INDEX sound velocities

In principle any physical constant may be useful for structural analysis of mixtures. For practical reasons those constants should be applied that can be easily determined. High demands should be made upon the accuracy of the determinations. For example the physical constants density, refractive index, kinematic viscosity, ultrasonic sound velocity and surface tension may be chosen. Combination of constants, e.g. in certain additive functions, is useful only when the constants in question have been determined with comparable accuracy. In this respect density and refractive index may be combined, whereas molecular weight, the determination of which is not so precise, cannot always be combined with refractive index and density. 

Fig. 45. Log v-n diagram for the determination of the ultrasonic sound velocity and the surface tension of saturated mineral oil fractions from their viscosity and refractive index.

Figure 2.20. Right part The polariton dispersion at a few tens of reciprocal centimeters below the bottom of the excitonic band, vs the wave vector, or the refractive index n = ck/w (notice the logarithmic scale). The arrows indicate transitions with creation of one acoustical phonon, with linear dispersion in k (with a sound velocity of 2000 m/s). For the transitions T, Tt, T3 the final momentum is negligible compared to the initial momentum, and the unidimensional picture suffices. For the transitions between T3 and the point A, the direction of the final wave vectors should be taken into account. Left part The density of states m( ) (2.141) of the polaritons in the same energy region. This diagram explains why the transitions T, will be much slower than the transitions around T3 and the point A. The very rapid increase of m( ) at a few reciprocal centimeters below E0 shows the effect of the thermal barrier.

Over 50 methods have been employed in the literature to determine CMC values of bile salt solutions (reviewed in [6]). These can be divided into two broad categories (a) methods requiring no physical or chemical additive in the bulk solution and (b) methods involving the use of an additive in the bulk solution. The former methods, also called non-invasive, include surface tension and the measurements of a variety of colligative bulk properties (conductivity, turbidimetry, osmometry, self-diffusion, refractive index, modal volumes, electrometric force) or electromagnetic bulk properties (NMR, sound velocity and adsorption, etc.), all as functions of bile salt concentration. The second set of methods, also called invasive, depends upon a change in some physical or chemical property of an additive which occurs with the formation of micelles. These include the spectral change of a water-soluble dye, micellar solubilization of a water-insoluble dye, interfacial tension at liquid-liquid interfaces, and partition coefficients between aqueous and immiscible non-polar phases. Whereas a detailed discussion of the merits and demerits of both approaches can be found elsewhere [6], non-invasive methods which are correctly utilized provide the most reliable CMC values. 

Mach number = ratio of velocity to the local sound velocity general index dimension of state vector polytropic index of gas expansion... 

In BS, the energy transfer between photons and phonons is very small (5x10 Hz/5xl0 " Hz=10 ) and hence ki and ks have the same length. Provided, acoustic attenuation is small (Tosc f2) the phase-sound velocity can be calculated from simple geometric arguments. Equations (15, 16) yield Eq. (17), where n is the refractive index of the sample, for the sound velocity v for the longitudinal mode. Equivalent equations hold for other polarizations. 

Fortunately, there exists the 90A-scattering geometry (see Fig. 9.2 b) which leaves the acoustic wave vector independent of the refractive index (for isotropic samples). For the scattering geometries shown in Fig. 9.2, the relationships between the sound velocity, the sound frequency, and the sound wavelength are given by Eqs. (20, 21, 22) respectively, with sin(qi/2) and v °(T) defined in Eqs. 

Thus, the choice of an incident radiation Aj defines k , whereas the choice of a scattering angle (usually 90° or 180") unambiguously determines and, henceforth, the Brillouin shifi related to each of the three acoustic modes with their own velocities. Typically, for an incident visible radiation, and a material characterized by an index of refraction about 1.5 and sound velocities of a few km/s, the Brillouin shift lies in the range of 10-30 GHz (0.33-1 cm ) in backscattering geometry. Obviously, the study of Brillouin lines requires a more consequent resoiution than the one of a conventional Raman spectrometer. 

Often an acousto-optic switch is used, for example, for argon lasers and cw dye lasers [648]. Its basic principle is explained in Fig. 6.6. A short ultrasonic pulse with acoustic frequency / and pulse duration T 1 //s is sent nit = to through a fused quartz plate inside the laser resonator. The acoustic wave produces a time-dependent spatially periodic modulation of the refractive index n(t,z), which acts as a Bragg grating with the grating constant A = Cs//, equal to the acoustic wavelength A where Cg is the sound velocity. When an optical wave Eocos((ot — k r) with the... 

J. Comely, C. Rogers, V.P. Manno, A. Philipossian, In situ temperature measurement during oxide chemical mechanical planarization, Mater. Res. Soc. Symp. Proc. 767 (2003). From Densitrak website at http //www.densitrak.com/index.php/products/anal)dical-flow-technologies-llc-densitrakandreg-d625-a0-00-01/ (last accessed November 2014). From Anton Parr website at http //www.anton-paar.com/us-en/products/details/density-and-sound-velocity-meter-dsa-5000-m/density-meter/ (last accessed November 2014). 

The critical micellar concentration of any detergent may be determined by a number of different methods, including the solubilization of insoluble dye, osmotic pressure, conductivity, surface tension, light scattering, nuclear magnetic resonance, refractive index, freezing point determination, vapor pressure, sound velocity, etc. (141). Each method may give a somewhat different value for CMC. 

Figure 5-1 shows that the longitudinal phonon velocity vl(p) decreases with decreasing p (increasing fco)- Note that the frequency shift of the peak is not completely due to the change of the sound velocity. In fact, also the refractive index changes with the density. Its value is well approximated by an interpolation between the refractive index of bulk silica... 

Figure 5-8. Upper left-hand side frame Refractive index profile at 514.5 nm of a three-layered Si02-Ti02 planar waveguide. Left-hand side column Calculated squared electric-field patterns of the five TE modes. Right-hand side column BriUouin experimental spectra (open circles), calculated spectra (dotted line), and convolution of the calculated spectra with the instrumental response (solid line). The longitudinal sound velocity used in the fit is vi = 5.9 km/s,for m= 0,1, 2, and 3, and Pl = 5.75 km/sjbr m = 4 (Chiasera, 2003b).

Figure 4.6. Variation of the sodium dodecyl sulfate CMC at temperatures between 20 and 30 C as obtained by various experimental methods. a, specific conductivity b, equivalent conductivity c, other conductance d, surface tension versus logarithm of concentration e, other relationships between surface tension and concentration f, absorbance g, solubilization h, light scattering i, other methods such as refractive index, emf, vapor pressure, sound velocity, and viscosity.

In fact, aerogels consist of a thin amorphous solid matrix network surrounded by nanoscale-sized pores, and therefore, they are reasonably described as transparent, highly porous, open-cell, extremely low-density materials. This extraordinary structure provides silica aerogels a variety of unique properties. For example, low thermal and electrical conductivity are a result of the low thermal conductivity of silica and nanometer pores sizes. The low thermal conductivity and other optical properties make them desirable for many applications. For example, they can be an attractive alternative in insulating applications, due to their high insulating value and environment-friendly production methods. They also possess low refractive index, low sound velocity, and low dielectric constant. 

In the field of cryogenics, as in many other phases of science and industry, the accurate measurement of temperature is a very critical matter. The measurement of temperature, however, is more difficult to accomplish than the measurement of many of the other physical properties of a substance. Unlike properties such as volume or length, temperature cannot be measured directly. It must be measured in terms of another property. Some of the physical properties that have been utilized include pressure of a gas, equilibrium pressure of a liquid with its vapor, electrical resistance, thermoelectric emf, magnetic susceptibility, volume of a liquid, length of a solid, refractive index, and velocity of sound in a gas. In addition, there are thermometers that respond to a temperature-dependent phenomenon rather than to a physical property. Included in this category are the optical pyrometer and the electrical noise thermometer. 

The sound velocity determination using the 90N-, 90R-, and 180-scattering geometries requires the knowledge of the refractive index, n, of the sample. For temperatures other than room temperature, the refractive indices of polymer specimens are often unknown. Usually the correct values are approximated by the room temperature values. Since the temperature coefficients of the refractive indices are on the order of 10 /K for many polymers, a temperature change of about 5 K produces a systematic error comparable with the sound frequency reproducibility of modem Brillouin spectrometers. Therefore, the omission of the temperature dependence on die refractive index is unacceptable for accurate investigations. 

Fig. 7. Sketch of the typical behavior of physical properties at The symbols indicated at each curve are V, sound velocity Gruneisen parameter c/ , elastic modulus 8, density n, refractive index ct, thermal expansion coefficient Cp, specific heat t], dynamic viscosity and Tj, longitudinal relaxation time.

At very low frequencies the movement of the panel will be controlled by the stiffness, as inertia is a dynamic force and cannot come into effect until the panel has measurable velocity. Stiffness controls the performance of the panel at low frequencies until resonance occurs. As the driving frequency increases, the resonance zone is passed and we enter the mass-controlled area. The increase in the sound-reduction index with frequency is approximately linear at this point, and can be represented by Figure 42.8. 

Evaluations of Rd and Y necessitate a knowledge of certain physical properties of the two liquids and the mixtures. The variation of refractive index with concentration is measured readily by refractometry, if I nT, — n21 is large. The coefficient of isothermal compressibility of a mixture t2 requires specialised equipment. Alternatively, it can be determined from the heat capacity and the coefficient of isentropic compressibility87, 88, the latter being yielded from velocity of sound data88. However, provided and 02 for the pure compounds are known, j312 is evaluated most conveniently on the basis of additivity, thus ... 

A f Frontal area of the bubble, cm2 b Dimensionless index B Substitution given in the text c Dimensionless index velocity of sound in the gas, cm/sec C Substitution given in the text proportionality constant [Eq. (108) chamber capacitance [Eq. (166)]... 

Colorless gas characteristic odor of rotten eggs odor threshold Ippm sweetish taste fumes in air flammable gas, bums with a pale blue flame refractive index at 589.3nm, 1.000644 at 0°C and 1 atm density 1.539 g/L at 0°C critical temperature 100.4°C critical pressure 88.9 atm liquefies at -60.7°C solidifies at -85.5°C velocity of sound 289 m/sec in H2S gas slightly soluble in water (0.4% at 20° C) pH of a saturated aqueous solution 4.5 slightly acidic diffusivity in water at 16°C, 1.77x10 cm /sec soluble in carbon disulfide, methanol, acetone very soluble in N-methylpyrrolidinone and alka-nolamines (salt formation occurs salt dissociates on heating) liquid H2S dissolves sulfur and SO2. 

We recall that c is the velocity of the molecules. The index on v means that we calculate the number of collisions necessary for reaction in the part of the zone where the reaction rate is highest and conditions are most conducive, so that i/min is the minimum value of v. Finally, tp is a dimensionless quantity of order (but less than) unity, algebraically (but not exponentially) dependent on the reaction mechanism, the activation heat, the temperatures T0 and TB, and the reagent concentrations. From the formula it is obvious first of all that u is always many times smaller than c, and less than the speed of sound. This fact will be important for the theory of detonation (Part II). 

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