GROUP THEORETICAL-ANALYSIS OF NUCLEAR-SPIN RELAXATION IN LIQUID-CRYSTALS AND MOLECULAR-SOLIDS

A comprehensive and general group theoretical analysis is presented of the time correlation functions (TCFs) governing nuclear spin relaxati on in anisotropic systems such as liquid crystals and molecular solids . Without invoking specific dynamic models, the consequences of time-r eversal invariance (detailed balance) and rotational symmetry are expl ored systematically. By constructing TCFs from irreducible tensor comp onents adapted to the crystal symmetry and making use of group theoret ical orthogonality relations, the most general and concise expression of the orientation dependence of the lab-frame TCFs is derived. Depend ing on the crystal symmetry, there are between 2 and 15 coefficients i n this expression: these are the irreducible crystal-frame TCFs associ ated with the irreducible representations of the crystal point group. The corresponding irreducible crystal-frame spectral densities constit ute the complete model-independent information content derivable from spin relaxation experiments. Explicit expressions for the irreducible crystal-frame TCFs and the associated angular functions are given for all crystallographic point groups. The combined effect of crystal symm etry and local (microstructure) symmetry is also investigated, as is t he effect of symmetry on TCF contributions from motions on multiple ti me scales. Furthermore, the relation of the TCFs to the independent or der parameters is established. While many of the new results are appli cable to a wide variety of spectroscopic techniques and systems, the e xplicit results have their greatest potential for spin relaxation stud ies of oriented lyotropic liquid crystals.