milliseconds, and the translation component of this motion is a direct result of diffu-
sion, which leads to a broader wavelength distribution of the scattered light compared
to the incident light. This analysis is the subject of dynamic light scattering, and yields
the distribution of diffusion coefficients of macromolecules in solution.
The diffusion coefficient is related to the particle size by an equation known as the
Stokes–Einstein relation. The parameter derived is the hydrodynamic radius, or
Stokes radius, which is the size of a spherical particle that would have the same
diffusion coefficient in a solution with the same viscosity. Most commonly, data from
dynamic light scattering are presented as a distribution of hydrodynamic radius rather
than wavelength of scattered light.
Notably, the hydrodynamic radius describes an idealised particle and can differ
significantly from the true physical size of a macromolecule. This is certainly true for
most proteins which are not strictly spherical and their hydrodynamic radius thus
depends on their shape and conformation.
In contrast to size exclusion chromatography, dynamic light scattering measures
the hydrodynamic radius directly and accurately, as the former method relies on
comparison with standard molecules and several assumptions.
Applications of dynamic light scattering include determination of diffusion coeffi-
cients and assessment of protein aggregation, and can aid many areasin praxi. For
instance, the development of ‘stealth’ drugs that can hide from the immune system or
certain receptors relies on the PEGylation of molecules. Since conjugation with PEG
(polyethylene glycol) increases the hydrodynamic size of the drug molecules dramat-
ically, dynamic light scattering can be used for product control and as a measure of
efficiency of the drug.12.6.3 Inelastic light scattering – Raman spectroscopy
When the incident light beam hits a molecule in its ground state, there is a low
probability that the molecule is excited and occupies the next higher vibrational state
(Figs. 12.3, 12.8). The energy needed for the excitation is a defined increment which
will be missing from the energy of the scattered light. The wavelength of the scattered
light is thus increased by an amount associated with the difference between two
vibrational states of the molecule (Stokes shift). Similarly, if the molecule is hit by
the incident light in its excited state and transitions to the next lower vibrational state,
the scattered light has higher energy than the incident light which results in a shift to
lower wavelengths (anti-Stokes shift). These lines constitute the Raman spectrum. If
the wavelength of the incident light is chosen such that it coincides with an absorp-
tion band of an electronic transition in the molecule, there is a significant increase in
the intensity of bands in the Raman spectrum. This technique is called resonance
Raman spectroscopy (see Section 13.2).12.7 Atomic spectroscopy
So far, all methods have dealt with probing molecular properties. In Section 12.1.2, we
discussed the general theory of electronic transitions and said that molecules give rise516 Spectroscopic techniques: I Photometric techniques