Scattering intensity, time-averaged

In static light scattering only the time average of the scattered intensity is recorded, while DLS measures the scattered intensity with a time resolution of milliseconds or even tenths of nanoseconds. These fluctuations in the scattered intensity can be related to dynamical processes within the sample. 

A variant of the zero average contrast method has been applied on a solution of a symmetric diblock copolymer of dPS and hPS in benzene [331]. The dynamic scattering of multicomponent solutions in the framework of the RPA approximation [324] yields the sum of two decay modes, which are represented by exponentials valid in the short time limit. For a symmetric diblock the results for the observable scattering intensity yields conditions for the cancellation of either of these modes. In particular the zero average contrast condition, i.e. a solvent scattering length density that equals the average of both... 

First, the shear layer thickness at various axial locations in the near field was quantified using time-averaged Mie-scattering images. The shear layer thickness was defined as the radial distance over which the average Mie-scattering intensity dropped from 90% to 10% of the core value. Figure 29.7 shows the results... 

We have focused on only the static (i.e., the time-averaged) measurements of intensities so far. However, one can also obtain the dynamic structure factor (i.e., as a function of time) from scattering experiments. The dynamic structure factor can then be used as a probe of the rheological behavior of the dispersions discussed in Chapter 4. 

Y ratio of the ensemble average to time average of the scattered intensity... 

Figure 4. Polymerization of GA induced by amine observed by light scattering. The normalized scattering intensity at a right angle, which is virtually equivalent to the average polymerization degree of GA under the conditions used here, is plotted against the time after the addition of amine to GA solution.

As long as the concentration of the small molecule is low (<5%), the scattered intensity due to concentration fluctuations will be negligible relative to the density or anisotropy fluctuations. In polystyrene, the HV spectrum will not have any contribution due to concentration fluctuations, but in principle there could be a contribution due to the diluent anisotropy. The average relaxation time will be determined by the longest time processes and thus should reflect only the polymer fluctuations. The data were collected near the end of the thermal polymerization of styrene. Average relaxation times were determined as a function of elapsed time during the final stages of the reaction... 

The methods of analyzing data for the concentration and angular dependence of the time-average scattering light intensity and the intensity-intensity time correlation function can be found in many LLS books and related literature. In this section, we will mainly concern ourselves with how to combine static and dynamic LLS results to characterize special polymers in regard not only to the average molar mass, but also to the molar mass and composition distributions. 

G (t) is a time average of the scatter intensity at time t, I(t), times the intensity at a time t later, or I (t + x) where x is on the order of msec or jxsec. The autocorrelation function is determined by the Coulter Model N4 for a number of values of x simultaneously, and the data is plotted as G (x) versus x. If the particles in the liquid are the same size and shape (i.e., spherical), and hence monodisperse, the curve of the autocorrelation function of the scattered light intensity is a single decaying exponential ... 

In static LLS [43], the angular dependence of the excess absolute time-averaged scattering intensity, known as the Rayleigh ratio Rw(< )> is measured. For a dilute solution measured at a relatively small angle (6), Rw(q) can be related to the weight average molar mass (Mw), the root mean square... 

Fig. 16. Apparent average hydrodynamic diameter (upper curves) and total scattering intensity in arbitrary units (lower curves) as a function of time following the addition of chymosin ( ) or controls (O). From Walstra et al. (1981), reproduced with permission.

---