Attenuation spectrum

Two models are available for interpreting attenuation spectra as a PSD in suspensions with chemically distinct, dispersed phases using the extended coupled phase theory.68 Both models assume that the attenuation spectrum of a mixture is composed of a superposition of component spectra. In the multiphase model, the PSD is represented as the sum of two log-normal distributions with the same standard deviation, that is, a bimodal distribution. The appearance of multiple solutions is avoided by setting a common standard deviation to the mean size of each distribution. This may be a poor assumption for the PSD (see section 11.3.2). The effective medium model assumes that only one target phase of a multidisperse system needs to be determined, while all other phases contribute to a homogeneous system, the so-called effective medium. Although not complicated by the possibility of multiple solutions, this model requires additional measurements to determine the density, viscosity, and acoustic attenuation of the effective medium. The attenuation spectrum of the effective medium is modeled via a polynomial fit, while the target phase is assumed to have a log-normal PSD.68 This model allows the PSD for mixtures of more than two phases to be determined. 

Ultrasonic Spectroscopy. Information on size distribution maybe obtained from the attenuation of sound waves traveling through a particle dispersion. Two distinct approaches are being used to extract particle size data from the attenuation spectrum an empirical approach based on the Bouguer-Lambert-Beer law (63) and a more fundamental or first-principle approach (64—66). The first-principle approach impHes that no caHbration is requited, but certain physical constants of both phases, ie, speed of sound, density, thermal coefficient of expansion, heat capacity, thermal conductivity. 

Riebel and Ldffler [240] obtained an acoustic attenuation spectrum with one transducer pair to infer the particle size distribution. Solids concentrations and particle size distribution were obtained using both the Phillips-Twomey algorithm (PTA) and the relaxation method. The PTA gives a least squares solution by simple linear matrix operations to yield a numerical inversion from the attenuation spectra to the size distribution... 

Remembering that ultrasonic spectroscopy measures the frequency spectrum of sound attenuation of suspensions from 0.01 pm to 1000 pm [3], the more difficult question (that cannot be answered here) will be how are the difftaction pattern and the attenuation spectrum related to size parameters of fttmed powders ... 

Attenuation spectra measured in the first run up to if = 80 are presented in Fig. 13. The results for if = 90 and R = 100 are not reported because fliey were found to vary appreciably. As the water concentration is increased, the attenuation spectrum rises in intensity and there is a distinct jump in the attenuation spectrum from if = 5- to if = 60 in the low-frequency range. This discontinuity is also reflected in the visual appearance, as at if = 60 the system becomes turbid. The smooth shape of the attenuation curve also... 

At R = 10 the acoustic method gave a slightly larger diameter than expected. This could be as a result of the constrained state of the bound water in the swollen reverse micelles. The water under these conditions may exhibit different thermal properties from those of the bulk water used in ttie particle size calculations. Also, at the low R values R< 10 or < 2.4% water), the attenuation spectrum is not very large as compared to the background heptane signal. 

The contribution of droplets to the attenuation spectrum then may become too low to be reliably distinguished from the background signal coming from heptane molecules and AOT micelles. 

Developed particles of AgHal-porous glass medium-composite, like those of AgHal film plates, represent particles of recovered metallic silver of colloid structure. Fig. 4a ptresents attenuation spectra of developed film plates PFG-03 (curve 1) and AgHal-PG (curve 2) after development to formulation PRG-1 so as to obtain developed silver particles of colloid structure. Curve 3 represents attenuation spectrum of diluted water preparation of Ag-PG sample of type 2, which is dispersed (powdered) and spread in water solution. 

In colloidal suspensions, the sound propagation is typically governed by the acoustophoretic motion of particles. For monodisperse spheroids that do not deviate too much from spherical shape (aspect ratio <10/1), the attenuation spectrum essentially reflects the volume specific surface area of the particles (Babick and Richter 2006). Similar results would probably be obtained for any convex particle shape. For particle aggregates, the inner structure is decisive. Regarding the type of quantity, acoustically measured size distributions are ideally volume weighted distributions (see comments in Sect. 2.2). 

In 2012, the first PSt-based GI POP was reported [20]. The fiber was obtained by preform-drawing and rod-in-tube methods. Its attenuation spectrum is shown in Figure 4.6 alongside that of the PMMA-based GI POF. The wth overtones of the aliphatic and aromatic C-H bonds are labeled as v and v, respectively. The attenuation of the PSt-based GI POF is 166-193 dB/km at 670-680 nm, which is significantly lower than the attenuation of the PMMA-based GI POF in the same region ( 240-270 dB/km). 

Figure A.10 Attenuation spectrum of PSt-based SI POF. Vg and v correspond to absorption wavelengths of aliphatic and aromatic C-H bonds, respectively. Shoulders in the region of lower wavelength of each...

---