Lattice Relaxation Phenomena

The MNDO equilibrium geometries in the Si and T1 states of the dimer, trimer, and tetramer are reported in Table 1, together with the ground-state geometry and the 

6 Geometric and Electronic Structure and Optical Response of Oligo- and Polythiophenes 

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This dependence on the dopants (at constant effective charge) can be understood in terms of interactions, ordering, and lattice relaxation phenomena. As a consequence, the local binding... 

The variations in conductivity with different dopants of the same valence can be understood in terms of defect interactions and lattice relaxation phenomena caused by the dopant the binding energies of the defect clusters and the effective mobility of the vacancies depend on the dopant size and concentration [35-37]. Doping with Sc " ", the ionic radius of which is almost identical to that of Zr" +, leads to the highest conductivity maximum (ca. 0.3S/cm at 1000°C) [38,39[. However, despite the high conductivity of Sc-doped zirconia... 

Experimental data on nitrogen obtained from spin-lattice relaxation time (Ti) in [71] also show that tj is monotonically reduced with condensation. Furthermore, when a gas turns into a liquid or when a liquid changes to the solid state, no breaks occur (Fig. 1.17). The change in density within the temperature interval under analysis is also shown in Fig. 1.17 for comparison. It cannot be ruled out that condensation of the medium results in increase in rotational relaxation rate primarily due to decrease in free volume. In the rigid sphere model used in [72] for nitrogen, this phenomenon is taken into account by introducing the factor g(ri) into the angular momentum relaxation rate... 

Methods of disturbing the Boltzmann distribution of nuclear spin states were known long before the phenomenon of CIDNP was recognized. All of these involve multiple resonance techniques (e.g. INDOR, the Nuclear Overhauser Effect) and all depend on spin-lattice relaxation processes for the development of polarization. The effect is referred to as dynamic nuclear polarization (DNP) (for a review, see Hausser and Stehlik, 1968). The observed changes in the intensity of lines in the n.m.r. spectrum are small, however, reflecting the small changes induced in the Boltzmann distribution. 

The relaxation phenomenon which has been discussed so far is within the linear viscoelastic range. Under large deformation, the global relaxation time has to include the contribution from the external work Aw done on the lattice site and takes the form (20)... 

Second, it is conceivable that amines quench triplet ketones before spin-lattice relaxation takes place within the three triplet sublevels 159>, which are populated unevenly 160>. In that event, radicals can be produced with their electron spins polarized. The CIDEP phenomenon 161>, whereby EPR emission is observed upon irradiation of ketones and very reactive substrates, may involve this mechanism. In fact, certain CIDNP observations may depend on rapid quenching of spin-polarized triplets 162>. 

In the first case, the energy is dissipated within the lattice as phonons, that is, vibrational, rotational and translational energy. The mechanism by which this dissipation occurs is known as spin-lattice relaxation. It is characterized by an exponential decay of energy as a function of time. The exponential time constant is denoted Tie and is called the spin-lattice relaxation time. In the second case the initial equilibrium may also be reached by a different process. There could be an energy exchange between the spins without transfer of energy to the lattice. This phenomenon, known as spin-spin relaxation is characterized by a time constant T2e called the spin-spin relaxation time. 

Since the first report (5) of a pronounced configurational dependence for the anomeric protons of monosaccharides in aqueous solutions, studies in this laboratory have shown (6), (7 ), (8), (9) that proton Ri-values have a variety of stereospecific dependencies and reflect the overall steric environment of a proton. In the following discussion, a brief introduction to the phenomenon of spin-lattice relaxation and to the measurement of proton Ri-values by pulse Fourier transform methods, will be... 

The first microscopic theory for the phenomenon of nuclear spin relaxation was presented by Bloembergen, Purcell and Pound (BPP) in 1948 [2]. They related the spin-lattice relaxation rate to the transition probabilities between the nuclear spin energy levels. The BPP paper constitutes the foundation on which most of the subsequent theory has been built, but contains some faults which were corrected by Solomon in 1955... 

The question of the nature of the superconducting state in the radical-ion salts can still not be unambiguously answered even after more than 20 years of intensive research. In the conventional superconductors, the phenomenon can be explained through the BCS theory by the formation of Cooper pairs. Here, the attractive interaction between two electrons is mediated by phonons. The total spin of the Cooper pairs is S = 0, and their total orbital angular momentum is I = 0. The pair wave-function is an s-function. The concept of the Cooper pairs as spin singlets can evidently also be applied to the radical-ion salts. This can for example be shown by measurements of the NMR spin-lattice relaxation time in the superconducting state [3]. 

In general, no large energy barriers are to be crossed for the motional phenomenon. The activation energy was evaluated by the relaxation values to be as small as 4.5 kj mol in PHTP, lower than a gauche/trans interconversion barrier [39]. Large librations of methylenes account for the short carbon spin-lattice relaxation times at room temperature. 

The width of NMR lines is related to the phenomenon of relaxation. This concept has been defined. There are two main relaxation processes in NMR, namely, spin-lattice or longitudinal, relaxation and spin-spin , or transverse, relaxation. Spin-lattice relaxation is the process by which the nuclei in the upper spin state lose energy externally to the crystal lattice (in a crystal) or, less effectively, to the surrounding liquid (in a solution). The speed at which spin-lattice relaxation occurs is characterized by the longitudinal relaxation time Ti. 

The evolution of spin-lattice relaxation times as a function of time was measured for the tricaprin/tristearin 50 50 (w/w) mixture at 40°C. At this temperature, tricaprin was liquid and tristearin was in the P form (checked by XRD measurements, results not shown). The Solid Fat Content (SFC) was 60%. The small deviation from theory (50%) was due to the presence of co-crystals which delay the melting of triceqjrin crystals. It is already known that the average crystal size increases as a fimction of time via the Ostwald Ripening phenomenon according to a power law model. The evolution of T for the present system is shown in Figure 1. 

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