Long-time decay free motion

A distinction should be made between free rotation and hindered rotation. In the case of free rotation, after a (5-pulse excitation the emission anisotropy decays from ro to 0 because the rotational motions of the molecules lead to a random orientation at long times. In the case of hindered rotations, the molecules cannot become randomly oriented at long times, and the emission anisotropy does not decay to zero but to a steady value, r (Figure 5.10). These two cases of free and hindered rotations will now be discussed. 

The translational diffusion of water molecules at the micellar surface also slows down, but only by about 20%. Thus, the translational motion is less affected than the rotational motion. This is due to the fact that the average mean-square displacement (which measures the translational dynamics) is dominated by the fast-moving free water molecules in the layer, while the long time slow decay of orientational relaxation is found to be dominated by the bovmd water molecules. 

The segmental motion of a polymer chain was successfully described by a bead-spring model, discussed by Rouse [17] in the so-called free-draining limit and by Zimm [18] in the hydrodynamic limit, de Gennes [19,20] calculated the coherent and incoherent intermediate scattering functions for both the Rouse and Zimm models. In the low Q and long time limit, the time decay of the intermediate scattering function depends on and and the Q dependence of the... 

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