The nanoscale phase behavior of a semicrystalline polymer is important for mechanical, thermal, optical and other macroscopic properties and can be analyzed well by thermal methods. Using quasi-isothermal (QI) heat capacity measurements, we investigate the formation behavior of the crystalline, mobile amorphous, and rigid amorphous fractions in poly(trimethylene terephthalate), PTT. The crystal and rigid amorphous phases comprise the total solid fraction in PTT at temperatures above T-g, the glass transition temperature of the mobile amorphous fraction. FIT was quasi-isothermally cooled step-wise from the melt which causes its crystalline fraction to be fixed below 451 K. Between the high temperature fulfillment of the T-g step and 451 K, the temperature dependent rigid amorphous fraction (RAF) is completely determined. For PTT, most of the RAF vitrifies between 451 K and T-g step by step during QI cooling after the crystals have formed. The constraints imposed by the crystal surfaces reduce the mobility of the highly entangled polymer chains. We suggest the vitrification of RAF proceeds outward away from the lamellar surfaces in a step by step manner during QI cooling. Upon reheating, devitrification of RAF occurs at a temperature above its previous vitrification temperature, due to the effects of densification brought by physical aging during the long period of quasi-isothermal treatment. Finally, we consider recent concepts related to jamming, which have been suggested to apply to filled polymer systems, and may also be applicable in describing constraints exerted by crystal lamellae upon the RAF. (C) 2011 Elsevier Ltd. All rights reserved.