# Biocompatible Dispersants for Carbon Nanomaterials
## 5 Factors Affecting Dispersion Efficiency  
The formation of micelles is a critical factor in the dispersion of carbon nanomaterials (CNMs) at high surfactant concentrations. The role of micelles depends heavily on the sur \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dispersant** & **CNM** & \(\eta\) **(\%)** & \(\eta^{*}\) **(\% kg.mmol\({}^{-1}\))** \\ \hline SDBS & MWCNT & 77 & 35 \\ SDBS & SWCNT & 93 & 4.7 \\ SDS & MWCNT & 63 & 7.5 \\ SDS & SWCNT & 40 & 1.3 \\ CTAB & MWCNT & 67 & 27 \\ CTAB & SWCNT & 37 & 2.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: \(\eta\) and \(\eta^{*}\) values for a range of CNT dispersions [27]. Table adapted with permission from [27] Copyright © 2015 American Chemical Society. factant used and its concentration relative to the CNMs. It is worth noting that, while not very well studied, the adsorption of surfactant molecules onto the surface of graphene is believed to result in the formation of novel 2D micelles [28; 29]. At low surfactant concentrations, individual dispersant molecules randomly adsorb onto the CNM surface. They then coalesce to form hemimicelles as their concentration increases. Finally, they encapsulate the carbon nanoparticle in a blanket micelle. The critical micelle concentration (CMC)--the concentration of surfactant above which micelles form in solution--of surfactants in CNM dispersions is higher than their CMC in water due to the adsorption of surfactant molecules onto the CNMs. When a surfactant concentration is increased above its \(C_{s,max}\), a phenomenon known as depletion attraction occurs [26; 30]. Depletion attraction causes the re-agglomeration of individual carbon nanomaterials (CNTs), which occurs due to the osmotic pressure exerted on the CNTs by the surfactant micelles. At a high enough micelle concentration, the depletion attraction forces eventually overcome the CNT repulsive forces and cause re-bundling of the fibres. Another mechanism of re-agglomeration known as surfactant induced flocculation was proposed by [PERSON] et al. [22]. Surfactant induced flocculation involves ionic head/tail surfactants forming a bilayer around the CNM, with their hydrophilic tails pointing out into solution. These tails interact with each other to cause re-bundling of CNMs; they do not provide steric hindrance due to their packing and relatively short chain lengths. Therefore, to achieve the best \(\eta^{*}\) value in biocompatible hybrid systems, the optimal surfactant concentration must be determined. For CNMs with curvature--fullerenes/carbon nano-onions (CNOs)/CNTs--curved or flexible hydrophobic regions in surfactants can be utilised to increase the surface coverage on the CNM, therefore increasing binding forces. This concept is known as complementarity [31]. Complementarity can also be applied to interatomic distances in the surfactant and CNM surface [32]. By optimising the curvature and interatomic distances in the hydrophobic regions of the surfactant molecule to match those of the CNM surface, enhanced binding and packing can be achieved, therefore increasing dispersion efficiency. Once bound to the dispersed CNT's surface, it is important to note that small-molecule dispersants, such as head/tail surfactants, exist in dynamic equilibrium with the surrounding solvent (meaning the dispersant molecules are reversibly bound). This dynamic equilibrium could negatively affect the biocompatibility of the final dispersion due to its reversible nature. For example, suppose a dynamic dispersion of a CNM-based therapeutic was to be injected. In that case, the resulting dilution of the solution in the bloodstream could drive desorption of the surfactant molecules, resulting in the re-aggregation of CNMs in the blood. In contrast to small-molecule surfactants, large polymer dispersants tend to wrap around the CNT surface (Figure 1).