= Polymer fraction-recovery balance
A \b[polymer fraction-recovery balance] accounts for material recovered in each sampled fraction after a <polymer> experiment, including retained solids, dissolved products, filter deposits and container rinses. It tests whether the fractions used to infer a <molar mass distribution> represent the intended population. A decrease in retained mass and a change in the <number-average molar mass> of the analyzed fraction are different observations.
First specify a <polymer recovery accounting basis>. Comparable dry masses can be summed when they describe the same material inventory; chemical transformation may instead require a conserved-element or repeat-unit inventory. For example, <ester hydrolysis> incorporates <water> into new end groups. Summing product mass as though it were unchanged original <polymer> mass then mixes accounting conventions. The manufacturer's decomposition diagram for <polyglycolic acid> explicitly distinguishes hydrolytic decomposition from later microbial degradation.<Kuredux Polyglycolic Acid Resin technical brochure by Kureha>[March 2022 brochure, PDF p. 2, decomposition diagram]{ref}
For an original closed repeat-unit bookkeeping model with no destruction of those units, let $U_0$ be the initial inventory. Write
$$
U_0=U_{\rm solid}+U_{\rm soluble}+U_{\rm other}+U_{\rm unrecovered},\qquad
r=\frac{U_{\rm solid}+U_{\rm soluble}+U_{\rm other}}{U_0}.
$$
Here $r$ is recovery on that specified basis. Material converted into unmeasured chemical products belongs in the unaccounted inventory until measured; a recovery deficit alone does not identify its chemical fate.
On a stipulated consistent mass-equivalent basis, start with 100 mg and recover 70 mg in solids, 20 mg in the soluble fraction and 5 mg in rinses. Recovery is 95%, leaving 5 mg unaccounted. The 30 mg decrease in retained solids is not evidence that all 30 mg was collected as soluble material: only 20 mg was measured there. Experimental <mass balance> requires those distinctions even when a single residue curve appears smooth.
Combining recovered <number-average molar masses> also requires counting chains rather than averaging the reported means by mass. If fraction $i$ has mass $m_i$ and correctly measured number-average molar mass $M_{n,i}$, its <amount of substance> of chains is $m_i/M_{n,i}$. Thus, for the combined measured fractions,
$$
M_{n,\rm combined}=\frac{\sum_i m_i}{\sum_i m_i/M_{n,i}}.
$$
An original example recovers 80 mg with $M_n=80\,\mathrm{kg\,mol^{-1}}$ and 20 mg with $M_n=2\,\mathrm{kg\,mol^{-1}}$. These correspond to $1\,\mathrm{\mu mol}$ and $10\,\mathrm{\mu mol}$ of chains. Their combined 100 mg divided by $11\,\mathrm{\mu mol}$ gives $M_n\approx9.09\,\mathrm{kg\,mol^{-1}}$. The mass-weighted average of the two reported means, $64.4\,\mathrm{kg\,mol^{-1}}$, is not their combined <number-average molar mass>. Missing fractions with unknown chain counts prevent this calculation from establishing the whole original population's mean.
A useful collection protocol measures initial material, retained residue, filtrate and rinses separately, with preparation blanks and stated drying conditions. Kureha's published water-exposure protocol measures filtered, dried solids, so that observable covers only one part of the balance.<Kuredux Polyglycolic Acid Resin technical brochure by Kureha>[PDF p. 3, Degradability test method]{ref} A <size-exclusion chromatography> trace of a selected fraction adds another measurement model: IUPAC defines that separation chiefly through hydrodynamic volume in porous non-adsorbing material.<Size-exclusion chromatography in the IUPAC Gold Book>[entry S05705, definition]{ref} Recovery, representativeness and the conversion from separation to <molar mass> must all be justified before interpreting a survivor distribution as the full degraded sample.
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