Figure 1. SAXS differential pattern of SDS dispersion in buffer.
Figure 2. Minimum and maximums of the reconstructed PDDF function indicate the characteristic distances within the particle.
Point C on Figure 2, at ~41 (A), may serve as an estimate of the average distance
between the opposite hydrophilic groups in the micelle. Point D, at ~55 (A), indicates the
maximum distance within the particle. Point B is the length of the average of all vectors
inside the micelle connecting parts with positive (hydrophilic) and negative
(hydrophobic) relative scattering densities.
The second analysis method, applied to the same experimental data, used the fitting of the experimental differential curve to a model based on the double core-shell structure. The two- shells model was introduced to more accurately mimic the outer part formed by hydrophilic heads. In this case, parameters of core and shells – size, scattering contrast and polydispersity – were refined to obtain the best fit with the differential pattern (Figure 3).
Figure 3. Core-shell model of micelle.
Refinement of the core-shell model returned the following parameters:
Core: radius = 15.5[A], σ=13%, ρ=-3.8; 1st shell: thickness = 3.8[A], σ=9%, ρ=2.8; 2nd shell: thickness = 1.9[A], σ=22%, ρ=5.9
The values above refer to σ as polydispersity and ρ as the relative (to water) scattering contrast.
The resulting distribution of scattering contrast in micelle associated with the relative (to water) electron density is also depicted in Figure 4.
Figure 4. Reconstruction of electron density contrast as function of distance from the particle centre.
The average distance between the centres of opposite hydrophilic groups calculated from the centre of the second shell is equal to ~40.5 [A].
Therefore, both methods result in comparable values for the particle size.
The advantage of the first method is flexibility and independence from the model. The second method demands the introduction of a realistic model, but fitting by model brings actual numerical values to the refined parameters.
* PDDF is a self-correlation function of relative scattering density within the particle. Maximums of PDDF function show the most populated vectors inside the particles connecting the areas with the largest scattering density.