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 (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \scriptstyle P(q)} ), which simply encodes the particle size/shape (because the structure factor is eliminated: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \scriptstyle S(c=0,q)=1} ). On the other hand, at high concentrations, particles interact strongly, leading to a non-trivial structure factor.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle I(c,q) = I(c=0,q) \times S(c,q)}
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S(c,q) = \frac{ I(c,q) }{ I(0,q) }}
From the solution structure factor (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \scriptstyle S(q)} ), one can calculate the second virial coefficient (A2):
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{S(c,q=0)} = 1 + 2 M A_2 c}
See Also
- Journal of Crystal Growth 2001, 232, 1-9.
- Methods in Enzymology 1997, Vol. 276, 100-110.
