Polymers 2022 , 14 , 3309
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with low refractive index [43] and applicable when the region of study is much larger than the primary particles and is much smaller than the floc aggregates (Equation (3)) [45].
1/R agg <<q<<1/R part
(3)
R agg is the radius of the aggregate and R part is the radius of the primary particle. For systems where the flocculation is very pronounced and the size of the flocs (secondary aggregation resulting from the aggregation of primary flocs) falls out of the applicability range of the RGB theory, the information about the flocs is provided by the scattering exponent (SE) [43,46]. The SE corresponds to the negative slope of the log-log plot of the scattered light intensity, versus q at large length-scales (low diffraction angles). In short, structural information about the flocs in a certain system can be obtained fromthed F for small-length scales (high diffraction angles) and from SE for high-length scales (small diffraction angles), as exemplified in Figure 2, corresponding to the primary and secondary aggregates, respectively.
Figure2. Example of the log-log plot of scattering light intensity versus q for the determination of the scattering exponent, SE (first region), and the fractal dimension, d F (second region). The structural information (d F and SE) of the flocs that were formed in the second flocculation study (best-performing samples) was obtained by outputting the raw data of the LDS equipment to an external spreadsheet (provided by Malvern Instruments) for the offline analysis of the data and for computing the angle of each detector and the intensity of light at each detector. Making use of Equation (2), the data was further computed into log-log plots of scattered light intensity versus the scattering wave vector (q) (Figure 2), when either d F or SE could be obtained. 2.6. Drainability and Retention Tests Drainability and retention tests were performed with the commercial CPAM and the cationic celluloses that presented the best performance in the LDS flocculation tests. Before carrying out the drainage tests, suspensions of the different required compo- nents were prepared. The same BEKP (presenting a refining degree of 17 ◦ SR) that was used to prepare the cationic celluloses was used for the drainability tests in the form of a 1 wt % solids content suspension. The PCC was prepared as a 1 wt % solids content suspension. The commercial CPAM and the produced cationic celluloses were prepared as 0.1 wt % solu- tions/suspensions (as described previously for the flocculation tests).
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