Optimizing your optical properties for colored materials

Introduction

Measuring the size of nanoparticles using laser diffraction can be a challenging endeavor, particularly selecting the optical properties. This is doubly true when analyzing colored nanoparticles such as ink pigments. 

Laser diffraction uses optical models to interpret scattering data to produce the final particle size distribution (PSD). In the Mastersizer 3000 software, two optical models are available – the Fraunhofer approximation and Mie theory. The former is only recommended when measuring particles >50 µm, whilst Mie theory can be used to analyze particles of all sizes. The difference between the two models lies in the assumptions made about the particles being measured. Fraunhofer assumes that only primary scattering effects are occurring, i.e., diffraction of light. To predict this, no information about the optical properties, such as the refractive and absorption indices, is required. In addition, Mie theory takes in to account secondary scattering effects – absorption, reflection, and refraction. For large particles, the secondary scattering effects are not statistically significant and will have limited influence on the PSD. As such, we do not really need to consider the optical properties when analyzing coarse particles. As particles become smaller, secondary scattering effects become more and more significant and so does the selection of the optical properties if we wish to correctly model how light interacts with the particles.

Materials gain their color from absorbing certain wavelengths of light whilst reflecting others. For example, a red material is red because it reflects light in the red portion of the visible spectrum. Conversely, it absorbs light strongly in the green and blue regions. The Mastersizer 3000 uses two different wavelengths of light – 633 nm (red) and 470 nm (blue).¹ Therefore, when colored materials are analyzed using the Mastersizer 3000, it is necessary to consider how both the refractive and absorption indices change when illumination moves from the red to blue wavelengths of the visible light spectrum.

This report details the study of the PSD of nanosized colored pigments with the aim of demonstrating how to determine the optimum optical properties for the material. Four organic based pigments, received directly from the manufacturer, were selected for the study:

• Magenta (red)
• Cyan (blue)
• Yellow 
• Black

Each sample was measured using a Mastersizer 3000 equipped with extended software features (version 3.89). A Hydro MV unit was used to disperse the particles, with water used as the dispersant. The samples were added dropwise until the desired obscuration was reached.

Red pigment 

Red pigments take their coloring from the absorption of wavelengths of light towards the green and blue regions of the visible light spectrum whilst reflecting those associated with red wavelengths. We would therefore expect a low value for the absorption index when considering the red wavelength component, and one that is higher when considering that of the blue absorption index value. Typically, refractive indices are lower for the blue light wavelength when measuring red materials. Knowing that we are analyzing organic pigments allows us to focus the range of suitable refractive indices. Inorganic pigments typically have higher values for their refractive index.

The optical property optimizer (OPO) allows users of the Mastersizer 3000 to scan different optical property configurations whilst assessing the fit of the data, which refers to the agreement between the captured scattering data and the scattering data predicted by the optical model. The residual values give an indication of the quality of the fit, with the percentage figure being the area between the two curves. The aim when assessing such small particles is to have the weighted residual be less than, or close to, 1%. Whilst doing this, the user can also see how changing optical properties alters the PSD, giving them an indication of the robustness of their selection. Within the OPO we have the option to adjust the optical properties for both the red and blue wavelengths independently.

Figure 1 shows the OPO set up for determining ideal optical properties for the red pigment. By applying the earlier discussed principles (blue light – higher absorbance, lower refractive index), we can see that a weighted residual value of 0.9% is achieved, with excellent agreement of the fit across the entire detector range, indicating an appropriate selection of optical properties for the material. This result was achieved even after considering the relatively high obscuration of the blue laser (19.3%) versus that of the red laser (3.24%). Removing the blue light from the analysis did not improve the weighted residual fit. Particular note should be paid to the excellent agreement on detectors 51 and 63 – these are known as the extinction detectors and can be used to give an indication of the value of the absorption index.

Blue pigment

Materials that appear blue do so due to absorption of red light and reflection of blue light. This high absorption of red wavelengths will mean that higher absorption index values will be observed when measuring with the red laser than the blue. There is also likely to be variation in the value associated with the refractive index between the two wavelengths. 

Figure 2 shows the OPO set up for determining ideal optical properties for the blue pigment. By applying the earlier discussed principles (red light – higher absorption and a different refractive index), we can see that a weighted residual value of 0.97% is achieved, with excellent agreement of the fit across the entire detector range, indicating an appropriate selection of optical properties for the material. 

Black Pigment

Black materials get their colour from absorbing all wavelengths of light – we can therefore expect both the refractive index and absorption index to be similar for both red and blue wavelengths. This makes our lives easier and within the OPO we can set the analysis settings to ‘same blue light settings.’ Figure 3 shows the OPO setup for determining the appropriate optical properties for a black pigment. By using the same optical properties for both red and blue wavelengths, a weighted residual value of 0.76% is achieved, once more indicating that we have selected optical properties that are appropriate for the material that we are analysing. The absorption value of 0.5 is unsurprising – black materials are highly absorbing of visible light, so we therefore have a fair absorption index being used.

Yellow pigment

The final material analyzed was a yellow pigment which gets its bright color from absorbing in the blue region of the visible light spectrum, and reflecting light with more red character. Our approach for selecting our optical properties for this pigment can therefore use the same logic as for our red pigment – high absorption value for blue, lower for red.

Figure 4 shows the OPO after having scanned different combinations of refractive index and absorption index, ranging from 1.3 – 1.8 and 0 – 1, respectively. 

Even after scanning this broad range for both red and blue lasers, the lowest weighted residual obtained was 6.03%, which is higher than the 1% we are aiming for. This needs to be investigated further – if we look at the laser obscuration for the blue light, a value of 71.7% is observed, much higher than the obscuration value recorded for the red laser light, which was 5.1%. This suggests that when measuring with the blue light, we have extreme amounts of multiple scattering, explaining why we cannot fit both red and blue laser light. As the majority of the scattering data comes from red laser light measurements, we should select conditions in which we generate repeatable red-light measurements. In order to do so, we can remove the blue light from our analysis. This is done within the advanced analysis settings by selecting ‘Remove Blue Light from Analysis.’

By removing the blue light from the analysis and focusing solely on the red-light measurement (applying the same logic of low absorbance for red light), you can see that we can achieve a much more agreeable fit across all detectors, with a weighted residual of 0.64%.

Comparison with DLS

Figure 6 shows the overlay of the PSDs obtained for each of the four colored pigments measured as part of this investigation using the Mastersizer 3000. The sizes of each ink are similar each other. The size of the particles was also measured using dynamic light scattering (DLS) with a Zetasizer Advance, which also showed that the four samples possess similar PSDs, with the reported sizes in-line with those obtained using a Mastersizer 3000.²

Conclusion

This work highlights the importance of considering changes in refractive and absorption indices with wavelength when measuring colored materials using the Mastersizer 3000. Analysis using both red and blue wavelengths of light was successful for red, blue, and black pigments. In cases where extreme multiple scattering events are likely to occur, i.e., when the blue laser obscuration is significantly higher than that of the red, the user may benefit from removing blue light from the analysis. This was the case when analyzing the yellow organic pigment.

1. Particles are measured with the shorter wavelength to give improved sensitivity during the measurement of small particles.
   
2. The slightly larger sizer reported by DLS is due to the results being reported as an intensity weighted distribution which is more biased towards coarse particles than the volume-weighted distribution that we get in laser diffraction.