= Selective-fragment-loss bias in polymer molar mass
\b[Selective-fragment-loss bias in polymer molar mass] arises when the chains retained or analyzed are not representative of the original molecular population. Preferential loss of short fragments can raise the measured <number-average molar mass> of the survivors even while the specimen loses mass and <chain scission> continues.
Let $M$ denote molar mass for a molecule drawn with equal probability from the original chain population. If its retention probability is $p(M)$, the number-average molar mass of retained chains is
$$
M_{n,\rm ret}=\frac{\mathbb E[Mp(M)]}{\mathbb E[p(M)]},
\qquad \mathbb E[p(M)]>0.
$$
Consequently
$$
M_{n,\rm ret}-\mathbb E[M]
=\frac{\operatorname{cov}(M,p(M))}{\mathbb E[p(M)]}.
$$
Retention favouring larger chains can make this difference positive. This is an original selection calculation; it does not assume a particular hydrolysis mechanism. If the intended measurand is explicitly the retained fraction, its correctly measured mean is not intrinsically erroneous. Bias appears when that mean is interpreted as the whole population's mean.
An original mixture has 90 chains at $1\,\mathrm{kg\,mol^{-1}}$ and ten at $100\,\mathrm{kg\,mol^{-1}}$. Its number-average molar mass is $10.9\,\mathrm{kg\,mol^{-1}}$. Removing all short chains leaves the survivor mean at 100, although only $90/1090\approx8.26\%$ of the initial chain mass has left. The large numerical increase does not imply chain growth.
A <weight-average molar mass> is a different statistic: $M_w=\sum_iN_iM_i^2/\sum_iN_iM_i$. The same initial mixture has $M_w\approx91.83\,\mathrm{kg\,mol^{-1}}$, showing why an averaging convention must accompany a reported molecular-mass value. Equal molecule weighting and equal mass weighting answer different questions.
Experimentally, distinguish residue, released soluble fragments and the fraction actually injected into the analytical instrument. A <polymer fraction-recovery balance> can compare their recovered mass. The manufacturer's <polyglycolic acid> test measures filtered dry residue after water exposure; it does not directly supply the chain distribution in the liquid that passed through.<Kuredux Polyglycolic Acid Resin technical brochure by Kureha>[PDF p. 3, Degradability test method]{ref}
<Size-exclusion chromatography> adds a further measurement model: IUPAC defines its separation chiefly through hydrodynamic volume in a porous, non-adsorbing material, not molecular mass alone.<Size-exclusion chromatography in the IUPAC Gold Book>[entry S05705, definition]{ref} Solubility, preparation losses, detector response and the mass calibration can therefore affect what distribution is inferred. Preserve the sampled fraction's identity instead of treating a cleaner chromatogram or a higher surviving mean as evidence that degradation reversed.
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