The cycle
The first amino acid is attached to a resin bead. Then a cycle repeats: remove the protecting group from the chain end, couple the next protected amino acid, wash. Because the chain is immobilised, purification between steps is a wash rather than an isolation, which is what makes the process practical.
When the chain is complete it is cleaved from the resin and the side-chain protecting groups are removed, usually in strongly acidic conditions.
Why length is limited
Each coupling is efficient but not perfect. At 99% efficiency per step a 30-residue peptide finishes at about 74% intact chains; at 50 residues, about 61%. The remainder are deletion sequences differing from the target by one or more residues — and being so similar, they are the hardest impurities to separate.
This compounding is the practical ceiling on synthesis, and the reason long chains are made biologically instead.
What it means for purity
A chromatographic purity figure on a synthetic peptide is largely a statement about how well those closely related chains were separated. That is a harder separation than removing an unrelated contaminant, which is why method matters.
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