A thin slab of polymeric material (B) is to be crosslinked by immersing it in a well-mixed solution containing the crosslinking agent, A. The process is controlled by the molecular diffusion of A into the slab. The crosslinking reaction is instantaneous, i.e., fast compared to the diffusion process, or diffusion is the rate-limiting step. The concentration of A at the slab-solution interface is maintained constant at CA0. The diffusion coefficient of A through the uncrosslinked polymer, DAe, is known. In the crosslinking reaction, one mole of A reacts with one mole of B to produce one mole of the crosslinked polymer. The density and molecular weight of B are denoted by B and Mb respectively.

A. Draw a diagram to understand the physical process.

B. Develop a mathematical expression for the time required to crosslink a slab as a function of its thickness 2H.