Mixing polymer cocktails: Diffusion and relaxation distributions of mixed and polydisperse poly (ethylene oxide) melts

Mixing polymer cocktails: Diffusion and relaxation distributions of mixed and polydisperse poly (ethylene oxide) melts Kevin Lindta, Carlos Matteaa, Siegfried Stapfa, Sarah Mailhiotb a Dept. of Technical Physics II, Technische Universität Ilmenau, D-98684 Ilmenau, Germany b Bruker BioSpin GmbH & Co. KG, D-76275 Ettlingen, Germany Motivation, Samples & Methods Polymers in the melt follow characteristic scaling dependences of their dynamics: diffusion and NMR relaxation [1-4] Self-diffusion is determined directly via PFG/CFG and indirectly from relaxation Relaxation possesses both weight and frequency dependence All theoretical and experimental work relies on welldefined polymers with narrow weight distribution, i.e. PDI = Mw/Mn< 1.1 is the assumption of a defined weight justified? are diffusion and relaxation single-component? how to determine and quantify distribution functions? What defines the dynamics in binary mixtures? T2decays of bulk and mixturesDiffusion of bulk polymers Relaxometry of bulk and mixtures Conclusions & Outlook References [1] de Gennes, P. G, J. Chem. Phys. 1971, 55, 572. [2] Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Clarendon: Oxford, 1986. [3] Fatkullin, N.; Kimmich, R., Adv. Polym. Sci. 2004, 170, 1−113. [4] Fatkullin, N.; Stapf, S.; Hofmann, M.; Meier, R.; Rossler, E. A., J. Non-Cryst. Solids 2015, 407, 309. Diffusion of mixtures Distribution of diffusion coefficients and T2 are non-vanishing even for commercial PEO with narrow distribution Enhanced distribution width for mixtures of different weights Effect of matrix (light, heavy) onto polymer diffusion and relaxation detected Protracted transition Rouse reptation dynamics also revealed by T1 dispersion Data analysis and theory requires taking into account molecular weight distribution even for apparently well-defined polymer melts and blends bulk T2depends strongly on Mw, up to 10 times longer in deuterated matrix Decays are non-exponential even for narrow molar mass distributions Diffusion measurements carried out at Bruker 11.7 T spectrometer with DiffBB gradient at 17 T/m and 29 T/m Relaxation measurements carried out at Bruker 7.0 T spectrometer with multipulse echo sequences Relaxometry measurements carried out with Stelar SpinMaster relaxometer between 0.05 mT and 0.5 T 10-3 10-2 10-1 100101102103 10-2 10-1 100 PEO Bulk, T = 358 K 3 kg/mol 6 kg/mol 11 kg/mol 30 kg/mol 95 kg/mol 220 kg/mol 1000 kg/mol T1 (s) n (MHz) ~n0.28 ~n0.39 10-3 10-2 10-1 100101102103 10-2 10-1 100 PEO Blend, T = 358 K 90% 2H 10 kg/mol 10% 1H 11 kg/mol 30 kg/mol 95 kg/mol 220 kg/mol T1 (s) n (MHz) ~n0.24 ~n0.32 left: Rouse function (M<Mcrit) vs. power-law function (M>Mcrit) in bulk according to reptation theory [1,2] right: longer T1and reduced power-law exponent in 90% deut. matrix due to (a) no intermolecular contribution (b) higher mobility in 10 kDa matrix 010 20 30 40 10-3 10-2 10-1 100PEO Bulk, T = 358 K S/A T2 (ms) 3 kg/mol 409(9) 6 kg/mol 234(6) 11 kg/mol 203(6) 30 kg/mol 35(2) 95 kg/mol 10.7(5) 220 kg/mol 11.8(5) 1000 kg/mol 9.3(4) S/A = e-t/T2 S/A t/T2 010 20 30 40 10-3 10-2 10-1 100PEO Blend, T = 358 K 90% 2H 10 kg/mol & 10% 1H S/A T2 (ms) 11 kg/mol 378(10) 30 kg/mol 185(6) 95 kg/mol 112(4) 220 kg/mol 88(3) S/A = e-t/T2 S/A t/T2 in bulk and deuterated matrix similar non-exponentiality for large Mw 02x1012 4x1012 6x1012 8x1012 1x1013 10-4 10-3 10-2 10-1 100 d = 3 ms, D = 200 ms data exp. fit 3 kg/mol 6 kg/mol 11 kg/mol 30 kg/mol d = 5 ms, D = 500 ms 95 kg/mol S/Smax g2d2g2(D-d/3) [s/m²] bulk linear poly (ethylene oxide) PEO-hLxxx and mixtures of 10% linear poly (ethylene oxide) PEO-hLxxx in 90% deuterated linear poly (ethylene oxide) PEO-dLxxx Molar mass distribution (GPC) 102103104105106 0 1 2 3 4 P(log M) Molar Mass [g/mol] 1H PEO 3 kg/mol 30 kg/mol 95 kg/mol Project number 238391017 name isotope Mw(g/mol ) Mn(g/mol) PDI PEO -hL3b 1 H 3060 2980 1.03 PEO -hL6a 1 H 6000 5850 1.03 PEO -hL11 1 H 11200 10800 1.04 PEO -hL30 1 H 29100 26400 1.10 PEO -hL95 1 H 94600 81900 1.16 PEO -hL220 1 H 220000 197000 1.12 PEO -dL10 2 H 11000 10100 1.09 PEO -dL300 2 H 310000 242000 1.28 0500 1000 1500 2000 2500 10-3 10-2 10-1 100PEO Blend, T = 358 K 90% 2H 10 kg/mol & 10% 1H A1e-t/t1 11 kg/mol 30 kg/mol 95 kg/mol 220 kg/mol integral/max [arb. unit] time [ms] We study linear poly (ethylene oxide) in bulk (1H) and in mixtures (10% 1H in 90% 2H) 0500 1000 1500 2000 2500 10-3 10-2 10-1 100PEO Bulk, T = 358 K A1e-t/t1 3 kg/mol 6 kg/mol 11 kg/mol 30 kg/mol 95 kg/mol 220 kg/mol 1000 kg/mol integral/max [arb. unit] time [ms] 10.5281/zenodo.17376125 Mixture I: 6 kDa with different PDI 102103104105 0.00 0.01 0.02 0.03 0.04 PDF(logM) M [g/mol] PEO-hL6b PDI = 1.06 / 1.09 (PSS/calc.) Mw (g/mol) = 6650 / 6448 Mn (g/mol) = 6170 / 5938 PEO-hL6a PDI = 1.03 (PSS) Mw (g/mol) = 6000 g/mol Mn (g/mol) = 5850 g/mol Mc w Mc n 102103104105 0.000 0.005 0.010 0.015 PDF(logM) M [g/mol] 0.44 * PEO-hL3b 0.18 * PEO-hL5 0.38 * PEO-hL10 hL6mix (sum) PDI = 1.52 (calc.) Mw (g/mol) = 6003 Mn (g/mol) = 3948 Mc w Mc n Purchased narrow 6 kDa vs. mixture of three different molar masses with the same mass average but larger PDI 1091010 1011 1012 1013 1014 10−5 10−4 10−3 10−2 10−1 100 Mw = 6 kg/mol T = 358 K, d = 3 ms, D = 200 ms PDI = 1.03 (hL6aa) PDI = 1.52 (hL6mixb) a 100% 1H 6 kg/mol b 44% 1H 3 kg/mol + 18% 1H 5 kg/mol + 38% 1H 10 kg/mol Smax norm g2d2g2(D-d/3) [s/m²] 343 358 373 10-12 10-11 Mw = 6 kg/mol d = 3 ms, D = 200 ms PDI = 1.03 (hL6aa) PDI = 1.52 (hL6mixb) a 100% 1H 6 kg/mol b 44% 1H 3 kg/mol + 18% 1H 5 kg/mol + 38% 1H 10 kg/mol Temperature [K] NNLS Means 10−15 10−14 10−13 10−12 10−11 10−10 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0 20 40 60 80 100 NNLS Weights [%] Log Normal PDF(lnD) Diffusion Coefficients [m²/s] Mw = 6 kg/mol (hL6a*) T = 358 K, d = 3 ms, D = 200 ms Log Normal Fit (1) NNLS Fit (9) *100% 1H 6 kg/mol 10−15 10−14 10−13 10−12 10−11 10−10 0.0 0.2 0.4 0.6 0.8 1.0 0 20 40 60 80 100 NNLS Weights [%] Log Normal PDF(lnD) Mw = 6 kg/mol, hL6mix* T = 358 K, d = 3 ms, D = 200 ms Log Normal Fit (2) NNLS Fit (9) *44% 1H 3 kg/mol + 18% 1H 5 kg/mol + 38% 1H 10 kg/mol 46.9% 53.0% 36% 64% 10−15 10−14 10−13 10−12 10−11 10−10 0.0 0.2 0.4 0.6 0.8 1.0 0 20 40 60 80 100 NNLS Weights [%] Log Normal PDF(lnD) Diffusion Coefficients [m²/s] Mw = 6 kg/mol, hL6mix* T = 358 K, d = 3 ms, D = 200 ms Log Normal Fit (3) NNLS Fit (9) 44% 1H 3 kg/mol + 18% 1H 5 kg/mol + 38% 1H 10 kg/mol 0.1% Top: larger average D in mixed sample Right: multiple components (2 or 3) identified in both log-normal and NNLS fit Mixture II: 10% 3 kDa in 90% deuterated 300 kDa 01×1013 2×1013 3×1013 4×1013 10-6 10-5 10-4 10-3 10-2 10-1 100 T = 358 K, d = 3 ms, D = 200 ms exp. fit hL3ba n = 1 hL3b-dL300b n = 3 a100% 1H 3 kg/mol b 10% 1H 3 kg/mol & 90% 2H 300 kg/mol Smax norm g2d2g2(D-d/3) [s/m²] 343 358 373 1E-14 1E-13 1E-12 1E-11 19(6)% 34(11)% 17(2)% 74(5)% 60(11)% 78(2)% 7.16(6)% 6.22(6)% 4.48(2)% T = 343 K, d = 3 ms, D = 200 ms hL3ba hL3b-dL300b a100% 1H 3 kg/mol b 10% 1H 3 kg/mol & 90% 2H 300 kg/mol D [m²/s] Temperature [K] 343 358 373 100 101 102 Mw = 3 kg/mol d = 3 ms, D = 200 ms hL3ba hL3b-dL300b a100% 1H 3 kg/mol b 10% 1H 3 kg/mol & 90% 2H 300 kg/mol Temperature [K] NNLS Spread 10−15 10−14 10−13 10−12 10−11 10−10 0.0 0.5 1.0 1.5 2.0 2.5 0 20 40 60 80 100 NNLS Weights [%] Log Normal PDF(lnD) Diffusion Coefficients [m²/s] Mw = 3 kg/mol (hL3b*) T = 358 K, d = 3 ms, D = 200 ms Log Normal Fit (1) NNLS Fit (4) *100% 1H 3 kg/mol 10−15 10−14 10−13 10−12 10−11 10−10 0.0 0.5 1.0 1.5 0 20 40 60 80 100 NNLS Weights [%] Log Normal PDF(lnD) Diffusion Coefficients [m²/s] Mw = 3 kg/mol (hL3b-dL300*) T = 358 K, d = 3 ms, D = 200 ms Log Normal Fit (2) NNLS Fit (10) *10% 1H 3 kg/mol & 90% 2H 300 kg/mol 93.9% 6.1% smaller D and broader distribution of 3 kDa in 300 kDa matrix 1% residual protons in the deuterated matrix are observable Mixture III: 10% in 90% deuterated 10 kDa 02x1012 4x1012 6x1012 8x1012 1x1013 10-4 10-3 10-2 10-1 100 in 90% 2H 10 kg/mol, T = 358 K d = 3 ms, D = 200 ms data exp. fit 10 kg/mol 30 kg/mol 95 kg/mol 220 kg/mol S/Smax g2d2g2(D-d/3) [s/m²] 103104105 10-14 10-13 10-12 10-11 T = 358 K Bulk with 90% 2H 10 kg/mol Dh [m2/s] (Mn+Mw)/2 [g/mol] ~M-1.96(15) ~M-1.35(5) non-exponential decays D~M-1.4 in mixtures weaker than D~M-2 in bulk [2,3]