scenario by means of the Bethe-Peierls approximation'
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Introduction
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Despite extensive extensive experimental and theoretical work, some aspects of the polymer glass formation still remain unresolved puzzles. In the present work we address one such unresolved problem related to the role of the surface in the glass formation. The glass transition in confined geometries has been in a focus of intensive experimental and theoretical investigations in several decades. Scientific disputes continue concerning whether depression [@DecreaseTg2; @DecreaseTg3; @DecreaseTg4; @DecreaseTg5; @DecreaseTg6; @DecreaseTg7; @SimulDecreaseTg; @TheorDecreaseTg] or enhancement [@IncreaseTg1a; @IncreaseTg; @IncreaseTgSurfEng; @IncrTgAttrSurf; @InctrTgAtrrSurf; @IncrTgNeutrSurf1; @IncrTgNeutrSurf2; @Saalwachter] of glass transition temperature $T_g$ is exerted by surface. The dynamic aspect of the slowing down of the cooperative molecular motions is attributed to the well-known mechanisms described by the classical theories. [@Adam_Gibbs; @Cohen_Grest; @Goetze] Despite some progress in understanding of the vitrification transition achieved with help of these theories, the driving mechanism of the cooperative motions near the glass transition is rather poorly understood. Restrictions imposed on these motions by the presence of interfaces in the system result in increasing of the enthalpy and reducing the entropy that can be described in terms of relevant characteristic length scales. According to the dynamic and calorimetric measurements, the 