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Notes: The out-of-plane anchoring strength at the interface between 4-n-pentyl-4'-cyanobiphenyl (5CB) and an obliquely evaporated SiO was measured as a function of temperature by applying the "high-electric-field technique'' recently developed by Yokoyama and van Sprang [J. Appl. Phys. 57, 4520 (1985)]. The orientational "extrapolation length''de for the interface was found to remain virtually constant at about 30 nm up to nearly 1 K below the clearing temperature Tc=308.4 K. At temperatures closer to Tc, however, it was observed to show an apparently critical increase, which approximately follows de∝[(Tc−T)/Tc]−0.45. At 0.043 K below Tc, de=183±3 nm, yielding the anchoring energy of (1.13±0.03)×10−5 J/m2. The implications of the observed temperature dependence are first investigated by extending Gibbs' surface thermodynamics to a nematic-wall interface, deriving a general relationship between the temperature variation of de and the surface excess entropy. In particular, it is concluded on thermodynamic grounds that the exponent of −0.45 can never be associated with a real critical behavior, but is indicative of the occurrence of crossover to a more singular or noncritical behavior. To draw specific connections between the temperature dependence of de and the orientational order near the interface,we develop a simple statistical mechanical theory of the anchoring strength, based on a van der Waals picture of the nematic-wall interface. We show that the extrapolation length consists of two essentially distinct contributions: one is from the anisotropic interactions at the interface and the other is unconventionally from the interfacial inhomogeneity of the order parameter itself. For the most relevant cases, the van der Waals theory states that a reduction of the anchoring strength should always be accompanied by a depression of the surface order parameter. By comparing the theory with the experiment, the surface order parameters just below and above Tc are found to be 0.04 and 0.01, respectively, in agreement with the estimates from the contact angle and the pretransitional birefringence experiments. It is also argued, based on the present model, that the order parameter inhomogeneity is predominantly responsible for the quasicritical behavior of the anchoring strength.