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: Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\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 (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\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.