G$$pferich erosion theory:

a$.$ Does G$$pferich erosion theory account for autocatalysis during polymer

degradation$/$erosion$?$

b$.$ Your research team at a startup company is working on using biodegradable

polymers as scaffolds to promote bone regeneration. You have found that a

polyanhydride, poly$($carboxyphenoxyhexane$)(PCH,$ structure shown below$),$ has

good mechanical properties for this application. However, porous bone scaffolds with

mean strut dimensions of $250m($as illustrated below$)$ degrade by surface erosion

and this causes the scaffold to loosen in its position when implanted at a bone defect.

Show that the erosion number calculated for this situation agrees with the

experimental observation.

c$.$ You'd like to engineer your PCH scaffolds to degrade by bulk erosion. Your

colleagues suggest that the problem could be overcome by blending PCH with

poly$($ethylene glycol$),$ which will phase separate and raise the average diffusion

constant of water in the matrix to a value one tenth that of water's natural self$-$

diffusion coefficient $($water diffusion in water$).$ Will this drive the scaffold to erode by a

bulk mechanism? $($Defend your answer with a calculation$).$ An alternative proposal is

to make the struts of the scaffold thinner. Which route would you pick an why?

PCH structure

Data for $PCH$ :

$=1\mathrm{.}05\frac{g}{c}{m}^3,$ degradation rate constant $k=1\mathrm{.}9s^{-1}$

$D_{H2O}($diffusion coefficient of water in $PCH)=1{10}^{-5}c{m}^2{s}^{-1}$