Radiation amplitude

The radiation amplitude is directly related to the amount of energy applied to the system. Exhaustive treatments require high irradiation amplitudes, for which probes are more suitable than baths. 

Table II. Mean relative quantity of calcium ions released by brain tissue pairs as a function of exposure to 147-MHz radiation, amplitude modulated at 16 Hz.

This manifold has been used for the USALLE of paracetamol from suppositories [17]. Hydrolysis of the analyte prior to reaction with o-cresol in the alkaline extractant medium was also favoured by US (the entire sample plug was irradiated in EC). Hydrolysis and formation of the reaction product displaced the extraction equilibrium, thus favouring extraction into the aqueous phase. The influence of the variables related to the dynamic manifold (namely, flow rate and sample volume), chemical variables (namely, NaOH and o-cresol concentrations) and temperature was studied using the univariate method on account of their independence on the other hand, those related to US (namely, probe position, radiation amplitude and pulse duration) were the subject of a multivariate study in which the latter two exhibited an insignificant but positive effect. Positioning the probe closest to the extraction coil was found to maximize extraction efficiency. The positive effect of US on extraction and analyte hydrolysis provides the overall enhancement shown in Fig. 6.4A, which shows the results obtained in the presence and absence of US. The time required for the development of the method was significantly shorter than that required by the United States Pharmacopoeia (USP) method. In addition, the latter produces emulsions that need about 30 min for phase separation after extraction. 

The manifold in Fig. 6.2B has been used to develop two methods for the extraction of two analytes from an aqueous phase, with or without a chemical reaction (viz. extraction of Fe(ll) into a dichloromethane/o-phenanthroline phase with the formation of the well-known red complex, and extraction of li into dichloromethane) [16]. Because both chemical systems are well known, chemical and flow-related variables were set at their reported optimum values, and US-related variables (namely, probe position, radiation amplitude and cycle duration) were optimized by using a multivariate approach. The temperature was kept constant throughout the experiments. The results for iodine (Fig. 6.4B) reveal that the presence of US results in poorer extraction of this analyte. On the other hand, those for the water Fe(ll)/o-phenantholine dichloromethane system reveal that the presence of US improves the extraction after several cycles (see Fig. 6.4C) however, the improvement is very slight, so it does not justify the use of ultrasound here. 

Figure 7.12. Plot of parameter K270 as a function of time at a variable US radiation amplitude. 3% ( ), 40% ( ) and 50% ( ). The effect of bubbling air during the oxidation process was studied at a radiation amplitude of 30% (x). (Reproduced with permission of Elsevier, Ref [74].)...

Usually, the sonicator system allows adjustment of the sonication interval, the radiation amplitude and its continuous or intermittent functioning. The optimum values of these three variables depend directly on the particular analyte to be leached and the type of matrix that contains it. 

Either two or more molecular levels of a molecule are excited coherently by a spectrally broad, short laser pulse (level-crossing and quantum-beat spectroscopy) or a whole ensemble of many atoms or molecules is coherently excited simultaneously into identical levels (photon-echo spectroscopy). This coherent excitation alters the spatial distribution or the time dependence of the total, emitted, or absorbed radiation amplitude, when compared with incoherent excitation. Whereas methods of incoherent spectroscopy measure only the total intensity, which is proportional to the population density and therefore to the square ir of the wave function iff, the coherent techniques, on the other hand, yield additional information on the amplitudes and phases of ir. 

Within the density-matrix formalism (Vol. 1, Sect. 2.9) the coherent techniques measure the off-diagonal elements pab of the density matrix, called the coherences, while incoherent spectroscopy only yields information about the diagonal elements, representing the time-dependent population densities. The off-diagonal elements describe the atomic dipoles induced by the radiation field, which oscillate at the field frequency radiation sources with the field amplitude Ak(r, t). Under coherent excitation the dipoles oscillate with definite phase relations, and the phase-sensitive superposition of the radiation amplitudes Ak results in measurable interference phenomena (quantum beats, photon echoes, free induction decay, etc.). 

The phase-factor exp[i q Ri] explicitly gives the phase relative to that of the noninteracting beam. The total radiation amplitude scattered into a given scattering vector ke, that is, a scattering momentum q, is the simple sum over all sites in the sample ... 

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