TABLE OF CONTENTS OF
`ESSENTIALS OF DYNAMIC NUCLEAR POLARIZATION'

Preface v

1   Spin Thermodynamics 1  
     1.1   Introduction   1  
     1.2   The Zeeman Interaction   3  
             1.2.1   Electron Spins   3  
             1.2.2   The Electron Zeeman Interaction   4  
             1.2.3   Nuclear Spins   6  
             1.2.4   The Nuclear Zeeman Interaction   6  
     1.3   Polarization   9  
             1.3.1   Expectation Values of Observables   9  
             1.3.2   The Density Matrix   10  
     1.4   Thermodynamic Equilibrium   12  
             1.4.1   The Microcanonical Ensemble   13  
             1.4.2   The Canonical Ensemble   15  
             1.4.3   Nuclear Spin 1/2   18  
     1.5   Thermodynamic Potentials   21  
             1.5.1   General Expressions   21  
             1.5.2   High Temperature Approximation   23  

2   Spin Dynamics 27
     2.1   Evolution of the Density Matrix   28
             2.1.1   The Liouville Equation   28  
             2.1.2   Solutions of the Liouville Equation   29  
     2.2   Motion of the Polarization Vector   30  
             2.2.1   The Bloch Equations   30  
             2.2.2   Coherent Precession of the Polarization Vector   32  
     2.3   Rotating Frames of Reference   34  
             2.3.1   Rotating Frames in Laboratory Space   34  
             2.3.2   Rotating Frames in State Space   34  
     2.4   Rate Equations   36  
             2.4.1   Transverse Relaxation   36  
             2.4.2   Rate Equation for the Polarization   39  
             2.4.3   General Two-Level Systems   42  

3   Spin Hamiltonian and Spectrum 45
     3.1   Elements of the Spin Hamiltonian   45
             3.1.1   Externally Applied Magnetic Fields   45  
             3.1.2   Dipolar Interaction   46  
             3.1.3   Step Operators   48  
     3.2   Truncation   50  
             3.2.1   Conservation of Energy   50  
             3.2.2   Average Hamiltonian Theory   53  
             3.2.3   The Spin Hamiltonian   54  
     3.3   The ESR Spectrum   56  
             3.3.1   Anisotropy of the $g$-Tensor   57  
             3.3.2   Hyperfine Interaction   59  
             3.3.3   Super-Hyperfine Interaction   62  
     3.4   Homogeneous Broadening   67  
             3.4.1   Mutual Interaction between Nuclear Spins   67  
             3.4.2   Mutual Interaction between Electron Spins   69  

4   CW Magnetic Resonance and Saturation 75
     4.1   CW ESR and Hole Burning   76
             4.1.1   The CW ESR Signal   76  
             4.1.2   Hole Burning   78  
     4.2   Spectral Diffusion   81  
             4.2.1   The Flip-Flop Hamiltonian   82  
             4.2.2   Rate Equations for Flip-Flop Transitions   83  
             4.2.3   The Total Flip-Flop Transition Rate   86  
             4.2.4   The Diffusion Equation   88  
     4.3   Provotorov's Theory   92  
             4.3.1   The Zeeman and the Non-Zeeman Reservoirs   93  
             4.3.2   The Provotorov Equations   97  
             4.3.3   Stationary Solutions of the Provotorov Equations   100  

5   Electron Spin Lattice Interactions 105
     5.1   Lattice Vibrations   106  
             5.1.1   The Lattice Hamiltonian   106  
             5.1.2   Phonon Modes   107  
             5.1.3   Lattice Temperature   110  
     5.2   Electron Spin-Lattice Relaxation   112  
             5.2.1   Spin-Lattice Coupling   112  
             5.2.2   Direct Spin-Lattice Relaxation Transitions   114  
             5.2.3   The Direct Spin-Lattice Relaxation Rate   116  
             5.2.4   The Raman, Orbach and other Processes   119  
     5.3   Magnetic Resonance Saturation and Relaxation   124  
             5.3.1   Spin-Lattice Relaxation and Spectral Diffusion   124  
             5.3.2   The Extended Provotorov Equations   127  
             5.3.3   Stationary Solutions of the Extended Provotorov Equations   130  

6   The Solid Effect 133
     6.1   DNP Mechanisms   133  
             6.1.1   The Solid Effect   133  
             6.1.2   Direct Nuclear Spin-Lattice Relaxation   136  
             6.1.3   Thermal Mixing   138  
     6.2   The Fundamental Transition of the Solid Effect   142  
             6.2.1   A Model System for the Solid Effect   142  
             6.2.2   The Tilted Rotating Frame   143  
             6.2.3   Rate Equations for the Polarization Transfer   148  
             6.2.4   The Polarization Transfer vs. Microwave Frequency   151  
     6.3   Nuclear Spin Diffusion   152  
             6.3.1   Spheres of Influence   153  
             6.3.2   Nuclear Spin Flip-Flop Transitions   155  
             6.3.3   The Diffusion Equation   158  
             6.3.4   The Diffusion Barrier   162  
     6.4   Polarization Transfer in the Solid Effect   164  
             6.4.1   Inhomogeneous Broadening and the Solid Effect   165  
             6.4.2   The Well-Resolved Solid Effect   168  
             6.4.3   The Differential Solid Effect   170  
             6.4.4   Microwave Induced Thermal Mixing   172  

7 Direct Nuclear Spin-Lattice Relaxation 175
     7.1   The Fundamental Transition   175  
             7.1.1   A Model System for Direct Nuclear Spin-Lattice Relaxation   175  
             7.1.2   Truncation   179  
             7.1.3   Transition Rates   181  
             7.1.4   Rate Equation for Nuclear Spin-Lattice Relaxation   183  
     7.2   Nuclear Spin-Lattice Relaxation and the Solid Effect   187  
             7.2.1   Nuclear Spin-Lattice Relaxation   188  
             7.2.2   Relaxation Limits on the Solid Effect   190  
             7.2.3   The Well-Resolved and Differential Solid Effect   193  

8   Thermal Mixing 195
     8.1   Triple Spin Flips   195  
             8.1.1   Model System for Triple Spin Flips   195  
             8.1.2   Truncation   198  
             8.1.3   Transition Rates   200  
             8.1.4   Rate Equation for the Nuclear Spin Polarization   203  
     8.2   Indirect Nuclear Spin-Lattice Relaxation   205  
             8.2.1   Decay of the Nuclear Spin Polarization   206  
             8.2.2   Equal Spin Temperature   209  
             8.2.3   Rate Equations for Indirect Nuclear Spin-Lattice Relaxation   210  
             8.2.4   Some Experimental Results   215  
     8.3   Triple Spin Flips and DNP   219  
             8.3.1   Triple Spin Flips and the Solid Effect   219  
             8.3.2   Thermal Mixing   222  
             8.3.3   Slow and Fast Thermal Mixing   227  
             8.3.4   The Cross Effect   231  

9   Coherent Polarization Transfer 235
     9.1   Introduction   235  
     9.2   The Hamiltonian for DNP Revisited   237  
             9.2.1   Multiple Nuclear Spins   237  
             9.2.2   Matrix Representation and Singular Value Decomposition   239  
             9.2.3   The Spectrum of Transition Matrix Elements $\sigma _{m\mu   $   242  
             9.2.4   Fictitious Spin ${\textstyle \frac {1   2     $   245  
     9.3   Polarization Transfer   248  
             9.3.1   Coherent Precession of a Polarization Vector   248  
             9.3.2   The Solid Effect   250  
             9.3.3   Nuclear Orientation Via Electron spin Locking (NOVEL)   255  
     9.4   The Integrated Solid Effect   259  
             9.4.1   Adiabatic Slow Passages   259  
             9.4.2   Polarization Transfer in the Integrated Solid Effect   261  

A   Units and Conversions 265

B   Rotations, Vectors and Tensors 267
     B.1   Rotations   267  
     B.2   Vectors and Tensors   269  

C   The Diffusion Equation 271
     C.1   The One-Dimensional Diffusion Equation   271  
     C.2   The Three-Dimensional Diffusion Equation   273  

D   Linear Differential Equations 275
     D.1   General Solutions   275  
     D.2   Limits for Rates and Time Constants   277  
{subsubsection   Example   277  

E   Singular Value Decomposition 279

F   Landau-Zener Theory 281

Bibliography 286

Index 293

Last update: 14 August 2016