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The backscattering geometry requires access to the sample cell from only one side, which means that the CCD should be located on the same side of incident laser beam to detect the scattered light. Although the angle between the incident and detected light is not as important as DLS, the location of CCD is still critical, because it is the boundary condition which influences the value of .
The parameter is a constant which reflects the contribution of short non-diffusive light paths to P s
[87, 112]; it plays important role in determination of the value0. Ultimately, as described in Equation(4.18), it affects the result of particle sizing through its influence on the relax time0. It is difficult to calculate because it requires the knowledge of low order scattering processes which is close to sample surface[40, 113]; and the low order scattering principally depends on the parallel polarization of the scattering[112]. So, to determine , the channels not only with perpendicular polarization, but also with parallel polarization should be detected. Some practical approaches have been proposed in previous studies, and the value of was presented. For example, Horne et al.[114] suggested an average value of 2for57
all particle sizes. Weitz et al.[87] experimentally observed that the value varies between 1.5 to 2.7 for various particle sizes and polarizations.
In practice, is found to depend on the actual experiment set-up, such as the detection angel, sample cell and surface reflections[40]. In this experiment, the sample cell and surface reflection was fixed. Therefore, in order to investigate the values of , the detector was located on different position to change the detector angles. Figure 4.9 shows the different CCD locations around the sample cell. The distance between the laser spot on sample cell and CCD camera in the vertical direction is expressed as D and in the horizontal direction d, both with unit of cm.
Figure 4.9 The CCD was placed at various locations to work out different values of γ.
For each experiment, the CCD was placed on a particular position. For each location, pictures were taken and processed to generate the autocorrelation function. Analysing the function and substituting the particle size into Equation(4.18)gives the value of . These values were used to construct a contour figure as shown Figure 4.10, wherethe sample cell was located at the left bottom corner with coordinate of (0, 0). In this graph, the legend with different colours reveals different values of , warm colour denotes high value and cold colour indicates low value. The high values are in the area of D=6-12cm and d=10-16cm, and the low values are on the top of the graph. Figure 4.11is the 3D view of contour map. Although, as shown in Figure 4.10 andFigure 4.11the experiment was carried out in a half field of the backscattering geometry, but it could be determined that the distribution of was identical for the other half field because of symmetrical geometry. From Equation(4.18), it is clearly
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that high value of is associated with slop of the logarithm plotting which represents quick decay. As noted in Weitz et al.[87], long paths decay quickly and short path decays slowly and Equation(4.11) is based on the diffusion approximation and central limit theorem, valid only for long paths. Therefore, the system is calibrated with the highest value of 2for the experiments which was conducted later on. For this particular value, CCD was set at the location marked as L. Hereby, for the DWS experiments, the CCD was positioned at location with D=7.5cm and d=14.5cm, and 2was recommended.
Figure 4.10 The contour plotting of γ.
Figure 4.11 3D view of the contour plotting of γ.
1.63 1.58 1.58 1.45 1.65 1.38 1.23 1.95 1.08 1.73 1.68 1.78 1.33 1.13 1.15 1.52 1.58 1.63 1.55 d(cm) Isolines of Coefficient--Gamma 2.02 1.83 1.93 1.25 1.98 1.8 1.8 1.15 1.6 1.43 1.08 1.7 1.63 0.8 0.85 1.08 1.6 1.58 1.38 0.95 D (c m ) 4 6 8 10 12 14 16 18 20 8 10 12 14 16 18 20 0.8 1 1.2 1.4 1.6 1.8 2 L L
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4.4
Summary
This chapter gives the details of particle sizing using DWS technique and discusses the DWS system calibration.
At first, optical microscope was used for a direct observation of particles under Brownian motion. The particle suspension was mounted to produce the specimen. In a wide image field of DM2500 M optical microscope, particles were observed clearly after the objective magnification and optical magnification. The pictures were taken and displayed on monitor, displaying particles were under Brownian motion.
The high speed CCD camera was set at a frame rate of 100000fps to take particle pictures with a resolution of 12832 pixels. For each experiment, 1572864 frames were collected in a time period of 15.7s. These images were taken in sequence with a time interval of 10-5s. All the pixels were ensemble-averaged to get the intensity correlation functions by the custom- written C++ program. The autocorrelation function was processed, and then g t2
1was plotted against time t. The logarithmically plotting of lng2
t 1against t produced a linear line with slope S. From the Stoke-Einstein relation, particle size can be obtained from2 2 2 2 16 B s n K T R S .
Although the DWS set-up was proved to be reliable, the system calibration was necessary. The frame rate, image resolution and light adsorption were considered in the calibration. Comparison between theoretical data and experimental results, it was found that the impact of absorption was minor and could be ignored. Besides, the parameter which is dependent on boundary conditions was also investigated. The experimental results revealed that in the backscattering geometry the values of depended on the CCD location. High value of appeared to be along paths scattering, and coincided with the diffusion approximation. Therefore, for the subsequent DWS experiments, 2 was used, and the CCD was positioned at the location with D=7.5cm and d=14.5cm.
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