## 3 Selected Methods and Experimental Approaches for Analysis of HS Structure
### Liquid State Investigations
#### 3.3.1 Scattering Techniques
On the right side it is graphically represented how the fractal dimension d\({}_{f}\) increases from approximately 1 for rod-like aggregates to 3 for ideally spherical structures, passing through intermediate shapes (e.g., d\({}_{f}\) = 2). difficult to determine, and instead, a lower limit of R\({}_{\rm g}\) was obtained. In subsequent investigations, the same authors reported an increase in the fractal dimensions of aggregates (from d\({}_{f}\) = 1.85 to 2.35) for two types of HA suspended in D\({}_{2}\)O (concentration = 3 mg/mL, pH = 5.0 and 0.1 M NaCl) after 48 h of equilibration at 4 \({}^{\circ}\)C and 11 \({}^{\circ}\)C and after 60 h at 22 \({}^{\circ}\)C, demonstrating that the increase in temperature somehow allowed a compaction of the humic material [171, 172]. One possible explanation is that the increase in kinetic energy was sufficient to allow functional group interactions to overcome some activation energy barrier. In their investigation, [PERSON] et al. [84] measured the wavelength dependence of the turbidity of humic particles in dilute suspensions in absence of background electrolytes, to obtain the respective fractal dimensions at various pH values and for different equilibration times at 25 \({}^{\circ}\)C. From fractal analysis, HA particles in aqueous suspension were observed to evolve as the pH and/or the equilibration time increased, from an almost compact, dense structure with either smooth surfaces (non-fractal particles) or corrugated surfaces (surface fractals), to less compact and irregular structures with increasingly rough surfaces (mass fractal). In a subsequent turbidimetric investigation carried out on aqueous suspensions of three HA standards, a general reduction of d\({}_{f}\) was observed upon increasing HA concentration, pH, or ionic strength due to added NaCl [85]. However, in the presence of CaCl\({}_{2}\), the HA particles existed as condensed structures with rippled and rough surfaces. [PERSON] et al. [173] performed high-performance size exclusion chromatography (HPSEC) to preliminary fractionate HS from Suwannee River natural organic matter and then used the multi-angle laser light scattering (MALLS) technique to measure the time-averaged angular dependence of the scattering of light by humic material in two phosphate buffer solutions. In 2.5 mM phosphate buffer, the weighted average molecular mass (M\({}_{\rm w}\)) and z-average particle radius (R\({}_{\rm z}\)) were, respectively, M\({}_{\rm w}\) = 25.7 \(\pm\) 7.5 kDa and R\({}_{\rm z}\) = 68.1 \(\pm\) 20.4 nm, the latter value being almost halved in the higher ionic strength solutions as a consequence of an increased macromolecular coiling. Those data supported the random coil hypothesis for macromolecular NOM species in aqueous solutions. A combination of DLS and SAXS techniques performed on dilute solutions of HA extracted from peat, yielded particle sizes R\({}_{\rm h}\) of the order of 50-100 nm at pH \(\sim\) 9 and low ionic strength, characterized by a loose, sponge-like inner structure with mass fractal dimension d\({}_{f}\) = 2.1-2.2 [174]. [PERSON] et al. [175] analyzed the non-perturbed AHA structure in aqueous solutions by using the noninvasive MALLS technique, giving an accurate in situ value for size and molecular weight of aggregates. All measurements were made immediately after the solutions were prepared to avoid long-term aggregation effects. The authors stated that from SEC fractionation experiments, three peaks were obtained in the 1-30 kDa range attributable to as many building blocks of AHA, although they could not be representative of the aggregation found in naturally occurring samples. By measuring the intensity of scattered light at various set angles, the values of M\({}_{\rm w}\) = 116.4 MDa and R\({}_{\rm g}\) = 436 nm were determined.