 Polymer fraction-recovery balance

A 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.^[ref]

For an original closed repeat-unit bookkeeping model with no destruction of those units, let $U_0$ be the initial inventory. WriteHere $r$ 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,An original example recovers 80 mg with $M_n=80\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$ and 20 mg with $M_n=2\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$. These correspond to $1\mu \mathrm{mol}$ and $10\mu \mathrm{mol}$ of chains. Their combined 100 mg divided by $11\mu \mathrm{mol}$ gives $M_n\approx 9.09\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$. The mass-weighted average of the two reported means, $64.4\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$, 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.^[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.^[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.