 Geometry-dependent erosion-rate inference

Geometry-dependent erosion-rate inference converts a measured polymer mass-loss rate into a polymer erosion front speed using an explicit model of specimen shape, exposed surfaces and density. The conversion is justified only if an inward-moving boundary actually describes the specimen. IUPAC's definition of polymer erosion concerns degradation progressing from the surface inward; loss of mass alone does not establish that spatial mechanism.^[ref]

An original constant-density calculation shows the geometric dependence. Write $q=-M^{\prime }/M$ for positive relative mass-loss rate and $v$ for positive inward boundary speed. For a sphere of radius $R$, a long cylinder of radius $R$ whose ends are protected, and a sheet of full thickness $h$ attacked on both large faces with negligible edge effects, respectively,These follow by differentiating $M=4\pi \rho R^3/3$, $M=\pi \rho R^2\ell$ with fixed length $\ell$, and $M=\rho Ah$ with fixed face area $A$. The radial boundaries obey $R^{\prime }=-v$; the two sheet boundaries give $h^{\prime }=-2v$. Exposing the cylinder ends or the sheet edges requires including their motion as well.

For stipulated $q=0.03\mathrm{da}{\mathrm{y}}^{-1}$ and current $R=1\mathrm{mm}$, the sphere implies $v=0.01\mathrm{mm}\mathrm{da}{\mathrm{y}}^{-1}$, whereas the end-protected cylinder implies $0.015\mathrm{mm}\mathrm{da}{\mathrm{y}}^{-1}$. A sheet with current $h=1\mathrm{mm}$ gives the latter speed under its two-face assumption. The identical relative mass slope therefore does not identify a unique front speed without geometry.

The retained mass fraction $f=M/M_0$ similarly impliesFor $f=0.729$, the respective radius ratios are 0.900 and approximately 0.854. These are original model predictions, not measurements of a particular polymer. A fit to retained mass cannot by itself select between the shapes or demonstrate a sharp front.

Even the relation between mass and volume needs checking. If a specimen remains spatially uniform but its density changes with time, $M=\rho V$ givesA density change contributes to the inferred relative mass slope independently of boundary motion. Nonuniform-density erosion inference requires the further spatial information hidden by this uniform-density equation. Swelling, fragment detachment and an extended reaction zone also challenge a sharp-front interpretation.

A discriminating experiment combines timed dry-mass measurements with radius or thickness measurements, imaging of cut specimens and chemical observations at different depths. Specify which faces were exposed, how drying was performed and whether dimensions were measured wet or dry. Kureha's polyglycolic acid test holds material in water, then filters and dries it before measuring retained solids.^[ref] That apparatus supplies a retained-mass curve; direct front or dimensional observations would be an additional measurement, rather than information already contained in that curve.