Dielectric polarization of cross-linked poly(ethylene oxide)—phenomenology

Highlights

• The dielectric behavior as fluctuation-dissipation behavior in thermodynamics sense of cross-linked PEO is discussed.

• The dielectric behavior is reflected in permittivity, real part of conductivity, dipole moment and finally loss modulus.

• Electric properties of polymers can be understood from the transport properties-molecular interactions relationship.

Abstract

Results of dielectric relaxation studies will be discussed. It turns out that competition of electric and structural relaxation coins permittivity and as a result conductivity mechanism at low temperature. It dominates long-ranging relaxation in the molten state. In the opposite limit of temperature, cross-linked poly(ethylene oxide) (PEO) with low mesh size can be transferred into super-cooled liquid state. Then, PEO behaves like a hydrogen-bonded liquid since crystallization is strongly suppressed. As a result, one observes slow Debye-like relaxation at low temperature. Beyond the low-frequency region, there appears an extended region between crossings of impedance components, where Z′ ≈ Z″ at acceptable approximation. It is coined by damped oscillation under action of the electric field. These effects lessen with increasing mesh size of the sample as clearly shown by M″(ω) spectra. The dipole moment of the PEO samples in molten state decreases only slightly with increasing mesh size.

Introduction

We are going to discuss dielectric properties of neat cross-linked poly(ethylene oxide), PEO(S–M), having different mesh sizes from molar mass M = 400 g/mol up to 6000 g/mol [1]. Properties are determined in a wide range of temperature. It turns out that dielectric responses are frequency dependent and thermally activated at high temperature.

Poly(ethylene oxide) is a polar polymer carrying longitudinal dipoles along the backbone. We may say one monomer represents a molecular dipole. Alignment of dipoles in an electric field leads to orientation polarization which is lifting thermal disorder. Thus, we expect that orientation of dipoles contributes to macroscopic polarization in the system. We mention in parenthesis, there is also a dipole component transverse to the field. However, its relaxation is quite fast and outside the frequency range of impedance spectroscopy.

There are two phases in PEO(S–M) samples below melting point, crystalline PEO and an elastomeric, liquid-like phase. The latter is not in equilibrium at low temperature owing to locked-in entropy of high molar mass polymers. Electric conductivity in polymers cannot be seen as Frenkel or Schottky mechanism [2,3]. Fluctuation–dissipation effects might be more adequate for describing conductivity in amorphous polymer phase [4].

Cross-linked PEO comprises permanent and reversible associations due to extended hydrogen bonding. The latter develop and decay in time scales of impedance spectroscopy. Experiments show that interactions between more or less disordered networks in amorphous phase allow for long-ranging motion of charged entities as well as strictly local relaxation. Both modes rule conductance of pure polymer systems, that is, one may observe long-ranging electric relaxation at very low and high temperature as well as strictly localized motions of charged entities. Hence, weak bonds underpin fluctuation–dissipation effects. There are quite a number of studies dealing with relationship between electric conductivity and structural relaxation in polymers [[5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18]]. Some low molar masses, polar polymers, display electric properties can be readily assigned to polymer electrolytes. It is well known that electric conductivity can be observed preferably in amorphous continuous phase region of the semi-crystalline material. In high molar mass PEO (10⁶ g/mol), one observes at melting temperature a jump of conductivity by two orders of magnitude [19]. The transition in conductivity Δσ does not appear in low molar mass PEO as we will see later in conductivity function over frequency.

Electric conductivity of neat PEO as a function of temperature displays a jump Δσ > 0 at melting temperature due to disappearing of crystalline domains at sufficiently high temperature or formation of continuous amorphous phase. In PEO with high cross-linking density, in some cases, the close-meshed network or cross-linked PEO with short ethylene oxide sequence prevents crystallization [13,20]. In this study, relaxation behavior of neat cross-linked PEO, formed by chains of low molar mass, will be elucidated.

Properties of PEO solutions are ruled by hydrogen bonding interactions in some cases [14]. Liquids which are rich in hydrogen bonding, e.g., monohydroxy alcohol and water, tend to clustering or formation of supra-molecular structures in super-cooled liquid state. Very often, these liquids show slow Debye-like dielectric relaxation in this condition [[15], [16], [17], [18]]. It is obvious that cross-linked PEO with different mesh sizes may display similar behavior if it can be transferred into super-cooled amorphous state. This is possible for the PEO network with the lowest molar mass of the ethylene oxide sequence, where crystallization can be prevented even at low temperatures [20]. Accordingly, two random networks in cross-linked PEO can be observed. One chemical in nature, the other one is rooted in hydrogen bonds leading to the formation of supra-molecular structures. These two networks respond differently to external changes. We will highlight in this study, chemical and physical network behave more or less separately in the neat system at low temperature.

Understanding of electric properties of polymers will be only possible when the relationship between transport properties and molecular interactions becomes transparent. This includes both internal clustering in the polymer as well as segmental interaction. Thus, the key point remains unraveling of complex interplay among molecular structure, hydrogen bond networks, and dynamics of charge transport. We see it chiefly as fluctuation–dissipation of electric field in dielectric system. In low molar mass, dilute aqueous electrolytes containing totally dissociated species, conductivity, and diffusivity are related by the famous Nernst-Einstein equation [21]. In the context of salt-free polymer electrolytes where competition between internal clustering and interaction between chain segments appear this framework might be replaced by fluctuations of electric field [22].

In this work, dynamics in neat cross-linked PEO with different mesh sizes will be discussed. It is the aim of this study to make this behavior more transparent by comparison of dielectric spectra of cross-linked PEO with different molar masses of the ethylene oxide sequence. Impedance spectroscopy is suitable to study dynamic electric properties of these systems. Data will be analyzed in terms of complex impedance ε∗, electric modulus Mʺ, and conductivity. Description of the basic quantities and formalisms is discussed by Chan and Kammer [23].