Volume scattering

Model Cell volume (Pi) Scattering volume (nl) Angles (degrees) Laser... 

One of the first approaches to study the microscopic kinetics i.e. state-to-state cross sections and reaction probabilities of a chemical reaction was the crossed molecular beam experiments. The principle of the method consists of intersecting two beams of the reactant molecules in a well-defined scattering volume and catching the product molecules in a suitable detector (Fig. 9.33). 

The beams of reactant molecules A and B intersect in a small scattering volume V. The product molecule C is collected in the detector. The detector can be rotated around the scattering centre. Various devices may be inserted in the beam path, i.e. between reactants and scattering volume and between scattering volume and product species to measure velocity or other properties. The angular distribution of the scattered product can be measured by rotating the detector in the plane defined by two molecular beams. The mass spectrophotometer can also be set to measure a specific molecular mass so that the individual product molecules are detected. 

Since the scattering volume is given by V = AC, where C is the thickness of sample,... 

The point of observation is at a large distance compared with the dimensions of any coherently illuminated scattering volume. 

Quantity used to characterize the scattered intensity at the scattering angle,0, defined as R 6) = ier / If V), where / is the intensity of the incident radiation, iff is the total intensity of scattered radiation observed at an angle 6 and a distance r from the point of scattering and V is the scattering volume. The factor /takes account of polarization phenomena. 

Fig. 1.5.2 Schematic diagrams of aerosol-vapor mixing manifolds. A The aerosol passes through the center tube while the reactant vapor (e.g., water vapor) is introduced through the capillaries (6). B (1) Inner tube for the liquid aerosol tlow, (2) outer tube for the humidified gas (e.g. helium), (3) cross section of the chamber, (4) variable reaction distance (X). (5) light beam. (6) illuminated light scattering volume, (7) light scattering cell. (From Ref. 37.)...

Up to this point we have considered only extinction by a single particle. However, the vast majority of extinction measurements involve collections of very many particles. Let us now consider such a collection, which is confined to a finite volume, the scattering volume. The total Poynting vector is... 

Rather than suspend a particle in the scattering volume for a time sufficient to make a scan with a conventional nephelometer, scattering data can be recorded rapidly during the short time it takes a particle to transit the scattering volume. This can be done in two ways (1) with a rotating detector or aperture (or both), or (2) with an array of fixed detectors. 

Calibration is invariably based on spheres, which means that an instrument can be used with confidence only for such particles. Of course, a response will duly be recorded if a nonspherical particle passes through the scattering volume. But what is the meaning of the equivalent radius corresponding to that response Is it the radius of a sphere of equal cross-sectional area Or equal surface area Or equal volume Or perhaps equal mean chord length Answers to these questions depend on the particular instrument and nonspherical particle comprehensive answers do not come easily because it is difficult to do calculations for nonspherical particles, even those of regular shape. 

The ratio (nl/nl) is the refractive index correction to the scattering volume [42], Equation (12) becomes the following expression [9] ... 

The observed ratio of detector intensities has to be corrected by a few factors in order to obtain the two Rayleigh ratios [10,15-18,41,42], Typical phenomena that must be corrected for are [10,41] (1) scattering volume, (2) refraction correction, (3) reflection correction, (4) absorption, (5) fluorescence, (6) polarization, and (7) sensitivity of photomultiplier. 

The correction of absorption depends on the geometry of the cell and of the scattering volume. Fortunately, in the KMX-6 instrument, the scattering volume is at the center of the cell and the incident and scattered beams are equally attenuated. Consequently the correction of absorption is reduced to the measure of the intensity of the transmitted beam for each concentration. 

The Siegert relation is valid except in the case of scattering volumes with a very small number of scatterers or when the motion of the scatterers is limited. We ignore the exceptions, which are rare in common uses of DLS, and consider only autocorrelations of the type shown in Equation (104). As mentioned above, modern DLS instruments use computer-controlled correlators to calculate the intensity autocorrelation function automatically and to obtain the results in terms of the function gi(s,/rf) therefore we only need to concern ourselves here with the interpretation of gi(s,td). 

Let us proceed to define appropriate coordinate systems (see Fig. 1 and Table 1). We use four different levels of coordinate frames in the averaging procedures of our model construction scheme to describe the molecular arrangement in the scattering volume. On the first level, System M describes the real structure of a segment, whereby the origin is fixed to a well-defined molecular unit System MC (second level) is defined in cylindrical coordinates with the symmetry axis given by the long axis of the rod-like molecular... 

It is these fluctuations that cause the inhomogeneities in the fluid and the reradiated waves. The total amplitude of the electric field at a distance R from the scattering volume is given by the summation of the contributions of the infinitesimal scattering elements and can be expressed as... 

In a standard beating experiment, a photomultiplier tube is used to detect the scattered light. Since the output photocurrent is proportional to the square of the electric field incident upon the tube, it is known as a square-law detector. Thus, if the scattered light contained only two frequencies, as would be the case if only two molecules were in the scattering volume (as in Figure 2), we find the magnitude of the photocurrent i to be... 

The existence of molecules often creates permanent intramolecular optical anisotropy. The optical anisotropy of the liquid is then due to fluctuations in the orientations of the molecules or molecular subunits. If we assign a symmetric traceless anisotropy tensor a to each molecule or molecular subunit in the scattering volume, then the relaxation function for collective optical anisotropy fluctuations can be expressed as... 

---