  Polymers adopt extended coil and compact globule states according to the
balance between entropy and interaction energies. The transition of a polymer
between an extended coil state and compact globule state can be induced by
changing thermodynamic force such as temperature to alter the energy/entropy
balance. Previously, this transition was theoretically studied by taking into
account the excluded-volume interaction between monomers of a polymer chain
using the partition function. For binary mixtures of a long polymer and short
polymers, the coil-globule transition can be induced by changing the
concentration of the shorter polymers. Here we investigate the transition
caused by short polymers by generalizing the partition function of the long
polymer to include the excluded-volume effect of short polymers. The
coil-globule transition is studied as a function of the concentration of mixed
polymers by systematically varying Flory's chi-parameters. We show that the
transition is caused by the interplay between the excluded-volume interaction
and the dispersion state of short polymers in the solvent. We also reveal that
the same results can be obtained by combining the mixing entropy and elastic
energy if the volume of a long polymer is properly defined.
