Anwendung

der NMR-Spektroskopie

in der Anorganischen Chemie

Literatur

Canet D.: „NMR-Konzepte und Methoden�, Springer-Verlag, New-York 1994

Farrar T.C., Becker E.D.: „Pulse and Fourier Transform NMR, Introduction to Theory and Methods�, Academic Press, New-York 1971

Fukushima E., Roeder S.B.W.: „Experimental Pulse NMR, A Nuts and Bolts Approach�, Addison-Wesley, Reading Mass. 1981

Fyfe C.A.: „Solid State NMR for Chemists�, C.F.C. Press, Guelph Ontario 1983

Poppov A.I., Hallenga K.: „Modern NMR Techniques and their Application in Chemistry�, Marcel Dekker Inc., New-York 1991

Duer, M. J. „Introduction to Solid-State NMR Spectroscopy�, Blackwell Publishing, 2004

Levitt, M. H. „ Spin Dynamics – Basics of Nuclear Magnetic Resonance, Wiley, 2005

Typische Streufunktionen von Materie

Vorbemerkungen

charakteristische Länge / m

10-10 10-9 10-8 10-7 10-6

mesoskopische Methodenlokale Methoden

IR/Raman

EXAFS

EELS

Mößbauer

Kleinwinkelstreuung

Lichtstreuung

MikroskopieFK-NMR

TEM

Charakteristische Längenskala verschiedener analytischer Methoden

Vorbemerkungen

Struktur auf intermediären Längenskalen (< 5 nm)

Amorphe Si3B3N7 Keramik

• Mikroskopisch homogen?

• Grad der Klusterung?

• Strukturmodell aus Kombinationvon Monte-Carlo-Simulationen und FK-NMR-Messungen

through-bond connectivities

through-space connectivities

Vorbemerkungen

a) Korrelation

Signalzuordnung

b) Struktur

Konnektivitäten, Abstände, Orientierung von Baugruppen

c) Dynamik

Chemischer Austausch, Konformationsänderungen, Rotation und Translation von Ionen, Molekülen

Angewandte Chemie 2002, 114, 3224-3259

1. Grundlagen

a) Einführung

Drehimpuls und magnetisches Moment, Zeeman-Aufspaltung, Besetzung der Energieniveaus im Boltzmann-Gleichgewicht

b) Relaxation

Übergänge zwischen den Energieniveaus, Verhältnis zwischen spontaner und induzierter Emission, Spin-Gitter- und Spin-Spin-Relaxation

c) Dynamik von Spins

rotierendes Koordinatensystem und effektives Magnetfeld, Pulse im rot. Koordinatensystem, Spin-Echos (Methoden zur Messung von T1 und T2)

Wichtige Wechselwirkungen

• Zeeman-Wechselwirkung

magnetische Moment µ eines Kerns im äußeren Magnetfeld B

!µ = γ I ⋅

!I

• Kerne besitzen einen Drehimpuls

• Mit Drehimpuls starr verbunden ist ein magnetisches Moment

• gI ist das gyromagnetische Verhältnis

!µ

!I

• Quantisierung des Drehimpulses

!µ = γ I ⋅ ! ⋅ I I +1( ) µz =mI ⋅ ! ⋅γ I

B0!µ

I = 1, g > 0

mI = 1

mI = 0

mI = -1

• Aufspaltung in 2I+1 Energieniveaus

Em = −!µ ⋅!B = −µz ⋅B0

= −m ⋅ ! ⋅γ I ⋅B0ω0

!B0 =

00B0

!

"

###

$

%

&&&

E

Kerne mit I = 1/2

Nucleus N. A. (%) Class [a] RC [b]g (note the sign

!)[107 rad s-1T-1]

X [MHz] Reference standard

1H 99.985 ©©©©© 5.67 103 26.7522 100.000000 SiMe4, 1% in CDCl33H - [12 years] - - 28.5350 106.6663984 3H1-SiMe43He 0.00014 © 3.51 10-3 -20.3801 76.178972 He gas13C 1.108 ©©© 1.00 6.7283 25.145020 SiMe4 1% in CDCl315N 0.37 ©© 2.19 10-2 -2.7126 10.136767 MeNO2 (neat)19F 100 ©©©©© 4.73 103 25.1815 94.094003 CFCl3 (neat)29Si 4.70 ©© 2.10 -5.3190 19.867187 SiMe4 1% in CDCl331P 100 ©©©© 3.77 102 10.8394 40.480747 H3PO4. 85 % aq57Fe 2.19 © 4.25 10-3 0.8687 3.237798 Fe(CO)5 (neat)

77Se 7.58 ©©© 3.02 5.1214 19.071523 Me2Se (neat)89Y 100 ©© 0.676 -1.3163 4.900200 Y3+ aq (H2O, D2O)103Rh 100 ©© 0.180 -0.8468 3.160000 No compound107Ag 51.82 ©© 0.198 -1.0878 4.047898 Ag+ ¥ aq109Ag 48.18 ©© 0.280 -1.2519 4.653623 Ag+ ¥ aq111Cd 12.75 ©©© 7.01 -5.7046 21.201877 Cd(ClO4)2 0.1M aq113Cd 12.26 ©©© 7.69 -5.9609 22.193173 CdMe2 (neat)115Sn 0.35 ©© 0.707 -8.8014 32.718780 SnMe4 (neat)117Sn 7.61 ©©© 19.9 -9.589 35.632295 SnMe4 (neat)119Sn 8.58 ©©© 25.7 -10.0318 37.290665 SnMe4 (neat)

Kerne mit I > ½ (Quadrupolkerne)

Nucleus N.A. (%) Spin I Class [a] Q [b]

[10-28 m2]g[107 rad s-1T-1]

X [MHz] ReferenceStandard

2H 0.015 1 ©©© 2.87 10-3 4.1066 15.350609 Si(CD3)4 (D12-TMS)6Li 7.42 1 ©©© -6.4 10-4 3.9371 14.716106 LiCl, D2O » 9.7 M7Li 92.58 3/2 ©©©© -3.7 10-3 10.3976 38.863790 LiCl, D2O » 9.7 M9Be 100 3/2 ©©©© 5.3 10-2 -3.7606 14.051820 BeSO4, D2O » 0.45 M10B 19.58 3 ©©© 8.5 10-2 2.8747 10.743657 F3B-OEt2 (CDCl3)11B 80.42 3/2 ©©©©© 4.1 10-2 8.5847 32.083971 F3B-OEt2 (CDCl3)14N 99.63 1 ©©© 1.67 10-2 1.9338 7.226324 MeNO2 (neat)

17º 0.037 5/2 © 6.11 10-2 -3.6280 13.556430 D2O (liquid)23Na 100 3/2 ©©©©© 0.10 7.0704 26.451921 NaBr, in D2O » 10 M25Mg 10.13 5/2 ©© 0.22 -1.6389 6.121643 MgCl2, D2O » 15 M27Al 100 5/2 ©©©©© 0.14 6.9762 26.056890 A(NO3)3, D2O, 1.1 M33S 0.76 3/2 © -6.4 10-2 2.0557 7.676020 (NH4)2SO4, D2O, sat.35Cl 75.53 3/2 ©©©© -8.2 10-2 2.6242 9.797931 KCl, D2O » 2.2 M37Cl 24.47 3/2 ©©©© -6.5 10-2 2.1844 8.155764 KCl, D2O » 2.2 M39K 93.1 3/2 ©©© 5.5 10-2 1.2499 4.666423 KI, D2O » 3.8 M43Ca 0.145 7/2 © -5 10-2 -1.8028 6.729996 CaCl2, D2O45Sc 100 7/2 ©©© -0.22 6.5088 24.291702 ScCl3, D2O, 1 M47Ti 7.28 5/2 ©© 0.29 -1.5106 5.637587 TiCl4 (neat)49Ti 5.51 7/2 ©© 0.24 -1.5110 5.639095 TiCl4 (neat)51V 99.76 7/2 ©©©©© -5.2 10-2 7.0492 26.302963 VOCl3 (neat)53Cr 9.55 3/2 © -0.15 -1.5077 5.652511 (NH4)2CrO4, D2O, 1 M55Mn 100 5/2 ©©©© 0.40 6.6453 24.789290 MnO4

- aq; sat.59Co 100 7/2 ©©©©© 0.42 6.3015 23.727074 K3[Co(CN)6], D2O,0.56 M

Ensemble schwach wechselwirkender Spins

B0 = 0 B0 ¹ 0

Verteilung der Spins

im thermischen

Gleichgewicht

Rückkehr der Magnetisierung ins

thermische Gleichgewicht

• Verhältnis spontaner (A) und induzierter (B) EmissionenA/B » 10-7 (Einsteinkoeffizienten)

• nur induzierte Prozesse relevant

• präparierte Zustände langlebig

• Relaxation ins thermische Gleichgewicht

• NMR eine phasenkohärente Spektroskopie

Wechselwirkungen Probe und Umgebung

Umgebung

• Thermische Fluktuationen

• RF-Felder

Spin-Gitter-Relaxation nach 90�-Puls

direkt nach 90�-Puls

Mx = M0; My = 0; Mz = 0

thermisches Gleichgewicht

Mx = 0; My = 0; Mz = M0

Spin-Gitter

Relaxation T1

B0 B0

• Angleichung an thermisches Gleichgewicht durch Energieabgabe an Umgebung

• Rate Proportional zur spektralen Dichte bei J(w=w0)

• Verlust der Phasenkohärenz

1T1∝ J(ω0)

Spin-Spin-Relaxation nach 90�-Puls

direkt nach 90�-Puls

Mx = M0; My = 0; Mz = 0Spin-Spin

Relaxation T2

B0 B0

• Verlust der Phasenkohärenz ohne Wechsel der Energieniveaus

• Entropieprozess

• Rate proportional zur spektralen Dichte bei w = 0 (J(0))

nach Zerfall des FID

Mx = 0; My = 0; Mz = 0

Relaxationsprozesse nach Anregung mit 90�-Puls

direkt nach 90�-Puls

Mx = M0; My = 0; Mz = 0

thermisches Gleichgewicht

Mx = 0; My = 0; Mz = M0

nach Zerfall des FID

Mx = 0; My = 0; Mz = 0

Spin-Gitter

Relaxation T1

Sp

in-G

itte

r

Rela

xati

on

T1

Sp

in-S

pin

Rela

xati

on

T2

Spin-Gitter-Relaxation als Sonde für lokale Dynamik

1H Spin-Gitter-Relaxation für

verschiedene molekulare

Glasbildner

ω0 = 2π 300MHz124507-8 Storek et al. J. Chem. Phys. 137, 124507 (2012)

FIG. 9. Mean spin-lattice relaxation times of 0.33Li2O + 0.67[xB2O3+ (1 – x)P2O5] recorded at Larmor frequencies of ωL = 2π × 117 MHz(open symbols) and ωL = 2π × 150 MHz (filled symbols). The ordinate axisrefers to x = 0.5. To avoid overlap the data for x = 0.3 and x = 1.0 wereshifted downwards and upwards, respectively, by one order of magnitude.Data for x = 0.0 were shifted by two orders of magnitude. For T > 450 K andbelow the minimum in ⟨T1⟩ the solid lines show fits to the data according toEq. (9) in conjunction with Eq. (10) and using the parameters given in Table Iand Sec. IV D. The glass transition temperatures, Tg, are indicated by dashedlines. The inset shows the compositional dependence of ⟨T1⟩ at T = 157 K.

1.0. Above 300 K, we observe single exponential magnetiza-tion recovery curves M(t) ∝ exp[–(t/T1)1–µ] with µ = 0 andbelow 300 K slight deviations from exponential magnetiza-tion recovery occur. At the lowest investigated temperatures,fits using the given Kohlrausch function yield µ = 0.04, ex-cept for x = 0 where µ = 0.16 below 200 K. In Fig. 9, wepresent the mean relaxation times, taken over the distributionunderlying the Kohlrausch function, ⟨T1⟩ = T1 (1 − µ)−1 #[(1– µ)−1], with # denoting Euler’s Gamma function. At the lowtemperature end, the spin-lattice relaxation times become al-most temperature independent and samples with increasingboron content exhibit shorter T1 as documented in the inset ofFig. 9.

With increasing temperature, T1 becomes significantlyshorter until at values of ⟨T1⟩ ≈ 0.1 s we find minima at 775,676, and 752 K for x = 0.0, 0.3, and 0.5, respectively.51 Forx = 0 this minimum occurs at temperatures substantiallyhigher than the glass transition temperature, whereas in thex = 0.3 and 0.5 samples, the temperature of the minimum ap-pears to coincide roughly with Tg. Unfortunately, for the mod-estly conducting oxide glasses under study, it is not possiblefor the Larmor frequencies used here to detect a T1 minimumbelow Tg for any of the glasses. A straightforward quanti-tative analysis of the data in Fig. 9 on the basis of Eq. (9)in conjunction with a single suitable spectral density seemstherefore not to be appropriate: For all the glasses except theone with x = 0.0, the T1 values measured on the differenttwo sides of the minimum, at low and high temperatures,refer to two different physical states. The high-temperatureside refers to the supercooled melt while the low-temperatureside refers to the glassy state. These different states can beexpected to be associated with different activation energiesand spectral densities.52 Therefore, we chose to estimate the

FIG. 10. Arrhenius representation of time constants for 0.33Li2O+ 0.67[0.5B2O3 + 0.5P2O5] acquired by different NMR techniques. Cor-relation times were evaluated from F2 measurements (black stars), from thespin-lattice relaxation time minimum (filled square), from the minimum inthe spin-spin relaxation times (filled diamond), and from the inflection pointof the weighting factor WQ(T) (open diamond), cf. Fig. 6(b). Conductivityrelaxation times τσ (red filled circles) were calculated according to Eq. (13).The solid line represents a fit using an Arrhenius law. The open circles corre-spond to mean spin-lattice relaxation times. The calorimetric glass transitiontemperature Tg = 732 K is indicated by the dashed line.

width parameter of the latter using the following procedure:For Cole-Davidson spectral densities, cf. Eq. (10), we ex-pect an asymmetrically shaped minimum with a “reduced”slope βCD'Ea in the low-temperature regime, ωLτ ≫ 1, ascompared to the behavior in the high-temperature limit, ωLτ

≪ 1, where the magnitude of the slope is simply 'Ea. How-ever, since the high-temperature regime does not occur in theglassy state, but rather above Tg in the (supercooled) liquid,it is not possible to obtain 'Ea by analyzing the T1 datain that regime. Therefore, for a determination of 'Ea wehave to resort to the various echo techniques that were ap-plied below Tg. For x = 0.5 the corresponding Arrhenius plot(see Fig. 10, below) is presented and discussed in detail inSec. V A 1. From these data and those of other concentra-tions τCD was evaluated via the Arrhenius relation, Eq. (4),yielding τ 0 and 'Ea as summarized in Table I. Use of theseactivation energies together with the “reduced” ones as ob-tained from fitting T1 in the slow-motion regime yields thedistribution parameter βCD = 0.28 ± 0.11 for x = 0.5. Forthe curve shown in Fig. 9 we set δ/2π = 86 kHz as theanisotropy parameter for x = 0.5. The curve describes thedata even above Tg into the supercooled liquid state with onlyslight deviations. According to Eqs. (9) and (10), the conditionfor the T1 minimum becomes ωLτCD = 1.88, which meansτCD = 2.0 ns at 752 K for x = 0.5. The corresponding anal-ysis yields βCD = 0.43 ± 0.13, δ/2π = 83 kHz, and τCD

= 1.4 ns for x = 0.0 and βCD = 0.30 ± 0.06, δ/2π = 82 kHz,and τCD = 1.6 ns for x = 0.3. The relatively good agree-ment between experimental data and calculated T1 curve, evenabove Tg, suggests that the activation energy is not altered dra-matically while passing through Tg. This is not entirely unex-pected for the decoupled ion conductors we deal with in thepresent investigation.52

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Spin-Gitter-Relaxation für

Lithiumborophosphatgläser

ω0 = 2π 117MHz

1/3 Li2O + 2/3[x B2O3 + (1-x) P2O5]

Präzesion der Magnetisierung

Kreiselgleichung

• makroskopische Magnetisierung präzediert um externes B-Feld mit der Lamorfrequenz w0

• analog zu einem Kreisel M!

B0

w0

Präzesion und FID

• Präzession der Magnetisierung erzeugt Wechselspannung U(t) in Messspule

• U(t) entspricht dem freien Induktionszerfall

B0

Rotierende Koordinatensystem

• Abtrennung der Präzession durch Transformation ins rotierende Koordinatensystem

• Magnetisierung im rotierenden Koordinatensystem:

• Magnetisierung rotiert um Beff

FID und Spektrum

Dw

Lösung durch Substitution:

FID und Spektrum

Dw

w

Adsorptionsanteil

Dispersionsanteil

Magnetisierung im rotierenden Koordinatensystem

• Magnetisierung präzediert im rotierenden Koordinatensystem um Beff

statischer Anteil

Puls

Magnetisierung während 90o-Puls

Laborkoordinatensystem

Komplexe Präzessions-bewegung

Rotierendes

Koordinatensystem

Einfache Präzessions-bewegung

B0

z‘

x‘y‘

M0

Kippwinkel a für „on-resonante� Anregung

• für „on-resonante� Anregung W = w0 folgt:

weff = g×B10

Rot. KO

xy

z

M a

90�-Puls: a = p/2 180�-Puls: a = p

• für a gilt:

• Pulslänge tp:

RF-Felder im rotierenden Koordinatensystem

Pulsanteil

„off-resonante� Anteile

Spin-Echo

Messung von T2

• Zerfall der transversalen Magnetisierung M+ = Mx + iMy

dM#

dt = −M# ' 1T* +# = M- ' ./0 123

CPMG (Carr Purcell Meiboom Gill) M+(t)

t/tDep

M0

02 4 6 8 10

Messung von T1

• Rückkehr der longitudinalen Magnetisierung Mzins thermische Gleichgewicht

dM4dt = M- − M4 ' 1T5

M4 = M- ' 1 − M- −M4-

M-' e/7 893

tW/T1

Inversion

(Mz0 = -M0)

Sättigung (Mz0 = 0)

N-2 Wiederholungen