Free volume,glass transition,and degree of branching in metallocene‐based propylene/α‐olefin copolymers: Positron lifetime,density, and differential scanning calorimetric studies

Positron annihilation lifetime spectroscopy (PALS), density, and differential scanning calorimetric (DSC) measurements were used to study systematically the variation of the glass‐transition temperature (T_g) and the size v and number density N_h of local free volumes in n‐alkyl‐branched polypropylenes. The samples were metallocene‐catalyzed propylene copolymers with different α‐olefins (from C₄ to C₁₆) and a different α‐olefin content (between 0 and 20 mol %). From the total specific volume and crystallinity the specific volume of the amorphous phase V_a was estimated and used to calculate the fractional free (hole) volume h and value of N_h. The variations of T_g, v, V_a, h, and N_h were related to the degree (number and length) of branching. T_g decreases and v increases linearly with the number and length of n‐alkyl branches. This behavior was attributed to an increased segmental mobility caused by branching. Both values, T_g and v, follow linear master curves as a function of the degree of branching (DB) if this is defined as the number of all side‐chain carbons with respect to a total of 1000 (main‐chain and side‐chain) carbons. Only propylene/1‐butene copolymers deviated from these relations. A linear relation between v and T_g was also found. The number density of holes was estimated to be N_h = 0.49(±0.07) nm^?3 and N_h′ = 0.58(±0.11) × 10²¹ g^?1, respectively. It shows a slight variation with the DB, which is also seen in the behavior of the specific volume V_a. This variation was explained by the appearance of sterical hindrances resulting from short‐chain branches that may prevent an efficient packing of the chains. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 434–453, 2002; DOI 10.1002/polb.10108