  Poly($para$-phenylene) has been recognized as one important family of
conducting polymers upon doping with donors or acceptors. This system possesses
a chain-like structure with infinite benzene rings linked with the single C-C
bond. Oligophenyls as models of poly($para$-phenylene) with short chains in the
\emph{para} position were found to exhibit superconductivity at transition
temperatures ranging from 3 K to 123 K upon dopant. Structural studies have
revealed that there exist the order-disorder transitions in many
\emph{p}-oligophenyls with almost doubled lattice constants in the \emph{b} and
\emph{c} directions at low temperatures, seemingly supporting the formation of
the charge-density-wave order. Such a transition is of relevance to the
understanding of the emergence of novel quantum functionality where
unconventional polaronic interactions are relevant for the new emerging theory
of superconductivity in this system. However, the accurate temperatures for the
order-disorder transitions amongst these \emph{p}-oligophenyls are still needed
to be determined. The chain length effects on the order-disorder transitions in
this system remain unknown. Here we report the systematic investigation of the
evolution of vibrational properties of the crystalline \emph{p}-oligophenyls
over a wide temperature range. The order-disorder transition is identified by
three indicators, the lowest energy peak together with the intensity ratios
between the 1280 cm$^{-1}$ and 1220 cm$^{-1}$ modes and between the two modes
at around 1600 cm$^{-1}$. A phase diagram of the order-disorder transition
temperature as well as the melting curve for \emph{p}-oligophenyls is thus
established. The former is found to increase with the chain length and
saturates at around 350 K for poly($para$-phenylene).
