Section 2.6.2.6.4. Inner surface area

According to Porod (1951, 1982), small-angle scattering curves behave asymptotically like I(Q) = constant × A_sQ⁻⁴ for large Q, where A_s is the inner surface of the sample. Theoretically, fitting a straight line to I(Q)Q⁴ versus Q⁴ (`Porod plot') at sufficiently large Q therefore yields a zero intercept, which is proportional to the internal surface; a slope can be interpreted as a residual constant background (including the self-term of the constant nuclear `form factor'), which may be used for slightly correcting the estimated background and consequently improving the quality of the data. For monodispersed particles, a particle surface can be deduced from the overall surface. The value of the surface area so determined depends on the maximal Q to which the scattering curve can be obtained with good statistics. This depends also on the magnitude of the background. At least for weakly scattering particles in mixtures of ¹H₂O and ²H₂O, and even more in pure ¹H₂O, the incoherent background level often cannot be determined precisely enough for interpreting the tail of the scattering curve in terms of the surface area.