Sum-frequency vibrational spectroscopy has been used to probe the chain orientation of polyvinyl alcohol at the surface after rubbing. The distribution function of the chain orientation is determined quantitatively. The orientational order parameter of the chains deduced from the distribution matches well with that of a liquid crystal monolayer deposited on the polymer, proving that the polymer surface can align a liquid crystal film through orientational epitaxy. [S0031-9007(99)09202-9] PACS numbers: 68.35.Bs, 42.65.Ky, 78.30.Jw Among modern strategic materials, polymers have become increasingly important in our daily life. In many applications, polymer interfaces play a pivotal role. Often it is the orientation and conformation of molecular units at a polymer surface that determine the polymer interfacial properties. For example, surface molecular orientation directly affects adhesion of a polymer to metals or semiconductors, which is vital to modern electronic devices and systems [1]. Surface molecular conformation of a biopolymer, such as protein, DNA, and RNA, strongly influences binding of ligands to a substrate and hence the enzymatic function of the biopolymer [2]. A polymer surface with oriented polymer chains could serve as a template for growing highly ordered polymeric or organic crystals superb in mechanical, electrical, thermal, or optical properties [3]. As a more specific case, rubbed polymer films have long been used in the liquid crystal display industry as substrates for obtaining the desired liquid crystal (LC) bulk alignment. Rubbing presumably modifies the polymer surface structure, and then aligns the LC [4,5]. To study how rubbing affects the polymer surface structure, a number of techniques have been used with varying degrees of success. Ellipsometry [6] and infrared spectroscopy [7] can measure rubbing-induced anisotropy in the surface region of a polymer film, but are incapable of probing the real surface because of their lack of surface specificity. Atomic force microscopy [8] can provide images of rubbed polymer surfaces although the spatial resolution may be limited. Near-edge x-ray absorption fine structure spectroscopy [9] can probe a surface layer of 1 nm thick and yield information on the orientational order parameter of a rubbed polymer surface.Recently, sum-frequency generation (SFG) vibrational spectroscopy has been demonstrated to be an effective surface analytical probe [10]. As a second-order nonlinear optical process, it is forbidden in media with inversion symmetry, but allowed at interfaces where the inversion symmetry is necessarily broken. Therefore it is particularly sensitive to the interfacial structure between two centrosymmetric media. When used to probe surface molecular orientation, it can provide information not only on the average molecular orientation and order parameter but also on the orientational distribution. We report here application of this technique to the study of surface alignment of polymer chains by rubbing. We take polyvinyl alcohol (PVA, ͓-C...