# Effect of Hydrophobic Silica Nanochannel Structure on the Running Speed of a Colloidal Damper
## 2 Structure and Fractal Description of the Silica Gel Nanochannel Structure  
### Silica Gel Nanochannel Structure and Its Parameters  
The basic structure of silica gel is composed of Si-O tetrahedrons stacked by chemical bonds. It has high porosity and large specific surface area. Hydrophobic silica gel is based on silica gel and coupled hydrophobic functional groups (e.g., benzene, alkyl (C4, C8, C18), etc.) with covalent bonds. Alkyl generally uses linear chains of silaneyl, and the chemical molecular expression is Si (CH\({}_{3}\)) \({}_{2}\)C\({}_{m}\)H\({}_{2m+1}\). Because water molecules are polar molecules, hydrophobic functional groups are generally nonpolar chains, as polar molecules and nonpolar molecules are mutually exclusive. Take the silaneyl studied in this paper as an example. The main structure of the alkyl chain is shown in Figure 1; the longer the alkyl, the better the symmetry, the better the nonpolarity, and the stronger the hydrophobic capacity [13; 14]. Figure 1: Alkyl chlorosilane molecule. The hydrophobic layer is attached to the surface of the modified silica gel. The thickness of the hydrophobic layer affects the structural parameters of the silica gel particles [9], including pore size distribution, average pore size, specific surface, pore volume, and porosity. The silica gel used in this paper was the Unisil hydrophobic silica gel produced by Suzhou Nano-micro Technology Co, Ltd. (Suzhou, China). Table 1 shows the parameters of the modified silica gel determined and calculated via the N\({}_{2}\) adsorption method. In the table, the trade name of the silica gel contains the basic parameters of each silica gel. For example, 10-100 C4 indicates that the particle size of the silica gel is 10 \(\upmu\)m, the pore size is 100 A, and the surface functional group is C4 silica gel. The digit \(M\) (4, 8, and 18) in the surface functional group denotes the number of graft molecules of alkyl, and the larger the value of \(m\), the stronger the hydrophobicity. The terms \(d_{a}\), \(2r_{a}\), \(S_{a}\), \(V_{a}\), and \(\rho_{a}\) denote the average particle size, average pore size, specific surface area, pore volume, and stacking density of the silica gel particles after modification, respectively. The terms \(\lambda_{min}\) and \(\lambda_{max}\) denote the minimum and maximum pore sizes of the hydrophobic silica nanochannels, respectively. Hydrophobic silica gel is a typical granular porous medium with complex pores. Figure 2 shows pore structure images of hydrophobic silica nanochannels with magnifications of 1000 and 100,000, obtained by scanning electron microscopy (SEM). For SEM, we used an FEI Quanta-200; the materials selected were 10-100 C18 and 10-300 C18 silicone, treated with surface gold spray for 15 min. It was determined that the silica gel microspheres (secondary particles) were made up of nanoparticles (primary particles) by necking and bonding. Attributable to the different tightness degrees of each primary particle, there were a number of gaps between the particles, forming nanoscale pore structures with different shapes distributed continuously within the nanoscale. Under multiple magnifications from 1000\(\times\) to 100,000\(\times\), the SEM images of the silicone showed that it is clearly geometric; the structure of silicone at this scale is a fractal structure of self-similarity. The silicone shown in the figure is due to advanced technology, so the shape of the secondary particles is a regular spherical shape, and the particle size distribution of the secondary particles is relatively singular. There is a greater randomness in the process of primary particle aggregation; the cluster size of primary particle aggregation varies, so the aperture distribution between secondary particles is wide [15]. A primary particle of 10-100 C18 silicone was measured using an SEM ruler, and the diameter was about 20-31 nm; for 10-300 C18 silicone, the primary particle size was about 100-110 nm.