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molecular mass, and thus ideal for determination ofM, since the contribution of small

solvent molecules can be neglected. In an ideal solution, the macromolecules are

entirely independent from each other, and the light scattering can be described as:

I

I 0

R¼PKcM ð 12 : 9 Þ

whereIyis the intensity of the scattered light at angley,I 0 is the intensity of the

incident light,Kis a constant proportional to the squared refractive index increment,c

is the concentration andRythe Rayleigh ratio.Pydescribes the angular dependence of

the scattered light.

For non-ideal solutions, interactions between molecules need to be considered. The

scattering intensity of real solutions has been calculated by Debye and takes into

account concentration fluctuations. This results in an additional correction term

comprising thesecond virial coefficientBwhich is a measure for the strength of

interactions between molecules:

Kc

R¼

1

P

1

Mþ^2 Bc



ð 12 : 10 Þ

Determination of molecular mass with multi-angle light scattering

In solution, there are only three methods for absolute determination of molecular mass:

membrane osmometry, sedimentation equilibrium centrifugation and light scattering.

These methods are absolute, because they do not require any reference to molecular mass

standards. In order to determine the molecular mass from light scattering, three param-

eters must be measured: the intensity of scattered light at different angles, the concen-

tration of the macromolecule and the specific refractive index increment of the solvent.

As minimum instrumentation, this requires a light source, amulti-angle light scattering

(MALS) detector, as well as a refractive index detector. These instruments can be used

in batch mode, but can also be connected to an HPLC to enable online determination

of the molecular mass of eluting macromolecules. The chromatography of choice is

size-exclusion chromatography(SEC), also called gel filtration (see Section 11.7), and

the combination of these methods is known as SEC–MALS. Unlike conventional size-

exclusion chromatography, the molecular mass determination from MALS is independ-

ent of the elution volume of the macromolecule. This is a valuable advantage, since the

retention time of a macromolecule on the size-exclusion column can depend on its shape

and conformation.

12.6.2 Quasi-elastic (dynamic) light scattering – photon
correlation spectroscopy

While intensity and angular distribution of scattered light yields information about

molecular mass and dimension of macromolecules, the wavelength analysis of scat-

tered light allows conclusions as to the transport properties of macromolecules. Due to

rotation and translation, macromolecules move into and out of a very small region in

the solution. This Brownian motion happens at a timescale of microseconds to

515 12.6 Light scattering