Response surface methodology (RSM) Central composite rotatable design (CCRD) Box-Behnken design (BBD) a b s t r a c t Box-Behnken (BBD) and central composite rotatable designs (CCRD) were used as statistical multivariate methods in the formulation optimization of fullerene loaded nano-emulsions. Effect of palm kernel oil ester (10-20%, w/w), emulsifier (5-10%, w/w) and xanthan gum (0.6-1.0%, w/w) as formulation variables on the particle size, -potential and viscosity of the nano-emulsions were investigated. Under the optimum conditions, CCRD model predicted the response values for particle size, -potential and viscosity were 153.6 nm, −53.4 mV and 42.1 Pa s, respectively. Nonetheless, BBD model suggested that the optimum conditions for a fullerene loaded nano-emulsion would gave particle size, -potential and viscosity of 151.6 nm, −53.8 mV and 43.1 Pa s, respectively. The actual response according to suggested compositions for both models showed excellent agreement with the predicted value with residual standard error (RSE) of less than 4%. Optimum nano-emulsions were stable during storage at 25 and 45 • C for 90 days and freeze-thaw cycle.

This research aims to formulate and to optimize a nanoemulsion-based formulation containing fullerene, an antioxidant, stabilized by a low amount of mixed surfactants using high shear and the ultrasonic emulsification method for transdermal delivery. Process parameters optimization of fullerene nanoemulsions was done by employing response surface methodology, which involved statistical multivariate analysis. Optimization of independent variables was investigated using experimental design based on Box–Behnken design and central composite rotatable design. An investigation on the effect of the homogenization rate (4,000–5,000 rpm), sonication amplitude (20%–60%), and sonication time (30–150 seconds) on the particle size, ζ-potential, and viscosity of the colloidal systems was conducted. Under the optimum conditions, the central composite rotatable design model suggested the response variables for particle size, ζ-potential, and viscosity of the fullerene nanoemulsion were 152.5 nm, −52.6 mV, and 44.6 pascal seconds, respectively. In contrast, the Box–Behnken design model proposed that preparation under the optimum condition would produce nanoemulsion with particle size, ζ-potential, and viscosity of 148.5 nm, −55.2 mV, and 39.9 pascal seconds, respectively. The suggested process parameters to obtain optimum formulation by both models yielded actual response values similar to the predicted values with residual standard error of <2%. The optimum formulation showed more elastic and solid-like characteristics due to the existence of a large linear viscoelastic region.