particle accuracy, and ease of use. The

Such an instrument consists of at least one source of high intensity, monochromatic 
light, a sample handling system to control the interaction of particles and incident 
light, and an array of high quality photodiodes to detect the scattered light over a 
wide range of angles. This last piece is the primary function of a laser diffraction 
instrument: to record angle and intensity of scattered light. This information is then 
input into an algorithm which, while complex, reduces to the following basic truth:
The algorithm, at its core, consists of an optical model with the mathematical 
transformations necessary to get particle size data from scattered light. However, 
not all optical models were created equally. 
THE IMPORTANCE OF OPTICAL MODEL
In the beginning there was the Fraunhofer Approximation and it was good. This 
model, which was popular in older laser diffraction instruments, makes certain 
assumptions (hence the approximation) to simplify the calculation. Particles are 
assumed:
•
to be spherical
•
to be opaque
•
to scatter equivalently at wide angles as narrow angles 
•
to interact with light in a different manner than the medium
Practically, these restrictions render the Fraunhofer Approximation a very poor 
choice for particle size analysis as measurement accuracy below roughly 20 microns 
is compromised.
The Mie scattering theory overcomes these limitations. Gustav Mie developed a 
closed form solution (not approximation) to Maxwell’s electromagnetic equations for 
scattering from spheres; this solution exceeds Fraunhofer to include sensitivity to 
smaller sizes (wide angle scatter), a wide range of opacity (i.e. light absorption), and 
the user need only provide the refractive index of particle and dispersing medium. 
Accounting for light that refracts through the particle (a.k.a. secondary scatter) 
allows for accurate measurement even in cases of significant transparency. The Mie
theory likewise makes certain assumptions that the particle:
•
is spherical
•
ensemble is homogeneous
•
refractive index of particle and surrounding medium is known
Figure 18 shows a graphical representation of Fraunhofer and Mie models using 
scattering intensity, scattering angle, and particle size (ref. 13). The two models 
begin to diverge around 20 microns and these differences become pronounced 
below 10 microns. Put simply, the Fraunhofer Approximation contributes a 
magnitude of error for micronized particles that is typically unacceptable to the 
user. A measurement of spherical glass beads is shown in Figure 19 and calculated 
using the Mie (red) and Fraunhofer (blue) models. The Mie result meets the material 
specification while the Fraunhofer result fails the specification and splits the peak.
The over-reporting of small particles (where Fraunhofer error is significant) is a
typical comparison result.
figure 18
|
REPRESENTATIONS OF
FRAUNHOFER (TOP) AND MIE
SCATTERING MODELS
Angle, energy and size are used
as parameters in these examples.
figure 19
|

tải về 7.54 Mb.

Chia sẻ với bạn bè của bạn: