Direct computation of the free volume fraction in amorphous polymers from positron lifetime measurements

Bandžuch, P.; Krištiak, J.; Šauša, O.; Zrubcová, J.

doi:10.1103/physrevb.61.8784

Cited by 43 publications

(35 citation statements)

References 18 publications

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“…This indicates that free e + are not localized and their wave functions feel relatively vast volume, consequently, their annihilation characteristics will be sensitive to the macroscopic properties. Therefore, the value of α + for PP is in excellent agreement with the reported linear thermal expansion coefficient (~1×10 -4 K -1 ) of the occupied volume in polymers [7,8]. We performed another fit (fit 2 in Fig.…”

Section: Introductionsupporting

confidence: 70%

On the consistency between positron annihilation lifetime and Doppler broadening results in polypropylene

Djourelov

Dauwe

Palacio

et al. 2007

Phys. Status Solidi (c)

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Polypropylene samples were measured as a function of the source exposure time at 20 K and as a function of the temperature (20-400 K) simultaneously by Positron Annihilation Lifetime (PAL) and Doppler Broadening (DB) spectroscopy. The peak shape parameter (S) measured by DB can be calculated as a sum of contributions of specific parameters corresponding to each positron state. The contributions are obtained by analysis of the PAL spectra. The confinement of positronium (Ps) in a free volume hole (FVH) determines the self annihilation shape parameter S sa of the para-Ps, the pick-off annihilation lifetime τ po , and supposes FVH size-dependence of the pick-off shape parameter S po . The ortho-Ps lifetime and shape parameters are used to compute S sa . In this way, the temperature and time dependences of the S parameter are modelled. The fit of this model to the experimental S parameter shows a stronger dependence of the S po on the FVH size (R) than the one as expected by taking into account only the Ps momentum. This result suggests that the penetration of Ps into the walls of the FVH must be properly considered and that the penetration depth depends on R itself.

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Section: Introductionsupporting

confidence: 70%

On the consistency between positron annihilation lifetime and Doppler broadening results in polypropylene

Djourelov

Dauwe

Palacio

et al. 2007

Phys. Status Solidi (c)

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“…This result is consistent with the expectation that the glass transition is not an iso-free volume point. [26][27][28] Table 2.…”

Section: Resultsmentioning

confidence: 99%

Effect of particle size on the glass transition

Larsen

Zukoski

2011

Phys. Rev. E

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The glass transition temperature of a broad class of molecules is shown to depend on molecular size. This dependency results from the size dependence of the pair potential. A generalized equation of state is used to estimate how the volume fraction at the glass transition depends on the size of the molecule, for rigid molecule glass-formers. The model shows that at a given pressure and temperature there is a size-induced glass transition: for molecules larger than a critical size, the volume fraction required to support the effective pressure due to particle attractions is above that which characterizes the glassy state. This observation establishes the boundary between nanoparticles, which exist in liquid form only as a dispersion in low molecular weight solvents, and large molecules which form liquids that have viscosities below those characterized by the glassy state.

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“…[27,32,33] Various groups have performed PALS experiments on PIB, and the most recent works were published by the Bratislava group. [34,35] In these works typically only the mean hole volume is determined as a function of the temperature. In ref.…”

Section: Introductionmentioning

confidence: 99%

“…In ref. [35] the hole fraction at the glass transition temperature T g was estimated from a relation between the coefficients of thermal expansion, but this calculation was based on a number of assumptions whose validity has yet to be confirmed. As we and others have discussed recently, a correlation of PALS results with V f , estimated from the total volume by employing the SS EOS, allows to estimate reasonable values for the hole density and the hole fraction.…”

Section: Introductionmentioning

confidence: 99%

Temperature and Pressure Dependence of the Free Volume in Polyisobutylene from Positron Lifetime and Pressure‐Volume‐Temperature Experiments

Kilburn

Wawryszczuk

Dlubek

et al. 2006

Macro Chemistry & Physics

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Summary: The microstructure of the free volume and its temperature and pressure dependence in PIB were studied by PVT experiments and PALS. Employing the Simha–Somcynsky equation of state, the hole‐free volume fraction h and the specific free and occupied volumes, Vf = hV and Vocc = (1 − h)V, respectively, and their expansivity and compressibility were calculated. From the PALS spectra analyzed using the LT9.0 software, the hole size distribution, the mean hole size 〈vh〉 and mean dispersion σh were calculated. From a comparison of 〈vh〉 with Vf, the hole density $N'_{\rm h}$ was obtained. It was found that PIB shows an unusual thermal expansion with glass‐like transitions at 210 K and 290 K (at 0 MPa). A similar behavior is observed for tan δ. It was found that at 296 K, 〈vh〉 decreases exponentially from 80 Å3 at 0.1 MPa to the extremely low value of 10 Å3 at 1 300 MPa. Starting from a fluctuation approach, the free‐volume fluctuations and the characteristic length scale (ξ) of dynamic heterogeneity of structural relaxation were estimated from σh. It was found that ξ increases from ≈1.5 nm to ≈1.9 nm when the temperature decreases from 293 K to the glass transition temperature Tg = 207 K (at 0 MPa) or the pressure increases from 0.1 MPa to 200 MPa (at 296 K).Fractional free volume and its mean fluctuation in PIB as determined from positron lifetime spectroscopy and PVT experiments analyzed with the Simha‐Somcynsky equation of state.imageFractional free volume and its mean fluctuation in PIB as determined from positron lifetime spectroscopy and PVT experiments analyzed with the Simha‐Somcynsky equation of state.

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Direct computation of the free volume fraction in amorphous polymers from positron lifetime measurements

Cited by 43 publications

References 18 publications

On the consistency between positron annihilation lifetime and Doppler broadening results in polypropylene

On the consistency between positron annihilation lifetime and Doppler broadening results in polypropylene

Effect of particle size on the glass transition

Temperature and Pressure Dependence of the Free Volume in Polyisobutylene from Positron Lifetime and Pressure‐Volume‐Temperature Experiments

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