Relaxation mechanisms autocorrelation function

The linear response theory [50,51] provides us with an adequate framework in order to study the dynamics of the hydrogen bond because it allows us to account for relaxational mechanisms. If one assumes that the time-dependent electrical field is weak, such that its interaction with the stretching vibration X-H Y may be treated perturbatively to first order, linearly with respect to the electrical field, then the IR spectral density may be obtained by the Fourier transform of the autocorrelation function G(t) of the dipole moment operator of the X-H bond ... 

When l l, the above gives the so-called cross-correlation functions and the associated cross-correlation rates (longitudinal and transverse). Crosscorrelation functions arise from the interference between two relaxation mechanisms (e.g., between the dipole-dipole and the chemical shielding anisotropy interactions, or between the anisotropies of chemical shieldings of two nuclei, etc.).40 When l = 1=2, one has the autocorrelation functions G2m(r) or simply... 

There is a large class of relaxation mechanisms which operate on molecules in motion in non-metailic samples. All but one, the spin-rotation interaction, depend on the fact that the change in the molecular orientation or translation modulates the field due to that particular interaction and creates a randomly varying field at the site of the nucleus in question. Any such random motion can have associated with it a special form of an autocorrelation function G(t), expressed in terms of a scalar product of the local field h(t) and the same local field at an earlier time h(0), which is a measure of... 

Rigorous statistical mechanical analysis indicates that the dielectric relaxation function 0(f) of an isotropic system in the linear response regime is equivalent to an autocorrelation function of a microscopic polarization p(f) fluctuating through the molecular motion at equilibrium (Cole, 1967 Kubo, 1957) ... 

Monte Carlo simulations with lattice models of chain dynamics have been concerned with segmental and with whole molecule relaxation. In each case the autocorrelation functions depend upon details of the lattice model. A cubic-lattice model, with random stifle bead motions has been used to study the relaxation of seven characteristics of instantaneous aspherical shape. Three decay functions are observed for iarge molecules with and without excluded volume considerations. The large difference in relaxation times and in their chain length dependence obtained here, and in earlier studies on including the excluded volume effect, is attributed to restrictions associated with the single bead mechanism, a view justified by simulations which obtained more flexible chains by... 

For the dipolar relaxation mechanism, the spin lattice relaxation time is sensitive to the reorientation dynamics of the CH bond vectors. Different orientations of the CH bond result in slightly different magnetic fields at the carbon nucleus and the modulation of this field allows the spin flips to occur. When we define ecn as the unit vector along a CH bond, the second Legendre polynomial of its autocorrelation function is given by... 

Molecular motions in polymer solutions or bulk pol3nners have been investigate by vaj ous spectroscopic techniques such as dielectric relaxation, H and C NMR, ESR, quasi-elastic Light Scattering or Neutron Scattering. However, there are still many unanswered questions concerning the type of orientation autocorrelation function able to describe local polymer motions in solution or in bulk and the size of these motions. Furthermore, for bulk polymers, the relation of these local motions to the glass transition phenomena observed in macroscopic mechanical measurements is controvertible... 

---