  Exact solutions for the elastic and thermodynamic properties for the wormlike
chain model are elaborated in terms of Mathieu functions. The smearing of the
classical Euler buckling instability for clamped polymers is analyzed for the
force-extension relation. Interestingly, at strong compression forces the
thermal fluctuations lead to larger elongations than for the elastic rod. The
susceptibility defined as the derivative of the force-extension relation
displays a prominent maximum at a force that approaches the critical Euler
buckling force as the persistence length is increased. We also evaluate the
excess entropy and heat capacity induced by the compresssion and find that they
vary non-monotonically with the load. These findings are corroborated by
pseudo-Brownian simulations.
