The need to reconsider traditional free volume theory for polymer electrolytes

Kilburn

Alam

2005

Summary: We analysed reported specific volume V from pressure‐volume‐temperature (PVT) experiments for poly(vinyl acetate) (PVAc) using the Simha‐Somcynsky equation of state (S‐S eos) and calculated the specific occupied volume, Vocc, and hole free volume, Vfh We found that Vocc shows almost no thermal expansion but is distinctly compressible (T > Tg). Due to this, Vfh = V − Vocc is not a unique function of V but can depend on the specific values of P and T giving rise to the particular value for V. We observed that with decreasing temperature the α‐relaxation detected via dielectric measurements slows down faster than the shrinkage of hole free volume Vfh would predict on the basis of the free volume theory of Cohen and Turnbull. Vfh becomes zero at approximately 65 K below the Vogel temperature T0, $T'_0 = T_0 - 65\,{\rm K}$. Plots of the α‐relaxation frequency log ωα versus 1/Vfh can be linearised when taking into account this discrepancy by substituting 1/Vfh by 1/(Vfh − ΔV) with $\Delta V = E_{{\rm fh}} (T_0 - T'_0 )$, or by including an energy term of the type exp[−E′/R(T − T0)] in the pre‐exponential factor of the frequency‐volume equation. Our results indicate that the α‐relaxation in PVAc operates via the Cohen‐Turnbull mechanism only when liquid‐like clusters of cells of the S‐S lattice appear which contain a hole free volume of three or more empty S‐S cells. For regions with a smaller number of empty cells an activation energy is required for allowing segmental motion via the cooperative rearranging of cells. The β‐(Johari‐Goldstein) relaxation which is a non‐cooperative, more local, process follows completely the free volume theory. The same seems to be true for the primitive (uncoupled) relaxation of the coupling model. magnified image

Section: Resultsmentioning

confidence: 99%

Section: Quantitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Temperature and Pressure Dependence of α‐Relaxation and Free Volume in Poly(vinyl acetate)

Kilburn

Alam

2005

The Structure of the Free Volume in Poly(styrene‐co‐acrylonitrile) from Positron Lifetime and Pressure Volume Temperature (PVT) Experiments

Pionteck

Kilburn

2004

Summary: The structure of the free volume and its temperature dependence between 25 and 190 °C of copolymers of styrene with acrylonitrile, SAN (0 to 50 mol‐% AN), is studied by pressure volume temperature (PVT) experiments and positron annihilation lifetime spectroscopy (PALS). In this first part of the work, PVT data are reported which were analysed with the Simha‐Somcynsky equation of state (S‐S eos) to estimate the volume fraction of holes, h, which constitute the excess free volume. The temperature and pressure dependence of the specific volume V, the specific occupied and free volume, Vocc = (1 − h)V and Vf = hV, and the corresponding isobaric expansivities and isothermal compressibilities for both the rubbery and glassy state, are estimated. We obtained the unexpected results that (i) the occupied volume changes its coefficient of thermal expansion at Tg from αocc,g ≈ 0.5αg ≈ 1 × 10−4 K−1 below Tg to almost zero above Tg and (ii) the isothermal compressibility of the occupied volume at zero pressure is rather high, κocc ≈ 2 × 10−4 MPa−1, and decreases only slightly at Tg. The variation of total, occupied, and free volume parameters with the composition of the SAN copolymers is discussed.Specific volume V of SAN50 as a function of temperature T and as selection of isobars (in MPa).magnified imageSpecific volume V of SAN50 as a function of temperature T and as selection of isobars (in MPa).

Temperature Dependence of Free Volume in Pure and Silica‐Filled Poly(dimethyl siloxane) from Positron Lifetime and PVT Experiments

Pionteck

et al. 2005

Summary:The microstructure of the free volume and its temperature dependence in two poly(dimethyl siloxane)s (PDMS), one in the pure state and the other filled with 35 wt.‐% of an in situ hydrophobized fumed silica with a specific surface area of 200–300 m2 · g−1, were studied by pressure‐volume‐temperature experiments (PVT, T = 22–156 °C, P = 10–200 MPa) and positron annihilation lifetime spectroscopy (PALS, T = −173–100 °C, P = 10−5 MPa). The Simha‐Somcynsky equation of state was used to estimate the hole free volume fraction, h, and free and occupied volumes, Vf = hV and Vocc = (1 − h)V, from the specific total volume, V. The PALS spectra were analyzed with the routine LT9.0, which allowed for a dispersion, σi, in all three of the lifetimes: the para‐positronium (p‐Ps, τ1), positron (e+, τ2), and ortho‐positronium (o‐Ps) lifetime (τ3). This kind of analysis delivered correct p‐Ps lifetime parameters, τ1, σ1, and I1. It was speculated that e+, like o‐Ps, undergoes Anderson localization at empty sites of the, static or dynamic, disordered structure. The hole size distribution, its mean value, 〈vh〉, and dispersion, σh, were calculated from the o‐Ps lifetimes. A comparison of 〈vh〉 with Vf was used to estimate the specific hole number, $N'_{\rm h}$. During melting of the semicrystalline samples at−38 °C (Tm), 〈vh〉 increased abruptly, and σh suddenly decreased. Both effects are explained by the disappearance of the rigid‐amorphous fraction (RAF) and, thus, a reduction in the dynamic heterogeneity. The following leveling‐off in 〈vh〉 and the low value of σh are attributed to the fast segmental relaxation in the PDMS melts which leads to a smearing of the molecule density distribution around a hole during the o‐Ps lifetime. magnified image