1. Particle Form Factor

Absolute intensity of SAXS from particulate system is typically written as below:

, where V is the sampling volume, r_e is the classical electron radius, rho_p, the electron density of particles, tilde_rho, the electron density of solution, N_p, the number of particles in the sampling volume, V_p, the volume of a particle, P(q) is the normalized form factor (P(0) = 1), and S(q) is the structure factor. f (= N_p * V_p / V) is the volume fraction of particles in solution. r_e * rho is called the scattering length density, and r_e^2*(rho_p - tilde_rho)^2 is called the contrast.

When particles are well dispersed in solution with a dilute concentration, tilde_rho can be approximated to the electron density of solvent.

Some simulations:

Small Angle Scattering from spherical particles.

Legend shows the radii of the particles.

Polydispersity in size damps oscillation in the form factor.

Around 20% of polydispersity completely damps oscillations for spherical particles.

Intensity at high q region, the so called Porod region, is proportional to the surface area of particle, or 2/3 power of the mean volume of polydisperse particle.