  We study a single statistical amphiphilic copolymer chain AB in a selective
solvent (e.g.water). Two situations are considered. In the annealed case,
hydrophilic (A) and hydrophobic (B) monomers are at local chemical equilibrium
and both the fraction of A monomers and their location along the chain can
vary, whereas in the quenched case (which is relevant to proteins), the
chemical sequence along the chain is fixed by synthesis. In both cases, the
physical behaviour depends on the average hydrophobicity of the polymer chain.
For a strongly hydrophobic chain (large fraction of B), we find an ordinary
continuous $\theta$ collapse, with a large conformational entropy in the
collapsed phase. For a weakly hydrophobic, or a hydrophilic chain, there is an
unusual first-order collapse transition. In particular, for the case of
Gaussian disorder, this discontinuous transition is driven by a change of sign
of the third virial coefficient. The entropy of this collapsed phase is
strongly reduced with respect to the $\theta$ collapsed phase. Email contact:
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