The local free volume, glass transition, and ionic conductivity in a polymer electrolyte: A positron lifetime study

Abstract

The size of free-volume holes in neat poly[(ethylene glycol)23dimethacrylate] [poly((EG)23DMA)] and in the same polymer doped with 0.6 mol/kg LiCF3SO3 have been studied as a function of temperature in the range between 100 and 370 K using positron annihilation lifetime spectroscopy. The results are compared with differential scanning calorimetry and ionic conductivity measurements. In both systems, the hole volume νh shows a typical glass-transition behavior, i.e., a small linear increase with temperature below the glass transition temperature Tg and a steeper increase above Tg. From these measurements Tg was estimated to be 233 K (neat polymer) and 240 K (polymer with salt) and the coefficients of the thermal expansion of the hole volume were determined. The fractional free volume (f=0.080) and the number density of holes (Nh=0.6 nm−3) were also estimated. Below Tg the average hole volume of the polymer electrolyte is larger than in the neat polymer. This is consistent with the bulky character of the CF3SO3− anion. Above Tg the salt-doped system shows the lower hole volume of the two systems, probably caused by a reduced segmental mobility as a consequence of the interactions of the Li+ ions with the ethylene oxide units of the polymer. Based on the free-volume theory of Cohen–Turnbull the ionic conductivity σ is correlated with the mean hole volume νh. A linear relation between log(σT 0.5) and 1/νh was observed to be valid for variations of the conductivity over several orders of magnitudes. From these plots critical hole sizes of γν*=0.65 nm3 (neat polymer) and 0.87 nm3 (polymer-salt system) were estimated. The parameters B and T0 of the Vogel–Tamman–Fulcher equation were also determined, as well as the apparent activation volume ΔVapp by pressure-dependent conductivity measurements. The cationic transference number in the polymer-salt system was determined by pulsed field gradient-nuclear magnetic resonance to be t+≈0.3.

Oxygen transport as a solid‐state structure probe for polymeric materials: A review

“…, which correlates with an N 0 value of about 4 ϫ 10 20 cm Ϫ3 determined for a range of polymers in various PALS studies, which considered either an average hole size [51][52][53] or a distribution of hole sizes. 54 The consistency with independent estimates of the hole size and hole density supports the simple physical model that views gas diffusion as the random hopping of an oxygen molecule from one excess-hole free volume hole to another.…”

The need to reconsider traditional free volume theory for polymer electrolytes

“…Free volume theory has found increasing use in the description of polymer electrolytes [1][2][3]. The primary reason, of course, is that it provides an easily understandable, qualitative explanation of many phenomena [4].…”

Electrical conductivity in glass-forming solid electrolytes: theory and experiment

“…Specifically, eqs. (4) and (6) show that both AV app ß, and AV tru increase as Vß, decreases and vice versa (The mathematical dependence is different in the two cases.). This explains the successful application of eq.…”

“…For example, Bamford et al [6] have adapted the free volume theory of Cohen and Turnbull to describe ionic conductivity. The result of that work is that the conductivity is given by…”

“…Several papers have appeared recently which discuss the effect of pressure on ionic conductivity in materials [1][2][3][4][5][6]. One quantity that is usually calculated from the pressure dependence of the conductivity is the apparent activation volume, AV app , defined ölncr by'…”