Dlubek free volume from PALS

Kilburn, D., Dlubek, G., Pionteck, J., Bamford, D., and Alam, M. A., Microstructure of free volume in SMA copolymers 1. Free volume from Simha-Somcynsky analysis of PVT experiments. Polymer, 46, 859-868 It. Local free volume from PALS, ibid., 869-876 (2005). 

FIGURE 11.9 Specific total, V, free Vf = hV, and occupied, Vqcc = (1 — h)V, volume of PC as a function of T at ambient P. h is the hole fraction calculated from V using the S-S equation of state. Open symbols, experimental data dots, S-S equation of state fits to the volume in the temperature range T>Tg-, stars, free volume calculated from Vf=N v,), where (Vf,) is the mean hole volume from PALS and is the specific hole density, assumed to be constant at N f = 0.67 X 10 g (corresponding to 0.81 nm at 300 K). (Adapted from Dlubek et al., [2007d].)... 

Dlubek, G., Bondarenko, V., Al-Qaradawi, I. Y., Kilburn, D., and Krause-Rehberg, R., Structure of free volume in SAN copolymers from positron lifetime and PVT experiments II. Local free volume from positron annihilation lifetime spectroscopy (PALS), Macromol. Chem. Phys., 205, 512-522 (2004c). 

Since the 1960s position annihilation lifetime spectroscopy (PALS) has been used to measure free-volume cell size and/or its content in liquids or solids. The three chapters of Part III discuss correlations between the PALS experimental values and those computed from the S-S theory. Chapter 10, by Consolati and Quasso, considers free volume in amorphous polymers Chapter 11, by Dlubek, its distribution from PALS and Chapter 12, by Jamieson et al., the free volume in heterogeneous polymer systems. These state of the art texts offer intriguing observations on the structure of polymeric systems and its variation with independent variables. In all cases, good correlation has been found between the free-volume quantity measured by PALS and its variability computed from the S-S equation of state. 

FIGURE 11.20 Schematic illustration of the spatial structure of the smallest representative subvolume derived from the volume fluctuations detected by PALS, (VVs) =1, at high temperatures (T 2Tg, the a -process) and at Tg (the cooperative a-process) and its relation to particle mobilities. Shown are empty spaces (represented by empty areas), which constitute the fluctuating free volume and particles (spheres). The larger empty spaces are probed by o-Ps (holes). Circles with dots represent particles considered at their movement near a hole, filled circles are particles with higher mobihty, and open circles are particles with lower mobility. The arrows indicate the possible movement of particles. (From Dlubek et al. [2006a].)... 

Finally, in this part we present an advanced classification of the different ranges of the temperature dependence of the free volume, as observed by PALS, and their physical origins. Figure 11.21 shows a systematic plot of the data of PFE from PALS and PVT experiments [Dlubek et al 2004e Dlubek, 2006]. We divide the entire temperature range into four regions and discuss their characteristic features as follows. 

The results of Dlubek et al. [2005a] indicate that between room temperature and the melting point, Vraf of PTFE, estimated as described above from Eqs. (12.45) and (12.46), is smaller than Vmaf- Below room temperature, however, the situation reverses and, at Tg, Vraf is distinctly larger than Vmaf- This behavior, which reflects the greater restriction of segmental mobility on the densification of the RAF as temperature is lowered, was also found to hold for the specific free volumes, Vy RAF and V/,maf - From comparison of the specific volume data versus the PALS results, Dlubek et al. conclude that the RAF contains more holes than the MAF. 

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