  The line-dipole approximation for the evaluation of the exciton transfer
integral, $J$, between conjugated polymer chains is rigorously justified. Using
this approximation, as well as the plane-wave approximation for the exciton
center-of-mass wavefunction, it is shown analytically that $J \sim L$ when the
chain lengths are smaller than the separation between them, or $J\sim L^{-1}$
when the chain lengths are larger than their separation, where $L$ is the
polymer length. Scaling relations are also obtained numerically for the more
realistic standing-wave approximation for the exciton center-of-mass
wavefunction, where it is found that for chain lengths larger than their
separation $J \sim L^{-1.8}$ or $J \sim L^{-2}$, for parallel or collinear
chains, respectively. These results have important implications for the
photo-physics of conjugated polymers and self-assembled molecular systems, as
the Davydov splitting in aggregates and the F\"orster transfer rate for exciton
migration decreases with chain lengths larger than their separation. This
latter result has obvious deleterious consequences for the performance of
polymer photovoltaic devices.
