Acylation of cellulose was carried out via Acetyl Chloride esterification, based on methodology by Org. Lett., 2005, 7, 1805-1808. 1 cm diameter agarose spheres were passed through a thin film of the polymer to coat. Thickness was then calculated by the difference in measured initial and final diameters (an average of 5 diameters, using 0.01 mm precision callipers).
The volatility and poor visible absorption of DCM posed a challenge in reliably measuring rates of diffusion though the polymer. We decided to base our modelling on the diffusion of indigo dye from within prepared beads, collecting the following spectrophotometric absorption data (calibrated to prepared concentration standards):
Alongside the experimental absorption data (red) we have plotted our theoretical lines of best fit. We predicted that system behaviour would be governed by Fick’s law, which states that:
i.e. that mass flux is proportional to a concentration gradient. Hence, we further predicted that the response of our system would follow the classic exponential asymptotic approach to a maximum value where the concentrations of dye both inside and outside the system were equal.
Thus our lines of best fit take the form:
φ = average concentration outside bead (g/ml)
A = equilibrium concentration (g/ml)
k = variable dictating rate of approach to equilibrium (min^-1)
t = time (min)
The value of k in each system was obtained through our parameter fitting algorithm.
Our results are tabulated below:
These results demonstrate that the polymer coating is indeed diffusion limiting due two simultaneous effects. Firstly, the rate at which the system reaches equilibrium concentration i.e. defined by the variable k which is itself a function of bead surface area, polymer diffusivity and coating thickness, is reduced in each of the systems. Furthermore, the maximum concentration reachable at the equilibrium point is itself a function of the thickness of the coating and decreases as the polymer thickness increases.