Coupling and time

The major chemical applications of NMR are derived from three secondary phenomena chemical shift", "spin-spin coupling" and time-dependent effects . 

In equation (Cl.4.14) the saturation parameter essentially defines a criterion to compare the time required for stimulated and spontaneous processes. If I then spontaneous coupling of the atom to the vacuum modes of the field is fast compared to the stimulated Rabi coupling and the field is considered weak. If s" 1 then the Rabi oscillation is fast compared to spontaneous emission and the field is said to be strong. Setting s equal to unity defines the saturation condition... 

Palladium (II) trifluoroacetate [42I96-3I-6] M 332.4, m 210"(dec). Suspend in trifluoroacetic acid and evaporate on a steam bath a couple of times. The residue is then dried in vacuum (40-80°) to a brown powder. [J Chem Soc 3632 7965 J Am Chem Soc 102 3572 1980.]... 

The determination of piezoelectric constants from current pulses is based on interpretation of wave shapes in the weak-coupling approximation. It is of interest to use the wave shapes to evaluate the degree of approximation involved in the various models of piezoelectric response. Such an evaluation is shown in Fig. 4.5, in which normalized current-time wave forms calculated from various models are shown for x-cut quartz and z-cut lithium niobate. In both cases the differences between the fully coupled and weakly coupled solutions are observed to be about 1%, which is within the accuracy limits of the calculations. Hence, for both quartz and lithium niobate, weakly coupled solutions appear adequate for interpretation of observed current-time waveforms. On the other hand, the adequacy of the uncoupled solution is significantly different for the two materials. For x-cut quartz the maximum error of about 1%-1.5% for the nonlinear-uncoupled solution is suitable for all but the most precise interpretation. For z-cut lithium niobate the maximum error of about 8% for the nonlinear-uncoupled solution is greater than that considered acceptable for most cases. The linear-uncoupled solution is seriously in error in each case as it neglects both strain and coupling. 

As more fuel is converted into combustion products per unit of volume and time, expansion flow becomes stronger. Higher flow velocities go hand in hand with more intense turbulence. This process feeds on itself that is, a positive feedback coupling comes into action. In the turbulent stage of flame propagation, a gas explosion may be described as a process of combustion-driven expansion flow with the turbulent expansion-flow structure acting as an uncontrolled positive feedback (Figure 3.2). 

The cycle of deprotection, coupling, and washing is repeated as many times as desired to add amino acid units to the growing chain. 

An interesting improvement from the classical treatment of the bond under stress was proposed by Crist et al, [101], Considering the chain as a set of N-coupled Morse oscillators, these authors determined the elongation and time to failure as a function of the axial stress. The results, reported in Fig. 20, show a decreasing correlation between the total elastic strain before failure and the level of applied force with the chain length. To break a chain within some reasonable time interval (for example <10-3s) requires, however, the same level of stress (a0.7 fb) as found from the simpler de Boer s model. 

In presence of molecular motion the NMR line shape will change. A particularly simple situation arises, if the motion is rapid on timescale defined by the inverse width of the spectrum in absence of motion 6 1. In this fast exchange limit, which in 2H NMR is reached for correlation times tc < 1CT7 s, the motion leads to a partially averaged quadrupole coupling and valuable information about the type of motion can directly be obtained from analysis of the resulting line shapes. The NMR frequency is then given by... 

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