Particle scattering beads

Figure 4.10. Theoretical dependence of translational diffusion coefficient of rods on location of bends. Theoretical relationships shown between translational diffusion coefficient (a), particle scattering factor at a scattering angle of 175.5° (b), and bend angle obtained using bead model with bends at ID and 2D from the end. Points above horizontal lines shown for D o,w and P(175.5°) are significantly different from those values for a straight rigid rod. The total rod length is 4.41). (reproduced from Silver, 1987).

The Mazur function can be used to calculate R ) and (R ) (n = 2,3,...), but its usefulness extends no more than that. Calculation of such important global polymer properties as mean-square radius of gyration, particle scattering function, intrinsic viscosity, and diffusion coefficient needs an analytical expression for l+,j(R), the distribution function for the distance R between specified beads i and j. We find no a priori reason for this function to be approximated by the Mazur function. Knowledge about Wij has increased in recent years mainly on the basis of computer simulation experiments. Some of the typical results from such work are described below. 

Figure 4.16. Relative particle scattering intensity over the solid angular range 5°-10 at X = 650 nm and rio= 1.0. Bottom solid curve m = 1.2-0/ top solid curve m = 1.5-0/ and solid curve with beads m = 1.5-0.5/. ...

Fig. 9.9 depicts some of the results from such trials. Despite some scatter in the angle range 95°-105°, it is readily seen that at 9< 95° none of the films ruptures, while at 0> 105° all the films rupture. Experiments with suspensions of solid particles (Teflon, hydrophobed glass beads and ground glass) showed that in the case of smooth particles, the defoaming... 

The radius of the spherical particle is r, and the relative refractive index, n, is the ratio (npln0) of the refractive index for the particle (np) to that of the suspending media (nc). As seen in Figure 11.1, particles with higher refractive indices scatter light more efficiently. The refractive index of polystyrene beads (1.6), generally used... 

As the aggregated particles become larger than 300 nm, other techniques become necessary for their detection. One useful option is that of dynamic hght scattering (DLS), which also provides size information based on the diffusivity (and can be calibrated with polystyrene beads). The DLS analysis of a non-aggregated and an aggregated virus preparation is shown in Fig. 6.6. 

For water analysis, the formulation of turbid standards is very difficult, so most water laboratories use a synthetic pol5mer suspension as a standard. The formazin polymer suspension is easy to make and more stable and reproducible than adding clay or other particles to water to prepare standards. Alternatively, suspensions of polymer beads of the appropriate size can be used as scattering standards. (See Standard Methods for the Examination of Water and Wastewater for details.)... 

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