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We study the thermodynamics of an exactly solvable model of aself-interacting partially directed self-avoiding walk (DSAW) in twodimensions, when a force is applied on one end of the chain. The critical forcefor the unfolding is determined exactly, as a function of the temperature,below the $\Theta$-transition. The transition is second order and characterizedby new critical exponents which are determined by a careful numerical analysis.The usual polymer critical index $\nu$ on the critical line, and another one,which we call $\zeta$, take a non-trivial value which is numerically close to2/3.Comment: 15 pages, 9 figure

Mechanical unfolding of directed polymers in a poor solvent: Critical exponents