Lambert S, Moustier S, Dussouillez Ph, Barakat M, Bottero J Y, Le Petit J, Ginestet P
CEREGE, UMR 6635 CNRS/Aix-Marseille III, Europôle de l'Arbois BP 80, 13545 Aix-en-Provence cedex 05, France.
J Colloid Interface Sci. 2003 Jun 15;262(2):384-90. doi: 10.1016/S0021-9797(03)00167-X.
This work aims at developing a more accurate measurement of the physical parameters of fractal dimension and the size distribution of large fractal aggregates by small-angle light scattering. The theory of multiple scattering has been of particular interest in the case of fractal aggregates for which Rayleigh theory is no longer valid. The introduction of multiple scattering theory into the interpretation of scattering by large bacterial aggregates has been used to calculate the fractal dimension and size distribution. The fractal dimension is calculated from the form factor F(q) at large scattering angles. At large angles the fractal dimension can also be computed by considering only the influence of the very local environment on the optical contrast around a subunit. The fractal dimensions of E. coli strains flocculated with two different cationic polymers have been computed by two techniques: static light scattering and confocal image analysis. The fractal dimensions calculated with both techniques at different flocculation times are very similar: between 1.90 and 2.19. The comparison between two completely independent techniques confirms the theoretical approach of multiple scattering of large flocs using the Mie theory. Size distributions have been calculated from light-scattering data taking into account the linear independence of the structure factor S(q) relative to each size class and using the fractal dimension measured from F(q) in the large-angle range or from confocal image analysis. The results are very different from calculations made using hard-sphere particle models. The size distribution is displaced toward the larger sizes when multiple scattering is considered. Using this new approach to the analysis of very large fractal aggregates by static light multiple scattering, the fractal dimension and size distribution can be calculated using two independent parts of the scattering curve.
这项工作旨在通过小角光散射开发一种更精确的方法来测量分形维数和大型分形聚集体的尺寸分布等物理参数。在分形聚集体的情况下，多次散射理论一直备受关注，因为瑞利理论在此不再适用。将多次散射理论引入对大型细菌聚集体散射的解释中，已被用于计算分形维数和尺寸分布。分形维数是根据大散射角处的形状因子F(q)计算得出的。在大角度下，分形维数也可以通过仅考虑非常局部的环境对亚基周围光学对比度的影响来计算。用两种技术计算了用两种不同阳离子聚合物絮凝的大肠杆菌菌株的分形维数：静态光散射和共聚焦图像分析。在不同絮凝时间用这两种技术计算出的分形维数非常相似：在1.90至2.19之间。两种完全独立的技术之间的比较证实了使用米氏理论对大型絮凝物进行多次散射的理论方法。已根据光散射数据计算尺寸分布，其中考虑了结构因子S(q)相对于每个尺寸类别的线性独立性，并使用在大角度范围内从F(q)或通过共聚焦图像分析测量的分形维数。结果与使用硬球粒子模型进行的计算有很大不同。当考虑多次散射时，尺寸分布向更大尺寸偏移。使用这种通过静态光多次散射分析非常大的分形聚集体的新方法，可以使用散射曲线的两个独立部分来计算分形维数和尺寸分布。
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