4.5) Porod law

The behavior of I(Q) at Q tending to infinity was investigated by Porod (Porod, 1951). He showed, in the system with clear interface between particle and surrounding solvent, the asymptotic trend of the scattering intensity for Q tending to infinity proportional to Q^-4, and it is readily related to the particle surface S,

, () (4.45)

which is called the "Porod law".

The Porod invariant (Porod, 1952) is an important integral characteristic of the scattering intensity,

. (4.46)

This invariant is proportional to the total scattered energy, because the factor Q² is due to the use of polar coordinates. For particle scattering, eqs. (4.7) and (4.8) give

, (4.47)

that is, I^total is proportional to the mean-square density fluctuation caused by a particle. The volume of a homogeneous particle can be readily obtained from the value of the invariant, since in this case,

. (4.48)

For the simple case of the spherical particle with radius R, one can experimentally obtain the curvature of the sphere from eq. (4.45) and (4.48),

. (4.49)