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We develop a model for charge trapping on conjugated polymer chains using acontinuous representation of the polymer. By constraining the motion to alongthe chain, we find that kinks along the chain serve as points of attraction andcan induce localization and spontaneous buckling of the chain. We implementthis in a model system of a conjugated polymer donor and fullerene acceptor tomimic a polymer based photovoltaic system. We find that geometric fluctuationsof the polymer give rise to deep potential energy traps at kinks which areoften stronger than the Coulomb interaction between the electron and hole.

Quantum motion of charges in $\pi$-conjugated polymers: kinkiness induces localization