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We solve a two dimensional model for polymer chain folding in the presence ofmechanical pulling force ($f$) exactly using equilibrium statistical mechanics.Using analytically derived expression for the partition function we determinethe phase diagram for the model in the $f$-temperature ($T$) plane. A squareroot singularity in the susceptibility indicates a second order phasetransition from a folded to an unfolded state at a critical force ($f_c$) inthe thermodynamic limit of infinitely long polymer chain. Surprisingly, thetemperature dependence of $f_c$ shows a reentrant phase transition, which isreflected in an increase in $f_c$ as $T$ increases below a threshold value. Fora range of $f$ values, the unfolded state is stable at both low and hightemperatures. The high temperature unfolded state is stabilized by entropywhereas the low temperature unfolded state is dominated by favorable energy.The exact calculation could serve as a bench mark for testing approximatetheories that are used in analyzing single molecule pulling experiments.

Exact solution of the Zwanzig-Lauritzen model of Polymer Crystallization under Tension