The application of the surface energy based solubility parameter theory for the rational design of polymer-functionalized MWCNTs† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c8cp07411a

Solubility parameter theories can be used to model the degree of polymer functionalization of MWCNTs in different solvent media.

Solution nuclear magnetic resonance (NMR) spectra were recorded at 298K on a 400 MHz Bruker AVANCE III HD. The samples were prepared using deuterated chloroform (99.8% D) purchased from Sigma-Aldrich.
The MALDI-TOF spectrum for the molecular weight characterization was recorded on a Bruker Microflex LT spectrometer. The samples were prepared using a polymer solution with a concentration of 2 mg/mL in THF, a 0.6 M solution of DCTB in THF and 0.06 M solution of silver trifluoracetate in THF. The silver trifluoroacetate to promote the ionization of the polymer 1 . For the analysis 10 µL of each solution were mixed in a vial. Afterwards 0.5 µL of the mixture was drop casted in the MALDI-TOF target.
Themogravimetric analysis was performed under nitrogen atmosphere in a Perkin Elmer Diamond TG/DTA6300 using a heating rate of 10 °C/minute. Gel permeation chromatography (GPC) data was obtained using a Shimadzu LC-20AD instrument with HPLC grade THF as the eluent flowing at 1.0 mL/min at 30 °C and calibrated using near monodisperse polystyrene standards.
Transmission Electron Microscopy images were recorded on a JEOL 3000F TEM microscope operating in an accelerating voltage of 300 kV. The samples were prepared by drop casting MWCNTs dispersions in acetone into lacey-carbon copper grids.

Hansen solubility parameters and calculation of the surface energy based solubility parameters
The calculation of the HSP surface energy based solubility parameters was performed according to Bergin Where ES,Total is the surface energy of the substance, δi are the Hansen solubility parameters (HSP) of the substance, and αi are empirical constants that are equal to αD = 1 and αP,H = 0.632. In addition, the total surface energy (ES,Total) of the solvents were calculated using the following equation: Where γ is the surface tension of the solvent and ΔSs is the solvents surface entropy that is equal to 0.1 mJ m -2 K -1 and can be considered constant for any organic solvent 2,3 . Finally, the surface energy based solubility parameter was calculated as follows: In the following

Synthesis of polystyrene by ATRP
The methodology for the synthesis of polystyrene was based on a procedure reported previously 8 . In a typical experiment 2-(4-bromomethyl)phenylpropionic acid (1.05 g, 4.34 mmol), copper (I) bromide (0.62g, 4.34 mmol), and 2,2-bipyridine (1.35g, 8.68 mmol) were added to a three-necked round bottom flask. The flask was fitted with a septum and the solid powders were flushed in vacuum and purged with argon in a Schlenck line, the evacuation procedure was repeated three times. Afterwards, 3.5 mL of DMF were added and the mixture was flushed in vacuum and purged with argon in a Schlenck line, the evacuation procedure was repeated three times. Under a nitrogen (N2) flow, 20 mL of deoxyganated styrene were added with a syringe to the reaction vessel and it was placed in an oil bath at 110 C for 3 hours. Afterwards, the reaction mixture was stopped and diluted in 200 mL of THF.
The mixture was vacuum filtered through a short neutral alumina column to remove the solid catalyst particles and the mixture was concentrated under vacuum and precipitated in methanol twice. The polymer was separated by vacuum filtration obtaining a light blue powder. 1 H NMR (Fig. S2) was consistent with the expected polystyrene spectrum and MALDI-TOF mass spectrometry (Fig. S3) showed that the difference of the molecular masses is equal to the expected mass of styrene monomers. 1 H NMR (450MHz, CDCl3): 7.10-6.50 ppm (broad, aromatic H), 2.5-1.1 ppm (broad, CH+CH2). The polymer number average molecular weight (Mn= 3333 g/mol) and weight average molecular weight (Mw=3609) were determined by GPC. MALDI-TOF mass spectrometry of the polymer showed a molecular weight separation of 104 g/mol consistent with the molecular weight of the styrene molecules ( Figure S2).

Figure S1
NMR spectrum of the polystyrene used during this study. The 1H signals corresponding to the aliphatic and aromatic hydrogens of the styrene monomers are tagged in blue.

Figure S2
MALDI-TOF mass spectrum of the polystyrene used during this study. The two most intense mass counts are highlighted.