Solid State NMR of Glass - Modelling NMR spectra of glass ... · PDF fileSolid State NMR of...

Click here to load reader

  • date post

    05-May-2018
  • Category

    Documents

  • view

    218
  • download

    1

Embed Size (px)

Transcript of Solid State NMR of Glass - Modelling NMR spectra of glass ... · PDF fileSolid State NMR of...

  • Solid State NMR of GlassModelling NMR spectra of glass from first-principles

    Thibault Charpentier

    CEA / IRAMIS / SIS2MLaboratoire de Structure et Dynamique par Resonance Magnetique

    GDR Verre, 9-13 April 2011

  • Introduction

    Basics of NMR: Interactions, MAS, MQMAS

    NMR of disordered Materials

    NMR from first-principles

  • Molecular Dynamics versus NMRContent of the tutorial

    I Basics of NMR interactions and spectra of solids

    I 1D-2D NMR experiments: Static, MAS and MQMAS spectra

    I NMR of disordered Materials

    I Structure: Molecular Dynamics Simulations (TD)

    I NMR parameters: DFT GIPAW calculations (TD)

    I NMR parameters & Simulations: specific NMR softwarepackages (fpNMR) (TD)

    I Principles of pulsed NMR

    I NMR Hamiltonian Art . . .

  • The Zeeman Interaction and Larmor FrequencyThe NMR spectrum of an isolated nucleus . . .

    m 1

    0

    0

    I=32

    B00

    B0=0

    m=3/2

    m=1/2

    m=1/2

    m=3/2 0

    The Zeeman effect

    0

    E=NB0

    0=N2

    B0

    The Larmor frequency and its NMRspectrum.

    No information on the chemical surrounding

    (~) H = ~N~I ~B0

  • NMR and the Periodic TableOne-half and quadrupolar nuclei

    I Isotope, Nuclear Spin

    I Natural Abundance

    I Gyromagnetic ratio (rad/s/T)0 = 20 = B0

    I Quadrupolar MomentQ (see Pyykko)

  • Pulsed NMRThe Basic NMR Experiment . . . One pulse !

    M0: Nuclear Magnetization at Equilibrium

    s s-msms-h

    p

    B0 M0 M0

    BRF

    M0

    FFT

    S t

    S

    ~M(0) = M0~z~M(p) = M0~x

    S(t) = M0ei0te

    tT2

    S() =

    0

    dt S(t)ei2t N1k=0

    S(tk)ei2tk = L ( 0)

    Lineshape L(): Gaussian, Lorentzian . . .

  • Pulsed NMRThe Basic NMR Experiment: Fourier Transform

    0 5000 10000 15000Time (s)

    -50-40-30-20-1001020304050Chemical shift ( ppm )

    23Na in Na2MoO4

    S(t) S()

  • NMR Interactions for NMR spectroscopistsEffects of the local magnetic fields . . .

    Electrons

    Phonons

    Nuclear Spins I Nuclear Spins SNMRNMR

    EPR

    MicroWaves, ....

    Bloc

    B0 BRF

    0

    E=N{B0Bloc }

    loc

    The NMR spectrum

    Information on the chemical surrounding

    (~) H = ~N~I {

    ~B0 + ~Bloc}

    = HZ + Hinter.

    (~) H = HZ + HCS + HQ + HJ + HD + . . .

    CS: Chemical Shift, Q: Quadrupolar, J: J couplings, D: Dipolar

  • NMR interactions for Quantum ChemistsThe effective Hamiltonian

    HS(NMR) = ~

    i

    i~Ii (1 ) ~B0 +

    i ,|Ii |1

    ~IiQii~Ii

    +~2

    2

    i

    j 6=i

    ij~Ii (Dij + Jij)~Ij

    ~B0 External static magnetic field

    ~BRF (t) External radiofrequency magnetic field (NMR signal)

    Internal Interactions

    ~Ii Nuclear spin operators ~i = i~~Ii Nuclear magnetic shielding tensor (chemical shift)

    Dij Nuclear magnetic dipolar coupling tensor (structure)

    Jij Indirect nuclear spin-spin coupling tensor

    Qii Nuclear quadrupolar coupling tensor ( |Ii | 1 )

  • The nature of NMR interactionsSecond-rank tensors (i.e. matrices) define NMR interactions.

    ~B(A)loc = A

    ~X =

    Axx Axy Axz

    Ayx Ayy Ayz

    Azx Azy Azz

    Xx

    Xy

    Xz

    HA = N~~I A ~X

    A ~X Interaction

    1 ~B0,~BRF Zeeman interaction

    ~B0 Magnetic Shielding DFT

    Q ~I Quadrupolar interaction DFT

    D ~S Dipolar interaction (spatial) structure

    J ~S Indirect J couplings (through bond) DFT

    DFT calculations output A in its tensorial (matrix) form relative to a

    reference frame(x , y , z) (crystal axes).

  • NMR Interactions: The Principal Axes System (PAS) IThe principal values

    AZZ

    AYYAXX

    B0B0

    z

    x

    y

    A =

    AXX 0 0

    0 AYY 0

    0 0 AZZ

    Isotropic Aiso =

    13Tr [A]

    Anisotropy A = AZZ AisoAsymmetry A = (AXX AYY ) /A

    with 0 A 1

    Calculations output the tensor in a reference frame (unit-cell definition).Its diagonalization (3D rotation) provides the principal values (A,) and

    its orientation with respect to the reference frame.Convention: |AZZ Aiso | |AXX Aiso | |AYY Aiso |

    AisoAZZ AYY AXX

  • NMR Interactions are Anisotropic . . .. . . NMR spectra of a single molecule (crystal)

    O

    C

    O

    C

    O

    C

    zz yy xx

    B0 B0 B0

    The NMR frequency depends on the orientation with respect to ~B0 0 = int()

    Single crystal NMR exists . . . but amorphous materials ?

  • NMR Interactions: The Principal Axes System (PAS) IIThe relative orientation of the PAS

    APAS = Aiso1

    + A

    12 (1 + A) 0 0

    0 12 (1 A) 0

    0 0 1

    A = X1A APASXA

    XA = R(A, A, A)

    = exp(iAIz) exp(iAIy ) exp(iAIz)

    (x , y , z): reference frame axis(A, A, A): Euler angles

    A NMR interaction is characterized by 6 parameters:Aiso , A, A, A, A, A.

    For a single interaction, (A, A, A) does not affect the powderlineshape but can be determined for single crystal NMR.

  • NMR Interactions are Anisotropic . . .. . . NMR spectrum (CSA) of a powder

    B0

    x

    y

    z

    ,

    =90 =0

    The powder average

    S(t) =

    sin dd

    exp {i(, )t}

  • NMR Interactions are Anisotropic . . .. . . but in liquids only the isotropic part in effective

    Motional averaging

    I Motions affect the anisotropiclineshape.

    I In the case of fast motionalaveraging (vs Larmorfrequency), a narrow line at theisotropic frequency.

    I Brownian Motion in liquid

    I Motions (fluctuations) induce

    Relaxation

    H ((t)) = Hiso + Hani ((t)) withHani ((t)) = 0 at the Larmor time scale ( 1/0)

  • The Zeeman Truncation in High Field NMROnly the part along B0 is NMR active to first order.

    AZZ

    AYYAXX

    B0B0

    z

    x

    y

    Azz

    In case of 1-spin interaction,only Azz (in the referenceframe) contributes to firstorder to the NMR frequency.

    Because B0 Bloc (or HZ Hint), wehave the secular approximation

    Hint H(1)CS + H(1)Q + H

    (2)Q + H

    (1)J + H

    (1)D . . .

    Typical strength of NMR interactionsI Z: 10-1000 MHz

    I CS: kHz

    I Q: MHz (up to second order)

    I D: kHz

    I J: Hz

  • NMR Interactions in generalAn overview . . .

    H () = C () R () () T()

    C () Constant Obtained from DFT (,Q)

    R() () Spatial Dependence Manipulated through (sample) motions

    R() () = 1 Isotropic Brownian motions in liquids

    T() Spin operators Manipulated through RF (spin rotation)

    T() Iz Chemical shift

    T(Q) I 2z First order quadrupolar interaction

    T(Q) Iz , I 3z Second order quadrupolar interaction

    T(D,J) IzSz Dipolar (heteronuclear) or J interactions

    T(D)II

    IAz IBz

    Dipolar (homonuclear) interaction+ 14

    (IA+ I

    B + I

    AI

    B+

    )

  • The Shielding / Chemical Shift TensorNMR frequency

    The secular contribution of the magnetic shielding is:

    HCS = ~I~B0 B0zz()Iz

    zz() = XX sin2 cos2 + YY sin

    2 sin2 + ZZ cos2

    = iso +CS2

    ((3 cos2 1) + CS sin2 cos 2

    )= iso + CSR20()

    NMR measure the chemical shift tensor (ppm):

    expiso (ppm) = 106

    ( ref

    ref

    )ref is a frequency reference value obtained from one tabulated

    reference compound, generally in liquid or in a solid (narrow peak,e.g. NaCl for 23Na.

  • The shielding / Chemical Shift TensorNMR static lineshape

    -200 -100 0 100 200ppm

    -200 -100 0 100 200ppm

    CSA > 0 CSA < 0

    = 0

    = 0.5

    = 1

  • The magnetic shieldingRelationshield with the chemical environment

    -120-110-100-90-80-70-6029Si chemical shift iso (ppm)

    O-O-SiO- O-

    O-SiOSiO- O-

    O-SiOSiOSi O-

    Si OSiOSiOSi O-

    Si OSiOSiOSi O Si

    Q(0) Q(1) Q(2) Q(3) Q(4)

    Q(1) SiOSi=180oQ(0)

    Q(1)

    Q(2)

    Q(3)

    Q(4)

    Tetrahedral silicon Q(n) units in silicates

  • The quadrupolar interactionfrom electric field gradient. Only for I 1.

    Because of its large strength (kHz-MHz), quadrupolar Hamiltonianare often accounted for up to second order (23Na,17O,27Al,11B. . . )

    depending on the local environment of the nucleus.

    The electric field gradient V is a symmetric traceless(VXX + VYY + VZZ = 0) tensor.

    CQ =eQ

    hVZZ , Q =

    VXX VYYVZZ

    ,Viso = 0

    CQ : quadrupolar couping constant, Q : quadrupolar asymmetryparameter.

  • The quadrupolar interactionTo first order. Only for I 1.

    The firt-order secular quadrupolar Hamiltonian is

    H(1)Q =

    CQ6I (2I 1)

    R20 () T20 , T20 =

    1

    6

    (3I 2z I (I + 1)

    )This I 2z yields the NMR frequency as

    m,m1 0 =1 2m

    2QR20 () =

    (1)Q ()

    The central transition 12 12 is not affected by H

    (1)Q .

    0Q1

    20

    Q1

    2

    I=1

    0

    0Q

    10Q1

    I=32

  • The quadrupolar interactionTo second order.

    The second-order secular quadrupolar Hamiltonian is (morecomplex)

    H(2)Q =

    1

    0

    (CQ

    6I (2I 1)

    )2

    l=0,2,4

    AlRl0()

    Rl0() =lk=l

    Bkl ()Dkl0 () ,D

    kl0 : Wigner rotation matrix elements

    Al = f (I 3z , Iz) and isotropic shift (SOQS) (2)Q = A

    0B00 ()

    The NMR frequency of the central transition can be written as

    1/2,+1/2() 0 = a0 + a2R20() + a4R40()

  • The quadrupolar interactionfrom electric field gradient

    -2000-1000010002000kHz

    -200-