4302 動態光散射儀 (Dynamic Light Scattering) 代工實例與結果解析 生醫暨非破壞性分析團隊 2016.10 updated
Which Size to Measure? Diameter Many techniques make the useful and convenient assumption that every particle is a sphere. The reported value is typically an equivalent spherical diameter. Vertical Projection Horizontal Projection Although this approach is simplistic and not perfectly accurate, the shapes of particles are such that the spherical assumptions doesn t cause problems. Problems can arise if the particles have a very large aspect ratio, such as fibers or needles. Fig 1 2
Intensity/ Number/ Volume Distribution Graphs Dynamic light scattering (DLS) is based on photon correlation spectroscopy technique and directly measures intensity (weighted) size distribution. The DelsaNano measures intensity distributions and optionally converts them to volume or number distributions. The following figure (Figure 2) shows the same standard sample but in 3 different ways of distribution (intensity/volume/number). 3
Which Size is Correct? Delsa Nano User s Manual Differential Intensity Distribution Differential volume Distribution Differential number Distribution Fig 2 In short, the answer to the dilemma is: The intensity result is always correct, so in most cases that should be the one chosen. Preferably the intensity as those data are closest to what is really measured without any additional assumption. 4
Particle size result interpretation: Number vs. Volume distribution Diameter= 1µm Volume= 0.52µm 3 % By Volume= 0.52/18.8 = 2.8% Diameter= 2µm Volume= 4.2µm 3 % By Volume= 4.2/18.8 = 22% Diameter= 3µm Volume= 14.1µm 3 % By Volume= 14.1/18.8 = 75% As an example, consider the nine particles shown in figure 3, three particles are 1μm, three are 2μm, and three are 3μm in size (diameter). Total Volume= 0.52+4.2+14.1= 18.8 Fig 3 5
Particle size result interpretation: Number vs. Volume distribution Fig 4 Fig 5 Building a number distribution for these particles will generate the result shown in Figure 4, where each particle size accounts for one third of the total. The same result was converted to a volume distribution, the result appears as Figure 5 where 75% of the total volume comes from the 3μm particles. Understand which technique was used and the basis of the calculations is a must! 6
Which Size is Correct? See the example below: particle species with size a and particle two of size b. There are N a particles with size a and N b particles with size b. %N a = %V a = %I a = Assuming that the particles are spherical, the particle volume is proportional to the size to the third power. For small, isotropic particles the scattering intensity from a spherical particle is proportional to the size to the sixth power. Therefore the short answer to this question is all there are correct. As long as it s clearly stated how the size was obtained and what distribution representation was considered. Effectively, the intensity distributions emphasize the larger particles in the distributions, while number distributions emphasize the smaller particles in the distribution. 7
Peak size or z-average size which one to pick in DLS? Cumulants Method In ISO13321 international standard the two parameters describing particle size distribution, i.e. the average PCS diameter and the polydispersity index PI, are determined by a variant of the socalled cumulants method. It s related to the overall mean size. Distribution analysis For the distribution analysis outcome is a distribution of different contributions from the size classes or bins, and peaks can be defined with a statistical mean and standard deviation of that specific peak. It s related to the distribution of different contributions. 8
Peak size or z-average size which one to pick in DLS? The key difference between these two algorithms: For a perfectly monodisperse sample, the two results should be the same, that is the z-average should be the same as the mean of the (one and only) peak in the distribution. In real applications, even for monodisperse samples, this is likely not the case and there will be small differences. For polydisperse samples, the two can not be the same, because the z- average will still be only a single number, whereas the distribution will show two or more peaks with corresponding mean and width. 9