymer Σ two-component decay food industry applications: solid fat content (SFC) in greases water content in bread
Manipulation by pulse sequences B 0 T 1 process B 0 90 pulse apparent rd FID T 2 process (B (recycle delay) 0 inhom.) more sophisticated experiments: rd some pulse (sequence) some other pulse (sequence) FID fast (MHz) dynamics: measure T 1 inversion recovery rd 180 pulse τ I = f(τ) slow (khz) dynamics: measure real T 2 Hahn echo (alt.: CPMG, multiple echoes) rd now also: more reliable separation of multiple mobile components! τ amplitude 180 pulse I = f(τ) τ fast decay intermediate decay slow decay time τ N
Other industrial applications Pharmaceutical Ind. Petroleum Industry Medical Research e.g. moisture in powders (free & bound) Consumer Products e.g. total hydrogen content of distillates e.g. live mice analyzer Polymer Applications e.g. fluoride in toothpaste
Chemometrics e.g., water, oil, and protein contents in seeds via T 1 or T 2 (inv.rec. or CPMG) amplitude fast decay intermediate decay slow decay multi-exponential fitting can be ambiguous! time idea: find sub-curves by linear-algebra techiques (principal-component analysis, PCA): K fixed time points N reference samples (known contents), a n data vectors to model an unknown a, T can often be a 2xK matrix, 2 principal components (PC1,2) and subcurves (p 1,2 ) are sufficient! eigenvectors (subcurves) n N p 1 p 2 k K A P PC1 0 0 PC2 0 0 T residuals, noise E
Applications of chemometrics oil seed treatment: water content of fish: T 1 H.T. Pedersen, L. Munck, S.B. Engelsen, J. Am. Oil Chem. Soc.. 77 (2000), 1069-1077 T 2 S.M. Jepsen, H.T. Pedersen, S.B. Engelsen, J. Sci.. Food Agric.. 79 (1999), 1793-1802
NMR cryoporometry Gibbs-Thompson: melting point depression of a finite-sized crystal: d 1 simple experiment: π/2 π d 2 rd τ τ remaining liquid (water) signal = f(t) reconstruct pore size distribution! NMR gas sorption (BET) J.H. Strange, M. Rahman, E.G. Smith, Phys. Rev. Lett.. 71 (1993), 3589-3591
NMR cryoporometry decomposition of pore-size mixtures: J.H. Strange, M. Rahman, E.G. Smith, Phys. Rev. Lett.. 71 (1993), 3589-3591
Advanced experiments polymer crystallinity and amorphous-phase mobility: measure dipolar-refocused FID and T 2 MSE-CPMG rd MSE FID τ τ τ I = f(nτ) domain sizes: measure spin diffusion improveddipolarfilter sequence rd selection spin diffusion τ diff MSE I mobile = f(τ diff ) network structure and dynamics: measure weak dipolar rd couplings MQ experiment I = f(τ DQ excitation DQ reconversion ) DQ τ DQ τ DQ
1 H NMR detection of polymer crystallization an old quantification problem dead time! f τ d c f a traditional partial solution solid echo x τ se ± y t=0 t=0 advanced solution mixed magic τ CPMG φ sandwich 1 echo φ 4 τ' 2τ 2τ τ τ initial φ 4 τ CPMG φ 4 t=0 N /2 φ 2 φ 3 φ 3 φ 3 φ 3 -φ 3 -φ 3 -φ 3 -φ 3 φ 2 τ' τ φ 2 τ φ τ φ 2 τ φ 2 τ φ 2 τ φ 2 τ φ τ φ 2 τ φ τ φ τ n MSE n MSE A. Maus. C. Hertlein, KS, Macromol. Chem. Phys. 207 (2006), 1150
Isothermal crystallization kinetics on the minispec poly(ε-caprolactone) at 40 C φ c dead time! magic echo improved method: signal / a.u. φ a t=0 N 90 80 70 60 50 40 30 20 10 FID-CPMG 2½ h 0 0.00 0.01 0.02 0.03 5 10 15 20 delay / ms signal / a.u. 90 80 70 60 50 40 30 20 10 t=0 N crystallinity MSE-CPMG amorphous phase mobility 0 0.00 0.01 0.02 0.03 5 10 15 20 delay / ms A. Maus. C. Hertlein, KS, Macromol. Chem. Phys. 207 (2006), 1150
Polymer crystallization: the problem
Polymer crystallization: spherulitic lamellar growth µm-mm scale: spherulites sub-µm scale: lamellae
Polymer crystallization: possible scenarios reeling-in, adjacent re-entry solidification model, fringed micelles, no large-scale diffusion new ideas: Olmsted et al. 1998: spinodal-like process? Strobl 2000: mesomorphic pre-phase?
Field (in)dependence and morphology effect spp crystallized at differect T c 1.0 0.8 f c = 21.6% f c = 24.5% 20 MHz norm. intensity 0.6 0.4 f m = 64% f m = 61% T 50% 0.43 ms 0.2 T 50% 0.28 ms 500 MHz norm. intensity 0.0 1.0 0.8 0.6 0.4 0.2 0.02 0.04 0.06 0.08 1 10 time / ms f c = 20.6% f c = 23.4% f m = 64% f m = 63% T 50% 0.30 ms } 100 µs 200 µs T c = 388 K 400 µs 100 µs 200 µs } T c = 368 K 400 µs T 50% 0.54 ms clear influence of morphology! lower T c faster cryst., solidificationtype more confined chains, faster relaxation 0.0 0.02 0.04 0.06 0.08 1 10 time / ms A. Maus. C. Hertlein, KS, Macromol. Chem. Phys. 207 (2006), 1150
Crystallization isotherms lin crystalline fraction f f c 0.25 0.20 0.15 0.10 0.05 secondary crystallization 0.00 phenomenological time dependence: Avrami equation f c (θ)=f [1-exp{-(Kθ) n }] n: growth dimensionality +1 for cont. nucleation +?for in-filling processes log crystalline fraction f f c 1 0.1 0.01 1E-3 1E-4 0 10000 20000 30000 40000 crystallization time θ / s A(θ) 20µs slope = 3 crystalline fraction immobilized fraction 1000 10000 crystallization time θ / s f c f ra equal trends for crystalline and immobilized fractions no indication for a multi-stage process A. Maus. C. Hertlein, KS, Macromol. Chem. Phys. 207 (2006), 1150
Domain sizes in phase-separated polymers domain sizes: measure spin diffusion dipolar filter sequence rd selection spin diffusion τ diff MSE I mobile = f(τ diff ) phase-separated system with mobility contrast intensity / a.u. 35 30 25 20 15 10 τ diff -dependent FIDs: compensate for fast T 1 relaxation at 20 MHz onlypossiblewith full MSE refocussing! 5 170.9 ms 0 0.0 0.1 0.2 0.3 0.4 time / ms spin diffusion time 0.5 ms 9.2 ms 23.0 ms 39.7 ms 68.7 ms 295.3 ms
Spin diffusion in lamellar copolymer systems selected soft (PB) fraction intensity [a.u.] 1,0 0,8 0,6 0,4 0,2 12.5 0,0 0 5 10 15 20 25 sqrt(t) [sqrt(ms)] d (2/ π)[d soft = eff t s,0 m ] ½ ~ 14.3 nm (t s,0 m ) ½ soft fraction in blend 14.3 nm TEM SBS/PS 40/60 Blend correlation with macroscopic properties (e.g. clarity ) HOPS project w/ Y. Thomann, R. Mülhaupt, BASF
NMR in networks: chain order parameter b(t) n S(n)
Segmental dynamics in networks reference direction time-dependent orientation correlation function C α (t) = <f(α)> t,n,n α(t) log C α ~1% fast segmental motions (ns µs) slow, cooperative processes (ms s) (?) log time n network chains, N segments each residual average orientation ~ backbone order parameter S b (local!) dependent on N -1 (~ crosslink density) changes with mechanical deformation!
The order parameter descriptor of uniaxial orientational order: S = P 2 (cos α) α 1.0 0.5 0.0-0.5 20 40 60 80 α S = 1 S 0.7 S 0 S = 0.5 (NMR: average... is over time!)
Dynamic averaging of NMR interactions dipolar coupling tensor D γ i γ j /r ij 3 B 0 τ c (T) D stat = D zz 30 khz! ± D(β) static spectrum D xx β D yy D zz intermediate τ c 1/D zz D res S b fast-limit spectrum
Why multiple-quantum spectroscopy? D res ~ S b real system vs. ~ 1/T 2 * T 2* subject to non-dipolar effects multi-spin couplings slowdynamics order distributions... 6420-2 -4 ppm 6420-2 -4 ppm more specific experiment! static dipolar doublequantum spectroscopy τ DQ τ DQ DQ excitation DQ reconversion
ideal real Transverse relaxation vs. MQ spectroscopy dipolar time evolution Φ = (2/3) Φ D res P 2 (cos β) τ spectra rd τ FT τ I = f(τ) FID/Hahn echo I dip = <cos Φ > structure structure + dynamics rd 0.5 DQ excitation τ DQ DQ MQ experiment I ΣMQ = <sin 2 Φ> + <cos 2 Φ> I ΣMQ DQ = <sin 2 Φ> DQ ΣMQ: dynamics only! DQ reconversion τ DQ 0.5 I = f(τ DQ) ndq = DQ/ΣMQ: structure only! freq. time τ mobile impurities (sol )
Magnitude and time dependence of S b S b D res n n C(t) = (1-S b2 ) P 2 (cos α(0)) P 2 (cos α(t)) +S b 2 n ~ MHz-scale pre-averaging; quasi-static order: cross-link density, S 1/N chain stretching/swelling distributions! n n β(t) ~ khz-scale slow motions; loss of correlation: cross-link mobility (?) or reptation of linear chains C(t) = S b 2 P 2 (cos β(0)) P 2 (cos β(t)) intermediate dynamics!
DQ data analysis order paramters monomodal PDMS network (47k), unswollen 1.0 220 K simulated spin system: DQ intensity 0.8 0.6 0.4 0.2 0.0 295 K 340K CH 3 semi-analytical fitting function monomer unit 0 2 4 6 8 10 12 14 16 18 20 excitation time τ DQ / ms Si α α C C D res = 130 Hz S 3% KS, J.-U. Sommer, et al., J. Chem. Phys. 119 (2003), 3468
Model case for a heterogeneous microstructure bimodal end-linked PDMS networks 0.6 linear superpositions of experimental data for net0 and net100 DQ intensity 0.4 0.2 best-fit (monomodal) 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 excitation time τ DQ % short chains: net0 (monomodal) net10 net20 net30 net50 net70 net90 net100 / ms 3.5 PDMS precursors: long chains: 47k short chains: 0.8k KS, J.-U. Sommer, et al., J. Chem. Phys. 119 (2003), 3468
Fitting of chain order distributions/heterogeneities integral inversion by Tikhonov regularization (Weese and Honerkamp, 1992) relative amplitude.008 100% 90%.006 70% 50%.004 30%.002 20% 10% 0 0% 0 400 800 1200 1600 D res / Hz KS, J.-U. Sommer, et al., J. Chem. Phys. 119 (2003), 3468 KS, J. Am. Chem. Soc. 125 (2003), 14684
Chain order distributions in natural rubber rel. amplitude 15 10 5 NR-A1 NR-A2 NR-A4 NR-A10 gamma distribution = expected result for Gaussian statistics <r 2 >= n l 2 0 r l 0 0 0.0 0.2 0.4 0.6 0.8 1.0 D res /2π / khz no indication for an influence of Gaussian chain statistics! network chain polydispersity (exponential distribution) does not appear either! cooperativity/packing reduces/homogenizes conformational space direct implications for chain entropy!! KS, B. Herrero, M. A. López-Manchado, Macromolecules 38 (2005) 9650-9660
Quantitative modelling: NMR vs. swelling crosslink density x c ~ 1/M c ~ 1/N ~ S b ~ D res 1/M c (NMR) / mol/kg 1/M c + 1/M e 0.80 0.60 0.40 0.20 NR-A NR-B 1/M e, NR slope = 2.05±0.06 slope = 1 0.00 0.00 0.05 0.10 0.15 0.20 1/M c (swelling) / mol/kg natural rubber: NMR overestimates order twice rescaling yields consistent results (M te = 10 kg/mol) semi-quantitative elastomer characterization! problems at the detail level validity of the Kuhn length model? of single-chain concepts in general? 1/M c + 1/M te KS, B. Herrero, M. A. López-Manchado, Macromolecules 38 (2005) 9650-9660
Chain dynamics: the Andersen-Weiss model I Gaussian (2nd-moment) assumption DQ experiment: τ DQ Φ A τ DQ Φ B I DQ = < sin Φ A sin Φ B > I ΣMQ = < sin Φ A sin Φ B > + < cos Φ A cos Φ B > comparison: Hahn echo relaxometry: Φ A τ echo ΦB I Hahn = < cos (Φ A + Φ B )> Gaussian distribution of interaction frequencies (mainly from the powder distribution) approximation of the trigonometric functions, simplification of the ensemble average: I DQ = sinh{<φ A Φ B >} exp{ <Φ A2 >} I ΣMQ = exp{<φ A Φ B >} exp{ <Φ A2 >} I Hahn = exp{ ½<(Φ A + Φ B )>} Φ = (2/3) Φ = τ D res P 2 (cos β t ) dt D res P 2 (cos β) τ KS, J. Chem. Phys. 120 (2004) 454 KS, A. Heuer, Macromolecules 39 (2006) 3291-3303
Experimental test of the Andersen-Weiss model calculate theoretical 1 H Hahn echo decay from experimental MQ data (natural rubber, 3 phr sulfur, 20 MHz spectrometer) rel. intensity 1.0 0.8 0.6 0.4 0.2 experimental Hahn echo theoretical Hahn echo 12 C 38 C 130 C normalized DQ build-up 0.0 0 1 2 3 4 5 evolution time / ms KS, A. Heuer, Macromolecules 39 (2006) 3291-3303
Chain dynamics: the Andersen-Weiss model II e.g. I DQ = sinh{<φ A Φ B >} exp{ <Φ A2 >} with Φ A,B = τ D res P 2 (cos α t ) dt requires integration of C(t) = P 2 (cos α 0 )P 2 (cos α t ) log C α S b 2 fast segmental motions (ns µs) slow, cooperative processes (ms s) old model: neglect fast processes C(t) = S b2 P 2 (cos β 0 )P 2 (cos β t ) = S b2 exp{ τ DQ /τ s } log time
Slow dynamics: temperature dependence vulcanized natural rubber, 3 phr sulfur normalized DQ build-up I ndq = I DQ /I ΣMQ I ΣMQ : exp. sum intensity decay I DQ : exp. DQ build-up 1.0 1.0 successful normalization procedure! norm. intensity 0.8 0.6 0.4 norm. intensity 0.8 0.6 0.4 285K 340K 403K ΣMQ DQ 0.2 0.2 0.0 0 2 4 6 DQ evolution time / ms 0.0 0 2 4 6 8 10 DQ evolution time / ms KS, A. Heuer, Macromolecules 39 (2006) 3291-3303
Slow-motion model 1 order parameter S b 0.1 ndq DQ ΣMQ T 0.01 g = 213 K 200 240 280 320 360 400 440 480 temperature / K expected plateau for D res from DQ-buildup unphysical result from sum intensity decay correlation time τ c / ms 100 10 1 0.1 0.01 1e-3 τ slow (DQ) τ slow (ΣMQ) T g = 213 K 200 240 280 320 360 400 440 480 temperature / K complete disagreement between the different τ c unphysical temperature dependence (not activated?) KS, A. Heuer, Macromolecules 39 (2006) 3291-3303
Fast and slow dynamics ΣMQ DQ ndq log C α S b 2 fast segmental motions (ns µs) slow, cooperative processes (ms s) old model: neglect fast processes new model: consider fast processes! importance of slow processes? log time
Better models 1.0 0.8 321K SMQ DQ exponential correlation function C(t) = (1-S b2 ) exp{-t/τ fast } + S b 2 exp. cf. τ fast norm. intensity 0.6 0.4 exp. cf. τ fast,τ slow power-law cf. exponential correlation function with slow decay C(t) = (1-S b2 ) exp{-t/τ fast } + S b2 exp{-t/τ slow } 0.2 0.0 0 2 4 6 8 10 12 14 DQ evolution time / ms power-law correlation function C(t) = (1-S b2 ) (τ 0 /t) κ + S b 2 for t > τ 0 validity/fitting limit! KS, A. Heuer, Macromolecules 39 (2006) 3291-3303
Better models correlation time τ c / ms power-law onset τ 0 / ms 100 10 1 0.1 0.01 1e-3 1e-4 0.01 1e-3 1e-4 1e-5 1e-6 WLF fit T g = 213 K 200 240 280 320 360 400 440 480 temperature / K exponential correlation function C(t) = (1-S b2 ) exp{-t/τ fast } + S b 2 1e-7 0.2 1e-8 T g = 213 K 0.0 200 240 280 320 360 400 440 480 temperature / K τ slow (DQ) τ slow (ΣMQ) τ fast (sim. fit) 1.2 1.0 0.8 0.6 0.4 power-law exponent κ no evidence for a slow process! KS, A. Heuer, Macromolecules 39 (2006) 3291-3303
Comparison with melt dynamics natural rubber, 3 phr sulfur (A3) vs. unvulcanized (lin) 1.0 NR-A3 NR-lin ndq norm. intensity 0.8 0.6 0.4 ΣMQ DQ 285K ΣMQ DQ 403K NR-A3 NR-lin 0.2 340K 0.0 0 2 4 6 8 10 DQ evolution time / ms 0 2 4 6 8 10 DQ evolution time / ms 0 2 4 6 DQ evolution time / ms no observable "plateau" value for S b influence of reptation dynamics! (isotropization on a timescale τ d ) KS, A. Heuer, Macromolecules 39 (2006) 3291-3303
Comparison of permanent networks and melts lin. poly(butadiene), 50% cis, 45% trans Graf, Heuer, Spiess, PRL 80 (1998) 5738 order parameter S b 1 0.1 0.01 ~ entanglement level S b,e T - T g / K NR-A3 NR-A04 NR-lin unobservable due to reptation! 0 40 80 120 160 200 240 segmental averaging at T = T g + 50K probes a length scale << a "local packing" (Doi-Edwards: a ~ entanglement length, associated with τ e ) slow segmental averaging, important when conformational space is large! no proper timescale separation (τ e, τ R, τ d )?
Study of gelation increasing crosslink density ω melt/solution percolation threshold elastomer rheology: F(ω) G(ω) η(ω)
Rheological determination of the gel point Winter/Chambon: gel point = loss tangent [ tan δ(ω) = ω η(ω)/g(ω) ] becomes independent of frequency tan δ 1000 100 10 1 0.1 gel point r = 0.423 50 rad/s 31.5 rad/s 19.9 rad/s 12.6 rad/s 7.9 rad/s 5.0 rad/s 3.15 rad/s 2.00 rad/s 1.26 rad/s 0.79 rad/s 0.50 rad/s bulk crosslinking of PDMS, varying stoichiometric ratio r time consuming! 0.35 0.40 0.45 0.50 r
norm. intensity 1.0 0.8 0.6 0.4 0.2 Gel point by low-field MQ NMR single-point detection of residual couplings comparisonwithrheology (Winter/Chambon) quantitative analysis: sol fraction, network properties bimodal structure at low conversion ΣMQ sol ndq 0.0 0 10 20 30 40 DQ evolution time / ms r = 0.36 r = 0.41 r = 0.47 r = 0.506 r = 0.56 r = 0.62 r = 0.67 ndq intensity @ 5 ms sol fraction statistical linking (vulcanization) 0.1 0.01 1E-3 PDMS 441 PDMS 424 noise 1E-4 0.00 0.02 0.04 0.40 0.50 0.60 0.70 r 1.0 0.8 0.6 0.4 0.2 PDMS 441 PDMS 424 0.0 0.00 0.02 0.04 0.40 0.50 0.60 0.70 r end-linking KS, M. Gottlieb, R. Liu, W. Oppermann, Macromolecules 40 (2007) 1555-1561
gel points Gelation kinetics by low-field MQ NMR ndq intensity @ 4 ms gel point time / s 0.20 0.16 0.12 0.08 0.04 0.00 0 5000 10000 15000 20000 gelation time / s 6000 4000 2000 DLS NMR c = 0.05 g/ml c = 0.04 g/ml c = 0.03 g/ml c = 0.02 g/ml τ NMR 0 0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 polymer concentration / g/ml 6000 4000 2000 gelation time constant / s dilute solutions of P(S-co-AMS) in toluene-d 8 real-time measurement of DQ intensities comparisonwithdls quantitative NMR analysis: 13-50% network chains 56-43% dangl. chains, loops, microgels 31-7% mobile sol KS, M. Gottlieb, R. Liu, W. Oppermann, Macromolecules 40 (2007) 1555-1561
Conclusions low field but high-end science easy set-up: insert sample, adjust gain, offset and 90 pulse, start polymer crystallinity, morphology, crystallization kinetics domain structures in block-copolymers in-depth elastomer characterization, new polymer physics detailed insights into gelation
Thanks very much... Andreas Maus Christopher Hertlein, G. Strobl (U Freiburg) Yi Thomann, R. Mülhaupt (U Freiburg) Jens-Uwe Sommer (ICSI Mulhouse/IPF Dresden) A. Vidal, B. Haidar, P. Ziegler, O. Spyckerelle (ICSI) Berta Herrero, M.A. López-Manchado (ICPT-CSIC, Madrid) Moshe Gottlieb (U of the Negev, Beer Sheva) Ruigang Liu, W. Oppermann (TU Clausthal) Landesstiftung Baden-Württemberg, DFG (SFBs 428 & 418), Fonds der Chemischen Industrie