What is the value of multi-angle DLS?

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1 What is the value of multi-angle DLS? A common question from users of dynamic light scattering (DLS) instrumentation is "what is the resolution of the technique". The rule of thumb response to this question is that DLS can resolve particles with size differences of circa 3X, e.g. 100 & 300 nm, but not 100 & 200 nm. Implied within this rule of thumb response, but not always recognized, is that the scattering from each particle size family is sufficient to be detected. However, if the scattering signal from one particle family is too small, compared to that from a second particle family, the lesser signal cannot be distinguished from the background noise, regardless of the resolving power of the technique. It is within this area of "resolution sensitivity" for mixtures of particle families that multi-angle dynamic light scattering may be of value. For particles much smaller than the wavelength of the incident light, the scattering is isotropic which means that the scattering intensity within the plane perpendicular to the plane of the incident light is independent of the angle of detection (see Figure 1). For 633 nm incident light, the Rayleigh or upper size limit for isotropic scattering is a hydrodynamic diameter of circa 100 nm. Figure 1: Isotropic (symmetrical) scattering profile for small particles. For particle sizes larger than the Rayleigh limit, the scattering is influenced by the optical properties of the particle, leading to asymmetric scattering profiles. Figure 2 shows a comparison of the scattering profiles for 60 and 1000 nm latex particles, and exemplifies the characteristic asymmetric scattering of large particles. It is noted here, that the scattering profiles in Figure 2 are independently normalized to coincide at zero angle.

2 Figure 2: Mie scattering profiles for 60 and 1000 nm latex spheres. Mie theory can be used to calculate the angle and particle size dependent scattering profile. Examples are given in Figure 3, which shows the calculated intensity traces for latex spheres at 80 and 100 degree scattering angles. The dashed lines in Figure 3 represent particle sizes that can be used to describe the influence of the scattering angle on the resolution sensitivity of DLS for a mixture of particle sizes. Consider for example, two mixtures of latex particles, one containing equal mass amounts of 60 and 800 nm particles, and a second containing equal mass amounts of 60 and 1000 nm particles. For the 1st mixture, the scattering intensity for both particle families is roughly equivalent (~0.4) at an 80 degree scattering angle. At a scattering angle of 100 degrees however, the magnitude of the intensity for the larger (800 nm) particle family is circa 6.5 times that of the smaller (60 nm) particle family. For this two angle example then, baseline resolution of a 60 and 800 nm mixture would be easier to achieve at an 80 degree scattering angle. For the 2nd mixture of 60 and 1000 nm latex particles, the scenario is reversed, with 100 degrees being the better of the two scattering angles for optimal resolution of the two particle families.

3 Figure 3: Particle size dependent scattering per particle volume for 80 and 100 degree scattering angles. Figure 4 shows the angular dependent intensity size distributions for a 60 and 1000 nm latex mixture, prepared by addition of 1 drop of 1000 nm (1% solids) and 4 drops of 60 nm (1% solids) to 10 ml of filtered 10 mm NaCl. Alternating colors are used to help distinguish the distributions.

4 Figure 4: Angle dependent intensity particle size distributions for a mixture of 60 & 1000 nm latex spheres. Qualitatively, the angular dependence predicted by Mie theory is clearly evident in the latex example shown in Figure 4. It is important to recognize however, that for all scattering angles > 30 degrees, both particle families are clearly resolved, with only the intensity ratio showing the Mie predicted angular dependence. For this particular example then, it would seem that there is very little added value derived from multiple scattering angles. However, if one is attempting to isolate trace amounts of particulates, then the ability to use the scattering angle to fine tune the intensity ratio would certainly be an advantage.

5 Additional Reading 1) C.S. Johnson and D.A. Gabriel (1981) Laser Light Scattering, Dover Publications Inc., New York. 2) ISO13321 (1996) Determination of Particle Size Distribution Part 8: Photon Correlation Spectroscopy, International Standards Organization. 3) C.F. Bohren, and D.R. Huffman (1983) Absorption and Scattering of Light by Small Particles, Wiley, New York. 4) C.H. van de Hulst (1981) Light Scattering by Small Particles, Dover, New York. 5) B.J. Berne and R. Pecora (1976) Dynamic Light Scattering with Applications to Chemistry, Biology and Physics, Wiley, New York. 6) B. Chu (1974) Laser Light Scattering, Academic Press, New York. 7) H.Z. Cummins and E.R. Pike (1974) Eds. Photon Correlation and Light Beating Spectroscopy. For additional questions or information regarding Malvern Instruments complete line of particle and materials characterization products, visit us at