  We explore the nematic ordering of the rod-like liquid crystals 5CB and 6CB,
embedded into parallel-aligned nanochannels in mesoporous silicon and silica
membranes as a function of mean channel radius (4.7<=R <=8.3 nm), and thus
geometrical confinement strength, by optical birefringence measurements in the
infrared region. The orientational order inside the nanochannels results in an
excess birefringence, which is proportional to the nematic order parameter. It
evolves continuously upon cooling with a precursor behavior, typical of a
paranematic state at high temperatures. These observations are compared with
the bulk behavior and analyzed within a phenomenological model. Such an
approach indicates that the strength of the nematic ordering fields sigma is
beyond a critical threshold sigma_c =1/2, that separates discontinuous from
continuous paranematic-to-nematic behavior. In agreement with the predictions
of the phenomenological approach a linear dependency of sigma on the inverse
channel radius is found and we can infer therefrom the critical channel radii,
R_c, separating continuous from discontinuous paranematic-to-isotropic
behavior, for 5CB (12.1 nm) and 6CB (14.0 nm). Our analysis suggests that the
tangential anchoring at the channel walls is of similar strength in mesoporous
silicon and mesoporous silica membranes. A comparison with the bulk phase
behavior reveals that the nematic order in nanoconfinement is significantly
affected by channel wall roughness leading to a reduction of the effective
nematic ordering.
