Consider a system with $0\mathrm{.}1M$ DMPA as a photoinitiator with a molar absorptivity of

$150\frac{L}{mo{l}^{**}(cm)}$ at $365nm$ and $)$ at $305nm($conventional

absorptivities$)$ in a $250$ micron thick sample. Neglect diffusion of the initiator and

products.

a$.$ Calculate the absorbed photon flux of $100m\frac{W}{c}{m}^2$ light split equally $($in terms

of energy$)$ between the two wavelengths as a function of depth at time zero.

b$.$ Assuming a quantum yield of $0\mathrm{.}6,$ an efficiency of $0\mathrm{.}8$ and that DMPA forms

two radicals that both initiate polymerization, what is the total radical

generation rate as a function of depth in the sample.

c$.$ At the top surface of the sample, how long will it be before $90\%$ of the initiator

has reacted, assuming no diffusion $($and only determining how long it takes at

the top surface $-$ not $90\%$ of the initiator throughout the entire sample$)?$

d$.$ For long exposures, what would happen $($describe qualitatively$)$ to the

initiation rate as a function of depth if the decomposition products absorbed

light more strongly than the initiator $($i$.$e$.,$ photodarkening$)?$ What if they

absorbed no light $($photobleaching$)?$