The nature of chain folding in polymers and the determination of the chain length at which folding occurs have been central questions in polymer science. The study of the formation of lamellar polymer crystals through chain folding has received a new impetus as a result of the recent synthesis of normal alkanes of strictly uniform chain lengths up to C(390) H(782). Chain folding is found in all such paraffins starting with C(150)H(302). As with polyethylenes obtained by conventional polymerization, the fold length in the normal alkanes varies with crystallization temperature, but it is always an integral reciprocal of the full chain length. This behavior indicates that the methyl end groups are located at the lamellar surface and that the fold itself must be sharp and adjacently reentrant.

High-quality positron lifetime measurements (70 million total counts) are reported for polyethylenes (PEs) of different crystallinities (X c ϭ 3-82%). The specific volumes of the crystalline and amorphous phases (V c and V a , respectively) were estimated from density and wide-angle X-ray scattering (WAXS) experiments. Some samples (those with low values of X c ) were branched PEs, and those with high values of X c were linear PEs for which X c was varied with changes in the crystallization temperature. Both V c and V a increase with decreasing X c in the range 0% Յ X c Յ 56% (the branched PEs) but are constant for X c Ն 56% (the linear PEs). The lifetime spectra were analyzed with the MELT and LIFSPECFIT routines. Artifacts that can appear in the spectrum analysis were checked via an analysis of computer-generated spectra. Four lifetime components appeared in all of the PEs; the two long-lived ones are attributed to pick-off annihilation of ortho-positronium (o-Ps) in crystalline regions ( 3 ) and in holes of the amorphous phase ( 4 ). With increasing X c , 3 decreases from about 1.2 to 1 ns, 4 decreases from 3.0 to 2.5 ns, and the intensity I 4 decreases from 29 to 0%. An increase in I 3 from 6 to 12% was observed. A comparison with simulations shows that the true I 3 value approaches 0 for X c 3 0%. The decrease in I 4 is weaker than the increase in X c ; this leads to the conclusion that the apparent specific o-Ps yield in the amorphous phase I 4 Xc increases with X c . Possible reasons for this surprising results are discussed. The fractional free hole volume [h ϭ (V a Ϫ V occ )/V a , where V occ is the crystalline occupied volume] was estimated from density and WAXS results. Between X c ϭ 0 and 56%, h decreases from 0.151 to 0.090, but it does not change further above X c ϭ 56%. The mean size (v) of the local free volumes (holes) estimated from 4 decreases from 200 to 150 Å 3 . The number density of holes (N h ) calculated from these values (N h ϭ h/v) also decreases from 0.8 to 0.6 nm Ϫ3 in the range 0% Յ X c Յ 56%. The values of V a , V c , h, and N h increase with an increasing degree of branching but do not vary for linear PEs. The possible influence of a crystalline-amorphous interfacial phase (three-phase model) on the observed lifetime parameters is also discussed.

The effect of cross-linking on the free-volume properties of poly(diethylene glycol bis(allyl carbonate)) networks was studied using a series of networks with progressively decreasing density of cross-links. The networks were prepared by bulk copolymerization of ethylene glycol bis(allyl carbonate) with an increasing amount of allyl ethoxyethyl carbonate. The mean free-volume hole radius (r) and the hole volume (v) as well as the hole radius and hole volume density distributions were estimated from positron lifetime measurements. It was found that with increasing concentration of monoallyl comonomer, the mean hole size increases from r = 0.250 nm (v = 0.066 nm3) for the pure diallyl component to 0.300 nm (0.114 nm3) for the 75% concentration of the monoallyl comonomer. Similarly, the hole size distributions shift to larger values. The local free-volume properties were correlated with the glass transition temperature and the specific volume. The comparison of the hole volume with the specific volume allowed us to estimate the number density of holes of ∼1 × 1027 m-3 and a free-volume hole fraction which increases with the concentration of the monoallyl from 0.066 to 0.113.

Positron annihilation lifetime spectroscopy (PALS), density, and differential scanning calorimetric (DSC) measurements were used to study systematically the variation of the glass‐transition temperature (Tg) and the size v and number density Nh 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 Va was estimated and used to calculate the fractional free (hole) volume h and value of Nh. The variations of Tg, v, Va, h, and Nh were related to the degree (number and length) of branching. Tg 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, Tg 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 Tg was also found. The number density of holes was estimated to be Nh = 0.49(±0.07) nm−3 and Nh′ = 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 Va. 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