title: Determination of Effective Particle Density for Sterically Stabilized Carbon Black Particles: Effect of Diblock Copolymer Stabilizer Composition.
abstract: Two poly(styrene-b-hydrogenated isoprene) (PS-PEP) copolymers and a poly(styrene-b-hydrogenated butadiene) (PS-PB) diblock copolymer of differing polystyrene content (20, 28 or 35 mol %) and molecular weight (117-183 kg mol(-1)) are examined. These copolymers form star-like micelles in n-dodecane, as judged by TEM, DLS, and SAXS studies. At ambient temperature, such micelles are known to adsorb intact onto a model colloidal substrate such as carbon black, conferring a high degree of dispersion (Growney, D. J.; Mykhaylyk, O. O.; Armes, S. P. Langmuir 2014, 30, 6047). Isotherms for micellar adsorption on carbon black at 20 °C are constructed using a supernatant depletion assay based on UV spectroscopy by utilizing the aromatic chromophore in the polystyrene block. Perhaps surprisingly, the diblock copolymer with the lowest polystyrene content has the strongest affinity for the carbon black particles. Assuming that the star-like diblock copolymer micelles adsorb onto carbon black to form hemi-micelles with a stabilizer layer thickness equal to the mean micelle radius, the effective particle density of the resulting sterically stabilized carbon black particles in n-dodecane can be estimated from the SAXS micelle dimensions based on geometric considerations. As an approximation, a spherical core-shell morphology was assumed, and the primary grain size of the carbon black particles was determined to be 74 nm diameter as judged by BET surface area analysis. Using this approach, effective particle densities of 0.90, 0.91, and 0.92 g cm(-3) were calculated for sterically stabilized carbon black particles prepared using the PS-PB20, PS-PEP28, and PS-PEP35 diblock copolymers, respectively. These densities are significantly lower than that of carbon black (1.89 g cm(-3)), which indicates that the sterically stabilized carbon black particles are substantially solvated. Since the rate of sedimentation of the sterically stabilized carbon black particles depends on the density difference between the effective particle density and that of n-dodecane (0.75 g cm(-3)), particle size analysis via analytical centrifugation incurs large sizing errors unless the above corrected effective particle densities are utilized. This is important because analytical centrifugation is a highly convenient technique for assessing the relative degree of dispersion of sterically stabilized carbon black particles, which are utilized to inkjet inks and coatings formulations.
authors.affiliation: †Department of Chemistry, University of Sheffield, Brook Hill, Sheffield, South Yorkshire S3 7HF, U.K.
authors.forename: David J
authors.initials: DJ
authors.lastname: Growney
authors.affiliation: †Department of Chemistry, University of Sheffield, Brook Hill, Sheffield, South Yorkshire S3 7HF, U.K.
authors.forename: Patrick W
authors.initials: PW
authors.lastname: Fowler
authors.affiliation: †Department of Chemistry, University of Sheffield, Brook Hill, Sheffield, South Yorkshire S3 7HF, U.K.
authors.forename: Oleksandr O
authors.initials: OO
authors.lastname: Mykhaylyk
authors.affiliation: †Department of Chemistry, University of Sheffield, Brook Hill, Sheffield, South Yorkshire S3 7HF, U.K.
authors.forename: Lee A
authors.initials: LA
authors.lastname: Fielding
authors.affiliation: †Department of Chemistry, University of Sheffield, Brook Hill, Sheffield, South Yorkshire S3 7HF, U.K.
authors.forename: Matthew J
authors.initials: MJ
authors.lastname: Derry
authors.affiliation: ‡BP Formulated Products Technology, Technology Centre, Whitchurch Hill, Pangbourne, RG8 7QR, U.K.
authors.forename: Najib
authors.initials: N
authors.lastname: Aragrag
authors.affiliation: ‡BP Formulated Products Technology, Technology Centre, Whitchurch Hill, Pangbourne, RG8 7QR, U.K.
authors.forename: Gordon D
authors.initials: GD
authors.lastname: Lamb
authors.affiliation: †Department of Chemistry, University of Sheffield, Brook Hill, Sheffield, South Yorkshire S3 7HF, U.K.
authors.forename: Steven P
authors.initials: SP
authors.lastname: Armes