Modern Solid State NMR strategies for the structural characterization of amorphous solids Leo van Wüllen

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1 Modern Solid State NMR strategies for the structural characterization of amorphous solids Leo van Wüllen Institute of Physical Chemistry University of Münster

2 The van Wüllen group at Münster Inorganic materials science Dr. Stefan Puls Dipl.-Phys. Sebstian Wegner solid state NMR methods development Dipl.-Chem. Thomas Köster Dr. Gregory Tricot

3 Today s menue The basics magnetic moments, precession B 0 and B 1 -fields how to obtain an NMR signal First examples phosphate glasses borosilicate glasses Internal interactions chemical shielding magn. dipole interactions elect. quadrupole interactions Magic Angle Spinning (MAS) NMR More examples and advanced techniques REDOR NMR Si-B-N-C ceramics MQMAS-NMR B O 3 -SiO glasses D-CPHETCOR M O-Al O 3 -P O 5 -glasses

4 The basics Nuclear magnetism Nuclear magnetic moment: Jˆ µ = γ = Iˆ γ I, the angular momentum, is subject to quantization laws, concerning both magnitude and orientation z m α I: spin quantum number m: orientational quantum number with m=-i,-i+1, I-1,I cos( α) = m I( I + 1)

5 The basics Detection of nuclear magnetism by application of a magnetic field B 0 H ˆ = ˆ = ˆ Z B I B γ B Z µ Z 0 Z 0 e.g. I = ½; two states with m = ½, - ½ E = 1 1 γ B E = γ B E E = ω B = 0 degenerate radio waves spectroscopic splitting: ω =γb 0 B > 0;non-degenerate NMR is element selective

6 The basics Solid State NMR Periodic Table 1 H 3 He 7 Li Be 3 Na 5 Mg 11 B 13 C 15 N 17 O 19 F Ne 7 Al 9 Si 31 P 33 S 35 Cl Ar 39 K 51 V 53 Cr 55 Mn 57 Fe 59 Co 61 Ni 65 Cu 67 Zn 71 Ga 73 Ge 75 As 77 Se 79 Br Kr 43 Ca 45 Sc 47 Ti 87 Rb Sr 89 Y 93 Nb 95 Mo Tc Ru 103 Rh 105 Pd 107 Ag 113 Cd 115 In 117 Sn 13 Sb 15 Te 17 I 19 Xe 91 Zr 133 Cs Hf Ta 183 W Re Os Ir 195 Pt Au 01 Ba La Hg 05 Tl 07 Pb Bi Po At Rn Fr Ra Ac Useful candidates for solid state NMR Low sensitivity In general no solid state NMR possible

7 The basics Macroscopic sample In a sample spins are distributed among energy levels ( Boltzmann-distribution)l z M 0 Macroscopic magnetization along B 0 No net magnetization in x- or y-direction Curie Law: I( I + 1) MZ = M = N γ B 3kT 0 0 x m = 1 1 m = + y NMR is quantitative!!

8 The basics Precession Precession of spins around external field similar to gyroscope B 0 z E E = ω 1 m = B 0 = 0 x y B 0 > 0 1 m = + NMR measures the precession (Larmor) frequency ω = γb 0

9 The basics The rotating frame To simplify the description of the magnetization s time dependence a rotating frame is introduced Laboratory frame B 0 z Rotating frame z µ y y x x

10 The basics The action of the B 1 -field remember: irradiation with electromagnetic wave, only B-part is used. This is linearly polarized. B = B + B lin R L = B cos( ωt) + isin( ωt) 1 + B cos( ωt) isin( ωt) = 1 B cos( ωt) 1 B l and B r are rotationg in xy-plane with frequencies ω L and ω L ; only the component with the correct precession sense can interact with the precessing magnetization.

11 The basics The action of the B 1 -field In laboratory frame: rotation of magnetization with ω 0 around B 0. B 1 rotates with ω 0 around z. In rotating frame: the part of B 1 with the corrent sense of precession is toggled to the y -axis. Magnetization will precess about this B 1 -field. If B 1 -field is on continuously, then the magnetization will precess in the zx -plane with frequency ω = γ B 1 This frequency is called the nutation frequency.

12 The basics The action of the B 1 -field z z M 0 M 0 x B 1 y 90 pulse: rotates the z-magnetization into the x-y-plane x 180 pulse: flips the z-magnetization into the z-direction B 1 y

13 The basics Measuring NMR spectra = Detection of Larmor frequencies present in the sample 1. B 1 field is irradiated for a short time t p along the x,y direction. If γb 1 t p = π/ then M z is flipped by 90 degrees (90 pulse) B 0 z B 0 z M 0 M 0 B 1 B 1 x y x y

14 The basics obtaining the NMR signal 90 pulse -> magnetization flip Free Induction Decay rf irradiation signal detection t/s NMR-Spectrum Fourier- Transformation ν/hz F( ω ) = f ( t) * e iωt dt

15 The basics Equipment magnet/console probe sample in rotor Macor ZrO Kel-F BN Vespel

16 The basics relaxation processes z z z M 0 M 0 y x T spin spin relaxation y x T 1 spin lattice relaxation y x

17 Internal interactions Why is NMR so cool? internal interactions inducing local electric and magnetic fields ˆ ˆ µ = γ I 1 H 1 H ˆ E = µ B= µ ˆ( B + B ) 0 int ν NMR signal depends on the immediate neighborhood of the nucleus H ˆ = H ˆ + H ˆ + H ˆ + H ˆ + H ˆ +... Zeeman RF Pulse Chem. Shift dipole quadrupole

18 Internal interactions Magnetic shielding Resonance frequency (bare nucleus): Effective magnetic field at nucleus: Resonance frequency (real sample) ω 0 = γb 0 B eff ω L = B0 (1 σ ) = γb (1 0 σ ) Chemical shift δ ω x L ω ω ref L ref L Effective magnetic field arises from shielding or deshielding of the external magnetic field by electrons Probe for electronic environment ( bonding)

19 Internal interactions Chemical Shielding Anisotropy Shielding is anisotropic in nature and can be described by its components in the molecular axis system B 0 1 ω =ω σ σ σ θ 3 L 0 1 iso ( z z x x )(3cos 1) orientational dependence of the resonance frequency θ Q 3 unit in phosphate glass

20 Internal interactions Chemical Shielding Anisotropy Shielding is anisotropic in nature and can be described by its components in the molecular axis system B 0 1 ω =ω σ σ σ θ 3 L 0 1 iso ( z z x x )(3cos 1) orientational dependence of the resonance frequency θ Q 3 unit in phosphate glass

21 Internal interactions example: 31 P NMR of phosphates Q 3 σ σ = 0 σ σ PAS 33 Q ω iso ω iso ω iso cubic axially symmetric asymmetric Q 1 σ 11 =σ =σ 33 σ 11 =σ <σ 33 σ 11 <σ <σ 33 Q 0 Probe for local symmetry ( bonding geometry)

22 Internal interactions Magnetic dipole interaction Magnetic moments of nearby spins affect the local magnetic field and thus the resonance frequency. Through-space interaction ˆ γγ µ IS I S 0 Hdip = I S (3cos 1) 3 Z Z β π r 4π ˆ ˆ B 0 β r IS S probe of internuclear distance I

23 Internal interactions Electric Quadrupole Interactions Quadrupolar interaction : For nuclei with I>1/ the spatial distribution of nuclear charge is not spherically symmetric described by quadrupolar moment probe for local symmetry

24 Internal interactions effect of quad. interaction on the NMR signal I = 3/ ĤZ (1) Hˆ Z + Hˆ Q central transition, independent of orientation satellite transitions, orientation dependence frequency

25 Internal interactions Strong quadrupolar coupling I = 3/ ĤZ (1) Hˆ Z + Hˆ Q Hˆ + Hˆ () Z Q Second-order perturbation theory only central transition observable anisotropic, orientation dependent ω ω (m) = m δ +ω Q Q 4 CS 0 Q { iso 0 ( I(I + 1) 3m ) 10 + ω ( ϑ, ϕ) I(I 1) 6 1 ( 8 + 1m 3) (3cos θ 1) 4 ( 18I(I + 1) 34m 5) (35cos θ 30 cos 3) } + ω ( ϑ, ϕ) θ+

26 Internal interactions Strong quadrupolar coupling eq 1 st order quadrupolar coupling constant C Q CQ = VZZ h asymmetry parameter η V V ηq = VZZ qeff CQ 3 r XX YY nd order frequency η = 0 η = 0.3 Non-axial EFG η = 1 ν ν ν

27 Internal interactions Solid State NMR element-selective locally selective quantitative experimentally flexible: Selective averaging B 0 E hν E= γ B 0 H = H Z + H D + H CS + H Q Internucl. distances Coordination numbers and symmetries

28 Internal interactions B 0 Magic Angle Spinning (MAS) D const H = (3cos Θ 1) 3 r static rotation axis Θ 1 Θ MAS iso 1 st order H ˆ = H ˆ + H ˆ + H ˆ + H ˆ +... Zeeman Chem. Shift dipole quadrupole

29 NMR and the structure of glasses Short range order B,Si,P O, N Li,Na,K chemical shielding quadrupolar interaction MAS-NMR, MQMAS-NMR directly bonded neighbors coordination numbers site quantification short range order 1-.5 Å

30 NMR and the structure of glasses Intermediate range order B,Si,P O, N Li,Na,K magnetic dipole interaction dipolar NMR REDOR, REAPDOR, CPMAS D HETCOR network former connectivities correlation former modifier intermediate range order.5-6 Å

31 NMR and the structure of glasses first examples Network depolymerisation in a Li O-P O 5 glass Q P- MAS- NMR Q Q 3 Q Li O Q 3 Q 1 Q Q δ/ppm

32 NMR and the structure of glasses first examples Boron speciation in a borosilicate glass BO 3 BO 4 δ iso C Q, η Q area δ iso area BO 4 in borate environment BO 3 in borate environment BO 4 in borosilicate environment BO 3 in borosilicate environment δ/ppm

TADB Cl 3 Si NH Cl B NH 3 -NH 4 Cl polycondensation Polyborosilazane N 100 C Pyrolysis Si 3 B 3 N 7

33 NMR and the structure of glasses more examples --- SiBNC Synthesis strategy and performance of Si 3 B 3 N 7 and SiBN 3 C Hi- Nicalon fibre ºC polycondensation of single source precursors TADB Cl 3 Si NH Cl B NH 3 -NH 4 Cl polycondensation Polyborosilazane N 100 C Pyrolysis Si 3 B 3 N 7 SiBN 3 C-fibre ºC CH 3 NH -CH 3 NH 3 Cl N- methylpolyborosilazane NH C N 100 C SiBN 3 C

34 NMR and the structure of glasses more examples --- SiBNC 9 Si 3 B 3 N 7 : MAS single pulse spectra 9 Si-MAS 11 B-MAS δ iso = -45.ppm SiN 4/3 δ iso = 30.4 ppm C Q =.9 MHz η = 0.1 BN 3/ δ/ppm δ/ppm

35 NMR and the structure of glasses more examples --- SiBNC intermediate range order nd coordination sphere boron nd coordination sphere silicon

36 NMR and the structure of glasses more examples --- SiBNC --- REDOR Modulation of dipolar coupling under MAS 11 B Magic- Angle Spinning (MAS) ˆ IS H D + ˆ IS H D = 0 - T r S I 9 Si Rotational Echo Double Resonance (REDOR) ˆ IS H D + + ˆ IS H D 0 T r Hˆ IS D = 1 Iˆ Sˆ sin( t) 3 Z Z ωr r I-channel π Puls ( 9 Si) ( Iˆ Iˆ ) z z

37 NMR and the structure of glasses more examples --- SiBNC --- REDOR REDOR S I 0 4 TR Hˆ IS D S 0 -S = f(r, NT S R ) 0 MAS-Spin echo S Hˆ IS D 0 4 TR

38 NMR and the structure of glasses more examples --- SiBNC --- REDOR 11 B-{ 9 Si}-REDOR Si 3 B 3 N 7 11 B Spin-Echo 0.8 ms.4 ms 4 ms 11 B-{ 9 Si}-REDOR S

39 NMR and the structure of glasses more examples --- SiBNC --- REDOR 11 B-{ 9 Si}-REDOR Si 3 B 3 N 7 11 B Spin-Echo 0.8 ms.4 ms 4 ms 11 B-{ 9 Si}-REDOR S/S ,0 S/S 0 0,8 0,6 0,4 0, 1 cos γγ µ = sin ϑ sinϕ sinϑdϑdϕ S π π S 1 I S 0 0 4πS NTR 3 0 8π 0 0 r 0,0 0,000 0,00 0,004 0,006 0,008 NT R /s

40 NMR and the structure of glasses more examples --- SiBNC --- REDOR 11 B- 9 Si-REDOR 9 Si-{ 11 B} RE(AP)DOR 1, B-Si threespin (d =.74Å) 1, Si-B threespin S/S 0 1,0 1,0 0,8 S/S 0 0,8 0,6 0,6 0,4 0,4 0, B-Si twospin 0, Si-B twospin 0,0 0,000 0,00 0,004 0,006 0,008 NT R /s 0,0 0,000 0,004 0,008 0,01 NT R /s 1.4 Si per BN 3/3 1.8 B per SiN 4/3

41 NMR and the structure of glasses more examples --- SiBNC Network model 11B-MAS 9Si-MAS 11B-{9Si}-REDOR 11B spin-echo 9Si-{11B}-REAPDOR 9Si spin-echo 1.4Si 4-5B 1.8B 6Si Si-N rich domains B-N rich domains

42 NMR and the structure of glasses more examples --- B O 3 SiO glasses mixing of network polyhedra or phase separation?? B O 3 SiO

43 NMR and the structure of glasses more examples --- B O 3 SiO glasses 11 B-MAS 9 Si-MAS xb O 3 = 0.8 xb O 3 = 0.7 xb O 3 = 0.6 xb O 3 = 0.5 xb O 3 = 0.4 xb O 3 = δ/ppm δ/ppm

44 NMR and the structure of glasses more examples --- B O 3 SiO glasses 11 B NMR static ω ω (m) = m δ +ω Q Q 4 CS 0 Q { iso 0 ( I(I + 1) 3m ) 10 + ω ( ϑ, ϕ) I(I 1) 6 1 ( 8 + 1m 3) (3cos θ 1) 4 ( 18I(I + 1) 34m 5) (35cos θ 30cos 3) } + ω ( ϑ, ϕ) θ+ 0.5 (3cos θ-1) = 0 MAS???

45 NMR and the structure of glasses more examples --- B O 3 SiO glasses 11 B NMR static ω ω (m) = m δ +ω Q Q 4 CS 0 Q { iso 0 ( I(I + 1) 3m ) 10 + ω ( ϑ, ϕ) I(I 1) 6 1 ( 8 + 1m 3) (3cos θ 1) 4 ( 18I(I + 1) 34m 5) (35cos θ 30cos 3) } + ω ( ϑ, ϕ) θ+ 0.5 (3cos θ-1) = 0 MAS 1,0 P l (cosθ) 0,5 l = ; 0.5 (3cos θ-1) l = 4; 0.15(35cos 4 θ -30cos θ+3)??? 0,0-0, θ/degrees

46 NMR and the structure of glasses more examples --- BSi-glasses --- MQMAS 11 B MQMAS-spectroscopy BSi-glass 0.8 B O SiO n t 1 t ppm -0 eliminate 4 th Legendrian and nd Legendrian I = 3/ -3/ I = 1/ -1/ ppm ppm eliminate nd Legendrian

47 NMR and the structure of glasses more examples --- BSi-glasses --- MQMAS Isotropic projections (F1) δ iso = 16.5 ppm BO 3/ in boroxol rings δ iso = 11.5 ppm free BO 3/ in borate- and mixed borosilicate matrix x(b O 3 )

48 NMR and the structure of glasses more examples --- BSi-glasses Quantum chemical calculations HF SCF; double ζ basis set: 19.3 ppm DFT; triple ζ basis set: 18.5 ppm HF SCF; double ζ basis set: 15. ppm DFT; triple ζ basis set: 1.5 ppm HF SCF; double ζ basis set: 13.0 ppm DFT; triple ζ basis set: 9.5ppm

49 NMR and the structure of glasses more examples --- BSi-glasses --- RE(AP)DOR 9 Si-{ 11 B} REAPDOR Statistical distribution of B in a 0.3 B O SiO glass 1, 1.7 B-neighbors per SiO 4/ 1,0 S/S 0 0,8 0,6 0,4 xb O 3 xsio , 1 B-neighbor per SiO 4/ 0,0 0,000 0,00 0,004 0,006 0,008 NT R /s

50 NMR and the structure of glasses more examples --- B O 3 SiO glasses glass-structure SiO matrix con only adopt a limited amount of B O 3, the limiting composition is 0.3 B O SiO. Excess B O 3 establishes a separate phase. area/% ppm ppm BO 3/ in boroxol rings (1-(1-x)f/x) free BO 3/ (1-(1-x)f/x) 0.3 and BO 3/ in borosilicate phase (1-x)f/x x B O 3

Topic 3: Periodicity OBJECTIVES FOR TODAY: Fall in love with the Periodic Table, Interpret trends in atomic radii, ionic radii, ionization energies &

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