Positron annihilation pressure-temperature

Dlubek, G., Shaikh, M. Q., Raetzke, K., Faupel, F., Pionteck, J., and Paluch, M. (2009) The temperature dependence of free volume in phenyl salicylate and its relation to structural d5mamics A positron annihilation lifetime and pressure-volume-temperature study, J. Chem. Phys. 130, 144906. 

The free-volume concept dates back to the Clausius [1880] equation of state. The need for postulating the presence of occupied and free space in a material has been imposed by the fluid behavior. Only recently has positron annihilation lifetime spectroscopy (PALS see Chapters 10 to 12) provided direct evidence of free-volume presence. Chapter 6 traces the evolution of equations of state up to derivation of the configurational hole-cell theory [Simha and Somcynsky, 1969 Somcynsky and Simha, 1971], in which the lattice hole fraction, h, a measure of the free-volume content, is given explicitly. Extracted from the pressure-volume-temperature PVT) data, the dependence, h = h T, P), has been used successfully for the interpretation of a plethora of physical phenomena under thermodynamic equilibria as well as in nonequilibrium dynamic systems. 

Beichel, W., Yu, Y, Dlubek, G., Krause Rehberg, R., Pionteck, J., Pfefferkorn, D., Bulut, S., Bejan, D., Friedrich, C. and Krossing, L, Free volume in ionic liquids A connection of experimentally accessible observables from positron annihilation lifetime spectroscopy and pressure-volume-temperature experiments with the molecular structure from X-ray diffraction data, Phys. Chem. Chem. Phys. 15, 8821-8830 (2013). 

The results summarized in Table 9 show that intrinsic porosity of the polymer, i.e. the fraction of its total volume accessible to N2 molecules at 77 K, can exceed 20% for the sample conditioned at high propylene pressure and room temperature, decreasing down to ca. 6% upon annealing in vacuum at 373 K. These results allow assuming that the variations in propylene permeability through a membrane described above apparently stem from the changes in the free volume structure, i.e. accessibility of the intrinsic micropores for the gas molecules. Similar conclusion on the expansion of the free volume hole size and the increase in the number of holes upon sorption of CO2 in polycarbonate has been made in [47] on the basis of positron annihilation lifetime spectroscopy investigations. 

Positrons emitted for a radioactive source (such as 22Na) into a polymeric matrix become thermalized and may annihilate with electrons or form positronium (Ps) (a bound state of an electron and positron). The detailed mechanism and models for the formation of positronium in molecular media can be found in Chapters 4 and 5 of this book. The para-positronium (p-Ps), where the positron and electron have opposite spin, decays quickly via self-annihilation. The long-lived ortho positronium (o-Ps), where the positron and electron have parallel spin, undergo so called pick-off annihilation during collisions with molecules. The o-Ps formed in the matrix is localized in the free volume holes within the polymer. Evidence for the localization of o-Ps in the free volume holes has been found from temperature, pressure, and crystallinity-dependent properties [12-14]. In a vacuum o-Ps has a lifetime of 142.1 ns. In the polymer matrix this lifetime is reduced to between 2 - 4 ns by the so-called pick-off annihilation with electrons from the surrounding molecule. The observed lifetime of the o-Ps (zj) depends on the reciprocal of the integral of the positron (p+(rj) and electron (p.(r)) densities at the region where the annihilation takes place ... 

In this part we present an example for the pressure dependence of hole-size distribution. In our experiments we could not vary the temperature but keep it constant at room temperature. Details of experiments are described by Goworek [2007]. Figure 11.7a displays the mean, T3 (= (T3)), and standard deviation, <73, of o-Ps lifetime distribution and the o-Ps intensity h of PIB at 296 K as a function of pressure, P [Kilburn et al., 2006]. All of these parameters exhibit an exponential-like decrease with increasing pressure, h shows a small hysteresis which can be attributed to positron irradiation effects. T3 decreases from 2.0 ns at P = 0.1 MPa to 0.83 ns at 1.3 GPa and from 0.45 ns to about 0.05 ns. The low value of T3 =0.83 ns is possibly the lowest o-Ps lifetime observed until now for polymers. A lifetime of 0.5 ns is the theoretical limit of the pickoff annihilation for disappearing hole sizes [see Eq. (11.3)]. In polytetratluoroethylene (PTFE) a second, medium o-Ps lifetime of about 1 ns has been resolved and attributed to o-Ps annihilation in the densely packed polymer crystals [Dlubek et al., 2005d]. 

Kilburn, D., Wawryszczuk, J., Dlubek, G., Pionteck, J., Hassler, R., and Alam, M. A., Temperature and pressure dependence of the free volume in poly isobutylene from positron lifetime and pressure-volume-temperarnreexperiments,Macromol. Chem. Phys., 207,721-734(2006b). Kim, S. H., Chung, J. W., Kang, T. J., Kwak, S.-Y, and Suzuki, T., Determination of the glass transition temperature of polymer/layered silicate nanocomposites from positronium annihilation lifetime measurements. Polymer, 48, 4271-4277 (2007). 

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