2.1 Basic Concepts of Conductivity Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
2.2 Early Dielectric and Conductivity Spectra of PEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
2.3 The Structural Analogue: Polyelectrolyte Multilayers and Their Conductivity . . . . 105
3 Conductivity Spectra of Dried PEC: Dependence on Temperature . . . . . . . . . . . . . . . . . . . . . . 107
3.1 Isothermal Conductivity Spectra of PEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.2 Temperature Dependence of the DC Conductivity of PEC . . . . . . . . . . . . . . . . . . . . . . . . . 109
3.3 Temperature-Dependent Ionic Conductivity as a Function of the Type of Alkali Ion 111
3.4 Modeling of Conductivity Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4 RH-Dependent Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.1 Conductivity Spectra of PEC at Constant RH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.2 RH Dependence of the DC Conductivity of PEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.3 Influence of the Alkali Ion Size in Hydrated PEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5 Scaling of Conductivity Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.1 Principle of Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.2 The Time–Temperature Superposition Principle in PEC . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5.3 The Time–Humidity Superposition Principle in PEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6 Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
1 Introduction
The unusual properties of polymer networks formed by the complexation of
oppositely charged polyions has already been the subject of very early research,
following the initial work of Bungenberg de Jong et al. [1]. In these early days,
polyelectrolyte complexes (PEC) had already been proposed as novel solid
materials for a range of applications such as membranes for filtration or in fuel
cells, as battery separators, as conductive coatings and so forth, as reviewed by
Michaels [2]. Nevertheless, research on polyelectrolyte complexes as a solid
material was sparse in the following decades. With the seminal work on the
dielectric properties of solid complexes by Michaels [3–5] almost forgotten, a lot
of research during the following years focused on soluble complexes in aqueous
solution, and various structural models were discussed on the basis of scattering and
other experiments. An overview is given by several review articles [6–8].
A major breakthrough was achieved with the advent of polyelectrolyte
multilayers (PEM), the layered analogue to PEC, formed by the so-called layerby-layer deposition of polyions with alternating sign of charge [9]. The process is
predominantly driven by multiple electrostatic interactions and is therefore very
versatile with respect to the different charged building blocks that can be employed
in multilayer formation. External parameters such as salt concentration [10], pH
value [11] or temperature [12] provide control of the layer thickness, which
typically lies in the range of 1 nm per layer. Research in the field of PEM has
vastly expanded in the past two decades, and there are numerous potential
applications such as containers, sensors, drug delivery, etc. Various review articles
provide information about structural aspects and summarize the properties of PEM
[13–16].
98
C. Cramer and M. Scho ¨nhoff
2.2 Early Dielectric and Conductivity Spectra of PEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
2.3 The Structural Analogue: Polyelectrolyte Multilayers and Their Conductivity . . . . 105
3 Conductivity Spectra of Dried PEC: Dependence on Temperature . . . . . . . . . . . . . . . . . . . . . . 107
3.1 Isothermal Conductivity Spectra of PEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.2 Temperature Dependence of the DC Conductivity of PEC . . . . . . . . . . . . . . . . . . . . . . . . . 109
3.3 Temperature-Dependent Ionic Conductivity as a Function of the Type of Alkali Ion 111
3.4 Modeling of Conductivity Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4 RH-Dependent Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.1 Conductivity Spectra of PEC at Constant RH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.2 RH Dependence of the DC Conductivity of PEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.3 Influence of the Alkali Ion Size in Hydrated PEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5 Scaling of Conductivity Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.1 Principle of Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.2 The Time–Temperature Superposition Principle in PEC . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5.3 The Time–Humidity Superposition Principle in PEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6 Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
1 Introduction
The unusual properties of polymer networks formed by the complexation of
oppositely charged polyions has already been the subject of very early research,
following the initial work of Bungenberg de Jong et al. [1]. In these early days,
polyelectrolyte complexes (PEC) had already been proposed as novel solid
materials for a range of applications such as membranes for filtration or in fuel
cells, as battery separators, as conductive coatings and so forth, as reviewed by
Michaels [2]. Nevertheless, research on polyelectrolyte complexes as a solid
material was sparse in the following decades. With the seminal work on the
dielectric properties of solid complexes by Michaels [3–5] almost forgotten, a lot
of research during the following years focused on soluble complexes in aqueous
solution, and various structural models were discussed on the basis of scattering and
other experiments. An overview is given by several review articles [6–8].
A major breakthrough was achieved with the advent of polyelectrolyte
multilayers (PEM), the layered analogue to PEC, formed by the so-called layerby-layer deposition of polyions with alternating sign of charge [9]. The process is
predominantly driven by multiple electrostatic interactions and is therefore very
versatile with respect to the different charged building blocks that can be employed
in multilayer formation. External parameters such as salt concentration [10], pH
value [11] or temperature [12] provide control of the layer thickness, which
typically lies in the range of 1 nm per layer. Research in the field of PEM has
vastly expanded in the past two decades, and there are numerous potential
applications such as containers, sensors, drug delivery, etc. Various review articles
provide information about structural aspects and summarize the properties of PEM
[13–16].
98
C. Cramer and M. Scho ¨nhoff