A thermodynamic approach to proton conductivity in acid-doped polybenzimidazole

Abstract

Conductivity measurement on films of acid-doped polybenzimidazole (PBI) was performed by impedance spectroscopy. A complete set of data for PBI–H₃PO₄ and PBI–H₂SO₄ complexes is reported as a function of temperature (30–90°C) and isostatic pressure (1–4000 bars). Experimental results indicate an activated mechanism for the proton migration. Isobar and isothermal conductivity data allow the determination of the characteristic thermodynamic parameters ΔV* (4–10 cm³ mol⁻¹), ΔH* (0.6–1.1 eV) and ΔS* (40–190 J mol⁻¹ K⁻¹). The dependence of these parameters on temperature and pressure is consistent with thermodynamic predictions. Based on a previous IR spectroscopic study of PBI–acid complexes, a microscopic model is developed, suggesting proton transfer from one imide site to another in which the anionic species participate by a Grotthus mechanism.

Introduction

In the last 20 years, protonic conductive polymers have been extensively studied for potential applications as electrolytes in fuel cells, electrochromic devices and hydrogen sensors [1]. The more common systems are obtained by dissolving a strong acid (i.e. phosphoric and sulphuric acids) in polymer chains containing basic sites. A classification of these complexes as a function of the polymer backbone basicity has been proposed by Lassègues [2]. Among them, H₃PO₄⁻ and H₂SO₄⁻ doped polybenzimidazole (PBI) are of a particular interest due to their thermal stability: these complexes are stable up to 200°C. Above this temperature, the dissolved acid begins to decompose [3], whereas the macromolecular chains remain stable up to about 600°C.

PBI is made of linear macromolecular chains whose monomer unit is:

Pure PBI can be considered as an insulator with an intrinsic conductivity of about 10⁻¹² S cm⁻¹ at 25°C [4]. Its glass transition temperature, T_g, is estimated as 420°C [5] and below this temperature, PBI is purely amorphous and can be considered as an organic glass. A strong acid (i.e. H₃PO₄ or H₂SO₄) dissolved in the macromolecular chains leads to an important protonic conductivity. The previously published results on conductivity arise from measurements performed on samples prepared according to two different methods. In the first one, the samples are in equilibrium with acidic solutions [6], [7], while in the second, the water is eliminated by a heating treatment in order to keep only the acid molecules in the PBI polymer [8], [9]. One of the most interesting features is that the ‘anhydrous’ systems exhibit an important protonic conductivity of about 10⁻² S cm⁻¹ at 130°C associated with a good mechanical behavior [6]. These properties make PBI–H₂SO₄ or PBI–H₃PO₄ complexes very attractive candidates as electrolytes for fuel cells [10], [11] or electrochemical hydrogen sensors [12], [13].

We have shown [6] that in PBI–acid complexes, the protonic conductivity is greatly influenced by the anionic species. This point has been discussed in the literature for other polymer/acid complexes [14]. A high protonic conductivity is associated with the amphoteric character of the counter anions, HSO₄⁻ or H₂PO₄⁻. The mechanism of this protonic migration is not yet established. The present work is an attempt to elucidate this mechanism using conductivity measurements of anhydrous mixtures of PBI–H₃PO₄ and PBI–H₂SO₄ as a function of temperature (30–90°C) and isostatic pressure (1–4000 bars).