095 Small angle X-ray scattering (SAXS) analysis of
nanoparticle size distribution -- dividing distribution function
(DDF) method and its verification
Weiguo Chu1 Jinyuan Zhang2 , Jianfeng Fang 2
1
The National Center for Nanoscience and Technology (NCNST) of China, Zhongguancun
NorthFirst Street No.2, 100080 Beijing, PR China wgchu@nanoctr.cn
2Central
Iron & Steel Research Institute, No.76 Xueyuan Nanlu, Haidian district Beijing,
P.R.China,100081
ABSTRACT
A dividing distribution function (DDF) method is proposed to evaluate nanoparticle size
distributions from small angle X-ray scattering (SAXS) data. The DDF method was
theoretically derived from the basic principle of SAXS. The integration equation between
scattering intensity and weighted particle size distribution function is transformed into a set of
linear equations through DDF method. The optimization of the coefficient matrix has been
also obtained. As a consequence, the continuous size distribution of nanoparticles, if so, will
be expressed as histograms. The DDF method is believed to have an apparent advantage
over other distribution function methods in SAXS in that the exact distribution function of
nanoparticle sizes is unnecessarily known a priori. Also, the DDF method has been
experimentally verified by TEM, PSC, Zeta potential methods. With the DDF method, size
distribution analysis has been successfully making on a number of different types of
nanoparticles such as metals, ceramics, polymers, suspension and so on. Detailed
comparison with other characterization methods for particle size is presented as well, and
nice agreement is obtained. Most importantly, SAXS data give the information on size
distributions of primary particles, even though the sample is not well dispersed, and the test
result is representative in statistics because of SAXS signals coming from a great number of
particles (~1010). The method is considered to be increasingly attractive to the international
community of nanotechnology.
Keywords: SAXS, nanoparticle, dividing distribution function (DDF)