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We have measured the positron annihilation lifetime spectra in an epoxy polymer using the electrotechnical laboratory (ETL) slow-positron facility as a function of positron energy from 0.2 to 3.0 keV. The ortho-positronium lifetime from the bulk increases near the surface while the intensity decreases. The results are interpreted in terms of a Ps free-volume model. A larger hole size and fraction near the polymeric surface are observed. A reduction of glass transition temperature near the surface is estimated from the WLF theory.