Static Light Scattering

Static light scattering is a classical method for the determination of molecular masses. In addition, information on particle shape and interactions, and even on superstructures, is accessible. With such enhanced evaluations, theoretical foundations become increasingly complex and a high level of certainty must be expected from the experimental data.

Compared to other methods for molecular mass determination, static light scattering is rather demanding in respect to the experimental setup and the experiment itself. It has the advantage, however, to provide an independent access to the basic property of mass, physically based on a totally different principle than Analytical Ultracentrifugation or size exclusion chromatography. This can be most helpful when dealing with complex systems. For example, aggregation numbers of micelles or masses of polymer coils are commonly determined via SLS.

Static light scattering is an absolute method and is most conveniently combined with Analytical Ultracentrifugation in respect to a comprehensive set of parameters and a complete characterisation of complex systems.

As per other scattering methods, Static Light Scattering is limited to monomodal systems. Under certain circumstances, distributions may be accessible, but

  • extensive assumptions may be neccessary, and
  • even enhanced evaluation methods cannot overcome the physical limitation due to the nature of light scattering.

The physical limitation is that scattering intensity increases with the sixth power of particle size: one single particle ten times as large as another will scatter light equivalent to 1,000,000 of the smaller particles. This puts strong restrictions on experiment and detection; the risk of misleading artefacts remains high.

For monomodal systems, however, SLS provides a most precise method for determining molecular masses. Unlike dynamic light scattering, measurement at varied angles are essential. Forthermore, dust is much more an issue in static measurements and can considerably affect the quality of results.

Light Scattering Setup
Figure 1: Light Scattering Setup

In Fig. 1, a light scattering setup is shown schematically. The Figure also shows how the scattering vector (q or s) is constructed. This vector is used for evaluation rather than the scattering angle.

The physical limitation with respect to particle sizes is found in static light scattering; the same limitation is known in dynamic light scattering. As scattering intensity decreases towards smaller particles with the sixth power of diameter, intensities become very weak and barely detectable for particles about one-twentieth of the incident wavelength in diameter. With high incident intensities and short wavelengths, it is possible to address particles of only several nanometers in size, corresponding to molecular masses of few thousands.

Scattering intensity is registered at multiple angles, from the dependence of intensity on the angle (or, rather, the scattering vector), the radius of gyration Rg is calculated. Together with the hydrodynamic radius Rh from dynamic light scattering, information on particle shape is available. Extrapolation of scattering intensity to zero scattering angle yields an apparent molecular mass. In Figure 2, a common evaluation method is shown, plotting a value derived from intensity and experimental parameters against the squared scattering vector; the y-axis intercept gives the reciprocal apparent molecular mass.

Zimmplot
Figure 2: Zimmplot

From a concentration series, the real molecular mass is obtained plotting apparent molecular masses against concentration and extrapolating to infinite dilution. The slope gives the second osmotic virial coefficient A2. Thus, the set of parameters accessible through SLS is M, Rg and A2.

Further information can be extracted using model-based fits to the scattering data. Shape and structural factors may be introduced and calculated from fit data.

For a normal evaluation with respect to the molecular mass, the only particle property required is the refractive index increment dn/dc. This property is known and tabled for many systems, if not, it is quite easy to measure. For the experiment, the crucial points to observe are:

  • extreme caution concerning dust and other impurities
  • high incident light intensity
  • precise temperature control
  • reasonable statistical significance of scattering data.

The SLS equipment in Nanolytics' laboratory guarantees the method's application right to its physical limits.