Polymer Brushes for Molecular Transport - Paul Braun Research ...

(Figure 1.4 (a)) is assumed to occur from molecular diffusion in the 2-dimensional plane of the
bleached region. The resulting fluorescence intensity versus distance profiles (i.e. concentration
files) are extracted after image analysis using a program written in C.[51, 52] Simulated
concentration profiles are generated following Fick’s law (Figure 1.4 (b), see derivations below),
and compared with the experimental results to determine the diffusion coefficient.
We consider the diffusion in our system occurring in an infinitely thin sheet in a long
circular cylinder in which the diffusion is uniform along the radial direction. The concentration
of diffusing molecules is a function of radius r and time t.[53]
∂C
1 ∂ ⎛ ∂C
⎞
= D ⎜r
⎟
(1.1)
∂t
r ∂r
⎝ ∂r
⎠
The initial concentration distribution is: C = 0, 0