## 1 Introduction  
Carbon nanomaterials (CNMs) have brought many new possibilities to human beings since their invention. CNMs, such as carbon nanotubes (CNTs), graphene, and carbon nanohorn (CNH), can be widely used in industry, pharmacy, and other fields such as water treatment, plant growth control, and AIDS treatment [1; 2; 3; 4; 5]. Nowadays, with the development of nanotechnology and the extension of human activity, the number of artificial nanomaterials released to the environment has increased in the last two decades. In this sense, the fate and transport of engineered nanoparticles are studied extensively [6; 7]. The existence of colloidal nanoparticles will change the fate and facilitate the transport of heavy metal pollutants, pathogens, etc., due to aggregation and co-transport [8; 9; 10]. The different transport behaviors of nanoparticles in porous media at different pH or electrolyte conditions have also been reported [11; 12]. Cations and anions, which exist widely in natural surface water, can reduce the energy barrier of colloidal systems and induce aggregation [13]. The charging behavior of particles can also change the aggregation of nanoparticles [14; 15; 16] and may also affect their transport in groundwater [17]. Therefore, the aggregation and charging of colloidal particles in different systems needs more attention. Ever since the carbon nanohorn (CNH) was invented by [PERSON] et al. [18], it has received extensive attention because it possesses a large specific surface area and high conductivity. A CNH can be produced by using CO\({}_{2}\) laser ablation of carbon at room temperature, and the product is a powder formed of graphitic particles with an average size of approximately 100 nm [18]. Oxidized carbon nanohorns (CNHoxs) were prepared with hydrogen peroxide treatment of the CNH. Figure 1 depicts a schematic diagram of the oxidation of a CNH. In the process of the oxidation, the tips of the CNH are opened, and some charged hydrophilic carboxyl groups (COO') are introduced; the porous structure allows molecules to access the inside of the CNHox and results in a larger specific surface area than a CNH. Figure 2 shows a transmission electron microscope (TEM) image of CNHox particles. This figure demonstrates that a single CNHox aggregate has a spherical structure, and that the mean diameter of CNHox aggregates is 96 \(\pm\) 20 nm [15]. To gain a better understanding of the aggregation-dispersion behaviors of colloidal particles, the classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory is usually employed by introducing only two forces, say, attractive van der Waals and repulsive electrical double-layer forces [19; 20; 21]. Colloidal systems, which follow the DLVO theory, show a slow aggregation regime, fast aggregation regime, and a critical coagulation concentration (CCC) between them. The aggregation rate increases with the electrolyte concentration in  
Figure 1: Schematic diagram of the oxidation of a CNH. Figure 2: Transmission electron micrograph images of CNHox particles [15] reused with permission from Elsevier. Irreversible aggregates of CNHox of approximately 100 nm can be seen. the slow aggregation regime. The aggregation rate reaches a plateau in the fast aggregation regime. Many research works about the aggregation of colloids or nanoparticles, such as polystyrene latex [22], Stober-type silica [23], and allophane [24], have been carried out and have proved that their aggregation behaviors follow the prediction of the DLVO theory. Although CNHox particles have a complex structure which contains a horn-shape single structure and a porous structure on their surface, the aggregation behaviors of bare CNHoxs in simple salt solutions were proved to follow the DLVO theory [15]. The addition of substances such as multivalent ions, polyelectrolytes, and surfactants, which possess high opposite charges, can induce the screening of a double layer or even charge neutralization [25; 26; 27]. When charge neutralization happens, the colloidal surface has net charge close to zero.