  An extensive study of single block copolymer knots containing two kinds of
monomers $A$ and $B$ is presented. The knots are in a solution and their
monomers are subjected to short range interactions that can be attractive or
repulsive. In view of possible applications in medicine and the construction of
intelligent materials, it is shown that several features of copolymer knots can
be tuned by changing the monomer configuration. A very fast and abrupt swelling
with increasing temperature is obtained in certain multiblock copolymers, while
the size and the swelling behavior at high temperatures may be controlled in
diblock copolymers. Interesting new effects appear in the thermal diagrams of
copolymer knots when their length is increased.
