Polymer light-emitting diodes with poly(2-decyloxy-1,4-phenylene), DO-PPP, as the luminescent polymer emit blue light with external quantum efficieny of similar to 3%. Using internal field emission (Fowler-Nordheim tunneling) in single carrier devices, the top of the pi band and the bottom of the pi* band have been determined for DO-PPP, and for poly(2-methoxy-5-(2'-ethyl-hexyloxy)-1,4-phenylene vinylene), MEH-PPV. For DO-PPP, the single particle pi-pi* energy gap is 3.4-3.6 eV; for MEH-PPV, the pi-pi* energy gap is 2.2-2.3 eV. Comparison with optical absorption (the optical gap) implies that the exciton binding energy is small; for both polymers, E(exc) less than or equal to 0.2 eV. Such small residual values are probably not significant in the presence of disorder broadening which is also 0.1-0.2 eV and in the presence of lattice relaxation with self-localization energies of approximately 0.2 eV.