ABSTRACT

The properties of complex particle systems typically depend on multivariate distributions of particle properties, like size and shape characteristics. Multidimensional particle property distributions can be a powerful tool to describe these systems. However, only few techniques exist which are able to simultaneously measure more than one property of individual particles in fast and efficient ways. It is shown how two-dimensional property spaces can be constructed by the combination of two univariate measurements to obtain bivariate particle size distributions. The proposed method is a general approach, which can be applied to a wide spectrum of particle systems and measurement devices. In this paper, the results of a case study are presented, which allow the estimation of bivariate distributions of length and diameter of nanorods, solely using univariate distributions of their particle mass and extinction-weighted sedimentation coefficient distributions. These quantities contain joint information about the particle lengths and diameters, which is used for the reconstruction. The method is validated in a simulation study in which the bivariate distribution to be reconstructed and the reconstruction parameters are varied. In addition, regularization techniques are introduced to reduce methodical errors. This approach can be transferred to other particle systems and measurement techniques, for which functional relationships between particle properties and measured quantities are well described.

摘要

复杂粒子系统的属性通常取决于粒子属性（如大小和形状特征）的多元分布。多维粒子属性分布可以是描述这些系统的强大工具。然而，仅存在极少数能够以快速且有效的方式同时测量单个颗粒的不止一种性质的技术。它显示了如何通过两个单变量测量值的组合来构造二维属性空间以获得双变量粒度分布。所提出的方法是一种通用方法，可以应用于各种粒子系统和测量设备。本文介绍了一个案例研究的结果，可以估算纳米棒的长度和直径的二元分布，仅使用其颗粒质量的单变量分布和消光加权沉降系数分布。这些量包含有关粒子长度和直径的联合信息，该信息用于重建。该方法在仿真研究中得到验证，在仿真研究中，要重构的双变量分布和重构参数均发生变化。另外，引入了正则化技术以减少方法错误。这种方法可以转移到其他粒子系统和测量技术中，对于它们的粒子特性和测量量之间的功能关系已经很好地描述了。这些量包含有关粒子长度和直径的联合信息，该信息用于重建。该方法在仿真研究中得到验证，在仿真研究中，要重构的双变量分布和重构参数均发生变化。另外，引入了正则化技术以减少方法错误。这种方法可以转移到其他粒子系统和测量技术中，对于它们的粒子特性和测量量之间的功能关系已经很好地描述了。这些量包含有关粒子长度和直径的联合信息，该信息用于重建。该方法在仿真研究中得到验证，在仿真研究中，要重构的双变量分布和重构参数均发生变化。此外，引入了正则化技术以减少方法错误。这种方法可以转移到其他粒子系统和测量技术中，对于它们的粒子特性和测量量之间的功能关系已经很好地描述了。