## 3 Results and Discussion
### Adsorbents Characteristics
#### 3.1.2 Structure of Nano-Sized Materials by XRD and Small-Angle X-ray Scattering  
In contrast to crystalline solids, which exhibit a regular and repeating pattern of atoms, the mesoporous carbons C1-C4 and the polymer materials P1, P2 show a lack of extensive ordering. Figure 6 shows the XRD patterns of the investigated mesoporous carbon materials (C1-C4). The first broad diffraction peak at 20 = 23\({}^{\circ}\) can be attributed to the amorphous carbon structures of the graphite plane C(002). The diffraction peak at 20 = 40-50\({}^{\circ}\) is due to the graphite structure and is labelled as C(100) and C(101). The broad nature of the XRD peaks indicates a low degree of graphitisation and identifies an amorphous carbon form. The position of the C(002) peaks for all carbon materials indicates a distance between the graphitic layers of 3.86 A (greater than 3.35 A for graphite (\(\sim\)26.7\({}^{\circ}\) of 20)). The amorphous structure of the polymer materials P1 and P2 was also confirmed. In this case, the XRD patterns (Figure 6) have no signals indicating impurities or other crystalline forms. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Carbon** & \(S_{\text{BET}}\) & \(S_{\text{mic}}\) & \(V_{\text{t}}\) & \(V_{mic}\) (t-plot) & \(D_{h}\) & \(D_{mo}\) (ads. & \(D_{mo}\) (des. BJH) \\  & [m\({}^{2}\)/g] & [m\({}^{2}\)/g] & [cm\({}^{3}\)/g] & [cm\({}^{2}\)/g] & [nm] & BJH) [nm] & [nm] \\ \hline C1 & 502 & 243 & 0.30 & 0.11 & 2.4 & 3.14 & 2.75 \\ C2 & 760 & 40 & 0.61 & 0.01 & 3.2 & 3.43 & 3.24 \\ C3 & 508 & 215 & 0.29 & 0.10 & 2.2 & 2.95 & 2.58 \\ C4 & 649 & 37 & 0.65 & 0.01 & 2.7 & 4.05 & 3.7 The properties of nanostructured carbon and polymer materials are related to the structure and arrangement of the domains on the nanoscale. To understand the relationship between the size, shape, and arrangement of nanostructures and their macroscopic behaviour, SAXS analysis for all investigated materials was performed. Particles embedded in a matrix material must have an electron density unlike the matrix to become visible in SAXS. When neither pores nor particles are present in a dilute phase, it is impossible to assign the SAXS distribution unambiguously to either pores or particles. The visibility increases with the difference in the electron densities between the two materials. It is a consequence of equation [67]. \[I_{1}(q)=I_{\epsilon}(q)4\pi(\Delta\rho)^{2}V\int\limits_{0}^{d}r^{2}\gamma_{ 0}(r)\frac{sinqr}{qr}dr \tag{15}\]  
where \(I_{1}(q)\) is the intensity of small-angle scattering from a single particle corresponding to point scattering, \(I_{\epsilon}(q)\) is scattering intensity by a single electron, \((\Delta\rho)^{2}\) is the difference between the electron densities of the particle and its surroundings, V is the volume of a particle, \(d\) is the maximum distance between points in a particle, (parameter referred to as the size of a particle), \(\gamma_{0}(r)\) the correlation function for a single particle, and r the distance between two points in a particle. The above equation (Equation (15)) shows that the SAXS intensity is directly proportional to the square of the difference between the electron density of the particle and the surroundings. The SAXS effect therefore occurs regardless of whether the electron density of the particles is higher (particles) or lower (voids) than the electron density of the surroundings. This means that the sign of the contrast has no effect at all. Voids in a matrix material appear with the same intensity as the material particles in a void matrix. It is solely the judgment of the experimenter which parts of the sample are considered as \"particles\". In the systems presented, the carbon material (or polymer materials) is considered as the matrix and the pores as scattering particles. The characterisation of such a system is based on other techniques (such as nitrogen adsorption/desorption at low temperature) that confirmed the presence of porosity in the nanometer range (suitable size of scattering objects for SAXS).