## 1 Introduction
The electrical double layer repulsion disappears and van der Waals attraction will be dominant in the interaction between particles, where the colloidal particles aggregate fast. Although the DLVO theory can be used in many colloidal systems, the existence of non-DLVO effects is well known. Due to the adsorption of oppositely charged substances, some patches with a different sign of charge appear. The adsorption of small amounts of oppositely charged substances will increase the heterogeneity on the particle surface. Therefore, patch-charge attraction happens. Electrical attraction will appear between the oppositely charged surfaces. This attraction can be affected by electrolyte concentration, macromolecule dosage, molecular masses, etc. [15; 26; 28]. A heterogeneously charged surface will have a larger patch-charge attraction than a homogenously charged surface. Not only can synthetic polyelectrolytes lead to non-DLVO interaction, but the effect of natural macromolecules, such as proteins and humic substances, also need more attention. [PERSON] et al. [23] have claimed that a low amount of adsorbed lysozyme (LSZ) promotes the aggregation of silica particles due to charge heterogeneity. The bridging effect plays an important role in the aggregation of silica particles in the presence of Suwannee River fulvic acid [29]. [PERSON] et al. have studied the initial aggregation kinetics of single-walled carbon nanotubes in the presence of natural organic matter, Suwannee River acid, bovine serum albumin, etc. [30]. While considering the fate and transport of colloidal particles, we cannot ignore some of the potential problems that the wide usage of CNHoxs may bring to the nanostructures of organism bodies. How a CNHox interacts with natural organic materials is highly discussed in many research studies. In previous studies, the biotoxicity of CNHoxs was proved by lots of researchers. [PERSON] et al. have studied the biotoxicity of CNHoxs on human cells [31]. Their result concluded that CNHs oxidized for 0.5 h have the highest toxicity, and thus the lowest cell viability. The effect of CNHox on the hatching rate and survival rate of zebrafish was also studied by [PERSON] et al., who have stated that the hatching rate and survival rate of zebrafish can be decreased by the addition of CNHoxs [32]. However, there is still a lack of research on the charging and aggregation-dispersion behaviors of CNHoxs with biological and environmental macromolecules such as proteins, polysaccharides, and humic substances, which are ubiquitous in natural environments. In previous research, the effects of high oppositely charged natural macromolecular materials on some colloidal particles' surface have been studied [23; 26]. If a CNHox is to be widely used in industrial production, the interaction between CNHoxs and proteins will be also non-negligible. Therefore, clarifying how proteins affect the aggregation and dispersion of CNHoxs in aqueous solution and the applicability of the DLVO theory are of great importance. In this study, the well-known model protein lysozyme (LSZ), which has been generally studied for its co-flocculation with many colloidal particles [23], is employed as model a protein. The charging and aggregation behaviors of CNHoxs in the presence of LSZ are studied to gain a better insight into the colloidal stability of CNHoxs in the presence of proteins. Non-DLVO interactions such as patch-charge attraction are concerned in this explanation of the aggregation-dispersion behavior of CNHox particles with protein molecules. With the usage of electrophoretic light scattering and time-resolved dynamic light scattering methods, the charging and aggregation-dispersion of CNHoxs are explored. The results obtained will be analyzed based on the DLVO theory.