Example:Virial coefficient

Interparticle interactions can be probed by measuring SAXS as a function of concentration (c). At low concentration, the particles do not interact. The scattering in this case is dominated by the form factor ($\scriptstyle P(q)$), which simply encodes the particle size/shape (because the structure factor is eliminated: $\scriptstyle S(c=0,q)=1$). On the other hand, at high concentrations, particles interact strongly, leading to a non-trivial structure factor.

$I(c,q)=I(c=0,q)\times S(c,q)$

$S(c,q)={\frac {I(c,q)}{I(0,q)}}$

From the solution structure factor ($\scriptstyle S(q)$), one can calculate the second virial coefficient (A₂):

${\frac {1}{S(c,q=0)}}=1+2MA_{2}c$

See Also

• Journal of Crystal Growth 2001, 232, 1-9.
• Methods in Enzymology 1997, Vol. 276, 100-110.