Because the laboratory gas-phase electronic spectra of only the three polyatomic bare carbon chains C3, C4 and C5 are available, we have made a further attempt to detect the origin bands of C4 (3789 Å) and C5 (5109 Å) in the diffuse cloud toward ζ Oph. The measurements provide an improved 3 σ limit to their column densities: N(C4)<=5×1011 cm-2 and N(C5)<=1×1011 cm-2, with a signal-to-noise ratio (S/N) of 42,000 and 31,000 Å-1, respectively, at a resolution of 110,000. The limits to N(C4) and N(C5) are lower than predictions from the chemical model used by Roueff and coworkers for such diffuse clouds. In conjunction with observations of related, hydrogen-containing polar chains in the millimeter region and laboratory studies of the electronic transitions of a number of homologous series, these results lead to interesting conclusions about the role of carbon chains as potential carriers of the diffuse interstellar bands (DIBs). First, the abundance and oscillator strength of smaller chains, say up to 10 atoms, are too small to account for the stronger DIBs. Second, because of the electronic configurations of these open-shell species, the lowest energy π-π transition does not have a large oscillator strength but the higher energy one in the UV does, and the chains would have to be prohibitively long for these absorptions to shift into the DIB 4000-9000 Å wavelength region. The exceptions are closed-shell systems such as the odd-numbered bare carbon chains, and the ones in the C15-C31 size range that have their very strong transitions in this region. These species should be a major goal for laboratory and subsequent astronomical studies.