  Vibrational heat transport in molecular junctions is a central issue in
different contemporary research areas like Chemistry, material science,
mechanical engineering, thermoelectrics and power generation. Our model system
consists of a chain of molecules which sandwiched between two solids that are
maintained at different temperatures. We employ quantum self-consistent
reservoir model, which is built on generalized quantum Langevin equation, to
investigate quantum effects and far from equilibrium conditions on thermal
conduction at nanoscale. The present self-consistent reservoir model can easily
mimic the phonon-phonon scattering mechanisms. Different thermal environments
are modelled as (i) Ohmic, (ii) sub-Ohmic, and (iii) super-Ohmic environment
and their effects are demonstrated for the thermal rectification properties of
the system with spring graded or mass graded feature. The behavior of heat
current across molecular junctions as a function of chain length, temperature
gradient and phonon scattering rate are studied. Further, our analysis reveals
the effects of vibrational mismatch between the solids phonon spectra on heat
transfer characteristics in molecular junctions for different thermal
environments.
