: An introduction to Solid State NMR spectroscopy Dr. Susanne Causemann (Solid State NMR specialist/ researcher) Interaction between nuclear spins and applied magnetic fields B 0 application of a static magnetic field (B 0 ) Nuclear spins without magnetic field: statistically orientated If a nd B 0 perpendicular magnetic field (B, rf pulse) is applied the net magnetization is rotated in the xy plane (in rotating frame) B Individual spins precess around their local experienced B loc field T relaxation: magnetization is build up (uneven density of arrows) due to fluctuations M = # nuclei i µ i L.G. Hanson, Conc. Magn. Reson. A,A(5), 9-40, (008)
Detection of transverse magnetization B 0 z y coil FID (free-induction decay) Fourier transformation * πt x transverse magnetization (oscillating) exp( t / * T ) t ν Rotating magnetic moment rotating magnetic field Electric field (Maxwell s equation) Sets electrons in a wire coil Oscillating current in coil = FID (close to the sample) in motion to summarize The NMR spectrometer is basically a device capable of - (i) magnetizing the nuclear spins with a large applied magnetic field - (ii) rotating the spin polarizations by radiofrequency pulses to produce transverse nuclear magnetization - (iii) detecting the small oscillating electric currents induced by the precessing transverse spin magnetization. To some extent, everything else is details. M. Levitt, spin dynamics, Wiley & sons, 00 4
The classical approach We deal with the macroscopic sizes i.e. the magnetization represented by the vector model Bloch s equation (describing magnetization in the rotating frame): M M M exp x = M x 0 * T exp y = M y 0 * T = t t t ( M z M 0 ) exp 0 z M 0 + T 5 The quantum mechanical approach - for the description of properties of individual spins - Multispin systems are represented by a spin density matrix 6
The Zeeman interaction = interaction of a nuclear magnetic moment with the B 0 -field - represented by the Zeeman-Hamilton operator: Z = µ B0 = γhb 0I z - Not all possible spin orientations relative to the B 0 -field have a well-defined energy. Only the nuclear spin eigenstates ( Zeeman states ) are associated with real, well-defined energy values ( energy eigenvalues ) Hˆ r ˆ ˆ γ = γmh B 0 gyromagnetic ratio h Planck constant m magnetic quantum number I, I,..., I -/ Em = E / E/ hb0 m M= = / = γ = ω L 7 The Zeeman interaction: Energy level diagrams in NMR General rules to construct them: the magnetic quantum number m has values from +I (nuclear spin) to I quantizied by steps of I, I,..., I for I=/ spin: the total number of energy eigenstates is I +, I is associated with the lowest energy level + = # energy levels due to the negative sign of = γmh E = ω B 0 m L for neighbored energy levels equidistant distance between the energy levels allowed transitions between neighbored levels only ( ± ) 8 4
The Zeeman interaction: Energy level diagrams in NMR for I=/ spins: ( H, C, 9 Si, P, 5 N ), + = # energy levels for I= spins: ( H, 6 Li, 4 N ),0, + = # energy levels 0 for I=/ spins: ( 7 Li, Na, 5 Cl, 79 Br, ),,, + = # energy levels E m 9 The Zeeman interaction: Energy level diagrams in NMR for I=/ spins: ( H, C, 9 Si, P, 5 N ) for I= spins: ( H, 6 Li, 4 N ) 0 for I=/ spins: ( 7 Li, Na, 5 Cl, 79 Br, ) Hypothetical pure Zeeman-Spectra? ω 0 ω ω ω 0 ω 0 ω 0 0 5
Internal interaction an overview Not much information! the carrier of information Internal interactions = interaction between the nuclear spin with internal magnetic and electronic fields Internal interaction an overview Magnetic shielding/chemical shift = indirect magnetic interaction of the external magnetic field and the nuclear spins through the involvement of electrons J-coupling B 0 uadrupolar couplings = electric interaction of spin >/ nuclei with the surrounding electric fields ( interaction between a quadrupolar moment with an electric field gradient) Direct dipole-dipole couplings = indirect magnetic interactions of nuclear spins with each other through the involvement of electrons Direct magnetic interactions of nuclear spins with each other 6
Internal interaction an overview ĤH int Chemical Shift Dipole-Dipole (short range) Dipole-Dipole (long range) J- coupling uadrupole coupling Solids Antropic liquids Isotropic liquids Internal interaction Hamilton operators Interactions are mathematically represented by Hamilton operators (Hamiltonians) ˆ = Hˆ + H tropic (orientation independent) Hˆ Reduced / eliminated by motional averaging tropic (orientation dependent, certain directions favoured) B 0 Magnetic shielding/chemical shift Hˆ = Hˆ uadrupolar couplings weak: strong: Hˆ = Hˆ H ˆ = Hˆ + () ( ) () Hˆ Direct dipole-dipole couplings homonulcear (i.e. H- H) ˆ = ˆ H D, II HD, II heteronuclear (i.e. H- C) ˆ = ˆ H D, IS HD, IS 4 7
Impact of motional averaging on a NMR spectrum all tropic internal interactions are averaged out due to Brown s molecular motion (complete motional averaging) in (rigid) solids: tropic interactions are (fully) present resulting in broad, featureless spectra 5 motional averaging Strength of internal magnetic interactions of solids and liquids are very different from each other due to motional averaging Modes of molecular motion internal molecular motion: -vibration -rotation around bonds translation: - diffusion - flow rotation 6 8
motional averaging in liquids and solids States of matter tropic Liquid (water) Intramolecular motion fast translation fast and tropic rotation fast and tropic tropic internal interactions are averaged out resulting in narrow NMR peaks tropic liquid /liquid crystal (soap film) fast fast and tropic fast and tropic tropic interactions are only partially averaged out resulting in more complicated NMR spectra solids can be fast, but usually restricted usually neglible restricted tropic interactions usually present leading to broad and complicated lines 7 motional averaging in liquids and solids Distinction solids liquids depends on mobility in the sample Distinction mobile immobile depends on timescale! Examples: - timescale: microseconds water resists deformations and appears as hard as a solid (you can test this by diving into a swimming pool stomach-first) - timescale: several centuries glass behaves like a liquid (windows of old chruches are thicker at the bottom than on the top. Glass has flowed under gravity like a liquid) Timescales are important! 8 9
Structural characterization Solution vs. solid state NMR H ˆ = Hˆ Energy of spin system: total Z All NMR spectra are results of the energy differences of the nuclear spin eigen states, which are shifted by internal spin interactions. RF int Solutions: Hˆ = Hˆ + int Hˆ J Structural parameters: - Isotropic chemical shift - J coupling Solids Hˆ int = Hˆ D, homo D, hetero () () Information overload! We need special solid state NMR techniques to obtain useful spectra! 9 Methods for structural characterization magic angle spinning (MAS)- setup B 0 θ 54.7 If the spinning is fast enough: θ = θ = 54. 7 θ How fast? Spinning frequency >> width of the static spectrum LiPSS-d7 LiPSS-d7 (static (static 7 7 LI LI solid solid echo echo NMR NMR spectrum) spectrum) LiPSS-d7 ( 7 LI MAS NMR ) M LiCl M LiCl 00000 50000 0-50000 -00000 ν( 7 Li)/Hz 0 0
Methods for structural characterization magic angle spinning (MAS) H ˆ = Hˆ int B 0θ (A) D, hetero D, homo proportional to: ( cos θ ) () () if θ=54.7 ( magic angle ) then ( cos ) = 0 θ Methods for structural characterization A simple experiment - one pulse MAS 90 (*) - (*) 90 pulse for spin-/ nuclei, special rules for quadrupolar nuclei Signal Exponential Growth.0 0.8 0.6 0.4 0. 0.0 0 4 6 8 Time (T Periods)!Note: very different measurement parameters compared to solution state NMR - often much shorter pulses (pulse length very important) - more power (000W amplifier) - acquisition time in order of few ms - very short dead time (-8 µs) - very short dwell times (0.5 to 0 µs) -Recyle delay: - 5 T quantitative -. T best S/N for a certain time period, but not quantitative
Methods for structural characterization MAS- the tropic line(s) and spinning sidebands If the spinning speed width of the static spectrum Spinning sidebands arise apart from the tropic line in distance of the spinning speed How to distinguish the tropic line from spinning sidebands? - position independent of spinning speed! Note: not necessarily the most intense line!! Note: for quantitative analysis spinning sidebands must be considered! D M. Duer, Introduction to Solid-State NMR spectroscopy, Blackwell Science (004) Methods for structural characterization TOSS MAS TOSS= total suppression of spinning sidebands - TOSS experiments are NOT quantitative! If more than one positions: Difficult to distinguish between spinning sidebands and tropic line solution: TOSS method -principle: the magnetization associated with the tropic lines is (almost fully) refocused, while the magnetization contributions of the spinning sidebands (ss) is destroyed -doesn t work well if there are many ss (small residual ss, phase distortions) M. Duer, Introduction to Solid-State NMR spectroscopy, Blackwell Science (004) 4
Study of dynamics in solids timescales and methods Timescale of dynamic process fast 0-9 to 0-6 s (local mobility like molecular vibrations and rotations) medium NMR time window 0-5 to 0 - s (ion jumps, chain mobility in polymers) slow 0 - to 0 s (chemical exchange) SS NMR method T relaxation studies Static lineshape analysis T ρ relaxation studies D exchange experiments 5 Study of dynamics in solids static lineshape analysis slow motion limit: τ c >>( ν) - motional narrowing: τ c ~( ν )- fast motion limit: τ c <<( ν) - ν/hz study of dynamic processes µs - ms 6 6
Study of dynamics in solids static lineshape analysis application example Estimation of activation energies for ion jumps in ion conducting materials 5K 498K 47K 449K 44K 99K 74K 50K 5K 00K 75K 50K 6K 0K 76K 00 50 00 50 0-50 -00-50 -00 δ( 7 Li)/ppm FWHH 500 000 500 000 500 000 500 T ON 50 00 50 00 50 400 450 500 550 T/K Waugh-Fedin equation [] : E a [ev].677 0 - T ON [K] [] J.S. Waugh, I. Fedin, Sov. Phys. Solid State, 4, 6, (96) 7 Study of dynamics in solids static lineshape analysis application example Estimation of activation energies for ion jumps in ion conducting materials Advantage - Good method complementary to conductivity studies, because mobility of an ion can be studied selectively - ion translation only is in the NMR time window, forward and back jumps are too fast Disadvantage - only mobile ions lead to motional narrowing, the degree of mobile relative to immobile ions is not known 8 4