Your hydrophobic particle may not remain hydrophobic once introduced to physiological fluids (culture medium, blood etc). Almost certainly, various biomolecules will adhere to it, forming a biomolecular 'corona'. The cells will encounter this corona, rather than the bare particle, and may well take it up. This will depend on the properties of the particle-corona composite.
If not functionalized, most carbon materials are indeed hydrophobic. So are CNTs. But the latter can penetrate cells, assuming a different mechanism than that of functionalized CNTs.
Entry of a molecule/particle into the cell can be through various mechanisms like endocytosis, pinocytosis, direct uptake and receptor mediated uptake. Usually nanomaterials whether hydrophobic/not enter through endocytosis and, receptor-mediated if functionalized.
Even if your carbon nanotubes would be hydrophilic, by taking a surface functionalization, the size shall be lower than ~200 nm to be effectively passed into a cell membrane through the pores.
Your hydrophobic particle may not remain hydrophobic once introduced to physiological fluids (culture medium, blood etc). Almost certainly, various biomolecules will adhere to it, forming a biomolecular 'corona'. The cells will encounter this corona, rather than the bare particle, and may well take it up. This will depend on the properties of the particle-corona composite.
The most typical cell internalization route for particles is the endocytosis, divided in different subtypes:
-- Phagocytosis
-- Pinocytosis
- Clathrin-dependent
- Clathrin-independent: macropinocytosis, caveolae-dependent and cav/clath-independent (further divided in 4 groups).
Another classification of endocytosis is based on material interaction with the cellular membrane components (receptor-mediated, adsorptive, fluid phase). However, this classification is less precise and often mistakenly used interchangeably with the previously described classification
Moreover, some particle could also penetrate the cell membrane, depending on size and surface characteristics, in a biocompatible or cytotoxic (destabilizing the phospholipid bilayer) way.
The category of endocytosis followed by the particles is strongly dependent on cell type and structural/physico-chemical particles features (mainly size, hydrophobicity and charge, shape and functionalization).
Moreover, the specific protein corona formation (due to medium/plasma proteins absorption on your particle surface) can also affect both the internalization mechanism and the uptake rate.
As Stuart and Ginevra have suggested you need to consider that your nanomaterials will adsorb proteins, lipids and sugars once they are dispersed in a biological fluids. I would suggest you read carefully the literature from Prof. Kenneth Dawson on the protein corona.
Other things you need to consider are the dispersant you use during/after synthesis and the state of aggregation of your nanomaterials in suspension. If you synthesise your nanomaterials in hydrophobic dispersants you need to change the dispersant to a water-based one. The dispersant may be highly toxic to cells. Hydrophobic NPs tend to aggregate heavily in water-based dispersions, therefore a strategy to stabilise them is needed. If your nanoparticles are aggregated when they come in contact with cells then indeed the aggregates may be too big to enter the cells via endocytosis. You have another check point here because this is also dependent on cell types, if you are using macrophages than pretty much anything from nano to micron size is taken up. Please tell us more or contact me in private if you would like to discuss more in detail.