Line broadening inhomogeneous

A. Meissner, P. Bloch, E. Humpfer, M. Spraul and O. W. Sorensen, Reduction of inhomogeneous line broadening in two-dimensional high-resolution MAS NMR spectra of molecules attached to swelled resins in solid-phase synthesis, J. Am. Chem. Soc., 1997, 119, 1787-1788. 

As introduced in Section 3.1, Forster theory assumes that there is no inhomogeneous line broadening, i.e. static disorder, in the spectra of donor emission and acceptor absorption. However, if one considers an ensemble of inhomoge-neously broadened spectra, the spectral overlap is given by ... 

The S groups stabilized at the solid surface can differ in their chemical nature. In the disordered (amorphous) solids, to which silica refers and which are of most practical and theoretical interest, the variations in the spatial structure are inevitable. These variations cause variations in the properties of even those S groups having chemically identical composition of their coordination spheres and give rise to the inhomogeneous line broadening in the spectra of these groups and to their kinetic inequivalence. In this work, special emphasis is placed on the questions associated with these problems. 

Isotropic scattering In addition to the dephasing time T2, the correlation time rc of the purely vibrational relaxation process can be measured, providing quantitative information on the question of homogeneous/inhomogeneous line broadening. 

An example is illustrated in Fig. 2. In case 1, there are two mechanisms operating one in the fast modulation limit, and one in the slow modulation limit. This is the classic case of combined homogeneous and inhomogeneous line broadening. In case 2, there is a single mechanism, but it is in the intermediate modulation region. The Raman hnewidths are identical... 

The Spectrum of fig. 3 demonstrates the use of the spin echo to remove inhomogeneous line broadening and the use of time proportional phase increments (TPPI) to restore the offset. Resolution is limited by truncation of the multiple quantum free induction decay and scale of reproduction. The actual linewidth is less than 2 Hz for all orders and suffices to resolve all allowed transitions of all orders. 

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