## 3 Selected Methods and Experimental Approaches for Analysis of HS Structure
### Liquid State Investigations
#### 3.3.1 Scattering Techniques
In many respects, small-angle X-ray (SAXS) and neutron (SANS) scattering can provide complimentary information over similar length-scales, a consequence of the difference in the way that each type of radiation interacts with matter [162]. Though X-rays are often ideal for studying samples with high-Z elements and therefore might seem an obvious choice for investigating mineral-based dispersions, the very presence of those high-Z elements masks the scattering from the low-Z elements in the organic component of natural aquatic colloids. Nevertheless, SAXS technique has been found to be useful for determining the fractal dimension, average molecular weight and particle size in aqueous dispersions of HS [163; 164]. SANS, on the other hand, does not suffer from any of these drawbacks, is a very penetrating radiation (and so is well suited to the study of optically opaque samples) and, importantly, can capitalize on the large differences in scattering behavior between hydrogen and deuterium. By dispersing colloidal material in aqueous matrices composed of varying ratios of H\({}_{2}\)O and D\({}_{2}\)O, it is possible to probe the different components of the system without substantively altering the physical chemistry of the system. This is of enormous potential importance for the study of natural aquatic colloids because of their complex mixed composition. SANS technique allows for the substitution of the water medium with its deuterated analogue (D\({}_{2}\)O) to increase the contrast between the organic compound of interest and the solvent, thanks to the substantial difference between the scattering lengths of hydrogen (H) and deuteron (D). The normalized SANS data are expressed as scattering cross section per unit volume of sample \(I(Q)\) where \(Q=\frac{4\pi}{\lambda}sin\frac{\theta}{\lambda}\) is the scattering vector, \(\lambda\) is the wavelength of the incident radiation and \(\theta\) is the scattering angle. The asymptotic expression of \(I(Q)\) for \(Q\to 0\) is described by the [PERSON]'s Gaussian law:  
\[I(Q)=I(0)\exp\left(-\frac{Q^{2}R_{g}^{2}}{3}\right) \tag{1}\]  
valid in the approximation of non-interacting particles, where \(I(0)\) is the extrapolated intensity at origin and R\({}_{g}\) is the particle radius of gyration or the mass-weighted root-mean-square deviation from the center of mass. Alternatively, assuming the shape of the particles, \(I(Q)\) of polydisperse anisotropic particles can be analyzed by modelling the experimental curves in the whole \(Q\) range. The latter approach implies the use of various fitting models in the general expression \(I(Q)=k\cdot L(Q)+b\), where the scattering law \(L(Q)\) describes how the scattering is modulated by size, shape and local order, \(k\) is a scale factor and \(b\) the incoherent scattered intensity. There are many expressions for \(L(Q)\) available in the literature that refer to a wide variety of 1D, 2D and 3D forms, different interaction potentials and different density correlation functions. The skill in interpreting small-angle scattering data is in finding a physically realistic \(L(Q)\) that fits the data better than any other. The difficulty with natural colloidal systems is that the colloidal objects responsible for the scattering are unlikely to be the simple regular geometric shapes (spheres, rods, ellipsoids of revolution, circular discs, etc...) for which there are a plethora of scattering functions. They often also exhibit size polydispersity. Polydispersity is actually relatively straightforward to handle in the data modelling, but broadening the size distribution has an effect comparable to degrading the data resolution. In most cases therefore, derived shape information is'representative', rather than definitive, and size information is averaged, albeit over a large statistical sample size. The application of fractal geometry allows for the determination of the mass distribution of the material within (mass fractals) or on the surface of the particles (surface fractals) [165].