Fractal and Rayleigh particle scattering for size determination

An established method for the determination of soot particle size distribution function is the combined use of optical measurements and analytical deconvolution techniques. Two problematical assumptions are commonly used with this approaches. First, the soot particles are assumed to be spherical, and Mie scattering theory is used to describe the particle-radiation interaction. The second assumption is that no small particle size distribution peak exists below the measurement sensitivity limit of Mie scattering and that the number distribution monotonically goes to zero as the size approaches zero.

To investigate the first assumption, the soot particles were assumed to be of fractal morphology in the Mie region, and the cross sections of the optical interactions with fractals were studied. The second assumption was evaluated by the cryodeposit collection of soot particles from a flame source, subsequent centrifugation of the melted sample, and optical analysis using diffusion broadening spectroscopy.

The scattering behavior of fractal objects was studied using two independent methods (Diffusion Limited Aggregation 4- Discrete Dipole Approximation and Structure Factor -f- Mean Field). Based on the scaling nature of fractal cluster N ~ r^D, the concept of a continuously variable dimensionality was developed and the structure factor S_D(q) was developed. S_D(q) elucidates the scattering behaviors, regimes and boundaries very well and leads to the famous Guinier law and Porod law at small-q and large-q respectively. Also, S_D(q) recovers integer dimensional structure factors if the Hausdorff dimension D is an integer number and furthermore S_D(X) connects the Euclidean geometry and fractal geometry. This approach also explains previous research results of other investigators. According to the results of this work, the critical size parameter XX_c. = 0.2 is a lower limit for the validation using static light scattering (SLS). If XX < 0.1 then the SLS is totally invalid because the Rayleigh scattering is independent of the scattering angle. Neither the fractality (structure dimension) nor the size can be distinguished in Rayleigh regime.

To determine the presence of particles for which XX < 0.1, dynamic light scattering (DLS) was utilized, and the use of DLS for the study of log-normal distributions was explored. Particles from a flame were collected in a cryodeposit, melted, centrifuged and separated by size, and DLS was used to investigate the possible existence, mean size, width and number of Rayleigh particles whose concentration exceeded the log-normal function prediction, because the size parameter(~ 0.3) of soot particle is very close to the XX_c in the visible light range. The theoretical foundations of DLS and lognormal distribution are discussed carefully. A new method of collecting particles to liquid is proposed and employed successfully. Some necessary calculations are given to estimate the efficiency and distortion of the collection. Finally we combine DLS, extinction, and centrifuge sedimentation methods to measure the size , number density N, and distribution width σ.