Advances in studying order and dynamics in condensed matter by NMR [Elektronische Ressource] / vorgelegt von Mihai Adrian Voda

Prof. Blümich

Sujets

• Physik

Informations

• Publié par: rheinisch-westfalischen_technischen_hochschule_-rwth-_aachen
• Publié le: 01 janvier 2006
• Nombre de lectures: 20
• Langue: Deutsch
• Poids de l'ouvrage: 2 Mo

Extrait

Advances in Studying Order and
Dynamics in Condensed Matter by NMR








Von der Fakultät für Mathematik, Informatik und Naturwissenschaften der
Rheinisch-Westfälischen Technischen Hochschule Aachen
zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften
genehmigte Dissertation



vorgelegt von
M.Sc. Mihai Adrian Voda
aus Ocna − Mures, Romania



Berichter: Universitätsprofessor Dr. Dr. h.c. Bernhard Blümich
Hochschuldozent PD Dr. Siegfried Stapf

Tag der mündlichen Prüfung: 13 Juli 2006
Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfügbar.
I
Content
Abbreviations and Symbols ..............................................................................................IV
Introduction ......................................................................................................................... 1
1 Theoretical Background .................................................................................................. 5
1.1 Introduction ................................................................................................................. 5
1.2 NMR signal ................................................................................................................. 6
1.2.1 Classical approach ................................................................................................ 6
1.2.2 Quantum mechanics treatment and the nuclear spin interactions......................... 9
2 Magnetic Field Inhomogeneities in Heterogeneous Liquid Mixtures: Simulations
and Measurements............................................................................................................. 15
2.1 Introduction ............................................................................................................... 15
2.2 Theory........................................................................................................................ 16
2.2.1 Sources of magnetic field inhomogeneities within a liquid sample ................... 16
2.2.2 Diffusion of liquids............................................................................................. 21
2.2.3 The simulation package Vector Fields OPERA-3d............................................ 22
2.3 Results and discussions 25
2.3.1 Magnetic field distortions introduced by a glass tube and a water sample ........ 25
2.3.2 Magnetic field distortions in heterogeneous liquid mixtures ............................. 32
2.3.3 Experiments that prove the simulated field inhomogeneities and line shifts ..... 36
2.4 Conclusions ............................................................................................................... 39
3 Stretched Elastomers Studied by Multiple Quantum NMR....................................... 41
3.1 Introduction 41
3.2 Theory........................................................................................................................ 42
3.2.1 The complex susceptibilities .............................................................................. 42
3.2.2 The dipolar interaction........................................................................................ 44
3.2.3 The van Vleck moments..................................................................................... 46
3.2.4 Multispin second van Vleck moment from the DQ build-up curve ................... 47
3.2.5 Multispin moments edited by the TQ build-up curve......................................... 51
II
3.3 Experimental ............................................................................................................. 53
3.3.1 Samples .............................................................................................................. 53
3.3.2 NMR experiments .............................................................................................. 53
3.4. Results and discussions ............................................................................................ 55
13.4.1 Sensitivity to the changes of H residual dipolar couplings in NR under uniaxial
elongation.......................................................................................................... 55
3.4.2 Residual dipolar moments edited by TQ build-up curves for natural rubber under
uniaxial elongation and compression ................................................................ 59
3.5. Conclusions .............................................................................................................. 62
4 Molecular Dynamic Heterogeneities of Thermoplastic Polyurethanes..................... 63
4.1 Introduction ............................................................................................................... 63
4.2 Experimental ............................................................................................................. 64
4.2.1 Samples 64
4.2.2 NMR measurements........................................................................................... 65
4.3 Double-Quantum dipolar filter.................................................................................. 66
4.4 Results and discussions ............................................................................................. 68
4.4.1 Proton NMR spectra and phase composition ..................................................... 68
4.4.2 Proton spin diffusivities ..................................................................................... 69
4.4.3 Dominant morphology of TPU samples. Effective domain sizes ...................... 73
4.4.4 Correlation between effective domain sizes, residual dipolar couplings, Young′s
modulus, and glass transition temperature ........................................................ 80
4.5 Conclusions ............................................................................................................... 85
5 Optimisation of Halbach Magnets Design Based on Field Simulations .................... 87
5.1 Introduction 87
5.2 Theory ....................................................................................................................... 87
5.3 Field simulations ....................................................................................................... 89
5.4 Results and discussions ............................................................................................. 91
5.4.1 Halbach-16 and its modified design................................................................... 91
5.4.2 Halbach-24 and its modified designs ................................................................. 94
5.5 Conclusions ............................................................................................................... 96

III
6 Conclusions ..................................................................................................................... 99
References ........................................................................................................................ 101




IV
Abbreviations and Symbols

NMR Nuclear Magnetic Resonance
MRI Magnetic Resonance Imaging
®MOUSE Mobile Universal Surface Explorer
B vector of the magnetic flux density
B static magnetic field vector 0
B rf field vector rf
B amplitude of the rf field 1
H vector of the magnetic field strength
M magnetic polarization p
M thermodynamic equilibrium magnetization vector 0
M components of the magnetization vector x,y,z
LFM magnetization in laboratory frame
μ magnetic dipole moment
i, j, k unit vectors
φ magnetic scalar potential
χ magnetic susceptibility m
χ ′, χ ′′ real and imaginary parts of the complex susceptibility
ω Larmor frequency 0
ω rf rf
ω precessing angular frequency in the rotating frame 1
Ω frequency offset in the rotating frame 0
μ magnetic permeability
γ gyromagnetic ratio of nucleus
I nuclear spin quantum number
k Boltzmann's constant B
h Planck's constant divided by 2 π
R relaxation matrix
T longitudinal relaxation time 1
T transverse relaxation time 2

V
∗T transverse relaxation time with inhomogeneous broadening 2
t rf pulse duration p
ρ density matrix
H Hamilton operator
H spin Hamiltonian S
()0
H secular dipolar Hamiltonian d
H double-quantum dipolar Hamiltonian DQ
Tr trace of a matrix
δ anisotropy parameter
η asymmetry param
σ isotropic chemical shift iso
P()cosθ associated Legendre polynomials n0
D diffusion coefficient
c concentration
MQ multiple-quantum
DQ double-quantum coherences
TQ triple-quantum
FQ four-quantum
f()ω the shape function
λ stretching ratio
thM the n moment of the resonance line n
d dipolar coupling constant of spins i and j ij
ijS site selective dynamic order parameter
R end-to-end vector
NR natural rubber
TPU thermoplastic polyurethane
HS hard segment
SS soft segm
AFM atomic force microscopy
SAXS small angle X-ray scattering
T glass transition temperature g
E Young ΄s modulus
d domain sizes R,M
Introduction
Introd